; 00-01Textbooks (general mathematics)Instructional exposition (textbooks, tutorial papers, etc.)00-XX ) 1 00-02Research monographs (general mathematics)Research exposition (monographs, survey articles)00-XX 00-99General mathematicsGeneral mathematics 00-XXGeneral mathematicsGeneral 00A05General mathematicsGeneral mathematics00Axx " F 00A06Mathematics for non-mathematiciansMathematics for nonmathematicians (engineering, social sciences, etc.)00Axx
00A07Problem booksProblem books00Axx ) 00A08Mathematical recreationRecreational mathematics [See also 97A20]00Axx 00A15BibliographiesBibliographies00Axx 00A17External book reviewsExternal book reviews00Axx00A991 . . 00A20Dictionaries and other general reference worksDictionaries and other general reference works00Axx 00A22FormulariesFormularies00Axx * 00A30Philosophy of mathematicsPhilosophy of mathematics [See also 03A05]00Axx % = 00A35Methodology of mathematics, didacticsMethodology of mathematics, didactics [See also 97Cxx, 97Dxx]00Axx O 00A69General applied mathematicsGeneral applied mathematics {For physics, see 00A79 and Sections 70 through 86}00Axx 00A71Theory of mathematical modelingTheory of mathematical modeling00Axx 00A72General methods of simulationGeneral methods of simulation00Axx 00A73Dimensional analysisDimensional analysis00Axx M 00A79PhysicsPhysics (use more specific entries from Sections 70 through 86 when possible)00Axx + 00A99Miscellaneous topics in general mathematicsMiscellaneous topics00Axx ) 00AxxTopics in general mathematicsGeneral and miscellaneous specific topics00-XX $ $ 00B05Collections of abstracts of lecturesCollections of abstracts of lectures00Bxx + + 00B10Collections of articles of general interestCollections of articles of general interest00Bxx : 9 00B15Collections of articles of miscellaneous specific interestCollections of articles of miscellaneous specific content00Bxx . . 00B20Proceedings of conferences of general interestProceedings of conferences of general interest00Bxx = = 00B25Proceedings of conferences of miscellaneous specific interestProceedings of conferences of miscellaneous specific interest00Bxx
00B30FestschriftenFestschriften00Bxx 00B50Volumes of selected translationsVolumes of selected translations00Bxx % % 00B55Miscellaneous volumes of translationsMiscellaneous volumes of translations00Bxx ! 2 00B60Collections of reprinted articlesCollections of reprinted articles [See also 01A75]00Bxx 0 0 00BxxConference proceedings and collections of papersConference proceedings and collections of papers00-XX G 01-00Reference works (history)General reference works (handbooks, dictionaries, bibliographies, etc.)01-XX ; 01-01Textbooks (history)Instructional exposition (textbooks, tutorial papers, etc.)01-XX 1 01-02Research monographs (history)Research exposition (monographs, survey articles)01-XX * + 01-06Proceedings of conferences, etc. (history)Proceedings, conferences, collections, etc.01-XX 01-08Computational methodsComputational methods01-XX $ $ 01-99History of mathematics and biographyHistory of mathematics and biography T 01-XXHistory and biographyHistory and biography [See also the classification number -03 in the other sections] 01A05General histories, source booksGeneral histories, source books01-XX 01A07EthnomathematicsEthnomathematics, general01-XX * 01A10Paleolithic or Neolithic mathematics, etc.Paleolithic, Neolithic01-XX # 01A12Native American mathematicsIndigenous cultures of the Americas01-XX ( 01A13Native African mathematicsOther indigenous cultures (non-European)01-XX . 01A15Pre-Greek mathematics of EuropeIndigenous European cultures (pre-Greek, etc.)01-XX 01A16Egyptian mathematicsEgyptian01-XX
01A17Babylonian mathematicsBabylonian01-XX 01A20Greek or Roman mathematicsGreek, Roman01-XX 01A25Chinese mathematicsChina01-XX 01A27Japanese mathematicsJapan01-XX 01A29Southeast Asian mathematicsSoutheast Asia01-XX 01A30Mathematics of Islam (Medieval)Islam (Medieval)01-XX 01A32Indian mathematicsIndia01-XX 01A35Mathematics in the medievalMedieval01-XX 7 $ 01A40Mathematics in the 15th and 16th centuries, Renaissance15th and 16th centuries, Renaissance01-XX 01A45Mathematics in the 17th century17th century01-XX 01A50Mathematics in the 18th century18th century01-XX 01A55Mathematics in the 19th century19th century01-XX 01A60Mathematics in the 20th century20th century01-XX 01A6121st centuryTwenty-first century01-XX01A65,01A671 ' 01A65Development of contemporary mathematicsContemporary01-XX " 01A67Future prospectives in mathematicsFuture prospectives01-XX 3 3 01A70Biographies, obituaries, personalia, bibliographiesBiographies, obituaries, personalia, bibliographies01-XX 01A72Schools of mathematicsSchools of mathematics01-XX & 01A73History of mathematics at universitiesUniversities01-XX D 01A74History of mathematics at institutions and academies (nonuniversity)Other institutions and academies01-XX U 01A75Collected or selected worksCollected or selected works; reprintings or translations of classics [See also 00B60]01-XX ) ) 01A80Sociology (and profession) of mathematicsSociology (and profession) of mathematics01-XX 01A85HistoriographyHistoriography01-XX01A991 01A90Bibliographic studiesBibliographic studies01-XX01A991 . 01A99Miscellaneous topics in history of mathematicsMiscellaneous topics01-XX $ G 03-00Reference works (mathematical logic)General reference works (handbooks, dictionaries, bibliographies, etc.)03-XX ; 03-01Textbooks (mathematical logic)Instructional exposition (textbooks, tutorial papers, etc.)03-XX ( 1 03-02Research monographs (mathematical logic)Research exposition (monographs, survey articles)03-XX U 03-03Historical (mathematical logic)Historical (must also be assigned at least one classification number from Section 01)03-XX 2 X 03-04Machine computation, programs (mathematical logic)Explicit machine computation and programs (not the theory of computation or programming)03-XX / + 03-06Proceedings of conferences (mathematical logic)Proceedings, conferences, collections, etc.03-XX 03-99Mathematical logicMathematical logic " 03-XXMathematical logicMathematical logic and foundations J 03A05Philosophical and criticalPhilosophical and critical {For philosophy of mathematics, see also 00A30}03-XX 03B05Classical propositional logicClassical propositional logic03Bxx 03B10First-order logicClassical first-order logic03Bxx " 03B15Higher-order logicHigher-order logic and type theory03Bxx > 03B20Subsystems of classical logicSubsystems of classical logic (including intuitionistic logic)03Bxx 03B22Abstract deductive systemsAbstract deductive systems03Bxx . M 03B25Decidability of theories and sets of sentencesDecidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]03Bxx ! R 03B30Foundations of classical theoriesFoundations of classical theories (including reverse mathematics) [See also 03F35]03Bxx ? 03B35Mechanical theorem provingMechanization of proofs and logical operations [See also 68T15]03Bxx 6 03B40Combinatory logicCombinatory logic and lambda-calculus [See also 68N18]03Bxx 03B42Logic of knowledge and beliefLogic of knowledge and belief03Bxx03B451 03B44Temporal logicTemporal logic03Bxx03B451 t 03B45Modal logic, etc.Modal logic {For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also 03F45}03Bxx ‘ 03B47Substructural logicsSubstructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}03Bxx03B46,03F501 0 03B48Probability logic, etc.Probability and inductive logic [See also 60A05]03Bxx 03B50Many-valued logicMany-valued logic03Bxx > 03B52Fuzzy logicFuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]03Bxx O 03B53Paraconsistent logicLogics admitting inconsistency (paraconsistent logics, discussive logics, etc.)03Bxx 03B55Intermediate logicsIntermediate logics03Bxx 03B60Other nonclassical logicOther nonclassical logic03Bxx 2 03B65Logic of natural languagesLogic of natural languages [See also 68T50, 91F20]03Bxx * 03B70Logic of programmingLogic in computer science [See also 68-XX]03Bxx 03B80Appl. of logicOther applications of logic03Bxx
& 03B99General logicNone of the above, but in this section03Bxx
03BxxGeneral logicGeneral logic03-XX D 03C05Universal algebra (model theory)Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]03Cxx 8 8 03C07Basic properties of first-order languages and structuresBasic properties of first-order languages and structures03Cxx ) = 03C10Quantifier elimination and related topicsQuantifier elimination, model completeness and related topics03Cxx
) 03C13Finite modelsFinite structures [See also 68Q15, 68Q19]03Cxx 03C15Countable modelsDenumerable structures03Cxx ' ' 03C20Ultraproducts and related constructionsUltraproducts and related constructions03Cxx 03C25Model-theoretic forcingModel-theoretic forcing03Cxx 03C30Other model constructionsOther model constructions03Cxx ) 03C35Categoricity, etc.Categoricity and completeness of theories03Cxx " ) 03C40Interpolation, etc. (model theory)Interpolation, preservation, definability03Cxx 5 03C45Stability (model theory)Classification theory, stability and related concepts03Cxx 7 03C50Models with special propertiesModels with special properties (saturated, rigid, etc.)03Cxx 03C52Properties of classes of modelsProperties of classes of models03Cxx 03C55Set-theoretic model theorySet-theoretic model theory03Cxx ? 03C57Recursion-theoretic model theoryEffective and recursion-theoretic model theory [See also 03D45]03Cxx 6 03C60Model-theoretic algebraModel-theoretic algebra [See also 08C10, 12Lxx, 13L05]03Cxx # 4 03C62Models of arithmetic and set theoryModels of arithmetic and set theory [See also 03Hxx]03Cxx " 0 03C64Model theory of ordered structuresModel theory of ordered structures; o-minimality03Cxx03C40,03C45,03C50,03C601 % % 03C65Models of other mathematical theoriesModels of other mathematical theories03Cxx ( ( 03C68Other classical first-order model theoryOther classical first-order model theory03Cxx 03C70Logic on admissible setsLogic on admissible sets03Cxx 03C75Other infinitary logicOther infinitary logic03Cxx * P 03C80Logic with extra quantifiers and operatorsLogic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]03Cxx % 03C85Higher-order model theorySecond- and higher-order model theory03Cxx 1 03C90Nonclassical modelsNonclassical models (Boolean-valued, sheaf, etc.)03Cxx 03C95Abstract model theoryAbstract model theory03Cxx - 03C98Applications of model theoryApplications of model theory [See also 03C60]03Cxx03C991 & 03C99Model theory (logic)None of the above, but in this section03Cxx 03CxxModel theory (logic)Model theory03-XX 03D03Rewriting systemsThue and Post systems, etc.03Dxx 4 ` 03D05Automata theory in connection with logical questionsAutomata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]03Dxx # 4 03D10Turing machines and related notionsTuring machines and related notions [See also 68Q05]03Dxx 1 03D15Complexity of computationComplexity of computation [See also 68Q15, 68Q17]03Dxx ; 03D20Recursive functionsRecursive functions and relations, subrecursive hierarchies03Dxx 4 03D25Recursively enumerable setsRecursively (computably) enumerable sets and degrees03Dxx 03D28Other Turing degree structuresOther Turing degree structures03Dxx03D301 03D30Degrees, other than r.e.Other degrees and reducibilities03Dxx / 03D35UndecidabilityUndecidability and degrees of sets of sentences03Dxx 9 03D40Word problems, etc. (logic)Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15]03Dxx & } 03D45Effectively presented structures, etc.Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]03Dxx 9 03D50Recursive equivalence typesRecursive equivalence types of sets and structures, isols03Dxx 03D55HierarchiesHierarchies03Dxx 3 E 03D60Recursion theory on ordinals, admissible sets, etc.Computability and recursion theory on ordinals, admissible sets, etc.03Dxx " $ 03D65Other generalized recursion theoryHigher-type and set recursion theory03Dxx 03D70Inductive definabilityInductive definability03Dxx ' 9 03D75Abstract and axiomatic recursion theoryAbstract and axiomatic computability and recursion theory03Dxx 2 03D80Appl. of recursion theoryApplications of computability and recursion theory03Dxx & 03D99Recursion theoryNone of the above, but in this section03Dxx " 03DxxRecursion theoryComputability and recursion theory03-XX 03E02Partition relationsPartition relations03Exx03E05,03E10,04A10,04A201 # / 03E04Ordered sets and their cofinalitiesOrdered sets and their cofinalities; pcf theory03Exx03E05,03E10,04A10,04A201 03E05Combinatorial set theory (logic)Other combinatorial set theory03Exx 03E10Ordinal and cardinal arithmeticOrdinal and cardinal numbers03Exx . 03E15Descriptive set theory (logic)Descriptive set theory [See also 28A05, 54H05]03Exx ) ) # 03E17Cardinal characteristics of the continuumCardinal characteristics of the continuum03Exx03E05,03E10,03E15,04A10,04A15,04A201 " L 03E20Other classical set theory (logic)Other classical set theory (including functions, relations, and set algebra)03Exx 0 ( 03E25Axiom of choice and related propositions (logic)Axiom of choice and related propositions03Exx 4 4 03E30Axiomatics of classical set theory and its fragmentsAxiomatics of classical set theory and its fragments03Exx 1 $ 03E35Consistency and independence results (set theory)Consistency and independence results03Exx % 2 03E40Other aspects of forcing (set theory)Other aspects of forcing and Boolean-valued models03Exx ; O 03E45Constructibility, ordinal definability, and related notionsInner models, including constructibility, ordinal definability, and core models03Exx + + 03E47Other notions of set-theoretic definabilityOther notions of set-theoretic definability03Exx 0 ' 03E50Continuum hypothesis and generalizations (logic)Continuum hypothesis and Martin's axiom03Exx 03E55Large cardinalsLarge cardinals03Exx 03E60Axiom of determinacy, etc.Determinacy principles03Exx ( 03E65Other hypotheses and axioms (set theory)Other hypotheses and axioms03Exx * 03E70Nonclassical set theoriesNonclassical and second-order set theories03Exx 03E72Fuzzy sets (logic)Fuzzy set theory03Exx 03E75Appl. of set theoryApplications of set theory03Exx & 03E99Set theory (logic)None of the above, but in this section03Exx
03ExxSet theory (logic)Set theory03-XX 03F03General aspects of proof theoryProof theory, general03Fxx ( 03F05Cut-elimination, etc.Cut-elimination and normal-form theorems03Fxx 03F07Structure of proofsStructure of proofs03Fxx 03F10Functionals in proof theoryFunctionals in proof theory03Fxx ( ( 03F15Recursive ordinals and ordinal notationsRecursive ordinals and ordinal notations03Fxx 03F20Complexity of proofsComplexity of proofs03Fxx ( ( 03F25Relative consistency and interpretationsRelative consistency and interpretations03Fxx $ $ 03F30First-order arithmetic and fragmentsFirst-order arithmetic and fragments03Fxx % B 03F35Higher-order arithmetic and fragmentsSecond- and higher-order arithmetic and fragments [See also 03B30]03Fxx ! 03F40Goedel numberings in proof theoryGödel numberings in proof theory03Fxx ' f 03F45Provability logics and related algebrasProvability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]03Fxx03B45,03F401 ' ' 03F50Metamathematics of constructive systemsMetamathematics of constructive systems03Fxx < 03F52Linear logic etc.Linear logic and other substructural logics [See also 03B47]03Fxx03F501 03F55Intuitionistic mathematicsIntuitionistic mathematics03Fxx # P 03F60Constructive and recursive analysisConstructive and recursive analysis [See also 03B30, 03D45, 26E40, 46S30, 47S30]03Fxx / 03F65Other constructive mathematicsOther constructive mathematics [See also 03D45]03Fxx & 03F99Metamathematics, etc.None of the above, but in this section03Fxx ) 03FxxMetamathematics, etc.Proof theory and constructive mathematics03-XX # ! 03G05Boolean algebras in algebraic logicBoolean algebras [See also 06Exx]03Gxx 1 0 03G10Lattices and related structures (algebraic logic)Lattices and related structures [See also 06Bxx]03Gxx
% 03G12Quantum logicQuantum logic [See also 06C15, 81P10]03Gxx % 2 03G15Cylindric and polyadic algebras, etc.Cylindric and polyadic algebras; relation algebras03Gxx / 5 03G20Post and Lukasiewicz algebras (algebraic logic)Lukasiewicz and Post algebras [See also 06D25, 06D30]03Gxx E 03G25Other algebras related to logicOther algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]03Gxx 7 03G30Categorical logicCategorical logic, topoi [See also 18B25, 18C05, 18C10]03Gxx & 03G99Algebraic logicNone of the above, but in this section03Gxx 03GxxAlgebraic logicAlgebraic logic03-XX ! U 03H05Nonstandard models in mathematicsNonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]03Hxx - C 03H10Appl. of nonstandard models to other sciencesOther applications of nonstandard models (economics, physics, etc.)03Hxx ? 03H15Nonstandard models of arithmeticNonstandard models of arithmetic [See also 11U10, 12L15, 13L05]03Hxx & 03H99Nonstandard modelsNone of the above, but in this section03Hxx # 03HxxNonstandard modelsNonstandard models [See also 03C62]03-XX G 05-00Reference works (combinatorics)General reference works (handbooks, dictionaries, bibliographies, etc.)05-XX ; 05-01Textbooks (combinatorics)Instructional exposition (textbooks, tutorial papers, etc.)05-XX # 1 05-02Research monographs (combinatorics)Research exposition (monographs, survey articles)05-XX U 05-03Historical (combinatorics)Historical (must also be assigned at least one classification number from Section 01)05-XX - X 05-04Machine computation, programs (combinatorics)Explicit machine computation and programs (not the theory of computation or programming)05-XX * + 05-06Proceedings of conferences (combinatorics)Proceedings, conferences, collections, etc.05-XX
05-99CombinatoricsCombinatorics
, 05-XXCombinatoricsCombinatorics {For finite fields, see 11Txx} F 05A05Combinatorial choice problemsCombinatorial choice problems (subsets, representatives, permutations)05Axx R 05A10Combinatorial functionsFactorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]05Axx " H 05A15Combinatorial enumeration problemsExact enumeration problems, generating functions [See also 33Cxx, 33Dxx]05Axx 05A16Asymptotic enumerationAsymptotic enumeration05Axx & 5 05A17Partitions of integres (combinatorics)Partitions of integers [See also 11P81, 11P82, 11P83]05Axx 05A18Partitions of setsPartitions of sets05Axx 05A19Combinatorial identitiesCombinatorial identities05Axx 05A20Combinatorial inequalitiesCombinatorial inequalities05Axx 0 05A30q-calculus and related topics$q$-calculus and related topics [See also 03Dxx]05Axx 05A40Umbral calculusUmbral calculus05Axx & 05A99Classical combinatorial problemsNone of the above, but in this section05Axx 05AxxClassical combinatorial problemsEnumerative combinatorics05-XX % 05B05Block designs (combinatorics)Block designs [See also 51E05, 62K10]05Bxx 05B07Triple systemsTriple systems05Bxx J 05B10Difference setsDifference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]05Bxx . 05B15Orthogonal arrays, etc.Orthogonal arrays, Latin squares, Room squares05Bxx $ 05B20(0,1)-matrices (combinatorics)Matrices (incidence, Hadamard, etc.)05Bxx ! ) 05B25Finite geometries (combinatorics)Finite geometries [See also 51D20, 51Exx]05Bxx . 05B30Other designs, configurationsOther designs, configurations [See also 51E30]05Bxx 4 05B35Matroids (combinatorics)Matroids, geometric lattices [See also 52B40, 90C27]05Bxx $ 3 05B40Packing and covering (combinatorics)Packing and covering [See also 11H31, 52C15, 52C17]05Bxx 8 05B45Tessellation and tiling problemsTessellation and tiling problems [See also 52C20, 52C22]05Bxx 05B50PolyominoesPolyominoes05Bxx & 05B99Designs and configurationsNone of the above, but in this section05Bxx I 05BxxDesigns and configurationsDesigns and configurations {For applications of design theory, see 94C30}05-XX 05C05TreesTrees05Cxx 05C07Degree sequencesDegree sequences05Cxx05C991 ; 05C10Topological graph theoryTopological graph theory, imbedding [See also 57M15, 57M25]05Cxx 05C12Distance in graphsDistance in graphs05Cxx # " 05C15Chromatic theory of graphs and mapsColoring of graphs and hypergraphs05Cxx 05C17Perfect graphsPerfect graphs05Cxx05C15,05C601 ' 05C20Directed graphs (digraphs)Directed graphs (digraphs), tournaments05Cxx 05C22Signed, gain and biased graphsSigned, gain and biased graphs05Cxx05C75,05C991 " 05C25Graphs and groupsGraphs and groups [See also 20F65]05Cxx 05C30Enumeration of graphs and mapsEnumeration of graphs and maps05Cxx " 05C35Extremal problems (graph theory)Extremal problems [See also 90C35]05Cxx ! 05C38Paths and cyclesPaths and cycles [See also 90B10]05Cxx 05C40ConnectivityConnectivity05Cxx 05C45Eulerian and Hamiltonian graphsEulerian and Hamiltonian graphs05Cxx 05C50Graphs and matricesGraphs and matrices05Cxx 05C55Generalized Ramsey theoryGeneralized Ramsey theory05Cxx # 6 05C60Isomorphism problems (graph theory)Isomorphism problems (reconstruction conjecture, etc.)05Cxx H 05C62Graph representationsGraph representations (geometric and intersection representations, etc.)05Cxx05C751 05C65HypergraphsHypergraphs05Cxx * * 05C69Dominating sets, independent sets, cliquesDominating sets, independent sets, cliques05Cxx05C35,05C701 - 05C70Factorization, etc.Factorization, matching, covering and packing05Cxx . . 05C75Structural characterization of types of graphsStructural characterization of types of graphs05Cxx 2 05C78Graph labellingGraph labelling (graceful graphs, bandwidth, etc.)05Cxx
05C80Random graphsRandom graphs05Cxx 05C83Graph minorsGraph minors05Cxx05C991 ( 05C85Graphic algorithmsGraph algorithms [See also 68R10, 68W05]05Cxx 05C90Appl. of graph theoryApplications05Cxx & 05C99Graph theoryNone of the above, but in this section05Cxx B 05CxxGraph theoryGraph theory {For applications of graphs, see 68R10, 90C35, 94C15}05-XX 05D05Extremal set theoryExtremal set theory05Dxx
05D10Ramsey theoryRamsey theory05Dxx 05D15Transversal (matching) theoryTransversal (matching) theory05Dxx & 05D40Probabilistic methods in combinatoricsProbabilistic methods05Dxx05A161 & 05D99Extremal combinatoricsNone of the above, but in this section05Dxx 05DxxExtremal combinatoricsExtremal combinatorics05-XX 05E05Symmetric functionsSymmetric functions05Exx A 05E10Tableaux, etc.Tableaux, representations of the symmetric group [See also 20C30]05Exx 6 N 05E15Combinatorial problems concerning the classical groupsCombinatorial problems concerning the classical groups [See also 22E45, 33C80]05Exx . 05E20Group actions on designs, etc.Group actions on designs, geometries and codes05Exx F 05E25Group actions on posets, etc.Group actions on posets and homology groups of posets [See also 06A11]05Exx , 05E30Association schemes, etc.Association schemes, strongly regular graphs05Exx & 5 05E35Orthogonal polynomials (combinatorics)Orthogonal polynomials [See also 33C45, 33C50, 33D45]05Exx & 05E99Algebraic combinatoricsNone of the above, but in this section05Exx 05ExxAlgebraic combinatoricsAlgebraic combinatorics05-XX $ G 06-00Reference works (ordered structures)General reference works (handbooks, dictionaries, bibliographies, etc.)06-XX ; 06-01Textbooks (ordered structures)Instructional exposition (textbooks, tutorial papers, etc.)06-XX ( 1 06-02Research monographs (ordered structures)Research exposition (monographs, survey articles)06-XX U 06-03Historical (ordered structures)Historical (must also be assigned at least one classification number from Section 01)06-XX 2 X 06-04Machine computation, programs (ordered structures)Explicit machine computation and programs (not the theory of computation or programming)06-XX / + 06-06Proceedings of conferences (ordered structures)Proceedings, conferences, collections, etc.06-XX - - 06-99Order, lattices, ordered algebraic structuresOrder, lattices, ordered algebraic structures > 06-XXOrdered structuresOrder, lattices, ordered algebraic structures [See also 18B35] 06A05Total orderTotal order06Axx
06A06Partial orderPartial order, general06Axx ' ' 06A07Combinatorics of partially ordered setsCombinatorics of partially ordered sets06Axx , 06A11Algebraic aspects of posetsAlgebraic aspects of posets [See also 05E25]06Axx06A08,06A091 E 06A12SemilatticesSemilattices [See also 20M10; for topological semilattices see 22A26]06Axx + ) 06A15Galois correspondences (ordered structures)Galois correspondences, closure operators06Axx & 06A99Ordered setsNone of the above, but in this section06Axx 06AxxOrdered setsOrdered sets06-XX 06B05Structure theory of latticesStructure theory06Bxx 06B10Ideals, etc. (lattices)Ideals, congruence relations06Bxx ! 06B15Representation theory of latticesRepresentation theory06Bxx 06B20Varieties of latticesVarieties of lattices06Bxx 06B23Complete latticesComplete lattices, completions06Bxx06A231 P 06B25Free lattices, etc.Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]06Bxx L 06B30Topological latticesTopological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]06Bxx ` 06B35Continuous latticesContinuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]06Bxx & 06B99LatticesNone of the above, but in this section06Bxx 06BxxLatticesLattices [See also 03G10]06-XX ' 06C05Modular latticesModular lattices, Desarguesian lattices06Cxx ( 06C10Geometric latticesSemimodular lattices, geometric lattices06Cxx T 06C15Complemented latticesComplemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]06Cxx # 4 06C20Complemented modular lattices, etc.Complemented modular lattices, continuous geometries06Cxx # & 06C99Lattices (modular and complemented)None of the above, but in this section06Cxx # ' 06CxxLattices (modular and complemented)Modular lattices, complemented lattices06-XX < # 06D05Structure and representation theory of distributive latticesStructure and representation theory06Dxx # 06D10Complete distributivity of latticesComplete distributivity06Dxx 06D15Pseudocomplemented latticesPseudocomplemented lattices06Dxx ! 06D20Heyting algebrasHeyting algebras [See also 03G25]06Dxx 5 06D22Frames etc.Frames, locales {For topological questions see 54-XX}06Dxx06D10,06D20,06D991
06D25Post algebrasPost algebras [See also 03G20]06Dxx & 9 06D30De Morgan algebras and generalizationsDe Morgan algebras, Lukasiewicz algebras [See also 03G20]06Dxx 06D35MV-algebrasMV-algebras06Dxx06D301 06D50Lattices and dualityLattices and duality06Dxx06D051 1 06D72Fuzzy lattices etc.Fuzzy lattices (soft algebras) and related topics06Dxx06D301 & 06D99Distributive latticesNone of the above, but in this section06Dxx 06DxxDistributive latticesDistributive lattices06-XX $ 06E05Structure theory of Boolean algebrasStructure theory06Exx # 06E10Complete Boolean algebrasChain conditions, complete algebras06Exx % % 06E15Stone space and related constructionsStone space and related constructions06Exx , 1 06E20Ring theoretic properties (Boolean algebras)Ring-theoretic properties [See also 16E50, 16G30]06Exx + c 06E25Boolean algebras with additional operationsBoolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]06Exx " 06E30Boolean functionsBoolean functions [See also 94C10]06Exx & 06E99Boolean algebrasNone of the above, but in this section06Exx 1 06ExxBoolean algebrasBoolean algebras (Boolean rings) [See also 03G05]06-XX / 06F05Ordered semigroupsOrdered semigroups and monoids [See also 20Mxx]06Fxx 06F07QuantalesQuantales06Fxx06F051 06F10Noether latticesNoether lattices06Fxx 06F15Ordered groupsOrdered groups [See also 20F60]06Fxx L 06F20Ordered abelian groups, etc.Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]06Fxx W 06F25Ordered algebraic structuresOrdered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80}06Fxx * L 06F30Order topologies (order-theoretic aspects)Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]06Fxx + 06F35BCK-algebras, etc.BCK-algebras, BCI-algebras [See also 03G25]06Fxx 4 & 06F99Ordered structures (connections with other sections)None of the above, but in this section06Fxx 4 06FxxOrdered structures (connections with other sections)Ordered structures06-XX + G 08-00Reference works (general algebraic systems)General reference works (handbooks, dictionaries, bibliographies, etc.)08-XX % ; 08-01Textbooks (general algebraic systems)Instructional exposition (textbooks, tutorial papers, etc.)08-XX / 1 08-02Research monographs (general algebraic systems)Research exposition (monographs, survey articles)08-XX & U 08-03Historical (general algebraic systems)Historical (must also be assigned at least one classification number from Section 01)08-XX 9 X 08-04Machine computation, programs (general algebraic systems)Explicit machine computation and programs (not the theory of computation or programming)08-XX 6 + 08-06Proceedings of conferences (general algebraic systems)Proceedings, conferences, collections, etc.08-XX 08-99General algebraic systemsGeneral algebraic systems 08-XXGeneral algebraic systemsGeneral algebraic systems ' 08A02General relational systemsRelational systems, laws of composition08Axx - 08A05Structure theory of general algebraic systemsStructure theory08Axx ( ! 08A30Subalgebras of general algebraic systemsSubalgebras, congruence relations08Axx * 08A35Endomorphisms on general algebraic systemsAutomorphisms, endomorphisms08Axx ' ( 08A40Operations on general algebraic systemsOperations, polynomials, primal algebras08Axx 08A45Equational compactnessEquational compactness08Axx ! 3 08A50Word problems (universal algebra)Word problems [See also 03D40, 06B25, 20F10, 68R15]08Axx 08A55Partial algebrasPartial algebras08Axx 08A60Unary algebrasUnary algebras08Axx 08A62Finitary algebrasFinitary algebras08Axx 08A65Infinitary algebrasInfinitary algebras08Axx 08A68Heterogeneous algebrasHeterogeneous algebras08Axx08A551 . 5 08A70Appl. of universal algebra in computer scienceApplications of universal algebra in computer science08Axx 08A72Fuzzy algebraic structuresFuzzy algebraic structures08Axx03E721 & 08A99Universal algebraNone of the above, but in this section08Axx % 08AxxUniversal algebraAlgebraic structures [See also 03C05]08-XX ) - 08B05Equational logic in varieties of algebrasEquational logic, Malcev (Maltsev) conditions08Bxx B 0 08B10Congruence modularity and generalizations in varieties of algebrasCongruence modularity, congruence distributivity08Bxx ! 08B15Lattices of varieties of algebrasLattices of varieties08Bxx &
08B20Free algebras in varieties of algebrasFree algebras08Bxx W 08B25Limits in varieties of algebrasProducts, amalgamated products, and other kinds of limits and colimits [See also 18A30]08Bxx + / 08B26Subdirect products in varieties of algebrasSubdirect products and subdirect irreducibility08Bxx 2 08B30Injectives or projectives in varieties of algebrasInjectives, projectives08Bxx & 08B99Varieties of algebrasNone of the above, but in this section08Bxx 08BxxVarieties of algebrasVarieties [See also 03C05]08-XX ' 08C05Categories of algebrasCategories of algebras [See also 18C05]08Cxx = 08C10Axiomatic model classesAxiomatic model classes [See also 03Cxx, in particular 03C60]08Cxx 08C15QuasivarietiesQuasivarieties08Cxx & 08C99Classes of algebrasNone of the above, but in this section08Cxx 08CxxOther classes of algebrasOther classes of algebras08-XX G 11-00Reference works (number theory)General reference works (handbooks, dictionaries, bibliographies, etc.)11-XX ; 11-01Textbooks (number theory)Instructional exposition (textbooks, tutorial papers, etc.)11-XX # 1 11-02Research monographs (number theory)Research exposition (monographs, survey articles)11-XX U 11-03Historical (number theory)Historical (must also be assigned at least one classification number from Section 01)11-XX - X 11-04Machine computation, programs (number theory)Explicit machine computation and programs (not the theory of computation or programming)11-XX * + 11-06Proceedings of conferences (number theory)Proceedings, conferences, collections, etc.11-XX
11-99Number theoryNumber theory
11-XXNumber theoryNumber theory ( G 11A05Multiplicative structure of the integersMultiplicative structure; Euclidean algorithm; greatest common divisors11Axx - 11A07Congruences, etc.Congruences; primitive roots; residue systems11Axx 11A15Power residues, etc.Power residues, reciprocity11Axx 9 11A25Arithmetic functions, etc.Arithmetic functions; related numbers; inversion formulas11Axx 11A41Elementary prime number theoryPrimes11Axx 11A51Factorization of numbersFactorization; primality11Axx . Y 11A55Continued fractions (number-theoretic results)Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]11Axx F 11A63Radix representationRadix representation; digital problems {For metric results, see 11K16}11Axx 1 11A67Representation systems for integers and rationalsOther representations11Axx & 11A99Elementary number theoryNone of the above, but in this section11Axx D 11AxxElementary number theoryElementary number theory {For analogues in number fields, see 11R04}11-XX 11B05Topology etc. of sets of numbersDensity, gaps, topology11Bxx 11B13Additive basesAdditive bases [See also 05B10]11Bxx ( 11B25Arithmetic progressionsArithmetic progressions [See also 11N13]11Bxx 11B34Representation functionsRepresentation functions11Bxx > 11B37RecurrencesRecurrences {For applications to special functions, see 33-XX}11Bxx ? 11B39Special numbers, etc.Fibonacci and Lucas numbers and polynomials and generalizations11Bxx 11B50Sequences (mod m)Sequences (mod $m$)11Bxx 3 11B57Farey sequencesFarey sequences; the sequences ${1^k, 2^k, \cdots}$11Bxx I 11B65Binomial coefficients, etc.Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]11Bxx + 11B68Bernoulli numbers, etc.Bernoulli and Euler numbers and polynomials11Bxx 11B73Bell and Stirling numbersBell and Stirling numbers11Bxx ! 11B75Combinatorial number theoryOther combinatorial number theory11Bxx - ! 11B83Special sequences of integers and polynomialsSpecial sequences and polynomials11Bxx 11B85Automata sequencesAutomata sequences11Bxx & 11B99Sequences and setsNone of the above, but in this section11Bxx 11BxxSequences and sets of numbersSequences and sets11-XX 11C08PolynomialsPolynomials [See also 13F20]11Cxx ' 11C20Matrices, determinantsMatrices, determinants [See also 15A36]11Cxx & 11C99Polynomials and matricesNone of the above, but in this section11Cxx 11CxxPolynomials and matricesPolynomials and matrices11-XX 11D04Linear diophantine equationsLinear equations11Dxx , 11D09Quadratic and bilinear diophantine equationsQuadratic and bilinear equations11Dxx ' 11D25Cubic and quartic diophantine equationsCubic and quartic equations11Dxx # * 11D41Higher degree diophantine equationsHigher degree equations; Fermat's equation11Dxx + + 11D45Counting solutions of Diophantine equationsCounting solutions of Diophantine equations11Dxx11N45,11D1 2 & 11D57Multiplicative and norm form diophantine equationsMultiplicative and norm form equations11Dxx 11D59Thue-Mahler equationsThue-Mahler equations11Dxx11D571 ! 11D61Exponential diophantine equationsExponential equations11Dxx % % 11D68Rational numbers as sums of fractionsRational numbers as sums of fractions11Dxx , 11D72Equations in many variablesEquations in many variables [See also 11P55]11Dxx ) 11D75Diophantine inequalitiesDiophantine inequalities [See also 11J25]11Dxx 11D79Congruences in many variablesCongruences in many variables11Dxx # ( 11D85Representation problems of integersRepresentation problems [See also 11P55]11Dxx 11D88p-adic and power series fields$p$-adic and power series fields11Dxx & 11D99Diophantine equationsNone of the above, but in this section11Dxx - 11DxxDiophantine equationsDiophantine equations [See also 11Gxx, 14Gxx]11-XX # # 11E04Quadratic forms over general fieldsQuadratic forms over general fields11Exx + + 11E08Quadratic forms over local rings and fieldsQuadratic forms over local rings and fields11Exx 11E10Forms over real fieldsForms over real fields11Exx , , 11E12Quadratic forms over global rings and fieldsQuadratic forms over global rings and fields11Exx 11E16General binary quadratic formsGeneral binary quadratic forms11Exx . P 11E20General ternary and quaternary quadratic formsGeneral ternary and quaternary quadratic forms; forms of more than two variables11Exx G 11E25Sums of squares, etcSums of squares and representations by other particular quadratic forms11Exx 11E39Bilinear and Hermitian formsBilinear and Hermitian forms11Exx . . 11E41Class numbers of quadratic and Hermitian formsClass numbers of quadratic and Hermitian forms11Exx X 11E45Analytic theory of formsAnalytic theory (Epstein zeta functions; relations with automorphic forms and functions)11Exx ) ( 11E57Arithmetic properties of classical groupsClassical groups [See also 14Lxx, 20Gxx]11Exx ) + 11E70K-theory of quadratic and Hermitian forms$K$-theory of quadratic and Hermitian forms11Exx , = 11E72Galois cohomology of linear algebraic groupsGalois cohomology of linear algebraic groups [See also 20G10]11Exx 11E76Forms of degree higher than twoForms of degree higher than two11Exx # R 11E81Algebraic theory of quadratic formsAlgebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]11Exx # ; 11E88Quadratic spaces; Clifford algebrasQuadratic spaces; Clifford algebras [See also 15A63, 15A66]11Exx 11E95p-adic theory of forms$p$-adic theory11Exx ! & 11E99Forms and linear algebraic groupsNone of the above, but in this section11Exx ! e 11ExxForms and linear algebraic groupsForms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}11-XX ! ! 11F03Modular and automorphic functionsModular and automorphic functions11Fxx / a 11F06Structure of modular groups and generalizationsStructure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]11Fxx 11F11Modular forms, one variableModular forms, one variable11Fxx 11F12Automorphic forms, one variableAutomorphic forms, one variable11Fxx $ $ 11F20Dedekind eta function, Dedekind sumsDedekind eta function, Dedekind sums11Fxx 7 5 11F22Relationship of automorphic forms to Lie algebras, etc.Relationship to Lie algebras and finite simple groups11Fxx ? . 11F23Relations of number theory with algebraic geometry and topologyRelations with algebraic geometry and topology11Fxx14-XX,57-XX1 @ @ 11F25Hecke-Petersson operators, differential operators (one variable)Hecke-Petersson operators, differential operators (one variable)11Fxx ! ! 11F27Theta series; Weil representationTheta series; Weil representation11Fxx ) ) 11F30Fourier coefficients of automorphic formsFourier coefficients of automorphic forms11Fxx 11F32Modular correspondences, etc.Modular correspondences, etc.11Fxx & J 11F33Congruences for (p-adic) modular formsCongruences for modular and $p$-adic modular forms [See also 14G20, 22E50]11Fxx " : 11F37Forms of half-integer weight, etc.Forms of half-integer weight; nonholomorphic modular forms11Fxx " | 11F41Hilbert modular forms and surfacesHilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]11Fxx = = 11F46Siegel modular groups and their modular and automorphic formsSiegel modular groups and their modular and automorphic forms11Fxx 11F50Jacobi formsJacobi forms11Fxx11F551 - - 11F52Modular forms associated to Drinfel'd modulesModular forms associated to Drinfel'd modules11Fxx11G09,11F111 B H 11F55Groups and their modular and automorphic forms (several variables)Other groups and their modular and automorphic forms (several variables)11Fxx 0 E 11F60Differential operators, etc. (several variables)Hecke-Petersson operators, differential operators (several variables)11Fxx B J 11F66Dirichlet series and functional equations related to modular formsDirichlet series and functional equations in connection with modular forms11Fxx + _ 11F67Special values of automorphic L-series, etcSpecial values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols11Fxx 6 Z 11F70Representation-theoretic methods in automorphic theoryRepresentation-theoretic methods; automorphic representations over local and global fields11Fxx & 11F72Spectral theorySpectral theory; Selberg trace formula11Fxx 11F75Cohomology of arithmetic groupsCohomology of arithmetic groups11Fxx 11F80Galois propertiesGalois representations11Fxx 5 11F85p-adic theory, local fields$p$-adic theory, local fields [See also 14G20, 22E50]11Fxx * & 11F99Discontinuous groups and automorphic formsNone of the above, but in this section11Fxx * ª 11FxxDiscontinuous groups and automorphic formsDiscontinuous groups and automorphic forms [See also 11R39, 11S37, 14-XX, 14Gxx, 14Kxx, 22Exx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}11-XX " 3 11G05Elliptic curves over global fieldsElliptic curves over global fields [See also 14H52]11Gxx ! 9 11G07Elliptic curves over local fieldsElliptic curves over local fields [See also 14G20, 14H52]11Gxx C 11G09Drinfel'd modules, etc.Drinfeld modules; higher-dimensional motives, etc. [See also 14L05]11Gxx # 8 11G10Abelian varieties of dimension $>1$Abelian varieties of dimension $\gtr 1$ [See also 14Kxx]11Gxx 6 G 11G15Complex multiplication and moduli of abelian varietiesComplex multiplication and moduli of abelian varieties [See also 14K22]11Gxx + 11G16Elliptic and modular unitsElliptic and modular units [See also 11R27]11Gxx 3 D 11G18Arithmetic aspects of modular and Shimura varietiesArithmetic aspects of modular and Shimura varieties [See also 14G35]11Gxx # 4 11G20Curves over finite and local fieldsCurves over finite and local fields [See also 14H25]11Gxx & > 11G25Varieties over finite and local fieldsVarieties over finite and local fields [See also 14G15, 14G20]11Gxx N 11G30Curves of arbitrary genusCurves of arbitrary genus or genus $\ne 1$ over global fields [See also 14H25]11Gxx - 11G35Varieties over global fieldsVarieties over global fields [See also 14G25]11Gxx + ` 11G40L-functions of varieties over global fields$L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]11Gxx ; 11G45Geometric class field theoryGeometric class field theory [See also 11R37, 14C35, 19F05]11Gxx 11G50HeightsHeights [See also 14G40]11Gxx11G351 * , 11G55Polylogarithms and relations with K-theoryPolylogarithms and relations with $K$-theory11Gxx19F27,11R42,14G101 & 11G99Arithmetic algebraic geometryNone of the above, but in this section11Gxx 4 Z 11GxxArithmetic algebraic geometry (Diophantine geometry)Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14-XX, 14Gxx, 14Kxx]11-XX 5 9 11H06Lattices and convex bodies (number theoretic results)Lattices and convex bodies [See also 11P21, 52C05, 52C07]11Hxx 11H16Nonconvex bodiesNonconvex bodies11Hxx 7 ; 11H31Lattice packing and covering (number-theoretic results)Lattice packing and covering [See also 05B40, 52C15, 52C17]11Hxx 11H46Products of linear formsProducts of linear forms11Hxx 11H50Minima of formsMinima of forms11Hxx 7 11H55Quadratic formsQuadratic forms (reduction theory, extreme forms, etc.)11Hxx 11H56Automorphism groups of latticesAutomorphism groups of lattices11Hxx 11H60Mean value and transfer theoremsMean value and transfer theorems11Hxx - 11H71Relations of number theory with coding theoryRelations with coding theory11Hxx11T711 & 11H99Geometry of numbersNone of the above, but in this section11Hxx B 11HxxGeometry of numbersGeometry of numbers {For applications in coding theory, see 94B75}11-XX ' ' 11J04Homogeneous approximation to one numberHomogeneous approximation to one number11Jxx / / 11J06Markov and Lagrange spectra and generalizationsMarkov and Lagrange spectra and generalizations11Jxx 4 4 11J13Simultaneous homogeneous approximation, linear formsSimultaneous homogeneous approximation, linear forms11Jxx + + 11J17Approximation by numbers from a fixed fieldApproximation by numbers from a fixed field11Jxx 11J20Inhomogeneous linear formsInhomogeneous linear forms11Jxx ) 11J25Diophantine inequalitiesDiophantine inequalities [See also 11D75]11Jxx 9 9 11J54Small fractional parts of polynomials and generalizationsSmall fractional parts of polynomials and generalizations11Jxx + + 11J61Approximation in non-Archimedean valuationsApproximation in non-Archimedean valuations11Jxx " " 11J68Approximation to algebraic numbersApproximation to algebraic numbers11Jxx ' ? 11J70Continued fractions and generalizationsContinued fractions and generalizations [See also 11A55, 11K50]11Jxx ( 11J71Distribution modulo oneDistribution modulo one [See also 11K06]11Jxx
/ 11J72IrrationalityIrrationality; linear independence over a field11Jxx 11J81Transcendence (general theory)Transcendence (general theory)11Jxx . . 11J82Measures of irrationality and of transcendenceMeasures of irrationality and of transcendence11Jxx
11J83Metric theory of numbersMetric theory11Jxx ( 11J85Algebraic independence resultsAlgebraic independence; Gelfond's method11Jxx * * 11J86Linear forms in logarithms; Baker's methodLinear forms in logarithms; Baker's method11Jxx 6 6 11J89Transcendence theory of elliptic and abelian functionsTranscendence theory of elliptic and abelian functions11Jxx / / 11J91Transcendence theory of other special functionsTranscendence theory of other special functions11Jxx 1 1 11J93Transcendence theory of Drinfel'd and $t$-modulesTranscendence theory of Drinfel'd and $t$-modules11Jxx11G09,11J991 @ # 11J95Results of diophantine approximation involving abelian varietiesResults involving abelian varieties11Jxx11G101 ) @ 11J97Analogues of methods in Nevanlinna theoryAnalogues of methods in Nevanlinna theory (work of Vojta et al.)11Jxx11J991 & 11J99Diophantine approximationNone of the above, but in this section11Jxx H 11JxxDiophantine approximationDiophantine approximation, transcendental number theory [See also 11K60]11-XX ' : 11K06General theory of distribution modulo 1General theory of distribution modulo $1$ [See also 11J71]11Kxx 7 11K16Normal numbers, etc.Normal numbers, radix expansions, etc. [See also 11A63]11Kxx 11K31Special sequencesSpecial sequences11Kxx / / 11K36Well-distributed sequences and other variationsWell-distributed sequences and other variations11Kxx < 11K38Irregularities of distributionIrregularities of distribution, discrepancy [See also 11Nxx]11Kxx ) + 11K41Continuous, p-adic and abstract analoguesContinuous, $p$-adic and abstract analogues11Kxx * 11K45Pseudo-random numbers, etc.Pseudo-random numbers; Monte Carlo methods11Kxx $ < 11K50Metric theory of continued fractionsMetric theory of continued fractions [See also 11A55, 11J70]11Kxx A i 11K55Metric theory of other number-theoretic algorithms and expansionsMetric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]11Kxx 7 * 11K60Diophantine approximation (probabilistic number theory)Diophantine approximation [See also 11Jxx]11Kxx 2 % 11K65Arithmetic functions (probabilistic number theory)Arithmetic functions [See also 11Nxx]11Kxx ( ( 11K70Harmonic analysis and almost periodicityHarmonic analysis and almost periodicity11Kxx & 11K99Probabilistic theoryNone of the above, but in this section11Kxx J 11KxxProbabilistic number theoryProbabilistic theory: distribution modulo $1$; metric theory of algorithms11-XX + + 11L03Trigonometric and exponential sums, generalTrigonometric and exponential sums, general11Lxx + 11L05Gauss and Kloosterman sumsGauss and Kloosterman sums; generalizations11Lxx 11L07Estimates on exponential sumsEstimates on exponential sums11Lxx 9 11L10Complete character sumsJacobsthal and Brewer sums; other complete character sums11Lxx 11L15Weyl sumsWeyl sums11Lxx 11L20Sums over primesSums over primes11Lxx 11L26Sums over arbitrary intervalsSums over arbitrary intervals11Lxx 11L40Estimates on character sumsEstimates on character sums11Lxx # & 11L99Exponential sums and character sumsNone of the above, but in this section11Lxx # B 11LxxExponential sums and character sumsExponential sums and character sums {For finite fields, see 11Txx}11-XX 1 11M06Riemannian zeta-function and Dirichlet L-function$\zeta (s)$ and $L(s, \chi)$11Mxx 3 11M20Real zeros of L(s,chi)Real zeros of $L(s, \chi)$; results on $L(1, \chi)$11Mxx % K 11M26Nonreal zeros of zeta(s) and L(s,chi)Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses11Mxx 11M35Other zeta functionsHurwitz and Lerch zeta functions11Mxx 3 ‘ 11M36Selberg zeta functions and regularized determinantsSelberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas11Mxx , , 11M38Zeta and $L$-functions in characteristic $p$Zeta and $L$-functions in characteristic $p$11Mxx11M411 ) ½ 11M41Other Dirichlet series and zeta functionsOther Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}11Mxx # 11M45Tauberian theoremsTauberian theorems [See also 40E05]11Mxx ' & 11M99Analytic theory of zeta and L-functionsNone of the above, but in this section11Mxx ' ' 11MxxAnalytic theory of zeta and L-functionsZeta and $L$-functions: analytic theory11-XX 11N05Distribution of primesDistribution of primes11Nxx ' 11N13Primes in progressionsPrimes in progressions [See also 11B25]11Nxx B B 11N25Distribution of integers with specified multiplicative constraintsDistribution of integers with specified multiplicative constraints11Nxx 11N30Turan theoryTurán theory [See also 30Bxx]11Nxx ! V 11N32Primes represented by polynomialsPrimes represented by polynomials; other multiplicative structure of polynomial values11Nxx 11N35SievesSieves11Nxx 11N36Appl. of sieve methodsApplications of sieve methods11Nxx * * 11N37Asymptotic results on arithmetic functionsAsymptotic results on arithmetic functions11Nxx = Q 11N45Asymptotic results on counting functions for other structuresAsymptotic results on counting functions for algebraic and topological structures11Nxx & & 11N56Rate of growth of arithmetic functionsRate of growth of arithmetic functions11Nxx A U 11N60Distribution functions (additive and positive multipl. functions)Distribution functions associated with additive and positive multiplicative functions11Nxx ( [ 11N64Characterization of arithmetic functionsOther results on the distribution of values or the characterization of arithmetic functions11Nxx 3 3 11N69Distribution of integers in special residue classesDistribution of integers in special residue classes11Nxx 6 [ 11N75Appl. of automorphic theory to multiplicative problemsApplications of automorphic functions and forms to multiplicative problems [See also 11Fxx]11Nxx 11N80Generalized primes and integersGeneralized primes and integers11Nxx & 11N99Multiplicative number theoryNone of the above, but in this section11Nxx 11NxxMultiplicative number theoryMultiplicative number theory11-XX 11P05Waring's problem and variantsWaring's problem and variants11Pxx # # 11P21Lattice points in specified regionsLattice points in specified regions11Pxx # A 11P32Additive questions involving primesGoldbach-type theorems; other additive questions involving primes11Pxx $ < 11P55Appl. of the Hardy-Littlewood methodApplications of the Hardy-Littlewood method [See also 11D85]11Pxx * * 11P70Inverse problems of additive number theoryInverse problems of additive number theory11Pxx11B751 0 11P81Elementary theory of partitionsElementary theory of partitions [See also 05A17]11Pxx 11P82Analytic theory of partitionsAnalytic theory of partitions11Pxx 5 5 11P83Partitions: congruences and congruential restrictionsPartitions; congruences and congruential restrictions11Pxx & 11P99Additive number theoryNone of the above, but in this section11Pxx " 11PxxAdditive number theoryAdditive number theory; partitions11-XX . 11R04Algebraic numbersAlgebraic numbers; rings of algebraic integers11Rxx ? 11R06Special algebraic numbersPV-numbers and generalizations; other special algebraic numbers11Rxx " 11R09Polynomials over global fieldsPolynomials (irreducibility, etc.)11Rxx 11R11Quadratic extensionsQuadratic extensions11Rxx 11R16Cubic and quartic extensionsCubic and quartic extensions11Rxx 11R18Cyclotomic extensionsCyclotomic extensions11Rxx ' ' 11R20Other abelian and metabelian extensionsOther abelian and metabelian extensions11Rxx 11R21Other number fieldsOther number fields11Rxx 11R23Iwasawa theoryIwasawa theory11Rxx 11R27Units and factorizationUnits and factorization11Rxx * * 11R29Class numbers, class groups, discriminantsClass numbers, class groups, discriminants11Rxx
11R32Galois theory for global fieldsGalois theory11Rxx 5 t 11R33Integral representations related to algebraic numbersIntegral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]11Rxx # 0 11R34Galois cohomology for global fieldsGalois cohomology [See also 12Gxx, 16H05, 19A31]11Rxx $ 11R37Class field theory for global fieldsClass field theory11Rxx 9 Q 11R39Langlands-Weil conjectures, nonabelian class field theoryLanglands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]11Rxx 6 I 11R42Zeta functions and L-functions of global number fieldsZeta functions and $L$-functions of number fields [See also 11M41, 19F27]11Rxx - 11R44Distribution of prime idealsDistribution of prime ideals [See also 11N05]11Rxx 11R45Density theoremsDensity theorems11Rxx & 11R47Other analytic theoryOther analytic theory [See also 11Nxx]11Rxx B B 11R52Quaternion and other division algebras: arithmetic, zeta functionsQuaternion and other division algebras: arithmetic, zeta functions11Rxx 9 Z 11R54Other algebras and orders, and their zeta and L-functionsOther algebras and orders, and their zeta and $L$-functions [See also 11S45, 16H05, 16Kxx]11Rxx 11R56Adele rings and groupsAdèle rings and groups11Rxx . ? 11R58Arithmetic theory of algebraic function fieldsArithmetic theory of algebraic function fields [See also 14-XX]11Rxx B 11R60Cyclotomic function fieldsCyclotomic function fields (class groups, Bernoulli objects, etc.)11Rxx11R581 ( ( 11R65Class groups and Picard groups of ordersClass groups and Picard groups of orders11Rxx , 11R70K-theory of global fields$K$-theory of global fields [See also 19Fxx]11Rxx 9 11R80Totally real fields, etc.Totally real and totally positive fields [See also 12J15]11Rxx * & 11R99Algebraic number theory over global fieldsNone of the above, but in this section11Rxx & N 11RxxAlgebraic number theory: global fieldsAlgebraic number theory: global fields {For complex multiplication, see 11G15}11-XX 11S05Polynomials over local fieldsPolynomials11Sxx ! ! 11S15Ramification and extension theoryRamification and extension theory11Sxx
11S20Galois theory for local fieldsGalois theory11Sxx ) 11S23Integral representations for local fieldsIntegral representations11Sxx " ) 11S25Galois cohomology for local fieldsGalois cohomology [See also 12Gxx, 16H05]11Sxx # ; 11S31Class field theory for local fieldsClass field theory; $p$-adic formal groups [See also 14L05]11Sxx 9 Q 11S37Langlands-Weil conjectures, nonabelian class field theoryLanglands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]11Sxx 5 8 11S40Zeta functions and L-functions of local number fieldsZeta functions and $L$-functions [See also 11M41, 19F27]11Sxx - S 11S45Algebras and orders, and their zeta functionsAlgebras and orders, and their zeta functions [See also 11R52, 11R54, 16H05, 16Kxx]11Sxx + 11S70K-theory of local fields$K$-theory of local fields [See also 19Fxx]11Sxx % Y 11S80Other analytic theory of local fieldsOther analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)11Sxx ( 11S85Other nonanalytic theory of local fieldsOther nonanalytic theory11Sxx 11S90Prehomogeneous vector spacesPrehomogeneous vector spaces11Sxx11M41,11S401 4 & 11S99Algebraic number theory over local and p-adic fieldsNone of the above, but in this section11Sxx 0 2 11SxxAlgebraic number theory: local and p-adic fieldsAlgebraic number theory: local and $p$-adic fields11-XX ' 11T06Polynomials over finite fields or ringsPolynomials11Txx 11T22CyclotomyCyclotomy11Txx 11T23Exponential sumsExponential sums11Txx # # 11T24Other character sums and Gauss sumsOther character sums and Gauss sums11Txx ! 11T30Structure theory of finite fieldsStructure theory11Txx 8 8 11T55Arithmetic theory of polynomial rings over finite fieldsArithmetic theory of polynomial rings over finite fields11Txx 11T60Finite upper half-planesFinite upper half-planes11Txx11F991 % 11T71Algebraic coding theoryAlgebraic coding theory; cryptography11Txx > & 11T99Finite fields and commutative rings (number-theoretic aspects)None of the above, but in this section11Txx = > 11TxxFinite fields and finite commutative rings (number-theoretic)Finite fields and commutative rings (number-theoretic aspects)11-XX % 11U05Decidability related to number theoryDecidability [See also 03B25]11Uxx 11U07Ultraproducts in number theoryUltraproducts [See also 03C20]11Uxx . 11U09Connections of number theory with model theoryModel theory [See also 03Cxx]11Uxx ' ' 11U10Nonstandard arithmetic in number theoryNonstandard arithmetic [See also 03H15]11Uxx ' & 11U99Connections of number theory with logicNone of the above, but in this section11Uxx ' 11UxxConnections of number theory with logicConnections with logic11-XX
11Y05FactorizationFactorization11Yxx 11Y11PrimalityPrimality11Yxx
' 11Y16AlgorithmsAlgorithms; complexity [See also 68Q25]11Yxx 11Y35Analytic computationsAnalytic computations11Yxx $ $ 11Y40Algebraic number theory computationsAlgebraic number theory computations11Yxx * * 11Y50Computer solution of Diophantine equationsComputer solution of Diophantine equations11Yxx 11Y55Calculation of integer sequencesCalculation of integer sequences11Yxx 11Y60Evaluation of constantsEvaluation of constants11Yxx 11Y65Continued fraction calculationsContinued fraction calculations11Yxx & 11Y70Values of arithmetic functionsValues of arithmetic functions; tables11Yxx & 11Y99Computational number theoryNone of the above, but in this section11Yxx , 11YxxComputational number theoryComputational number theory [See also 11-04]11-XX $ + 11Z05Miscellaneous appl. of number theoryMiscellaneous applications of number theory11-XX G 12-00Reference works (field theory)General reference works (handbooks, dictionaries, bibliographies, etc.)12-XX ; 12-01Textbooks (field theory)Instructional exposition (textbooks, tutorial papers, etc.)12-XX " 1 12-02Research monographs (field theory)Research exposition (monographs, survey articles)12-XX U 12-03Historical (field theory)Historical (must also be assigned at least one classification number from Section 01)12-XX , X 12-04Machine computation, programs (field theory)Explicit machine computation and programs (not the theory of computation or programming)12-XX ) + 12-06Proceedings of conferences (field theory)Proceedings, conferences, collections, etc.12-XX 12-99Field theory and polynomialsField theory and polynomials 12-XXField theory and polynomialsField theory and polynomials , 12D05Factorization of real or complex polynomialsPolynomials: factorization12Dxx B _ 12D10Algebraic theorems of location of zeros of polynomials over R or CPolynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}12Dxx e 12D15Formally real fieldsFields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]12Dxx & 12D99Real and complex fieldsNone of the above, but in this section12Dxx 12DxxReal and complex fieldsReal and complex fields12-XX " 12E05Polynomials over general fieldsPolynomials (irreducibility, etc.)12Exx ' 12E10Special polynomials over general fieldsSpecial polynomials12Exx 12E12Algebraic equationsEquations12Exx A 12E15Skew fields over special fieldsSkew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]12Exx ' ' 12E20Finite fields (field-theoretic aspects)Finite fields (field-theoretic aspects)12Exx 3 3 12E25Hilbertian fields; Hilbert's irreducibility theoremHilbertian fields; Hilbert's irreducibility theorem12Exx 12E30Field arithmeticField arithmetic12Exx12E25,12F121 & 12E99General field theoryNone of the above, but in this section12Exx 12ExxGeneral field theoryGeneral field theory12-XX 12F05Algebraic extensionsAlgebraic extensions12Fxx
# 12F10Galois theorySeparable extensions, Galois theory12Fxx 12F12Inverse Galois theoryInverse Galois theory12Fxx 12F15Inseparable extensionsInseparable extensions12Fxx 12F20Transcendental extensionsTranscendental extensions12Fxx & 12F99Field extensionsNone of the above, but in this section12Fxx 12FxxField extensionsField extensions12-XX 0 12G05Galois cohomologyGalois cohomology [See also 14F22, 16H05, 16K50]12Gxx 12G10Cohomological dimensionCohomological dimension12Gxx # & 12G99Homological methods in field theoryNone of the above, but in this section12Gxx # " 12GxxHomological methods in field theoryHomological methods (field theory)12-XX % 12H05Differential algebraDifferential algebra [See also 13Nxx]12Hxx # 12H10Difference algebraDifference algebra [See also 39Axx]12Hxx 0 12H20Abstract differential equationsAbstract differential equations [See also 34Mxx]12Hxx 7 12H25p-adic differential equations$p$-adic differential equations [See also 11S80, 14G20]12Hxx & 12H99Differential algebraNone of the above, but in this section12Hxx # 12HxxDifferential algebra, etc.Differential and difference algebra12-XX
12J05Normed fieldsNormed fields12Jxx
12J10Valued fieldsValued fields12Jxx 12J12Formally p-adic fieldsFormally $p$-adic fields12Jxx 12J15Ordered fieldsOrdered fields12Jxx 12J17Topological semi-fieldsTopological semifields12Jxx ) 12J20General valuation theoryGeneral valuation theory [See also 13A18]12Jxx C 12J25Non-Archimedean valued fieldsNon-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]12Jxx ? 12J27Krasner-Tate algebrasKrasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]12Jxx & 12J99Topological fieldsNone of the above, but in this section12Jxx 12JxxTopological fieldsTopological fields12-XX 12K05Near-fieldsNear-fields [See also 16Y30]12Kxx 12K10Semi-fieldsSemifields [See also 16Y60]12Kxx & 12K99Generalizations of fieldsNone of the above, but in this section12Kxx 12KxxGeneralizations of fieldsGeneralizations of fields12-XX $ 12L05Decidability related to field theoryDecidability [See also 03B25]12Lxx 12L10Ultraproducts in field theoryUltraproducts [See also 03C20]12Lxx 12L12Model theory for fieldsModel theory [See also 03C60]12Lxx ! ' 12L15Nonstandard arithmetic for fieldsNonstandard arithmetic [See also 03H15]12Lxx & & 12L99Connections of field theory with logicNone of the above, but in this section12Lxx & 12LxxConnections of field theory with logicConnections with logic12-XX 5 5 12Y05Computational aspects of field theory and polynomialsComputational aspects of field theory and polynomials12-XX 0 G 13-00Reference works (commutative rings and algebras)General reference works (handbooks, dictionaries, bibliographies, etc.)13-XX * ; 13-01Textbooks (commutative rings and algebras)Instructional exposition (textbooks, tutorial papers, etc.)13-XX 4 1 13-02Research monographs (commutative rings and algebras)Research exposition (monographs, survey articles)13-XX + U 13-03Historical (commutative rings and algebras)Historical (must also be assigned at least one classification number from Section 01)13-XX > X 13-04Machine computation, programs (commutative rings and algebras)Explicit machine computation and programs (not the theory of computation or programming)13-XX ; + 13-06Proceedings of conferences (commutative rings and algebras)Proceedings, conferences, collections, etc.13-XX 13-99Commutative rings and algebrasCommutative rings and algebras 13-XXCommutative rings and algebrasCommutative rings and algebras 13A02Graded ringsGraded rings [See also 16W50]13Axx 13A05DivisibilityDivisibility13Axx # 13A10Radical theory on commutative ringsRadical theory13Axx # # 13A15Ideals; multiplicative ideal theoryIdeals; multiplicative ideal theory13Axx $ 5 13A18Valuations and their generalizationsValuations and their generalizations [See also 12J20]13Axx 4 \ 13A30Associated graded rings of ideals and related topicsAssociated graded rings of ideals (Rees ring, form ring), analytic spread and related topics13Axx w 13A35Characteristic p methodsCharacteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also 13B22]13Axx I 13A50Invariant theoryActions of groups on commutative rings; invariant theory [See also 14L24]13Axx & 13A99General commutative ring theoryNone of the above, but in this section13Axx 13AxxGeneral commutative ring theoryGeneral commutative ring theory13-XX $ 13B02Extension theory (commutative rings)Extension theory13Bxx !
13B05Galois theory (commutative rings)Galois theory13Bxx ' 13B10Automorphisms, etc. (commutative rings)Morphisms13Bxx 13B21Integral dependenceIntegral dependence13Bxx 8 n 13B22Integral closure; integrally closed rings, related ringsIntegral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)13Bxx # # 13B24Going up; going down; going betweenGoing up; going down; going between13Bxx " A 13B25Polynomials over commutative ringsPolynomials over commutative rings [See also 11C08, 13F20, 13M10]13Bxx 13B30LocalizationQuotients and localization13Bxx 13B35Completion of ringsCompletion [See also 13J10]13Bxx \ 13B40Etale extensions, etc.Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]13Bxx & 13B99Ring extensionsNone of the above, but in this section13Bxx " " 13BxxRing extensions and related topicsRing extensions and related topics13-XX ( " 13C05Structure of modules (commutative rings)Structure, classification theorems13Cxx 7 13C10Projective modules, etc.Projective and free modules and ideals [See also 19A13]13Cxx % 13C11Injective modules etc.Injective and flat modules and ideals13Cxx 13C12Torsion modulesTorsion modules and ideals13Cxx 2 13C13Other special types of modules (commutative rings)Other special types13Cxx ' 13C14Cohen-Macaulay modulesCohen-Macaulay modules [See also 13H10]13Cxx * 7 13C15Dimension theory, etc. (commutative rings)Dimension theory, depth, related rings (catenary, etc.)13Cxx 13C20Class groupsClass groups [See also 11R29]13Cxx 8 W 13C40Linkage, complete intersections and determinantal idealsLinkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]13Cxx & 13C99Theory of modules and idealsNone of the above, but in this section13Cxx % 13CxxTheory of modules (commutative rings)Theory of modules and ideals13-XX 13D02SyzygiesSyzygies and resolutions13Dxx . h 13D03(Co)homology of commutative rings and algebras(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)13Dxx ) 13D05Homological dimension (commutative rings)Homological dimension13Dxx 0 13D07Homological functors on modulesHomological functors on modules (Tor, Ext, etc.)13Dxx13D02,13D051 L 13D10Infinitesimal methods, etc.Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]13Dxx E 13D15K-theory (commutative rings)Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]13Dxx / 13D22Homological conjecturesHomological conjectures (intersection theorems)13Dxx13D03,13H151 13D25ComplexesComplexes13Dxx $ & 13D30Torsion theories (commutative rings)Torsion theory [See also 13C12, 18E40]13Dxx , : 13D40Hilbert-Samuel functions and Poincare seriesHilbert-Samuel and Hilbert-Kunz functions; Poincaré series13Dxx ! 13D45Local cohomologyLocal cohomology [See also 14B15]13Dxx ' & 13D99Homological methods (commutative rings)None of the above, but in this section13Dxx ' \ 13DxxHomological methods (commutative rings)Homological methods {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}13-XX 13E05Noetherian rings and modulesNoetherian rings and modules13Exx 7 13E10Artinian rings and modulesArtinian rings and modules, finite-dimensional algebras13Exx & L 13E15Rings and modules of finite generationRings and modules of finite generation or presentation; number of generators13Exx ' & 13E99Chain conditions, finiteness conditionsNone of the above, but in this section13Exx ' ' 13ExxChain conditions, finiteness conditionsChain conditions, finiteness conditions13-XX 4 : 13F05Dedekind and Pruefer rings and their generalizationsDedekind, Prüfer and Krull rings and their generalizations13Fxx # # 13F07Euclidean rings and generalizationsEuclidean rings and generalizations13Fxx 13F10Principal ideal ringsPrincipal ideal rings13Fxx - > 13F15Factorial rings, unique factorization domainsFactorial rings, unique factorization domains [See also 14M05]13Fxx X 13F20Polynomial ringsPolynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]13Fxx * 13F25Formal power series ringsFormal power series rings [See also 13J05]13Fxx 13F30Valuation ringsValuation rings [See also 13A18]13Fxx 13F40Excellent ringsExcellent rings13Fxx 13F45Seminormal ringsSeminormal rings13Fxx - - 13F50Rings with straightening laws, Hodge algebrasRings with straightening laws, Hodge algebras13Fxx # E 13F55Face and Stanley-Reisner rings etc.Face and Stanley-Reisner rings; simplicial complexes [See also 55U10]13Fxx13F501 & 13F99Arithmetic ringsNone of the above, but in this section13Fxx ( 13FxxArithmetic ringsArithmetic rings and other special rings13-XX 13G05Integral domainsIntegral domains13-XX 13H05Regular local ringsRegular local rings13Hxx L 13H10Special types of local ringsSpecial types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]13Hxx & 7 13H15Multiplicity theory and related topicsMultiplicity theory and related topics [See also 14C17]13Hxx & 13H99Local ringsNone of the above, but in this section13Hxx 13HxxLocal rings and generalizationsLocal rings and semilocal rings13-XX # 13J05Power series ringsPower series rings [See also 13F25]13Jxx . 13J07Analytic algebras and ringsAnalytical algebras and rings [See also 32B05]13Jxx + 13J10Complete rings, completionComplete rings, completion [See also 13B35]13Jxx 13J15Henselian ringsHenselian rings [See also 13B40]13Jxx 13J20Global topological ringsGlobal topological rings13Jxx 13J25Commutative ordered ringsOrdered rings [See also 06F25]13Jxx $ 13J30Real algebraReal algebra [See also 12D15, 14Pxx]13Jxx12D15,14P991 & 13J99Topological ringsNone of the above, but in this section13Jxx 5 13JxxTopological ringsTopological rings and modules [See also 16W60, 16W80]13-XX 13K05Witt vectors and related ringsWitt vectors and related rings13-XX % D 13L05Appl. of logic to commutative algebraApplications of logic to commutative algebra [See also 03Cxx, 03Hxx]13-XX % 13M05Structure of finite commutative ringsStructure13Mxx ) 13M10Polynomials over finite commutative ringsPolynomials13Mxx & 13M99Finite commutative ringsNone of the above, but in this section13Mxx B 13MxxFinite commutative ringsFinite commutative rings {For number-theoretic aspects, see 11Txx}13-XX * 13N05Differential algebra (commutative algebra)Modules of differentials13Nxx I 13N10Rings of differential operatorsRings of differential operators and their modules [See also 16S32, 32C38]13Nxx 13N15DerivationsDerivations13Nxx13B101 & 13N99Differential algebraNone of the above, but in this section13Nxx , 13NxxDifferential algebraDifferential algebra [See also 12H05, 14F10]13-XX + 13P05Polynomials, factorizationPolynomials, factorization [See also 12Y05]13Pxx ! 1 13P10Polynomial ideals, Groebner basesPolynomial ideals, Gröbner bases [See also 13F20]13Pxx , & 13P99Computational aspects of commutative algebraNone of the above, but in this section13Pxx , = 13PxxComputational aspects of commutative algebraComputational aspects of commutative algebra [See also 68W30]13-XX $ G 14-00Reference works (algebraic geometry)General reference works (handbooks, dictionaries, bibliographies, etc.)14-XX ; 14-01Textbooks (algebraic geometry)Instructional exposition (textbooks, tutorial papers, etc.)14-XX ( 1 14-02Research monographs (algebraic geometry)Research exposition (monographs, survey articles)14-XX U 14-03Historical (algebraic geometry)Historical (must also be assigned at least one classification number from Section 01)14-XX 2 X 14-04Machine computation, programs (algebraic geometry)Explicit machine computation and programs (not the theory of computation or programming)14-XX / + 14-06Proceedings of conferences (algebraic geometry)Proceedings, conferences, collections, etc.14-XX 14-99Algebraic geometryAlgebraic geometry 14-XXAlgebraic geometryAlgebraic geometry - 14A05Relevant commutative algebraRelevant commutative algebra [See also 13-XX]14Axx 14A10VarietiesVarieties and morphisms14Axx 14A15SchemesSchemes and morphisms14Axx ( * 14A20Generalizations (algebraic spaces, etc.)Generalizations (algebraic spaces, stacks)14Axx ' ! 14A22Noncommutative algebraic geometry, etc.Noncommutative algebraic geometry14Axx * 14A25Elementary questions of algebraic geometryElementary questions14Axx ! & 14A99Foundations of algebraic geometryNone of the above, but in this section14Axx ! 14AxxFoundations of algebraic geometryFoundations14-XX " : 14B05Singularities (algebraic geometry)Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]14Bxx , 5 14B07Deformations of singularities (local theory)Deformations of singularities [See also 14D15, 32S30]14Bxx & 14B10Infinitesimal methodsInfinitesimal methods [See also 13D10]14Bxx K 14B12Local deformation theoryLocal deformation theory, Artin approximation, etc. [See also 13B40, 13D10]14Bxx ( 14B15Local cohomologyLocal cohomology [See also 13D45, 32C36]14Bxx 14B20Formal neighborhoodsFormal neighborhoods14Bxx , @ 14B25Local structure of maps (algebraic geometry)Local structure of morphisms: étale, flat, etc. [See also 13B40]14Bxx14E401 & 14B99Local algebraic geometryNone of the above, but in this section14Bxx 14BxxLocal algebraic geometryLocal theory14-XX * 14C05ParametrizationParametrization (Chow and Hilbert schemes)14Cxx 14C15Rational equivalence ringsChow groups and rings14Cxx Y 14C17Intersection theoryIntersection theory, characteristic classes, intersection multiplicities [See also 13H15]14Cxx , , 14C20Divisors, linear systems, invertible sheavesDivisors, linear systems, invertible sheaves14Cxx
$ 14C21Webs, netsPencils, nets, webs [See also 53A60]14Cxx
14C22Picard groupsPicard groups14Cxx 14C25Algebraic cyclesAlgebraic cycles14Cxx \ 14C30Transcendental methodsTranscendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture14Cxx 14C34Torelli problemTorelli problem [See also 32G20]14Cxx & @ 14C35Appl. of methods of algebraic K-theoryApplications of methods of algebraic $K$-theory [See also 19Exx]14Cxx - 14C40Riemann-Roch theoremsRiemann-Roch theorems [See also 19E20, 19L10]14Cxx & 14C99Cycles and subschemesNone of the above, but in this section14Cxx 14CxxCycles and subschemesCycles and subschemes14-XX : 14D05Structure of familiesStructure of families (Picard-Lefschetz, monodromy, etc.)14Dxx 14D06Fibrations, degenerationsFibrations, degenerations14Dxx14H99,14J991 . 14D07Variation of Hodge structuresVariation of Hodge structures [See also 32G20]14Dxx 0 14D10Arithmetic ground fieldsArithmetic ground fields (finite, local, global)14Dxx ; 14D15(Formal) deformationsFormal methods; deformations [See also 13D10, 14B07, 32Gxx]14Dxx ] 14D20Algebraic moduli problemsAlgebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}14Dxx A { 14D21Appl. of vector bundles and moduli spaces in mathematical physicsApplications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)14Dxx14D201 14D22Fine and coarse moduli spacesFine and coarse moduli spaces14Dxx & 14D99Families, fibrationsNone of the above, but in this section14Dxx 14DxxFamilies, fibrationsFamilies, fibrations14-XX 14E05Birational correspondencesRational and birational maps14Exx ; ; 14E07Birational automorphisms, Cremona group and generalizationsBirational automorphisms, Cremona group and generalizations14Exx 14E08Rationality questionsRationality questions14Exx14G05,14M201 L 14E15Global theory of singularitiesGlobal theory and resolution of singularities [See also 14B05, 32S20, 32S45]14Exx ' 14E20Coverings, fundamental group (mappings)Coverings [See also 14H30]14Exx & 14E22Ramification problemsRamification problems [See also 11S15]14Exx
14E25Embeddings (algebraic varieties)Embeddings14Exx 2 14E30Minimal modelsMinimal model program (Mori theory, extremal rays)14Exx & 14E99Mappings and correspondencesNone of the above, but in this section14Exx 14ExxMappings and correspondencesBirational geometry14-XX
[ 14F05Sheaves, etc.Vector bundles, sheaves, related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]14Fxx ? 14F10Special sheavesDifferentials and other special sheaves [See also 13Nxx, 32C38]14Fxx # 14F17Vanishing theoremsVanishing theorems [See also 32L20]14Fxx $ 8 14F20Grothendieck cohomology and topologyÉtale and other Grothendieck topologies and cohomologies14Fxx 0 14F22Brauer groups of schemesBrauer groups of schemes [See also 12G05, 16K50]14Fxx13A201 % % 14F25Classical real and complex cohomologyClassical real and complex cohomology14Fxx + 14F30p-adic cohomology$p$-adic cohomology, crystalline cohomology14Fxx $ 4 14F35Homotopy theory (algebraic geometry)Homotopy theory; fundamental groups [See also 14H30]14Fxx 1 14F40De Rham cohomologyde Rham cohomology [See also 14C30, 32C35, 32L10]14Fxx 14F42Motivic cohomologyMotivic cohomology14Fxx14F991 & h 14F43Other algebro-geometric (co)homologiesOther algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)14Fxx14F32,14F991 - 14F45Topological properties of algebraic varietiesTopological properties14Fxx & 14F99Cohomology theoryNone of the above, but in this section14Fxx 3 $ 14FxxHomology and Cohomology theory (algebraic geometry)(Co)homology theory [See also 13Dxx]14-XX & 14G05Rationality questions, rational pointsRational points14Gxx $ X 14G10Zeta-functions and related questionsZeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)14Gxx 14G15Finite ground fieldsFinite ground fields14Gxx 14G20p-adic ground fieldsLocal ground fields14Gxx 14G22Rigid analytic geometryRigid analytic geometry14Gxx14G201 14G25Global ground fieldsGlobal ground fields14Gxx & + 14G27Non algebraically closed ground fieldsOther nonalgebraically closed ground fields14Gxx g 14G32Universal profinite groupsUniversal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)14Gxx14D20,14H30,20E181 < 14G35Modular and Shimura varietiesModular and Shimura varieties [See also 11F41, 11F46, 11G18]14Gxx K 14G40Arithmetic varieties and schemesArithmetic varieties and schemes; Arakelov theory; heights [See also 11G50]14Gxx 3 M 14G50Applications of algebraic geometry to coding theoryApplications to coding theory and cryptography [See also 94A60, 94B27, 94B40]14Gxx94B271 & 14G99Special ground fieldsNone of the above, but in this section14Gxx * A 14GxxSpecial ground fields, arithmetic problemsArithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]14-XX 5 14H05Algebraic functionsAlgebraic functions; function fields [See also 11R58]14Hxx # 14H10Families, algebraic moduli (curves)Families, moduli (algebraic)14Hxx " 3 14H15Families, analytic moduli (curves)Families, moduli (analytic) [See also 30F10, 32Gxx]14Hxx 2 14H20Singularities, local ringsSingularities, local rings [See also 13Hxx, 14B05]14Hxx ! 7 14H25Arithmetic ground fields (curves)Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]14Hxx % 4 14H30Coverings, fundamental group (curves)Coverings, fundamental group [See also 14E20, 14F35]14Hxx
14H37AutomorphismsAutomorphisms14Hxx14E091 * 14H40JacobiansJacobians, Prym varieties [See also 32G20]14Hxx 9 14H42Theta functionsTheta functions; Schottky problem [See also 14K25, 32G20]14Hxx & & 14H45Special curves and curves of low genusSpecial curves and curves of low genus14Hxx 14H50Space curvesPlane and space curves14Hxx 1 14H51Special divisorsSpecial divisors (gonality, Brill-Noether theory)14Hxx14C201 . 14H52Elliptic curvesElliptic curves [See also 11G05, 11G07, 14Kxx]14Hxx D 14H55Riemann surfacesRiemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]14Hxx A 14H60Vector bundles on curvesVector bundles on curves and their moduli [See also 14D20, 14F05]14Hxx % 14H70Automorphisms of curvesRelationships with integrable systems14Hxx14H991 . 14H81Relationships of algebraic curves with physicsRelationships with physics14Hxx14H991 & 14H99CurvesNone of the above, but in this section14Hxx 14HxxCurvesCurves14-XX 5 2 14J10Families, algebraic moduli, classification (surfaces)Families, moduli, classification: algebraic theory14Jxx * V 14J15Analytic moduli, classification (surfaces)Moduli, classification: analytic theory; relations with modular forms [See also 32G13]14Jxx % 14J17Singularities of surfacesSingularities [See also 14B05, 14E15]14Jxx # > 14J20Arithmetic ground fields (surfaces)Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]14Jxx : 14J25Special surfacesSpecial surfaces {For Hilbert modular surfaces, see 14G35}14Jxx 14J26Surfaces (rational and ruled)Rational and ruled surfaces14Jxx 14J27Elliptic surfacesElliptic surfaces14Jxx # 14J28K3-surfaces, etc.$K3$ surfaces and Enriques surfaces14Jxx 14J29Surfaces of general typeSurfaces of general type14Jxx 14J30Special 3-folds$3$-folds14Jxx % 14J32Calabi-Yau manifoldsCalabi-Yau manifolds, mirror symmetry14Jxx 14J35Special 4-folds$4$-folds14Jxx 14J40Special n-folds$n$-folds ($n>4$)14Jxx 14J45Fano varietiesFano varieties14Jxx : : 14J50Automorphisms of surfaces and higher-dimensional varietiesAutomorphisms of surfaces and higher-dimensional varieties14Jxx 5 l 14J60Vector bundles on surfaces and higher-order varietiesVector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]14Jxx
14J70HypersurfacesHypersurfaces14Jxx G 14J80Topology of surfacesTopology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)14Jxx14J991 0 14J81Relationships of algebraic surfaces with physicsRelationships with physics14Jxx14J991 ) & 14J99Surfaces and higher-dimensional varietiesNone of the above, but in this section14Jxx ) J 14JxxSurfaces and higher-dimensional varietiesSurfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}14-XX 14K02IsogenyIsogeny14Kxx % 14K05Algebraic theory of abelian varietiesAlgebraic theory14Kxx 4 1 14K10Algebraic moduli, classification (abelian varieties)Algebraic moduli, classification [See also 11G15]14Kxx ! 14K12Subvarieties of abelian varietiesSubvarieties14Kxx14K051 , > 14K15Arithmetic ground fields (abelian varieties)Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]14Kxx 4 4 14K20Analytic theory; abelian integrals and differentialsAnalytic theory; abelian integrals and differentials14Kxx * ' 14K22Complex multiplication (abelian varieties)Complex multiplication [See also 11G15]14Kxx 14K25Theta-functionsTheta functions [See also 14H42]14Kxx 8 14K30Picard schemes, higher JacobiansPicard schemes, higher Jacobians [See also 14H40, 32G20]14Kxx & 14K99Abelian varieties and schemesNone of the above, but in this section14Kxx 14KxxAbelian varieties and schemesAbelian varieties and schemes14-XX
4 14L05Formal groupsFormal groups, $p$-divisible groups [See also 55N22]14Lxx 14L10Group varietiesGroup varieties14Lxx
14L15Group schemesGroup schemes14Lxx K 14L17Affine algebraic groupsAffine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]14Lxx + + 14L24Geometric invariant theory of group schemesGeometric invariant theory [See also 13A50]14Lxx14D251 % I 14L30Group actions on varieties or schemesGroup actions on varieties or schemes (quotients) [See also 13A50, 14L24]14Lxx $ < 14L35Classical groups (geometric aspects)Classical groups (geometric aspects) [See also 20Gxx, 51N30]14Lxx * * 14L40Other algebraic groups (geometric aspects)Other algebraic groups (geometric aspects)14Lxx & 14L99Algebraic groupsNone of the above, but in this section14Lxx W 14LxxAlgebraic groupsAlgebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}14-XX $ d 14M05Varieties defined by ring conditionsVarieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]14Mxx 14M06LinkageLinkage [See also 13C40]14Mxx 14M07Low-codimension problemsLow codimension problems14Mxx ' 14M10Complete intersectionsComplete intersections [See also 13C40]14Mxx ( 14M12Determinantal varietiesDeterminantal varieties [See also 13C40]14Mxx ! I 14M15Grassmannians, Schubert varietiesGrassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]14Mxx E 14M17Homogeneous spacesHomogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]14Mxx " 14M20Rational varietiesRational and unirational varieties14Mxx 2 14M25Toric varieties, etc.Toric varieties, Newton polyhedra [See also 52B20]14Mxx & 14M30SupervarietiesSupervarieties [See also 32C11, 58A50]14Mxx & 14M99Special varietiesNone of the above, but in this section14Mxx 14MxxSpecial algebraic varietiesSpecial varieties14-XX 4 & 14N05Projective techniques (classical algebraic geometry)Projective techniques [See also 51N35]14Nxx 3 - 14N10Enumerative problems (classical algebraic geometry)Enumerative problems (combinatorial problems)14Nxx ( % 14N15Classical problems in algebraic geometryClassical problems, Schubert calculus14Nxx14M151 " " 14N20Configurations of linear subspacesConfigurations of linear subspaces14Nxx14N051 14N25Varieties of low degreeVarieties of low degree14Nxx14N051 14N30Adjunction problemsAdjunction problems14Nxx14C201 = 14N35Quantum cohomologyGromov-Witten invariants, quantum cohomology [See also 53D45]14Nxx14N101 & 14N99Classical algebraic geometryNone of the above, but in this section14Nxx 4 14NxxClassical algebraic geometryProjective and enumerative geometry [See also 51-XX]14-XX $ 14P05Real algebraic setsReal algebraic sets [See also 12Dxx]14Pxx % % 14P10Semialgebraic sets and related spacesSemialgebraic sets and related spaces14Pxx # ; 14P15Real analytic and semianalytic setsReal analytic and semianalytic sets [See also 32B20, 32C05]14Pxx 4 14P20Nash functions and manifoldsNash functions and manifolds [See also 32C07, 58A07]14Pxx $ $ 14P25Topology of real algebraic varietiesTopology of real algebraic varieties14Pxx ) & 14P99Real algebraic and real analytic geometryNone of the above, but in this section14Pxx ) ) 14PxxReal algebraic and real analytic geometryReal algebraic and real analytic geometry14-XX 14Q05CurvesCurves14Qxx 14Q10Surfaces, hypersurfacesSurfaces, hypersurfaces14Qxx 14Q15Higher dimensional varietiesHigher-dimensional varieties14Qxx 14Q20EffectivityEffectivity14Qxx + & 14Q99Computational aspects of algebraic geometryNone of the above, but in this section14Qxx + J 14QxxComputational aspects of algebraic geometryComputational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]14-XX " " 14R05Classification of affine varietiesClassification of affine varieties14Rxx14J991
R 14R10Affine spacesAffine spaces (automorphisms, embeddings, exotic structures, cancellation problem)14Rxx14E09,14E251 14R15Jacobian problemJacobian problem14Rxx14E091 ! 9 14R20Group actions on affine varietiesGroup actions on affine varieties [See also 13A50, 14L30]14Rxx14L301 " 14R25Affine fibrationsAffine fibrations [See also 14D06]14Rxx14D991 & 14R99Affine geometryNone of the above, but in this section14Rxx14J991 14RxxAffine geometryAffine geometry14-XX G 15-00Reference works (linear algebra)General reference works (handbooks, dictionaries, bibliographies, etc.)15-XX ; 15-01Textbooks (linear algebra)Instructional exposition (textbooks, tutorial papers, etc.)15-XX $ 1 15-02Research monographs (linear algebra)Research exposition (monographs, survey articles)15-XX U 15-03Historical (linear algebra)Historical (must also be assigned at least one classification number from Section 01)15-XX . X 15-04Machine computation, programs (linear algebra)Explicit machine computation and programs (not the theory of computation or programming)15-XX + + 15-06Proceedings of conferences (linear algebra)Proceedings, conferences, collections, etc.15-XX 15-99Linear and multilinear algebraLinear and multilinear algebra - - 15-XXLinear and multilinear algebra; matrix theoryLinear and multilinear algebra; matrix theory
& 15A03Vector spacesVector spaces, linear dependence, rank15-XX ' 2 15A04Linear transformations (linear algebra)Linear transformations, semilinear transformations15-XX ! 15A06Linear equations (linear algebra)Linear equations15-XX & 15A09Matrix inversionMatrix inversion, generalized inverses15-XX ) 15A12Conditioning of matricesConditioning of matrices [See also 65F35]15-XX P 15A15Special matrix functionsDeterminants, permanents, other special matrix functions [See also 19B10, 19B14]15-XX . 15A18Eigenvalues of matrices, etc.Eigenvalues, singular values, and eigenvectors15-XX + 15A21Canonical forms, etc.Canonical forms, reductions, classification15-XX 15A22Matrix pencilsMatrix pencils [See also 47A56]15-XX 15A23Factorization of matricesFactorization of matrices15-XX 15A24Matrix equationsMatrix equations and identities15-XX
15A27Commutativity of matricesCommutativity15-XX ! 15A29Inverse problems in matrix theoryInverse problems15-XX05A181 < 15A30Algebraic systems of matricesAlgebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]15-XX > 15A33Matrices over special ringsMatrices over special rings (quaternions, finite fields, etc.)15-XX % 15A36Matrices of integersMatrices of integers [See also 11C20]15-XX 15A39Linear inequalitiesLinear inequalities15-XX 3 3 15A42Inequalities involving eigenvalues and eigenvectorsInequalities involving eigenvalues and eigenvectors15-XX - - 15A45Miscellaneous inequalities involving matricesMiscellaneous inequalities involving matrices15-XX + > 15A48Positive matrices and their generalizationsPositive matrices and their generalizations; cones of matrices15-XX 15A51Stochastic matricesStochastic matrices15-XX 15A52Random matricesRandom matrices15-XX 5 15A54Matrices over function ringsMatrices over function rings in one or more variables15-XX 9 15A57Other types of matricesOther types of matrices (Hermitian, skew-Hermitian, etc.)15-XX - p 15A60Appl. of functional analysis to matrix theoryNorms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]15-XX ? 15A63Bilinear forms, etc.Quadratic and bilinear forms, inner products [See mainly 11Exx]15-XX 15A66Clifford algebrasClifford algebras, spinors15-XX $ 15A69Multilinear algebraMultilinear algebra, tensor products15-XX G 15A72Vector and tensor algebraVector and tensor algebra, theory of invariants [See also 13A50, 14L24]15-XX $ 15A75Exterior algebra, etc.Exterior algebra, Grassmann algebras15-XX ! ! 15A78Other algebras built from modulesOther algebras built from modules15-XX ! ( 15A90Appl. of matrix theory to physicsApplications of matrix theory to physics15-XX & 15A99Miscellaneous topics in linear algebraMiscellaneous topics15-XX + G 16-00Reference works (assoc. rings and algebras)General reference works (handbooks, dictionaries, bibliographies, etc.)16-XX % ; 16-01Textbooks (assoc. rings and algebras)Instructional exposition (textbooks, tutorial papers, etc.)16-XX / 1 16-02Research monographs (assoc. rings and algebras)Research exposition (monographs, survey articles)16-XX & U 16-03Historical (assoc. rings and algebras)Historical (must also be assigned at least one classification number from Section 01)16-XX 9 X 16-04Machine computation, programs (assoc. rings and algebras)Explicit machine computation and programs (not the theory of computation or programming)16-XX 6 + 16-06Proceedings of conferences (assoc. rings and algebras)Proceedings, conferences, collections, etc.16-XX 16-99Associative rings and algebrasAssociative rings and algebras D 16-XXAssociative rings and algebrasAssociative rings and algebras {For the commutative case, see 13-XX} = L 16B50Category-theoretic methods and results in associative algebraCategory-theoretic methods and results (except as in 16D90) [See also 18-XX]16Bxx ) & 16B70Appl. of logic to associative ring theoryApplications of logic [See also 03Cxx]16Bxx / & 16B99Miscellaneous topics in associative ring theoryNone of the above, but in this section16Bxx 8 16BxxGeneral and miscellaneous topics associative ring theoryGeneral and miscellaneous16-XX 1 16D10General module theory (assoc. rings and algebras)General module theory16Dxx % 16D20Bimodules (assoc. rings and algebras)Bimodules16Dxx * 16D252-sided ideals (assoc. rings and algebras)Ideals16Dxx < 6 16D30Maximal and prime 2-sided ideals (assoc. rings and algebras)Infinite-dimensional simple rings (except as in 16Kxx)16Dxx 9 > 16D40Free, etc. modules and ideals (assoc. rings and algebras)Free, projective, and flat modules and ideals [See also 19A13]16Dxx C 8 16D50Injective modules, self-injective rings (assoc. rings and algebras)Injective modules, self-injective rings [See also 16L60]16Dxx 7 9 16D60(Semi-)simple modules, etc. (assoc. rings and algebras)Simple and semisimple modules, primitive rings and ideals16Dxx = Y 16D70Structure and classification of associative ring and algebrasStructure and classification (except as in 16Gxx), direct sum decomposition, cancellation16Dxx ? 4 16D80Other classes of modules and ideals (assoc. rings and algebras)Other classes of modules and ideals [See also 16G50]16Dxx - x 16D90Module categories (assoc. rings and algebras)Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality16Dxx 9 & 16D99Modules, bimodules and ideals (assoc. rings and algebras)None of the above, but in this section16Dxx 9 16DxxModules, bimodules and ideals (assoc. rings and algebras)Modules, bimodules and ideals16-XX 16E05Syzygies etcSyzygies, resolutions, complexes16Exx16E101 2 16E10Homological dimensions (assoc. rings and algebras)Homological dimension16Exx D 16E20K-theory of noncommutative ringsGrothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50]16Exx + 0 16E30Homological functors on associative modulesHomological functors on modules (Tor, Ext, etc.)16Exx 1 L 16E40Homology and cohomology theories for assoc. rings(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)16Exx - - 16E45Differential graded algebras and applicationsDifferential graded algebras and applications16Exx16E991 - - 16E50Von Neumann regular rings and generalizationsvon Neumann regular rings and generalizations16Exx 7 L 16E60Semihereditary and hereditary assoc. rings and algebrasSemihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.16Exx d 16E65Homological conditions on ringsHomological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)16Exx16E991 1 & 16E99Homological methods in noncommutative ring theoryNone of the above, but in this section16Exx 6 Z 16ExxHomological methods and results in associative algebraHomological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}16-XX ! ! 16G10Representations of Artinian ringsRepresentations of Artinian rings16Gxx 5 5 16G20Representations of quivers and partially ordered setsRepresentations of quivers and partially ordered sets16Gxx 6 U 16G30Representations of orders, etc. over commutative ringsRepresentations of orders, lattices, algebras over commutative rings [See also 16H05]16Gxx 2 16G50Cohen-Macaulay modules (assoc. rings and algebras)Cohen-Macaulay modules16Gxx 7 . 16G60Representation type of noncommutative rings and modulesRepresentation type (finite, tame, wild, etc.)16Gxx & P 16G70Auslander-Reiten sequences and quiversAuslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers16Gxx 9 & 16G99Representation theory of noncommutative rings and modulesNone of the above, but in this section16Gxx : + 16GxxRepresentation theory of noncommutative rings and algebrasRepresentation theory of rings and algebras16-XX 5 Z 16H05Orders and arithmetic, separable associative algebrasOrders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45]16-XX ! 4 16K20Finite-dimensional division ringsFinite-dimensional {For crossed products, see 16S35}16Kxx / 16K40Infinite dimensional and general division ringsInfinite-dimensional and general16Kxx
% 16K50Brauer groupsBrauer groups [See also 12G05, 14F22]16Kxx13A201 & 16K99Division ringsNone of the above, but in this section16Kxx * A 16KxxDivision rings and semi-simple Artin ringsDivision rings and semisimple Artin rings [See also 12E15, 15A30]16-XX ( 7 16L30Noncommutative local and semilocal ringsNoncommutative local and semilocal rings, perfect rings16Lxx & 16L60Quasi-Frobenius ringsQuasi-Frobenius rings [See also 16D50]16Lxx & 16L99Noncommutative local ringsNone of the above, but in this section16Lxx . 16LxxNoncommutative local rings and generalizationsLocal rings and generalizations16-XX % % 16N20Jacobson radical, quasimultiplicationJacobson radical, quasimultiplication16Nxx / / 16N40Nil and nilpotent radicals, sets, ideals, ringsNil and nilpotent radicals, sets, ideals, rings16Nxx 1 16N60Prime and semiprime assoc. ringsPrime and semiprime rings [See also 16D60, 16U10]16Nxx & I 16N80General radicals and associative ringsGeneral radicals and rings {For radicals in module categories, see 16S90}16Nxx / & 16N99Radicals and radical properties of assoc. ringsNone of the above, but in this section16Nxx / ( 16NxxRadicals and radical properties of assoc. ringsRadicals and radical properties of rings16-XX 8 k 16P10Finite associative rings and finite-dimensional algebrasFinite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx}16Pxx & 16P20Associative Artinian rings and modulesArtinian rings and modules16Pxx ( 16P40Associative Noetherian rings and modulesNoetherian rings and modules16Pxx - 2 16P50Localization and associative Noetherian ringsLocalization and Noetherian rings [See also 16U20]16Pxx - g 16P60Chain conditions on annihilators and summandsChain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension16Pxx 5 R 16P70Chain conditions on other classes of submodules, etc.Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence16Pxx D ' 16P90Growth rate, Gel'fand-Kirillov dimension (assoc. rings and algebras)Growth rate, Gelfand-Kirillov dimension16Pxx / & 16P99Forms of finiteness (assoc. rings and algebras)None of the above, but in this section16Pxx / B 16PxxForms of finiteness (assoc. rings and algebras)Chain conditions, growth conditions, and other forms of finiteness16-XX 7 16R10Varieties of rings and algebras$T$-ideals, identities, varieties of rings and algebras16Rxx I 16R20Semiprime p.i.rings, etc.Semiprime p.i. rings, rings embeddable in matrices over commutative rings16Rxx < 16R30Trace rings and invariant theory (assoc. rings and algebras)Trace rings and invariant theory16Rxx > > 16R40Identities other than those of matrices over commutative ringsIdentities other than those of matrices over commutative rings16Rxx ) H 16R50Other kinds of identities of assoc. ringsOther kinds of identities (generalized polynomial, rational, involution)16Rxx * & 16R99Associative rings with polynomial identityNone of the above, but in this section16Rxx * 16RxxAssociative rings with polynomial identityRings with polynomial identity16-XX 4 b 16S10Associative rings determined by universal propertiesRings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)16Sxx ( V 16S15Finite generation, finite presentabilityFinite generation, finite presentability, normal forms (diamond lemma, term-rewriting)16Sxx ' ' 16S20Centralizing and normalizing extensionsCentralizing and normalizing extensions16Sxx ; @ 16S30Universal enveloping algebras of Lie algebras (associative)Universal enveloping algebras of Lie algebras [See mainly 17B35]16Sxx + 7 16S32Associative rings of differential operatorsRings of differential operators [See also 13N10, 32C38]16Sxx = 16S34Group rings (assoc. rings)Group rings [See also 20C05, 20C07], Laurent polynomial rings16Sxx " . 16S35Twisted and skew group rings, etc.Twisted and skew group rings, crossed products16Sxx 6 G 16S36Ordinary and skew polynomial rings and semigroup ringsOrdinary and skew polynomial rings and semigroup rings [See also 20M25]16Sxx 16S37Quadratic algebrasQuadratic and Koszul algebras16Sxx16S991 5 5 16S38Rings arising from non-commutative algebraic geometryRings arising from non-commutative algebraic geometry16Sxx16S991 & 7 16S40Smash products of general Hopf actionsSmash products of general Hopf actions [See also 16W30]16Sxx 1 16S50Endomorphism rings: matrix ringsEndomorphism rings; matrix rings [See also 15-XX]16Sxx 8 8 16S60Rings of functions, subdirect products, sheaves of ringsRings of functions, subdirect products, sheaves of rings16Sxx ) 16S70Extensions of associative rings by idealsExtensions of rings by ideals16Sxx 3 - 16S80Deformation theory of associative ring and algebrasDeformations of rings [See also 13D10, 14D15]16Sxx + … 16S90Maximal ring of quotients, torsion theoriesMaximal ring of quotients, torsion theories, radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}16Sxx B & 16S99Associative rings and algebras arising under various constructionsNone of the above, but in this section16Sxx B 6 16SxxAssociative rings and algebras arising under various constructionsRings and algebras arising under various constructions16-XX ! 16U10Integral domains (noncommutative)Integral domains16Uxx . 0 16U20Rings of quotients (assoc. rings and algebras)Ore rings, multiplicative sets, Ore localization16Uxx ! ! 16U30Divisibility, noncommutative UFDsDivisibility, noncommutative UFDs16Uxx 8 16U60Units, groups of units, etc. (assoc. rings and algebras)Units, groups of units16Uxx ' ' 16U70Commutativity theorems for assoc. ringsCenter, normalizer (invariant elements)16Uxx < 16U80Generalizations of commutativity (assoc. rings and algebras)Generalizations of commutativity16Uxx . & 16U99Conditions on elements of noncommutative ringsNone of the above, but in this section16Uxx 2 16UxxConditions on elements (assoc. rings and algebras)Conditions on elements16-XX ! e 16W10Associative rings with involutionRings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]16Wxx 16W20Morphisms of associative ringsAutomorphisms and endomorphisms16Wxx 2 16W22Actions of groups and semigroupsActions of groups and semigroups; invariant theory16Wxx16W201 @ $ 16W25Derivations, actions of Lie algebras (assoc. rings and algebras)Derivations, actions of Lie algebras16Wxx ) f 16W30Hopf algebras (assoc. rings and algebras)Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05]; rings, modules, etc. on which these act16Wxx ( G 16W35Ring-theoretic aspects of quantum groupsRing-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]16Wxx16W301 $ 16W50Graded associative rings and modulesGraded rings and modules16Wxx 9 Œ 16W55"Super" (or "skew") structure (assoc. rings and algebras)``Super'' (or ``skew'') structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66}16Wxx < X 16W60Filtrations and valuations, etc. (assoc. rings and algebras)Valuations, completions, formal power series and related constructions [See also 13Jxx]16Wxx 2 16W70Filtered rings etc.Filtered rings; filtrational and graded techniques16Wxx16W601 5 A 16W80Topological and ordered associative rings and modulesTopological and ordered rings and modules [See also 06F25, 13Jxx]16Wxx ; & 16W99Noncommutative rings and algebras with additional structureNone of the above, but in this section16Wxx ; , 16WxxNoncommutative rings and algebras with additional structureRings and algebras with additional structure16-XX
16Y30Near-ringsNear-rings [See also 12K05]16Yxx 16Y60SemiringsSemirings [See also 12K10]16Yxx 1 & 16Y99Generalizations of associative rings and algebrasNone of the above, but in this section16Yxx ' 5 16YxxGeneralizations of associative algebrasGeneralizations {For nonassociative rings, see 17-XX}16-XX * ; 16Z05Computational aspects of associative ringsComputational aspects of associative rings [See also 68W30]16-XX16-041 . G 17-00Reference works (nonassoc. rings and algebras)General reference works (handbooks, dictionaries, bibliographies, etc.)17-XX ( ; 17-01Textbooks (nonassoc. rings and algebras)Instructional exposition (textbooks, tutorial papers, etc.)17-XX 2 1 17-02Research monographs (nonassoc. rings and algebras)Research exposition (monographs, survey articles)17-XX ) U 17-03Historical (nonassoc. rings and algebras)Historical (must also be assigned at least one classification number from Section 01)17-XX < X 17-04Machine computation, programs (nonassoc. rings and algebras)Explicit machine computation and programs (not the theory of computation or programming)17-XX 9 + 17-06Proceedings of conferences (nonassoc. rings and algebras)Proceedings, conferences, collections, etc.17-XX 17-08Computational methodsComputational methods17-XX ! ! 17-99Nonassociative rings and algebrasNonassociative rings and algebras ! ! 17-XXNonassociative rings and algebrasNonassociative rings and algebras ( 17A01General theory of nonassociative algebraGeneral theory17Axx 17A05Power-associative ringsPower-associative rings17Axx 17A15Noncommutative Jordan algebrasNoncommutative Jordan algebras17Axx 17A20Flexible algebrasFlexible algebras17Axx 3 $ 17A30Nonassociative algebras satisfying other identitiesAlgebras satisfying other identities17Axx 17A32Leibniz algebrasLeibniz algebras17Axx17A301 17A35Division algebrasDivision algebras17Axx ! + 17A36Automorphisms and other operatorsAutomorphisms, derivations, other operators17Axx 17A40Ternary compositionsTernary compositions17Axx & 17A42Other n-ary compositionsOther $n$-ary compositions $(n \ge 3)$17Axx 6 17A45Quadratic algebrasQuadratic algebras (but not quadratic Jordan algebras)17Axx
17A50Nonassociative free algebrasFree algebras17Axx = 17A60Structure theory of general nonassociative rings and algebrasStructure theory17Axx 17A65Radical theoryRadical theory17Axx
17A70SuperalgebrasSuperalgebras17Axx 17A75Composition algebrasComposition algebras17Axx 17A80Valued algebrasValued algebras17Axx & 17A99General nonassociative ringsNone of the above, but in this section17Axx 17AxxGeneral nonassociative ringsGeneral nonassociative rings17-XX $ 17B01Identities, free Lie algebrasIdentities, free Lie (super)algebras17Bxx 17B05Structure theory of Lie algebrasStructure theory17Bxx 1 + 17B10Representations of Lie algebras, algebraic theoryRepresentations, algebraic theory (weights)17Bxx 0 17B15Representations of Lie algebras, analytic theoryRepresentations, analytic theory17Bxx " 5 17B20Simple and semisimple Lie algebrasSimple, semisimple, reductive (super)algebras (roots)17Bxx 17B25Exceptional Lie algebrasExceptional (super)algebras17Bxx # 17B30Solvable, nilpotent Lie algebrasSolvable, nilpotent (super)algebras17Bxx , 5 17B35Universal enveloping algebras (Lie algebras)Universal enveloping (super)algebras [See also 16S30]17Bxx ' m 17B37Quantum groups and related deformationsQuantum groups (quantized enveloping algebras) and related deformations [See also 16W35, 20G42, 81R50, 82B23]17Bxx 1 + 17B40Automorphisms and other operators on Lie algebrasAutomorphisms, derivations, other operators17Bxx ' B 17B45Lie algebras of linear algebraic groupsLie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]17Bxx 17B50Modular Lie algebrasModular Lie (super)algebras17Bxx - * 17B55Homological methods in theory of Lie algebrasHomological methods in Lie (super)algebras17Bxx ! 17B56Cohomology of Lie algebrasCohomology of Lie (super)algebras17Bxx * o 17B60Lie rings associated with other structuresLie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]17Bxx 17B62Lie bialgebrasLie bialgebras17Bxx17B991 17B63Poisson algebrasPoisson algebras17Bxx17B991 ! 9 17B65Infinite-dimensional Lie algebrasInfinite-dimensional Lie (super)algebras [See also 22E65]17Bxx 2 : 17B66Lie algebras of vector fields and related algebrasLie algebras of vector fields and related (super) algebras17Bxx ? 17B67Kac-Moody algebrasKac-Moody (super)algebras (structure and representation theory)17Bxx 17B68Virasoro and related algebrasVirasoro and related algebras17Bxx A 17B69Vertex operatorsVertex operators; vertex operator algebras and related structures17Bxx 17B70Graded Lie algebrasGraded Lie (super)algebras17Bxx 17B75Color Lie (super)algebrasColor Lie (super)algebras17Bxx17B701 2 " 17B80Applications of Lie algebras to integrable systemsApplications to integrable systems17Bxx17B991 ' 17B81Applications of Lie algebras to physicsApplications to physics17Bxx & 17B99Lie algebrasNone of the above, but in this section17Bxx > 17BxxLie algebrasLie algebras and Lie superalgebras {For Lie groups, see 22Exx}17-XX % % 17C05Identities and free Jordan structuresIdentities and free Jordan structures17Cxx # 17C10Structure theory of Jordan algebrasStructure theory17Cxx 17C17RadicalsRadicals17Cxx % 17C20Simple and semisimple Jordan algebrasSimple, semisimple algebras17Cxx " " 17C27Idempotents, Peirce decompositionsIdempotents, Peirce decompositions17Cxx 4 17C30Automorphisms and other operators on Jordan algebrasAssociated groups, automorphisms17Cxx 17C36Associated manifoldsAssociated manifolds17Cxx 17C37Associated geometriesAssociated geometries17Cxx 17C40Exceptional Jordan structuresExceptional Jordan structures17Cxx - C 17C50Jordan rings associated with other structuresJordan structures associated with other structures [See also 16W10]17Cxx 17C55Finite dimensional structuresFinite-dimensional structures17Cxx 17C60Division algebrasDivision algebras17Cxx / G 17C65Jordan structures on Banach spaces and algebrasJordan structures on Banach spaces and algebras [See also 46H70, 46L70]17Cxx 17C70Super structuresSuper structures17Cxx 17C90Appl. to physicsApplications to physics17Cxx & 17C99Jordan algebrasNone of the above, but in this section17Cxx - 17CxxJordan algebrasJordan algebras (algebras, triples and pairs)17-XX 17D05Alternative ringsAlternative rings17Dxx # 17D10Mal'tsev rings and algebrasMalcev (Maltsev) rings and algebras17Dxx 17D15Right alternative ringsRight alternative rings17Dxx 2 17D20(gamma,delta)-rings$(\gamma, \delta)$-rings, including $(1,-1)$-rings17Dxx 17D25Lie-admissible algebrasLie-admissible algebras17Dxx 17D92Genetic algebrasGenetic algebras17Dxx ' & 17D99Other nonassociative rings and algebrasNone of the above, but in this section17Dxx ) ' 17DxxSpecial nonassociative rings and algebrasOther nonassociative rings and algebras17-XX ! G 18-00Reference works (category theory)General reference works (handbooks, dictionaries, bibliographies, etc.)18-XX ; 18-01Textbooks (category theory)Instructional exposition (textbooks, tutorial papers, etc.)18-XX % 1 18-02Research monographs (category theory)Research exposition (monographs, survey articles)18-XX U 18-03Historical (category theory)Historical (must also be assigned at least one classification number from Section 01)18-XX / X 18-04Machine computation, programs (category theory)Explicit machine computation and programs (not the theory of computation or programming)18-XX , + 18-06Proceedings of conferences (category theory)Proceedings, conferences, collections, etc.18-XX $ $ 18-99Category theory, homological algebraCategory theory, homological algebra $ Û 18-XXCategory theory, homological algebraCategory theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology} $ 18A05Basic definitions of category theoryDefinitions, generalizations18Axx ) = 18A10Generalizations of the notion of categoryGraphs, diagram schemes, precategories [See especially 20L05]18Axx % F 18A15Relations of category theory to logicFoundations, relations to logic and deductive systems [See also 03-XX]18Axx I 18A20Special classes of morphismsEpimorphisms, monomorphisms, special classes of morphisms, null morphisms18Axx 5 18A22Special properties of functorsSpecial properties of functors (faithful, full, etc.)18Axx & 18A23Natural morphismsNatural morphisms, dinatural morphisms18Axx $ 18A25Comma categoriesFunctor categories, comma categories18Axx { 18A30LimitsLimits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)18Axx U 18A32Factorization of morphismsFactorization of morphisms, substructures, quotient structures, congruences, amalgams18Axx Z 18A35Complete categoriesCategories admitting limits (complete categories), functors preserving limits, completions18Axx Z 18A40Adjoint functorsAdjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)18Axx ) & 18A99General theory of categories and functorsNone of the above, but in this section18Axx ) ) 18AxxGeneral theory of categories and functorsGeneral theory of categories and functors18-XX 4 18B05Category of setsCategory of sets, characterizations [See also 03-XX]18Bxx ) 18B10Category of relationsCategory of relations, additive relations18Bxx 9 18B15Universal categoriesEmbedding theorems, universal categories [See also 18E20]18Bxx N 18B20Categories of automata, etc.Categories of machines, automata, operative categories [See also 03D05, 68Qxx]18Bxx 18B25TopoiTopoi [See also 03G30]18Bxx I 18B30Categories of topological spacesCategories of topological spaces and continuous mappings [See also 54-XX]18Bxx 0 F 18B35Generalizations of lattices viewed as categoriesPreorders, orders and lattices (viewed as categories) [See also 06-XX]18Bxx . b 18B40Generalizations of groups viewed as categoriesGroupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]18Bxx & 18B99Special categoriesNone of the above, but in this section18Bxx 18BxxSpecial categoriesSpecial categories18-XX - 18C05Equational categoriesEquational categories [See also 03C05, 08C05]18Cxx M 18C10Algebraic theories, etc.Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]18Cxx „ 18C15TriplesTriples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]18Cxx 6 18C20Algebras associated with monadsAlgebras and Kleisli categories associated with monads18Cxx 18C30Sketches and generalizationsSketches and generalizations18Cxx18C101 - - 18C35Accessible and locally presentable categoriesAccessible and locally presentable categories18Cxx18C10,18B991 ) A 18C50Categorical semantics of formal languagesCategorical semantics of formal languages [See also 68Q55, 68Q65]18Cxx18C10,18B991 ! & 18C99Categories and algebraic theoriesNone of the above, but in this section18Cxx ! 18CxxCategories and algebraic theoriesCategories and theories18-XX C 18D052-categories and generalizationsDouble categories, $2$-categories, bicategories and generalizations18Dxx u 18D10Monoidal categoriesMonoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]18Dxx I 18D15Closed categoriesClosed categories (closed monoidal and Cartesian closed categories, etc.)18Dxx 8 18D20Enriched categoriesEnriched categories (over closed or monoidal categories)18Dxx # 18D25Strong functorsStrong functors, strong adjunctions18Dxx 18D30Fibered categoriesFibered categories18Dxx 6 18D35Structured objects in a categoryStructured objects in a category (group objects, etc.)18Dxx 18D50OperadsOperads [See also 55P48]18Dxx18D10,55U35,18C15,18G991 & 18D99Categories with structureNone of the above, but in this section18Dxx 18DxxCategories with structureCategories with structure18-XX 18E05Additive categories, etc.Preadditive, additive categories18Exx $ $ 18E10Exact categories, abelian categoriesExact categories, abelian categories18Exx 18E15Grothendieck categoriesGrothendieck categories18Exx ( # 18E20Imbedding theorems of abelian categoriesEmbedding theorems [See also 18B15]18Exx 18E25Derived functors, etc.Derived functors and satellites18Exx + 18E30Derived categories, etc.Derived categories, triangulated categories18Exx 18E35Localization of categoriesLocalization of categories18Exx 2 18E40Torsion theoriesTorsion theories, radicals [See also 13D30, 16S90]18Exx & 18E99Abelian categoriesNone of the above, but in this section18Exx 18ExxAbelian categoriesAbelian categories18-XX 18F05Local categories and functorsLocal categories and functors18Fxx ( 18F10Grothendieck topologiesGrothendieck topologies [See also 14F20]18Fxx < 18F15Abstract manifolds, etc.Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]18Fxx # C 18F20Categorical methods in sheaf theoryPresheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]18Fxx z 18F25Algebraic K-theory, etc.Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]18Fxx 2 18F30Grothendieck groupsGrothendieck groups [See also 13D15, 16E20, 19Axx]18Fxx & 18F99Categories and geometryNone of the above, but in this section18Fxx 18FxxCategories and geometryCategories and geometry18-XX 0 @ 18G05Projectives and injectives (homological algebra)Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]18Gxx ! < 18G10Resolutions (homological algebra)Resolutions; derived functors [See also 13D02, 16E05, 18E25]18Gxx > 18G15Ext and Tor, generalizationsExt and Tor, generalizations, Künneth formula [See also 55U25]18Gxx - 18G20Homological dimensionHomological dimension [See also 13D05, 16E10]18Gxx 0 18G25Relative homological algebraRelative homological algebra, projective classes18Gxx D 18G30Simplicial objects in a categorySimplicial sets, simplicial objects (in a category) [See also 55U10]18Gxx % ' 18G35Chain complexes (homological algebra)Chain complexes [See also 18E30, 55U15]18Gxx ( 4 18G40Spectral sequences (homological algebra)Spectral sequences, hypercohomology [See also 55Txx]18Gxx 18G50Nonabelian homological algebraNonabelian homological algebra18Gxx 18G55Nonabelian homotopical algebraHomotopical algebra18Gxx A 18G60Other (co)homologiesOther (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]18Gxx & 18G99Homological algebraNone of the above, but in this section18Gxx G 18GxxHomological algebraHomological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]18-XX G 19-00Reference works (K-theory)General reference works (handbooks, dictionaries, bibliographies, etc.)19-XX ; 19-01Textbooks (K-theory)Instructional exposition (textbooks, tutorial papers, etc.)19-XX 1 19-02Research monographs (K-theory)Research exposition (monographs, survey articles)19-XX U 19-03Historical (K-theory)Historical (must also be assigned at least one classification number from Section 01)19-XX ( X 19-04Machine computation, programs (K-theory)Explicit machine computation and programs (not the theory of computation or programming)19-XX % + 19-06Proceedings of conferences (K-theory)Proceedings, conferences, collections, etc.19-XX 19-99K-theoryK-theory " 19-XXK-Theory$K$-theory [See also 16E20, 18F25] 1 19A13Stability for projective modulesStability for projective modules [See also 13C10]19Axx 19A15Efficient generation ($K\sb 0$)Efficient generation19Axx 6 19A22Frobenius induction, etc.Frobenius induction, Burnside and representation rings19Axx " 19A31K$\sb 0$ of group rings and orders$K_0$ of group rings and orders19Axx 19A49K$\sb 0$ of other rings$K_0$ of other rings19Axx & 19A99Grothendieck groups and $K\sb 0$None of the above, but in this section19Axx 5 19AxxGrothendieck groups and $K\sb 0$Grothendieck groups and $K_0$ [See also 13D15, 18F30]19-XX " 19B10Stable range conditions (K$\sb 1$)Stable range conditions19Bxx & 19B14Stability for linear groups ($K\sb 1$)Stability for linear groups19Bxx 0 19B28$K\sb 1$ of group rings$K_1$ of group rings and orders [See also 57Q10]19Bxx ' - 19B37Congruence subgroup problems (K$\sb 1$)Congruence subgroup problems [See also 20H05]19Bxx & 19B99Whitehead groups and $K\sb 1$None of the above, but in this section19Bxx 19BxxWhitehead groups and $K\sb 1$Whitehead groups and $K_1$19-XX ( 19C09Central extensions, etc.Central extensions and Schur multipliers19Cxx 0 - 19C20Symbols, presentations and stability of K$\sb 2$Symbols, presentations and stability of $K_2$19Cxx 19C30$K\sb 2$ and the Brauer group$K_2$ and the Brauer group19Cxx 19C40Excision for K$\sb 2$Excision for $K_2$19Cxx & 19C99Steinberg groups and $K\sb 2$None of the above, but in this section19Cxx 19CxxSteinberg groups and $K\sb 2$Steinberg groups and $K_2$19-XX 19D06Q- and plus-constructions$Q$- and plus-constructions19Dxx 19D10Algebraic K-theory of spacesAlgebraic $K$-theory of spaces19Dxx ( . 19D23Symmetric monoidal categories (K-theory)Symmetric monoidal categories [See also 18D10]19Dxx # % 19D25Karoubi-Villamayor-Gersten K-theoryKaroubi-Villamayor-Gersten $K$-theory19Dxx 19D35Negative K-theory, etc.Negative $K$-theory, NK and Nil19Dxx ! 19D45Higher symbols, etc.Higher symbols, Milnor $K$-theory19Dxx ( B 19D50Computations of higher K-theory of ringsComputations of higher $K$-theory of rings [See also 13D15, 16E20]19Dxx H 19D55K-theory and homology$K$-theory and homology; cyclic homology and cohomology [See also 18G60]19Dxx & 19D99Higher algebraic K-theoryNone of the above, but in this section19Dxx 19DxxHigher algebraic K-theoryHigher algebraic $K$-theory19-XX & 19E08K-theory of schemes$K$-theory of schemes [See also 14C35]19Exx ? 19E15Algebraic cycles (K-theory)Algebraic cycles and motivic cohomology [See also 14C25, 14C35]19Exx . 3 19E20Relations of K-theory with cohomology theoriesRelations with cohomology theories [See also 14Fxx]19Exx & 19E99K-theory in geometryNone of the above, but in this section19Exx 19ExxK-theory in geometry$K$-theory in geometry19-XX / 19F05Generalized class field theoryGeneralized class field theory [See also 11G45]19Fxx ! ' 19F15Symbols and arithmetic (K-theory)Symbols and arithmetic [See also 11R37]19Fxx h 19F27Etale cohomology, etc.Étale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]19Fxx & 19F99K-theory in number theoryNone of the above, but in this section19Fxx 3 19FxxK-theory in number theory$K$-theory in number theory [See also 11R70, 11S70]19-XX 19G05Stability for quadratic modulesStability for quadratic modules19Gxx % 19G12Witt groups of ringsWitt groups of rings [See also 11E81]19Gxx * 19G24L-theory of group rings$L$-theory of group rings [See also 11E81]19Gxx 8 19G38Hermitian K-theoryHermitian $K$-theory, relations with $K$-theory of rings19Gxx & 19G99K-theory of formsNone of the above, but in this section19Gxx $ 19GxxK-theory of forms$K$-theory of forms [See also 11Exx]19-XX - * 19J05Finiteness and other obstructions in K$\sb 0$Finiteness and other obstructions in $K_0$19Jxx 19J10Whitehead (and related) torsionWhitehead (and related) torsion19Jxx % 19J25Surgery obstructions (K-theory)Surgery obstructions [See also 57R67]19Jxx ( 19J35Obstructions to group actions (K-theory)Obstructions to group actions19Jxx & & 19J99Obstructions of K-theory from topologyNone of the above, but in this section19Jxx 19JxxObstructions from topologyObstructions from topology19-XX ! 19K14$K\sb 0$ as an ordered group$K_0$ as an ordered group, traces19Kxx % 19K33EXT and K-homologyEXT and $K$-homology [See also 55N22]19Kxx . 19K35Kasparov theory (KK-theory)Kasparov theory ($KK$-theory) [See also 58J22]19Kxx $ 19K56Index theory (K-theory)Index theory [See also 58J20, 58J22]19Kxx & 19K99K-theory and operator algebrasNone of the above, but in this section19Kxx C 19KxxK-theory and operator algebras$K$-theory and operator algebras [See mainly 46L80, and also 46M20]19-XX ' 19L10Riemann-Roch theorems, etc.Riemann-Roch theorems, Chern characters19Lxx 3 19L20J-homomorphism, etc.$J$-homomorphism, Adams operations [See also 55Q50]19Lxx 1 19L41Connective K-theoryConnective $K$-theory, cobordism [See also 55N22]19Lxx C 19L47Equivariant K-theoryEquivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]19Lxx ) $ 19L64Computations, geometric appl. of K-theoryComputations, geometric applications19Lxx & 19L99Topological K-theoryNone of the above, but in this section19Lxx 5 19LxxTopological K-theoryTopological $K$-theory [See also 55N15, 55R50, 55S25]19-XX ( 19M05Miscellaneous appl. of K-theoryMiscellaneous applications of $K$-theory19-XX G 20-00Reference works (group theory)General reference works (handbooks, dictionaries, bibliographies, etc.)20-XX ; 20-01Textbooks (group theory)Instructional exposition (textbooks, tutorial papers, etc.)20-XX " 1 20-02Research monographs (group theory)Research exposition (monographs, survey articles)20-XX U 20-03Historical (group theory)Historical (must also be assigned at least one classification number from Section 01)20-XX , X 20-04Machine computation, programs (group theory)Explicit machine computation and programs (not the theory of computation or programming)20-XX ) + 20-06Proceedings of conferences (group theory)Proceedings, conferences, collections, etc.20-XX 20-99Group theory and generalizationsGroup theory and generalizations 20-XXGroup theoryGroup theory and generalizations 3 $ 20A05Axiomatics and elementary properties (group theory)Axiomatics and elementary properties20Axx . > 20A10Metamathematical considerations (group theory)Metamathematical considerations {For word problems, see 20F10}20Axx % 20A15Appl. of logic to group theoryApplications of logic to group theory20Axx & 20A99Foundations of group theoryNone of the above, but in this section20Axx 20AxxFoundations of group theoryFoundations20-XX , 20B05General theory for finite permutation groupsGeneral theory for finite groups20Bxx . " 20B07General theory for infinite permutation groupsGeneral theory for infinite groups20Bxx / 20B10Characterization theorems of permutation groupsCharacterization theorems20Bxx 20B15Uniprimitive permutation groupsPrimitive groups20Bxx - ! 20B20Multiply transitive finite permutation groupsMultiply transitive finite groups20Bxx / # 20B22Multiply transitive infinite permutation groupsMultiply transitive infinite groups20Bxx 6 | 20B25Finite automorphism groups of miscellaneous structuresFinite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]20Bxx 8 - 20B27Infinite automorphism groups of miscellaneous structuresInfinite automorphism groups [See also 12F10]20Bxx " 20B30General theory of symmetric groupsSymmetric groups20Bxx 20B35Subgroups of symmetric groupsSubgroups of symmetric groups20Bxx * 20B40Computational methods (permutation groups)Computational methods20Bxx & 20B99Permutation groupsNone of the above, but in this section20Bxx 20BxxPermutation groupsPermutation groups20-XX = ? 20C05Group rings of finite groups and their modules (group theory)Group rings of finite groups and their modules [See also 16S34]20Cxx ? A 20C07Group rings of infinite groups and their modules (group theory)Group rings of infinite groups and their modules [See also 16S34]20Cxx ( ( 20C08Hecke algebras and their representationsHecke algebras and their representations20Cxx20C991 ) ) 20C10Integral representations of finite groupsIntegral representations of finite groups20Cxx ' ) 20C11p-adic representations of finite groups$p$-adic representations of finite groups20Cxx + + 20C12Integral representations of infinite groupsIntegral representations of infinite groups20Cxx 1 ' 20C15Ordinary representations and characters of groupsOrdinary representations and characters20Cxx 0 & 20C20Modular representations and characters of groupsModular representations and characters20Cxx 4 * 20C25Projective representations and multipliers of groupsProjective representations and multipliers20Cxx * * 20C30Representations of finite symmetric groupsRepresentations of finite symmetric groups20Cxx , , 20C32Representations of infinite symmetric groupsRepresentations of infinite symmetric groups20Cxx , , 20C33Representations of finite groups of Lie typeRepresentations of finite groups of Lie type20Cxx " " 20C34Representations of sporadic groupsRepresentations of sporadic groups20Cxx ) 0 20C35Appl. of group representations to physicsApplications of group representations to physics20Cxx 1 20C40Computational methods (representations of groups)Computational methods20Cxx & 20C99Representation theory of groupsNone of the above, but in this section20Cxx ^ 20CxxRepresentation theory of groupsRepresentation theory of groups [See also 19A22 (for representation rings and Burnside rings)]20-XX 6 / 20D05Classification of simple and nonsolvable finite groupsClassification of simple and nonsolvable groups20Dxx 8 I 20D06Simple groups: alternating groups and groups of Lie typeSimple groups: alternating groups and groups of Lie type [See also 20Gxx]20Dxx % 20D08Simple groups: sporadic finite groupsSimple groups: sporadic groups20Dxx m 20D10Solvable finite groupsSolvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks [See also 20F17]20Dxx 20D15Nilpotent finite groupsNilpotent groups, $p$-groups20Dxx @ 20D20Sylow subgroups of finite groupsSylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure20Dxx " + 20D25Special subgroups of finite groupsSpecial subgroups (Frattini, Fitting, etc.)20Dxx 1 20D30Series and lattices of subgroups of finite groupsSeries and lattices of subgroups20Dxx $ 20D35Subnormal subgroups of finite groupsSubnormal subgroups20Dxx & 20D40Products of subgroups of finite groupsProducts of subgroups20Dxx
20D45Automorphisms of finite groupsAutomorphisms20Dxx 6 % 20D60Arithmetic and combinatorial problems on finite groupsArithmetic and combinatorial problems20Dxx & 20D99Abstract finite groupsNone of the above, but in this section20Dxx 20DxxAbstract finite groupsAbstract finite groups20-XX 20E05Free nonabelian groupsFree nonabelian groups20Exx 0 f 20E06Free products and generalizations (group theory)Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations20Exx " 20E07Subgroup theorems (group theory)Subgroup theorems; subgroup growth20Exx ' 20E08Groups acting on treesGroups acting on trees [See also 20F65]20Exx ' & 20E10Varieties of groups and generalizationsQuasivarieties and varieties of groups20Exx * F 20E15Chains and lattices of subgroups of groupsChains and lattices of subgroups, subnormal subgroups [See also 20F22]20Exx 20E18Profinite groupsLimits, profinite groups20Exx + D 20E22Extensions and other compositions of groupsExtensions, wreath products, and other compositions [See also 20J05]20Exx 20E25Local properties of groupsLocal properties20Exx 1 ' 20E26Residual properties of groups and generalizationsResidual properties and generalizations20Exx 20E28Maximal subgroups of groupsMaximal subgroups20Exx 20E32Infinite simple groupsSimple groups [See also 20D05]20Exx $ 20E34General structure theorems of groupsGeneral structure theorems20Exx 3 3 20E36General theorems concerning automorphisms of groupsGeneral theorems concerning automorphisms of groups20Exx 3 20E42Groups with a BN-pair; buildingsGroups with a $BN$-pair; buildings [See also 51E24]20Exx 20E45Conjugacy classesConjugacy classes20Exx20E991 9 & 20E99Structure and classification of infinite or finite groupsNone of the above, but in this section20Exx 9 9 20ExxStructure and classification of infinite or finite groupsStructure and classification of infinite or finite groups20-XX ( 20F05Presentations of groupsGenerators, relations, and presentations20Fxx " H 20F06Cancellation theory (group theory)Cancellation theory; application of van Kampen diagrams [See also 57M05]20Fxx 20F10Decision problems (group theory)Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]20Fxx " 20F12Commutator calculus (group theory)Commutator calculus20Fxx $ 3 20F14Series of groups and generalizationsDerived series, central series, and generalizations20Fxx 6 20F16Solvable groupsSolvable groups, supersolvable groups [See also 20D10]20Fxx 6 20F17Formations of groupsFormations of groups, Fitting classes [See also 20D10]20Fxx ! 20F18Nilpotent groupsNilpotent groups [See also 20D15]20Fxx 0 0 20F19Generalizations of solvable and nilpotent groupsGeneralizations of solvable and nilpotent groups20Fxx 2 2 20F22Other classes of groups defined by subgroup chainsOther classes of groups defined by subgroup chains20Fxx # 20F24FC-groups and generalizationsFC-groups and their generalizations20Fxx . 20F28Automorphism groups of groupsAutomorphism groups of groups [See also 20E36]20Fxx @ E 20F29Representations of groups as automorphism groups of alg. systemsRepresentations of groups as automorphism groups of algebraic systems20Fxx * B 20F34Fundamental groups and their automorphismsFundamental groups and their automorphisms [See also 57M05, 57Sxx]20Fxx 20F36Braid groups; Artin groupsBraid groups; Artin groups20Fxx , , 20F38Other groups related to topology or analysisOther groups related to topology or analysis20Fxx # 20F40Associated Lie structures on groupsAssociated Lie structures20Fxx 20F45Engel conditions on groupsEngel conditions20Fxx & & 20F50Periodic groups; locally finite groupsPeriodic groups; locally finite groups20Fxx 5 20F55Coxeter groupsReflection and Coxeter groups [See also 22E40, 51F15]20Fxx ! 20F60Ordered groups (group aspects)Ordered groups [See mainly 06F15]20Fxx 5 20F65Geometric group theoryGeometric group theory [See also 05C25, 20E08, 57Mxx]20Fxx20F321 1 20F67Hyperbolic groups etc.Hyperbolic groups and nonpositively curved groups20Fxx20F321 20F69Asymptotic properties of groupsAsymptotic properties of groups20Fxx20F321 , & 20F99Special aspects of infinite or finite groupsNone of the above, but in this section20Fxx , , 20FxxSpecial aspects of infinite or finite groupsSpecial aspects of infinite or finite groups20-XX 0 20G05Representation theory of linear algebraic groupsRepresentation theory20Gxx , 20G10Cohomology theory of linear algebraic groupsCohomology theory20Gxx - - 20G15Linear algebraic groups over arbitrary fieldsLinear algebraic groups over arbitrary fields20Gxx & F 20G20Linear algebraic groups over the realsLinear algebraic groups over the reals, the complexes, the quaternions20Gxx < < 20G25Linear algebraic groups over local fields and their integersLinear algebraic groups over local fields and their integers20Gxx = = 20G30Linear algebraic groups over global fields and their integersLinear algebraic groups over global fields and their integers20Gxx A ? 20G35Linear algebraic groups over ad\`eles and other rings and schemesLinear algebraic groups over adèles and other rings and schemes20Gxx * * 20G40Linear algebraic groups over finite fieldsLinear algebraic groups over finite fields20Gxx e 20G42Quantum groupsQuantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50]20Gxx16W30,17B371 + 20G45Appl. of linear algebraic groups to physicsApplications to physics20Gxx & 20G99Linear algebraic groupsNone of the above, but in this section20Gxx * Ö 20GxxLinear algebraic groups (classical groups)Linear algebraic groups (classical groups) {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}20-XX $ M 20H05Congruence subgroups (matrix groups)Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]20Hxx 8 O 20H10Fuchsian groups and their generalizations (group theory)Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]20Hxx 9 g 20H15Other geometric groups, including crystallographic groupsOther geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]20Hxx 20H20Other matrix groups over fieldsOther matrix groups over fields20Hxx 20H25Other matrix groups over ringsOther matrix groups over rings20Hxx & & 20H30Other matrix groups over finite fieldsOther matrix groups over finite fields20Hxx & 20H99Other groups of matricesNone of the above, but in this section20Hxx ) 20HxxOther groups of matricesOther groups of matrices [See also 15A30]20-XX # # 20J05Homological methods in group theoryHomological methods in group theory20Jxx 20J06Cohomology of finite groupsCohomology of groups20Jxx 20J15Category of groupsCategory of groups20Jxx 4 & 20J99Connections of group theory with homological algebraNone of the above, but in this section20Jxx 4 8 20JxxConnections of group theory with homological algebraConnections with homological algebra and category theory20-XX 20K01Finite abelian groupsFinite abelian groups20Kxx = 20K10Torsion abelian groups, etc.Torsion groups, primary groups and generalized primary groups20Kxx ( 20K15Torsion free abelian groups, finite rankTorsion-free groups, finite rank20Kxx * " 20K20Torsion free abelian groups, infinite rankTorsion-free groups, infinite rank20Kxx 20K21Mixed abelian groupsMixed groups20Kxx " " 20K25Direct sums, etc. (abelian groups)Direct sums, direct products, etc.20Kxx 20K27Subgroups of abelian groupsSubgroups20Kxx 1 20K30Morphisms of abelian groupsAutomorphisms, homomorphisms, endomorphisms, etc.20Kxx
20K35Extensions of abelian groupsExtensions20Kxx 4 # 20K40Homological and categorical methods (abelian groups)Homological and categorical methods20Kxx $ + 20K45Topological methods (abelian groups)Topological methods [See also 22A05, 22B05]20Kxx & 20K99Abelian groupsNone of the above, but in this section20Kxx 20KxxAbelian groupsAbelian groups20-XX « 20L05GroupoidsGroupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}20-XX 8 20M05Free semigroupsFree semigroups, generators and relations, word problems20Mxx 20M07Varieties of semigroupsVarieties of semigroups20Mxx & 20M10General structure theory of semigroupsGeneral structure theory20Mxx 20M11Radical theory on semigroupsRadical theory20Mxx 20M12Ideal theory of semigroupsIdeal theory20Mxx 20M14Commutative semigroupsCommutative semigroups20Mxx 20M15Mappings of semigroupsMappings of semigroups20Mxx 20M17Regular semigroupsRegular semigroups20Mxx 20M18Inverse semigroupsInverse semigroups20Mxx 20M19Orthodox semigroupsOrthodox semigroups20Mxx # B 20M20Semigroups of transformations, etc.Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]20Mxx 3 K 20M25Semigroup rings, multiplicative semigroups of ringsSemigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]20Mxx ; 20M30Representation of semigroupsRepresentation of semigroups; actions of semigroups on sets20Mxx 0 O 20M35Semigroups in automata theory, linguistics, etc.Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]20Mxx 2 F 20M50Connections of semigroups with homological algebraConnections of semigroups with homological algebra and category theory20Mxx
& 20M99SemigroupsNone of the above, but in this section20Mxx
20MxxSemigroupsSemigroups20-XX / / 20N02Sets with a single binary operation (groupoids)Sets with a single binary operation (groupoids)20Nxx # 20N05Loops (group theory)Loops, quasigroups [See also 05Bxx]20Nxx 2 20N10Ternary systems (group theory)Ternary systems (heaps, semiheaps, heapoids, etc.)20Nxx 20N15n-ary systems (group theory)$n$-ary systems $(n\ge 3)$20Nxx 20N20Hypergroups (group theory)Hypergroups20Nxx 20N25Fuzzy groupsFuzzy groups [See also 03E72]20Nxx & 20N99Generalizations of groupsNone of the above, but in this section20Nxx 20NxxOther generalizations of groupsOther generalizations of groups20-XX # 6 20P05Probability methods in group theoryProbabilistic methods in group theory [See also 60Bxx]20-XX $ G 22-00Reference works (topological groups)General reference works (handbooks, dictionaries, bibliographies, etc.)22-XX ; 22-01Textbooks (topological groups)Instructional exposition (textbooks, tutorial papers, etc.)22-XX ( 1 22-02Research monographs (topological groups)Research exposition (monographs, survey articles)22-XX U 22-03Historical (topological groups)Historical (must also be assigned at least one classification number from Section 01)22-XX 2 X 22-04Machine computation, programs (topological groups)Explicit machine computation and programs (not the theory of computation or programming)22-XX / + 22-06Proceedings of conferences (topological groups)Proceedings, conferences, collections, etc.22-XX 22-99Topological groups, Lie groupsTopological groups, Lie groups ~ 22-XXTopological groups, Lie groupsTopological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} ' ' 22A05Structure of general topological groupsStructure of general topological groups22Axx & & 22A10Analysis on general topological groupsAnalysis on general topological groups22Axx # # 22A15Structure of topological semigroupsStructure of topological semigroups22Axx " " 22A20Analysis on topological semigroupsAnalysis on topological semigroups22Axx B S 22A22Topological groupoids (including differentiable and Lie groupoids)Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]22Axx < < 22A25Representations of general topological groups and semigroupsRepresentations of general topological groups and semigroups22Axx / R 22A26Topological lattices, etc. (topological groups)Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]22Axx < = 22A30Other topological algebraic systems and their representationOther topological algebraic systems and their representations22Axx & 22A99Topological algebraic systemsNone of the above, but in this section22Axx l 22AxxTopological algebraic systemsTopological and differentiable algebraic systems {For topological rings and fields, see 12Jxx, 13Jxx, 16W80}22-XX . . 22B05General properties and structure of LCA groupsGeneral properties and structure of LCA groups22Bxx ) ) 22B10Structure of group algebras of LCA groupsStructure of group algebras of LCA groups22Bxx
& 22B99LCA groupsNone of the above, but in this section22Bxx + + 22BxxLocally compact abelian groups (LCA groups)Locally compact abelian groups (LCA groups)22-XX 22C05Compact topological groupsCompact groups22-XX : : 22D05General properties and structure of locally compact groupsGeneral properties and structure of locally compact groups22Dxx 1 1 22D10Unitary representations of locally compact groupsUnitary representations of locally compact groups22Dxx / / 22D12Other representations of locally compact groupsOther representations of locally compact groups22Dxx ( ( 22D15Group algebras of locally compact groupsGroup algebras of locally compact groups22Dxx ! ! 22D20Representations of group algebrasRepresentations of group algebras22Dxx 4 V 22D25Operator algebras arising from group representations$C^*$-algebras and $W$*-algebras in relation to group representations [See also 46Lxx]22Dxx 1 22D30Induced representations of locally compact groupsInduced representations22Dxx ) 22D35Duality theorems (locally compact groups)Duality theorems22Dxx ) 22D40Ergodic theory on groupsErgodic theory on groups [See also 28Dxx]22Dxx - - 22D45Automorphism groups of locally compact groupsAutomorphism groups of locally compact groups22Dxx ) & 22D99Locally compact groups and their algebrasNone of the above, but in this section22Dxx ) ) 22DxxLocally compact groups and their algebrasLocally compact groups and their algebras22-XX / 22E05Local Lie groupsLocal Lie groups [See also 34-XX, 35-XX, 58H05]22Exx 6 G 22E10General properties and structure of complex Lie groupsGeneral properties and structure of complex Lie groups [See also 32M05]22Exx 3 3 22E15General properties and structure of real Lie groupsGeneral properties and structure of real Lie groups22Exx 4 4 22E20General properties and structure of other Lie groupsGeneral properties and structure of other Lie groups22Exx ! ! 22E25Nilpotent and solvable Lie groupsNilpotent and solvable Lie groups22Exx 4 r 22E27Representations of nilpotent and solvable Lie groupsRepresentations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)22Exx ' ? 22E30Analysis on real and complex Lie groupsAnalysis on real and complex Lie groups [See also 33C80, 43-XX]22Exx 22E35Analysis on p-adic Lie groupsAnalysis on $p$-adic Lie groups22Exx 8 22E40Discrete subgroups of Lie groupsDiscrete subgroups of Lie groups [See also 20Hxx, 32Nxx]22Exx " 4 22E41Continuous cohomology (Lie groups)Continuous cohomology [See also 57R32, 57Txx, 58H10]22Exx 1 1 22E43Structure and representation of the Lorentz groupStructure and representation of the Lorentz group22Exx C ‚ 22E45Analytic repres.of Lie and linear algebraic groups over real fieldsRepresentations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}22Exx 0 / 22E46Semi-simple Lie groups and their representationsSemisimple Lie groups and their representations22Exx ; j 22E47Repres. of Lie and real algebraic groups: algebraic methodsRepresentations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]22Exx < U 22E50Repres. of Lie and linear algebraic groups over local fieldsRepresentations of Lie and linear algebraic groups over local fields [See also 20G05]22Exx = f 22E55Repres. of Lie and linear algebraic groups over global fieldsRepresentations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]22Exx P 22E60Lie algebras of Lie groupsLie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx}22Exx U 22E65Infinite-dimensional Lie groupsInfinite-dimensional Lie groups and their Lie algebras [See also 17B65, 58B25, 58H05]22Exx % Q 22E67Loop groups and related constructionsLoop groups and related constructions, group-theoretic treatment [See also 58D05]22Exx W 22E70Appl. of Lie groups to physicsApplications of Lie groups to physics; explicit representations [See also 81R05, 81R10]22Exx
& 22E99Lie groupsNone of the above, but in this section22Exx
ƒ 22ExxLie groupsLie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90}22-XX / p 22F05General theory of group and pseudogroup actionsGeneral theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}22Fxx22A99,57S201 7 22F10Measurable group actionsMeasurable group actions [See also 22D40, 28Dxx, 37Axx]22Fxx22D40,28Dxx1 § 22F30Homogeneous spacesHomogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups see especially 22E40}22Fxx57M60,57Sxx,22E401 + + 22F50Groups as automorphisms of other structuresGroups as automorphisms of other structures22Fxx22Axx,46Lxx1 22FxxNoncompact transformation groupsNoncompact transformation groups22-XX G 26-00Reference works (real functions)General reference works (handbooks, dictionaries, bibliographies, etc.)26-XX ; 26-01Textbooks (real functions)Instructional exposition (textbooks, tutorial papers, etc.)26-XX $ 1 26-02Research monographs (real functions)Research exposition (monographs, survey articles)26-XX U 26-03Historical (real functions)Historical (must also be assigned at least one classification number from Section 01)26-XX . X 26-04Machine computation, programs (real functions)Explicit machine computation and programs (not the theory of computation or programming)26-XX + + 26-06Proceedings of conferences (real functions)Proceedings, conferences, collections, etc.26-XX 26-99Real functionsReal functions 26-XXReal functionsReal functions [See also 54C30] $ H 26A03Elementary topology of the real lineFoundations: limits and generalizations, elementary topology of the line26Axx 26A06One-variable calculusOne-variable calculus26Axx ) 26A09Elementary functions of one real variableElementary functions26Axx 0 Z 26A12Rate of growth of functions of one real variableRate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]26Axx 4 â 26A15Continuity and related questions (one real variable)Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}26Axx + 26A16Lipschitz classes, etc. (one real variable)Lipschitz (Hölder) classes26Axx + = 26A18Iteration of functions of one real variableIteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]26Axx 0 k 26A21Classification of functions of one real variableClassification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50]26Axx 1 z 26A24Differentiation of functions of one real variableDifferentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]26Axx 6 m 26A27Nondifferentiability of functions of one real variableNondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives26Axx A M 26A30Real functions of one real variable with other special propertiesSingular functions, Cantor functions, functions with other special properties26Axx 5 $ 26A33Fractional derivatives and integrals (real functions)Fractional derivatives and integrals26Axx 4 26A36Antidifferentiation (functions of one real variable)Antidifferentiation26Axx 3 4 26A39Special integrals of functions of one real variableDenjoy and Perron integrals, other special integrals26Axx 4 B 26A42Ordinary integrals of functions of one real variableIntegrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]26Axx 2 / 26A45Functions of bounded variation (one real variable)Functions of bounded variation, generalizations26Axx 3 26A46Absolutely continuous functions (one real variable)Absolutely continuous functions26Axx 8 $ 26A48Monotonic functions, generalizations (one real variable)Monotonic functions, generalizations26Axx . 26A51Convexity, generalizations (one real variable)Convexity, generalizations26Axx & 26A99Functions of one real variableNone of the above, but in this section26Axx 26AxxFunctions of one real variableFunctions of one variable26-XX A ( 26B05Continuity and differentiation questions (several real variables)Continuity and differentiation questions26Bxx 9 M 26B10Implicit function theorems, etc. (several real variables)Implicit function theorems, Jacobians, transformations with several variables26Bxx 26B12Calculus of vector functionsCalculus of vector functions26Bxx $ 9 26B15Integration (several real variables)Integration: length, area, volume [See also 28A75, 51M25]26Bxx . 26B20Integral formulasIntegral formulas (Stokes, Gauss, Green, etc.)26Bxx 6 26B25Convexity and generalizations (several real variables)Convexity, generalizations26Bxx > ? 26B30Absolutely continuous functions, etc. (several real variables)Absolutely continuous functions, functions of bounded variation26Bxx 9 M 26B35Special properties of functions of several real variablesSpecial properties of functions of several variables, Hölder conditions, etc.26Bxx D - 26B40Representation and superposition of functions of sev. real variablesRepresentation and superposition of functions26Bxx # & 26B99Functions of several real variablesNone of the above, but in this section26Bxx # 26BxxFunctions of several real variablesFunctions of several variables26-XX 1 > 26C05Polynomials: analytic properties (real variables)Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]26Cxx / = 26C10Polynomials: location of zeros (real variables)Polynomials: location of zeros [See also 12D10, 30C15, 65H05]26Cxx # # 26C15Rational functions (real variables)Rational functions [See also 14Pxx]26Cxx 0 & 26C99Polynomials, rational functions (real variables)None of the above, but in this section26Cxx 0 26CxxPolynomials, rational functions (real variables)Polynomials, rational functions26-XX 8 8 26D05Inequalities for trigonometric functions and polynomialsInequalities for trigonometric functions and polynomials26Dxx 4 / 26D07Inequalities involving other types of real functionsInequalities involving other types of functions26Dxx @ J 26D10Inequalities involving derivatives, diff. and integral operatorsInequalities involving derivatives and differential and integral operators26Dxx = + 26D15Inequalities for sums, series and integrals of real functionsInequalities for sums, series and integrals26Dxx 0 26D20Analytical inequalities involving real functionsOther analytical inequalities26Dxx % & 26D99Inequalities involving real functionsNone of the above, but in this section26Dxx % Ž 26DxxInequalities involving real functionsInequalities {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15}26-XX / 26E05Real-analytic functionsReal-analytic functions [See also 32B05, 32C05]26Exx . ? 26E10Infinitely differentiable real functions, etc.$C^\infty$-functions, quasi-analytic functions [See also 58C25]26Exx 4 L 26E15Calculus of functions on infinite-dimensional spacesCalculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]26Exx B a 26E20Calculus of functions taking values in infinite-dimensional spacesCalculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]26Exx ^ 26E25Set-valued real functionsSet-valued functions [See also 28B20, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx}26Exx ) 26E30Non-Archimedean real analysisNon-Archimedean analysis [See also 12J25]26Exx 3 26E35Nonstandard real analysisNonstandard analysis [See also 03H05, 28E05, 54J05]26Exx + 26E40Constructive real analysisConstructive real analysis [See also 03F60]26Exx + 26E50Fuzzy real analysisFuzzy real analysis [See also 03E72, 28E10]26Exx 26E60MeansMeans [See also 47A64]26Exx26A24,26D151 % & 26E99Miscellaneous topics in real analysisNone of the above, but in this section26Exx % % 26ExxMiscellaneous topics in real analysisMiscellaneous topics [See also 58Cxx]26-XX ) G 28-00Reference works (measure and integration)General reference works (handbooks, dictionaries, bibliographies, etc.)28-XX # ; 28-01Textbooks (measure and integration)Instructional exposition (textbooks, tutorial papers, etc.)28-XX - 1 28-02Research monographs (measure and integration)Research exposition (monographs, survey articles)28-XX $ U 28-03Historical (measure and integration)Historical (must also be assigned at least one classification number from Section 01)28-XX 7 X 28-04Machine computation, programs (measure and integration)Explicit machine computation and programs (not the theory of computation or programming)28-XX 4 + 28-06Proceedings of conferences (measure and integration)Proceedings, conferences, collections, etc.28-XX 28-99Measure and integrationMeasure and integration > 28-XXMeasure and integrationMeasure and integration {For analysis on manifolds, see 58-XX} € 28A05Classes of setsClasses of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]28Axx % % 28A10Real- or complex-valued set functionsReal- or complex-valued set functions28Axx " . 28A12Measures and their generalizationsContents, measures, outer measures, capacities28Axx R 28A15Differentiation of set functionsAbstract differentiation theory, differentiation of set functions [See also 26A24]28Axx & _ 28A20Measurable and nonmeasurable functionsMeasurable and nonmeasurable functions, sequences of measurable functions, modes of convergence28Axx < < 28A25Integration with respect to measures and other set functionsIntegration with respect to measures and other set functions28Axx C 28A33Spaces of measuresSpaces of measures, convergence of measures [See also 46E27, 60Bxx]28Axx ( ( 28A35Measures and integrals in product spacesMeasures and integrals in product spaces28Axx * * 28A50Integration and disintegration of measuresIntegration and disintegration of measures28Axx 28A51Measure-theoretic lifting theoryLifting theory [See also 46G15]28Axx + < 28A60Measures on Boolean rings, measure algebrasMeasures on Boolean rings, measure algebras [See also 54H10]28Axx L 28A75Geometric measure theoryLength, area, volume, other geometric measure theory [See also 26B15, 49Q15]28Axx 28A78Hausdorff measuresHausdorff and packing measures28Axx 28A80FractalsFractals [See also 37Fxx]28Axx & 28A99Classical measure theoryNone of the above, but in this section28Axx 28AxxClassical measure theoryClassical measure theory28-XX 1 D 28B05Vector-valued set functions etc. (measure theory)Vector-valued set functions, measures and integrals [See also 46G10]28Bxx & @ 28B10(Semi-)group-valued set functions etc.Group- or semigroup-valued set functions, measures and integrals28Bxx 1 C 28B15Set functions, etc. with values in ordered spacesSet functions, measures and integrals with values in ordered spaces28Bxx ‡ 28B20Set-valued set functions etc.Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]28Bxx 1 & 28B99Set functions etc. with values in abstract spacesNone of the above, but in this section28Bxx 1 D 28BxxSet functions etc. with values in abstract spacesSet functions, measures and integrals with values in abstract spaces28-XX ) | 28C05Integration theory via linear functionalsIntegration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures28Cxx 0 k 28C10Set functions and measures on topological groupsSet functions and measures on topological groups, Haar measures, invariant measures [See also 22Axx, 43A05]28Cxx 0 O 28C15Set functions and measures on topological spacesSet functions and measures on topological spaces (regularity of measures, etc.)28Cxx @ – 28C20Set functions and measures and integrals in infinite-dim. spacesSet functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]28Cxx > & 28C99Set functions and measures on spaces with additional structureNone of the above, but in this section28Cxx 6 ] 28CxxSet functions etc. on spaces with additional structureSet functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]28-XX " " 28D05Measure-preserving transformationsMeasure-preserving transformations28Dxx B G 28D10One-parameter continuous families of measure-preserving transformsOne-parameter continuous families of measure-preserving transformations28Dxx 4 4 28D15General groups of measure-preserving transformationsGeneral groups of measure-preserving transformations28Dxx . 28D20Entropy and other measure-theoretic invariantsEntropy and other invariants28Dxx & 28D99Measure-theoretic ergodic theoryNone of the above, but in this section28Dxx b 28DxxMeasure-theoretic ergodic theoryMeasure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]28-XX 2 28E05Nonstandard measure theoryNonstandard measure theory [See also 03H05, 26E35]28Exx 3 28E10Fuzzy measuresFuzzy measure theory [See also 03E72, 26E50, 94D05]28Exx + + 28E15Other connections with logic and set theoryOther connections with logic and set theory28Exx & & 28E99Miscellaneous topics of measure theoryNone of the above, but in this section28Exx & & 28ExxMiscellaneous topics in measure theoryMiscellaneous topics in measure theory28-XX 3 G 30-00Reference works (functions of one complex variable)General reference works (handbooks, dictionaries, bibliographies, etc.)30-XX - ; 30-01Textbooks (functions of one complex variable)Instructional exposition (textbooks, tutorial papers, etc.)30-XX 7 1 30-02Research monographs (functions of one complex variable)Research exposition (monographs, survey articles)30-XX , U 30-03Historical (functions of a complex variable)Historical (must also be assigned at least one classification number from Section 01)30-XX ? X 30-04Machine computation, programs (functions of a complex variable)Explicit machine computation and programs (not the theory of computation or programming)30-XX < + 30-06Proceedings of conferences (functions of a complex variable)Proceedings, conferences, collections, etc.30-XX 30-99Functions of a complex variableFunctions of a complex variable F 30-XXFunctions of a complex variableFunctions of a complex variable {For analysis on manifolds, see 58-XX} ) _ 30A05Monogenic properties of complex functionsMonogenic properties of complex functions (including polygenic and areolar monogenic functions)30Axx " " 30A10Inequalities in the complex domainInequalities in the complex domain30Axx ' & 30A99General properties of complex functionsNone of the above, but in this section30Axx 7 30AxxGeneral properties of functions of one complex variableGeneral properties30-XX # ( 30B10Power series (one complex variable)Power series (including lacunary series)30Bxx * 30B20Random power series (one complex variable)Random power series30Bxx 8 3 30B30Boundary behavior of power series (one complex variable)Boundary behavior of power series, over-convergence30Bxx , 30B40Analytic continuation (one complex variable)Analytic continuation30Bxx ( X 30B50Series expansions (one complex variable)Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]30Bxx , 7 30B60Completeness problems (one complex variable)Completeness problems, closure of a system of functions30Bxx 0 + 30B70Continued fractions (function-theoretic results)Continued fractions [See also 11A55, 40A15]30Bxx ( & 30B99Series expansions (one complex variable)None of the above, but in this section30Bxx 3 30BxxSeries expansions (functions of a complex variable)Series expansions30-XX " 30C10Polynomials (one complex variable)Polynomials30Cxx 1 ¿ 30C15Zeros of polynomials, etc. (one complex variable)Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}30Cxx % % 30C20Conformal mappings of special domainsConformal mappings of special domains30Cxx - - 30C25Covering theorems in conformal mapping theoryCovering theorems in conformal mapping theory30Cxx - > 30C30Numerical methods in conformal mapping theoryNumerical methods in conformal mapping theory [See also 65E05]30Cxx $ $ 30C35General theory of conformal mappingsGeneral theory of conformal mappings30Cxx 1 ! 30C40Kernel functions and appl. (one complex variable)Kernel functions and applications30Cxx 6 a 30C45Special classes of univalent and multivalent functionsSpecial classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)30Cxx < < 30C50Coefficient problems for univalent and multivalent functionsCoefficient problems for univalent and multivalent functions30Cxx 5 5 30C55General theory of univalent and multivalent functionsGeneral theory of univalent and multivalent functions30Cxx $ $ 30C62Quasiconformal mappings in the planeQuasiconformal mappings in the plane30Cxx = > 30C65Quasiconformal mappings in R$\sp n$ and other generalizationsQuasiconformal mappings in $R^n$, other generalizations30Cxx A P 30C70Extremal problems for (quasi-)conformal mappings, variat. methodsExtremal problems for conformal and quasiconformal mappings, variational methods30Cxx ? J 30C75Extremal problems for (quasi-)conformal mappings, other methodsExtremal problems for conformal and quasiconformal mappings, other methods30Cxx . d 30C80Maximum principle, etc. (one complex variable)Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination30Cxx 2 C 30C85Capacity and harmonic measure in the complex planeCapacity and harmonic measure in the complex plane [See also 31A15]30Cxx & 30C99Geometric function theoryNone of the above, but in this section30Cxx 30CxxGeometric function theoryGeometric function theory30-XX * z 30D05Functional equations in the complex domainFunctional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]30Dxx ; ; 30D10Representations of entire functions by series and integralsRepresentations of entire functions by series and integrals30Dxx # 8 30D15Special classes of entire functionsSpecial classes of entire functions and growth estimates30Dxx " 30D20General theory of entire functionsEntire functions, general theory30Dxx ' % 30D30General theory of meromorphic functionsMeromorphic functions, general theory30Dxx - ) 30D35Distribution of values (one complex variable)Distribution of values, Nevanlinna theory30Dxx + 30D40Cluster sets, etc.Cluster sets, prime ends, boundary behavior30Dxx 2 30D45Normal functions, etc.Bloch functions, normal functions, normal families30Dxx y 30D50Blaschke products, etc.Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part30Dxx 30D55H (sup p)-classes${H}^p$-classes30Dxx - 30D60Other classes of functionsQuasi-analytic and other classes of functions30Dxx & 30D99Entire and meromorphic functionsNone of the above, but in this section30Dxx 4 4 30DxxEntire and meromorphic functions, and related topicsEntire and meromorphic functions, and related topics30-XX ' 30E05Moment problems, etc.Moment problems, interpolation problems30Exx # # 30E10Approximation in the complex domainApproximation in the complex domain30Exx 0 0 30E15Asymptotic representations in the complex domainAsymptotic representations in the complex domain30Exx " f 30E20Integration (one complex variable)Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]30Exx ) ( 30E25Boundary value problems, complex analysisBoundary value problems [See also 45Exx]30Exx 6 & 30E99Miscellaneous topics of analysis in the complex domainNone of the above, but in this section30Exx 6 6 30ExxMiscellaneous topics of analysis in the complex domainMiscellaneous topics of analysis in the complex domain30-XX C 30F10Compact Riemann surfacesCompact Riemann surfaces and uniformization [See also 14H15, 32G15]30Fxx & & 30F15Harmonic functions on Riemann surfacesHarmonic functions on Riemann surfaces30Fxx ) ) 30F20Classification theory of Riemann surfacesClassification theory of Riemann surfaces30Fxx 30F25Ideal boundary theoryIdeal boundary theory30Fxx ! ! 30F30Differentials on Riemann surfacesDifferentials on Riemann surfaces30Fxx ) V 30F35Fuchsian groups and automorphic functionsFuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]30Fxx 30F40Kleinian groupsKleinian groups [See also 20H10]30Fxx < 30F45Conformal metricsConformal metrics (hyperbolic, Poincaré, distance functions)30Fxx 30F50Klein surfacesKlein surfaces30Fxx # 30F60Teichmueller theoryTeichmüller theory [See also 32G15]30Fxx ' & 30F99Riemann surfaces (one complex variable)None of the above, but in this section30Fxx ' 30FxxRiemann surfaces (one complex variable)Riemann surfaces30-XX . ^ 30G06Non-Archimedean function theory (one variable)Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]30Gxx < < 30G12Finely holomorphic functions and topological function theoryFinely holomorphic functions and topological function theory30Gxx ; J 30G20Generalizations of analytic functions of Bers or Vekua typeGeneralizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)30Gxx 30G25Discrete analytic functionsDiscrete analytic functions30Gxx : Q 30G30Other generalizations of analytic functions (one variable)Other generalizations of analytic functions (including abstract-valued functions)30Gxx = = 30G35Functions of hypercomplex variables and generalized variablesFunctions of hypercomplex variables and generalized variables30Gxx & 30G99Generalized function theoryNone of the above, but in this section30Gxx 30GxxGeneralized function theoryGeneralized function theory30-XX ) H 30H05Spaces and algebras of analytic functionsSpaces and algebras of analytic functions [See also 32A38, 46Exx, 46J15]30-XX " G 31-00Reference works (potential theory)General reference works (handbooks, dictionaries, bibliographies, etc.)31-XX ; 31-01Textbooks (potential theory)Instructional exposition (textbooks, tutorial papers, etc.)31-XX & 1 31-02Research monographs (potential theory)Research exposition (monographs, survey articles)31-XX U 31-03Historical (potential theory)Historical (must also be assigned at least one classification number from Section 01)31-XX 0 X 31-04Machine computation, programs (potential theory)Explicit machine computation and programs (not the theory of computation or programming)31-XX - + 31-06Proceedings of conferences (potential theory)Proceedings, conferences, collections, etc.31-XX 31-99Potential theoryPotential theory @ 31-XXPotential theoryPotential theory {For probabilistic potential theory, see 60J45} * . 31A05Harmonic functions, etc. (two-dimensional)Harmonic, subharmonic, superharmonic functions31Axx @ H 31A10Integral representations of harmonic functions (two-dimensional)Integral representations, integral operators, integral equations methods31Axx " K 31A15Potentials, etc. (two-dimensional)Potentials and capacity, harmonic measure, extremal length [See also 30C85]31Axx 2 0 31A20Boundary behavior of harmonic functions (two-dim.)Boundary behavior (theorems of Fatou type, etc.)31Axx > # 31A25Boundary value and inverse problems (two-dim.potential theory)Boundary value and inverse problems31Axx 4 D 31A30Biharmonic (etc.) functions and equations (two-dim.)Biharmonic, polyharmonic functions and equations, Poisson's equation31Axx ? ' 31A35Connections of potential theory with diff. equations (two-dim.)Connections with differential equations31Axx & 31A99Two-dimensional potential theoryNone of the above, but in this section31Axx 31AxxTwo-dimensional potential theoryTwo-dimensional theory31-XX - . 31B05Harmonic functions, etc. (higher-dimensional)Harmonic, subharmonic, superharmonic functions31Bxx C H 31B10Integral representations of harmonic functions (higher-dimensional)Integral representations, integral operators, integral equations methods31Bxx % * 31B15Potentials, etc. (higher-dimensional)Potentials and capacities, extremal length31Bxx B # 31B20Boundary value and inverse problems (higher-dim. potential theory)Boundary value and inverse problems31Bxx 5 31B25Boundary behavior of harmonic functions (higher-dim.)Boundary behavior31Bxx 7 3 31B30Biharmonic (etc.) functions and equations (higher-dim.)Biharmonic and polyharmonic equations and functions31Bxx B ' 31B35Connections of potential theory with diff. equations (higher-dim.)Connections with differential equations31Bxx # & 31B99Higher-dimensional potential theoryNone of the above, but in this section31Bxx # 31BxxHigher-dimensional potential theoryHigher-dimensional theory31-XX , . 31C05Generalizations of harmonic (etc.) functionsHarmonic, subharmonic, superharmonic functions31Cxx , = 31C10Pluriharmonic and plurisubharmonic functionsPluriharmonic and plurisubharmonic functions [See also 32U05]31Cxx ( V 31C12Potential theory on Riemannian manifoldsPotential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]31Cxx # 31C15Generalizations of potentials, etc.Potentials and capacities31Cxx / 31C20Discrete potential theory, etc.Discrete potential theory and numerical methods31Cxx 31C25Dirichlet spacesDirichlet spaces31Cxx ' 31C35Martin boundary theoryMartin boundary theory [See also 60J50]31Cxx 31C40Fine potential theoryFine potential theory31Cxx 8 31C45Nonlinear potential theory, etc.Other generalizations (nonlinear potential theory, etc.)31Cxx # & 31C99Generalizations in potential theoryNone of the above, but in this section31Cxx # 31CxxGeneralizations in potential theoryOther generalizations31-XX 31D05Axiomatic potential theoryAxiomatic potential theory31-XX ? G 32-00Reference works (several complex variables and analytic spaces)General reference works (handbooks, dictionaries, bibliographies, etc.)32-XX % ; 32-01Textbooks (several complex variables)Instructional exposition (textbooks, tutorial papers, etc.)32-XX / 1 32-02Research monographs (several complex variables)Research exposition (monographs, survey articles)32-XX : U 32-03Historical (several complex variables and analytic spaces)Historical (must also be assigned at least one classification number from Section 01)32-XX 9 X 32-04Machine computation, programs (several complex variables)Explicit machine computation and programs (not the theory of computation or programming)32-XX 6 + 32-06Proceedings of conferences (several complex variables)Proceedings, conferences, collections, etc.32-XX : : 32-99Functions of several complex variables and analytic spacesFunctions of several complex variables and analytic spaces : e 32-XXFunctions of several complex variables and analytic spacesSeveral complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} . ! 32A05Power series, etc. (several complex variables)Power series, series of functions32Axx 4 32A07Special domains in $C^n$Special domains (Reinhardt, Hartogs, circular, tube)32Axx ) 32A10Holomorphic functions (several variables)Holomorphic functions32Axx * 32A12Multifunctions (several complex variables)Multifunctions32Axx32A991 $ 32A15Entire functions (several variables)Entire functions32Axx 9 32A17Special families of functions (several complex variables)Special families of functions32Axx ! 32A18Bloch functions etc.Bloch functions, normal functions32Axx32A371 & & 32A19Normal families of functions, mappingsNormal families of functions, mappings32Axx32A171 ) 32A20Meromorphic functions (several variables)Meromorphic functions32Axx & h 32A22Estimates in several complex variablesNevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30}32Axx D B 32A25Integral representation of holomorphic functions (several variables)Integral representations; canonical kernels (Szegó, Bergman, etc.)32Axx S 32A26Integral representationsIntegral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)32Axx32A251 4 ) 32A27Local theory of residues (several complex variables)Local theory of residues [See also 32C30]32Axx 7 Ê 32A30Generalizations of function theory to several variablesOther generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}32Axx ( G 32A35$H^p$-spaces (several complex variables)${H}^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]32Axx 32A36Bergman spacesBergman spaces32Axx32A371 3 32A37Spaces of holomorphic functions (several variables)Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]32Axx 6 @ 32A38Algebras of holomorphic functions of several variablesAlgebras of holomorphic functions [See also 30H05, 46J10, 46J15]32Axx32E251 > * 32A40Boundary behavior of holomorphic functions (several variables)Boundary behavior of holomorphic functions32Axx ! 32A45Hyperfunctions (complex analysis)Hyperfunctions [See also 46F15]32Axx . A 32A50Harmonic analysis of several complex variablesHarmonic analysis of several complex variables [See mainly 43-XX]32Axx32A991 32A55Singular integralsSingular integrals32Axx32A991 7 " 32A60Zero sets of holomorphic functions of several variablesZero sets of holomorphic functions32Axx32A101 @ , 32A65Banach algebra techniques in theory of several complex variablesBanach algebra techniques [See mainly 46Jxx]32Axx32E25,32E991 = 1 32A70Functional analysis techniques in theory of several variablesFunctional analysis techniques [See mainly 46Exx]32Axx32A991 * & 32A99Holomorphic functions of several variablesNone of the above, but in this section32Axx 2 2 32AxxHolomorphic functions of several complex variablesHolomorphic functions of several complex variables32-XX % ; 32B05Analytic algebras and generalizationsAnalytic algebras and generalizations, preparation theorems32Bxx - 32B10Germs of analytic setsGerms of analytic sets, local parametrization32Bxx 32B15Analytic subsets of affine spaceAnalytic subsets of affine space32Bxx 8 32B20Semi-analytic sets, etc.Semi-analytic sets and subanalytic sets [See also 14P15]32Bxx # # 32B25Triangulation and related questionsTriangulation and related questions32Bxx & 32B99Local analytic geometryNone of the above, but in this section32Bxx 3 2 32BxxLocal analytic geometry (several complex variables)Local analytic geometry [See also 13-XX and 14-XX]32-XX " E 32C05Real-analytic manifolds and spacesReal-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]32Cxx B 32C07Real-analytic setsReal-analytic sets, complex Nash functions [See also 14P15, 14P20]32Cxx $ $ 32C09Embedding of real analytic manifoldsEmbedding of real analytic manifolds32Cxx32F251 4 32C11Complex supergeometryComplex supergeometry [See also 14A22, 14M30, 58A50]32Cxx 32C15Complex spacesComplex spaces32Cxx 32C18Topology of analytic spacesTopology of analytic spaces32Cxx 32C20Normal analytic spacesNormal analytic spaces32Cxx 32C22Embedding of analytic spacesEmbedding of analytic spaces32Cxx32C18,32C20,32C251 ! ! 32C25Analytic subsets and submanifoldsAnalytic subsets and submanifolds32Cxx ' X 32C30Integration on analytic sets and spacesIntegration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27}32Cxx & E 32C35Analytic sheaves and cohomology groupsAnalytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]32Cxx # # 32C36Local cohomology of analytic spacesLocal cohomology of analytic spaces32Cxx " 32C37Duality theorems (analytic spaces)Duality theorems32Cxx 3 f 32C38Sheaves of differential operators (analytic spaces)Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15]32Cxx " 3 32C55The Levi problem in complex spacesThe Levi problem in complex spaces; generalizations32Cxx32E991 # 32C81Appl. of analytic spaces to physicsApplications to physics32Cxx ! & 32C99General theory of analytic spacesNone of the above, but in this section32Cxx ! 32CxxGeneral theory of analytic spacesAnalytic spaces32-XX 32D05Domains of holomorphyDomains of holomorphy32Dxx 32D10Envelopes of holomorphyEnvelopes of holomorphy32Dxx 4 32D15Continuation of analytic objects (several variables)Continuation of analytic objects32Dxx 3 32D20Removable singularities (several complex variables)Removable singularities32Dxx 32D25Non-Archimedean function theoryNon-Archimedean function theory ) & 32D99Analytic continuation (several variables)None of the above, but in this section32Dxx ) 32DxxAnalytic continuation (several variables)Analytic continuation32-XX % 7 32E05Holomorphically convex complex spacesHolomorphically convex complex spaces, reduction theory32Exx 32E10Stein spaces and manifoldsStein spaces, Stein manifolds32Exx 32E20Polynomial convexityPolynomial convexity32Exx - D 32E30Holomorphic approximation (several variables)Holomorphic and polynomial approximation, Runge pairs, interpolation32Exx C 1 32E35Global boundary behavior of holomorphic functions of sev. variablesGlobal boundary behavior of holomorphic functions32Exx 32E40The Levi problemThe Levi problem32Exx32E991 & 32E99Holomorphic convexityNone of the above, but in this section32Exx 32ExxHolomorphic convexityHolomorphic convexity32-XX 32F10$q$-convexity, etc.$q$-convexity, $q$-concavity32Fxx 32F17Other notions of convexityOther notions of convexity32Fxx32F99,32E991 , 32F18Finite-type conditions (geometric convexity)Finite-type conditions32Fxx32F991 / / 32F27Topological consequences of geometric convexityTopological consequences of geometric convexity32Fxx32F991 . I 32F32Analytical consequences of geometric convexityAnalytical consequences of geometric convexity (vanishing theorems, etc.)32Fxx32F99,32L20,32L151 % % 32F45Invariant metrics and pseudodistancesInvariant metrics and pseudodistances32Fxx32H151 & 32F99Geometric convexityNone of the above, but in this section32Fxx 32FxxGeometric convexityGeometric convexity32-XX " H 32G05Deformations of complex structuresDeformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]32Gxx " , 32G07Deformations of special structuresDeformations of special (e.g. CR) structures32Gxx 32G08Deformations of fiber bundlesDeformations of fiber bundles32Gxx * 32G10Deformations of submanifoldsDeformations of submanifolds and subspaces32Gxx p 32G13Analytic moduli problemsAnalytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15]32Gxx F 32G15Teichm\"uller theoryModuli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]32Gxx [ 32G20Period matricesPeriod matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]32Gxx t 32G34Moduli and deformations for ODEModuli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx]32Gxx 7 32G81Appl. of deformations of analytic structures to physicsApplications to physics32Gxx # & 32G99Deformations of analytic structuresNone of the above, but in this section32Gxx # # 32GxxDeformations of analytic structuresDeformations of analytic structures32-XX ' D 32H02Holomorphic mappings on analytic spacesHolomorphic mappings, (holomorphic) embeddings and related questions32Hxx ' 32H04Meromorphic mappings on analytic spacesMeromorphic mappings32Hxx + 32H12Boundary uniqueness of holomorphic mappingsBoundary uniqueness of mappings32Hxx32H401 : W 32H25Picard type theorems and generalizations (analytic spaces)Picard-type theorems and generalizations {For function-theoretic properties, see 32A22}32Hxx . ] 32H30Value distribution theory in higher dimensionsValue distribution theory in higher dimensions {For function-theoretic properties, see 32A22}32Hxx $ 32H35Proper mappings, etc.Proper mappings, finiteness theorems32Hxx 9 32H40Boundary regularity of holomorphic maps on anlytic spacesBoundary regularity of mappings32Hxx : 32H50Iteration problems for holomorphic maps on analytic spacesIteration problems32Hxx ' & 32H99Holomorphic mappings on analytic spacesNone of the above, but in this section32Hxx ' ( 32HxxHolomorphic mappings on analytic spacesHolomorphic mappings and correspondences32-XX # # 32J05Compactification of analytic spacesCompactification of analytic spaces32Jxx 7 32J10Algebraic dependence theorems (compact analytic spaces)Algebraic dependence theorems32Jxx " 32J15Compact surfaces (analytic spaces)Compact surfaces32Jxx ! 32J17Compact 3-folds (analytic spaces)Compact $3$-folds32Jxx / 32J18Compact $n$-folds $(n \ge 4)$ (analytic spaces)Compact $n$-folds32Jxx , = 32J25Transcendental methods of algebraic geometryTranscendental methods of algebraic geometry [See also 14C30]32Jxx 9 32J27Compact K\"ahler manifoldsCompact Kähler manifolds: generalizations, classification32Jxx + 32J81Appl. of compact analytic spaces to physicsApplications to physics32Jxx & 32J99Compact analytic spacesNone of the above, but in this section32Jxx a 32JxxCompact analytic spacesCompact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx}32-XX ' 32K05Banach analytic spacesBanach analytic spaces [See also 58Bxx]32Kxx 1 32K07Formal and graded complex spacesFormal and graded complex spaces [See also 58C50]32Kxx $ S 32K15Differentiability on analytic spacesDifferentiable functions on analytic spaces, differentiable spaces [See also 58C25]32Kxx " & 32K99Generalizations of analytic spacesNone of the above, but in this section32Kxx " ” 32KxxGeneralizations of analytic spacesGeneralizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)32-XX - ' 32L05Holomorphic fiber bundles and generalizationsHolomorphic bundles and generalizations32Lxx & p 32L10Sections of holomorphic vector bundlesSheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]32Lxx ! 32L15Bundle convexityBundle convexity [See also 32F10]32Lxx $ 32L20Vanishing theorems (analytic spaces)Vanishing theorems32Lxx & 2 32L25Twistor theory, etc. (analytic spaces)Twistor theory, double fibrations [See also 53C28]32Lxx # 32L81Holomorphic fiber spaces in physicsApplications to physics32Lxx & 32L99Holomorphic fiber spacesNone of the above, but in this section32Lxx ) 32LxxHolomorphic fiber spacesHolomorphic fiber spaces [See also 55Rxx]32-XX % Q 32M05Automorphism groups of complex spacesComplex Lie groups, automorphism groups acting on complex spaces [See also 22E10]32Mxx 5 32M10Homogeneous complex manifoldsHomogeneous complex manifolds [See also 14M17, 57T15]32Mxx % 8 32M12Almost homogeneous manifolds (spaces)Almost homogeneous manifolds and spaces [See also 14M17]32Mxx " l 32M15Symmetric spaces (analytic spaces)Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]32Mxx ( 7 32M17Automorphism groups of ${\Bbb C}^n$ etc.Automorphism groups of ${\bf C}^n$ and affine manifolds32Mxx32M051 32M25Complex vector fieldsComplex vector fields32Mxx32S651 , & 32M99Complex spaces with a group of automorphismsNone of the above, but in this section32Mxx , , 32MxxComplex spaces with a group of automorphismsComplex spaces with a group of automorphisms32-XX D D 32N05General theory of automorphic functions of several complex variablesGeneral theory of automorphic functions of several complex variables32Nxx . 32N10Automorphic forms of several complex variablesAutomorphic forms32Nxx * * 32N15Automorphic functions in symmetric domainsAutomorphic functions in symmetric domains32Nxx 1 & 32N99Automorphic functions (several complex variables)None of the above, but in this section32Nxx 1 ; 32NxxAutomorphic functions (several complex variables)Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]32-XX ’ 32P05Non-Archimedean complex analysisNon-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)32-XX 32Q05Negative curvature manifoldsNegative curvature manifolds32Qxx32C101 32Q10Positive curvature manifoldsPositive curvature manifolds32Qxx32C101 32Q15K\"ahler manifoldsKähler manifolds32Qxx32C17,32J271 * 32Q20K\"ahler-Einstein manifoldsKähler-Einstein manifolds [See also 53Cxx]32Qxx53C25,32L071 32Q25Calabi-Yau theoryCalabi-Yau theory32Qxx32J17,32J18,14J321 32Q28Stein manifoldsStein manifolds32Qxx32E101 32Q30UniformizationUniformization32Qxx32C101 2 2 32Q35Complex manifolds as subdomains of Euclidean spaceComplex manifolds as subdomains of Euclidean space32Qxx32C101 32Q40Embedding theoremsEmbedding theorems32Qxx32C101 - - 32Q45Hyperbolic and Kobayashi hyperbolic manifoldsHyperbolic and Kobayashi hyperbolic manifolds32Qxx32H201 ( ( 32Q55Topological aspects of complex manifoldsTopological aspects of complex manifolds32Qxx32C101 32Q57Classification theoremsClassification theorems32Qxx32C10,32J15,32J17,32J181 32Q60Almost complex manifoldsAlmost complex manifolds32Qxx53C151 32Q65Pseudoholomorphic curvesPseudoholomorphic curves32Qxx58D101 & 32Q99Complex manifoldsNone of the above, but in this section32Qxx1 32QxxComplex manifoldsComplex manifolds32-XX % $ 32S05Local singularities (analytic spaces)Local singularities [See also 14J17]32Sxx " " 32S10Invariants of analytic local ringsInvariants of analytic local rings32Sxx * ; 32S15Equisingularity (topological and analytic)Equisingularity (topological and analytic) [See also 14E15]32Sxx 0 I 32S20Global theory of singularities (analytic spaces)Global theory of singularities; cohomological properties [See also 14E15]32Sxx * ; 32S22Relations with arrangements of hyperplanesRelations with arrangements of hyperplanes [See also 52C35]32Sxx52B30,32S201 0 7 32S25(Hyper-) Surface singularities (analytic spaces)Surface and hypersurface singularities [See also 14J17]32Sxx / @ 32S30Deformations of singularities (analytic spaces)Deformations of singularities; vanishing cycles [See also 14B07]32Sxx ( @ 32S35Mixed Hodge theory of singular varietiesMixed Hodge theory of singular varieties [See also 14C30, 14D07]32Sxx > @ 32S40Monodromy; relations with differential equations and D-modulesMonodromy; relations with differential equations and $D$-modules32Sxx 3 ; 32S45Resolution of singularities, etc. (analytic spaces)Modifications; resolution of singularities [See also 14E15]32Sxx D O 32S50Topological aspects with respect to singularities on analytic spacesTopological aspects: Lefschetz theorems, topological classification, invariants32Sxx D 32S55Milnor fibrationMilnor fibration; relations with knot theory [See also 57M25, 57Q45]32Sxx ' P 32S60Stratifications, etc. (analytic spaces)Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]32Sxx * 9 32S65Singularities of holomorphic vector fieldsSingularities of holomorphic vector fields and foliations32Sxx - ! 32S70Operations on singularities (analytic spaces)Other operations on singularities32Sxx & 32S99Singularities (analytic spaces)None of the above, but in this section32Sxx32S701
32SxxSingularitiesSingularities [See also 58Kxx]32-XX 32T05Domains of holomorphyDomains of holomorphy32Txx32D051 32T15Strongly pseudoconvex domainsStrongly pseudoconvex domains32Txx32F151 32T20Worm domainsWorm domains32Txx32F151 32T25Finite type domainsFinite type domains32Txx32F151 C C 32T27Geometric and analytic invariants on weakly pseudoconvex boundariesGeometric and analytic invariants on weakly pseudoconvex boundaries32Txx32F151 32T35Exhaustion functionsExhaustion functions32Txx32F151 32T40Peak functionsPeak functions32Txx32E251 & 32T99Pseudoconvex domainsNone of the above, but in this section32Txx1 32TxxPseudoconvex domainsPseudoconvex domains32-XX . ? 32U05Plurisubharmonic functions and generalizationsPlurisubharmonic functions and generalizations [See also 31C10]32Uxx32F051 % % 32U10Plurisubharmonic exhaustion functionsPlurisubharmonic exhaustion functions32Uxx32F051 32U15General pluripotential theoryGeneral pluripotential theory32Uxx32F051 # # 32U20Capacity theory and generalizationsCapacity theory and generalizations32Uxx31B15,31C15,32F991 32U25Lelong numbersLelong numbers32Uxx32F051 32U30Removable setsRemovable sets32Uxx32F99,32D201 32U35Pluricomplex Green functionsPluricomplex Green functions32Uxx32F051 32U40CurrentsCurrents32Uxx32C301 & 32U99Pluripotential theoryNone of the above, but in this section32Uxx1 32UxxPluripotential theoryPluripotential theory32-XX 0 32V05CR structures etc.CR structures, CR operators, and generalizations32Vxx32C161 32V10CR functionsCR functions32Vxx32C161 % % 32V15CR manifolds as boundaries of domainsCR manifolds as boundaries of domains32Vxx32C161 32V20Analysis on CR manifoldsAnalysis on CR manifolds32Vxx32C161 C C 32V25Extension of functions and other analytic objects from CR manifoldsExtension of functions and other analytic objects from CR manifolds32Vxx32C16,32D151 32V30Embeddings of CR manifoldsEmbeddings of CR manifolds32Vxx32C161 & & 32V35Finite type conditions on CR manifoldsFinite type conditions on CR manifolds32Vxx32C161 & & 32V40Real submanifolds in complex manifoldsReal submanifolds in complex manifolds32Vxx32F251 & 32V99CR manifoldsNone of the above, but in this section32Vxx1 32VxxCR ManifoldsCR manifolds32-XX = = 32W05$\overline\partial$ and $\overline\partial$-Neumann operators$\overline\partial$ and $\overline\partial$-Neumann operators32Wxx32F20,35N151 A A 32W10$\overline\partial_b$ and $\overline\partial_b$-Neumann operators$\overline\partial_b$ and $\overline\partial_b$-Neumann operators32Wxx32F20,35N151 32W20Complex Monge-Amp\`ere operatorsComplex Monge-Ampère operators32Wxx32F07,35J991 9 9 32W25Pseudodifferential operators in several complex variablesPseudodifferential operators in several complex variables32Wxx35S051 ) ) 32W30Heat kernels in several complex variablesHeat kernels in several complex variables32Wxx58G11,35K991 8 8 32W50Other partial differential equations of complex analysisOther partial differential equations of complex analysis32Wxx35A201 + & 32W99Differential operators in several variablesNone of the above, but in this section32Wxx1 + + 32WxxDifferential operators in several variablesDifferential operators in several variables32-XX # G 33-00Reference works (special functions)General reference works (handbooks, dictionaries, bibliographies, etc.)33-XX ; 33-01Textbooks (special functions)Instructional exposition (textbooks, tutorial papers, etc.)33-XX ' 1 33-02Research monographs (special functions)Research exposition (monographs, survey articles)33-XX U 33-03Historical (special functions)Historical (must also be assigned at least one classification number from Section 01)33-XX 1 X 33-04Machine computation, programs (special functions)Explicit machine computation and programs (not the theory of computation or programming)33-XX . + 33-06Proceedings of conferences (special functions)Proceedings, conferences, collections, etc.33-XX 33-99Special functionsSpecial functions è 33-XXSpecial functionsSpecial functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx} ' 33B10Elementary functionsExponential and trigonometric functions33Bxx # 33B15Gamma-functions, etc.Gamma, beta and polygamma functions33Bxx # ^ 33B20Incomplete beta and gamma functionsIncomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)33Bxx 33B30Higher logarithm functionsHigher logarithm functions33Bxx33B99,33E201 & 33B99Elementary classical functionsNone of the above, but in this section33Bxx 33BxxElementary classical functionsElementary classical functions33-XX " + 33C05Classical hypergeometric functionsClassical hypergeometric functions, $_2F_1$33Cxx 6 33C10Cylinder functions, etc.Bessel and Airy functions, cylinder functions, $_0F_1$33Cxx " @ 33C15Confluent hypergeometric functionsConfluent hypergeometric functions, Whittaker functions, $_1F_1$33Cxx ! * 33C20Generalized hypergeometric seriesGeneralized hypergeometric series, $_pF_q$33Cxx ; 33C45Orthogonal polynomials and functions of hypergeometric typeOrthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]33Cxx 2 2 33C47Other special orthogonal polynomials and functionsOther special orthogonal polynomials and functions33Cxx33C451 ; s 33C50Hypergeometric functions and integrals in several variablesOrthogonal polynomials and functions in several variables expressible in terms of special functions in one variable33Cxx A A 33C52Orthogonal polynomials and functions associated with root systemsOrthogonal polynomials and functions associated with root systems33Cxx33C50,33C801 . 33C55Elliptic integrals as hypergeometric functionsSpherical harmonics33Cxx 6 U 33C60Hypergeometric integrals and functions defined by themHypergeometric integrals and functions defined by them ($E$, $G$ and ${H}$ functions)33Cxx % % 33C65Appell, Horn and Lauricella functionsAppell, Horn and Lauricella functions33Cxx 5 5 33C67Hypergeometric functions associated with root systemsHypergeometric functions associated with root systems33Cxx33C70,33C801 A A 33C70Other hypergeometric functions and integrals in several variablesOther hypergeometric functions and integrals in several variables33Cxx . . 33C75Elliptic integrals as hypergeometric functionsElliptic integrals as hypergeometric functions33Cxx C 8 33C80Connections of theory of special functions with groups and algebrasConnections with groups and algebras, and related topics33Cxx ! 33C90Appl. of hypergeometric functionsApplications33Cxx & 33C99Hypergeometric functionsNone of the above, but in this section33Cxx 33CxxHypergeometric functionsHypergeometric functions33-XX 1 5 33D05q-gamma functions, q-beta functions and integrals$q$-gamma functions, $q$-beta functions and integrals33Dxx . < 33D15Basic hypergeometric functions of one variableBasic hypergeometric functions in one variable, ${}_r\phi_s$33Dxx A K 33D45Basic hypergeometric functions and integrals in several variablesBasic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)33Dxx 9 € 33D50Orthogonal polynomials and functions in several variablesOrthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable33Dxx33D451 C e 33D52Basic orthogonal polynomials and functions assoc. with root systemsBasic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)33Dxx33D801 < < 33D60Basic hypergeometric integrals and functions defined by themBasic hypergeometric integrals and functions defined by them33Dxx $ $ 33D65Bibasic functions and multiple basesBibasic functions and multiple bases33Dxx ; ; 33D67Basic hypergeometric functions associated with root systemsBasic hypergeometric functions associated with root systems33Dxx33D801 A G 33D70Basic hypergeometric functions and integrals in several variablesOther basic hypergeometric functions and integrals in several variables33Dxx 4 f 33D80Connections with groups, algebras and related topicsConnections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics33Dxx ' 33D90Appl. of basic hypergeometric functionsApplications33Dxx & 33D99Basic hypergeometric functionsNone of the above, but in this section33Dxx 33DxxBasic hypergeometric functionsBasic hypergeometric functions33-XX 33E05Elliptic functions and integralsElliptic functions and integrals33Exx , 33E10Spheroidal wave functions, etc.Lamé, Mathieu, and spheroidal wave functions33Exx , , 33E12Mittag-Leffler functions and generalizationsMittag-Leffler functions and generalizations33Exx33E151 33E15Other wave functionsOther wave functions33Exx 33E17Painlev\'e-type functionsPainlevé-type functions33Exx33E301 ) / 33E20Functions defined by series and integralsOther functions defined by series and integrals33Exx > K 33E30Functions coming from diff., difference and integral equationsOther functions coming from differential, difference and integral equations33Exx ' ? 33E50Special functions in characteristic $p$Special functions in characteristic $p$ (gamma functions, etc.)33Exx33E991 & 33E99Special functionsNone of the above, but in this section33Exx 33ExxOther special functionsOther special functions33-XX , ( 33F05Numerical approximation of special functionsNumerical approximation [See also 65D20]33Fxx33-041 ) N 33F10Symbolic computation of special functionsSymbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]33Fxx33C99,33Cxx,68W301 * & 33F99Computational aspects of special functionsNone of the above, but in this section33Fxx33-041 * 33FxxComputational aspects of special functionsComputational aspects33-XX 1 G 34-00Reference works (ordinary differential equations)General reference works (handbooks, dictionaries, bibliographies, etc.)34-XX + ; 34-01Textbooks (ordinary differential equations)Instructional exposition (textbooks, tutorial papers, etc.)34-XX 5 1 34-02Research monographs (ordinary differential equations)Research exposition (monographs, survey articles)34-XX , U 34-03Historical (ordinary differential equations)Historical (must also be assigned at least one classification number from Section 01)34-XX ? X 34-04Machine computation, programs (ordinary differential equations)Explicit machine computation and programs (not the theory of computation or programming)34-XX < + 34-06Proceedings of conferences (ordinary differential equations)Proceedings, conferences, collections, etc.34-XX % % 34-99Ordinary differential equations (ODE)Ordinary differential equations (ODE) % 34-XXOrdinary differential equations (ODE)Ordinary differential equations ! 34A05Methods of solution of ODEExplicit solutions and reductions34Axx E 34A09Implicit equationsImplicit equations, differential-algebraic equations [See also 65L80]34Axx b 34A12Initial value problems for ODEInitial value problems, existence, uniqueness, continuous dependence and continuation of solutions34Axx c 34A25Analytical theory of ODEAnalytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]34Axx + + 34A26Geometric methods in differential equationsGeometric methods in differential equations34Axx % 34A30Linear ODE and systemsLinear equations and systems, general34Axx " ( 34A34Nonlinear ODE and systems, generalNonlinear equations and systems, general34Axx ( 34A35ODE of infinite orderDifferential equations of infinite order34Axx 34A36Discontinuous equationsDiscontinuous equations34Axx34A991 $ $ 34A37Differential equations with impulsesDifferential equations with impulses34Axx * 34A40Differential inequalities (ODE)Differential inequalities [See also 26D20]34Axx - J 34A45Theoretical approximation of solutions of ODETheoretical approximation of solutions {For numerical analysis, see 65Lxx}34Axx 34A55Inverse problems of ODEInverse problems34Axx % / 34A60ODE with multivalued right-hand sidesDifferential inclusions [See also 49J24, 49K24]34Axx & 34A99General theory of ODENone of the above, but in this section34Axx 34AxxGeneral theory ODEGeneral theory34-XX % 34B05Linear boundary value problems of ODELinear boundary value problems34Bxx 8 R 34B07Linear boundary value problems with nonlinear dependenceLinear boundary value problems with nonlinear dependence on the spectral parameter34Bxx34B05,34B991 ' ' 34B08Multi-parameter boundary value problemsMulti-parameter boundary value problems34Bxx34B05,34B991 1 1 34B09Boundary value problems with an indefinite weightBoundary value problems with an indefinite weight34Bxx34B05,34B991 " " 34B10Multipoint boundary value problemsMultipoint boundary value problems34Bxx ( ! 34B15Nonlinear boundary value problems of ODENonlinear boundary value problems34Bxx * * 34B16Singular nonlinear boundary value problemsSingular nonlinear boundary value problems34Bxx34B15,34B991 7 7 34B18Positive solutions of nonlinear boundary value problemsPositive solutions of nonlinear boundary value problems34Bxx34B151 # # 34B20Weyl theory and its generalizationsWeyl theory and its generalizations34Bxx ' 34B24Sturm-Liouville theorySturm-Liouville theory [See also 34Lxx]34Bxx 34B27Green functionsGreen functions34Bxx / 34B30Special ODESpecial equations (Mathieu, Hill, Bessel, etc.)34Bxx % % 34B37Boundary value problems with impulsesBoundary value problems with impulses34Bxx34A37,34B05,34B15,34B991 - - 34B40Boundary value problems on infinite intervalsBoundary value problems on infinite intervals34Bxx34B05,34B15,34B991 . . 34B45Boundary value problems on graphs and networksBoundary value problems on graphs and networks34Bxx34B05,34B991 34B60Applications of theory of BVPApplications34Bxx34B991 & 34B99Boundary value problems for ODENone of the above, but in this section34Bxx % H 34BxxBoundary value problems (BVP) for ODEBoundary value problems {For ordinary differential operators, see 34Lxx}34-XX 3 : 34C05Qualitative theory of some special solutions of ODELocation of integral curves, singular points, limit cycles34Cxx ? ‰ 34C07Theory of limit cycles of polynomial and analytic vector fieldsTheory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)34Cxx34C05,58F211 / j 34C08Connections of ODE with real algebraic geometryConnections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)34Cxx14P99,34C05,58F211 6 = 34C10Qualitative theory of oscillations of ODE: Zeros, etc.Oscillation theory, zeros, disconjugacy and comparison theory34Cxx 4 , 34C11Qualitative theory of solutions of ODE: Growth, etc.Growth, boundedness, comparison of solutions34Cxx 34C12Monotone systemsMonotone systems34Cxx34C35,34C991 34C14Symmetries, invariantsSymmetries, invariants34Cxx34A26,34C99,58F351 * + 34C15Nonlinear oscillations of solutions of ODENonlinear oscillations, coupled oscillators34Cxx ! C 34C20Transformation of ODE and systemsTransformation and reduction of equations and systems, normal forms34Cxx 34C23Bifurcation (periodic solutions)Bifurcation [See mainly 37Gxx]34Cxx 34C25Periodic solutions of ODEPeriodic solutions34Cxx 34C26Relaxation oscillationsRelaxation oscillations34Cxx34C15,34C99,34E991 34C27Almost periodic solutions of ODEAlmost periodic solutions34Cxx + 4 34C28Other types of "recurrent" solutions of ODEComplex behavior, chaotic systems [See mainly 37Dxx]34Cxx 34C29Averaging methodAveraging method34Cxx 34C30Manifolds of solutions of ODEManifolds of solutions34Cxx , % 34C37Homoclinic and heteroclinic solutions of ODEHomoclinic and heteroclinic solutions34Cxx " 34C40ODE on manifoldsEquations and systems on manifolds34Cxx # # 34C41Equivalence, asymptotic equivalenceEquivalence, asymptotic equivalence34Cxx34C99,34E991 34C45Method of integral manifoldsMethod of integral manifolds34Cxx
34C55HysteresisHysteresis34Cxx34C99,47H301 ) 34C60Applications of qualitative theory of ODEApplications34Cxx34C99,58F401 & & 34C99Qualitative theory of solutions of ODENone of the above, but in this section34Cxx & # 34CxxQualitative theory of solutions of ODEQualitative theory [See also 37-XX]34-XX 34D05Asymptotic stability of ODEAsymptotic properties34Dxx % 34D08Lyapunov exponentsCharacteristic and Lyapunov exponents34Dxx 34D09Dichotomy, trichotomyDichotomy, trichotomy34Dxx34C11,34D991
34D10Stability perturbations of ODEPerturbations34Dxx 34D15Singular perturbations of ODESingular perturbations34Dxx 34D20Lyapunov stability of ODELyapunov stability34Dxx 34D23Global stabilityGlobal stability34Dxx34D99,58F121 < 34D30Structural stability of ODEStructural stability and analogous concepts [See also 37C20]34Dxx * # 34D35Stability of manifolds of solutions of ODEStability of manifolds of solutions34Dxx 34D40Ultimate boundednessUltimate boundedness34Dxx
" 34D45AttractorsAttractors [See also 37C70, 37D45]34Dxx & 34D99Stability theory of ODENone of the above, but in this section34Dxx ( 34DxxStability theory of ODEStability theory [See also 37C75, 93Dxx]34-XX 34E05Asymptotic expansions (ODE)Asymptotic expansions34Exx 34E10Asymptotic perturbations (ODE)Perturbations, asymptotics34Exx 34E13Multiple scale methodsMultiple scale methods34Exx34E991 7 & 34E15Asymptotic singular perturbations, general theory (ODE)Singular perturbations, general theory34Exx 0 34E18Methods of nonstandard analysis in theory of ODEMethods of nonstandard analysis34Exx03H05,34E991 0 9 34E20Asymptotic singular perturbations, methods (ODE)Singular perturbations, turning point theory, WKB methods34Exx & 34E99Asymptotic theory of ODENone of the above, but in this section34Exx 34ExxAsymptotic theory of ODEAsymptotic theory34-XX D 34F05ODE with randomnessEquations and systems with randomness [See also 34K50, 60H10, 93E03]34-XX ( 34G10Linear ODE in abstract spacesLinear equations [See also 47D06, 47D09]34Gxx + 34G20Nonlinear ODE in abstract spacesNonlinear equations [See also 47Hxx, 47Jxx]34Gxx 34G25Evolution inclusionsEvolution inclusions34Gxx34A60,34G201 & 34G99ODE in abstract spacesNone of the above, but in this section34Gxx ] 34GxxODE in abstract spacesDifferential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]34-XX ' / 34H05ODE in connection with control problemsControl problems [See also 49J25, 49K25, 93C15]34-XX 3 34K05General theory of functional-differential equationsGeneral theory34Kxx ( ( 34K06Linear functional-differential equationsLinear functional-differential equations34Kxx34K051 - & 34K07Theoretical approximation of solutions of FDETheoretical approximation of solutions34Kxx34A45,34K05,34K991 = 34K10Boundary value problems for functional-differential equationsBoundary value problems34Kxx 7 34K11Oscillation theory of functional-differential equationsOscillation theory34Kxx34C10,34K151 < , 34K12Properties of solutions of functional-differential equationsGrowth, boundedness, comparison of solutions34Kxx34C11,34K151 7 34K13Periodic solutions of functional differential equationsPeriodic solutions34Kxx34C25,34K15,58F221 > 34K14Almost periodic solutions of functional differential equationsAlmost periodic solutions34Kxx34C27,34K151 ? C 34K17Transformation of functional-differential equations and systemsTransformation and reduction of equations and systems, normal forms34Kxx34A25,34C20,34K15,58F361 7 34K18Bifurcation theory of functional differential equationsBifurcation theory34Kxx34C23,34K15,58F141 34K19Invariant manifoldsInvariant manifolds34Kxx34C30,34K15,58F991 5 34K20Stability theory of functional-differential equationsStability theory34Kxx . ' 34K23Complex (chaotic) behavior of solutions of FDEComplex (chaotic) behavior of solutions34Kxx34D45,34K15,58F131 6 34K25Asymptotic theory of functional-differential equationsAsymptotic theory34Kxx ; 34K26Singular perturbations of functional-differential equationsSingular perturbations34Kxx34E15,34K05,34K991 + $ 34K28Numerical approximation of solutions of FDENumerical approximation of solutions34Kxx34A45,34K99,65Lxx1 ? 34K29Inverse problems in theory of functional-differential equationsInverse problems34Kxx34A55,34K991 4 ; 34K30Functional-differential equations in abstract spacesEquations in abstract spaces [See also 34Gxx, 47Dxx, 47Jxx]34Kxx A / 34K35Functional-differential equations connected with control problemsControl problems [See also 49J25, 49K25, 93C15]34Kxx 34K40Neutral equationsNeutral equations34Kxx 34K45Equations with impulsesEquations with impulses34Kxx34A37,34K991 2 34K50Stochastic delay equationsStochastic delay equations [See also 34F05, 60Hxx]34Kxx 1 34K60Applications of functional-differential equationsApplications34Kxx34K991 ! & 34K99Functional-differential equationsNone of the above, but in this section34Kxx ' N 34KxxFunctional-differential equations, etc.Functional-differential and differential-difference equations [See also 37-XX]34-XX 34L05General spectral theory for ODEGeneral spectral theory34Lxx $ 8 34L10Eigenfunction expansions, etc. (ODE)Eigenfunction expansions, completeness of eigenfunctions34Lxx * 1 34L15Estimation of eigenvalues for OD operatorsEstimation of eigenvalues, upper and lower bounds34Lxx , I 34L16Numerical approximation of eigenvalues, etc.Numerical approximation of eigenvalues and of other parts of the spectrum34Lxx34L99,65L991 7 K 34L20Asymptotic distribution of eigenvalues for OD operatorsAsymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions34Lxx 34L25Scattering theory (ODE)Scattering theory34Lxx ) ) 34L30Nonlinear ordinary differential operatorsNonlinear ordinary differential operators34Lxx * ? 34L40Particular ordinary differential operatorsParticular operators (Dirac, one-dimensional Schrödinger, etc.)34Lxx & 34L99Ordinary differential operatorsNone of the above, but in this section34Lxx 0 34LxxOrdinary differential operatorsOrdinary differential operators [See also 47E05]34-XX 34M05Entire and meromorphic solutionsEntire and meromorphic solutions34Mxx30D99,34A201 34M10Oscillation, growth of solutionsOscillation, growth of solutions34Mxx30D99,34A201 A Q 34M15Algebraic aspects of differential equations in the complex domainAlgebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)34Mxx34A201 @ 34M20Nonanalytic aspects differential equations in the complex domainNonanalytic aspects34Mxx34A201 & & 34M25Formal solutions, transform techniquesFormal solutions, transform techniques34Mxx34A201 34M30Asymptotics, summation methodsAsymptotics, summation methods34Mxx30E15,34A20,34E05,34E991 C C 34M35Singularities, monodromy, local behavior of solutions, normal formsSingularities, monodromy, local behavior of solutions, normal forms34Mxx32G34,32S65,32S99,34A201 34M37Resurgence phenomenaResurgence phenomena34Mxx34A20,34E991 ( ? 34M40Stokes phenomena and connection problemsStokes phenomena and connection problems (linear and nonlinear)34Mxx34A201 + + 34M45Differential equations on complex manifoldsDifferential equations on complex manifolds34Mxx34A201 6 E 34M50Inverse problems in theory of DE in the complex domainInverse problems (Riemann-Hilbert, inverse differential Galois, etc.)34Mxx30E99,34A201 & ] 34M55Painlev\'e and other special equationsPainlevé and other special equations; classification, hierarchies; isomonodromic deformations34Mxx32G34,34A20,34A341 4 u 34M60Singular perturbation problems in the complex domainSingular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]34Mxx34A20,34E201 , & 34M99Differential equations in the complex domainNone of the above, but in this section34Mxx34A201 , E 34MxxDifferential equations in the complex domainDifferential equations in the complex domain [See also 30Dxx, 32G34]34-XX 0 G 35-00Reference works (partial differential equations)General reference works (handbooks, dictionaries, bibliographies, etc.)35-XX * ; 35-01Textbooks (partial differential equations)Instructional exposition (textbooks, tutorial papers, etc.)35-XX 4 1 35-02Research monographs (partial differential equations)Research exposition (monographs, survey articles)35-XX + U 35-03Historical (partial differential equations)Historical (must also be assigned at least one classification number from Section 01)35-XX > X 35-04Machine computation, programs (partial differential equations)Explicit machine computation and programs (not the theory of computation or programming)35-XX ; + 35-06Proceedings of conferences (partial differential equations)Proceedings, conferences, collections, etc.35-XX $ $ 35-99Partial differential equations (PDE)Partial differential equations (PDE) $ 35-XXPartial differential equations (PDE)Partial differential equations / ) 35A05General existence and uniqueness theorems (PDE)General existence and uniqueness theorems35Axx - ? 35A07Local existence and uniqueness theorems (PDE)Local existence and uniqueness theorems [See also 35Hxx, 35Sxx]35Axx 35A08Fundamental solutions of PDEFundamental solutions35Axx 35A10Cauchy-Kowalewski theoremsCauchy-Kovalevskaya theorems35Axx 35A15Variational methods (PDE)Variational methods35Axx 35A17ParametricesParametrices35Axx35A991 35A18Wave front setsWave front sets35Axx35A991 35A20Analytic methods (PDE)Analytic methods, singularities35Axx 35A21Propagation of singularitiesPropagation of singularities35Axx35A20,35A211 , 35A22Transform methods (PDE)Transform methods (e.g. integral transforms)35Axx 35A25Other special methods (PDE)Other special methods35Axx b 35A27Sheaf-theoretic methods (PDE)Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]35Axx ) J 35A30Geometric theory for PDE, transformationsGeometric theory, characteristics, transformations [See also 58J70, 58J72]35Axx - Q 35A35Theoretical approximation to solutions of PDETheoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx}35Axx & 35A99General theory of PDENone of the above, but in this section35Axx 35AxxGeneral theory PDEGeneral theory35-XX $ { 35B05General behavior of solutions of PDEGeneral behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)35Bxx 35B10Periodic solutions of PDEPeriodic solutions35Bxx 35B15Almost periodic solutions of PDEAlmost periodic solutions35Bxx
35B20Perturbations (PDE)Perturbations35Bxx 35B25Singular perturbations (PDE)Singular perturbations35Bxx g 35B27Homogenization, etc.Homogenization; partial differential equations in media with periodic structure [See also 74Qxx, 76M50]35Bxx ; X 35B30Dependence of solutions of PDE on initial and boundary dataDependence of solutions of PDE on initial and boundary data, parameters [See also 37Cxx]35Bxx # 35B32Bifurcation (PDE)Bifurcation [See also 37Gxx, 37K50]35Bxx 35B33Critical exponentsCritical exponents35Bxx35B991
35B34ResonancesResonances35Bxx35B991 35B35Stability of solutions of PDEStability, boundedness35Bxx ' F 35B37PDE in connection with control problemsPDE in connection with control problems [See also 49J20, 49K20, 93C20]35Bxx 35B38Critical pointsCritical points35Bxx35B99,58E051 ' 35B40Asymptotic behavior of solutions of PDEAsymptotic behavior of solutions35Bxx
35B41AttractorsAttractors35Bxx35B99,58F121 35B42Inertial manifoldsInertial manifolds35Bxx35B991 35B45A priori estimatesA priori estimates35Bxx 35B50Maximum principles (PDE)Maximum principles35Bxx P 35B60Continuation of solutions of PDEContinuation and prolongation of solutions of PDE [See also 58A15, 58A17, 58Hxx]35Bxx - 35B65Smoothness of solutions of PDESmoothness and regularity of solutions of PDE35Bxx * & 35B99Qualitative properties of solutions of PDENone of the above, but in this section35Bxx + # 35BxxQualitative properties of solutions of PDEsQualitative properties of solutions35-XX 35C05Solutions of PDE in closed formSolutions in closed form35Cxx $ 35C10Series solutions of PDESeries solutions, expansion theorems35Cxx , , 35C15Integral representations of solutions of PDEIntegral representations of solutions of PDE35Cxx ) 35C20Asymptotic expansions of solutions of PDEAsymptotic expansions35Cxx # & 35C99Representations of solutions of PDENone of the above, but in this section35Cxx # 35CxxRepresentations of solutions of PDERepresentations of solutions35-XX ) " 35D05Existence of generalized solutions of PDEExistence of generalized solutions35Dxx * # 35D10Regularity of generalized solutions of PDERegularity of generalized solutions35Dxx & 35D99Generalized solutions of PDENone of the above, but in this section35Dxx 7 35DxxGeneralized solutions of PDEGeneralized solutions of partial differential equations35-XX 6 35E05Fundamental solutions (PDE with constant coefficients)Fundamental solutions35Exx 5 35E10Convexity properties (PDE with constant coefficients)Convexity properties35Exx 8 35E15Initial value problems of PDE with constant coefficientsInitial value problems35Exx 0 35E20General theory of PDE with constant coefficientsGeneral theory35Exx & 35E99PDE with constant coefficientsNone of the above, but in this section35Exx A 35ExxPDE with constant coefficientsEquations and systems with constant coefficients [See also 35N05]35-XX ( ( 35F05General theory of first order linear PDEGeneral theory of linear first-order PDE35Fxx 1 M 35F10Initial value problems for first order linear PDEInitial value problems for linear first-order PDE, linear evolution equations35Fxx 2 2 35F15Boundary value problems for first order linear PDEBoundary value problems for linear first-order PDE35Fxx + + 35F20General theory of first order nonlinear PDEGeneral theory of nonlinear first-order PDE35Fxx 4 S 35F25Initial value problems for first order nonlinear PDEInitial value problems for nonlinear first-order PDE, nonlinear evolution equations35Fxx 5 5 35F30Boundary value problems for first order nonlinear PDEBoundary value problems for nonlinear first-order PDE35Fxx & 35F99General first order PDENone of the above, but in this section35Fxx ) 35FxxGeneral first order PDEGeneral first-order equations and systems35-XX ) ) 35G05General theory of linear higher-order PDEGeneral theory of linear higher-order PDE35Gxx 2 N 35G10Initial value problems for linear higher-order PDEInitial value problems for linear higher-order PDE, linear evolution equations35Gxx 3 3 35G15Boundary value problems for linear higher-order PDEBoundary value problems for linear higher-order PDE35Gxx , , 35G20General theory of nonlinear higher-order PDEGeneral theory of nonlinear higher-order PDE35Gxx 5 T 35G25Initial value problems for nonlinear higher-order PDEInitial value problems for nonlinear higher-order PDE, nonlinear evolution equations35Gxx 6 6 35G30Boundary value problems for nonlinear higher-order PDEBoundary value problems for nonlinear higher-order PDE35Gxx & 35G99General higher order PDENone of the above, but in this section35Gxx * 35GxxGeneral higher order PDEGeneral higher-order equations and systems35-XX 35H10Hypoelliptic equationsHypoelliptic equations35Hxx35H051 35H20Subelliptic equationsSubelliptic equations35Hxx35H051 35H30Quasi-elliptic equationsQuasi-elliptic equations35Hxx35H051 & 35H99Close-to-elliptic equationsNone of the above, but in this section35Hxx35H051 35HxxClose-to-elliptic equationsClose-to-elliptic equations35-XX ] 35J05Laplace equation, etc.Laplace equation, reduced wave equation (Helmholtz), Poisson equation [See also 31Axx, 31Bxx]35Jxx % 35J10Schroedinger operatorSchrödinger operator [See also 35Pxx]35Jxx ( 2 35J15Second order elliptic equations, generalGeneral theory of second-order, elliptic equations35Jxx 4 8 35J20Second order elliptic equations, variational methodsVariational methods for second-order, elliptic equations35Jxx 8 < 35J25Second order elliptic equations, boundary value problemsBoundary value problems for second-order, elliptic equations35Jxx ( J 35J30Higher order elliptic equations, generalGeneral theory of higher-order, elliptic equations [See also 31A30, 31B30]35Jxx 5 8 35J35Higher order elliptic equations, variational problemsVariational methods for higher-order, elliptic equations35Jxx 8 < 35J40Higher order elliptic equations, boundary value problemsBoundary value problems for higher-order, elliptic equations35Jxx & ) 35J45Systems of elliptic equations, generalGeneral theory of elliptic systems of PDE35Jxx 2 ( 35J50Systems of elliptic equations, variational methodsVariational methods for elliptic systems35Jxx 6 , 35J55Systems of elliptic equations, boundary value problemsBoundary value problems for elliptic systems35Jxx 35J60Nonlinear elliptic equationsNonlinear PDE of elliptic type35Jxx 2 m 35J65(Nonlinear) BVP for (non)linear elliptic equationsNonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE35Jxx 2 , 35J67Boundary values of solutions of elliptic equationsBoundary values of solutions to elliptic PDE35Jxx % : 35J70Elliptic equations of degenerate typeElliptic partial differential equations of degenerate type35Jxx = Y 35J85Unilateral problems; variational inequalities (elliptic type)Unilateral problems and variational inequalities for elliptic PDE [See also 35R35, 49J40]35Jxx & 35J99Elliptic equations and systemsNone of the above, but in this section35Jxx N 35JxxElliptic equations and systemsPartial differential equations of elliptic type [See also 58Jxx, 58J10, 58J20]35-XX
35K05Heat equationHeat equation35Kxx ) 3 35K10Second order parabolic equations, generalGeneral theory of second-order, parabolic equations35Kxx 8 < 35K15Second order parabolic equations, initial value problemsInitial value problems for second-order, parabolic equations35Kxx 9 = 35K20Second order parabolic equations, boundary value problemsBoundary value problems for second-order, parabolic equations35Kxx ) 3 35K25Higher order parabolic equations, generalGeneral theory of higher-order, parabolic equations35Kxx 8 < 35K30Higher order parabolic equations, initial value problemsInitial value problems for higher-order, parabolic equations35Kxx 9 = 35K35Higher order parabolic equations, boundary value problemsBoundary value problems for higher-order, parabolic equations35Kxx ' * 35K40Systems of parabolic equations, generalGeneral theory of parabolic systems of PDE35Kxx 6 , 35K45Systems of parabolic equations, initial value problemsInitial value problems for parabolic systems35Kxx 7 - 35K50Systems of parabolic equations, boundary value problemsBoundary value problems for parabolic systems35Kxx 35K55Nonlinear parabolic equationsNonlinear PDE of parabolic type35Kxx 35K57Reaction-diffusion equationsReaction-diffusion equations35Kxx 3 o 35K60(Nonlinear) BVP for (non)linear parabolic equationsNonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE35Kxx & ; 35K65Parabolic equations of degenerate typeParabolic partial differential equations of degenerate type35Kxx ) 35K70Ultraparabolic (etc.) problemsUltraparabolic, pseudoparabolic PDE, etc.35Kxx > Z 35K85Unilateral problems; variational inequalities (parabolic type)Unilateral problems and variational inequalities for parabolic PDE [See also 35R35, 49J40]35Kxx & & 35K90Abstract parabolic evolution equationsAbstract parabolic evolution equations35Kxx35K22,35K99,34Gxx,35R201 & 35K99Parabolic equations and systemsNone of the above, but in this section35Kxx L 35KxxParabolic equations and systemsParabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]35-XX
35L05Wave equationWave equation35Lxx * 4 35L10Second order hyperbolic equations, generalGeneral theory of second-order, hyperbolic equations35Lxx 9 = 35L15Second order hyperbolic equations, initial value problemsInitial value problems for second-order, hyperbolic equations35Lxx : > 35L20Second order hyperbolic equations, boundary value problemsBoundary value problems for second-order, hyperbolic equations35Lxx * 4 35L25Higher order hyperbolic equations, generalGeneral theory of higher-order, hyperbolic equations35Lxx 9 = 35L30Higher order hyperbolic equations, initial value problemsInitial value problems for higher-order, hyperbolic equations35Lxx : > 35L35Higher order hyperbolic equations, boundary value problemsBoundary value problems for higher-order, hyperbolic equations35Lxx ' 7 35L40First order hyperbolic systems, generalGeneral theory of hyperbolic systems of first-order PDE35Lxx 6 @ 35L45First order hyperbolic systems, initial value problemsInitial value problems for hyperbolic systems of first-order PDE35Lxx 7 A 35L50First order hyperbolic systems, boundary value problemsBoundary value problems for hyperbolic systems of first-order PDE35Lxx & 35L55Higher order hyperbolic systemsHyperbolic systems of higher-order PDE35Lxx * , 35L60First-order nonlinear hyperbolic equationsNonlinear first-order PDE of hyperbolic type35Lxx 35L65Conservation lawsConservation laws35Lxx 0 35L67Shocks, etc.Shocks and singularities [See also 58Kxx, 76L05]35Lxx + - 35L70Second order nonlinear hyperbolic equationsNonlinear second-order PDE of hyperbolic type35Lxx / 3 35L75Nonlinear hyperbolic PDE of higher $(>2)$ orderNonlinear hyperbolic PDE of higher ($\gtr 2$) order35Lxx ' ! 35L80Hyperbolic equations of degenerate typeHyperbolic PDE of degenerate type35Lxx 35L82Pseudohyperbolic equationsPseudohyperbolic equations35Lxx35L991 ? X 35L85Unilateral problems; variational inequalities (hyperbolic type)Unilateral problems; variational inequalities for hyperbolic PDE [See also 35R35, 49J40]35Lxx ' ' 35L90Abstract hyperbolic evolution equationsAbstract hyperbolic evolution equations35Lxx35L99,34Gxx,35R201 & 35L99Hyperbolic equations and systemsNone of the above, but in this section35Lxx B 35LxxHyperbolic equations and systemsPartial differential equations of hyperbolic type [See also 58J45]35-XX 35M10PDE of mixed typePDE of mixed type35Mxx 35M20PDE of composite typePDE of composite type35Mxx & 35M99PDE of special typeNone of the above, but in this section35Mxx . w 35MxxPartial differential equations of special typePartial differential equations of special type (mixed, composite, etc.) {For degenerate types, see 35J70, 35K65, 35L80}35-XX 8 1 35N05Overdetermined systems of PDE with constant coefficientsOverdetermined systems with constant coefficients35Nxx A ; 35N10Overdetermined systems of PDE with variable coefficients, generalOverdetermined systems with variable coefficients (general)35Nxx 2 h 35N15$\bar\partial$-Neumann problem and generalizations$\overline\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]35Nxx & 35N99Overdetermined systems of PDENone of the above, but in this section35Nxx 8 < 35NxxOverdetermined systems of partial differential equationsOverdetermined systems [See also 58Hxx, 58Jxx, 58J10, 58J15]35-XX 35P05General spectral theory of PDEGeneral spectral theory of PDE35Pxx / @ 35P10Eigenfunction expansions, etc. for PD operatorsCompleteness of eigenfunctions, eigenfunction expansions for PDO35Pxx * 1 35P15Estimation of eigenvalues for PD operatorsEstimation of eigenvalues, upper and lower bounds35Pxx 7 A 35P20Asymptotic distribution of eigenvalues for PD operatorsAsymptotic distribution of eigenvalues and eigenfunctions for PDO35Pxx * 35P25Scattering theory (PDE)Scattering theory for PDE [See also 47A40]35Pxx . @ 35P30Nonlinear eigenvalue problems for PD operatorsNonlinear eigenvalue problems, nonlinear spectral theory for PDO35Pxx 8 & 35P99Spectral theory and eigenvalue problems for PD operatorsNone of the above, but in this section35Pxx 8 i 35PxxSpectral theory and eigenvalue problems for PD operatorsSpectral theory and eigenvalue problems for partial differential operators [See also 47Axx, 47Bxx, 47F05]35-XX 2 2 35Q05Euler-Poisson-Darboux equation and generalizationsEuler-Poisson-Darboux equation and generalizations35Qxx 7 35Q15Riemann-Hilbert problemsRiemann-Hilbert problems [See also 30E25, 31A25, 31B20]35Qxx " A 35Q30Stokes and Navier-Stokes equationsStokes and Navier-Stokes equations [See also 76D05, 76D07, 76N10]35Qxx * * 35Q35Other equations arising in fluid mechanicsOther equations arising in fluid mechanics35Qxx 35Q40PDE from quantum mechanicsEquations from quantum mechanics35Qxx 35Q51SolitonsSolitons [See also 37K40]35Qxx ` 35Q53KdV-like equationsKdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) [See also 37K10]35Qxx + ; 35Q55NLS-like (nonlinear Schroedinger) equationsNLS-like (nonlinear Schrödinger) equations [See also 37K10]35Qxx = 35Q58Other completely integrable PDEOther completely integrable equations [See also 37J35, 37K10]35Qxx ( . 35Q60PDE of electromagnetic theory and opticsEquations of electromagnetic theory and optics35Qxx 35Q72Other PDE from mechanicsOther equations from mechanics35Qxx 35Q75PDE in relativityPDE in relativity35Qxx ( / 35Q80Appl. of PDE in areas other than physicsApplications of PDE in areas other than physics35Qxx + & 35Q99PDE of mathematical physics and other areasNone of the above, but in this section35Qxx + f 35QxxPDE of mathematical physics and other areasEquations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]35-XX + + 35R05PDE with discontinuous coefficients or dataPDE with discontinuous coefficients or data35Rxx ) i 35R10Difference-partial differential equationsPartial functional-differential or differential-difference equations, with or without deviating arguments35Rxx ( ( 35R12Impulsive partial differential equationsImpulsive partial differential equations35Rxx35R10,35R991 " Š 35R15PDE on infinite-dimensional spacesPartial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]35Rxx ' ® 35R20Partial operator-differential equationsPartial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]35Rxx ! ! 35R25Improperly posed problems for PDEImproperly posed problems for PDE35Rxx : 35R30Inverse problems for PDEInverse problems (undetermined coefficients, etc.) for PDE35Rxx 35R35Free boundary problems for PDEFree boundary problems for PDE35Rxx ! ! 35R45Partial differential inequalitiesPartial differential inequalities35Rxx 0 35R50PDE of infinite orderPartial differential equations of infinite order35Rxx ? 35R60PDE with randomnessPartial differential equations with randomness [See also 60H15]35Rxx % % 35R70PDE with multivalued right-hand sidesPDE with multivalued right-hand sides35Rxx " & 35R99Miscellaneous topics involving PDENone of the above, but in this section35Rxx " ± 35RxxMiscellaneous topics involving PDEMiscellaneous topics involving partial differential equations {For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see also 60H15}35-XX . 35S05General theory of pseudodifferential operatorsGeneral theory of PsDO35Sxx 7 35S10Initial value problems for pseudodifferential operatorsInitial value problems for PsDO35Sxx 8 35S15Boundary value problems for pseudodifferential operatorsBoundary value problems for PsDO35Sxx 35S30Fourier integral operatorsFourier integral operators35Sxx 3 i 35S35Topological aspects of pseudodifferential operatorsTopological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]35Sxx 35S50Paradifferential operatorsParadifferential operators35Sxx & 35S99Pseudodifferential operatorsNone of the above, but in this section35Sxx p 35SxxPseudodifferential operatorsPseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]35-XX > G 37-00General reference works (Dynamical systems and ergodic theory)General reference works (handbooks, dictionaries, bibliographies, etc.)37-XX28-00,34-00,39-00,54H20,58-001 ? ; 37-01Instructional exposition (Dynamical systems and ergodic theory)Instructional exposition (textbooks, tutorial papers, etc.)37-XX28-01,34-01,39-01,58-011 : 1 37-02Research exposition (Dynamical systems and ergodic theory)Research exposition (monographs, survey articles)37-XX28-02,34-02,39-02,58-001 1 U 37-03Historical (Dynamical systems and ergodic theory)Historical (must also be assigned at least one classification number from Section 01)37-XX28-03,34-03,39-03,58-031 D X 37-04Machine computation, programs (Dynamical systems and ergodic theory)Explicit machine computation and programs (not the theory of computation or programming)37-XX28-04,34-04,39-04,58-041 A + 37-06Proceedings of conferences (Dynamical systems and ergodic theory)Proceedings, conferences, collections, etc.37-XX28-06,34-06,39-06,58-061 " " 37-99Dynamic systems and ergodic theoryDynamic systems and ergodic theory $ f ) 37-XXDynamical systems and ergodic theoryDynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]28Dxx,34Cxx,39-XX,35Bxx,54H20,58Fxx,70-XX1 " " 37A05Measure-preserving transformationsMeasure-preserving transformations37Axx28D051 G G 37A10One-parameter continuous families of measure-preserving transformationsOne-parameter continuous families of measure-preserving transformations37Axx28D101 3 G 37A15General groups of measure-preserving transformationGeneral groups of measure-preserving transformations [See mainly 22Fxx]37Axx22D40,28D15,58F111 " 37A17Homogeneous flowsHomogeneous flows [See also 22Fxx]37Axx22D40,28D99,58F111 : : 37A20Orbit equivalence, cocycles, ergodic equivalence relationsOrbit equivalence, cocycles, ergodic equivalence relations37Axx28D05,28D10,28D151 # # 37A25Ergodicity, mixing, rates of mixingErgodicity, mixing, rates of mixing37Axx28D05,58F11,60F991 3 c 37A30Ergodic theorems, spectral theory, Markov operatorsErgodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}37Axx28D05,28D10,28D15,47A35,58F111 9 37A35Invariants of ergodic theoryEntropy and other invariants, isomorphism, classification37Axx28D20,47A35,58F111 = 37A40Nonsingular transformationsNonsingular (and infinite-measure preserving) transformations37Axx28D051 D C 37A45Relations of ergodic theory with number theory and harmonic analysisRelations with number theory and harmonic analysis [See also 11Kxx]37Axx28D99,11Kxx1 0 U 37A50Relations ergodic theory with probability theoryRelations with probability theory and stochastic processes [See also 60Fxx and 60G10]37Axx60F05,60F15,60F201 = > 37A55Relations of ergodic theory with the theory of $C^*$-algebrasRelations with the theory of $C^*$-algebras [See mainly 46L55]37Axx28D99,46L551 * ; 37A60Dynamical systems in statistical mechanicsDynamical systems in statistical mechanics [See also 82Cxx]37Axx28D99,82Cxx1 & 37A99Ergodic theoryNone of the above, but in this section37Axx28D991 37AxxErgodic theoryErgodic theory [See also 28Dxx]37-XX 9 d 37B05Transformations and group actions with special propertiesTransformations and group actions with special properties (minimality, distality, proximality, etc.)37Bxx54H151 ) 37B10Symbolic dynamicsSymbolic dynamics [See also 37Cxx, 37Dxx]37Bxx28D99,54H20,58F03,58F991 37B15Cellular automataCellular automata37Bxx54H20,58F08,68Q801 37B20Notions of recurrenceNotions of recurrence37Bxx34C35,54H20,58F991 7 # 37B25Lyapunov functions and stabilityLyapunov functions and stability; attractors, repellers37Bxx34C35,34D20,34D45,54H20,58F10,58F121 " " 37B30Index theory, Morse-Conley indicesIndex theory, Morse-Conley indices37Bxx34C35,55M99,57R99,54H20,58F991 * O 37B35Gradient-like and recurrent behavior, etc.Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets37Bxx54H20,58F991 37B40Topological entropyTopological entropy37Bxx54C70,54H20,58F991 37B45Continua theory in dynamicsContinua theory in dynamics37Bxx54F15,54H20,58F991 8 8 37B50Multi-dimensional shifts of finite type, tiling dynamicsMulti-dimensional shifts of finite type, tiling dynamics37Bxx28D99,54H20,58F991 37B55Nonautonomous dynamical systemsNonautonomous dynamical systems37Bxx34C35,54H20,58F991 & 37B99Topological dynamicsNone of the above, but in this section37Bxx54H20,54H99,58F991 % 37BxxTopological dynamicsTopological dynamics [See also 54H20]37-XX # # 37C05Smooth mappings and diffeomorphismsSmooth mappings and diffeomorphisms37Cxx57R35,58C25,58F991 5 5 37C10Vector fields, flows, ordinary differential equationsVector fields, flows, ordinary differential equations37Cxx34C35,34C40,57R25,58F25,58F991 0 Y 37C15Topological and differentiable equivalence, etc.Topological and differentiable equivalence, conjugacy, invariants, moduli, classification37Cxx34C99,58F991 ( ( 37C20Generic properties, structural stabilityGeneric properties, structural stability37Cxx34C99,34D30,58F10,58F991 7 7 # 37C25Fixed points, periodic points, fixed-point index theoryFixed points, periodic points, fixed-point index theory37Cxx34C05,55M20,57R99,58F03,58F08,58F201 * * 37C27Periodic orbits of vector fields and flowsPeriodic orbits of vector fields and flows37Cxx34C25,58F221 " " 37C29Homoclinic and heteroclinic orbitsHomoclinic and heteroclinic orbits37Cxx34C23,34C37,58F14,58F991 3 t 37C30Functional analytic techniques in dynamical systemsZeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems37Cxx58F20,58F991 37C35Orbit growthOrbit growth37Cxx58F991 ) : 37C40Smooth ergodic theory, invariant measuresSmooth ergodic theory, invariant measures [See also 37Dxx]37Cxx28D99,58F111 % % 37C45Dimension theory of dynamical systemsDimension theory of dynamical systems37Cxx28A78,28A99,58F991 > 37C50Approximate trajectoriesApproximate trajectories (pseudotrajectories, shadowing, etc.)37Cxx58F991 4 4 37C55Periodic and quasiperiodic flows and diffeomorphismsPeriodic and quasiperiodic flows and diffeomorphisms37Cxx34C27,34C35,58F25,58F271 & 7 37C60Nonautonomous smooth dynamical systemsNonautonomous smooth dynamical systems [See also 37B55]37Cxx34C35,34C99,58F991 37C65Monotone flowsMonotone flows37Cxx34C35,58F251 / / 37C70Attractors and repellers, topological structureAttractors and repellers, topological structure37Cxx34D45,54H20,58F121 37C75Stability theoryStability theory37Cxx34Dxx,54H20,58F121 ) ) 37C80Symmetries, equivariant dynamical systemsSymmetries, equivariant dynamical systems37Cxx58F35,58F991 > t 37C85Dynamics of group actions other than $\bbfZ$ and $\bbfR$, etc.Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]37Cxx57R30,57Sxx,58F991 & 37C99Smooth dynamical systemsNone of the above, but in this section37Cxx34C35,58F991 ( @ 37CxxSmooth dynamical systems: general theorySmooth dynamical systems: general theory [See also 34Cxx, 34Dxx]37-XX 37D05Hyperbolic orbits and setsHyperbolic orbits and sets37Dxx58F09,58F151 37D10Invariant manifold theoryInvariant manifold theory37Dxx58F15,58F991 37D15Morse-Smale systemsMorse-Smale systems37Dxx58F091 ? 37D20Uniformly hyperbolic systemsUniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)37Dxx58F15,58F991 H 37D25Nonuniformly hyperbolic systemsNonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)37Dxx58F15,58F991 5 5 37D30Partially hyperbolic systems and dominated splittingsPartially hyperbolic systems and dominated splittings37Dxx58F15,58F991 C C 37D35Thermodynamic formalism, variational principles, equilibrium statesThermodynamic formalism, variational principles, equilibrium states37Dxx58F11,58F15,58F991 7 \ 37D40Dynamical systems of geometric origin and hyperbolicityDynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)37Dxx58F171 $ $ 37D45Strange attractors, chaotic dynamicsStrange attractors, chaotic dynamics37Dxx58F12,58F13,58F141 % 7 37D50Hyperbolic systems with singularitiesHyperbolic systems with singularities (billiards, etc.)37Dxx58F15,58F991 * & 37D99Dynamical systems with hyperbolic behaviorNone of the above, but in this section37Dxx58F15,58F991 * * 37DxxDynamical systems with hyperbolic behaviorDynamical systems with hyperbolic behavior37-XX ? 37E05Maps of the intervalMaps of the interval (piecewise continuous, continuous, smooth)37Exx26A18,39B12,58F03,58F08,58F991 37E10Maps of the circleMaps of the circle37Exx58F03,58F991 1 37E15Combinatorial dynamicsCombinatorial dynamics (types of periodic orbits)37Exx58F991 . 37E20Universality, renormalizationUniversality, renormalization [See also 37F25]37Exx58F991 37E25Maps of trees and graphsMaps of trees and graphs37Exx58F991 9 9 37E30Homeomorphisms and diffeomorphisms of planes and surfacesHomeomorphisms and diffeomorphisms of planes and surfaces37Exx59F991 37E35Flows on surfacesFlows on surfaces37Exx34C35,57R99,58F991
37E40Twist mapsTwist maps37Exx58F991 37E45Rotation numbers and vectorsRotation numbers and vectors37Exx58F991 ! & 37E99Low-dimensional dynamical systemsNone of the above, but in this section37Exx58F991 ! ! 37ExxLow-dimensional dynamical systemsLow-dimensional dynamical systems37-XX 37F05Relations and correspondencesRelations and correspondences37Fxx32H50,58F231 < b 37F10Polynomials; rational maps; entire and meromorphic functionsPolynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]37Fxx30D05,32H50,58F231 3 3 37F15Expanding maps; hyperbolicity; structural stabilityExpanding maps; hyperbolicity; structural stability37Fxx30D05,32H50,58F231 37F20Combinatorics and topologyCombinatorics and topology37Fxx30D05,32H50,58F231 37F25RenormalizationRenormalization37Fxx30D05,32H50,58F231 5 ` 37F30Quasiconformal methods and Teichm\"uller theory, etc.Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems37Fxx30C99,30F35,30F40,30F60,58F231 + + 37F35Conformal densities and Hausdorff dimensionConformal densities and Hausdorff dimension37Fxx30D05,32H50,58F231 37F40Geometric limitsGeometric limits37Fxx30D05,32H50,58F231 / K 37F45Holomorphic families of dynamical systems, etc.Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations37Fxx30D05,32H50,58F231 2 H 37F50Small divisors, rotation domains and linearizationSmall divisors, rotation domains and linearization; Fatou and Julia sets37Fxx30D05,32H50,58F231 ( G 37F75Holomorphic foliations and vector fieldsHolomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]37Fxx32S65,34A20,58F181 & 37F99Complex dynamical systemsNone of the above, but in this section37Fxx30D05,32H50,58F231 1 37FxxComplex dynamical systemsComplex dynamical systems [See also 30D05, 32H50]37-XX 37G05Normal formsNormal forms37Gxx34C20,58F361 37G10Bifurcations of singular pointsBifurcations of singular points37Gxx34C23,58F141 0 0 # 37G15Bifurcations of limit cycles and periodic orbitsBifurcations of limit cycles and periodic orbits37Gxx34C05,34C23,34C25,58F14,58F21,58F221 7 7 37G20Hyperbolic singular points with homoclinic trajectoriesHyperbolic singular points with homoclinic trajectories37Gxx34C23,34C37,58F141 7 7 37G25Bifurcations connected with nontransversal intersectionBifurcations connected with nontransversal intersection37Gxx34C23,58F141 2 2 37G30Infinite nonwandering sets arising in bifurcationsInfinite nonwandering sets arising in bifurcations37Gxx34C23,58F141 ! ! 37G35Attractors and their bifurcationsAttractors and their bifurcations37Gxx58F12,58F141 * * 37G40Symmetries, equivariant bifurcation theorySymmetries, equivariant bifurcation theory37Gxx34C23,58F14,58F351 & 37G99Bifurcation theoryNone of the above, but in this section37Gxx34C23,58F141 = 37GxxBifurcation theoryLocal and nonlocal bifurcation theory [See also 34C23, 34K18]37-XX A R 37H05Foundations, general theory of cocycles, algebraic ergodic theoryFoundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]37Hxx22D40,28D15,58F11,58F991 ; m / 37H10Random and stochastic difference and differential equationsGeneration, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]37Hxx34F05,34K50,39A99,35R60,60H10,60H15,60H99,93Exx1 1 W 37H15Multiplicative ergodic theory, Lyapunov exponentsMultiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]37Hxx28D99,34D08,34F05,58F111 # # 37H20Bifurcation theoryBifurcation theory [See also 37Gxx]37Hxx34C23,34F05,34K50,39A99,35R60,58F141 & A 37H99Random dynamical systemsNone of the above, but in this section37Hxx34F05,34K50,35R60,39A99,47B80,47H40,58F99,60H10,60H15,60H99,93Exx1 S 37HxxRandom dynamical systemsRandom dynamical systems [See also 15A52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]37-XX / ? 37J05Relations with symplectic geometry and topologyGeneral theory, relations with symplectic geometry and topology37Jxx53C15,58F05,70Gxx,70H051 ! ! 37J10Symplectic mappings, fixed pointsSymplectic mappings, fixed points37Jxx58F05,70H05,70H151 V 37J15Symmetries, etc.Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]37Jxx58F05,58F35,70H05,70H331 37J20Bifurcation problemsBifurcation problems37Jxx34C23,58F05,58F14,70H05,70K991 37J25Stability problemsStability problems37Jxx34Dxx,58F05,58F12,70K15,70K201 9 9 37J30Obstructions to integrability (nonintegrability criteria)Obstructions to integrability (nonintegrability criteria)37Jxx58F05,58F07,70H051 # X 37J35Completely integrable systems, etc.Completely integrable systems, topological structure of phase space, integration methods37Jxx58F05,58F07,70H051 I ) 37J40Perturbations, etc.Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion37Jxx34C29,34C99,58F05,58F27,58F30,70H05,70K991 2 [ 37J45Periodic, homoclinic and heteroclinic orbits, etc.Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods37Jxx34C25,34C37,58F05,58F14,58F221 % % 37J50Action-minimizing orbits and measuresAction-minimizing orbits and measures37Jxx58E99,58F05,58F991 37J55Contact systemsContact systems [See also 53D10]37Jxx53C15,58F99,70F99,70H991 / 37J60Nonholonomic dynamical systemsNonholonomic dynamical systems [See also 70F25]37Jxx58F99,70F251 + & 37J99Finite-dimensional Hamiltonian etc. systemsNone of the above, but in this section37Jxx58F99,70H991 + l 37JxxFinite-dimensional Hamiltonian etc. systemsFinite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]37-XX M ) 37K05Hamiltonian structures, etc.Hamiltonian structures, symmetries, variational principles, conservation laws37Kxx35A15,35A30,35Qxx,58F05,58F07,58F37,58F391 " p 37K10Completely integrable systems etc.Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)37Kxx35Q51,35Q53,35Q55,35Q58,58F071 6 W / 37K15Integration by inverse spectral and scattering methodsIntegration of completely integrable systems by inverse spectral and scattering methods37Kxx34A55,34L40,34L25,35Q51,35Q53,35Q55,35Q58,58F071 ' W 37K20Relations with algebraic geometry, etc.Relations with algebraic geometry, complex analysis, special functions [See also 14H70]37Kxx14H99,35Qxx,58F071 $ $ 37K25Relations with differential geometryRelations with differential geometry37Kxx53C99,35Qxx,58F071 # O 37K30Relations with algebraic structuresRelations with infinite-dimensional Lie algebras and other algebraic structures37Kxx17B99,35Qxx,58F071 ( & ) 37K35Lie-B\"acklund and other transformationsLie-Bäcklund and other transformations37Kxx35A30,35Q51,35Q53,35Q55,35Q58,58F37,58G371 0 0 # 37K40Soliton theory, asymptotic behavior of solutionsSoliton theory, asymptotic behavior of solutions37Kxx35B40,35Q51,35Q53,35Q55,35Q58,58F071 # 37K45Stability problemsStability problems37Kxx35B35,35Qxx,58D25,58F07,58F12,58F391 37K50Bifurcation problemsBifurcation problems37Kxx35B32,35Qxx,58D25,58F14,58F391 3 3 37K55Perturbations, KAM for infinite-dimensional systemsPerturbations, KAM for infinite-dimensional systems37Kxx35B20,35Qxx,58D25,58F30,58F391 ! 37K60Lattice dynamicsLattice dynamics [See also 37L60]37Kxx35Q99,58F39,70K991 5 Y 37K65Hamiltonian systems on groups of diffeomorphisms etc.Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics37Kxx58D05,58D25,58F051 ( & 37K99Infinite-dimensional Hamiltonian systemsNone of the above, but in this section37Kxx35Qxx,58F05,58F991 ( @ 37KxxInfinite-dimensional Hamiltonian systemsInfinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]37-XX 9 9 ) 37L05General theory, nonlinear semigroups, evolution equationsGeneral theory, nonlinear semigroups, evolution equations37Lxx34G20,35Bxx,35K22,35L99,47H20,58D25,58F391 8 8 # 37L10Normal forms, center manifold theory, bifurcation theoryNormal forms, center manifold theory, bifurcation theory37Lxx34G20,35B32,58D25,58F14,58F36,58F391 > 37L15Stability problems of infinite-dimensional Hamiltonian systemsStability problems37Lxx34G20,35B35,58D25,58F12,58F391 6
37L20Symmetries of infinite-dimensional Hamiltonian systemsSymmetries37Lxx34G20,35A30,58D25,58F35,58F391 6 6 37L25Inertial manifolds and other invariant attracting setsInertial manifolds and other invariant attracting sets37Lxx34G20,35B40,58D25,58F12,58F391 3 37L30Attractors and their dimensionsAttractors and their dimensions, Lyapunov exponents37Lxx34G20,35B40,58F12,58F391 37L40Invariant measuresInvariant measures37Lxx35B99,58D25,58F391 ! ! 37L45Hyperbolicity; Lyapunov functionsHyperbolicity; Lyapunov functions37Lxx35B99,58F15,58F391 ) Q 37L50perturbations of Hamiltonian systems etc.Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems37Lxx34G20,47H20,58D25,58F30,58F391 2 b 37L55Infinite-dimensional random dynamical systems etc.Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]37Lxx35R60,60H10,60H151 ! 37L60Lattice dynamicsLattice dynamics [See also 37K60]37Lxx35Q99,58F99,70K99,82C991 B 8 37L65Approximation methods for infinite-dimensional Hamiltonian systemsSpecial approximation methods (nonlinear Galerkin, etc.)37Lxx35A35,58F39,58F99,65M991 2 & # 37L99Infinite-dimensional dissipative dynamical systemsNone of the above, but in this section37Lxx34G20,35Bxx,35Qxx,47H20,58D25,58F391 2 J 37LxxInfinite-dimensional dissipative dynamical systemsInfinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]37-XX
37M05SimulationSimulation37Mxx58F99,65C20,65C991 37M10Time series analysisTime series analysis37Mxx58F99,65U051 37M15Symplectic integratorsSymplectic integrators37Mxx58F99,65L991 . . 37M20Computational methods for bifurcation problemsComputational methods for bifurcation problems37Mxx58F14,58F99,65L991 ( z 37M25Computational methods for ergodic theoryComputational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)37Mxx58F991 B & 37M99Approximation methods and numerical treatment of dynamical systemsNone of the above, but in this section37Mxx58F99,65-XX1 B S 37MxxApproximation methods and numerical treatment of dynamical systemsApproximation methods and numerical treatment of dynamical systems [See also 65Pxx]37-XX 6 W 37N05Dynamical systems in classical and celestial mechanicsDynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]37Nxx58F05,58F40,70F15,70Hxx,70Kxx1 B | 37N10Dynamical systems in fluid mechanics, oceanography and meteorologyDynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]37Nxx58F40,76-XX,86A05,86A101 $ 7 37N15Dynamical systems in solid mechanicsDynamical systems in solid mechanics [See mainly 74Hxx]37Nxx58F40,73-XX1 . e 37N20Dynamical systems in other branches of physicsDynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)37Nxx58F40,78-XX,81-XX,83-XX1 ? 37N25Dynamical systems in biologyDynamical systems in biology [See mainly 92-XX, but also 91-XX]37Nxx58F40,92-XX1 ' ' 37N30Dynamical systems in numerical analysisDynamical systems in numerical analysis37Nxx58F40,65-XX1 37N35Dynamical systems in controlDynamical systems in control37Nxx58F40,49-XX,93-XX1 / / 37N40Dynamical systems in optimization and economicsDynamical systems in optimization and economics37Nxx58F40,90-XX1 ! & 37N99Applications of dynamical systemsNone of the above, but in this section37Nxx58F401 ! 37NxxApplications of dynamical systemsApplications37-XX & G 39-00Reference works (functional equations)General reference works (handbooks, dictionaries, bibliographies, etc.)39-XX ; 39-01Textbooks (functional equations)Instructional exposition (textbooks, tutorial papers, etc.)39-XX * 1 39-02Research monographs (functional equations)Research exposition (monographs, survey articles)39-XX ! U 39-03Historical (functional equations)Historical (must also be assigned at least one classification number from Section 01)39-XX 4 X 39-04Machine computation, programs (functional equations)Explicit machine computation and programs (not the theory of computation or programming)39-XX 1 + 39-06Proceedings of conferences (functional equations)Proceedings, conferences, collections, etc.39-XX # # 39-99Difference and functional equationsDifference and functional equations # # 39-XXDifference and functional equationsDifference and functional equations & 39A05General theory of difference equationsGeneral39Axx 39A10Difference equationsDifference equations, additive39Axx ! [ 39A11Stability of difference equationsStability and asymptotics of difference equations; oscillatory and periodic solutions, etc.39Axx & & 39A12Discrete version of topics in analysisDiscrete version of topics in analysis39Axx / @ 39A13Difference equations, scaling ($q$-differences)Difference equations, scaling ($q$-differences) [See also 33Dxx]39Axx39A10,39A701 N 39A20Generalized difference equationsMultiplicative and other generalized difference equations, e.g. of Lyness type39Axx39A10,39A701 % 39A70Difference operatorsDifference operators [See also 47B39]39Axx & 39A99Difference equationsNone of the above, but in this section39Axx 7 39AxxDifference equationsDifference equations {For dynamical systems, see 37-XX}39-XX & 39B05General theory of functional equationsGeneral39Bxx " R 39B12Iteraterative functional equationsIteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]39Bxx ' 4 39B22Functional equations for real functionsEquations for real functions [See also 26A51, 26B25]39Bxx * 0 39B32Functional equations for complex functionsEquations for complex functions [See also 30D05]39Bxx ( . 39B42Matrix and operator functional equationsMatrix and operator equations [See also 47Jxx]39Bxx < ? 39B52Functional equations for functions with more general domainsEquations for functions with more general domains and/or ranges39Bxx 5 5 39B55Orthogonal additivity and other conditional equationsOrthogonal additivity and other conditional equations39Bxx39B05,39B42,39B521 ` 39B62Systems of functional equationsFunctional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]39Bxx 3 0 39B72Functional inequalities involving unknown functionsSystems of functional equations and inequalities39Bxx 4 E 39B82Stability, separation, extension, and related topicsStability, separation, extension, and related topics [See also 46A22]39Bxx39B10,46A221 & 39B99Functional equationsNone of the above, but in this section39Bxx 6 39BxxFunctional equationsFunctional equations and inequalities [See also 30D05]39-XX ! G 40-00Reference works (sequences, etc.)General reference works (handbooks, dictionaries, bibliographies, etc.)40-XX ; 40-01Textbooks (sequences, etc.)Instructional exposition (textbooks, tutorial papers, etc.)40-XX % 1 40-02Research monographs (sequences, etc.)Research exposition (monographs, survey articles)40-XX U 40-03Historical (sequences, etc.)Historical (must also be assigned at least one classification number from Section 01)40-XX / X 40-04Machine computation, programs (sequences, etc.)Explicit machine computation and programs (not the theory of computation or programming)40-XX , + 40-06Proceedings of conferences (sequences, etc.)Proceedings, conferences, collections, etc.40-XX 40-99Sequences, etc.Sequences, etc. 40-XXSequences, etc.Sequences, series, summability # 2 40A05Convergence of series and sequencesConvergence and divergence of series and sequences40Axx ' 40A10Convergence of integralsConvergence and divergence of integrals40Axx " B 40A15Convergence of continued fractionsConvergence and divergence of continued fractions [See also 30B70]40Axx / 40A20Convergence of infinite productsConvergence and divergence of infinite products40Axx s 40A25Approximation to limiting valuesApproximation to limiting values (summation of series, etc.) {For the Euler-Maclaurin summation formula, see 65B15}40Axx 0 ? 40A30Convergence of series and sequences of functionsConvergence and divergence of series and sequences of functions40Axx * & 40A99Convergence of infinite limiting processesNone of the above, but in this section40Axx * 9 40AxxConvergence of infinite limiting processesConvergence and divergence of infinite limiting processes40-XX r 40B05Multiple sequences and seriesMultiple sequences and series {(should also be assigned at least one other classification number in this section)}40-XX 40C05Matrix methods in summabilityMatrix methods40Cxx 40C10Integral methods in summabilityIntegral methods40Cxx ) V 40C15Function theoretic methods in summabilityFunction-theoretic methods (including power series methods and semicontinuous methods)40Cxx & 40C99General summability methodsNone of the above, but in this section40Cxx 40CxxGeneral summability methodsGeneral summability methods40-XX 40D05General summability theoremsGeneral theorems40Dxx 40D09Structure of summability fieldsStructure of summability fields40Dxx * 40D10Tauberian constants, etc.Tauberian constants and oscillation limits40Dxx + + 40D15Convergence factors and summability factorsConvergence factors and summability factors40Dxx % ) 40D20Bounded fields of summability methodsSummability and bounded fields of methods40Dxx " 40D25Inclusion theorems, etc.Inclusion and equivalence theorems40Dxx & 40D99Direct theorems on summabilityNone of the above, but in this section40Dxx 40DxxDirect theorems on summabilityDirect theorems on summability40-XX 40E05Tauberian theorems, generalTauberian theorems, general40Exx $ 40E10Growth estimates in Tauberian theoryGrowth estimates40Exx 40E15Lacunary inversion theoremsLacunary inversion theorems40Exx 40E20Tauberian constantsTauberian constants40Exx & 40E99Inversion theoremsNone of the above, but in this section40Exx 40ExxInversion theoremsInversion theorems40-XX 40F05Special cases of summabilityAbsolute and strong summability40-XX , 40G05Traditional summability methodsCesàro, Euler, Nörlund and Hausdorff methods40Gxx $ 40G10Power series methodsAbel, Borel and power series methods40Gxx & 40G99Special methods of summabilityNone of the above, but in this section40Gxx 40GxxSpecial methods of summabilitySpecial methods of summability40-XX * * 40H05Functional analytic methods in summabilityFunctional analytic methods in summability40-XX " A 40J05Summability in abstract structuresSummability in abstract structures [See also 43A55, 46A35, 46B15]40-XX / G 41-00Reference works (approximations and expansions)General reference works (handbooks, dictionaries, bibliographies, etc.)41-XX ) ; 41-01Textbooks (approximations and expansions)Instructional exposition (textbooks, tutorial papers, etc.)41-XX 3 1 41-02Research monographs (approximations and expansions)Research exposition (monographs, survey articles)41-XX * U 41-03Historical (approximations and expansions)Historical (must also be assigned at least one classification number from Section 01)41-XX = X 41-04Machine computation, programs (approximations and expansions)Explicit machine computation and programs (not the theory of computation or programming)41-XX : + 41-06Proceedings of conferences (approximations and expansions)Proceedings, conferences, collections, etc.41-XX 41-99Approximations and expansionsApproximations and expansions é 41-XXApproximation theoryApproximations and expansions {For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx}
( 41A05InterpolationInterpolation [See also 42A15 and 65D05]41-XX X 41A10Approximation by polynomialsApproximation by polynomials {For approximation by trigonometric polynomials, see 42A10}41-XX 41A15Spline approximationSpline approximation41-XX Z 41A17Inequalities in approximationInequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-type inequalities)41-XX # # 41A20Approximation by rational functionsApproximation by rational functions41-XX 41A21Pade approximationPadé approximation41-XX , 41A25Degree of approximation, etc.Rate of convergence, degree of approximation41-XX ( 41A27Inverse theorems in approximation theoryInverse theorems41-XX 41A28Simultaneous approximationSimultaneous approximation41-XX 41A29Approximation with constraintsApproximation with constraints41-XX / / 41A30Approximation by other special function classesApproximation by other special function classes41-XX A 41A35Approximation by operatorsApproximation by operators (in particular, by integral operators)41-XX # # 41A36Approximation by positive operatorsApproximation by positive operators41-XX
41A40SaturationSaturation41-XX 41A44Best constantsBest constants41-XX - - 41A45Approximation by arbitrary linear expressionsApproximation by arbitrary linear expressions41-XX 0 D 41A46Approximation by arbitrary nonlinear expressionsApproximation by arbitrary nonlinear expressions; widths and entropy41-XX % 41A50Best approximationBest approximation, Chebyshev systems41-XX 41A52Uniqueness of best approximationUniqueness of best approximation41-XX 41A55Approximate quadraturesApproximate quadratures41-XX H 41A58Series expansionsSeries expansions (e.g. Taylor, Lidstone series, but not Fourier series)41-XX $ Z 41A60Asymptotic problems in approximationAsymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]41-XX ' l 41A63Multidimensional approximation problemsMultidimensional problems (should also be assigned at least one other classification number in this section)41-XX _ 41A65Abstract approximation theoryAbstract approximation theory (approximation in normed linear spaces and other abstract spaces)41-XX $ $ 41A80Remainders in approximation formulasRemainders in approximation formulas41-XX , 41A99Miscellaneous topics in approximation theoryMiscellaneous topics41-XX " G 42-00Reference works (Fourier analysis)General reference works (handbooks, dictionaries, bibliographies, etc.)42-XX ; 42-01Textbooks (Fourier analysis)Instructional exposition (textbooks, tutorial papers, etc.)42-XX & 1 42-02Research monographs (Fourier analysis)Research exposition (monographs, survey articles)42-XX U 42-03Historical (Fourier analysis)Historical (must also be assigned at least one classification number from Section 01)42-XX 0 X 42-04Machine computation, programs (Fourier analysis)Explicit machine computation and programs (not the theory of computation or programming)42-XX - + 42-06Proceedings of conferences (Fourier analysis)Proceedings, conferences, collections, etc.42-XX 42-99Fourier analysisFourier analysis 42-XXFourier analysisFourier analysis : 42A05Trigonometric polynomialsTrigonometric polynomials, inequalities, extremal problems42Axx 42A10Trigonometric approximationTrigonometric approximation42Axx 42A15Trigonometric interpolationTrigonometric interpolation42Axx Œ 42A16Fourier coefficients, etc.Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}42Axx H 42A20Convergence trigonometric seriesConvergence and absolute convergence of Fourier and trigonometric series42Axx # H 42A24Summability of trigonometric seriesSummability and absolute summability of Fourier and trigonometric series42Axx % [ 42A32Trigonometric series of special typesTrigonometric series of special types (positive coefficients, monotonic coefficients, etc.)42Axx % M 42A38Fourier type transforms, one variableFourier and Fourier-Stieltjes transforms and other transforms of Fourier type42Axx 42A45Multipliers, one variableMultipliers42Axx 9 42A50Singular integrals, one variableConjugate functions, conjugate series, singular integrals42Axx D 42A55Lacunary seriesLacunary series of trigonometric and other functions; Riesz products42Axx ) 42A61Probabilistic methods in Fourier analysisProbabilistic methods42Axx , f 42A63Uniqueness of trigonometric expansions, etc.Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization42Axx ! ! 42A65Completeness of sets of functionsCompleteness of sets of functions42Axx 42A70Trigonometric moment problemsTrigonometric moment problems42Axx & M 42A75Periodic functions and generalizationsClassical almost periodic functions, mean periodic functions [See also 43A60]42Axx 42A82Positive definite functionsPositive definite functions42Axx 42A85Convolution (Fourier analysis)Convolution, factorization42Axx & 42A99Fourier analysis in one variableNone of the above, but in this section42Axx 42AxxFourier analysis in one variableFourier analysis in one variable42-XX 2 42B05Fourier series and coefficients, several variablesFourier series and coefficients42Bxx 6 42B08Summability of trigonometric series, several variablesSummability42Bxx * M 42B10Fourier type transforms, several variablesFourier and Fourier-Stieltjes transforms and other transforms of Fourier type42Bxx 42B15Multipliers, several variablesMultipliers42Bxx % + 42B20Singular integrals, several variablesSingular integrals (Calderón-Zygmund, etc.)42Bxx * 42B25Maximal functionsMaximal functions, Littlewood-Paley theory42Bxx 42B30Hp-spaces (Fourier analysis)$H^p$-spaces42Bxx , , 42B35Function spaces arising in harmonic analysisFunction spaces arising in harmonic analysis42Bxx42B991 % & 42B99Fourier analysis in several variablesNone of the above, but in this section42Bxx % P 42BxxFourier analysis in several variablesFourier analysis in several variables {For automorphic theory, see mainly 11F30}42-XX 6 S 42C05General theory of orthogonal functions and polynomialsOrthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]42Cxx . \ 42C10Fourier series in special orthogonal functionsFourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)42Cxx 1 ` 42C15Series and expansions in general function systemsSeries of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions42Cxx = O 42C20Rearrangements and other transformations of orthogonal seriesRearrangements and other transformations of Fourier and other orthogonal series42Cxx 1 1 42C25Uniqueness and localization for orthogonal seriesUniqueness and localization for orthogonal series42Cxx C ! 42C30Completeness of sets of functions of non-trigonom. Fourier analysisCompleteness of sets of functions42Cxx 42C40WaveletsWavelets42Cxx42C15,42C991 & 42C99Non-trigometric Fourier analysisNone of the above, but in this section42Cxx " ! 42CxxNon-trigonometric Fourier analysisNontrigonometric Fourier analysis42-XX , G 43-00Reference works (abstract harmonic analysis)General reference works (handbooks, dictionaries, bibliographies, etc.)43-XX & ; 43-01Textbooks (abstract harmonic analysis)Instructional exposition (textbooks, tutorial papers, etc.)43-XX 0 1 43-02Research monographs (abstract harmonic analysis)Research exposition (monographs, survey articles)43-XX ' U 43-03Historical (abstract harmonic analysis)Historical (must also be assigned at least one classification number from Section 01)43-XX : X 43-04Machine computation, programs (abstract harmonic analysis)Explicit machine computation and programs (not the theory of computation or programming)43-XX 7 + 43-06Proceedings of conferences (abstract harmonic analysis)Proceedings, conferences, collections, etc.43-XX 43-99Abstract harmonic analysisAbstract harmonic analysis X 43-XXAbstract harmonic analysisAbstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx} ' 43A05Measures on groups, etc.Measures on groups and semigroups, etc.43-XX 2 43A07Means on groups, etc.Means on groups, semigroups, etc.; amenable groups43-XX , 43A10Measure algebras on groups, etc.Measure algebras on groups, semigroups, etc.43-XX 3 B 43A15Lp-spaces and other function spaces on groups, etc.$L^p$-spaces and other function spaces on groups, semigroups, etc.43-XX % * 43A17Analysis on ordered groups, Hp-theoryAnalysis on ordered groups, ${H}^p$-theory43-XX * 43A20L1 algebras on groups, etc.$L^1$-algebras on groups, semigroups, etc.43-XX @ L 43A22Homomorphisms and multipliers of function spaces on groups, etc.Homomorphisms and multipliers of function spaces on groups, semigroups, etc.43-XX 9 J 43A25Fourier type transforms on locally compact abelian groupsFourier and Fourier-Stieltjes transforms on locally compact abelian groups43-XX 2 U 43A30Fourier type transforms on nonabelian groups, etc.Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.43-XX . . 43A32Other transforms and operators of Fourier typeOther transforms and operators of Fourier type43-XX + 7 43A35Positive definite functions on groups, etc.Positive definite functions on groups, semigroups, etc.43-XX ! ! 43A40Character groups and dual objectsCharacter groups and dual objects43-XX " . 43A45Spectral synthesis on groups, etc.Spectral synthesis on groups, semigroups, etc.43-XX * T 43A46Special sets in abstract harmonic analysisSpecial sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)43-XX 7 7 43A50Convergence of Fourier series and of inverse transformsConvergence of Fourier series and of inverse transforms43-XX # @ 43A55Summability methods on groups, etc.Summability methods on groups, semigroups, etc. [See also 40J05]43-XX ) ˜ 43A60Almost periodic functions on groups, etc.Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions43-XX ( 43A62Hypergroups (abstract harmonic analysis)Hypergroups43-XX < Q 43A65Representations of groups, etc. (abstract harmonic analysis)Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]43-XX 3 K 43A70Analysis on specific locally compact abelian groupsAnalysis on specific locally compact abelian groups [See also 11R56, 22B05]43-XX # # 43A75Analysis on specific compact groupsAnalysis on specific compact groups43-XX " " 43A77Analysis on general compact groupsAnalysis on general compact groups43-XX % 6 43A80Analysis on other specific Lie groupsAnalysis on other specific Lie groups [See also 22Exx]43-XX 43A85Analysis on homogeneous spacesAnalysis on homogeneous spaces43-XX 0 2 43A90Spherical functions (abstract harmonic analysis)Spherical functions [See also 22E45, 22E46, 33C65]43-XX ( $ 43A95Categorical methods in harmonic analysisCategorical methods [See also 46Mxx]43-XX ) 43A99Miscellaneous topics in harmonic analysisMiscellaneous topics43-XX % G 44-00Reference works (integral transforms)General reference works (handbooks, dictionaries, bibliographies, etc.)44-XX ; 44-01Textbooks (integral transforms)Instructional exposition (textbooks, tutorial papers, etc.)44-XX ) 1 44-02Research monographs (integral transforms)Research exposition (monographs, survey articles)44-XX U 44-03Historical (integral transforms)Historical (must also be assigned at least one classification number from Section 01)44-XX 3 X 44-04Machine computation, programs (integral transforms)Explicit machine computation and programs (not the theory of computation or programming)44-XX 0 + 44-06Proceedings of conferences (integral transforms)Proceedings, conferences, collections, etc.44-XX 44-99Integral transformsIntegral transforms æ 44-XXIntegral transformsIntegral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10} # 44A05General integral transformsGeneral transforms [See also 42A38]44-XX 44A10Laplace transformLaplace transform44-XX 44A12Radon transformRadon transform [See also 92C55]44-XX , 44A15Special transformsSpecial transforms (Legendre, Hilbert, etc.)44-XX ( 44A20Integral transforms of special functionsTransforms of special functions44-XX 44A30Multiple transformsMultiple transforms44-XX 44A35ConvolutionConvolution44-XX 6 44A40Calculus of Mikusinski, etc.Calculus of Mikusi\'nski and other operational calculi44-XX 44A45Classical operational calculusClassical operational calculus44-XX 44A55Discrete operational calculusDiscrete operational calculus44-XX 44A60Moment problemsMoment problems44-XX D 44A99Miscellaneous topics of integral transforms and operational calculusMiscellaneous topics44-XX $ G 45-00Reference works (integral equations)General reference works (handbooks, dictionaries, bibliographies, etc.)45-XX ; 45-01Textbooks (integral equations)Instructional exposition (textbooks, tutorial papers, etc.)45-XX ( 1 45-02Research monographs (integral equations)Research exposition (monographs, survey articles)45-XX U 45-03Historical (integral equations)Historical (must also be assigned at least one classification number from Section 01)45-XX 2 X 45-04Machine computation, programs (integral equations)Explicit machine computation and programs (not the theory of computation or programming)45-XX / + 45-06Proceedings of conferences (integral equations)Proceedings, conferences, collections, etc.45-XX 45-99Integral equationsIntegral equations 45-XXIntegral equationsIntegral equations 45A05Linear integral equationsLinear integral equations45-XX 45B05Fredholm integral equationsFredholm integral equations45-XX ( 9 45C05Eigenvalue problems (integral equations)Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]45-XX , 45D05Volterra integral equationsVolterra integral equations [See also 34A12]45-XX . ? 45E05Integral equations with kernels of Cauchy typeIntegral equations with kernels of Cauchy type [See also 35J15]45Exx * i 45E10Integral equations of the convolution typeIntegral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]45Exx & 45E99Singular integral equationsNone of the above, but in this section45Exx O 45ExxSingular integral equationsSingular integral equations [See also 30Exx, 44-XX, 30E20, 30E25, 44A15, 44A35]45-XX 0 0 45F05Systems of nonsingular linear integral equationsSystems of nonsingular linear integral equations45Fxx ! 1 45F10Multiple integral equations, etc.Dual, triple, etc., integral and series equations45Fxx - - 45F15Systems of singular linear integral equationsSystems of singular linear integral equations45Fxx $ & 45F99Systems of linear integral equationsNone of the above, but in this section45Fxx $ $ 45FxxSystems of linear integral equationsSystems of linear integral equations45-XX % % 45G05Singular nonlinear integral equationsSingular nonlinear integral equations45Gxx ( " 45G10Nonsingular nonlinear integral equationsOther nonlinear integral equations45Gxx ' ' 45G15Systems of nonlinear integral equationsSystems of nonlinear integral equations45Gxx 4 45GxxNonlinear integral equationsNonlinear integral equations [See also 47H30, 47Jxx]45-XX 5 . 45H05Integral equations with miscellaneous special kernelsMiscellaneous special kernels [See also 44A15]45-XX ' F 45J05Integro-ordinary differential equationsIntegro-ordinary differential equations [See also 34K05, 34K30, 47G20]45-XX & E 45K05Integro-partial differential equationsIntegro-partial differential equations [See also 34K30, 35R10, 47G20]45-XX < J 45L05Theoretical approximation of solutions of integral equationsTheoretical approximation of solutions {For numerical analysis, see 65Rxx}45-XX ' 45M05Asymptotic theory of integral equationsAsymptotics45Mxx & 45M10Stability theory of integral equationsStability theory45Mxx ( 45M15Periodic solutions of integral equationsPeriodic solutions45Mxx ( 45M20Positive solutions of integral equationsPositive solutions45Mxx 7 & 45M99Qualitative behavior of solutions of integral equationsNone of the above, but in this section45Mxx 7 45MxxQualitative behavior of solutions of integral equationsQualitative behavior45-XX % B 45N05Integral equations in abstract spacesAbstract integral equations, integral equations in abstract spaces45-XX * 45P05Integral operatorsIntegral operators [See also 47B38, 47G10]45-XX 45Q05Inverse problemsInverse problems45-XX35R30,45A051 * 45R05Random integral equationsRandom integral equations [See also 60H20]45-XX60H201 % G 46-00Reference works (functional analysis)General reference works (handbooks, dictionaries, bibliographies, etc.)46-XX ; 46-01Textbooks (functional analysis)Instructional exposition (textbooks, tutorial papers, etc.)46-XX ) 1 46-02Research monographs (functional analysis)Research exposition (monographs, survey articles)46-XX U 46-03Historical (functional analysis)Historical (must also be assigned at least one classification number from Section 01)46-XX 3 X 46-04Machine computation, programs (functional analysis)Explicit machine computation and programs (not the theory of computation or programming)46-XX 0 + 46-06Proceedings of conferences (functional analysis)Proceedings, conferences, collections, etc.46-XX 46-99Functional analysisFunctional analysis Z 46-XXFunctional analysisFunctional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} ' ' 46A03General theory of locally convex spacesGeneral theory of locally convex spaces46Axx # - 46A04Locally convex Frechet spaces, etc.Locally convex Fréchet spaces and (DF)-spaces46Axx % % 46A08Barrelled spaces, bornological spacesBarrelled spaces, bornological spaces46Axx : q 46A11Spaces determined by compactness or summability propertiesSpaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)46Axx 0 P 46A13Spaces defined by inductive or projective limitsSpaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]46Axx s 46A16Non-locally convex linear spacesNot locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)46Axx " < 46A17Bornologies and related structuresBornologies and related structures; Mackey convergence, etc.46Axx , ¥ 46A19Generalizations of topological linear spacesOther ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R}$, etc.)46Axx + 46A20Duality theory of topological linear spacesDuality theory46Axx 2 a 46A22Extension and lifting of functionals and operatorsTheorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]46Axx ( 1 46A25Reflexivity of topological linear spacesReflexivity and semi-reflexivity [See also 46B10]46Axx - Y 46A30Open mappings and closed graph theorems, etc.Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)46Axx 3 w 46A32Topological linear spaces of linear operators, etc.Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]46Axx 2 & 46A35Summability and bases in topological linear spacesSummability and bases [See also 46B15]46Axx ! Q 46A40Ordered topological linear spacesOrdered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]46Axx B 46A45Sequence spacesSequence spaces (including Köthe sequence spaces) [See also 46B45]46Axx . > 46A50Compactness in topological linear spaces, etc.Compactness in topological linear spaces; angelic spaces, etc.46Axx & I 46A55Convexity in topological linear spacesConvex sets in topological linear spaces; Choquet theory [See also 52A07]46Axx ( 46A61Graded Fr\'echet spaces etc.Graded Fréchet spaces and tame operators46Axx46A04,46A991 ' / 46A63Topological invariants of linear spacesTopological invariants ((DN), ($\Omega$), etc.)46Axx46A04,46A991 h 46A70Saks spaces and their dualsSaks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)46Axx 46A80Modular spacesModular spaces46Axx & 46A99Topological linear spacesNone of the above, but in this section46Axx 0 Q 46AxxTopological linear spaces and related structuresTopological linear spaces and related structures {For function spaces, see 46Exx}46-XX 8 8 46B03Isomorphic theory (including renorming) of Banach spacesIsomorphic theory (including renorming) of Banach spaces46Bxx ! ! 46B04Isometric theory of Banach spacesIsometric theory of Banach spaces46Bxx 46B07Local theory of Banach spacesLocal theory of Banach spaces46Bxx . ? 46B08Ultraproduct techniques in Banach space theoryUltraproduct techniques in Banach space theory [See also 46M07]46Bxx , = 46B09Probabilistic methods in Banach space theoryProbabilistic methods in Banach space theory [See also 60Bxx]46Bxx ( ( 46B10Duality and reflexivity in normed spacesDuality and reflexivity [See also 46A25]46Bxx & & 46B15Summability and bases in normed spacesSummability and bases [See also 46A35]46Bxx ' . 46B20Geometry and structure of normed spacesGeometry and structure of normed linear spaces46Bxx " C 46B22Spaces with Radon-Nikodym propertyRadon-Nikodym, Krein-Milman and related properties [See also 46G10]46Bxx > - 46B25Classical Banach spaces in the general theory of normed spacesClassical Banach spaces in the general theory46Bxx 46B26Nonseparable Banach spacesNonseparable Banach spaces46Bxx . d 46B28Normed linear spaces of linear operators, etc.Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]46Bxx - 46B40Ordered normed spacesOrdered normed spaces [See also 46A40, 46B42]46Bxx ' 46B42Banach latticesBanach lattices [See also 46A40, 46B40]46Bxx ' 46B45Banach sequence spacesBanach sequence spaces [See also 46A45]46Bxx ( 46B50Compactness in normed spacesCompactness in Banach (or normed) spaces46Bxx46A50,46B991 * ; 46B70Interpolation between normed linear spacesInterpolation between normed linear spaces [See also 46M35]46Bxx & & 46B99Normed linear spaces and Banach spacesNone of the above, but in this section46Bxx & X 46BxxNormed linear spaces and Banach spacesNormed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}46-XX - h 46C05Geometry and topology of inner product spacesHilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)46Cxx l 46C07Hilbert subspaces etc.Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]46Cxx46C05,46C99,46B70,46M351 # # 46C15Characterizations of Hilbert spacesCharacterizations of Hilbert spaces46Cxx $ ] 46C20Spaces with indefinite inner productSpaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]46Cxx ! U 46C50Generalizations of inner productsGeneralizations of inner products (semi-inner products, partial inner products, etc.)46Cxx $ & 46C99Inner product spaces, Hilbert spacesNone of the above, but in this section46Cxx $ _ 46CxxInner product spaces, Hilbert spacesInner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}46-XX 6 < 46E05Lattices of functions defined by smoothness propertiesLattices of continuous, differentiable or analytic functions46Exx A M 46E10Topological linear spaces of functions with smoothness propertiesTopological linear spaces of continuous, differentiable or analytic functions46Exx ; A 46E15Banach spaces of functions defined by smoothness propertiesBanach spaces of continuous, differentiable or analytic functions46Exx < B 46E20Hilbert spaces of functions defined by smoothness propertiesHilbert spaces of continuous, differentiable or analytic functions46Exx ' ™ 46E22Hilbert spaces with reproducing kernelsHilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]46Exx : w 46E25Rings and algebras of functions with smoothness propertiesRings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}46Exx * 46E27Spaces of measuresSpaces of measures [See also 28A33, 46Gxx]46Exx — 46E30Spaces of measurable functionsSpaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)46Exx " [ 46E35Sobolev spaces and generalizationsSobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems46Exx 1 H 46E39Sobolev spaces of functions of discrete variablesSobolev (and similar kinds of) spaces of functions of discrete variables46Exx ! / 46E40Spaces of vector-valued functionsSpaces of vector- and operator-valued functions46Exx > o 46E50Spaces of holomorphic functions on infinite-dimensional spacesSpaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]46Exx & & 46E99Linear function spaces and their dualsNone of the above, but in this section46Exx & h 46ExxLinear function spaces and their dualsLinear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}46-XX = i 46F05Topological linear spaces of test functions and distributionsTopological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]46Fxx 5 46F10Operations with distributions (generalized functions)Operations with distributions46Fxx * B 46F12Integral transforms in distribution spacesIntegral transforms in distribution spaces [See also 42-XX, 44-XX]46Fxx $ J 46F15Hyperfunctions, analytic functionalsHyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]46Fxx 6 l 46F20Distributions as boundary values of analytic functionsDistributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]46Fxx 4 = 46F25Generalized functions on infinite-dimensional spacesDistributions on infinite-dimensional spaces [See also 58C35]46Fxx , U 46F30Generalized functions for nonlinear analysisGeneralized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)46Fxx46F05,46F10,46F991 & 46F99Generalized functions, etc.None of the above, but in this section46Fxx J 46FxxGeneralized functions, etc.Distributions, generalized functions, distribution spaces [See also 46T30]46-XX ' * 46G05Derivatives, etc. (functional analysis)Derivatives [See also 46T20, 58C20, 58C25]46Gxx & > 46G10Vector-valued measures and integrationVector-valued measures and integration [See also 28Bxx, 46B22]46Gxx 2 J 46G12Measures and integration on abstract linear spacesMeasures and integration on abstract linear spaces [See also 28C20, 46T12]46Gxx " 3 46G15Functional analytic lifting theoryFunctional analytic lifting theory [See also 28A51]46Gxx L 46G20Infinite dimensional holomorphyInfinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]46Gxx L 46G25(Spaces of) multilinear mappings(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]46Gxx46B28,46G20,46E501 4 & 46G99Measures, etc. involving infinite-dimensional spacesNone of the above, but in this section46Gxx 4 q 46GxxMeasures, etc. involving infinite-dimensional spacesMeasures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]46-XX & & 46H05General theory of topological algebrasGeneral theory of topological algebras46Hxx . 46H10Ideals and subalgebras of topological algebrasIdeals and subalgebras46Hxx ' ' 46H15Representations of topological algebrasRepresentations of topological algebras46Hxx 4 1 46H20Structure and classification of topological algebrasStructure, classification of topological algebras46Hxx X 46H25Topological modulesNormed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)46Hxx + < 46H30Functional calculus in topological algebrasFunctional calculus in topological algebras [See also 47A60]46Hxx ! 4 46H35Topological algebras of operatorsTopological algebras of operators [See mainly 47Lxx]46Hxx 46H40Automatic continuityAutomatic continuity46Hxx # ; 46H70Nonassociative topological algebrasNonassociative topological algebras [See also 46K70, 46L70]46Hxx & 46H99Topological algebras, etc.None of the above, but in this section46Hxx ’ 46HxxTopological algebras, etc.Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}46-XX 2 2 46J05General theory of commutative topological algebrasGeneral theory of commutative topological algebras46Jxx ' K 46J10Banach algebras of continuous functionsBanach algebras of continuous functions, function algebras [See also 46E25]46Jxx + { 46J15Banach algebras of differentiable functionsBanach algebras of differentiable or analytic functions, ${H}^p$-spaces [See also 30D55, 30H05, 32A35, 32A37, 32A38, 42B30]46Jxx * " 46J20Ideals of commutative topological algebrasIdeals, maximal ideals, boundaries46Jxx 3 3 46J25Representations of commutative topological algebrasRepresentations of commutative topological algebras46Jxx / 46J30Subalgebras of commutative topological algebrasSubalgebras46Jxx = = 46J40Structure, classification of commutative topological algebrasStructure, classification of commutative topological algebras46Jxx 46J45Radical Banach algebrasRadical Banach algebras46Jxx @ & 46J99Commutative Banach algebras and commutative topological algebrasNone of the above, but in this section46Jxx @ Q 46JxxCommutative Banach algebras and commutative topological algebrasCommutative Banach algebras and commutative topological algebras [See also 46E25]46-XX ' 6 46K05General theory of rings with involutionGeneral theory of topological algebras with involution46Kxx ( 7 46K10Representations of rings with involutionRepresentations of topological algebras with involution46Kxx 46K15Hilbert algebrasHilbert algebras46Kxx 8 8 46K50Nonselfadjoint (sub)algebras in algebras with involutionNonselfadjoint (sub)algebras in algebras with involution46Kxx 6 N 46K70Nonassociative topological algebras with an involutionNonassociative topological algebras with an involution [See also 46H70, 46L70]46Kxx % & 46K99Rings and algebras with an involutionNone of the above, but in this section46Kxx 3 D 46KxxTopological (rings and) algebras with an involutionTopological (rings and) algebras with an involution [See also 16W10]46-XX 46L05General theory of C*-algebrasGeneral theory of $C^*$-algebras46Lxx ! 46L06Tensor products of C*-algebrasTensor products of $C^*$-algebras46Lxx46L05,46M051 < 46L07Operator spaces etc.Operator spaces and completely bounded maps [See also 47L25]46Lxx46L05,46B28,47D15,47D251
46L08C*-modules$C^*$-modules46Lxx46L05,46H251 46L09Free products of C*-algebrasFree products of $C^*$-algebras46Lxx46L05,46M991 & & 46L10General theory of von Neumann algebrasGeneral theory of von Neumann algebras46Lxx 46L30States of C*-algebrasStates46Lxx * * 46L35Classifications and factors of C*-algebrasClassifications of $C^*$-algebras, factors46Lxx # # 46L37Subfactors and their classificationSubfactors and their classification46Lxx
46L40Automorphisms of C*-algebrasAutomorphisms46Lxx $ ' 46L45Decomposition theory for C*-algebrasDecomposition theory for $C^*$-algebras46Lxx & & 46L51Noncommutative measure and integrationNoncommutative measure and integration46Lxx46L501 46L52Noncommutative function spacesNoncommutative function spaces46Lxx46L501 ) ) 46L53Noncommutative probability and statisticsNoncommutative probability and statistics46Lxx46L501 + + 46L54Free probability and free operator algebrasFree probability and free operator algebras46Lxx46L501 F 46L55Noncommutative dynamical systemsNoncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]46Lxx " C 46L57Derivations etc. in $C^*$-algebrasDerivations, dissipations and positive semigroups in $C^*$-algebras46Lxx 1 l 46L60Appl. of selfadjoint operator algebras to physicsApplications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]46Lxx 46L65Quantizations etc.Quantizations, deformations46Lxx46L60,46L991 , D 46L70Nonassociative selfadjoint operator algebrasNonassociative selfadjoint operator algebras [See also 46H70, 46K70]46Lxx g 46L80K-theory and operator algebras$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]46Lxx 6 46L85Noncommutative topologyNoncommutative topology [See also 58B32, 58B34, 58J22]46Lxx $ C 46L87Noncommutative differential geometryNoncommutative differential geometry [See also 58B32, 58B34, 58J22]46Lxx = a 46L89Other "noncommutative" mathematics based on C*-algebra theoryOther ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]46Lxx & 46L99Selfadjoint operator algebrasNone of the above, but in this section46Lxx j 46LxxSelfadjoint operator algebrasSelfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.) [See also 22D25, 47Lxx]46-XX , . 46M05Tensor products of topological linear spacesTensor products [See also 46A32, 46B28, 47A80]46Mxx
% 46M07UltraproductsUltraproducts [See also 46B08, 46S20]46Mxx D 1 46M10Projective / injective objects in categories of topol. linear spacesProjective and injective objects [See also 46A22]46Mxx 3 P 46M15Functors on categories of topological linear spacesCategories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}46Mxx * D 46M18Homological methods in functional analysisHomological methods (exact sequences, right inverses, lifting, etc.)46Mxx46M20,46M991 4 ’ 46M20Methods of algebraic topology in functional analysisMethods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]46Mxx 3 D 46M35Abstract interpolation of topological linear spacesAbstract interpolation of topological vector spaces [See also 46B70]46Mxx < 0 46M40Inductive and projective limits of topological linear spacesInductive and projective limits [See also 46A13]46Mxx * & 46M99Categorical methods in functional analysisNone of the above, but in this section46Mxx * B 46MxxCategorical methods in functional analysisMethods of category theory in functional analysis [See also 18-XX]46-XX B R 46N10Appl. of functional analysis in optimization and math. programmingApplications in optimization, convex analysis, mathematical programming, economics46Nxx C 3 46N20Appl. of functional analysis to differential and integral equationsApplications to differential and integral equations46Nxx A 1 46N30Appl. of functional analysis in probability theory and statisticsApplications in probability theory and statistics46Nxx 2 3 46N40Appl. of functional analysis in numerical analysisApplications in numerical analysis [See also 65Jxx]46Nxx / 46N50Appl. of functional analysis in quantum physicsApplications in quantum physics46Nxx 3 # 46N55Appl. of functional analysis in statistical physicsApplications in statistical physics46Nxx : * 46N60Appl. of functional analysis in biology and other sciencesApplications in biology and other sciences46Nxx & 46N99Appl. of functional analysisNone of the above, but in this section46Nxx B 46NxxAppl. of functional analysisMiscellaneous applications of functional analysis [See also 47Nxx]46-XX : 46S10Functional analysis over fields (not R, C, or quaternions)Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]46Sxx 0 46S20Nonstandard functional analysisNonstandard functional analysis [See also 03H05]46Sxx 1 46S30Constructive functional analysisConstructive functional analysis [See also 03F60]46Sxx * 46S40Fuzzy functional analysisFuzzy functional analysis [See also 03E72]46Sxx 2 9 46S50Functional analysis in probabilistic metric spacesFunctional analysis in probabilistic metric linear spaces46Sxx ) _ 46S60Functional analysis on "super"-structuresFunctional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]46Sxx46S99,58A50,58C501 & 46S99Nonclassical functional analysisNone of the above, but in this section46Sxx B 46SxxNonclassical functional analysisOther (nonclassical) types of functional analysis [See also 47Sxx]46-XX ? D 46T05Infinite-dimensional manifolds in nonlinear functional analysisInfinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]46Txx58Bxx,58Dxx1 6 46T10Manifolds of mappings in nonlinear functional analysisManifolds of mappings46Txx58Dxx1 7 ~ 46T12Measures and integrals in nonlinear functional analysisMeasure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]46Txx28C20,46G12,60Hxx1 C 3 46T20Continuous and differentiable maps in nonlinear functional analysisContinuous and differentiable maps [See also 46G05]46Txx46G05,58Cxx1 1 ! 46T25Holomorphic maps in nonlinear functional analysisHolomorphic maps [See also 46G20]46Txx46G20,58C101 ; L 46T30Distributions and generalized functions on nonlinear spacesDistributions and generalized functions on nonlinear spaces [See also 46Fxx]46Txx46Fxx,58C991 & 46T99Nonlinear functional analysisNone of the above, but in this section46Txx46G99,58B99,58C99,58D991 C 46TxxNonlinear functional analysisNonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]46-XX ! G 47-00Reference works (operator theory)General reference works (handbooks, dictionaries, bibliographies, etc.)47-XX ; 47-01Textbooks (operator theory)Instructional exposition (textbooks, tutorial papers, etc.)47-XX % 1 47-02Research monographs (operator theory)Research exposition (monographs, survey articles)47-XX U 47-03Historical (operator theory)Historical (must also be assigned at least one classification number from Section 01)47-XX / X 47-04Machine computation, programs (operator theory)Explicit machine computation and programs (not the theory of computation or programming)47-XX , + 47-06Proceedings of conferences (operator theory)Proceedings, conferences, collections, etc.47-XX 47-99Operator theoryOperator theory 47-XXOperator theoryOperator theory " I 47A05General theory of linear operatorsGeneral (adjoints, conjugates, products, inverses, domains, ranges, etc.)47Axx / 47A06multivalued linear operatorsLinear relations (multivalued linear operators)47Axx47A05,47A991 " + 47A07Forms on topological linear spacesForms (bilinear, sesquilinear, multilinear)47Axx47A05,47A991 * 47A10Spectrum and resolvent of linear operatorsSpectrum, resolvent47Axx 47A11Local spectral propertiesLocal spectral properties47Axx # ! 47A12Numerical range of linear operatorsNumerical range, numerical radius47Axx ; 47A13Several-variable spectral theorySeveral-variable operator theory (spectral, Fredholm, etc.)47Axx ' 47A15Invariant subspaces of linear operatorsInvariant subspaces47Axx 47A16(Hyper-)cyclic vectorsCyclic and hypercyclic vectors47Axx47A99,47B991 3 # 47A20Extensions and related concepts of linear operatorsDilations, extensions, compressions47Axx
47A25Spectral setsSpectral sets47Axx . 47A30Operator norms and inequalitiesNorms (inequalities, more than one norm, etc.)47Axx " & 47A35Ergodic theory of linear operatorsErgodic theory [See also 28Dxx, 37Axx]47Axx % 0 47A40Scattering theory of linear operatorsScattering theory [See also 34L25, 35P25, 81Uxx]47Axx > > 47A45Canonical models for contractions and nonselfadjoint operatorsCanonical models for contractions and nonselfadjoint operators47Axx 7 U 47A46Chains (nests) of projections or of invariant subspacesChains (nests) of projections or of invariant subspaces, integrals along chains, etc.47Axx47A15,47A45,47A991 f 47A48Operator colligationsOperator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.47Axx 5 K 47A50Equations and inequalities involving linear operatorsEquations and inequalities involving linear operators, with vector unknowns47Axx " 47A52Ill-posed problems etc.Ill-posed problems, regularization47Axx47A50,65J10,65J201 ) B 47A53(Semi-)Fredholm operators; index theories(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]47Axx ' 47A55Perturbation theory of linear operatorsPerturbation theory47Axx + 47A56Functions whose values are linear operatorsFunctions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)47Axx @ f 47A57Operator methods in interpolation, moment and extension problemsOperator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]47Axx 47A58Operator approximation theoryOperator approximation theory47Axx 47A60Functional calculus of operatorsFunctional calculus47Axx < < 47A62Equations involving linear operators, with operator unknownsEquations involving linear operators, with operator unknowns47Axx 47A63Operator inequalities, etc.Operator inequalities47Axx47A631 ' 47A64Operator means etc.Operator means, shorted operators, etc.47Axx47A631 $ 47A65Structure theory of linear operatorsStructure theory47Axx $ T 47A66(Non)quasitriangular operators, etc.Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators47Axx ) 47A67Representation theory of linear operatorsRepresentation theory47Axx ( H 47A68Factorization theory of linear operatorsFactorization theory (including Wiener-Hopf and spectral factorizations)47Axx , = 47A70Eigenfunction expansions of linear operators(Generalized) eigenfunction expansions; rigged Hilbert spaces47Axx & $ 47A75Eigenvalue problems (linear operators)Eigenvalue problems [See also 49R50]47Axx - 47A80Tensor products of operatorsTensor products of operators [See also 46M05]47Axx ) & 47A99General theory of single linear operatorsNone of the above, but in this section47Axx ) " 47AxxGeneral theory of single linear operatorsGeneral theory of linear operators47-XX , … 47B06Riesz operators and eigenvalue distributionsRiesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators47Bxx + + 47B07Operators defined by compactness propertiesOperators defined by compactness properties47Bxx + y 47B10Operators defined by summability propertiesOperators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]47Bxx M 47B15Hermitian and normal operatorsHermitian and normal operators (spectral measures, functional calculus, etc.)47Bxx / 47B20Subnormal operators, etc.Subnormal operators, hyponormal operators, etc.47Bxx / / 47B25Symmetric and selfadjoint operators (unbounded)Symmetric and selfadjoint operators (unbounded)47Bxx . ‡ 47B32Operators in reproducing-kernel Hilbert spacesOperators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]47Bxx47A45,47B38,46E221 47B33Composition operatorsComposition operators47Bxx47B381 47B34Kernel operatorsKernel operators47Bxx47B381 ‡ 47B35Toeplitz operators, etc.Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]47Bxx ) = 47B36Jacobi (tridiagonal) operators (matrices)Jacobi (tridiagonal) operators (matrices) and generalizations47Bxx39A70,47B25,47B37,47B391 " Q 47B37Operators on sequence spaces, etc.Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)47Bxx & 47B38Operators on function spacesOperators on function spaces (general)47Bxx & % 47B39Difference operators (operator theory)Difference operators [See also 39A70]47Bxx H 47B40Decomposable operators, etc.Spectral operators, decomposable operators, well-bounded operators, etc.47Bxx " 0 47B44Accretive operators, etc. (linear)Accretive operators, dissipative operators, etc.47Bxx @ 4 47B47Derivations and linear operators defined by algebraic conditionsCommutators, derivations, elementary operators, etc.47Bxx 47B48Operators on Banach algebrasOperators on Banach algebras47Bxx 0 1 47B49Transformers (=operators on spaces of operators)Transformers (= operators on spaces of operators)47Bxx . > 47B50Operators on a space with an indefinite metricOperators on spaces with an indefinite metric [See also 46C50]47Bxx 47B60Operators on ordered spacesOperators on ordered spaces47Bxx $ . 47B65Positive and order bounded operatorsPositive operators and order-bounded operators47Bxx ! 47B80Random operatorsRandom operators [See also 60H25]47Bxx # & 47B99Special classes of linear operatorsNone of the above, but in this section47Bxx # # 47BxxSpecial classes of linear operatorsSpecial classes of linear operators47-XX ! 47C05Operators in topological algebrasOperators in algebras47Cxx 47C10Operators in *-algebrasOperators in $^*$-algebras47Cxx + 47C15Operators in C*-algebras, etc.Operators in $C^*$- or von Neumann algebras47Cxx 8 & 47C99Single linear operators as elements of algebraic systemsNone of the above, but in this section47Cxx < < 47CxxIndividual linear operators as elements of algebraic systemsIndividual linear operators as elements of algebraic systems47-XX ^ 47D03(Semi)groups of linear operatorsGroups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}47Dxx 7 O 47D06One-parameter semigroups and linear evolution equationsOne-parameter semigroups and linear evolution equations [See also 34G10, 34K30]47Dxx % [ 47D07Markov semigroups of linear operatorsMarkov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}47Dxx ( & 47D08Schr\"odinger and Feynman-Kac semigroupsSchrödinger and Feynman-Kac semigroups47Dxx35J10,47D06,47D071 : T 47D09Operator cosine functions and higher-order Cauchy problemsOperator sine and cosine functions and higher-order Cauchy problems [See also 34G10]47Dxx 47D60C-semigroups$C$-semigroups47Dxx47D03,47D061 47D62Integrated semigroupsIntegrated semigroups47Dxx47D03,47D061 % & 47D99Algebraic systems of linear operatorsNone of the above, but in this section47Dxx % Q 47DxxAlgebraic systems of linear operatorsGroups and semigroups of linear operators, their generalizations and applications47-XX 7 47E05Ordinary differential operatorsOrdinary differential operators [See also 34Bxx, 34Lxx]47-XX 6 47F05Partial differential operatorsPartial differential operators [See also 35Pxx, 58Jxx]47-XX # 47G10Integral operatorsIntegral operators [See also 45P05]47Gxx D 47G20Integro-differential operatorsIntegro-differential operators [See also 34K30, 35R10, 45J05, 45K05]47Gxx 4 47G30Pseudodifferential operatorsPseudodifferential operators [See also 35Sxx, 58Jxx]47Gxx , & 47G99Integral operators and their generalizationsNone of the above, but in this section47Gxx , Q 47GxxIntegral operators and their generalizationsIntegral, integro-differential, and pseudodifferential operators [See also 58Jxx]47-XX 3 47H04Set-valued operatorsSet-valued operators [See also 28B20, 54C60, 58C06]47Hxx , , 47H05Monotone operators (with respect to duality)Monotone operators (with respect to duality)47Hxx % 0 47H06Accretive operators, etc. (nonlinear)Accretive operators, dissipative operators, etc.47Hxx 7 c 47H07Positive operators on ordered topological linear spacesMonotone and positive operators on ordered Banach spaces or other ordered topological vector spaces47Hxx * ³ 47H09Mappings defined by "shrinking" propertiesNonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.)47Hxx C 3 47H10Fixed point theorems for nonlinear operators on topol.linear spacesFixed-point theorems [See also 54H25, 55M20, 58C30]47Hxx
% 47H11Degree theoryDegree theory [See also 55M25, 58C30]47Hxx $ $ 47H14Perturbations of nonlinear operatorsPerturbations of nonlinear operators47Hxx47H15,47H991 ! ! 47H20Semigroups of nonlinear operatorsSemigroups of nonlinear operators47Hxx l 47H30Particular nonlinear operatorsParticular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.) [See also 45Gxx, 45P05]47Hxx ! 47H40Random operatorsRandom operators [See also 60H25]47Hxx 47H50Potential operatorsPotential operators47Hxx47H15,47H991 $ 5 47H60Multilinear and polynomial operatorsMultilinear and polynomial operators [See also 46G25]47Hxx46G20,47H991 & 47H99Nonlinear operatorsNone of the above, but in this section47Hxx h 47HxxNonlinear operatorsNonlinear operators and their properties {For global and geometric aspects, see 58-XX, especially 58Cxx}47-XX 1 1 47J05Equations involving nonlinear operators (general)Equations involving nonlinear operators (general)47Jxx47H151 47J06Nonlinear ill-posed problemsNonlinear ill-posed problems47Jxx47H15,47H17,65J15,65J201 7 R 47J07Abstract inverse mapping and implicit function theoremsAbstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]47Jxx46G05,47H15,58C151 47J10Nonlinear eigenvalue problemsNonlinear eigenvalue problems47Jxx47H12,58E07,58E091 3 47J15Abstract bifurcation theoryAbstract bifurcation theory [See also 58E07, 58E09]47Jxx47H15,58E07,58E091 * S 47J20Inequalities involving nonlinear operatorsVariational and other types of inequalities involving nonlinear operators (general)47Jxx47H19,49J401 : : 47J25Methods for solving nonlinear operator equations (general)Methods for solving nonlinear operator equations (general)47Jxx47H17,65J151 $ 47J30Variational methodsVariational methods [See also 58Exx]47Jxx47H15,58Exx1 _ 47J35Nonlinear evolution equationsNonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 58D25]47Jxx34G20,35R20,58D251 # # 47J40Equations with hysteresis operatorsEquations with hysteresis operators47Jxx47H301 & & 47J99None of the above, but in this sectionNone of the above, but in this section47Jxx47H991 8 w 47JxxEquations and inequalities involving nonlinear operatorsEquations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}47-XX 5 47L05Linear spaces of operatorsLinear spaces of operators [See also 46A32 and 46B28]47Lxx46B28,47D151 " 3 47L07Convex sets and cones of operatorsConvex sets and cones of operators [See also 46A55]47Lxx47D201 , J 47L10Algebras of operators on Banach spaces, etc.Algebras of operators on Banach spaces and other topological linear spaces47Lxx47D301 ' ' 47L15Operator algebras with symbol structureOperator algebras with symbol structure47Lxx46L99,47D25,47D301 47L20Operator idealsOperator ideals47Lxx47D501 , > 47L25Operator spaces (=matricially normed spaces)Operator spaces (= matricially normed spaces) [See also 46L07]47Lxx46L05,47D251 , , 47L30Abstract operator algebras on Hilbert spacesAbstract operator algebras on Hilbert spaces47Lxx46Lxx,47D251 47L35Nest algebras, CSL algebrasNest algebras, CSL algebras47Lxx47D251 - - 47L40Limit algebras, subalgebras of $C^*$-algebrasLimit algebras, subalgebras of $C^*$-algebras47Lxx46L05,47D251 ? ? 47L45Dual algebras; weakly closed singly generated operator algebrasDual algebras; weakly closed singly generated operator algebras47Lxx47D271 47L50Dual spaces of operator algebrasDual spaces of operator algebras47Lxx47D351 5 5 47L55Representations of (nonselfadjoint) operator algebrasRepresentations of (nonselfadjoint) operator algebras47Lxx47D251 > > 47L60Algebras of unbounded operators; partial algebras of operatorsAlgebras of unbounded operators; partial algebras of operators47Lxx47D401 4 4 47L65Crossed product algebras (analytic crossed products)Crossed product algebras (analytic crossed products)47Lxx46L05,46L55,47D251 / / 47L70Nonassociative nonselfadjoint operator algebrasNonassociative nonselfadjoint operator algebras47Lxx46K99,47D251 & & 47L75Other nonselfadjoint operator algebrasOther nonselfadjoint operator algebras47Lxx47D251 ' V # 47L80Algebras of specific types of operatorsAlgebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)47Lxx46L05,47B35,47D30,47D25,47G10,47G301 , , 47L90Applications of operator algebras to physicsApplications of operator algebras to physics47Lxx47D45,47N50,47N551 & & 47L99None of the above, but in this sectionNone of the above, but in this section47Lxx47D991 ' 9 47LxxLinear spaces and algebras of operatorsLinear spaces and algebras of operators [See also 46Lxx]47-XX A R 47N10Appl. of operator theory in optimization, math. programming, etc.Applications in optimization, convex analysis, mathematical programming, economics47Nxx ? 3 47N20Appl. of operator theory to differential and integral equationsApplications to differential and integral equations47Nxx = 1 47N30Appl. of operator theory in probability theory and statisticsApplications in probability theory and statistics47Nxx . 3 47N40Appl. of operator theory in numerical analysisApplications in numerical analysis [See also 65Jxx]47Nxx + 47N50Appl. of operator theory in quantum physicsApplications in quantum physics47Nxx / # 47N55Appl. of operator theory in statistical physicsApplications in statistical physics47Nxx 6 * 47N60Appl. of operator theory in biology and other sciencesApplications in biology and other sciences47Nxx : . 47N70Appl. of operator theory in systems theory, circuits, etc.Applications in systems theory, circuits, etc.47Nxx & 47N99Appl. of operator theoryNone of the above, but in this section47Nxx > 47NxxAppl. of operator theoryMiscellaneous applications of operator theory [See also 46Nxx]47-XX @ m 47S10Operator theory over fields other than R or C or the quaternionsOperator theory over fields other than R, C or the quaternions; non-Archimedean operator theory47Sxx , 47S20Nonstandard operator theoryNonstandard operator theory [See also 03H05]47Sxx - 47S30Constructive operator theoryConstructive operator theory [See also 03F60]47Sxx & 47S40Fuzzy operator theoryFuzzy operator theory [See also 03E72]47Sxx 5 5 47S50Operator theory in probabilistic metric linear spacesOperator theory in probabilistic metric linear spaces47Sxx & 47S99Nonclassical operator theoryNone of the above, but in this section47Sxx > 47SxxNonclassical operator theoryOther (nonclassical) types of operator theory [See also 46Sxx]47-XX ( G 49-00Reference works (calculus of variations)General reference works (handbooks, dictionaries, bibliographies, etc.)49-XX " ; 49-01Textbooks (calculus of variations)Instructional exposition (textbooks, tutorial papers, etc.)49-XX , 1 49-02Research monographs (calculus of variations)Research exposition (monographs, survey articles)49-XX # U 49-03Historical (calculus of variations)Historical (must also be assigned at least one classification number from Section 01)49-XX 6 X 49-04Machine computation, programs (calculus of variations)Explicit machine computation and programs (not the theory of computation or programming)49-XX 3 + 49-06Proceedings of conferences (calculus of variations)Proceedings, conferences, collections, etc.49-XX 8 8 49-99Calculus of variations and optimal control; optimizationCalculus of variations and optimal control; optimization e 49-XXCalculus of variationsCalculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] 5 ) 49J05Free problems in one independent variable (existence)Free problems in one independent variable49Jxx : 2 49J10Free problems in several independent variables (existence)Free problems in two or more independent variables49Jxx - B 49J15Optimal control problems with ODE (existence)Optimal control problems involving ordinary differential equations49Jxx - A 49J20Optimal control problems with PDE (existence)Optimal control problems involving partial differential equations49Jxx < 5 49J22Optimal control problems with integral equations (existence)Optimal control problems involving integral equations49Jxx A K 49J24Optimal control problems with differential inclusions (existence)Optimal control problems involving differential inclusions [See also 34A60]49Jxx D U 49J25Optimal control problems with equations with ret. arguments (exist.)Optimal control problems involving equations with retarded arguments [See also 34K35]49Jxx 7 3 49J27Optimal control problems in abstract spaces (existence)Problems in abstract spaces [See also 90C48, 93C25]49Jxx = ` 49J30Optimal solutions belonging to restricted classes (existence)Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)49Jxx 49J35Minimax problems (existence)Minimax problems49Jxx 6 G 49J40Variational methods including variational inequalitiesVariational methods including variational inequalities [See also 47J20]49Jxx < < 49J45Optimal control problems inv. semicontinuity and convergenceMethods involving semicontinuity and convergence; relaxation49Jxx % = 49J50Frechet and Gateaux differentiabilityFréchet and Gateaux differentiability [See also 46G05, 58C20]49Jxx 6 + 49J52Nonsmooth analysis (other weak concepts of optimality)Nonsmooth analysis [See also 46G05, 58C50]49Jxx # I 49J53Set-valued and variational analysisSet-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]49Jxx49J52,49J27,49K271 & . 49J55Optimal stochastic control (existence)Problems involving randomness [See also 93E20]49Jxx & & 49J99Existence theory for optimal solutionsNone of the above, but in this section49Jxx & 49JxxExistence theory for optimal solutionsExistence theories49-XX 7 ) 49K05Free problems in one independent variable (nec./ suff.)Free problems in one independent variable49Kxx < 2 49K10Free problems in several independent variables (nec./ suff.)Free problems in two or more independent variables49Kxx / 2 49K15Optimal control problems with ODE (nec./ suff.)Problems involving ordinary differential equations49Kxx / 1 49K20Optimal control problems with PDE (nec./ suff.)Problems involving partial differential equations49Kxx > % 49K22Optimal control problems with integral equations (nec./ suff.)Problems involving integral equations49Kxx C ; 49K24Optimal control problems with differential inclusions (nec./ suff.)Problems involving differential inclusions [See also 34A60]49Kxx A E 49K25Optimal control problems with equations with ret.arguments (nec.)Problems involving equations with retarded arguments [See also 34K35]49Kxx 9 3 49K27Optimal control problems in abstract spaces (nec./ suff.)Problems in abstract spaces [See also 90C48, 93C25]49Kxx 1 1 49K30Optimal solutions belonging to restricted classesOptimal solutions belonging to restricted classes49Kxx , 49K35Minimax problems (necessity and sufficiency)Minimax problems49Kxx A 7 49K40Sensitivity of optimal solutions in the presence of perturbationsSensitivity, stability, well-posedness [See also 90C31]49Kxx 6 . 49K45Optimal stochastic control (necessity and sufficiency)Problems involving randomness [See also 93E20]49Kxx 2 & 49K99Necessary and sufficient conditions for optimalityNone of the above, but in this section49Kxx 2 = 49KxxNecessary and sufficient conditions for optimalityNecessary conditions and sufficient conditions for optimality49-XX : 49L20Dynamic programming method (infinite-dimensional problems)Dynamic programming method49Lxx 49L25Viscosity solutionsViscosity solutions49Lxx & 49L99Caratheodory theories, etc.None of the above, but in this section49Lxx 7 49LxxCaratheodory theories, etc.Hamilton-Jacobi theories, including dynamic programming49-XX A % 49M05Methods of successive approximation based on necessary conditionsMethods based on necessary conditions49Mxx 2 2 49M15Methods of Newton-Raphson, Galerkin and Ritz typesMethods of Newton-Raphson, Galerkin and Ritz types49Mxx 49M20Methods of relaxation typeMethods of relaxation type49Mxx 49M25Finite difference methodsDiscrete approximations49Mxx 49M27Decomposition methodsDecomposition methods49Mxx 49M29Multiplier methodsMethods involving duality49Mxx A I 49M30Methods of successive approximation, not based on necessary cond.Other methods, not based on necessary conditions (penalty function, etc.)49Mxx % = 49M37Methods of nonlinear programming typeMethods of nonlinear programming type [See also 90C30, 65Kxx]49Mxx $ & 49M99Methods of successive approximationsNone of the above, but in this section49Mxx $ < 49MxxMethods of successive approximationsMethods of successive approximations [See also 90Cxx, 65Kxx]49-XX 0 49N05Linear optimal control problemsLinear optimal control problems [See also 93C05]49Nxx ) 49N10Linear-quadratic optimal control problemsLinear-quadratic problems49Nxx 49N15Duality theory (optimization)Duality theory49Nxx 49N20Periodic optimizationPeriodic optimization49Nxx " " 49N25Impulsive optimal control problemsImpulsive optimal control problems49Nxx 4 5 49N30Optimal control problems with incomplete informationProblems with incomplete information [See also 93C41]49Nxx + 49N35Closed-loop controlsOptimal feedback synthesis [See also 93B52]49Nxx * 49N45Inverse problems in calculus of variationsInverse problems49Nxx 5 49N60Regularity of solutions in the calculus of variationsRegularity of solutions49Nxx 49N70Differential gamesDifferential games49Nxx90D251 49N75Pursuit and evasion gamesPursuit and evasion games49Nxx90D261 6 N 49N90Applications of optimal control and differential gamesApplications of optimal control and differential games [See also 90C90, 93C95]49Nxx49N55,90D801 ) & 49N99Miscellaneous problems of optimal controlNone of the above, but in this section49Nxx 49NxxMiscellaneous topicsMiscellaneous topics49-XX ) ( 49Q05Minimal surfaces (calculus of variations)Minimal surfaces [See also 53A10, 58E12]49Qxx 5 C 49Q10Optimization of the shape other than minimal surfacesOptimization of shapes other than minimal surfaces [See also 90C90]49Qxx 49Q12Sensitivity analysisSensitivity analysis49Qxx . l 49Q15Geometric measure and integration theory, etc.Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]49Qxx ; = 49Q20Variational problems in geometric measure-theoretic settingVariational problems in a geometric measure-theoretic setting49Qxx # & 49Q99Manifolds in calculus of variationsNone of the above, but in this section49Qxx # 49QxxManifolds in calculus of variationsManifolds [See also 58Exx]49-XX 0 A # 49R50Variational methods for eigenvalues of operatorsVariational methods for eigenvalues of operators [See also 47A75]49-XX49Rxx,49R05,49R10,49R15,49R20,49R991 ! ! 49S05Variational principles of physicsVariational principles of physics49-XX G 51-00Reference works (geometry)General reference works (handbooks, dictionaries, bibliographies, etc.)51-XX ; 51-01Textbooks (geometry)Instructional exposition (textbooks, tutorial papers, etc.)51-XX 1 51-02Research monographs (geometry)Research exposition (monographs, survey articles)51-XX U 51-03Historical (geometry)Historical (must also be assigned at least one classification number from Section 01)51-XX ( X 51-04Machine computation, programs (geometry)Explicit machine computation and programs (not the theory of computation or programming)51-XX % + 51-06Proceedings of conferences (geometry)Proceedings, conferences, collections, etc.51-XX 51-99GeometryGeometry , 51-XXGeometryGeometry {For algebraic geometry, see 14-XX} + ( 51A05General theory of linear incidence geometryGeneral theory and projective geometries51Axx / ( 51A10Homomorphism, etc. in linear incidence geometryHomomorphism, automorphism and dualities51Axx % 51A15Geometric structures with parallelismStructures with parallelism51Axx ! 51A20Configuration theorems (geometry)Configuration theorems51Axx * & 51A25Algebraization (linear incidence geometry)Algebraization [See also 12Kxx, 20N05]51Axx # # 51A30Desarguesian and Pappian geometriesDesarguesian and Pappian geometries51Axx - - 51A35Non-Desarguesian affine and projective planesNon-Desarguesian affine and projective planes51Axx 51A40Translation planes, etc.Translation planes and spreads51Axx : : 51A45Incidence structures imbeddable into projective geometriesIncidence structures imbeddable into projective geometries51Axx 4 4 51A50Polar geometry, symplectic spaces, orthogonal spacesPolar geometry, symplectic spaces, orthogonal spaces51Axx & 51A99Linear incidence geometryNone of the above, but in this section51Axx 51AxxLinear incidence geometryLinear incidence geometry51-XX . 51B05General theory of nonlinear incidence geometryGeneral theory51Bxx 51B10Moebius geometriesMöbius geometries51Bxx 51B15Laguerre geometriesLaguerre geometries51Bxx 51B20Minkowski geometriesMinkowski geometries51Bxx 51B25Lie geometriesLie geometries51Bxx & 51B99Nonlinear incidence geometryNone of the above, but in this section51Bxx 51BxxNonlinear incidence geometryNonlinear incidence geometry51-XX
* 51C05Ring geometryRing geometry (Hjelmslev, Barbilian, etc.)51-XX 51D05Abstract geometriesAbstract (Maeda) geometries51Dxx ' ' 51D10Abstract geometries with exchange axiomAbstract geometries with exchange axiom51Dxx $ $ 51D15Abstract geometries with parallelismAbstract geometries with parallelism51Dxx 0 51D20Combinatorial geometriesCombinatorial geometries [See also 05B25, 05B35]51Dxx & 51D25Lattices of subspaces (geometry)Lattices of subspaces [See also 05B35]51Dxx ( 9 51D30Continuous geometries and related topicsContinuous geometries and related topics [See also 06Cxx]51Dxx & 51D99Geometric closure systemsNone of the above, but in this section51Dxx 51DxxGeometric closure systemsGeometric closure systems51-XX & 51E05General block designs (geometry)General block designs [See also 05B05]51Exx 51E10Steiner systems (geometry)Steiner systems51Exx - 51E12Generalized quadranglesGeneralized quadrangles, generalized polygons51Exx ; : 51E14Finite partial geometries (general), nets, fractial spreadsFinite partial geometries (general), nets, partial spreads51Exx 51E15Affine and projective planesAffine and projective planes51Exx 4 E 51E20Combinatorial structures in finite projective spacesCombinatorial structures in finite projective spaces [See also 05Bxx]51Exx 51E21Blocking sets, ovals, k-arcsBlocking sets, ovals, $k$-arcs51Exx & 7 51E22Linear codes and caps in Galois spacesLinear codes and caps in Galois spaces [See also 94B05]51Exx ' 51E23Spreads and packing problems (geometry)Spreads and packing problems51Exx & & 51E24Buildings and the geometry of diagramsBuildings and the geometry of diagrams51Exx ! ! 51E25Other finite nonlinear geometriesOther finite nonlinear geometries51Exx 51E26Other finite linear geometriesOther finite linear geometries51Exx ! 2 51E30Other finite incidence structuresOther finite incidence structures [See also 05B30]51Exx & 51E99Finite geometryNone of the above, but in this section51Exx 0 0 51ExxFinite geometry and special incidence structuresFinite geometry and special incidence structures51-XX 51F05Absolute planesAbsolute planes51Fxx 51F10Absolute spacesAbsolute spaces51Fxx _ 51F15Reflection groups and geometriesReflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]51Fxx ' - 51F20Congruence and orthogonality (geometry)Congruence and orthogonality [See also 20H05]51Fxx ( . 51F25Orthogonal and unitary groups (geometry)Orthogonal and unitary groups [See also 20H05]51Fxx & 51F99Metric geometryNone of the above, but in this section51Fxx 51FxxMetric geometryMetric geometry51-XX 7 51G05Ordered geometriesOrdered geometries (ordered incidence structures, etc.)51-XX & 51H05General theory of topological geometryGeneral theory51Hxx ' ' 51H10Topological linear incidence structuresTopological linear incidence structures51Hxx * * 51H15Topological nonlinear incidence structuresTopological nonlinear incidence structures51Hxx # 4 51H20Topological geometries on manifoldsTopological geometries on manifolds [See also 57-XX]51Hxx ( @ 51H25Geometries with differentiable structureGeometries with differentiable structure [See also 53Cxx, 53C70]51Hxx , = 51H30Geometries with algebraic manifold structureGeometries with algebraic manifold structure [See also 14-XX]51Hxx & 51H99Topological geometryNone of the above, but in this section51Hxx 51HxxTopological geometryTopological geometry51-XX " 51J05General theory of incidence groupsGeneral theory51Jxx 51J10Projective incidence groupsProjective incidence groups51Jxx 51J15Kinematic spacesKinematic spaces51Jxx C G 51J20Representation of incidence groups by near-fields and near-algebrasRepresentation by near-fields and near-algebras [See also 12K05, 16Y30]51Jxx & 51J99Incidence groupsNone of the above, but in this section51Jxx 51JxxIncidence groupsIncidence groups51-XX # 51K05General theory of distance geometryGeneral theory51Kxx 51K10Synthetic differential geometrySynthetic differential geometry51Kxx & 51K99Distance geometryNone of the above, but in this section51Kxx 51KxxDistance geometryDistance geometry51-XX . . 51L05Geometry of orders of nondifferentiable curvesGeometry of orders of nondifferentiable curves51Lxx 51L10Directly differentiable curvesDirectly differentiable curves51Lxx $ & 51L15n-vertex theorems via direct methods$n$-vertex theorems via direct methods51Lxx 51L20Geometry of orders of surfacesGeometry of orders of surfaces51Lxx & 51L99Geometric order structuresNone of the above, but in this section51Lxx + 51LxxGeometric order structuresGeometric order structures [See also 53C75]51-XX + + 51M04Elementary problems in Euclidean geometriesElementary problems in Euclidean geometries51Mxx 2 2 51M05Euclidean geometries (general) and generalizationsEuclidean geometries (general) and generalizations51Mxx 9 9 51M09Elementary problems in hyperbolic and elliptic geometriesElementary problems in hyperbolic and elliptic geometries51Mxx @ @ 51M10Hyperbolic and elliptic geometries (general) and generalizationsHyperbolic and elliptic geometries (general) and generalizations51Mxx 51M15Geometric constructionsGeometric constructions51Mxx - C 51M16Inequalities and extremum problems (geometry)Inequalities and extremum problems {For convex problems, see 52A40}51Mxx M 51M20Regular figures in spacePolyhedra and polytopes; regular figures, division of spaces [See also 51F15]51Mxx " ( 51M25Length, area and volume (geometry)Length, area and volume [See also 26B15]51Mxx ) : 51M30Line geometries and their generalizationsLine geometries and their generalizations [See also 53A25]51Mxx C 51M35Synthetic treatment of fundamental manifolds in projective geometrySynthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]51Mxx & 51M99Real and complex geometryNone of the above, but in this section51Mxx 51MxxReal and complex geometryReal and complex geometry51-XX , 51N05Descriptive geometryDescriptive geometry [See also 65D17, 68U07]51Nxx 51N10Affine analytic geometryAffine analytic geometry51Nxx 51N15Projective analytic geometryProjective analytic geometry51Nxx 51N20Euclidean analytic geometryEuclidean analytic geometry51Nxx 2 2 51N25Analytic geometry with other transformation groupsAnalytic geometry with other transformation groups51Nxx 4 51N30Geometry of classical groupsGeometry of classical groups [See also 20Gxx, 14L35]51Nxx ) : 51N35Questions of classical algebraic geometryQuestions of classical algebraic geometry [See also 14Nxx]51Nxx ! & 51N99Analytic and descriptive geometryNone of the above, but in this section51Nxx ! ! 51NxxAnalytic and descriptive geometryAnalytic and descriptive geometry51-XX l 51P05Geometry and physicsGeometry and physics (should also be assigned at least one other classification number from Sections 70--86)51-XX . G 52-00Reference works (convex and discrete geometry)General reference works (handbooks, dictionaries, bibliographies, etc.)52-XX ( ; 52-01Textbooks (convex and discrete geometry)Instructional exposition (textbooks, tutorial papers, etc.)52-XX 2 1 52-02Research monographs (convex and discrete geometry)Research exposition (monographs, survey articles)52-XX ) U 52-03Historical (convex and discrete geometry)Historical (must also be assigned at least one classification number from Section 01)52-XX < X 52-04Machine computation, programs (convex and discrete geometry)Explicit machine computation and programs (not the theory of computation or programming)52-XX 9 + 52-06Proceedings of conferences (convex and discrete geometry)Proceedings, conferences, collections, etc.52-XX 52-99Convex and discrete geometryConvex and discrete geometry 52-XXConvex and discrete geometryConvex and discrete geometry - # 52A01Axiomatic and generalized geometric convexityAxiomatic and generalized convexity52Axx < * 52A05Convex sets without dimension restrictions (convex geometry)Convex sets without dimension restrictions52Axx : 9 52A07Convex sets in topological vector spaces (convex geometry)Convex sets in topological vector spaces [See also 46A55]52Axx 5 H 52A10Convex sets in 2 dimensions (including convex curves)Convex sets in $2$ dimensions (including convex curves) [See also 53A04]52Axx 7 Q 52A15Convex sets in 3 dimensions (including convex surfaces)Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45]52Axx V 52A20Convex sets in n dimensionsConvex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]52Axx 2 Z 52A21Finite dimensional Banach spaces (convex geometry)Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]52Axx ( @ 52A22Random convex sets and integral geometryRandom convex sets and integral geometry [See also 53C65, 60D05]52Axx 52A27Approximation by convex setsApproximation by convex sets52Axx < 52A30Variants of convex setsVariants of convex sets (star-shaped, ($m, n$)-convex, etc.)52Axx % 4 52A35Helly-type theorems (convex geometry)Helly-type theorems and geometric transversal theory52Axx ) ) 52A37Other problems of combinatorial convexityOther problems of combinatorial convexity52Axx & 3 52A38Length, area, volume (convex geometry)Length, area, volume [See also 26B15, 28A75, 49Q20]52Axx 2 52A39Mixed volumes and related topics (convex geometry)Mixed volumes and related topics52Axx . " 52A40Geometric inequalities, etc. (convex geometry)Inequalities and extremum problems52Axx 6 < 52A41Convex functions and convex programs (convex geometry)Convex functions and convex programs [See also 26B25, 90C25]52Axx " " 52A55Spherical and hyperbolic convexitySpherical and hyperbolic convexity52Axx & 52A99General convexityNone of the above, but in this section52Axx 52AxxGeneral geometric convexityGeneral convexity52-XX ' Q 52B05Combinatorial properties of convex setsCombinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]52Bxx 52B10Three-dimensional polytopesThree-dimensional polytopes52Bxx 52B11n-dimensional polytopes$n$-dimensional polytopes52Bxx A A 52B12Special polytopes (linear programming, centrally symmetric, etc.)Special polytopes (linear programming, centrally symmetric, etc.)52Bxx 52B15Symmetry properties of polytopesSymmetry properties of polytopes52Bxx # v 52B20Lattice polytopes (convex geometry)Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]52Bxx 52B22ShellabilityShellability52Bxx52B30,52B11,52B40,52B201 ) 52B35Gale and other diagrams (convex geometry)Gale and other diagrams52Bxx 52B40Matroids (convex geometry)Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]52Bxx : 52B45Dissections and valuationsDissections and valuations (Hilbert's third problem, etc.)52Bxx 4 ž 52B55Computational aspects related to geometric convexityComputational aspects related to convexity {For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx]52Bxx $ $ 52B60Isoperimetric problems for polytopesIsoperimetric problems for polytopes52Bxx 52B70Polyhedral manifoldsPolyhedral manifolds52Bxx & 52B99Polytopes and polyhedraNone of the above, but in this section52Bxx 52BxxPolytopes and polyhedraPolytopes and polyhedra52-XX * K 52C05Lattices and convex bodies in 2 dimensionsLattices and convex bodies in $2$ dimensions [See also 11H06, 11H31, 11P21]52Cxx * K 52C07Lattices and convex bodies in n dimensionsLattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]52Cxx 7 G 52C10Erdoes problems and related topics of discrete geometryErdös problems and related topics of discrete geometry [See also 11Hxx]52Cxx 8 > 52C15Packing and covering in 2 dimensions (discrete geometry)Packing and covering in $2$ dimensions [See also 05B40, 11H31]52Cxx 8 > 52C17Packing and covering in n dimensions (discrete geometry)Packing and covering in $n$ dimensions [See also 05B40, 11H31]52Cxx + 1 52C20Tilings in 2 dimensions (discrete geometry)Tilings in $2$ dimensions [See also 05B45, 51M20]52Cxx + 1 52C22Tilings in n dimensions (discrete geometry)Tilings in $n$ dimensions [See also 05B45, 51M20]52Cxx 52C23Quasicrystals, aperiodic tilingsQuasicrystals, aperiodic tilings52Cxx52C20,52C221 & 7 52C25Rigidity and flexibility of structuresRigidity and flexibility of structures [See also 70B15]52Cxx / / 52C26Circle packings and discrete conformal geometryCircle packings and discrete conformal geometry52Cxx52C15,52C171 , , 52C30Planar arrangements of lines and pseudolinesPlanar arrangements of lines and pseudolines52Cxx52B30,52B401 * ; 52C35Arrangements of points, flats, hyperplanesArrangements of points, flats, hyperplanes [See also 32S22]52Cxx52B30,52B401 52C40Oriented matroidsOriented matroids52Cxx52B401 0 A 52C45Combinatorial complexity of geometric structuresCombinatorial complexity of geometric structures [See also 68U05]52Cxx52B55,68U051 & 52C99Discrete geometryNone of the above, but in this section52Cxx 52CxxDiscrete geometryDiscrete geometry52-XX ' G 53-00Reference works (differential geometry)General reference works (handbooks, dictionaries, bibliographies, etc.)53-XX ! ; 53-01Textbooks (differential geometry)Instructional exposition (textbooks, tutorial papers, etc.)53-XX + 1 53-02Research monographs (differential geometry)Research exposition (monographs, survey articles)53-XX " U 53-03Historical (differential geometry)Historical (must also be assigned at least one classification number from Section 01)53-XX 5 X 53-04Machine computation, programs (differential geometry)Explicit machine computation and programs (not the theory of computation or programming)53-XX 2 + 53-06Proceedings of conferences (differential geometry)Proceedings, conferences, collections, etc.53-XX 53-99Differential geometryDifferential geometry 53-XXDifferential geometryDifferential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} 53A04Curves in Euclidean spaceCurves in Euclidean space53Axx 53A05Surfaces in Euclidean spaceSurfaces in Euclidean space53Axx ? E 53A07Higher-dimension and -codimension surfaces in Euclidean n-spaceHigher-dimensional and -codimensional surfaces in Euclidean $n$-space53Axx 9 X 53A10Minimal surfaces, surfaces with prescribed mean curvatureMinimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]53Axx 53A15Affine differential geometryAffine differential geometry53Axx "
53A17Kinematics (differential geometry)Kinematics53Axx 53A20Projective differential geometryProjective differential geometry53Axx 53A25Differential line geometryDifferential line geometry53Axx 53A30Conformal differential geometryConformal differential geometry53Axx # # 53A35Non-Euclidean differential geometryNon-Euclidean differential geometry53Axx % % 53A40Other special differential geometriesOther special differential geometries53Axx 53A45Vector and tensor analysisVector and tensor analysis53Axx 9 9 53A55Differential invariants (local theory), geometric objectsDifferential invariants (local theory), geometric objects53Axx ( 53A60Geometry of websGeometry of webs [See also 14C21, 20N05]53Axx & 53A99Classical differential geometryNone of the above, but in this section53Axx 53AxxClassical differential geometryClassical differential geometry53-XX 53B05Linear and affine connectionsLinear and affine connections53Bxx 53B10Projective connectionsProjective connections53Bxx 53B15Other connectionsOther connections53Bxx 53B20Local Riemannian geometryLocal Riemannian geometry53Bxx 53B21Methods of Riemannian geometryMethods of Riemannian geometry53Bxx # 53B25Local submanifoldsLocal submanifolds [See also 53C40]53Bxx # # 53B30Lorentz metrics, indefinite metricsLorentz metrics, indefinite metrics53Bxx % 3 53B35Complex differential geometry (local)Hermitian and Kählerian structures [See also 32Cxx]53Bxx * 2 53B40Finsler spaces and generalizations (local)Finsler spaces and generalizations (areal metrics)53Bxx / 53B50Appl. of local differential geometry to physicsApplications to physics53Bxx & 53B99Local differential geometryNone of the above, but in this section53Bxx 53BxxLocal differential geometryLocal differential geometry53-XX 53C05Connections, general theoryConnections, general theory53Cxx 1 ` 53C07Special connections and metrics on vector bundlesSpecial connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]53Cxx 53C10G-structures$G$-structures53Cxx " C 53C12Foliations (differential geometry)Foliations (differential geometric aspects) [See also 57R30, 57R32]53Cxx ! [ 53C15Geometric structures on manifoldsGeneral geometric structures on manifolds (almost complex, almost product structures, etc.)53Cxx 53C17Sub-Riemannian geometrySub-Riemannian geometry53Cxx53C201 F 53C20Riemannian manifolds (global)Global Riemannian geometry, including pinching [See also 31C12, 58B20]53Cxx ' ^ 53C21Methods of Riemannian geometry (global)Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]53Cxx 53C22GeodesicsGeodesics [See also 58E10]53Cxx ( ( 53C23Global topological methods (a la Gromov)Global topological methods (à la Gromov)53Cxx 53C24Rigidity resultsRigidity results53Cxx53C20,53C231 7 53C25Special Riemannian manifoldsSpecial Riemannian manifolds (Einstein, Sasakian, etc.)53Cxx 1 C 53C26Hyper-K\"ahler and quaternionic K\"ahler geometryHyper-Kähler and quaternionic Kähler geometry, ``special'' geometry53Cxx53C25,53C551 53C27Spin and Spin$^c$ geometrySpin and Spin$^c$ geometry53Cxx53C25,57R151 53C28Twistor methodsTwistor methods [See also 32L25]53Cxx32L25,53C561 53C29Issues of holonomyIssues of holonomy53Cxx53C05,53C101 ; 53C30Homogeneous manifoldsHomogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]53Cxx ( ( 53C35Symmetric spaces (differential geometry)Symmetric spaces [See also 32M15, 57T15]53Cxx & & 53C38Calibrations and calibrated geometriesCalibrations and calibrated geometries53Cxx53C421 $ $ 53C40Submanifolds (differential geometry)Global submanifolds [See also 53B25]53Cxx " d 53C42Immersions (differential geometry)Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]53Cxx / @ 53C43Differential geometric aspects of harmonic mapsDifferential geometric aspects of harmonic maps [See also 58E20]53Cxx58E201 3 3 53C44Geometric evolution equations (mean curvature flow)Geometric evolution equations (mean curvature flow)53Cxx58E12,53C21,351 - > 53C45Global surface theory (a la A.D. Aleksandrov)Global surface theory (convex surfaces à la A. D. Aleksandrov)53Cxx 4 4 53C50Lorentz manifolds, manifolds with indefinite metricsLorentz manifolds, manifolds with indefinite metrics53Cxx & 2 53C55Complex differential geometry (global)Hermitian and Kählerian manifolds [See also 32Cxx]53Cxx # 4 53C56Other complex differential geometryOther complex differential geometry [See also 32Cxx]53Cxx + C 53C60Finsler spaces and generalizations (global)Finsler spaces and generalizations (areal metrics) [See also 58B20]53Cxx ` 53C65Integral geometryIntegral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]53Cxx + - 53C70Direct methods (G-spaces of Busemann, etc.)Direct methods ($G$-spaces of Busemann, etc.)53Cxx 1 53C75Geometric orders, order geometryGeometric orders, order geometry [See also 51Lxx]53Cxx 0 53C80Appl. of global differential geometry to physicsApplications to physics53Cxx & 53C99Global differential geometryNone of the above, but in this section53Cxx a 53CxxGlobal differential geometryGlobal differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]53-XX 53D05Symplectic manifolds, generalSymplectic manifolds, general53Dxx58F05,70H051 53D10Contact manifolds, generalContact manifolds, general53Dxx58F05,70H051 % % 53D12Lagrangian submanifolds; Maslov indexLagrangian submanifolds; Maslov index53Dxx58F05,70H051 . . 53D15Almost contact and almost symplectic manifoldsAlmost contact and almost symplectic manifolds53Dxx53C151 53D17Poisson manifoldsPoisson manifolds53Dxx58F05,70H051 # # 53D20Momentum maps; symplectic reductionMomentum maps; symplectic reduction53Dxx58F05,70H05,70H331 53D22Canonical transformationsCanonical transformations53Dxx58F05,70H151 53D25Geodesic flowsGeodesic flows53Dxx58F171 & & 53D30Symplectic structures of moduli spacesSymplectic structures of moduli spaces53Dxx58D27,58F051 1 B 53D35Global theory of symplectic and contact manifoldsGlobal theory of symplectic and contact manifolds [See also 57Rxx]53Dxx57R15,57R571 1 1 53D40Floer homology and cohomology, symplectic aspectsFloer homology and cohomology, symplectic aspects53Dxx58E05,58D101 A R 53D45Gromov-Witten invariants, quantum cohomology, Frobenius manifoldsGromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]53Dxx58D29,58D10,14N101 53D50Geometric quantizationGeometric quantization53Dxx58F06,81S101 ' ' 53D55Deformation quantization, star productsDeformation quantization, star products53Dxx58F06,81S101 % & 53D99Symplectic geometry, contact geometryNone of the above, but in this section53Dxx58F051 % D 53DxxSymplectic geometry, contact geometrySymplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]53-XX ) 53Z05Appl. of differential geometry to physicsApplications to physics53-XX " G 54-00Reference works (general topology)General reference works (handbooks, dictionaries, bibliographies, etc.)54-XX ; 54-01Textbooks (general topology)Instructional exposition (textbooks, tutorial papers, etc.)54-XX & 1 54-02Research monographs (general topology)Research exposition (monographs, survey articles)54-XX U 54-03Historical (general topology)Historical (must also be assigned at least one classification number from Section 01)54-XX 0 X 54-04Machine computation, programs (general topology)Explicit machine computation and programs (not the theory of computation or programming)54-XX - + 54-06Proceedings of conferences (general topology)Proceedings, conferences, collections, etc.54-XX 54-99General topologyGeneral topology M 54-XXGeneral topologyGeneral topology {For the topology of manifolds of all dimensions, see 57Nxx} & = 54A05Topological spaces and generalizationsTopological spaces and generalizations (closure spaces, etc.)54Axx d 54A10Several topologies on one setSeveral topologies on one set (change of topology, comparison of topologies, lattices of topologies)54Axx 54A15Syntopogeneous structuresSyntopogeneous structures54Axx V 54A20Convergence in general topologyConvergence in general topology (sequences, filters, limits, convergence spaces, etc.)54Axx , } 54A25Cardinality properties of topological spacesCardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}54Axx 7 5 54A35Consistency and independence results (general topology)Consistency and independence results [See also 03E35]54Axx 54A40Fuzzy topologyFuzzy topology [See also 03E72]54Axx & 54A99Generalities of general topologyNone of the above, but in this section54Axx 54AxxGeneralities of general topologyGeneralities54-XX 54B05Subspaces (general topology)Subspaces54Bxx ! 54B10Product spaces (general topology)Product spaces54Bxx ( 54B15Quotient spaces, etc. (general topology)Quotient spaces, decompositions54Bxx + + 54B17Adjunction spaces and similar constructionsAdjunction spaces and similar constructions54Bxx 54B20HyperspacesHyperspaces54Bxx ' $ 54B30Categorical methods in general topologyCategorical methods [See also 18B30]54Bxx 54B35SpectraSpectra54Bxx ' 54B40Sheaves, etc. (general topology)Presheaves and sheaves [See also 18F20]54Bxx ' & 54B99Basic constructions in general topologyNone of the above, but in this section54Bxx & 54BxxBasic constructions (general topology)Basic constructions54-XX 54C05Continuous mapsContinuous maps54Cxx 54C08Generalizations of continuityWeak and generalized continuity54Cxx " @ 54C10Special maps on topological spacesSpecial maps on topological spaces (open, closed, perfect, etc.)54Cxx
54C15RetractionRetraction54Cxx ' 54C20Extension of maps on topological spacesExtension of maps54Cxx 54C25Imbedding of topological spacesEmbedding54Cxx + & 54C30Real-valued functions on topological spacesReal-valued functions [See also 26-XX]54Cxx " ' 54C35Function spaces (general topology)Function spaces [See also 46Exx, 58D15]54Cxx : 8 54C40Algebraic properties of function spaces (general topology)Algebraic properties of function spaces [See also 46J10]54Cxx 54C45C- and C*-imbedding$C$- and $C^*$-embedding54Cxx 7 2 54C50Special sets of topological spaces defined by functionsSpecial sets defined by functions [See also 26A21]54Cxx , • 54C55Absolute neighborhood retracts and extensorsAbsolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]54Cxx $ 54C56Shape theoryShape theory [See also 55P55, 57N25]54Cxx 5 54C60Set-valued mapsSet-valued maps [See also 26E25, 28B20, 47H04, 58C06]54Cxx 54C65Continuous selectionsSelections [See also 28B20]54Cxx 54C70Topological entropyEntropy54Cxx & 54C99Maps and spaces defined by mapsNone of the above, but in this section54Cxx 0 54CxxMaps and spaces defined by mapsMaps and general types of spaces defined by maps54-XX 8 54D05Connectedness (general aspects)Connected and locally connected spaces (general aspects)54Dxx , 54D10Lower separation axiomsLower separation axioms ($T_0$--$T_3$, etc.)54Dxx _ 54D15Higher separation axiomsHigher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)54Dxx < 54D20Covering properties (noncompact)Noncompact covering properties (paracompact, Lindelöf, etc.)54Dxx ! ) 54D25"P-minimal" and "P-closed" spaces``$P$-minimal'' and ``$P$-closed'' spaces54Dxx 54D30CompactnessCompactness54Dxx S 54D35CompactificationsExtensions of spaces (compactifications, supercompactifications, completions, etc.)54Dxx
54D40RemaindersRemainders54Dxx ' 54D45Local compactness, etc.Local compactness, $\sigma$-compactness54Dxx
54D50k-spaces$k$-spaces54Dxx 54D55Sequential spacesSequential spaces54Dxx ( ( 54D60Realcompactness and realcompactificationRealcompactness and realcompactification54Dxx 54D65SeparabilitySeparability54Dxx 54D70Base propertiesBase properties54Dxx > 54D80Special constructions of spacesSpecial constructions of spaces (spaces of ultrafilters, etc.)54Dxx / & 54D99Fairly general properties of topological spacesNone of the above, but in this section54Dxx / 54DxxFairly general properties of topological spacesFairly general properties54-XX ( ( 54E05Proximity structures and generalizationsProximity structures and generalizations54Exx & & 54E15Uniform structures and generalizationsUniform structures and generalizations54Exx 54E17Nearness spacesNearness spaces54Exx - 54E18p-spaces, etc.$p$-spaces, $M$-spaces, $\sigma$-spaces, etc.54Exx ( 54E20Stratifiable spaces, etc.Stratifiable spaces, cosmic spaces, etc.54Exx 54E25Semimetric spacesSemimetric spaces54Exx 54E30Moore spacesMoore spaces54Exx 54E35Metric spaces, metrizabilityMetric spaces, metrizability54Exx 54E40Special maps on metric spacesSpecial maps on metric spaces54Exx ' 54E45Compactness in metric spacesCompact (locally compact) metric spaces54Exx 54E50Complete metric spacesComplete metric spaces54Exx 54E52Baire category, Baire spacesBaire category, Baire spaces54Exx 54E55BitopologiesBitopologies54Exx 54E70Probabilistic metric spacesProbabilistic metric spaces54Exx ) & 54E99Topological spaces with richer structuresNone of the above, but in this section54Exx ) 54ExxTopological spaces with richer structuresSpaces with richer structures54-XX u 54F05Ordered topological spacesLinearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]54Fxx 54F15Continua and generalizationsContinua and generalizations54Fxx & > 54F35Higher dimensional local connectednessHigher-dimensional local connectedness [See also 55Mxx, 55Nxx]54Fxx # ! 54F45Dimension theory (general topology)Dimension theory [See also 55M10]54Fxx @ 54F50Spaces of dimension $\le 1$Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]54Fxx 54F55Unicoherence, multicoherenceUnicoherence, multicoherence54Fxx 2 2 54F65Topological characterizations of particular spacesTopological characterizations of particular spaces54Fxx ( & 54F99Special properties of topological spacesNone of the above, but in this section54Fxx ( 54FxxSpecial properties of topological spacesSpecial properties54-XX $ 0 54G05Extremally disconnected spaces, etc.Extremally disconnected spaces, $F$-spaces, etc.54Gxx
54G10P-spaces$P$-spaces54Gxx 54G12Scattered spacesScattered spaces54Gxx 54G15Pathological spacesPathological spaces54Gxx " 54G20Counterexamples (general topology)Counterexamples54Gxx & 54G99Peculiar topological spacesNone of the above, but in this section54Gxx 54GxxPeculiar topological spacesPeculiar spaces54-XX , u 54H05Descriptive set theory (topological aspects)Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]54Hxx 0 A 54H10Topological representations of algebraic systemsTopological representations of algebraic systems [See also 22-XX]54Hxx ( # 54H11Topological groups (topological aspects)Topological groups [See also 22A05]54Hxx * 2 54H12Topological lattices (topological aspects)Topological lattices, etc. [See also 06B30, 06F30]54Hxx . Z 54H13Topological fields, etc. (topological aspects)Topological fields, rings, etc. [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80}54Hxx + C 54H15Transformation groups of topological spacesTransformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]54Hxx , 54H20Topological dynamicsTopological dynamics [See also 28Dxx, 37Bxx]54Hxx * < 54H25Fixed-point theorems in topological spacesFixed-point and coincidence theorems [See also 47H10, 55M20]54Hxx 5 & 54H99Connections of general topology with other structuresNone of the above, but in this section54Hxx 5 / 54HxxConnections of general topology with other structuresConnections with other structures, applications54-XX % 54J05Nonstandard topologyNonstandard topology [See also 03H05]54-XX $ G 55-00Reference works (algebraic topology)General reference works (handbooks, dictionaries, bibliographies, etc.)55-XX ; 55-01Textbooks (algebraic topology)Instructional exposition (textbooks, tutorial papers, etc.)55-XX ( 1 55-02Research monographs (algebraic topology)Research exposition (monographs, survey articles)55-XX U 55-03Historical (algebraic topology)Historical (must also be assigned at least one classification number from Section 01)55-XX 2 X 55-04Machine computation, programs (algebraic topology)Explicit machine computation and programs (not the theory of computation or programming)55-XX / + 55-06Proceedings of conferences (algebraic topology)Proceedings, conferences, collections, etc.55-XX 55-99Algebraic topologyAlgebraic topology 55-XXAlgebraic topologyAlgebraic topology 55M05Topological dualityDuality55Mxx % ! 55M10Dimension theory (algebraic topology)Dimension theory [See also 54F45]55Mxx / 55M15Absolute neighborhood retractsAbsolute neighborhood retracts [See also 54C55]55Mxx 2 . 55M20Fixed points and coincidences (algebraic topology)Fixed points and coincidences [See also 54H25]55Mxx 55M25Degree, etc.Degree, winding number55Mxx * B 55M30Lyusternik-Shnirel'man category of a spaceLjusternik-Schnirelman (Lyusternik-Shnirelman) category of a space55Mxx J 55M35Finite groups of transformationsFinite groups of transformations (including Smith theory) [See also 57S17]55Mxx & 55M99Classical algebraic topologyNone of the above, but in this section55Mxx & P 55MxxClassical topics of algebraic topologyClassical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}55-XX
55N05Cech typesCech types55Nxx 55N07Steenrod-Sitnikov homologiesSteenrod-Sitnikov homologies55Nxx 55N10Singular theorySingular theory55Nxx H 55N15K-theory (algebraic topology)$K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}55Nxx , < 55N20Generalized homology and cohomology theoriesGeneralized (extraordinary) homology and cohomology theories55Nxx $ e 55N22Bordism and cobordism theories, etc.Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]55Nxx 8 8 55N25Homology with local coefficients, equivariant cohomologyHomology with local coefficients, equivariant cohomology55Nxx / 55N30Sheaf cohomologySheaf cohomology [See also 18F20, 32C35, 32L10]55Nxx $ $ 55N33Intersection homology and cohomologyIntersection homology and cohomology55Nxx 55N34Elliptic cohomologyElliptic cohomology55Nxx55N35,55N20,58G10,58G12,11F111 55N35Other homology theoriesOther homology theories55Nxx 2 2 55N40Axioms for homology theory and uniqueness theoremsAxioms for homology theory and uniqueness theorems55Nxx 55N45Products and intersectionsProducts and intersections55Nxx # 4 55N91Equivariant homology and cohomologyEquivariant homology and cohomology [See also 19L47]55Nxx & 55N99Homology and cohomology theoriesNone of the above, but in this section55Nxx 1 55NxxHomology and cohomology theoriesHomology and cohomology theories [See also 57Txx]55-XX + + 55P05Homotopy extension properties, cofibrationsHomotopy extension properties, cofibrations55Pxx 55P10Homotopy equivalencesHomotopy equivalences55Pxx 55P15Classification of homotopy typeClassification of homotopy type55Pxx 55P20Eilenberg-MacLane spacesEilenberg-Mac Lane spaces55Pxx 55P25Spanier-Whitehead dualitySpanier-Whitehead duality55Pxx 55P30Eckmann-Hilton dualityEckmann-Hilton duality55Pxx 55P35Loop spacesLoop spaces55Pxx 55P40SuspensionsSuspensions55Pxx 55P42Stable homotopy theoryStable homotopy theory, spectra55Pxx ! N 55P43Spectra with additional structureSpectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)55Pxx55P42,55U35,55P471 55P45H-spaces and duals${H}$-spaces and duals55Pxx 55P47Infinite loop spacesInfinite loop spaces55Pxx - 55P48Loop space machines, operadsLoop space machines, operads [See also 18D50]55Pxx55P47,55U35,55P421 $ 55P55Shape theoryShape theory [See also 54C56, 55Q07]55Pxx 55P57Proper homotopy theoryProper homotopy theory55Pxx55P15,55P99,55P551 55P60Localization and completionLocalization and completion55Pxx 55P62Rational homotopy theoryRational homotopy theory55Pxx 55P65Homotopy functorsHomotopy functors55Pxx , 55P91Equivariant homotopy theoryEquivariant homotopy theory [See also 19L47]55Pxx @ @ 55P92Relations between equivariant and nonequivariant homotopy theoryRelations between equivariant and nonequivariant homotopy theory55Pxx55P911 & 55P99Homotopy theoryNone of the above, but in this section55Pxx 5 55PxxHomotopy theoryHomotopy theory {For simple homotopy type, see 57Q10}55-XX ! 2 55Q05General theory of homotopy groupsHomotopy groups, general; sets of homotopy classes55Qxx 55Q07Shape groupsShape groups55Qxx 55Q10Stable homotopy groupsStable homotopy groups55Qxx & & 55Q15Whitehead products and generalizationsWhitehead products and generalizations55Qxx 3 55Q20Homotopy groups of wedges, etc.Homotopy groups of wedges, joins, and simple spaces55Qxx 55Q25Hopf invariantsHopf invariants55Qxx 55Q35Operations in homotopy groupsOperations in homotopy groups55Qxx 55Q40Homotopy groups of spheresHomotopy groups of spheres55Qxx 55Q45Stable homotopy of spheresStable homotopy of spheres55Qxx
55Q50J-morphism$J$-morphism [See also 19L20]55Qxx 55Q51$v_n$-periodicity$v_n$-periodicity55Qxx55P42,55Q10,55N22,55N201 ! ! 55Q52Homotopy groups of special spacesHomotopy groups of special spaces55Qxx 55Q55Cohomotopy groupsCohomotopy groups55Qxx 8 55Q70Homotopy groups of special typesHomotopy groups of special types [See also 55N05, 55N07]55Qxx , 55Q91Equivariant homotopy groupsEquivariant homotopy groups [See also 19L47]55Qxx & 55Q99Homotopy groupsNone of the above, but in this section55Qxx 55QxxHomotopy groupsHomotopy groups55-XX 55R05Fiber spacesFiber spaces55Rxx
55R10Fiber bundlesFiber bundles55Rxx 55R12TransferTransfer55Rxx 55R15ClassificationClassification55Rxx / @ 55R20Spectral sequences and homology of fiber spacesSpectral sequences and homology of fiber spaces [See also 55Txx]55Rxx ' ! 55R25Sphere bundles and vector space bundlesSphere bundles and vector bundles55Rxx ) - 55R35Classifying spaces of groups and H-spacesClassifying spaces of groups and ${H}$-spaces55Rxx 55R37Maps between classifying spacesMaps between classifying spaces55Rxx55R351 6 N 55R40Homology of classifying spaces, characteristic classesHomology of classifying spaces, characteristic classes [See also 57Txx, 57R20]55Rxx " D 55R45Homology and homotopy of BO and BUHomology and homotopy of $B{\rm O}$ and $B{\rm U}$; Bott periodicity55Rxx 0 p 55R50Stable classes of vector space bundles, K-theoryStable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}55Rxx 55R55Fiberings with singularitiesFiberings with singularities55Rxx 6 55R60Microbundles and block bundlesMicrobundles and block bundles [See also 57N55, 57Q50]55Rxx + + 55R65Generalizations of fiber spaces and bundlesGeneralizations of fiber spaces and bundles55Rxx 55R70Fibrewise topologyFibrewise topology55Rxx55Rxx1 . . 55R80Discriminantal varieties, configuration spacesDiscriminantal varieties, configuration spaces55Rxx55R35,55R99,57M25,57R451 $ 5 55R91Equivariant fiber spaces and bundlesEquivariant fiber spaces and bundles [See also 19L47]55Rxx & 55R99Fiber spaces and bundlesNone of the above, but in this section55Rxx L 55RxxFiber spaces and bundlesFiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]55-XX 55S05Primary cohomology operationsPrimary cohomology operations55Sxx 55S10Steenrod algebraSteenrod algebra55Sxx 55S12Dyer-Lashof operationsDyer-Lashof operations55Sxx # 55S15Symmetric products, etc.Symmetric products, cyclic products55Sxx * * 55S20Secondary and higher cohomology operationsSecondary and higher cohomology operations55Sxx 9 S 55S25K-theory operations and generalized cohomology operations$K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]55Sxx 55S30Massey productsMassey products55Sxx 55S35Obstruction theoryObstruction theory55Sxx % % 55S36Extension and compression of mappingsExtension and compression of mappings55Sxx 55S37Classification of mappingsClassification of mappings55Sxx # # 55S40Sectioning fiber spaces and bundlesSectioning fiber spaces and bundles55Sxx ! 55S45Postnikov system, k-invariantsPostnikov systems, $k$-invariants55Sxx ' 8 55S91Equivariant operations and obstructionsEquivariant operations and obstructions [See also 19L47]55Sxx & 55S99Operations and obstructionsNone of the above, but in this section55Sxx 55SxxOperations and obstructionsOperations and obstructions55-XX 55T05General spectral sequencesGeneral55Txx 55T10Serre spectral sequencesSerre spectral sequences55Txx 55T15Adams spectral sequencesAdams spectral sequences55Txx " 3 55T20Eilenberg-Moore spectral sequencesEilenberg-Moore spectral sequences [See also 57T35]55Txx 55T25Generalized cohomologyGeneralized cohomology55Txx & 55T99Spectral sequencesNone of the above, but in this section55Txx * 55TxxSpectral sequencesSpectral sequences [See also 18G40, 55R20]55-XX 55U05Abstract complexesAbstract complexes55Uxx 55U10Semisimplicial complexesSimplicial sets and complexes55Uxx 55U15Chain complexesChain complexes55Uxx 2 2 55U20Universal coefficient theorems, Bockstein operatorUniversal coefficient theorems, Bockstein operator55Uxx ' & 55U25Homology of a product, Kuenneth formulaHomology of a product, Künneth formula55Uxx % 55U30Duality (applied homological algebra)Duality55Uxx & 55U35Abstract homotopy theoryAbstract and axiomatic homotopy theory55Uxx 6 55U40Topological categoriesTopological categories, foundations of homotopy theory55Uxx / & 55U99Applied homological algebra and category theoryNone of the above, but in this section55Uxx / @ 55UxxApplied homological algebra and category theoryApplied homological algebra and category theory [See also 18Gxx]55-XX G 57-00Reference works (manifolds)General reference works (handbooks, dictionaries, bibliographies, etc.)57-XX ; 57-01Textbooks (manifolds)Instructional exposition (textbooks, tutorial papers, etc.)57-XX 1 57-02Research monographs (manifolds)Research exposition (monographs, survey articles)57-XX U 57-03Historical (manifolds)Historical (must also be assigned at least one classification number from Section 01)57-XX ) X 57-04Machine computation, programs (manifolds)Explicit machine computation and programs (not the theory of computation or programming)57-XX & + 57-06Proceedings of conferences (manifolds)Proceedings, conferences, collections, etc.57-XX 57-99Manifolds and cell complexesManifolds and cell complexes ? 57-XXManifolds and cell complexesManifolds and cell complexes {For complex manifolds, see 32Qxx} < 57M05Fundamental group, etc.Fundamental group, presentations, free differential calculus57Mxx # # 57M07Topological methods in group theoryTopological methods in group theory57Mxx 57M10Covering spacesCovering spaces57Mxx 57M12Special coveringsSpecial coverings, e.g. branched57Mxx , 57M15Relations with graph theoryRelations with graph theory [See also 05Cxx]57Mxx 57M20Two-dimensional complexesTwo-dimensional complexes57Mxx ; 57M25Knots and links in the 3-sphereKnots and links in $S^3$ {For higher dimensions, see 57Q45}57Mxx # # 57M27Invariants of knots and 3-manifoldsInvariants of knots and 3-manifolds57Mxx57M25,57N101 ( . 57M30Wild knots and surfaces, wild imbeddingsWild knots and surfaces, etc., wild embeddings57Mxx 7 7 57M35Dehn's lemma, sphere theorem, loop theorem, asphericityDehn's lemma, sphere theorem, loop theorem, asphericity57Mxx 3 K 57M40Characterizations of Euclidean 3-space and 3-sphereCharacterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12]57Mxx 1 1 57M50Geometric structures on low-dimensional manifoldsGeometric structures on low-dimensional manifolds57Mxx 57M60Group actions in low dimensionsGroup actions in low dimensions57Mxx & 57M99Low-dimensional topologyNone of the above, but in this section57Mxx 57MxxLow-dimensional topologyLow-dimensional topology57-XX * 57N05Topology of Euclidean 2-space, 2-manifoldsTopology of $E^2$, $2$-manifolds57Nxx 2 57N10Topology of general 3-manifoldsTopology of general $3$-manifolds [See also 57Mxx]57Nxx * , 57N12Topology of Euclidean 3-space and 3-sphereTopology of $E^3$ and $S^3$ [See also 57M40]57Nxx * 8 57N13Topology of Euclidean 4-space, 4-manifoldsTopology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]57Nxx * : 57N15Topology of Euclidean n-space, n-manifoldsTopology of $E^n$, $n$-manifolds ($4 < n < \infty$)57Nxx ! 2 # 57N16Geometric structures on manifoldsGeometric structures on manifolds [See also 57M50]57Nxx57M50,57N05,57N10,57N13,57N15,57N701 % % 57N17Topology of topological vector spacesTopology of topological vector spaces57Nxx * ; 57N20Topology of infinite-dimensional manifoldsTopology of infinite-dimensional manifolds [See also 58Bxx]57Nxx % 57N25ShapesShapes [See also 54C56, 55P55, 55Q07]57Nxx 57N30EngulfingEngulfing57Nxx 1 57N35Imbeddings and immersions (topological manifolds)Embeddings and immersions57Nxx 57N37Isotopy and pseudo-isotopyIsotopy and pseudo-isotopy57Nxx 57N40Neighborhoods of submanifoldsNeighborhoods of submanifolds57Nxx 57N45Flatness and tamenessFlatness and tameness57Nxx ! ) 57N50(n-1)-sphere in Euclidean n-space$S^{n-1}\subset E^n$, Schoenflies problem57Nxx 6 57N55Microbundles and block bundlesMicrobundles and block bundles [See also 55R60, 57Q50]57Nxx 57N60CellularityCellularity57Nxx 57N65Algebraic topology of manifoldsAlgebraic topology of manifolds57Nxx 57N70Cobordism and concordanceCobordism and concordance57Nxx # # 57N75General position and transversalityGeneral position and transversality57Nxx 57N80StratificationsStratifications57Nxx & 57N99Topological manifoldsNone of the above, but in this section57Nxx 57NxxTopological manifoldsTopological manifolds57-XX ) ) 57P05Local properties of generalized manifoldsLocal properties of generalized manifolds57Pxx 57P10Poincare duality spacesPoincaré duality spaces57Pxx & 57P99Generalized manifoldsNone of the above, but in this section57Pxx & 57PxxGeneralized manifoldsGeneralized manifolds [See also 18F15]57-XX 57Q05General topology of complexesGeneral topology of complexes57Qxx Z 57Q10Simple homotopy type, etc.Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]57Qxx , , 57Q12Wall finiteness obstruction for CW-complexesWall finiteness obstruction for CW-complexes57Qxx 57Q15Triangulating manifoldsTriangulating manifolds57Qxx 57Q20Cobordism (PL-topology)Cobordism57Qxx ; 57Q25Comparison of PL-structuresComparison of PL-structures: classification, Hauptvermutung57Qxx 57Q30Engulfing (PL-topology)Engulfing57Qxx ' 57Q35Imbeddings and immersions (PL-topology)Embeddings and immersions57Qxx 57Q37Isotopy (PL-topology)Isotopy57Qxx 57Q40Regular neighborhoodsRegular neighborhoods57Qxx 0 N 57Q45Knots and links in high dimensions (PL-topology)Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}57Qxx , 6 57Q50Microbundles and block bundles (PL-topology)Microbundles and block bundles [See also 55R60, 57N55]57Qxx 57Q55Approximations (PL-topology)Approximations57Qxx ' 57Q60Cobordism and concordance (PL-topology)Cobordism and concordance57Qxx 1 # 57Q65General position and transversality (PL-topology)General position and transversality57Qxx 57Q91Equivariant PL-topologyEquivariant PL-topology57Qxx & 57Q99PL-topologyNone of the above, but in this section57Qxx 57QxxPL-topologyPL-topology57-XX
57R05TriangulatingTriangulating57Rxx 57R10SmoothingSmoothing57Rxx 57R12Smooth approximationsSmooth approximations57Rxx # L 57R15Specialized structures on manifoldsSpecialized structures on manifolds (spin manifolds, framed manifolds, etc.)57Rxx 57R17Symplectic and contact topologySymplectic and contact topology57Rxx57R151 57R19Algebraic topology on manifoldsAlgebraic topology on manifolds57Rxx " " 57R20Characteristic classes and numbersCharacteristic classes and numbers57Rxx , = 57R22Topology of vector bundles and fiber bundlesTopology of vector bundles and fiber bundles [See also 55Rxx]57Rxx 57R25Vector fields, frame fieldsVector fields, frame fields57Rxx ? i 57R27Controllability of vector fields on C-infinity (etc.) manifoldsControllability of vector fields on $C^\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]57Rxx 57R30Foliations; geometric theoryFoliations; geometric theory57Rxx ! K 57R32Classifying spaces for foliationsClassifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]57Rxx / 57R35Differentiable mappings (differential topology)Differentiable mappings57Rxx "
57R40Imbeddings (differential topology)Embeddings57Rxx "
57R42Immersions (differential topology)Immersions57Rxx ( ( 57R45Singularities of differentiable mappingsSingularities of differentiable mappings57Rxx 57R50DiffeomorphismsDiffeomorphisms57Rxx 57R52Isotopy (differential topology)Isotopy57Rxx 57R55Differentiable structuresDifferentiable structures57Rxx " " 57R56Topological quantum field theoriesTopological quantum field theories57Rxx57R57,58D291 3 t 57R57Appl. of global analysis to structures on manifoldsApplications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]57Rxx 57R58Floer homologyFloer homology57Rxx57R57,55N35,58E051 % % 57R60Homotopy spheres, Poincare conjectureHomotopy spheres, Poincaré conjecture57Rxx 57R65Surgery and handlebodiesSurgery and handlebodies57Rxx ! 2 57R67Surgery obstructions, Wall groupsSurgery obstructions, Wall groups [See also 19J25]57Rxx ) ) 57R70Critical points and critical submanifoldsCritical points and critical submanifolds57Rxx 57R75O- and SO-cobordismO- and SO-cobordism57Rxx ' 8 57R77Complex cobordism (U- and SU-cobordism)Complex cobordism (U- and SU-cobordism) [See also 55N22]57Rxx 57R80h- and s-cobordism$h$- and $s$-cobordism57Rxx 57R85Equivariant cobordismEquivariant cobordism57Rxx ) 57R90Other types of cobordismOther types of cobordism [See also 55N22]57Rxx + + 57R91Equivariant algebraic topology of manifoldsEquivariant algebraic topology of manifolds57Rxx 57R95Realizing cycles by submanifoldsRealizing cycles by submanifolds57Rxx & 57R99Differential topologyNone of the above, but in this section57Rxx ˆ 57RxxDifferential topologyDifferential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}57-XX 8 E 57S05Topological properties of groups of homeomorphisms, etc.Topological properties of groups of homeomorphisms or diffeomorphisms57Sxx 57S10Compact groups of homeomorphismsCompact groups of homeomorphisms57Sxx 4 4 57S15Compact Lie groups of differentiable transformationsCompact Lie groups of differentiable transformations57Sxx 57S17Finite transformation groupsFinite transformation groups57Sxx ( ( 57S20Noncompact Lie groups of transformationsNoncompact Lie groups of transformations57Sxx # # 57S25Groups acting on specific manifoldsGroups acting on specific manifolds57Sxx ' ' 57S30Discontinuous groups of transformationsDiscontinuous groups of transformations57Sxx ! & 57S99Topological transformation groupsNone of the above, but in this section57Sxx ! N 57SxxTopological transformation groupsTopological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]57-XX
57T05Hopf algebrasHopf algebras [See also 16W30]57Txx % % 57T10Homology and cohomology of Lie groupsHomology and cohomology of Lie groups57Txx ; ; 57T15Homology and cohomology of homogeneous spaces of Lie groupsHomology and cohomology of homogeneous spaces of Lie groups57Txx < < 57T20Homotopy groups of topological groups and homogeneous spacesHomotopy groups of topological groups and homogeneous spaces57Txx # ' 57T25Homology and cohomology of H-spacesHomology and cohomology of ${H}$-spaces57Txx 3 57T30Bar and cobar constructionsBar and cobar constructions [See also 18G55, 55Uxx]57Txx + J 57T35Appl. of Eilenberg-Moore spectral sequencesApplications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]57Txx + & 57T99Homology and homotopy of topological groupsNone of the above, but in this section57Txx B B 57TxxHomology and homotopy of topological groups and related structuresHomology and homotopy of topological groups and related structures57-XX ! G 58-00Reference works (global analysis)General reference works (handbooks, dictionaries, bibliographies, etc.)58-XX ; 58-01Textbooks (global analysis)Instructional exposition (textbooks, tutorial papers, etc.)58-XX % 1 58-02Research monographs (global analysis)Research exposition (monographs, survey articles)58-XX U 58-03Historical (global analysis)Historical (must also be assigned at least one classification number from Section 01)58-XX / X 58-04Machine computation, programs (global analysis)Explicit machine computation and programs (not the theory of computation or programming)58-XX , + 58-06Proceedings of conferences (global analysis)Proceedings, conferences, collections, etc.58-XX & & 58-99Global analysis, analysis on manifoldsGlobal analysis, analysis on manifolds T 58-XXGlobal analysisGlobal analysis, analysis on manifolds {For geometric integration theory, see 49Q15} 2 4 58A03Topos-theoretic approach to differential manifoldsTopos-theoretic approach to differentiable manifolds58Axx ' % 58A05Foundations of differentiable manifoldsDifferentiable manifolds, foundations58Axx 8 58A07Real-analytic manifolds, etc.Real-analytic and Nash manifolds [See also 14P20, 32C07]58Axx 58A10Differential formsDifferential forms58Axx 58A12de Rham theory (global analysis)de Rham theory [See also 14Fxx]58Axx 2 58A14Hodge theory (global analysis)Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]58Axx - - 58A15Exterior differential systems (Cartan theory)Exterior differential systems (Cartan theory)58Axx 58A17Pfaffian systemsPfaffian systems58Axx 58A20JetsJets58Axx 58A25Currents (global analysis)Currents [See also 32C30, 53C65]58Axx & 8 58A30Vector distributions (global analysis)Vector distributions (subbundles of the tangent bundles)58Axx 58A32Natural bundlesNatural bundles58Axx58A05,58A201 ! 58A35Stratified sets (global analysis)Stratified sets [See also 32S60]58Axx % 58A40Differential spaces (global analysis)Differential spaces58Axx & ; 58A50Supermanifolds, etc. (global analysis)Supermanifolds and graded manifolds [See also 14A22, 32C11]58Axx * & 58A99General theory of differentiable manifoldsNone of the above, but in this section58Axx * ; 58AxxGeneral theory of differentiable manifoldsGeneral theory of differentiable manifolds [See also 32Cxx]58-XX 7 " 58B05Topological questions of infinite-dimensional manifoldsHomotopy and topological questions58Bxx = 58B10Differentiability questions in infinite-dimensional manifoldsDifferentiability questions58Bxx 9 / 58B12Questions of holomorphy in infinite-dimensional manifoldsQuestions of holomorphy [See also 32-XX, 46G20]58Bxx 5 $ 58B15Fredholm structures on infinite-dimensional manifoldsFredholm structures [See also 47A53]58Bxx 6 J 58B20Geometric structures on infinite-dimensional manifoldsRiemannian, Finsler and other geometric structures [See also 53C20, 53C60]58Bxx ? ^ 58B25Group structures and generalizations on infinite-dim. manifoldsGroup structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]58Bxx 58B32Geometry of quantum groupsGeometry of quantum groups58Bxx58B301 % % 58B34Noncommutative geometry (a la Connes)Noncommutative geometry (à la Connes)58Bxx58B301 & 58B99Infinite-dimensional manifoldsNone of the above, but in this section58Bxx 58BxxInfinite-dimensional manifoldsInfinite-dimensional manifolds58-XX " 58C05Real-valued functions on manifoldsReal-valued functions58Cxx % E 58C06Set-valued mappings etc. on manifoldsSet valued and function-space valued mappings [See also 47H04, 54C60]58Cxx . ! 58C07Continuity properties of mappings on manifoldsContinuity properties of mappings58Cxx / ! 58C10Holomorphic maps on manifolds (global analysis)Holomorphic maps [See also 32-XX]58Cxx , 1 58C15Implicit function theorems etc. on manifoldsImplicit function theorems; global Newton methods58Cxx / G 58C20Generalized differentiation theory on manifoldsDifferentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]58Cxx 2 58C25Differentiable maps on manifolds (global analysis)Differentiable maps58Cxx ! 2 58C30Fixed point theorems on manifoldsFixed point theorems on manifolds [See also 47H10]58Cxx @ 58C35Integration on manifoldsIntegration on manifolds; measures on manifolds [See also 28Cxx]58Cxx < 58C40Spectral theory on manifoldsSpectral theory; eigenvalue problems [See also 47J10, 58E07]58Cxx . 58C50Analysis on supermanifolds, etc.Analysis on supermanifolds or graded manifolds58Cxx & 58C99Calculus on manifoldsNone of the above, but in this section58Cxx I 58CxxCalculus on manifoldsCalculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]58-XX 9 Q 58D05Groups of diffeomorphisms and homeomorphisms as manifoldsGroups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]58Dxx , D 58D07Groups and semigroups of nonlinear operatorsGroups and semigroups of nonlinear operators [See also 17B65, 47H20]58Dxx # # 58D10Spaces of imbeddings and immersionsSpaces of imbeddings and immersions58Dxx - 58D15Manifolds of mappingsManifolds of mappings [See also 46T10, 54C35]58Dxx & 58D17Manifolds of metricsManifolds of metrics (esp. Riemannian)58Dxx 9 % 58D19Global group actions and symmetry properties on manifoldsGroup actions and symmetry properties58Dxx S 58D20Measures on manifolds of mapsMeasures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]58Dxx ) e 58D25Differential equations in function spacesEquations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]58Dxx C 5 58D27Moduli problems for diff.geometric structures on spaces of mappingsModuli problems for differential geometric structures58Dxx C * 58D29Moduli problems for topological structures on manifolds of mappingsModuli problems for topological structures58Dxx 4 ^ 58D30Spaces and manifolds of mappings in appl. to physicsApplications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)58Dxx & 58D99Spaces and manifolds of mappingsNone of the above, but in this section58Dxx a 58DxxSpaces and manifolds of mappingsSpaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]58-XX j 58E05Abstract critical point theoryAbstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)58Exx 58E07Abstract bifurcation theoryAbstract bifurcation theory58Exx " " 58E09Group-invariant bifurcation theoryGroup-invariant bifurcation theory58Exx ( N 58E10Appl. of bifurcation theory to geodesicsApplications to the theory of geodesics (problems in one independent variable)58Exx / 58E11Critical metrics in infinite-dimensional spacesCritical metrics58Exx 0 Y 58E12Appl. of variational methods to minimal surfacesApplications to minimal surfaces (problems in two independent variables) [See also 49Q05]58Exx B d 58E15Appl. of variational methods to extremal problems in sev.variablesApplication to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.58Exx + C 58E17Pareto optimality, etc., appl. to economicsPareto optimality, etc., applications to economics [See also 90C29]58Exx 1 $ 58E20Harmonic maps between infinite-dimensional spacesHarmonic maps [See also 53C43], etc.58Exx . 6 58E25Appl. of variational methods to control theoryApplications to control theory [See also 49-XX, 93-XX]58Exx 5 58E30Variational principles on infinite-dimensional spacesVariational principles58Exx * * 58E35Variational inequalities (global problems)Variational inequalities (global problems)58Exx
58E40Group actionsGroup actions58Exx ; 58E50Appl. of variational methods in infinite-dimensional spacesApplications58Exx 3 & 58E99Variational problems in infinite-dimensional spacesNone of the above, but in this section58Exx 3 3 58ExxVariational problems in infinite-dimensional spacesVariational problems in infinite-dimensional spaces58-XX A 58H05Pseudogroups on manifoldsPseudogroups and differentiable groupoids [See also 22A22, 22E65]58Hxx ; j 58H10Cohomology of classifying spaces for pseudogroup structuresCohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]58Hxx . 2 58H15Global deformations of structures on manifoldsDeformations of structures [See also 32Gxx, 58J10]58Hxx 0 & 58H99Pseudogroups and general structures on manifoldsNone of the above, but in this section58Hxx 0 J 58HxxPseudogroups and general structures on manifoldsPseudogroups, differentiable groupoids and general structures on manifolds58-XX / @ 58J05Elliptic equations on manifolds, general theoryElliptic equations on manifolds, general theory [See also 35-XX]58Jxx58G031 ; 58J10Differential complexesDifferential complexes [See also 35Nxx]; elliptic complexes58Jxx58G051 58J15Relations with hyperfunctionsRelations with hyperfunctions58Jxx58G071 - E 58J20Index theory and related fixed point theoremsIndex theory and related fixed point theorems [See also 19K56, 46L80]58Jxx58G101 B 58J22Exotic index theoriesExotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]58Jxx58G121 58J26Elliptic generaElliptic genera58Jxx11F11,58G10,58G121 ' ' 58J28Eta-invariants, Chern-Simons invariantsEta-invariants, Chern-Simons invariants58Jxx58G10,58G251 58J30Spectral flowsSpectral flows58Jxx58G10,58G251 $ $ 58J32Boundary value problems on manifoldsBoundary value problems on manifolds58Jxx58G201 ) ) 58J35Heat and other parabolic equation methodsHeat and other parabolic equation methods58Jxx58G111 58J37Perturbations; asymptoticsPerturbations; asymptotics58Jxx58G181 > O 58J40Pseudodifferential and Fourier integral operators on manifoldsPseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]58Jxx58G151 7 7 58J42Noncommutative global analysis, noncommutative residuesNoncommutative global analysis, noncommutative residues58Jxx58G15,58B301 % 58J45Hyperbolic equationsHyperbolic equations [See also 35Lxx]58Jxx58G161 4 4 58J47Propagation of singularities; initial value problemsPropagation of singularities; initial value problems58Jxx58G171 7 H 58J50Spectral problems; spectral geometry; scattering theorySpectral problems; spectral geometry; scattering theory [See also 35Pxx]58Jxx58G251 6 6 58J52Determinants and determinant bundles, analytic torsionDeterminants and determinant bundles, analytic torsion58Jxx58G261 58J53IsospectralityIsospectrality58Jxx58G251 58J55BifurcationBifurcation [See also 35B32]58Jxx58G281 * F 58J60Relations with special manifold structuresRelations with special manifold structures (Riemannian, Finsler, etc.)58Jxx58G301 8 W 58J65Diffusion processes and stochastic analysis on manifoldsDiffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]58Jxx58G321 " 3 58J70Invariance and symmetry propertiesInvariance and symmetry properties [See also 35A30]58Jxx58G351 0 U 58J72Correspondences and other transformation methodsCorrespondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]58Jxx58G371 58J90ApplicationsApplications58Jxx58G401 & & 58J99None of the above, but in this sectionNone of the above, but in this section58Jxx58G991 C b 58JxxPartial differential equations on manifolds; differential operatorsPartial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]58-XX ) ) 58K05Critical points of functions and mappingsCritical points of functions and mappings58Kxx58C27,32S051 58K10MonodromyMonodromy58Kxx58C271 " " 58K15Topological properties of mappingsTopological properties of mappings58Kxx58C271 - - 58K20Algebraic and analytic properties of mappingsAlgebraic and analytic properties of mappings58Kxx58C27,32S05,32S151 58K25StabilityStability58Kxx58C271
58K30Global theoryGlobal theory58Kxx58C27,57R451 58K35Catastrophe theoryCatastrophe theory58Kxx58C281 / / 58K40Classification; finite determinacy of map germsClassification; finite determinacy of map germs58Kxx58C271 3 3 58K45Singularities of vector fields, topological aspectsSingularities of vector fields, topological aspects58Kxx58F14,58C271 58K50Normal formsNormal forms58Kxx58F36,58C271 58K55Asymptotic behaviorAsymptotic behavior58Kxx58C27,58G181 58K60Deformation of singularitiesDeformation of singularities58Kxx58C27,32S391 58K65Topological invariantsTopological invariants58Kxx58C271 58K70Symmetries, equivarianceSymmetries, equivariance58Kxx58C271 & & 58K99None of the above, but in this sectionNone of the above, but in this section58Kxx58C271 . F 58KxxTheory of singularities and catastrophe theoryTheory of singularities and catastrophe theory [See also 32Sxx, 37-XX]58-XX # 58Z05Appl. of global analysis to physicsApplications to physics58-XX $ G 60-00Reference works (probability theory)General reference works (handbooks, dictionaries, bibliographies, etc.)60-XX ; 60-01Textbooks (probability theory)Instructional exposition (textbooks, tutorial papers, etc.)60-XX ( 1 60-02Research monographs (probability theory)Research exposition (monographs, survey articles)60-XX U 60-03Historical (probability theory)Historical (must also be assigned at least one classification number from Section 01)60-XX 2 X 60-04Machine computation, programs (probability theory)Explicit machine computation and programs (not the theory of computation or programming)60-XX / + 60-06Proceedings of conferences (probability theory)Proceedings, conferences, collections, etc.60-XX ? P 60-08Computational methods (not classified at a more specific level)Computational methods (not classified at a more specific level) [See also 65C50]60-XX60-041 + + 60-99Probability theory and stochastic processesProbability theory and stochastic processes + ~ 60-XXProbability theory and stochastic processesProbability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} 60A05Axioms of probability theoryAxioms; other general questions60Axx F 60A10Probabilistic measure theoryProbabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}60Axx ! & 60A99Foundations of probability theoryNone of the above, but in this section60Axx ! ! 60AxxFoundations of probability theoryFoundations of probability theory60-XX * * 60B05Probability measures on topological spacesProbability measures on topological spaces60Bxx # # 60B10Convergence of probability measuresConvergence of probability measures60Bxx / @ 60B11Probability theory on linear topological spacesProbability theory on linear topological spaces [See also 28C20]60Bxx A M 60B12Limit theorems for vector-valued random variables (inf.-dim.case)Limit theorems for vector-valued random variables (infinite-dimensional case)60Bxx A 60B15Probability measures on groupsProbability measures on groups, Fourier transforms, factorization60Bxx ( & 60B99Probability theory on general structuresNone of the above, but in this section60Bxx ( : 60BxxProbability theory on general structuresProbability theory on algebraic and topological structures60-XX 60C05Combinatorial probabilityCombinatorial probability60-XX O 60D05Geometric probabilityGeometric probability, stochastic geometry, random sets [See also 52A22, 53C65]60-XX + 60E05General theory of probability distributionsDistributions: general theory60Exx " 8 60E07Infinitely divisible distributionsInfinitely divisible distributions; stable distributions60Exx ' * 60E10Transforms of probability distributionsCharacteristic functions; other transforms60Exx " " 60E15Inequalities in probability theoryInequalities; stochastic orderings60Exx ) & 60E99Distribution theory in probability theoryNone of the above, but in this section60Exx ) + 60ExxDistribution theory in probability theoryDistribution theory [See also 62Exx, 62Hxx]60-XX % 60F05Weak limit theoremsCentral limit and other weak theorems60Fxx 60F10Large deviationsLarge deviations60Fxx 60F15Strong limit theoremsStrong theorems60Fxx 0 60F17Functional limit theoremsFunctional limit theorems; invariance principles60Fxx
60F20Zero-one lawsZero-one laws60Fxx 60F25Lp-limit theorems (probability)$L^p$-limit theorems60Fxx & 60F99Limit theorems (probability)None of the above, but in this section60Fxx & 60FxxLimit theorems (probability)Limit theorems [See also 28Dxx, 60B12]60-XX # # 60G05Foundations of stochastic processesFoundations of stochastic processes60Gxx & 60G07General theory of stochastic processesGeneral theory of processes60Gxx 60G09ExchangeabilityExchangeability60Gxx 60G10Stationary processesStationary processes60Gxx 60G12General second order processesGeneral second-order processes60Gxx 60G15Gaussian processesGaussian processes60Gxx 60G17Sample path propertiesSample path properties60Gxx 60G18Self-similar processesSelf-similar processes60Gxx 60G20Generalized stochastic processesGeneralized stochastic processes60Gxx " 60G25Prediction theoryPrediction theory [See also 62M20]60Gxx ( . 60G30Induced measures of stochastic processesContinuity and singularity of induced measures60Gxx V 60G35Appl. of stochastic processesApplications (signal detection, filtering, etc.) [See also 62M20, 93E10, 93E11, 94Axx]60Gxx R 60G40Optimal stoppingStopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]60Gxx # # 60G42Martingales with discrete parameterMartingales with discrete parameter60Gxx % % 60G44Martingales with continuous parameterMartingales with continuous parameter60Gxx " " 60G46Martingales and classical analysisMartingales and classical analysis60Gxx 60G48Generalizations of martingalesGeneralizations of martingales60Gxx $ 2 60G50Sums of independent random variablesSums of independent random variables; random walks60Gxx % % 60G51Processes with independent incrementsProcesses with independent increments60Gxx60J301 60G52Stable processesStable processes60Gxx60G991 60G55Point processesPoint processes60Gxx 60G57Random measuresRandom measures60Gxx
60G60Random fieldsRandom fields60Gxx " ( 60G70Extreme value theory (probability)Extreme value theory; extremal processes60Gxx & 60G99Stochastic processesNone of the above, but in this section60Gxx 60GxxStochastic processesStochastic processes60-XX 60H05Stochastic integralsStochastic integrals60Hxx < < 60H07Stochastic calculus of variations and the Malliavin calculusStochastic calculus of variations and the Malliavin calculus60Hxx * ; 60H10Stochastic ordinary differential equationsStochastic ordinary differential equations [See also 34F05]60Hxx ) : 60H15Stochastic partial differential equationsStochastic partial differential equations [See also 35R60]60Hxx 60H20Stochastic integral equationsStochastic integral equations60Hxx / 60H25Random operators, etc.Random operators and equations [See also 47B80]60Hxx 2 60H30Appl. of stochastic analysisApplications of stochastic analysis (to PDE, etc.)60Hxx . @ 60H35Computational methods for stochastic equationsComputational methods for stochastic equations [See also 65C30]60Hxx60H10,60H15,60H20,60H991 60H40White noise theoryWhite noise theory60Hxx60G99,60H991 & 60H99Stochastic analysisNone of the above, but in this section60Hxx $ 60HxxStochastic analysisStochastic analysis [See also 58J65]60-XX ( ( 60J05Markov processes with discrete parameterMarkov processes with discrete parameter60Jxx % % 60J10Markov chains with discrete parameterMarkov chains with discrete parameter60Jxx " Ž 60J20Appl. of discrete Markov processesApplications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]60Jxx & 7 60J22Computational methods in Markov chainsComputational methods in Markov chains [See also 65C40]60Jxx60J10,60J27,60-041 * * 60J25Markov processes with continuous parameterMarkov processes with continuous parameter60Jxx ' ' 60J27Markov chains with continuous parameterMarkov chains with continuous parameter60Jxx G 60J35Transition functionsTransition functions, generators and resolvents [See also 47D03, 47D07]60Jxx 60J40Right processesRight processes60Jxx 6 60J45Probabilistic potential theoryProbabilistic potential theory [See also 31Cxx, 31D05]60Jxx 60J50Boundary theory (probability)Boundary theory60Jxx # 60J55Additive functionalsLocal time and additive functionals60Jxx 60J57Multiplicative functionalsMultiplicative functionals60Jxx $ 60J60Diffusion processesDiffusion processes [See also 58J65]60Jxx 60J65Brownian motionBrownian motion [See also 58J65]60Jxx b 60J70Appl. of diffusion theoryApplications of diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]60Jxx 60J75Jump processesJump processes60Jxx : 60J80Branching processesBranching processes (Galton-Watson, birth-and-death, etc.)60Jxx 4 60J85Appl. of branching processesApplications of branching processes [See also 92Dxx]60Jxx & 60J99Markov processesNone of the above, but in this section60Jxx 60JxxMarkov processesMarkov processes60-XX 60K05Renewal theoryRenewal theory60Kxx / 60K10Appl. of renewal theoryApplications (reliability, demand theory, etc.)60Kxx / 60K15Markov renewal processesMarkov renewal processes, semi-Markov processes60Kxx ! ` 60K20Appl. of Markov renewal processesApplications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]60Kxx ' 60K25Queueing theoryQueueing theory [See also 68M20, 90B22]60Kxx N 60K30Appl. of queueing theoryApplications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]60Kxx k 60K35Interacting random processesInteracting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]60Kxx 60K37Processes in random environmentsProcesses in random environments60Kxx60K99,60J801 " / 60K40Physical appl. of random processesOther physical applications of random processes60Kxx & 60K99Special processesNone of the above, but in this section60Kxx 60KxxSpecial processesSpecial processes60-XX G 62-00Reference works (statistics)General reference works (handbooks, dictionaries, bibliographies, etc.)62-XX ; 62-01Textbooks (statistics)Instructional exposition (textbooks, tutorial papers, etc.)62-XX 1 62-02Research monographs (statistics)Research exposition (monographs, survey articles)62-XX U 62-03Historical (statistics)Historical (must also be assigned at least one classification number from Section 01)62-XX * X 62-04Machine computation, programs (statistics)Explicit machine computation and programs (not the theory of computation or programming)62-XX ' + 62-06Proceedings of conferences (statistics)Proceedings, conferences, collections, etc.62-XX
62-07Data analysis (statistics)Data analysis62-XX 62-09Graphical methods in statisticsGraphical methods62-XX
62-99StatisticsStatistics
62-XXStatisticsStatistics % % 62A01Foundational and philosophical topicsFoundational and philosophical topics62-XX62Axx1 62B05Sufficient statisticsSufficient statistics and fields62Bxx - 62B10Statistical information theoryInformation-theoretic topics [See also 94A17]62Bxx % ! 62B15Comparison of statistical experimentsTheory of statistical experiments62Bxx ' & 62B99Statistical sufficiency and informationNone of the above, but in this section62Bxx ' 62BxxStatistical sufficiency and informationSufficiency and information62-XX 5 62C05General considerations in statistical decision theoryGeneral considerations62Cxx 5 62C07Complete class results in statistical decision theoryComplete class results62Cxx 7 62C10Bayesian problemsBayesian problems; characterization of Bayes procedures62Cxx ) 9 62C12Empirical statistical decision proceduresEmpirical decision procedures; empirical Bayes procedures62Cxx
62C15statistical admissibilityAdmissibility62Cxx 62C20Statistical minimax proceduresMinimax procedures62Cxx ( 62C25Compound decision problems in statisticsCompound decision problems62Cxx & 62C99Statistical decision theoryNone of the above, but in this section62Cxx C 62CxxStatistical decision theoryDecision theory [See also 90B50, 91B06; for game theory, see 91A35]62-XX 62D05Statistical sampling theorySampling theory, sample surveys62-XX - % 62E10Structure theory of statistical distributionsCharacterization and structure theory62Exx ' 62E15Exact distribution theory in statisticsExact distribution theory62Exx ; / 62E17Approximations to statistical distributions (nonasymptotic)Approximations to distributions (nonasymptotic)62Exx , 62E20Asymptotic distribution theory in statisticsAsymptotic distribution theory62Exx & 62E99Statistical distribution theoryNone of the above, but in this section62Exx $ 62ExxStatistical distribution theoryDistribution theory [See also 60Exx]62-XX 62F03Parametric hypothesis testingHypothesis testing62Fxx ) 62F05Asymptotic properties of parametric testsAsymptotic properties of tests62Fxx , 62F07Statistical ranking and selection proceduresRanking and selection62Fxx 62F10Point estimationPoint estimation62Fxx . # 62F12Asymptotic properties of parametric estimatorsAsymptotic properties of estimators62Fxx 62F15Bayesian inferenceBayesian inference62Fxx # 62F25Parametric confidence regions, etc.Tolerance and confidence regions62Fxx ' 62F30Statistical inference under constraintsInference under constraints62Fxx " " 62F35Robustness and adaptive proceduresRobustness and adaptive procedures62Fxx 1 62F40Resampling methodsBootstrap, jackknife and other resampling methods62Fxx62F99,62G091 & 62F99Parametric inferenceNone of the above, but in this section62Fxx 62FxxParametric inferenceParametric inference62-XX
62G05Nonparametric estimationEstimation62Gxx 62G07Curve estimationDensity estimation62Gxx 62G08Nonparametric regressionNonparametric regression62Gxx62G05,62J02,62G991 62G09Statistical resampling methodsResampling methods62Gxx 62G10Nonparametric hypothesis testingHypothesis testing62Gxx & 62G15Nonparametric confidence regions, etc.Tolerance and confidence regions62Gxx # 62G20Nonparametric asymptotic efficiencyAsymptotic properties62Gxx 2 62G30Order statistics, etc.Order statistics; empirical distribution functions62Gxx , , 62G32Statistics of extreme values; tail inferenceStatistics of extreme values; tail inference62Gxx62G30,62G991
62G35Nonparametric robustnessRobustness62Gxx & 62G99Nonparametric inferenceNone of the above, but in this section62Gxx 62GxxNonparametric inferenceNonparametric inference62-XX % 62H05Multivariate structure theoryCharacterization and structure theory62Hxx ( 62H10Multivariate distributions of statisticsDistribution of statistics62Hxx $ $ 62H11Directional data; spatial statisticsDirectional data; spatial statistics62Hxx
62H12Multivariate estimationEstimation62Hxx 62H15Multivariate hypothesis testingHypothesis testing62Hxx 62H17Contingency (statistics)Contingency tables62Hxx $ B 62H20Statistical measures of associationsMeasures of association (correlation, canonical correlation, etc.)62Hxx A 62H25Factor analysis, etc.Factor analysis and principal components; correspondence analysis62Hxx D 62H30Statistical classification, etc.Classification and discrimination; cluster analysis [See also 68T10]62Hxx 62H35Image analysisImage analysis62Hxx62H99,62M401 & 62H99Multivariate analysisNone of the above, but in this section62Hxx & 62HxxMultivariate analysisMultivariate analysis [See also 60Exx]62-XX 62J02General nonlinear regressionGeneral nonlinear regression62Jxx 62J05Linear regressionLinear regression62Jxx & 62J07Ridge regressionRidge regression; shrinkage estimators62Jxx # 62J10Analysis of variance, etc.Analysis of variance and covariance62Jxx 62J12Generalized linear modelsGeneralized linear models62Jxx 62J15Multiple comparisonsPaired and multiple comparisons62Jxx 62J20Regression diagnosticsDiagnostics62Jxx & 62J99Linear statistical inferenceNone of the above, but in this section62Jxx 62JxxLinear statistical inferenceLinear inference, regression62-XX 62K05Optimal statistical designsOptimal designs62Kxx
62K10Statistical block designsBlock designs62Kxx 62K15Factorial statistical designsFactorial designs62Kxx 62K20Response surface designsResponse surface designs62Kxx62K05,62K991 62K25Robust parameter designsRobust parameter designs62Kxx62K991 & 62K99Experimental statistical designNone of the above, but in this section62Kxx & 62KxxExperimental statistical designDesign of experiments [See also 05Bxx]62-XX 62L05Sequential statistical designsSequential design62Lxx 62L10Sequential statistical analysisSequential analysis62Lxx 62L12Sequential estimationSequential estimation62Lxx ( 62L15Optimal stopping (statistics)Optimal stopping [See also 60G40, 91A60]62Lxx 62L20Stochastic approximationStochastic approximation62Lxx & 62L99Sequential statistical methodsNone of the above, but in this section62Lxx 62LxxSequential statistical methodsSequential methods62-XX $ $ 62M02Markov processes: hypothesis testingMarkov processes: hypothesis testing62Mxx 62M05Markov processes: estimationMarkov processes: estimation62Mxx + + 62M07Non-Markovian processes: hypothesis testingNon-Markovian processes: hypothesis testing62Mxx # # 62M09Non-Markovian processes: estimationNon-Markovian processes: estimation62Mxx @ 62M10Time series, etc. (statistics)Time series, auto-correlation, regression, etc. [See also 91B84]62Mxx 62M15Spectral analysis of processesSpectral analysis62Mxx E 62M20Prediction, etc. (statistics)Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]62Mxx 62M30Statistics of spatial processesSpatial processes62Mxx 62M40Statistics of random fieldsRandom fields; image analysis62Mxx " " 62M45Neural nets and related approachesNeural nets and related approaches62Mxx62M991 # & 62M99Inference from stochastic processesNone of the above, but in this section62Mxx # # 62MxxInference from stochastic processesInference from stochastic processes62-XX 62N01Censored data modelsCensored data models62Nxx62G99,62G05,62G07,62G101
62N02EstimationEstimation62Nxx62G05,62G07,62F10,62F11,62F121 62N03TestingTesting62Nxx62G10,62F03,62F04,62F051 - 62N05Reliability, etc. (statistics)Reliability and life testing [See also 90B25]62Nxx # & 62N99Survival analysis and censored dataNone of the above, but in this section62Nxx # 62NxxEngineering statisticsSurvival analysis and censored data62-XX C < 62P05Appl. of statistics to actuarial sciences and financial mathematicsApplications to actuarial sciences and financial mathematics62Pxx , 62P10Appl. of statistics to biologyApplications to biology and medical sciences62Pxx 0 0 62P12Applications to environmental and related topicsApplications to environmental and related topics62Pxx62P10,62P991 ! 62P15Appl. of statistics to psychologyApplications to psychology62Pxx * 62P20Appl. of statistics to economicsApplications to economics [See also 91Bxx]62Pxx & 62P25Appl. of statistics to social sciencesApplications to social sciences62Pxx ( ( 62P30Applications in engineering and industryApplications in engineering and industry62Pxx62N05,62N10,62N991 % 62P35Applications of statistics to physicsApplications to physics62Pxx62P991 & 62P99Appl. of statisticsNone of the above, but in this section62Pxx + 62PxxAppl. of statisticsApplications [See also 90-XX, 91-XX, 92-XX]62-XX 62Q05Statistical tablesStatistical tables62-XX $ G 65-00Reference works (numerical analysis)General reference works (handbooks, dictionaries, bibliographies, etc.)65-XX ; 65-01Textbooks (numerical analysis)Instructional exposition (textbooks, tutorial papers, etc.)65-XX ( 1 65-02Research monographs (numerical analysis)Research exposition (monographs, survey articles)65-XX U 65-03Historical (numerical analysis)Historical (must also be assigned at least one classification number from Section 01)65-XX 2 X 65-04Machine computation, programs (numerical analysis)Explicit machine computation and programs (not the theory of computation or programming)65-XX 65-05Experimental papersExperimental papers65-XX / + 65-06Proceedings of conferences (numerical analysis)Proceedings, conferences, collections, etc.65-XX 65-99Numerical analysisNumerical analysis 65-XXNumerical analysisNumerical analysis 65A05TablesTables65-XX 0 65B05Extrapolation to the limitExtrapolation to the limit, deferred corrections65Bxx 65B10Summation of seriesSummation of series65Bxx 65B15Euler-Maclaurin formulaEuler-Maclaurin formula65Bxx & 65B99Acceleration of convergenceNone of the above, but in this section65Bxx 65BxxAcceleration of convergenceAcceleration of convergence65-XX 65C05Monte Carlo methodsMonte Carlo methods65Cxx 65C10Random number generationRandom number generation65Cxx * 65C20Models (numerical methods)Models, numerical methods [See also 68U20]65Cxx . . 65C30Stochastic differential and integral equationsStochastic differential and integral equations65Cxx65U05,65L99,65M99,65N99,65R991 , 65C35Stochastic particle methodsStochastic particle methods [See also 82C80]65Cxx65C991 65C40Computational Markov chainsComputational Markov chains65Cxx65U051 + + 65C50Other computational problems in probabilityOther computational problems in probability65Cxx65U051 $ $ 65C60Computational problems in statisticsComputational problems in statistics65Cxx65U051 & 65C99Numerical simulationNone of the above, but in this section65Cxx v 65CxxNumerical simulationProbabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see 68U20 and 60H35}65-XX !
65D05Interpolation (numerical methods)Interpolation65Dxx 65D07Splines (numerical methods)Splines65Dxx 65D10SmoothingSmoothing, curve fitting65Dxx ' ' 65D15Algorithms for functional approximationAlgorithms for functional approximation65Dxx 7 H 65D17Computer aided design (modeling of curves and surfaces)Computer aided design (modeling of curves and surfaces) [See also 68U07]65Dxx , D 65D18Computer graphics and computational geometryComputer graphics and computational geometry [See also 51N05, 68U05]65Dxx65Y251 I 65D20Computation of special functionsComputation of special functions, construction of tables [See also 33F05]65Dxx 65D25Numerical differentiationNumerical differentiation65Dxx 65D30Numerical integrationNumerical integration65Dxx ' 65D32Quadrature formulas (numerical methods)Quadrature and cubature formulas65Dxx & 65D99Numerical approximationNone of the above, but in this section65Dxx j 65DxxNumerical approximationNumerical approximation and computational geometry {Primarily algorithms; for theory, see 41-XX and 68Uxx}65-XX % v 65E05Numerical methods in complex analysisNumerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see 30C30}65-XX ! 6 65F05Direct methods for linear systemsDirect methods for linear systems and matrix inversion65Fxx $ 5 65F10Iterative methods for linear systemsIterative methods for linear systems [See also 65N22]65Fxx & 65F15Eigenvalues (numerical linear algebra)Eigenvalues, eigenvectors65Fxx 65F18Inverse eigenvalue problemsInverse eigenvalue problems65Fxx65F151 1 & 65F20Overdetermined systems (numerical linear algebra)Overdetermined systems, pseudoinverses65Fxx 65F22Ill-posedness, regularizationIll-posedness, regularization65Fxx65F20,65F991 , 65F25Orthogonalization (numerical linear algebra)Orthogonalization65Fxx 65F30Other matrix algorithmsOther matrix algorithms65Fxx - ; 65F35Matrix norms, etc. (numerical linear algebra)Matrix norms, conditioning, scaling [See also 15A12, 15A60]65Fxx ' 65F40Determinants (numerical linear algebra)Determinants65Fxx 65F50Sparse matricesSparse matrices65Fxx & 65F99Numerical linear algebraNone of the above, but in this section65Fxx 65FxxNumerical linear algebraNumerical linear algebra65-XX - - 65G20Algorithms with automatic result verificationAlgorithms with automatic result verification65Gxx65G10,65G991 65G30Interval and finite arithmeticInterval and finite arithmetic65Gxx65G101 $ $ 65G40General methods in interval analysisGeneral methods in interval analysis65Gxx65G101 65G50Roundoff errorRoundoff error65Gxx65G051 & 65G99Error analysisNone of the above, but in this section65Gxx $ 65GxxError analysisError analysis and interval analysis65-XX . 65H05Single nonlinear equations (numerical methods)Single equations65Hxx 2 65H10Systems of nonlinear equations (numerical methods)Systems of equations65Hxx D F 65H17Eigenvalue and bifurcation problems of nonlinear algebraic equationsEigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]65Hxx - E 65H20Global methods, including homotopy approachesGlobal methods, including homotopy approaches [See also 58C30, 90C30]65Hxx / & 65H99Nonlinear algebraic or transcendental equationsNone of the above, but in this section65Hxx / / 65HxxNonlinear algebraic or transcendental equationsNonlinear algebraic or transcendental equations65-XX 6 65J05General theory of numerical methods in abstract spacesGeneral theory65Jxx 3 2 65J10Equations with linear operators (numerical methods)Equations with linear operators (do not use 65Fxx)65Jxx 6 5 65J15Equations with nonlinear operators (numerical methods)Equations with nonlinear operators (do not use 65Hxx)65Jxx @ ) 65J20Improperly posed problems (numerical methods in abstract spaces)Improperly posed problems; regularization65Jxx 65J22Inverse problemsInverse problems65Jxx65J201 % & 65J99Numerical analysis in abstract spacesNone of the above, but in this section65Jxx % % 65JxxNumerical analysis in abstract spacesNumerical analysis in abstract spaces65-XX , ; 65K05Mathematical programming (numerical methods)Mathematical programming {Algorithms; for theory see 90Cxx}65Kxx + ? 65K10Optimization techniques (numerical methods)Optimization and variational techniques [See also 49Mxx, 93B40]65Kxx ? & 65K99Numerical methods for mathematical programming and optimizationNone of the above, but in this section65Kxx > A 65KxxNumerical methods in mathematical programming and optimizationMathematical programming, optimization and variational techniques65-XX 2 65L05Initial value problems for ODE (numerical methods)Initial value problems65Lxx 1 0 65L06Multistep, Runge-Kutta, and extrapolation methodsMultistep, Runge-Kutta and extrapolation methods65Lxx 8 1 65L07Numerical investigation of stability of solutions of ODENumerical investigation of stability of solutions65Lxx 5 65L08Improperly posed problems for ODE (numerical methods)Improperly posed problems65Lxx 65L09Inverse problemsInverse problems65Lxx65L081 3 65L10Boundary value problems for ODE (numerical methods)Boundary value problems65Lxx ! 65L12Finite difference methods for ODEFinite difference methods65Lxx / 65L15Eigenvalue problems for ODE (numerical methods)Eigenvalue problems65Lxx & . 65L20Stability of numerical methods for ODEStability and convergence of numerical methods65Lxx $ 65L50Mesh generation and refinement (ODE)Mesh generation and refinement65Lxx @ 65L60Finite numerical methods for ODEFinite elements, Rayleigh-Ritz, Galerkin and collocation methods65Lxx ( 65L70Error bounds (numerical methods for ODE)Error bounds65Lxx , , 65L80Methods for differential-algebraic equationsMethods for differential-algebraic equations65Lxx65L991 & 65L99Numerical methods for ODENone of the above, but in this section65Lxx 65LxxNumerical methods for ODEOrdinary differential equations65-XX & 65M06Finite difference methods (IVP of PDE)Finite difference methods65Mxx ; . 65M12Stability and convergence of numerical methods (IVP of PDE)Stability and convergence of numerical methods65Mxx 65M15Error bounds (IVP of PDE)Error bounds65Mxx 65M20Method of lines (IVP of PDE)Method of lines65Mxx % 65M25Method of characteristics (numerical)Method of characteristics65Mxx 9 65M30Improperly posed problems (IVP of PDE, numerical methods)Improperly posed problems65Mxx 65M32Inverse problemsInverse problems65Mxx65M301 + 65M50Mesh generation and refinement (IVP of PDE)Mesh generation and refinement65Mxx 4 ' 65M55Multigrid methods; domain decomposition (IVP of PDE)Multigrid methods; domain decomposition65Mxx % C 65M60Finite numerical methods (IVP of PDE)Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65Mxx 6 ) 65M70Spectral, collocation and related methods (IVP of PDE)Spectral, collocation and related methods65Mxx & 65M99Numerical methods for IVP of PDENone of the above, but in this section65Mxx 9 ` 65MxxNumerical methods for initial value problems (IVP) of PDEPartial differential equations, initial value and time-dependent initial-boundary value problems65-XX & 65N06Finite difference methods (BVP of PDE)Finite difference methods65Nxx ; . 65N12Stability and convergence of numerical methods (BVP of PDE)Stability and convergence of numerical methods65Nxx 65N15Error bounds (BVP of PDE)Error bounds65Nxx 65N21Inverse problemsInverse problems65Nxx65N991 . 9 65N22Solution of discretized equations (BVP of PDE)Solution of discretized equations [See also 65Fxx, 65Hxx]65Nxx 6 65N25Numerical methods for eigenvalue problems (BVP of PDE)Eigenvalue problems65Nxx % C 65N30Finite numerical methods (BVP of PDE)Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods65Nxx ) 65N35Collocation methods (BVP of PDE)Spectral, collocation and related methods65Nxx % 65N38Boundary element methods (BVP of PDE)Boundary element methods65Nxx 65N40Methods of lines (BVP of PDE)Method of lines65Nxx 2 % 65N45Method of contraction of the boundary (BVP of PDE)Method of contraction of the boundary65Nxx + 65N50Mesh generation and refinement (BVP of PDE)Mesh generation and refinement65Nxx 4 ' 65N55Multigrid methods; domain decomposition (BVP of PDE)Multigrid methods; domain decomposition65Nxx & 65N99Numerical methods for BVP of PDENone of the above, but in this section65Nxx : 7 65Nxxnumerical methods for boundary value problems (BVP) of PDEPartial differential equations, boundary value problems65-XX 4 4 65P10Hamiltonian systems including symplectic integratorsHamiltonian systems including symplectic integrators65Pxx58F051 65P20Numerical chaosNumerical chaos65Pxx58F131 65P30Bifurcation problemsBifurcation problems65Pxx58E07,47H171 65P40Nonlinear stabilitiesNonlinear stabilities65Pxx58F101 & & 65P99None of the above, but in this sectionNone of the above, but in this section65Pxx58F991 ' 8 65PxxNumerical problems in dynamical systemsNumerical problems in dynamical systems [See also 37Mxx]65-XX * 9 65Q05Numerical methods for functional equationsDifference and functional equations, recurrence relations65-XX ' 65R10Integral transforms (numerical methods)Integral transforms65Rxx & 65R20Integral equations (numerical methods)Integral equations65Rxx A 65R30Improperly posed problems (integral equations, numerical methods)Improperly posed problems65Rxx 65R32Inverse problemsInverse problems65Rxx65R301 7 & 65R99Numerical methods for integral equations and transformsNone of the above, but in this section65Rxx 7 ' 65RxxNumerical methods for integral equations and transformsIntegral equations, integral transforms65-XX ' 65S05Graphical methods of numerical analysisGraphical methods65-XX - - 65T40Trigonometric approximation and interpolationTrigonometric approximation and interpolation65Txx65T101 $ $ 65T50Discrete and fast Fourier transformsDiscrete and fast Fourier transforms65Txx65T201 65T60WaveletsWavelets65Txx65T20,65T991 % & 65T99Numerical methods in Fourier analysisNone of the above, but in this section65Txx % % 65TxxNumerical methods in Fourier analysisNumerical methods in Fourier analysis65-XX ( 65Y05Parallel computation (numerical methods)Parallel computation65Yxx 0 0 65Y10Algorithms for specific classes of architecturesAlgorithms for specific classes of architectures65Yxx 65Y15Packaged methodsPackaged methods65Yxx 2 C 65Y20Complexity and performance of numerical algorithmsComplexity and performance of numerical algorithms [See also 68Q25]65Yxx ( & 65Y99Computer aspects of numerical algorithmsNone of the above, but in this section65Yxx ( ( 65YxxComputer aspects of numerical algorithmsComputer aspects of numerical algorithms65-XX 65Z05Applications to physicsApplications to physics65-XX65P05,65M99,65N991 " G 68-00Reference works (computer science)General reference works (handbooks, dictionaries, bibliographies, etc.)68-XX ; 68-01Textbooks (computer science)Instructional exposition (textbooks, tutorial papers, etc.)68-XX & 1 68-02Research monographs (computer science)Research exposition (monographs, survey articles)68-XX U 68-03Historical (computer science)Historical (must also be assigned at least one classification number from Section 01)68-XX 0 X 68-04Machine computation, programs (computer science)Explicit machine computation and programs (not the theory of computation or programming)68-XX - + 68-06Proceedings of conferences (computer science)Proceedings, conferences, collections, etc.68-XX 68-99Computer scienceComputer science ‡ 68-XXComputer scienceComputer science {For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area} 68M01GeneralGeneral68Mxx68M051 / . 68M07Mathematical problems of computer architecturesMathematical problems of computer architecture68Mxx 8 68M10Computer networksNetwork design and communication [See also 68R10, 90B18]68Mxx 68M12Network protocolsNetwork protocols68Mxx68M101 68M14Distributed systemsDistributed systems68Mxx68M101 + 9 68M15Reliability and testing of computer systemsReliability, testing and fault tolerance [See also 94C12]68Mxx 0 D 68M20Performance evaluation of computer systems, etc.Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]68Mxx & 68M99Computer system organizationNone of the above, but in this section68Mxx 68MxxComputer system organizationComputer system organization68-XX 68N01GeneralGeneral68Nxx68N051 68N15Programming languagesProgramming languages68Nxx 68N17Logic programmingLogic programming68Nxx * ; 68N18Functional programming and lambda calculusFunctional programming and lambda calculus [See also 03B40]68Nxx68N15,03B401 W 68N19Other programming techniquesOther programming techniques (object-oriented, sequential, concurrent, automatic, etc.)68Nxx68N991 68N20Compilers and generatorsCompilers and interpreters68Nxx 68N25Monitors and operating systemsOperating systems68Nxx , g 68N30Mathematical aspects of software engineeringMathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)68Nxx68N99,68Q601 & 68N99SoftwareNone of the above, but in this section68Nxx 68NxxSoftwareSoftware68-XX 68P01GeneralGeneral68Pxx68P99,68Pxx1 68P05Data structuresData structures68Pxx 68P10Searching and sortingSearching and sorting68Pxx 68P15Database theoryDatabase theory68Pxx ! ! 68P20Information storage and retrievalInformation storage and retrieval68Pxx ' 68P25Data encryptionData encryption [See also 94A60, 81P68]68Pxx y 68P30Coding and information theoryCoding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]68Pxx68P99,94A291 & 68P99Theory of dataNone of the above, but in this section68Pxx 68PxxTheory of dataTheory of data68-XX 68Q01GeneralGeneral68Qxx68Q99,68Qxx1 E 68Q05Models of computationModels of computation (Turing machines, etc.) [See also 03D10, 81P68]68Qxx d 68Q10Modes of computationModes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]68Qxx ! i 68Q15Complexity classes of computationComplexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]68Qxx $ u 68Q17Computational difficulty of problemsComputational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]68Qxx68Q25,68Q151 ( 9 68Q19Descriptive complexity and finite modelsDescriptive complexity and finite models [See also 03C13]68Qxx03C131 - > 68Q25Analysis of algorithms and problem complexityAnalysis of algorithms and problem complexity [See also 68W40]68Qxx < 68Q30Algorithmic information theoryAlgorithmic information theory (Kolmogorov complexity, etc.)68Qxx . 68Q32Computational learning theoryComputational learning theory [See also 68T05]68Qxx68T05,68Q991 68Q42Rewriting systemsGrammars and rewriting systems68Qxx < 68Q45Formal languagesFormal languages and automata [See also 03D05, 68Q70, 94A45]68Qxx ( 68Q55SemanticsSemantics [See also 03B70, 06B35, 18C50]68Qxx * V 68Q60Specification and verification of programsSpecification and verification (program logics, model checking, etc.) [See also 03B70]68Qxx , = 68Q65Abstract data types; algebraic specificationAbstract data types; algebraic specification [See also 18C50]68Qxx B 68Q70Algebraic theory of automataAlgebraic theory of languages and automata [See also 18B20, 20M35]68Qxx " 68Q80Cellular and array automataCellular automata [See also 37B15]68Qxx ; s 68Q85Models and methods for concurrent and distributed computingModels and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)68Qxx68Q101 & 68Q99Theory of computingNone of the above, but in this section68Qxx 68QxxTheory of computingTheory of computing68-XX 68R01GeneralGeneral68Rxx68R99,68Rxx1 1
68R05Combinatorics in connection with computer scienceCombinatorics68Rxx 0 2 68R10Graph theory in connection with computer scienceGraph theory [See also 05Cxx, 90B10, 90B35, 90C35]68Rxx 68R15Combinatorics on wordsCombinatorics on words68Rxx 4 & 68R99Discrete mathematics in relation to computer scienceNone of the above, but in this section68Rxx 4 4 68RxxDiscrete mathematics in relation to computer scienceDiscrete mathematics in relation to computer science68-XX ) 68T01Artificial intelligence (general aspects)General68Txx 5 68T05Learning and adaptive systemsLearning and adaptive systems [See also 68Q32, 91E40]68Txx I 68T10Pattern recognitionPattern recognition, speech recognition {For cluster analysis, see 62H30}68Txx > 68T15Theorem provingTheorem proving (deduction, resolution, etc.) [See also 03B35]68Txx 5 68T20Problem solvingProblem solving (heuristics, search strategies, etc.)68Txx 68T27AI logicsLogic in artificial intelligence68Txx 68T30Knowledge representationKnowledge representation68Txx N 68T35AI software systemsLanguages and software systems (knowledge-based systems, expert systems, etc.)68Txx 68T37Reasoning under uncertaintyReasoning under uncertainty68Txx68T27,68T301 68T40RoboticsRobotics [See also 93C85]68Txx70B15,93C85,68T991 & & 68T45Machine vision and scene understandingMachine vision and scene understanding68Txx68U101 , 68T50Natural language processingNatural language processing [See also 03B65]68Txx68S051 & 68T99Artificial intelligenceNone of the above, but in this section68Txx 68TxxArtificial intelligenceArtificial intelligence68-XX 68U01GeneralGeneral68Uxx68U99,68Uxx1 : 68U05Computational geometry, etc.Computer graphics; computational geometry [See also 65D18]68Uxx & 68U07Computer aided designComputer-aided design [See also 65D17]68Uxx 68U10Image processingImage processing68Uxx ( 68U15Text processingText processing; mathematical typography68Uxx
68U20SimulationSimulation [See also 65Cxx]68Uxx N 68U35Information systemsInformation systems (hypertext navigation, interfaces, decision support, etc.)68Uxx68U991 & 68U99Computing methodologiesNone of the above, but in this section68Uxx ( 68UxxComputing methodologiesComputing methodologies and applications68-XX 68W01GeneralGeneral68Wxx68Q201 68W05Nonnumerical algorithmsNonnumerical algorithms68Wxx68Q201 68W10Parallel algorithmsParallel algorithms68Wxx68Q221 68W15Distributed algorithmsDistributed algorithms68Wxx68Q221 68W20Randomized algorithmsRandomized algorithms68Wxx68Q201 68W25Approximation algorithmsApproximation algorithms68Wxx68Q201 . i 68W30Symbolic computation and algebraic computationSymbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]68Wxx68Q401 68W35VLSI algorithmsVLSI algorithms68Wxx68Q351 ' 68W40Analysis of algorithmsAnalysis of algorithms [See also 68Q25]68Wxx68Q251 & & 68W99None of the above, but in this sectionNone of the above, but in this section68Wxx68Q201
_ 68WxxAlgorithmsAlgorithms {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 68Rxx}68-XX 4 G 70-00Reference works (mechanics of particles and systems)General reference works (handbooks, dictionaries, bibliographies, etc.)70-XX . ; 70-01Textbooks (mechanics of particles and systems)Instructional exposition (textbooks, tutorial papers, etc.)70-XX 8 1 70-02Research monographs (mechanics of particles and systems)Research exposition (monographs, survey articles)70-XX / U 70-03Historical (mechanics of particles and systems)Historical (must also be assigned at least one classification number from Section 01)70-XX B X 70-04Machine computation, programs (mechanics of particles and systems)Explicit machine computation and programs (not the theory of computation or programming)70-XX 8 70-05Experimental papers (mechanics of particles and systems)Experimental work70-XX ? + 70-06Proceedings of conferences (mechanics of particles and systems)Proceedings, conferences, collections, etc.70-XX : 70-08Computational methods (mechanics of particles and systems)Computational methods70-XX " " 70-99Mechanics of particles and systemsMechanics of particles and systems " z 70-XXMechanics of particles and systemsMechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX} + 70A05Axiomatics, foundations (general mechanics)Axiomatics, foundations70-XX 70B05Kinematics of particleKinematics of a particle70Bxx 70B10Kinematics of a rigid bodyKinematics of a rigid body70Bxx
1 70B15MechanismsMechanisms, robots [See also 68T40, 70Q05, 93C85]70Bxx
& 70B99KinematicsNone of the above, but in this section70Bxx
70BxxKinematicsKinematics [See also 53A17]70-XX 70C20StaticsStatics70-XX 70E05Motion of the gyroscopeMotion of the gyroscope70Exx , 70E15Motion of rigid bodiesFree motion of a rigid body [See also 70M20]70Exx ) ) 70E17Motion of a rigid body with a fixed pointMotion of a rigid body with a fixed point70Exx70E151 6 G 70E18Motion of a rigid body in contact with a solid surfaceMotion of a rigid body in contact with a solid surface [See also 70F25]70Exx70E15,70F251 * - 70E20Perturbation methods for Euler's equationsPerturbation methods for rigid body dynamics70Exx 70E40Integrable cases of motionIntegrable cases of motion70Exx70E15,70H05,58F071 " " 70E45Higher-dimensional generalizationsHigher-dimensional generalizations70Exx70E15,58F05,58F071 70E50Stability problemsStability problems70Exx34Dxx,70K15,70K201 70E55Dynamics of multibody systemsDynamics of multibody systems70Exx70E991 9 70E60Robot dynamics and controlRobot dynamics and control [See also 68T40, 70Q05, 93C85]70Exx70B15,70Q05,93C851 & 70E99Dynamics of a rigid bodyNone of the above, but in this section70Exx 1 70ExxDynamics of a rigid bodyDynamics of a rigid body and of multibody systems70-XX 70F05Two-body problemTwo-body problems70Fxx 70F07Three-body problemThree-body problems70Fxx 70F10n-body problem$n$-body problems70Fxx 70F15Celestial mechanicsCelestial mechanics70Fxx 1 1 70F16Collisions in celestial mechanics, regularizationCollisions in celestial mechanics, regularization70Fxx70F10,70F15,70F351 70F17Inverse problemsInverse problems70Fxx70F991 70F20Holonomic systemsHolonomic systems70Fxx 70F25Nonholonomic systemsNonholonomic systems70Fxx
) 70F35CollisionsCollision of rigid or pseudo-rigid bodies70Fxx 70F40Problems with frictionProblems with friction70Fxx70F991 70F45Infinite particle systemsInfinite particle systems70Fxx70F99,70H05,58F05,58F991 ! & 70F99Dynamics of a system of particlesNone of the above, but in this section70Fxx ! @ 70FxxDynamics of a system of particlesDynamics of a system of particles, including celestial mechanics70-XX T 70G10Generalized coordinates etc.Generalized coordinates; event, impulse-energy, configuration, state, or phase space70Gxx 0 0 70G40Topological and differential-topological methodsTopological and differential-topological methods70Gxx57R99,58F05,58F07,58F99,70H991 ’ 70G45Differential-geometric methodsDifferential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]70Gxx53C15,53C80,58F05,70G051 70G55Algebraic geometry methodsAlgebraic geometry methods70Gxx58F99,70H991 70G60Dynamical systems methodsDynamical systems methods70Gxx34C35,58F05,58F401 - - 70G65Symmetries, Lie-group and Lie-algebra methodsSymmetries, Lie-group and Lie-algebra methods70Gxx22E70,58F35,70H331 70G70Functional-analytic methodsFunctional-analytic methods70Gxx47H99,70H991 70G75Variational methodsVariational methods70Gxx49J40,49S05,58E99,70H25,70H301 , & 70G99General representations of dynamical systemsNone of the above, but in this section70Gxx , 8 70GxxGeneral representations of dynamical systemsGeneral models, approaches, and methods [See also 37-XX]70-XX 70H03Lagrange's equationsLagrange's equations70Hxx70H35,58F051 70H05Hamilton's equationsHamilton's equations70Hxx 8 8 70H06Completely integrable systems and methods of integrationCompletely integrable systems and methods of integration70Hxx58F05,58F07,70H051 70H07Nonintegrable systemsNonintegrable systems70Hxx34C99,58F05,70H051 1 1 70H08Nearly integrable Hamiltonian systems, KAM theoryNearly integrable Hamiltonian systems, KAM theory70Hxx34C99,58F05,58F30,70H051 70H09Perturbation theoriesPerturbation theories70Hxx34C29,58F05,58F30,70H051 70H11Adiabatic invariantsAdiabatic invariants70Hxx34C99,34E99,70H05,70K991 & & 70H12Periodic and almost periodic solutionsPeriodic and almost periodic solutions70Hxx34C25,34C27,58F22,70H051 70H14Stability problemsStability problems70Hxx34D99,58F12,70K15,70K201 ( 70H15Canonical transformationsCanonical and symplectic transformations70Hxx 70H20Hamilton-Jacobi equationsHamilton-Jacobi equations70Hxx 70H25Hamilton's principleHamilton's principle70Hxx 0 70H30Other variational principles (general mechanics)Other variational principles70Hxx
k 70H33SymmetriesSymmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction70Hxx 70H40Relativistic dynamicsRelativistic dynamics70Hxx 3 R 70H45Constrained dynamics, Dirac's theory of constraintsConstrained dynamics, Dirac's theory of constraints [See also 70F20, 70F25, 70Gxx]70Hxx58F99,70F20,70F25,70G99,70H991 70H50Higher-order theoriesHigher-order theories70Hxx58F05,70H991 $ & 70H99Hamiltonian and Lagrangian mechanicsNone of the above, but in this section70Hxx $ 5 70HxxHamiltonian and Lagrangian mechanicsHamiltonian and Lagrangian mechanics [See also 37Jxx]70-XX ! 70J10Normal modes of linear vibrationsModal analysis70Jxx ' 70J25Stability of linear oscillatory motionsStability70Jxx 70J30Free motions, etc.Free motions70Jxx 70J35Forced motionsForced motions70Jxx 70J40Parametric resonancesParametric resonances70Jxx / H 70J50Discretization of structural vibration problemsSystems arising from the discretization of structural vibration problems70Jxx70J99,73K121 & 70J99Linear vibration theoryNone of the above, but in this section70Jxx + 70JxxLinear vibration theory (general mechanics)Linear vibration theory70-XX ( " 70K05Phase plane analysis (general mechanics)Phase plane analysis, limit cycles70Kxx 7 70K20Stability of nonlinear oscillations (general mechanics)Stability70Kxx 70K25Free motionsFree motions70Kxx 70K28Parametric resonancesParametric resonances70Kxx ( 70K30Nonlinear resonances (general mechanics)Nonlinear resonances70Kxx " 70K40Forced motions (general mechanics)Forced motions70Kxx $ $ 70K42Equilibria and periodic trajectoriesEquilibria and periodic trajectories70Kxx34C05,34C25,70K05,70K101 ) ) 70K43Quasi-periodic motions and invariant toriQuasi-periodic motions and invariant tori70Kxx34C27,58F27,58F30,70H051 ( ( 70K44Homoclinic and heteroclinic trajectoriesHomoclinic and heteroclinic trajectories70Kxx34C37,58F14,70K991 70K45Normal formsNormal forms70Kxx34C20,58F05,58F36,70H051 / 70K50Transition to stochasticity (general mechanics)Bifurcations and instability70Kxx . ? 70K55Transition to stochasticity (chaotic behavior)Transition to stochasticity (chaotic behavior) [See also 37D45]70Kxx58F13,70K501 70K60General perturbation schemesGeneral perturbation schemes70Kxx34C29,58F30,70H05,70K991 70K65Averaging of perturbationsAveraging of perturbations70Kxx34C29,58F30,70H05,70K991 " " 70K70Systems with slow and fast motionsSystems with slow and fast motions70Kxx34C29,34E99,70K991 70K75Nonlinear modesNonlinear modes70Kxx34C15,70K991 & 70K99Nonlinear motionsNone of the above, but in this section70Kxx * * 70KxxNonlinear oscillations (general mechanics)Nonlinear dynamics [See also 34Cxx, 37-XX]70-XX % " 70L05Random vibrations (general mechanics)Random vibrations [See also 74H50]70-XX 70M20Orbital mechanicsOrbital mechanics70-XX
70P05Variable massVariable mass, rockets70-XX < 70Q05Control of mechanical systemsControl of mechanical systems [See also 49-XX, 93Cxx, 93Dxx]70-XX . . 70S05Lagrangian formalism and Hamiltonian formalismLagrangian formalism and Hamiltonian formalism70Sxx58F05,70G50,70H051 70S10Symmetries and conservation lawsSymmetries and conservation laws70Sxx58E15,58F35,70H33,81T131 # # 70S15Yang-Mills and other gauge theoriesYang-Mills and other gauge theories70Sxx58E15,70G50,81T131 & & 70S20More general nonquantum field theoriesMore general nonquantum field theories70Sxx70G50,81T991 & & 70S99None of the above, but in this sectionNone of the above, but in this section70Sxx70G501 E 70SxxClassical field theoriesClassical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]70-XX 0 G 74-00Reference works (mechanics of deformable solids)General reference works (handbooks, dictionaries, bibliographies, etc.)74-XX73-001 * ; 74-01Textbooks (mechanics of deformable solids)Instructional exposition (textbooks, tutorial papers, etc.)74-XX73-011 4 1 74-02Research monographs (mechanics of deformable solids)Research exposition (monographs, survey articles)74-XX73-021 + U 74-03Historical (mechanics of deformable solids)Historical (must also be assigned at least one classification number from Section 01)74-XX73-031 > X 74-04Machine computation, programs (mechanics of deformable solids)Explicit machine computation and programs (not the theory of computation or programming)74-XX73-041 2 74-05Experimental work (mechanics of deformable solids)Experimental work74-XX73-051 ; + 74-06Proceedings of conferences (mechanics of deformable solids)Proceedings, conferences, collections, etc.74-XX73-061 74-99Mechanics of deformable solidsMechanics of deformable solids 74-XXMechanics of deformable solidsMechanics of deformable solids73-XX1 74A05Kinematics of deformationKinematics of deformation74Axx73A05,73B991 74A10StressStress74Axx73A05,73B991 74A15ThermodynamicsThermodynamics74Axx73B30,80A10,80A151 74A20Theory of constitutive functionsTheory of constitutive functions74Axx73B051 , , 74A25Molecular, statistical, and kinetic theoriesMolecular, statistical, and kinetic theories74Axx73B99,82B99,82C991 74A30Nonsimple materialsNonsimple materials74Axx73B181 74A35Polar materialsPolar materials74Axx73B251 ( ( 74A40Random materials and composite materialsRandom materials and composite materials74Axx73B27,73B35,73K201 74A45Theories of fracture and damageTheories of fracture and damage74Axx73M251 5 5 74A50Structured surfaces and interfaces, coexistent phasesStructured surfaces and interfaces, coexistent phases74Axx73B30,80A22,82B26,82B991 74A55Theories of friction (tribology)Theories of friction (tribology)74Axx73T051 74A60Micromechanical theoriesMicromechanical theories74Axx73S101 74A65Reactive materialsReactive materials74Axx80A99,92E991 3 & 74A99Generalities, etc. of continuum mechanics of solidsNone of the above, but in this section74Axx73A05,73B991 3 F 74AxxGeneralities, etc. of continuum mechanics of solidsGeneralities, axiomatics, foundations of continuum mechanics of solids74-XX 74B05Classical linear elasticityClassical linear elasticity74Bxx73C021 ' ' 74B10Linear elasticity with initial stressesLinear elasticity with initial stresses74Bxx73C991 + T 74B15Equations linearized about a deformed stateEquations linearized about a deformed state (small deformations superposed on large)74Bxx73C02,73C50,73C991 74B20Nonlinear elasticityNonlinear elasticity74Bxx73C501 & 74B99Elasitc materialsNone of the above, but in this section74Bxx73C991 74BxxElastic materialsElastic materials74-XX ' ^ 74C05Small-strain, rate-independent theoriesSmall-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)74Cxx73E05,73E991 % M 74C10Small-strain, rate-dependent theoriesSmall-strain, rate-dependent theories (including theories of viscoplasticity)74Cxx73E60,73E991 ' H 74C15Large-strain, rate-independent theoriesLarge-strain, rate-independent theories (including nonlinear plasticity)74Cxx73E99,73G20,73G991 % % 74C20Large-strain, rate-dependent theoriesLarge-strain, rate-dependent theories74Cxx73E99,73G991 & 74C99Plastic materials, etc.None of the above, but in this section74Cxx73E99,73G991 F 74CxxPlastic materials, etc.Plastic materials, materials of stress-rate and internal-variable type74-XX 74D05Linear constitutive equationsLinear constitutive equations74Dxx73F05,73Fxx1 74D10Nonlinear constitutive equationsNonlinear constitutive equations74Dxx73G25,73G991 4 & 74D99Materials of strain-rate type and history type, etc.None of the above, but in this section74Dxx73F99,73G991 4 ž 74DxxMaterials of strain-rate type and history type, etc.Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)74-XX
74E05InhomogeneityInhomogeneity74Exx73B271
74E10AnisotropyAnisotropy74Exx73B401 74E15Crystalline structureCrystalline structure74Exx73B991 74E20GranularityGranularity74Exx73B99,73E991 74E25TextureTexture74Exx73B991 74E30Composite and mixture propertiesComposite and mixture properties74Exx73B27,73B99,73K201 74E35Random structureRandom structure74Exx73B351 74E40Chemical structureChemical structure74Exx80A99,92E991 + & 74E99Material properties given special treatmentNone of the above, but in this section74Exx73B991 + + 74ExxMaterial properties given special treatmentMaterial properties given special treatment74-XX 74F05Thermal effectsThermal effects74Fxx73B301 O 74F10Fluid-solid interactionsFluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)74Fxx73K70,76S051 74F15Electromagnetic effectsElectromagnetic effects74Fxx73R05,78A991 74F20Mixture effectsMixture effects74Fxx73B99,80A991 74F25Chemical and reactive effectsChemical and reactive effects74Fxx80A99,92E991 . & 74F99Coupling of solid mechanics with other effectsNone of the above, but in this section74Fxx73B991 . . 74FxxCoupling of solid mechanics with other effectsCoupling of solid mechanics with other effects74-XX 74G05Explicit solutionsExplicit solutions74Gxx73C02,73E99,73F99,73G991 # \ 74G10Analytic approximation of solutionsAnalytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)74Gxx73C99,73E99,73F99,73G991 $ $ 74G15Numerical approximation of solutionsNumerical approximation of solutions74Gxx73Vxx1 4 4 # 74G20Local existence of solutions (near a given solution)Local existence of solutions (near a given solution)74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 # 74G25Global existence of solutionsGlobal existence of solutions74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 # 74G30Uniqueness of solutionsUniqueness of solutions74Gxx35Q72,73C15,73C35,73E99,73F99,73G991 # 74G35Multiplicity of solutionsMultiplicity of solutions74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 # 74G40Regularity of solutionsRegularity of solutions74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 # 74G45Bounds for solutionsBounds for solutions74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 74G50Saint-Venant's principleSaint-Venant's principle74Gxx73C101 ! ! # 74G55Qualitative behavior of solutionsQualitative behavior of solutions74Gxx35Q72,73C02,73C35,73E99,73F99,73G991 74G60Bifurcation and bucklingBifurcation and buckling74Gxx73C99,73E99,73F99,73G99,73H051 74G65Energy minimizationEnergy minimization74Gxx73C99,73E99,73F99,73G99,73V251 $ $ 74G70Stress concentrations, singularitiesStress concentrations, singularities74Gxx73B50,73C991 74G75Inverse problemsInverse problems74Gxx35Q72,35R30,73C991 # & 74G99Equilibrium (steady-state) problemsNone of the above, but in this section74Gxx73C99,73E99,73F99,73G991 # # 74GxxEquilibrium (steady-state) problemsEquilibrium (steady-state) problems74-XX # 74H05Explicit solutionsExplicit solutions74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx1 # \ 74H10Analytic approximation of solutionsAnalytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)74Hxx73C99,73D991 $ $ 74H15Numerical approximation of solutionsNumerical approximation of solutions74Hxx73Vxx1 # 74H20Existence of solutionsExistence of solutions74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx1 # 74H25Uniqueness of solutionsUniqueness of solutions74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx1 # 74H30Regularity of solutionsRegularity of solutions74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx1 , , ) 74H35Singularities, blowup, stress concentrationsSingularities, blowup, stress concentrations74Hxx35Q72,73B50,73C02,73Dxx,73E50,73F15,73Gxx1 # 74H40Long-time behavior of solutionsLong-time behavior of solutions74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx1
74H45VibrationsVibrations74Hxx73D30,73D35,73K121 74H50Random vibrationsRandom vibrations74Hxx73D99,73K351 ) 74H55StabilityStability74Hxx35Q72,73C02,73Dxx,73E50,73F15,73Gxx,73H101 74H60Dynamical bifurcationDynamical bifurcation74Hxx73D99,73H101 74H65Chaotic behaviorChaotic behavior74Hxx58F13,58F40,73D35,73K121 & 74H99Dynamical problemsNone of the above, but in this section74Hxx73C99,73D991 74HxxDynamical problemsDynamical problems74-XX 74J05Linear wavesLinear waves74Jxx35Q72,73D991
74J10Bulk wavesBulk waves74Jxx73D151
74J15Surface wavesSurface waves74Jxx73D201 74J20Wave scatteringWave scattering74Jxx35P25,35Q72,73D251 74J25Inverse problemsInverse problems74Jxx35Q72,35R30,73D501 74J30Nonlinear wavesNonlinear waves74Jxx35Q72,73D991 74J35Solitary wavesSolitary waves74Jxx35Q51,73D35,73D991 " " 74J40Shocks and related discontinuitiesShocks and related discontinuities74Jxx35Q72,35L67,73D05,73D401 & 74J99WavesNone of the above, but in this section74Jxx35Q72,73D991 74JxxWavesWaves74-XX 74K05StringsStrings74Kxx73K031 2 2 74K10Rods (beams, columns, shafts, arches, rings, etc.)Rods (beams, columns, shafts, arches, rings, etc.)74Kxx73K051 74K15MembranesMembranes74Kxx73K101 74K20PlatesPlates74Kxx73K101 74K25ShellsShells74Kxx73K151 74K30JunctionsJunctions74Kxx73K991
74K35Thin filmsThin films74Kxx73C99,73K991 & 74K99Thin bodies, structuresNone of the above, but in this section74Kxx73K991 74KxxThin bodies, structuresThin bodies, structures74-XX , 74L05Geophysical solid mechanicsGeophysical solid mechanics [See also 86-XX]74Lxx73N201 74L10Soil and rock mechanicsSoil and rock mechanics74Lxx73Q051 . 74L15Biomechanical solid mechanicsBiomechanical solid mechanics [See also 92C10]74Lxx73P20,92C101 $ & 74L99Special subfields of solid mechanicsNone of the above, but in this section74Lxx73-XX1 $ $ 74LxxSpecial subfields of solid mechanicsSpecial subfields of solid mechanics74-XX 3 D 74M05Control, switches and devices (``smart materials'')Control, switches and devices (``smart materials'') [See also 93Cxx]74Mxx73K50,93C20,93C951 74M10FrictionFriction74Mxx70F99,73T051 74M15ContactContact74Mxx73T051 74M20ImpactImpact74Mxx73D051 74M25MicromechanicsMicromechanics74Mxx73S101 + & 74M99Special kind of problems of solid mechanicsNone of the above, but in this section74Mxx73-XX1 74MxxSpecial kind of problemsSpecial kinds of problems74-XX 74N05CrystalsCrystals74Nxx73B10,73B99,73C50,82D251 74N10Displacive transformationsDisplacive transformations74Nxx73B301 74N15Analysis of microstructureAnalysis of microstructure74Nxx73B30,73B99,73S101 74N20Dynamics of phase boundariesDynamics of phase boundaries74Nxx73B30,80A221 # # 74N25Transformations involving diffusionTransformations involving diffusion74Nxx73B30,80A20,80A221 74N30Problems involving hysteresisProblems involving hysteresis74Nxx73B30,47H30,80A991 & 74N99Phase transformations in solidsNone of the above, but in this section74Nxx73B301 E 74NxxPhase transformations in solidsPhase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]74-XX ! ! 74P05Compliance or weight optimizationCompliance or weight optimization74Pxx49Q10,49Q99,73K401 74P10Optimization of other propertiesOptimization of other properties74Pxx49Q10,49Q99,73K401 74P15Topological methodsTopological methods74Pxx49Q10,49Q99,73K401 74P20Geometrical methodsGeometrical methods74Pxx49Q10,49Q99,73K401 & 74P99Optimization solid mechanicsNone of the above, but in this section74Pxx49Q10,49Q99,73K401 74PxxOptimization solid mechanicsOptimization [See also 49Qxx]74-XX & & 74Q05Homogenization in equilibrium problemsHomogenization in equilibrium problems74Qxx35B27,73B27,73K201 5 5 74Q10Homogenization and oscillations in dynamical problemsHomogenization and oscillations in dynamical problems74Qxx35B27,73B27,73K201 74Q15Effective constitutive equationsEffective constitutive equations74Qxx35B27,73B27,73K201 74Q20Bounds on effective propertiesBounds on effective properties74Qxx35B27,73B27,73K201 5 & 74Q99Homogenization, determination of effective propertiesNone of the above, but in this section74Qxx35B27,73B27,73K201 5 5 74QxxHomogenization, determination of effective propertiesHomogenization, determination of effective properties74-XX 74R05Brittle damageBrittle damage74Rxx73M251 74R10Brittle fractureBrittle fracture74Rxx73M251 74R15High-velocity fractureHigh-velocity fracture74Rxx73M251 74R20Anelastic fracture and damageAnelastic fracture and damage74Rxx73M251 & 74R99Fracture and damageNone of the above, but in this section74Rxx73M251 74RxxFracture and damageFracture and damage74-XX 74S05Finite element methodsFinite element methods74Sxx65M60,65N30,73V051 74S10Finite volume methodsFinite volume methods74Sxx65M99,65N99,73V201 74S15Boundary element methodsBoundary element methods74Sxx65M99,65N38,65R20,73V101 74S20Finite difference methodsFinite difference methods74Sxx65M06,65N06,73V151 74S25Spectral and related methodsSpectral and related methods74Sxx65M70,65N35,73V201 74S30Other numerical methodsOther numerical methods74Sxx65Mxx,65Nxx,73V201 $ & 74S99Numerical methods in solid mechanicsNone of the above, but in this section74Sxx65M99,65N99,73V991 $ 0 74SxxNumerical methods in solid mechanicsNumerical methods [See also 65-XX, 74G15, 74H15]74-XX ! G 76-00Reference works (fluid mechanics)General reference works (handbooks, dictionaries, bibliographies, etc.)76-XX ; 76-01Textbooks (fluid mechanics)Instructional exposition (textbooks, tutorial papers, etc.)76-XX % 1 76-02Research monographs (fluid mechanics)Research exposition (monographs, survey articles)76-XX U 76-03Historical (fluid mechanics)Historical (must also be assigned at least one classification number from Section 01)76-XX / X 76-04Machine computation, programs (fluid mechanics)Explicit machine computation and programs (not the theory of computation or programming)76-XX % 76-05Experimental papers (fluid mechanics)Experimental work76-XX , + 76-06Proceedings of conferences (fluid mechanics)Proceedings, conferences, collections, etc.76-XX 76-99Fluid mechanicsFluid mechanics U 76-XXFluid mechanicsFluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} 76A02Foundations of fluid mechanicsFoundations of fluid mechanics76Axx 76A05Non-Newtonian fluidsNon-Newtonian fluids76Axx 76A10Viscoelastic fluidsViscoelastic fluids76Axx 76A15Liquid crystalsLiquid crystals [See also 82D30]76Axx 76A20Thin fluid filmsThin fluid films76Axx76A99,76D991 76A25Superfluids (classical aspects)Superfluids (classical aspects)76Axx76A99,82D501 - & 76A99Foundations, constitutive equations, rheologyNone of the above, but in this section76Axx ) - 76AxxFoundations, constitutive equations, etc.Foundations, constitutive equations, rheology76-XX , = 76B03Existence, uniqueness, and regularity theoryExistence, uniqueness, and regularity theory [See also 35Q35]76Bxx35Q35,76Bxx1 76B07Free-surface potential flowsFree-surface potential flows76Bxx35Q35,76B10,76B15,76B991 s 76B10Free-streamline theory and appl.Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing76Bxx d 76B15Wave motions (fluid mechanics)Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30, 35Q53]76Bxx
76B20Ship wavesShip waves76Bxx & 76B25Solitary waves, etc. (inviscid fluids)Solitary waves [See also 35Q51]76Bxx . 76B45CapillarityCapillarity (surface tension) [See also 76D45]76Bxx 76B47Vortex flowsVortex flows76Bxx35Q35,76C051 76B55Internal wavesInternal waves76Bxx35Q35,76C10,76V051 " 76B60Atmospheric wavesAtmospheric waves [See also 86A10]76Bxx76C15,86A101 $ 76B65Rossby wavesRossby waves [See also 86A05, 86A10]76Bxx76C20,86A05,86A101 ) ) 76B70Stratification effects in inviscid fluidsStratification effects in inviscid fluids76Bxx76V051 < 76B75Flow control and optimizationFlow control and optimization [See also 49Q10, 93C20, 93C95]76Bxx49Q10,76B99,93C20,93C951 0 & 76B99Incompressible inviscid fluids, potential theoryNone of the above, but in this section76Bxx 0 76BxxIncompressible inviscid fluids, potential theoryIncompressible inviscid fluids76-XX , D 76D03Existence, uniqueness, and regularity theoryExistence, uniqueness, and regularity theory [See also 35Q30, 35Q35]76Dxx35Q30,76D051 ( ( 76D05Navier-Stokes equations (fluid dynamics)Navier-Stokes equations [See also 35Q30]76Dxx < T 76D06Statistical solutions of Navier-Stokes and related equationsStatistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]76Dxx35Q30,35Q35,76D05,76M35,60H301 & 76D07Stokes flowsStokes and related (Oseen, etc.) flows76Dxx 76D08Lubrication theoryLubrication theory76Dxx 76D09Viscous-inviscid interactionViscous-inviscid interaction76Dxx76B99,76C99,76D991 - H 76D10Boundary-layer theory (incompressible fluids)Boundary-layer theory, separation and reattachment, higher-order effects76Dxx 76D17Viscous vortex flowsViscous vortex flows76Dxx76D05,76D991 76D25Wakes and jets (viscous fluids)Wakes and jets76Dxx * * 76D27Other free-boundary flows; Hele-Shaw flowsOther free-boundary flows; Hele-Shaw flows76Dxx76D99,76S051 & 76D33Waves in incompressible viscous fluidsWaves76Dxx . 76D45CapillarityCapillarity (surface tension) [See also 76B45]76Dxx ( ( 76D50Stratification effects in viscous fluidsStratification effects in viscous fluids76Dxx76D99,76V051 < 76D55Flow control and optimizationFlow control and optimization [See also 49Q10, 93C20, 93C95]76Dxx49Q10,76D99,93C20,93C951 & 76D99Incompressible viscous fluidsNone of the above, but in this section76Dxx 76DxxIncompressible viscous fluidsIncompressible viscous fluids76-XX 76E05Stability of parallel flowsParallel shear flows76Exx
76E06ConvectionConvection76Exx76E99,76R05,76R101 76E07RotationRotation76Exx76E10,76E99,76U051 . . 76E09Stability and instability of nonparallel flowsStability and instability of nonparallel flows76Exx76E991 ( 1 76E15Convective instability (fluid mechanics)Absolute and convective instability and stability76Exx % % 76E17Interfacial stability and instabilityInterfacial stability and instability76Exx76E10,76E991 76E19Compressibility effectsCompressibility effects76Exx76E99,76N991 @ 76E20Instability of flows in natureStability and instability of geophysical and astrophysical flows76Exx 3 N 76E25Instabilities in presence of electromagnetic forcesStability and instability of magnetohydrodynamic and electrohydrodynamic flows76Exx # 76E30Nonlinear effects (fluid mechanics)Nonlinear effects76Exx & 76E99Hydrodynamic stabilityNone of the above, but in this section76Exx 76ExxHydrodynamic stabilityHydrodynamic stability76-XX 76F02FundamentalsFundamentals76Fxx76Fxx1 , 76F05Homogeneous isotropic turbulenceIsotropic turbulence; homogeneous turbulence76Fxx 76F06Transition to turbulenceTransition to turbulence76Fxx76E99,76F991 76F10Shear flowsShear flows76Fxx 9 76F20Turbulence via chaos techniquesDynamical systems approach to turbulence [See also 37-XX]76Fxx 76F25Turbulent transport, mixingTurbulent transport, mixing76Fxx76F99,76R991 3 D 76F30Renormalization and other field-theoretical methodsRenormalization and other field-theoretical methods [See also 81T99]76Fxx76F99,81T991 - 76F35Convective turbulenceConvective turbulence [See also 76E15, 76Rxx]76Fxx76E15,76F99,76R991 76F40Turbulent boundary layersTurbulent boundary layers76Fxx76D10,76F99,76N201 76F45Stratification effectsStratification effects76Fxx76F99,76V051 76F50Compressibility effectsCompressibility effects76Fxx76F99,76N991 0 76F55Statistical turbulence modelingStatistical turbulence modeling [See also 76M35]76Fxx76F99,76M35,82C991 76F60$k$-$\varepsilon$ modeling$k$-$\varepsilon$ modeling76Fxx76F991 8 8 76F65Direct numerical and large eddy simulation of turbulenceDirect numerical and large eddy simulation of turbulence76Fxx76F99,76M251 76F70Control of turbulent flowsControl of turbulent flows76Fxx76F99,93C20,93C951
& 76F99TurbulenceNone of the above, but in this section76Fxx
) 76FxxTurbulenceTurbulence [See also 37-XX, 60Gxx, 60Jxx]76-XX ' ' 76G25General aerodynamics and subsonic flowsGeneral aerodynamics and subsonic flows76-XX 76H05Transonic flowsTransonic flows76-XX 76J20Supersonic flowsSupersonic flows76-XX 76K05Hypersonic flowsHypersonic flows76-XX , 76L05Shock waves (fluid mechanics)Shock waves and blast waves [See also 35L67]76-XX 76M10Finite element methodsFinite element methods76Mxx 76M12Finite volume methodsFinite volume methods76Mxx76M251 76M15Boundary element methodsBoundary element methods76Mxx 76M20Finite difference methodsFinite difference methods76Mxx 76M22Spectral methodsSpectral methods76Mxx76M251 76M23Vortex methodsVortex methods76Mxx76M251 76M25Other numerical methodsOther numerical methods76Mxx 76M27Visualization algorithmsVisualization algorithms76Mxx76M251 ( ( 76M28Particle methods and lattice-gas methodsParticle methods and lattice-gas methods76Mxx76M251 76M30Variational methodsVariational methods76Mxx 76M35Stochastic analysisStochastic analysis76Mxx 76M40Complex-variables methodsComplex-variables methods76Mxx76M991 * * 76M45Asymptotic methods, singular perturbationsAsymptotic methods, singular perturbations76Mxx76M991 76M50HomogenizationHomogenization76Mxx35B27,76D30,76M991 # # 76M55Dimensional analysis and similarityDimensional analysis and similarity76Mxx76M991 0 0 76M60Symmetry analysis, Lie group and algebra methodsSymmetry analysis, Lie group and algebra methods76Mxx22E70,76M991 & 76M99Basic methods in fluid mechanicsNone of the above, but in this section76Mxx 1 76MxxBasic methods in fluid mechanicsBasic methods in fluid mechanics [See also 65-XX]76-XX K 76N10Compressible fluids, generalExistence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]76Nxx 76N15Gas dynamics, generalGas dynamics, general76Nxx 76N17Viscous-inviscid interactionViscous-inviscid interaction76Nxx76N991 76N20Boundary layer theoryBoundary-layer theory76Nxx 76N25Flow control and optimizationFlow control and optimization76Nxx49Q10,76N99,93C20,93C951 - & 76N99Compressible fluids and gas dynamics, generalNone of the above, but in this section76Nxx - - 76NxxCompressible fluids and gas dynamics, generalCompressible fluids and gas dynamics, general76-XX E 76P05Molecular or atomic structureRarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]76-XX 76Q05Density waves (fluid mechanics)Hydro- and aero-acoustics76-XX 76R05Forced convectionForced convection76Rxx 76R10Free convectionFree convection76Rxx 76R50DiffusionDiffusion [See also 60J60]76Rxx & 76R99Diffusion and convectionNone of the above, but in this section76Rxx * 76RxxDiffusion and convection (fluid mechanics)Diffusion and convection76-XX * 76S05Flows in porous mediaFlows in porous media; filtration; seepage76-XX ( ( 76T10Liquid-gas two-phase flows, bubbly flowsLiquid-gas two-phase flows, bubbly flows76Txx76D99,76N99,76T051 76T15Dusty-gas two-phase flowsDusty-gas two-phase flows76Txx76T051 76T20SuspensionsSuspensions76Txx76T051 & 76T25Granular flowsGranular flows [See also 74C99, 74E20]76Txx73B99,73E99,76A991 76T30Three or more component flowsThree or more component flows76Txx76T051 & & 76T99None of the above, but in this sectionNone of the above, but in this section76Txx76T051 76TxxTwo-phase and multiphase flowsTwo-phase and multiphase flows76-XX 76U05Rotating fluidsRotating fluids76-XX $ * 76V05Interacting phases (fluid mechanics)Reaction effects in flows [See also 80A32]76-XX + - 76W05Flows in presence of electromagnetic forcesMagnetohydrodynamics and electrohydrodynamics76-XX
I 76X05Plasmic flowsIonized gas flow in electromagnetic fields; plasmic flow [See also 82D10]76-XX L 76Y05Nonclassical hydrodynamicsQuantum hydrodynamics and relativistic hydrodynamics [See also 83C55, 85A30]76-XX $ 76Z05Physiological flowsPhysiological flows [See also 92C35]76Zxx
! 76Z10BiopropulsionBiopropulsion in water and in air76Zxx & 76Z99Biological fluid mechanicsNone of the above, but in this section76Zxx 9 76ZxxBiological fluid mechanicsBiological fluid mechanics [See also 74F10, 74L15, 92Cxx]76-XX 0 G 78-00Reference works (optics, electromagnetic theory)General reference works (handbooks, dictionaries, bibliographies, etc.)78-XX * ; 78-01Textbooks (optics, electromagnetic theory)Instructional exposition (textbooks, tutorial papers, etc.)78-XX 4 1 78-02Research monographs (optics, electromagnetic theory)Research exposition (monographs, survey articles)78-XX + U 78-03Historical (optics, electromagnetic theory)Historical (must also be assigned at least one classification number from Section 01)78-XX > X 78-04Machine computation, programs (optics, electromagnetic theory)Explicit machine computation and programs (not the theory of computation or programming)78-XX 4 78-05Experimental papers (optics, electromagnetic theory)Experimental work78-XX ; + 78-06Proceedings of conferences (optics, electromagnetic theory)Proceedings, conferences, collections, etc.78-XX 78-99Optics, electromagnetic theoryOptics, electromagnetic theory > 78-XXOptics, electromagnetic theoryOptics, electromagnetic theory {For quantum optics, see 81V80} 0 78A02Foundations of optics and electromagnetic theoryFoundations78Axx 78A05Geometric opticsGeometric optics78Axx 78A10Physical opticsPhysical optics78Axx 78A15Electron opticsElectron optics78Axx 78A20Space charge wavesSpace charge waves78Axx 78A25General electromagnetic theoryElectromagnetic theory, general78Axx 78A30Electro- and magnetostaticsElectro- and magnetostatics78Axx 78A35Motion of charged particlesMotion of charged particles78Axx 78A40Waves and radiationWaves and radiation78Axx 8 78A45Diffraction, scattering (optics)Diffraction, scattering [See also 34E20 for WKB methods]78Axx 78A46Inverse scattering problemsInverse scattering problems78Axx78A451 78A48optics in special mediaComposite media; random media78Axx78A551 78A50Antennas, wave-guidesAntennas, wave-guides78Axx 4 78A55Technical appl. of optics and electromagnetic theoryTechnical applications78Axx F 78A60Lasers, etc.Lasers, masers, optical bistability, nonlinear optics [See also 81V80]78Axx 5 / 78A70Biological appl. of optics and electromagnetic theoryBiological applications [See also 91D30, 92C30]78Axx : ‹ 78A97Mathematically heuristic optics and electromagnetic theoryMathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)78Axx 9 78A99Miscellaneous topics in optics and electromagnetic theoryMiscellaneous topics78Axx 78AxxGeneralGeneral78-XX 78M05Method of moments (optics)Method of moments78Mxx78-081 78M10Finite element methods (optics)Finite element methods78Mxx65M60,65N30,78-081 ! 78M15Boundary element methods (optics)Boundary element methods78Mxx65N38,78-081 " 78M20Finite difference methods (optics)Finite difference methods78Mxx65M06,65N06,78-081 78M25Numerical methods in opticsOther numerical methods78Mxx65Mxx,65Nxx,78-081 78M30Variational methods (optics)Variational methods78Mxx65Mxx,65Nxx,78-081 78M35Asymptotic analysis (optics)Asymptotic analysis78Mxx65M12,65N12,78-081 78M40HomogenizationHomogenization78Mxx78-081 78M50Optimization (optics)Optimization78Mxx78-081 $ & 78M99Basic mathematical methods in opticsNone of the above, but in this section78Mxx78-081 $
78MxxBasic mathematical methods in opticsBasic methods78-XX * G 80-00Reference works (classical thermodynamics)General reference works (handbooks, dictionaries, bibliographies, etc.)80-XX $ ; 80-01Textbooks (classical thermodynamics)Instructional exposition (textbooks, tutorial papers, etc.)80-XX . 1 80-02Research monographs (classical thermodynamics)Research exposition (monographs, survey articles)80-XX % U 80-03Historical (classical thermodynamics)Historical (must also be assigned at least one classification number from Section 01)80-XX 8 X 80-04Machine computation, programs (classical thermodynamics)Explicit machine computation and programs (not the theory of computation or programming)80-XX . 80-05Experimental papers (classical thermodynamics)Experimental work80-XX 5 + 80-06Proceedings of conferences (classical thermodynamics)Proceedings, conferences, collections, etc.80-XX ' ' 80-99Classical thermodynamics, heat transferClassical thermodynamics, heat transfer ' Q 80-XXClassical thermodynamics, heat transferClassical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15} ' 80A05Foundations of classical thermodynamicsFoundations80Axx 0 80A10Classical thermodynamicsClassical thermodynamics, including relativistic80Axx + 80A17Thermodynamics of continuaThermodynamics of continua [See also 74A15]80Axx731 ! 80A20Heat and mass transferHeat and mass transfer, heat flow80Axx 5 80A22Stefan problems, etc.Stefan problems, phase changes, etc. [See also 74Nxx]80Axx ! 80A23Inverse problems (thermodynamics)Inverse problems80Axx
80A25Combustion, interior ballisticsCombustion80Axx 0 80A30Chemical kineticsChemical kinetics [See also 76V05, 92C45, 92E20]80Axx 1 80A32Chemically reacting flowsChemically reacting flows [See also 92C45, 92E20]80Axx % & 80A50Thermodynamical problems in chemistryChemistry (general) [See mainly 92Exx]80Axx 0 & 80A99Miscellaneous topics in classical thermodynamicsNone of the above, but in this section80Axx 80AxxThermodynamics and heat transferThermodynamics and heat transfer80-XX 80M10Finite element methodsFinite element methods80Mxx80-08,65M60,65N301 80M15Boundary element methodsBoundary element methods80Mxx80-08,65N381 80M20Finite difference methodsFinite difference methods80Mxx80-08,65N06,65M061 80M25Other numerical methodsOther numerical methods80Mxx80-08,65P051 80M30Variational methodsVariational methods80Mxx80-08,65M99,65N991 80M35Asymptotic analysisAsymptotic analysis80Mxx80-08,651 80M40HomogenizationHomogenization80Mxx80-08,651 80M50OptimizationOptimization80Mxx80-08,65K101 & & 80M99None of the above, but in this sectionNone of the above, but in this section80Mxx80-08,651
80MxxBasic methodsBasic methods80-XX G 81-00Reference works (quantum theory)General reference works (handbooks, dictionaries, bibliographies, etc.)81-XX ; 81-01Textbooks (quantum theory)Instructional exposition (textbooks, tutorial papers, etc.)81-XX $ 1 81-02Research monographs (quantum theory)Research exposition (monographs, survey articles)81-XX U 81-03Historical (quantum theory)Historical (must also be assigned at least one classification number from Section 01)81-XX . X 81-04Machine computation, programs (quantum theory)Explicit machine computation and programs (not the theory of computation or programming)81-XX $ 81-05Experimental papers (quantum theory)Experimental papers81-XX + + 81-06Proceedings of conferences (quantum theory)Proceedings, conferences, collections, etc.81-XX & 81-08Computational methods (quantum theory)Computational methods81-XX 81-99Quantum theoryQuantum theory 81-XXQuantum TheoryQuantum theory 2 81P05General and philosophical topics in quantum theoryGeneral and philosophical81Pxx ( O 81P10Logical foundations of quantum mechanicsLogical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]81Pxx 81P15Quantum measurement theoryQuantum measurement theory81Pxx ; ; 81P20Stochastic mechanics (including stochastic electrodynamics)Stochastic mechanics (including stochastic electrodynamics)81Pxx , D 81P68Quantum computation and quantum cryptographyQuantum computation and quantum cryptography [See also 68Q05, 94A60]81Pxx81P991 5 & 81P99Axiomatics, foundations, philosophy of quantum theoryNone of the above, but in this section81Pxx 5 # 81PxxAxiomatics, foundations, philosophy of quantum theoryAxiomatics, foundations, philosophy81-XX @ o 81Q05Closed and approximate solutions to quantum-mechanical equationsClosed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations81Qxx - J 81Q10Selfadjoint operator theory in quantum theorySelfadjoint operator theory in quantum theory, including spectral analysis81Qxx > > 81Q15Perturbation theories for operators and differential equationsPerturbation theories for operators and differential equations81Qxx + 9 81Q20Semi-classical techniques in quantum theorySemiclassical techniques including WKB and Maslov methods81Qxx o 81Q30Feynman integrals and graphsFeynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40]81Qxx $ + 81Q40Integral equations in quantum theoryBethe-Salpeter and other integral equations81Qxx
81Q50Quantum chaosQuantum chaos [See also 37Dxx]81Qxx 81Q60Supersymmetric quantum mechanicsSupersymmetric quantum mechanics81Qxx Q 81Q70Differential-geometric methodsDifferential-geometric methods, including holonomy, Berry and Hannay phases, etc.81Qxx81Q20,81Q991 9 & 81Q99General mathematical topics and methods in quantum theoryNone of the above, but in this section81Qxx 9 9 81QxxGeneral mathematical topics and methods in quantum theoryGeneral mathematical topics and methods in quantum theory81-XX > m 81R05Repres. of finite-dim. groups and algebras from quantum theoryFinite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]81Rxx @ Ì 81R10Repres. of infinite-dim. groups and algebras from quantum theoryInfinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]81Rxx ! 9 81R12Relations with integrable systemsRelations with integrable systems [See also 17Bxx, 37J35]81Rxx58F071 0 81R15Operator algebra methodsOperator algebra methods [See also 46Lxx, 81T05]81Rxx81T051 81R20Covariant wave equationsCovariant wave equations81Rxx , + 81R25Spinor and twistor methods in quantum theorySpinor and twistor methods [See also 32L25]81Rxx ! B 81R30Coherent states in quantum theoryCoherent states [See also 22E45]; squeezed states [See also 81V80]81Rxx 81R40Symmetry breakingSymmetry breaking81Rxx > D 81R50Quantum groups and related algebraic methods in quantum theoryQuantum groups and related algebraic methods [See also 16W35, 17B37]81Rxx 81R60Noncommutative geometryNoncommutative geometry81Rxx58B301 % & 81R99Groups and algebras in quantum theoryNone of the above, but in this section81Rxx % % 81RxxGroups and algebras in quantum theoryGroups and algebras in quantum theory81-XX & $ 81S05Commutation relations (quantum theory)Commutation relations and statistics81Sxx * > 81S10Geometric quantization, symplectic methodsGeometry and quantization, symplectic methods [See also 53D50]81Sxx 81S20Stochastic quantizationStochastic quantization81Sxx 81S25Quantum stochastic calculusQuantum stochastic calculus81Sxx ( 8 81S30Phase space methods in quantum mechanicsPhase space methods including Wigner distributions, etc.81Sxx # 81S40Path integrals in quantum mechanicsPath integrals [See also 58D30]81Sxx 6 & 81S99General quantum mechanics and problems of quantizationNone of the above, but in this section81Sxx 6 6 81SxxGeneral quantum mechanics and problems of quantizationGeneral quantum mechanics and problems of quantization81-XX 1 81T05Axiomatic quantum field theoryAxiomatic quantum field theory; operator algebras81Txx ! ! 81T08Constructive quantum field theoryConstructive quantum field theory81Txx 81T10Model quantum field theoriesModel quantum field theories81Txx ; 81T13Gauge theoriesYang-Mills and other gauge theories [See also 53C07, 58E15]81Txx ' ' 81T15Perturbative methods of renormalizationPerturbative methods of renormalization81Txx * * 81T16Nonperturbative methods of renormalizationNonperturbative methods of renormalization81Txx 81T17Renormalization group methodsRenormalization group methods81Txx 81T18Feynman diagramsFeynman diagrams81Txx 0 0 81T20Quantum field theory on curved space backgroundsQuantum field theory on curved space backgrounds81Txx 81T25Quantum field theory on latticesQuantum field theory on lattices81Txx 81T27Continuum limitsContinuum limits81Txx W 81T30String and superstring theoriesString and superstring theories; other extended objects (e.g., branes) [See also 83E30]81Txx $ > 81T40Two-dimensional field theories, etc.Two-dimensional field theories, conformal field theories, etc.81Txx 2 81T45Topological field theoriesTopological field theories [See also 57R56, 58Dxx]81Txx81T70,58D291 81T50Anomalies in field theoryAnomalies81Txx 81T60Supersymmetric field theoriesSupersymmetric field theories81Txx 3 D 81T70Quantization in field theory; cohomological methodsQuantization in field theory; cohomological methods [See also 58D29]81Txx > 81T75Noncommutative geometry methodsNoncommutative geometry methods [See also 46L85, 46L87, 58B34]81Txx58B30,81V22,81T131 , ! 81T80Simulation and numerical modelling of fieldsSimulation and numerical modeling81Txx & 81T99Quantum field theoryNone of the above, but in this section81Txx 9 G 81TxxQuantum field theory and related classical field theoriesQuantum field theory; related classical field theories [See also 70Sxx]81-XX " E 81U052-body potential scattering theory$2$-body potential scattering theory [See also 34E20 for WKB methods]81Uxx " $ 81U10n-body potential scattering theory$n$-body potential scattering theory81Uxx " " 81U15Exactly and quasi-solvable systemsExactly and quasi-solvable systems81Uxx82B231 81U20S-matrix theory, etc.$S$-matrix theory, etc.81Uxx 8 ' 81U30Dispersion theory, dispersion relations (quantum theory)Dispersion theory, dispersion relations81Uxx , 81U40Inverse scattering problems (quantum theory)Inverse scattering problems81Uxx " & 81U99Scattering theory (quantum theory)None of the above, but in this section81Uxx " > 81UxxScattering theory (quantum theory)Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]81-XX 4 81V05Strong interactionStrong interaction, including quantum chromodynamics81Vxx 4 81V10Electromagnetic interactionElectromagnetic interaction; quantum electrodynamics81Vxx 81V15Weak interactionWeak interaction81Vxx 4 81V17Gravitational interactionGravitational interaction [See also 83Cxx and 83Exx]81Vxx 81V19Other fundamental interactionsOther fundamental interactions81Vxx ' 81V22Unified theories of elementary partclesUnified theories81Vxx 81V25Other elementary particle theoryOther elementary particle theory81Vxx * 81V35Appl. of quantum theory to nuclear physicsNuclear physics81Vxx ) 81V45Appl. of quantum theory to atomic physicsAtomic physics81Vxx , " 81V55Appl. of quantum theory to molecular physicsMolecular physics [See also 92E10]81Vxx , % 81V70Appl. of quantum theory to many-body systemsMany-body theory; quantum Hall effect81Vxx ) 81V80Appl. of quantum theory to quantum opticsQuantum optics81Vxx 4 & 81V99Appl. of quantum theory to specific physical systemsNone of the above, but in this section81Vxx 4 ) 81VxxAppl. of quantum theory to specific physical systemsApplications to specific physical systems81-XX ' G 82-00Reference works (statistical mechanics)General reference works (handbooks, dictionaries, bibliographies, etc.)82-XX ! ; 82-01Textbooks (statistical mechanics)Instructional exposition (textbooks, tutorial papers, etc.)82-XX + 1 82-02Research monographs (statistical mechanics)Research exposition (monographs, survey articles)82-XX " U 82-03Historical (statistical mechanics)Historical (must also be assigned at least one classification number from Section 01)82-XX 5 X 82-04Machine computation, programs (statistical mechanics)Explicit machine computation and programs (not the theory of computation or programming)82-XX + 82-05Experimental papers (statistical mechanics)Experimental papers82-XX 2 + 82-06Proceedings of conferences (statistical mechanics)Proceedings, conferences, collections, etc.82-XX - 82-08Computational methods (statistical mechanics)Computational methods82-XX * * 82-99Statistical mechanics, structure of matterStatistical mechanics, structure of matter * * 82-XXStatistical mechanics, structure of matterStatistical mechanics, structure of matter 0 82B03Foundations of equilibrium statistical mechanicsFoundations82Bxx 5 5 82B05Classical equilibrium statistical mechanics (general)Classical equilibrium statistical mechanics (general)82Bxx 3 3 82B10Quantum equilibrium statistical mechanics (general)Quantum equilibrium statistical mechanics (general)82Bxx A 82B20Lattice systemsLattice systems (Ising, dimer, Potts, etc.) and systems on graphs82Bxx - - 82B21Continuum models (systems of particles, etc.)Continuum models (systems of particles, etc.)82Bxx % 82B23Exactly solvable modelsExactly solvable models; Bethe ansatz82Bxx 1 82B24Interface problems (equilibrium)Interface problems; diffusion-limited aggregation82Bxx 82B26Phase transitions (general)Phase transitions (general)82Bxx 82B27Critical phenomenaCritical phenomena82Bxx . 82B28Renormalization group methodsRenormalization group methods [See also 81T17]82Bxx + 82B30Statistical thermodynamicsStatistical thermodynamics [See also 80-XX]82Bxx 7 82B31Stochastic methods in equilibrium statistical mechanicsStochastic methods82Bxx N 82B35Irreversible thermodynamicsIrreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]82Bxx 82B40Kinetic theory of gasesKinetic theory of gases82Bxx * L 82B41Random walks, etc. (statistical mechanics)Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]82Bxx 82B43PercolationPercolation [See also 60K35]82Bxx L 82B44Disordered systemsDisordered systems (random Ising models, random Schrödinger operators, etc.)82Bxx 6 Q 82B80Numerical methods in equilibrium statistical mechanicsNumerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]82Bxx ! & 82B99Equilibrium statistical mechanicsNone of the above, but in this section82Bxx ! ! 82BxxEquilibrium statistical mechanicsEquilibrium statistical mechanics82-XX 3 82C03Foundations of time-dependent statistical mechanicsFoundations82Cxx D D 82C05Classical dynamic and nonequilibrium statistical mechanics (general)Classical dynamic and nonequilibrium statistical mechanics (general)82Cxx C C 82C10Quantum dynamics and nonequilibrium statistical mechanics (general)Quantum dynamics and nonequilibrium statistical mechanics (general)82Cxx C 82C20Dynamic lattice systemsDynamic lattice systems (kinetic Ising, etc.) and systems on graphs82Cxx 5 82C21Dynamic continuum modelsDynamic continuum models (systems of particles, etc.)82Cxx - 82C22Interacting particle systemsInteracting particle systems [See also 60K35]82Cxx 0 82C23Exactly solvable dynamic modelsExactly solvable dynamic models [See also 37K60]82Cxx 0 1 82C24Interface problems (dynamic and non-equilibrium)Interface problems; diffusion-limited aggregation82Cxx 6 6 82C26Dynamic and nonequilibrium phase transitions (general)Dynamic and nonequilibrium phase transitions (general)82Cxx 82C27Dynamic critical phenomenaDynamic critical phenomena82Cxx % 6 82C28Dynamic renormalization group methodsDynamic renormalization group methods [See also 81T17]82Cxx : C 82C31Stochastic methods in time-dependent statistical mechanicsStochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]82Cxx * 82C32Neural netsNeural nets [See also 68T05, 91E40, 92B20]82Cxx = 82C35Irreversible thermodynamicsIrreversible thermodynamics, including Onsager-Machlup theory82Cxx 82C40Kinetic theory of gasesKinetic theory of gases82Cxx Q 82C41Dynamics of random walks, etc.Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]82Cxx + 82C43Time-dependent percolationTime-dependent percolation [See also 60K35]82Cxx ; 82C44Dynamics of disordered systemsDynamics of disordered systems (random Ising systems, etc.)82Cxx 82C70Transport processesTransport processes82Cxx 9 9 82C80Numerical methods of time-dependent statistical mechanicsNumerical methods (Monte Carlo, series resummation, etc.)82Cxx $ & 82C99Time-dependent statistical mechanicsNone of the above, but in this section82Cxx B A 82CxxTime-dependent statistical mechanics (dynamic and non-equilibrium)Time-dependent statistical mechanics (dynamic and nonequilibrium)82-XX 82D05GasesGases82Dxx 82D10PlasmasPlasmas82Dxx 82D15LiquidsLiquids82Dxx 82D20SolidsSolids82Dxx 7 82D25CrystalsCrystals {For crystallographic group theory, see 20H15}82Dxx O 82D30Random media, etc.Random media, disordered materials (including liquid crystals and spin glasses)82Dxx 82D35MetalsMetals82Dxx 82D37SemiconductorsSemiconductors82Dxx82D991 82D40Magnetic materialsMagnetic materials82Dxx 82D45FerroelectricsFerroelectrics82Dxx 82D50SuperfluidsSuperfluids82Dxx 82D55SuperconductorsSuperconductors82Dxx 82D60PolymersPolymers82Dxx ) 82D75Nuclear reactor theoryNuclear reactor theory; neutron transport82Dxx " & 82D99Appl. to specific physical systemsNone of the above, but in this section82Dxx " 2 82DxxAppl. to specific physical systemsApplications to specific types of physical systems82-XX G 83-00Reference works (relativity)General reference works (handbooks, dictionaries, bibliographies, etc.)83-XX ; 83-01Textbooks (relativity)Instructional exposition (textbooks, tutorial papers, etc.)83-XX 1 83-02Research monographs (relativity)Research exposition (monographs, survey articles)83-XX U 83-03Historical (relativity)Historical (must also be assigned at least one classification number from Section 01)83-XX * X 83-04Machine computation, programs (relativity)Explicit machine computation and programs (not the theory of computation or programming)83-XX 83-05Experimental papers (relativity)Experimental work83-XX ' + 83-06Proceedings of conferences (relativity)Proceedings, conferences, collections, etc.83-XX " 83-08Computational methods (relativity)Computational methods83-XX # # 83-99Relativity and gravitational theoryRelativity and gravitational theory # # 83-XXRelativity and gravitational theoryRelativity and gravitational theory 83A05Special relativitySpecial relativity83-XX 6 ( 83B05Observational and experimental questions of relativityObservational and experimental questions83-XX N 83C05Einstein's equationsEinstein's equations (general structure, canonical formalism, Cauchy problems)83Cxx 83C10Equations of motionEquations of motion83Cxx 8 83C15Closed form solutions of equations in general relativityExact solutions83Cxx 7 N 83C20Classes of solutions of equations in general relativityClasses of solutions; algebraically special solutions, metrics with symmetries83Cxx 2 83C22Electromagnetic fields, Einstein-Maxwell equationsEinstein-Maxwell equations83Cxx - % 83C25Approximation procedures (general relativity)Approximation procedures, weak fields83Cxx & : 83C27Discrete methods in general relativityLattice gravity, Regge calculus and other discrete methods83Cxx * H 83C30Asymptotic procedures (general relativity)Asymptotic procedures (radiation, news functions, {\scr H}-spaces, etc.)83Cxx 83C35Gravitational wavesGravitational waves83Cxx = 83C40Groups of motions, etc.Gravitational energy and conservation laws; groups of motions83Cxx ' ' 83C45Quantization of the gravitational fieldQuantization of the gravitational field83Cxx * 0 83C47Quantum field theory on curved space-timesMethods of quantum field theory [See also 81T20]83Cxx 83C50Electromagnetic fieldsElectromagnetic fields83Cxx " T 83C55Hydrodynamics (general relativity)Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)83Cxx 83C57Black holesBlack holes83Cxx 0 4 83C60Spinor and twistor methods in general retativitySpinor and twistor methods; Newman-Penrose formalism83Cxx " 3 83C65Methods of noncommutative geometryMethods of noncommutative geometry [See also 58B34]83Cxx58B30,83C991 1 83C75Space-time singularities, etc.Space-time singularities, cosmic censorship, etc.83Cxx 83C80Analogues in lower dimensionsAnalogues in lower dimensions83Cxx81T40,83C991 & 83C99General relativityNone of the above, but in this section83Cxx 83CxxGeneral relativityGeneral relativity83-XX 9 ^ 83D05Relativistic gravitational theories other than Einstein'sRelativistic gravitational theories other than Einstein's, including asymmetric field theories83-XX 83E05GeometrodynamicsGeometrodynamics83Exx ! 2 83E15Higher-dimensional field theoriesKaluza-Klein and other higher-dimensional theories83Exx 0 83E30String and superstring theoriesString and superstring theories [See also 81T30]83Exx 83E50SupergravitySupergravity83Exx 4 & 83E99Unified, higher-dimensional and super field theoriesNone of the above, but in this section83Exx 4 83ExxUnified field theories, etc.Unified, higher-dimensional and super field theories83-XX 83F05Relativistic cosmologyCosmology83-XX , G 85-00Reference works (astronomy and astrophysics)General reference works (handbooks, dictionaries, bibliographies, etc.)85-XX & ; 85-01Textbooks (astronomy and astrophysics)Instructional exposition (textbooks, tutorial papers, etc.)85-XX 0 1 85-02Research monographs (astronomy and astrophysics)Research exposition (monographs, survey articles)85-XX ' U 85-03Historical (astronomy and astrophysics)Historical (must also be assigned at least one classification number from Section 01)85-XX : X 85-04Machine computation, programs (astronomy and astrophysics)Explicit machine computation and programs (not the theory of computation or programming)85-XX 0 85-05Experimental papers (astronomy and astrophysics)Experimental work85-XX 7 + 85-06Proceedings of conferences (astronomy and astrophysics)Proceedings, conferences, collections, etc.85-XX 2 85-08Computational methods (astronomy and astrophysics)Computational methods85-XX 85-99Astronomy and astrophysicsAstronomy and astrophysics ? 85-XXAstronomy and astrophysicsAstronomy and astrophysics {For celestial mechanics, see 70F15} , 85A04General topics of astronomy and astrophysicsGeneral85-XX 85A05Galactic and stellar dynamicsGalactic and stellar dynamics85-XX 85A15Galactic and stellar structureGalactic and stellar structure85-XX 85A20Stellar atmospheresPlanetary atmospheres85-XX 85A25Radiative transferRadiative transfer85-XX 7 8 85A30Hydrodynamic and hydromagnetic problems in astrophysicsHydrodynamic and hydromagnetic problems [See also 76Y05]85-XX 85A35Statistical astronomyStatistical astronomy85-XX 1 85A40Nonrelativistic cosmologyCosmology {For relativistic cosmology, see 83F05}85-XX 2 85A99Miscellaneous topics in astronomy and astrophysicsMiscellaneous topics85-XX G 86-00Reference works (geophysics)General reference works (handbooks, dictionaries, bibliographies, etc.)86-XX ; 86-01Textbooks (geophysics)Instructional exposition (textbooks, tutorial papers, etc.)86-XX 1 86-02Research monographs (geophysics)Research exposition (monographs, survey articles)86-XX U 86-03Historical (geophysics)Historical (must also be assigned at least one classification number from Section 01)86-XX * X 86-04Machine computation, programs (geophysics)Explicit machine computation and programs (not the theory of computation or programming)86-XX 86-05Experimental papers (geophysics)Experimental work86-XX ' + 86-06Proceedings of conferences (geophysics)Proceedings, conferences, collections, etc.86-XX " 86-08Computational methods (geophysics)Computational methods86-XX
86-99GeophysicsGeophysics
" 86-XXGeophysicsGeophysics [See also 76U05, 76V05] 86A04General topics of geophysicsGeneral86-XX $ Q 86A05Hydrology, hydrography, oceanographyHydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]86-XX W 86A10MeteorologyMeteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]86-XX
86A15SeismologySeismology86-XX $ $ 86A17Global dynamics, earthquake problemsGlobal dynamics, earthquake problems86-XX 86A20Potentials, prospectingPotentials, prospecting86-XX ! 86A22Inverse problems in geophysicsInverse problems [See also 35R30]86-XX 8 86A25Geo-electricity and geomagnetismGeo-electricity and geomagnetism [See also 76W05, 78A25]86-XX 86A30GeodesyGeodesy, mapping problems86-XX
86A32GeostatisticsGeostatistics86-XX
86A40GlaciologyGlaciology86-XX 86A60Geological problemsGeological problems86-XX " 86A99Miscellaneous topics in geophysicsMiscellaneous topics86-XX G 90-00Reference works (optimization)General reference works (handbooks, dictionaries, bibliographies, etc.)90-XX ; 90-01Textbooks (optimization)Instructional exposition (textbooks, tutorial papers, etc.)90-XX " 1 90-02Research monographs (optimization)Research exposition (monographs, survey articles)90-XX U 90-03Historical (optimization)Historical (must also be assigned at least one classification number from Section 01)90-XX , X 90-04Machine computation, programs (optimization)Explicit machine computation and programs (not the theory of computation or programming)90-XX ) + 90-06Proceedings of conferences (optimization)Proceedings, conferences, collections, etc.90-XX $ 90-08Computational methods (optimization)Computational methods90-XX 90-99OptimizationOptimization - 90-XXOptimizationOperations research, mathematical programming 90B05Inventory managementInventory, storage, reservoirs90Bxx 90B06Transportation, logisticsTransportation, logistics90Bxx 90B10Flows in networksNetwork models, deterministic90Bxx * 90B15Flows in networks with stochastic elementsNetwork models, stochastic90Bxx . 90B18Communication networksCommunication networks [See also 68M10, 94A05]90Bxx90B121 90B20Highway trafficTraffic problems90Bxx * 90B22Queues and serviceQueues and service [See also 60K25, 68M20]90Bxx J 90B25Reliability, etc.Reliability, availability, maintenance, inspection [See also 60K10, 62N05]90Bxx 90B30Production modelsProduction models90Bxx 1 90B35Scheduling theoryScheduling theory, deterministic [See also 68M20]90Bxx . 90B36Scheduling theory, stochasticScheduling theory, stochastic [See also 68M20]90Bxx90B35,60K101
90B40Search theorySearch theory90Bxx ! X 90B50Multiple-criteria decision makingManagement decision making, including multiple objectives [See also 90C31, 91A35, 91B06]90Bxx ' 90B60Marketing, advertisingMarketing, advertising [See also 91B60]90Bxx ; 90B70Theory of organizations, etc.Theory of organizations, manpower planning [See also 91D35]90Bxx 1 90B80Discrete location and assignmentDiscrete location and assignment [See also 90C10]90Bxx 90B85Continuous locationContinuous location90Bxx 90B90Case-oriented studies in ORCase-oriented studies90Bxx * & 90B99Operations research and management scienceNone of the above, but in this section90Bxx ) * 90BxxOperations research and management sienceOperations research and management science90-XX 90C05Linear programmingLinear programming90Cxx 90C06Large-scale problemsLarge-scale problems90Cxx & J 90C08Special problems of linear programmingSpecial problems of linear programming (transportation, multi-index, etc.)90Cxx 90C09Boolean programmingBoolean programming90Cxx 90C10Integer programmingInteger programming90Cxx 90C11Mixed integer programmingMixed integer programming90Cxx 90C15Stochastic programmingStochastic programming90Cxx 90C20Quadratic programmingQuadratic programming90Cxx 90C22Semidefinite programmingSemidefinite programming90Cxx90C301 90C25Convex programmingConvex programming90Cxx 90C26Nonconvex programmingNonconvex programming90Cxx 90C27Combinatorial programmingCombinatorial optimization90Cxx ! $ 90C29Multi-objective programming, etc.Multi-objective and goal programming90Cxx 90C30Nonlinear programmingNonlinear programming90Cxx / 90C31Sensitivity, etc.Sensitivity, stability, parametric optimization90Cxx 90C32Fractional programmingFractional programming90Cxx 90C33Complementarity problemsComplementarity problems90Cxx 90C34Semi-infinite programmingSemi-infinite programming90Cxx 9 90C35Network programmingProgramming involving graphs or networks [See also 90C27]90Cxx $ 90C39Dynamic programmingDynamic programming [See also 49L20]90Cxx ) 90C40Markov decision processes, etc.Markov and semi-Markov decision processes90Cxx / 90C46Optimality conditions, dualityOptimality conditions, duality [See also 49N15]90Cxx90C30,49N151 ! 90C47Minimax problemsMinimax problems [See also 49K35]90Cxx49J35,49K351 90C48Programming in abstract spacesProgramming in abstract spaces90Cxx " 90C49Methods of reduced gradient typeExtreme-point and pivoting methods90Cxx90C08,90C301 90C51Interior-point methodsInterior-point methods90Cxx90C05,90C20,90C25,90C301 90C52Methods of reduced gradient typeMethods of reduced gradient type90Cxx90C301 90C53Methods of quasi-Newton typeMethods of quasi-Newton type90Cxx90C301 0 0 90C55Methods of successive quadratic programming typeMethods of successive quadratic programming type90Cxx90C30,90C201 90C56Derivative-free methodsDerivative-free methods90Cxx90C301 : : 90C57Polyhedral combinatorics, branch-and-bound, branch-and-cutPolyhedral combinatorics, branch-and-bound, branch-and-cut90Cxx90C271 $ $ 90C59Approximation methods and heuristicsApproximation methods and heuristics90Cxx90C301 @ X 90C60Abstract computational complexity for math. programming problemsAbstract computational complexity for mathematical programming problems [See also 68Q25]90Cxx 90C70Fuzzy programmingFuzzy programming90Cxx ! ( 90C90Appl. of mathematical programmingApplications of mathematical programming90Cxx & 90C99Mathematical programmingNone of the above, but in this section90Cxx 0 90CxxMathematical programmingMathematical programming [See also 49Mxx, 65Kxx]90-XX 8 G 91-00General reference works (Social and behavioral sciences)General reference works (handbooks, dictionaries, bibliographies, etc.)91-XX90-001 9 ; 91-01Instructional exposition (Social and behavioral sciences)Instructional exposition (textbooks, tutorial papers, etc.)91-XX90-011 4 1 91-02Research exposition (Social and behavioral sciences)Research exposition (monographs, survey articles)91-XX90-021 + U 91-03Historical (Social and behavioral sciences)Historical (must also be assigned at least one classification number from section 01)91-XX90-031 A X 91-04Machine computation and programs (Social and behavioral sciences)Explicit machine computation and programs (not the theory of computation or programming)91-XX90-041 ; + 91-06Proceedings of conferences (Social and behavioral sciences)Proceedings, conferences, collections, etc.91-XX90-061 6 91-08Computational methods (Social and behavioral sciences)Computational methods91-XX90-081 91-99Social and behavioral sciencesSocial and behavioral sciences 6 91-XXSocial and behavioral sciencesGame theory, economics, social and behavioral sciences90-XX,92-XX1 91A052-person games2-person games91Axx90D051 91A06$n$-person games, $n>2$$n$-person games, $n>2$91Axx90D061 91A10Noncooperative gamesNoncooperative games91Axx90D101 91A12Cooperative gamesCooperative games91Axx90D121 " " 91A13Games with infinitely many playersGames with infinitely many players91Axx90D131 91A15Stochastic gamesStochastic games91Axx90D151 91A18Games in extensive formGames in extensive form91Axx90D40,90D991 91A20Multistage and repeated gamesMultistage and repeated games91Axx90D201 91A22Evolutionary gamesEvolutionary games91Axx90D40,90D991 # 91A23Differential gamesDifferential games [See also 49N70]91Axx90D251 = 91A24Positional gamesPositional games (pursuit and evasion, etc.) [See also 49N75]91Axx90D26,90D421
91A25Dynamic gamesDynamic games91Axx90D25,90D261 91A26Rationality, learningRationality, learning91Axx90D35,90D40,90A051 91A28Signaling, communicationSignaling, communication91Axx90D40,90D991 ) 91A30Utility theory for gamesUtility theory for games [See also 91B16]91Axx90D35,90A101 8 91A35Decision theory for gamesDecision theory for games [See also 62Cxx, 91B06, 90B50]91Axx90D351 91A40Game-theoretic modelsGame-theoretic models91Axx90D401 91A43Games involving graphsGames involving graphs91Axx90D431 & & 91A44Games involving topology or set theoryGames involving topology or set theory91Axx90D441 91A46Combinatorial gamesCombinatorial games91Axx90D461 91A50Discrete-time gamesDiscrete-time games91Axx90D501 91A55Games of timingGames of timing91Axx90D551 91A60Probabilistic games; gamblingProbabilistic games; gambling91Axx90D601 91A65Hierarchical gamesHierarchical games91Axx90D651 91A70Spaces of gamesSpaces of games91Axx90D701 91A80Applications of game theoryApplications of game theory91Axx90D801 # 91A90Experimental studies in game theoryExperimental studies91Axx90D991 & 91A99Game theoryNone of the above, but in this section91Axx90D991 91AxxGame theoryGame theory91-XX 0 W 91B02Fundamental topics on applicability to economicsFundamental topics (basic mathematics, methodology; applicable to economics in general)91Bxx90A05,90A991 . 91B06Decision theoryDecision theory [See also 62Cxx, 90B50, 91A35]91Bxx90A051 91B08Individual preferencesIndividual preferences91Bxx90A061 91B10Group preferencesGroup preferences91Bxx90A071
91B12Voting theoryVoting theory91Bxx90A281
91B14Social choiceSocial choice91Bxx90A081 91B16Utility theoryUtility theory91Bxx90A101 91B18Public goodsPublic goods91Bxx90A271 ! ! 91B24Price theory and market structurePrice theory and market structure91Bxx90A121
< 91B26Market modelsMarket models (auctions, bargaining, bidding, selling, etc.)91Bxx90A601 91B28Finance etc.Finance, portfolios, investment91Bxx90A091 91B30Risk theory etc.Risk theory, insurance91Bxx90A461 91B32Resource and cost allocationResource and cost allocation91Bxx90A801 % 91B38Production theory etc.Production theory, theory of the firm91Bxx90A111 91B40Labor market etc.Labor market, contracts91Bxx90A501 91B42Consumer behavior etc.Consumer behavior, demand theory91Bxx90A401 91B44Informational economicsInformational economics91Bxx90A351 91B50Equilibrium in economicsEquilibrium: general theory91Bxx90A141 ( 91B52Special types of equilibria in economicsSpecial types of equilibria91Bxx90A561 91B54Special types of economiesSpecial types of economies91Bxx90A531 % 91B60General economic models etc.General economic models, trade models91Bxx90A151 & 91B62Dynamic economic models etc.Dynamic economic models, growth models91Bxx90A161 ; 91B64Macro-economic modelsMacro-economic models (monetary models, models of taxation)91Bxx90A701 91B66Multisectoral modelsMultisectoral models91Bxx90A171 91B68Matching modelsMatching models91Bxx90A991 91B70Stochastic modelsStochastic models91Bxx90A191 91B72Spatial modelsSpatial models91Bxx90A251 91B74Models of real-world systemsModels of real-world systems91Bxx90A581 N 91B76Environmental economicsEnvironmental economics (natural resource models, harvesting, pollution, etc.)91Bxx90A301 2 91B82Statistical methods in economicsStatistical methods; economic indices and measures91Bxx90A191 . 91B84Economic time series analysisEconomic time series analysis [See also 62M10]91Bxx90A201 & 91B99Mathematical economicsNone of the above, but in this section91Bxx90A991 4 91BxxMathematical economicsMathematical economics {For econometrics, see 62P20}91-XX 91C05Measurement theoryMeasurement theory91Cxx92G051 ! ! 91C15One- and multidimensional scalingOne- and multidimensional scaling91Cxx92G151
91C20ClusteringClustering [See also 62D05]91Cxx92G301 0 & 91C99general topics of social and behavioral sciencesNone of the above, but in this section91Cxx92G991 0 J 91CxxGeneral topics of social and behavioral sciencesSocial and behavioral sciences: general topics {For statistics, see 62-XX}91-XX / 91D10Models of societies etc.Models of societies, social and urban evolution91Dxx92H101 % % 91D20Mathematical geography and demographyMathematical geography and demography91Dxx92H201 91D25Spatial modelsSpatial models [See also 91B72]91Dxx92H251 91D30Social networksSocial networks91Dxx92H301 ( 91D35Manpower systemsManpower systems [See also 91B40, 90B70]91Dxx92H351 & 91D99Mathematical sociologyNone of the above, but in this section91Dxx92H991 / 91DxxMathematical sociologyMathematical sociology (including anthropology)91-XX 91E10Cognitive psychologyCognitive psychology91Exx92J101 . . 91E30Psychophysics and psychophysiology; perceptionPsychophysics and psychophysiology; perception91Exx92J301 $ 91E40Memory and learningMemory and learning [See also 68T05]91Exx92J401 91E45Measurement and performanceMeasurement and performance91Exx92J451 & 91E99Mathematical psychologyNone of the above, but in this section91Exx92J991 91ExxMathematical psychologyMathematical psychology91-XX 91F10History etc.History, political science91Fxx92K101 # 91F20LinguisticsLinguistics [See also 03B65, 68T50]91Fxx92K201 $ & 91F99Other social and behavioral sciencesNone of the above, but in this section91Fxx92K991 $ = 91FxxOther social and behavioral sciencesOther social and behavioral sciences (mathematical treatment)91-XX + G 92-00Reference works (appl. to natural sciences)General reference works (handbooks, dictionaries, bibliographies, etc.)92-XX % ; 92-01Textbooks (appl. to natural sciences)Instructional exposition (textbooks, tutorial papers, etc.)92-XX / 1 92-02Research monographs (appl. to natural sciences)Research exposition (monographs, survey articles)92-XX & U 92-03Historical (appl. to natural sciences)Historical (must also be assigned at least one classification number from Section 01)92-XX 9 X 92-04Machine computation, programs (appl. to natural sciences)Explicit machine computation and programs (not the theory of computation or programming)92-XX 6 + 92-06Proceedings of conferences (appl. to natural sciences)Proceedings, conferences, collections, etc.92-XX 1 92-08Computational methods (appl. to natural sciences)Computational methods92-XX ( ( 92-99Appl. of mathematics in natural sciencesAppl. of mathematics in natural sciences ( " 92-XXAppl. of mathematics to natural sciencesBiology and other natural sciences " " 92B05General biology and biomathematicsGeneral biology and biomathematics92Bxx 92B10Taxonomy, etc.Taxonomy, statistics92Bxx & 92B15General biostatisticsGeneral biostatistics [See also 62P10]92Bxx ! R 92B20General theory of neural networksNeural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx]92Bxx & 92B99Mathematical biologyNone of the above, but in this section92Bxx 92BxxMathematical biology in generalMathematical biology in general92-XX
92C05BiophysicsBiophysics92Cxx 92C10BiomechanicsBiomechanics [See also 74L15]92Cxx ( 92C15Developmental biology, etc.Developmental biology, pattern formation92Cxx
92C17Cell movementCell movement (chemotaxis, etc.)92Cxx92C30,92C45,92C99,92D501 92C20Neural biologyNeural biology92Cxx
92C30PhysiologyPhysiology (general)92Cxx # 92C35Physiological flowsPhysiological flow [See also 76Z05]92Cxx 92C37Cell biologyCell biology92Cxx92C30,92C40,92C991 92C40Biochemistry, etc.Biochemistry, molecular biology92Cxx [ 92C45Kinetics in biochemical problemsKinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]92Cxx % 92C50Medical appl. of mathematical biologyMedical applications (general)92Cxx
@ 92C55TomographyBiomedical imaging and signal processing [See also 44A12, 65R10]92Cxx 92C60Medical epidemiologyMedical epidemiology92Cxx
92C80Plant biologyPlant biology92Cxx92C991 & 92C99Medical topics etc.None of the above, but in this section92Cxx * 92CxxMedical topics etc.Physiological, cellular and medical topics92-XX * 92D10GeneticsGenetics {For genetic algebras, see 17D92}92Dxx 92D15Problems related to evolutionProblems related to evolution92Dxx 92D20Protein sequences, DNA sequencesProtein sequences, DNA sequences92Dxx 92D25Population dynamicsPopulation dynamics (general)92Dxx 92D30EpidemiologyEpidemiology92Dxx 92D40EcologyEcology92Dxx 92D50Animal behaviorAnimal behavior92Dxx & 92D99Genetics and population dynamicsNone of the above, but in this section92Dxx 92DxxGenetics and population dynamicsGenetics and population dynamics92-XX U 92E10Molecular structuresMolecular structure (graph-theoretic methods, methods of differential topology, etc.)92Exx 8 92E20Chemical flows, reactions, etc.Classical flows, reactions, etc. [See also 80A30, 80A32]92Exx ! & 92E99Appl. of mathematics to chemistryNone of the above, but in this section92Exx ' 92ExxchemistryChemistry {For biochemistry, see 92C40}92-XX . 92F05Appl. of mathematics to other natural sciencesOther natural sciences92-XX % G 93-00Reference works (systems and control)General reference works (handbooks, dictionaries, bibliographies, etc.)93-XX ; 93-01Textbooks (systems and control)Instructional exposition (textbooks, tutorial papers, etc.)93-XX ) 1 93-02Research monographs (systems and control)Research exposition (monographs, survey articles)93-XX U 93-03Historical (systems and control)Historical (must also be assigned at least one classification number from Section 01)93-XX 3 X 93-04Machine computation, programs (systems and control)Explicit machine computation and programs (not the theory of computation or programming)93-XX 0 + 93-06Proceedings of conferences (systems and control)Proceedings, conferences, collections, etc.93-XX 93-99Systems and controlSystems and control 8 93-XXSystems theory; controlSystems theory; control {For optimal control, see 49-XX} 93A05Axiomatic system theoryAxiomatic system theory93Axx 93A10General systemsGeneral systems93Axx 93A13Hierarchical systemsHierarchical systems93Axx 93A14Decentralized systemsDecentralized systems93Axx 93A15Large scale systemsLarge scale systems93Axx ! ? 93A30Mathematical modelling of systemsMathematical modeling (models of systems, model-matching, etc.)93Axx & 93A99General systems theoryNone of the above, but in this section93Axx 93AxxGeneral systems theoryGeneral93-XX 93B03Attainable setsAttainable sets93Bxx 93B05ControllabilityControllability93Bxx
93B07ObservabilityObservability93Bxx 93B10Canonical structure of systemsCanonical structure93Bxx 93B11System structure simplificationSystem structure simplification93Bxx 93B12Variable structure systemsVariable structure systems93Bxx / # 93B15Realizability of systems from input-output dataRealizations from input-output data93Bxx 93B17System transformationTransformations93Bxx 93B18Linearizability of systemsLinearizations93Bxx 93B20Minimal systems representationsMinimal systems representations93Bxx # 93B25Algebraic theory of control systemsAlgebraic methods93Bxx # / 93B27Geometric methods in systems theoryGeometric methods (including algebro-geometric)93Bxx , @ 93B28Operator-theoretic methods in systems theoryOperator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]93Bxx 0 93B29Differential-geometric methods in systems theoryDifferential-geometric methods93Bxx 93B30System identificationSystem identification93Bxx + 93B35Sensitivity (robustness) of control systemsSensitivity (robustness)93Bxx 93B36$H^\infty$-control${H}^\infty$-control93Bxx ' 93B40Computational methods in systems theoryComputational methods93Bxx 93B50Synthesis problemsSynthesis problems93Bxx # > 93B51Design techniques in systems theoryDesign techniques (robust design, computer-aided design, etc.)93Bxx 93B52Feedback controlFeedback control93Bxx 93B55Pole and zero placement problemsPole and zero placement problems93Bxx % 93B60Eigenvalue problems in systems theoryEigenvalue problems93Bxx 4 & 93B99Controllability, observability, and system structureNone of the above, but in this section93Bxx 4 4 93BxxControllability, observability, and system structureControllability, observability, and system structure93-XX 93C05Linear control systemsLinear systems93Cxx 93C10Nonlinear control systemsNonlinear systems93Cxx D 93C15Control systems governed by ODESystems governed by ordinary differential equations [See also 34H05]93Cxx C 93C20Control systems governed by PDESystems governed by partial differential equations [See also 35B37]93Cxx 5 F 93C23Systems governed by functional-differential equationsSystems governed by functional-differential equations [See also 34K35]93Cxx93C22,49J25,49K251 " 93C25Control systems in abstract spacesSystems in abstract spaces93Cxx 6 J 93C30Control systems governed by other functional relationsSystems governed by functional relations other than differential equations93Cxx / 93C35Multivariable, multidimensional control systemsMultivariable systems93Cxx 93C40Adaptive control systemsAdaptive control93Cxx , $ 93C41Control problems with incomplete informationProblems with incomplete information93Cxx
93C42Fuzzy controlFuzzy control93Cxx 93C55Discrete-time control systemsDiscrete-time systems93Cxx 93C57Sampled-data control systemsSampled-data systems93Cxx 93C62Digital control systemsDigital systems93Cxx 93C65Discrete event systemsDiscrete event systems93Cxx93C55,93C831 & . 93C70Time-scale analysis and related topicsTime-scale analysis and singular perturbations93Cxx
93C73Perturbations in control systemsPerturbations93Cxx 93C80Frequency-response methodsFrequency-response methods93Cxx $ < 93C83Control problems involving computersControl problems involving computers (process control, etc.)93Cxx ? 93C85Automated control systemsAutomated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]93Cxx 93C95Appl. of control theoryApplications93Cxx & 93C99Control systems, guided systemsNone of the above, but in this section93Cxx 93CxxControl systems, guided systemsControl systems, guided systems93-XX ; N 93D05Lyapunov and other classical stabilities of control systemsLyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)93Dxx # 93D09Robust stability of control systemsRobust stability93Dxx ( ( 93D10Popov-type stability of feedback systemsPopov-type stability of feedback systems93Dxx $ $ 93D15Stabilization of systems by feedbackStabilization of systems by feedback93Dxx ' 93D20Asymptotic stability of control systemsAsymptotic stability93Dxx ! 93D21Adaptive and robust stabilizationAdaptive or robust stabilization93Dxx 7 93D25Input-output approaches to stability of control systemsInput-output approaches93Dxx $ $ 93D30Scalar and vector Lyapunov functionsScalar and vector Lyapunov functions93Dxx & 93D99Stability of control systemsNone of the above, but in this section93Dxx 93DxxStability of control systemsStability93-XX $ 93E03General theory of stochastic systemsStochastic systems, general93Exx . ) 93E10Estimation and detection in stochastic controlEstimation and detection [See also 60G35]93Exx 93E11Filtering in stochastic controlFiltering [See also 60G35]93Exx * 93E12System identification (stochastic systems)System identification93Exx # 93E14Data smoothing (stochastic systems)Data smoothing93Exx 93E15Stochastic stabilityStochastic stability93Exx $ 93E20Optimal stochastic control (systems)Optimal stochastic control93Exx 7 ! 93E24Least squares and related methods in stochastic controlLeast squares and related methods93Exx + 93E25Computational methods in stochastic controlOther computational methods93Exx ( ( 93E35Stochastic learning and adaptive controlStochastic learning and adaptive control93Exx ) & 93E99Stochastic systems and stochastic controlNone of the above, but in this section93Exx 93ExxStochastic systems and controlStochastic systems and control93-XX / G 94-00Reference works (information and communication)General reference works (handbooks, dictionaries, bibliographies, etc.)94-XX ) ; 94-01Textbooks (information and communication)Instructional exposition (textbooks, tutorial papers, etc.)94-XX 3 1 94-02Research monographs (information and communication)Research exposition (monographs, survey articles)94-XX * U 94-03Historical (information and communication)Historical (must also be assigned at least one classification number from Section 01)94-XX = X 94-04Machine computation, programs (information and communication)Explicit machine computation and programs (not the theory of computation or programming)94-XX : + 94-06Proceedings of conferences (information and communication)Proceedings, conferences, collections, etc.94-XX 94-99Information and communicationInformation and communication ' 94-XXInformation and communicationInformation and communication, circuits , 94A05Communication theoryCommunication theory [See also 60G35, 90B18]94Axx E 94A08Image processingImage processing (compression, reconstruction, etc.) [See also 68U10]94Axx94A12,68U101 4 4 94A11Application of orthogonal functions in communicationApplication of orthogonal functions in communication94Axx
6 94A12Signal theorySignal theory (characterization, reconstruction, etc.)94Axx 94A13Detection theoryDetection theory94Axx 94A14Modulation and demodulationModulation and demodulation94Axx $ , 94A15General topics of information theoryInformation theory, general [See also 62B10]94Axx 94A17Measures of informationMeasures of information, entropy94Axx 94A20Sampling theorySampling theory94Axx42A32,42C101 94A24Coding theorems (Shannon theory)Coding theorems (Shannon theory)94Axx
94A29Source codingSource coding [See also 68P30]94Axx 94A34Rate-distortion theoryRate-distortion theory94Axx 94A40Channel modelsChannel models94Axx ) A 94A45Codes in connection with formal languagesPrefix, length-variable, comma-free codes [See also 20M35, 68Q45]94Axx 94A50Theory of questionnairesTheory of questionnaires94Axx < 94A55Shift register sequencesShift register sequences and sequences over finite alphabets94Axx + 94A60CryptographyCryptography [See also 11T71, 14G50, 68P25]94Axx ! ! 94A62Authentication and secret sharingAuthentication and secret sharing94Axx94A601 & 94A99Communication and informationNone of the above, but in this section94Axx 94AxxCommunication, informationCommunication, information94-XX 94B05General theory of linear codesLinear codes, general94Bxx 94B10Convolutional codesConvolutional codes94Bxx 5 94B12Combined modulation schemesCombined modulation schemes (including trellis codes)94Bxx 94B15Cyclic codesCyclic codes94Bxx 94B20Burst-correcting codesBurst-correcting codes94Bxx 94B25Combinatorial codesCombinatorial codes94Bxx " X 94B27Geometric methods in coding theoryGeometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]94Bxx 94B30Majority codesMajority codes94Bxx 94B35DecodingDecoding94Bxx ( 94B40Arithmetic codesArithmetic codes [See also 11T71, 14G50]94Bxx & & 94B50Synchronization error-correcting codesSynchronization error-correcting codes94Bxx 94B60Other types of codesOther types of codes94Bxx 94B65Bounds on codesBounds on codes94Bxx 94B70Error probability for codesError probability94Bxx = j 94B75Appl. of convex sets and geometry of numbers in coding theoryApplications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31]94Bxx & 94B99error-correcting codesNone of the above, but in this section94Bxx : 94BxxTheory of error-correcting codesTheory of error-correcting codes and error-detecting codes94-XX 94C05Analytic circuit theoryAnalytic circuit theory94Cxx T 94C10Switching theorySwitching theory, application of Boolean algebra; Boolean functions [See also 06E30]94Cxx 94C12Fault detectionFault detection; testing94Cxx . 4 94C15Appl. of graph theory to circuits and networksApplications of graph theory [See also 05Cxx, 68R10]94Cxx / . 94C30Appl. of design theory to circuits and networksApplications of design theory [See also 05Bxx]94Cxx & 94C99Circuits, networksNone of the above, but in this section94Cxx 94CxxCircuits, networksCircuits, networks94-XX 5 ` 94D05Fuzzy sets and logic in connection with communicationFuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]94-XX ' G 97-00Reference works (Mathematics education)General reference works (handbooks, dictionaries, bibliographies, etc.)97-XX ! ; 97-01Textbooks (Mathematics education)Instructional exposition (textbooks, tutorial papers, etc.)97-XX + 1 97-02Research monographs (Mathematics education)Research exposition (monographs, survey articles)97-XX " U 97-03Historical (Mathematics education)Historical (must also be assigned at least one classification number from Section 01)97-XX 5 X 97-04Machine computation, programs (Mathematics education)Explicit machine computation and programs (not the theory of computation or programming)97-XX 2 + 97-06Proceedings of conferences (mathematics education)Proceedings, conferences, collections, etc.97-XX 97-99Mathematics educationMathematics education 97-XXMathematics educationMathematics education ) 97A20Recreational mathematicsRecreational mathematics [See also 00A08]97Axx " $ 97A40Sociological issues of mathematicsSociological issues [See also 97C60]97Axx 97A80StandardsStandards [See also 97B70]97Axx 97A90Fiction and gamesFiction and games97Axx ) 97AxxGeneral topics in educational mathematicsGeneral97-XX ! ! 97B10Educational research and planningEducational research and planning97Bxx 97B20General educationGeneral education97Bxx 97B30Vocational educationVocational education97Bxx 97B40Higher educationHigher education97Bxx 2 97B50Teacher educationTeacher education {For research aspects see 97C70}97Bxx 4 97B60Out-of-school educationOut-of-school education. Adult and further education97Bxx B 97B70Syllabuses etc.Syllabuses. Curriculum guides, official documents [See also 97A80]97Bxx * & 97B99Educational policy and educational systemsNone of the above, but in this section97Bxx * * 97BxxEducational policy and educational systemsEducational policy and educational systems97-XX : 97C20Affective aspectsAffective aspects (motivation, anxiety, persistence, etc.)97Cxx \ 97C30Student learning and thinkingStudent learning and thinking (misconceptions, cognitive development, problem solving, etc.)97Cxx
Q 97C40AssessmentAssessment (large scale assessment, validity, reliability, etc.) [See also 97D10]97Cxx 1 x 97C50Theoretical perspectives in mathematics educationTheoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.) [See also 97D20]97Cxx S 97C60Sociological aspects of learningSociological aspects of learning (culture, group interactions, equity issues, etc.)97Cxx + X 97C70Teachers, and research on teacher educationTeachers, and research on teacher education (teacher development, etc.) [See also 97B50]97Cxx @ ” 97C80Technological tools and other materials in teaching and learningTechnological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)97Cxx u 97C90Teaching and curriculumTeaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )97Cxx 3 & 97C99Psychology of and research in mathematics educationNone of the above, but in this section97Cxx 3 3 97CxxPsychology of and research in mathematics educationPsychology of and research in mathematics education97-XX , = 97D10Comparative studies on mathematics educationComparative studies on mathematics education [See also 97C40]97Dxx : V 97D20Philosophical etc. contributions to mathematical educationPhilosophical and theoretical contributions to mathematical education [See also 97C50]97Dxx 5 5 97D30Goals of mathematics teaching. Curriculum developmentGoals of mathematics teaching. Curriculum development97Dxx ) v 97D40Teaching methods and classroom techniquesTeaching methods and classroom techniques. Lesson preparation. Educational principles {For research aspects see 97Cxx}97Dxx 1 R 97D50Teaching problem solving and heuristic strategiesTeaching problem solving and heuristic strategies {For research aspects see 97Cxx}97Dxx 97D60Achievement control and ratingAchievement control and rating97Dxx < O 97D70Diagnosis, analysis and remediation of learning difficultiesDiagnosis, analysis and remediation of learning difficulties and student errors97Dxx 0 0 97D80Teaching units, draft lessons and master lessonsTeaching units, draft lessons and master lessons97Dxx ( & 97D99Education and instruction in mathematicsNone of the above, but in this section97Dxx ( ( 97DxxEducation and instruction in mathematicsEducation and instruction in mathematics97-XX ] 97U20Evaluation of textbooksAnalysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom97Uxx ! 97U30Teatcher manualsTeacher manuals and planning aids97Uxx : 97U40Problem books, etc.Problem books; student competitions, examination questions97Uxx 8 97U50Computer assisted instructionComputer assisted instruction and programmed instruction97Uxx V 97U60Manipulative materialsManipulative materials and their use in the classroom {For research aspects see 97C80}97Uxx [ 97U70Technological toolsTechnological tools (computers, calculators, software, etc.) and their use in the classroom97Uxx . 97U80Audiovisual mediaAudiovisual media and their use in instruction97Uxx & 97U99Educational material and mediaNone of the above, but in this section97Uxx 6 6 97UxxEducational material and media. Educational technologyEducational material and media. Educational technology97-XX