* 00-XX General
00-01 Instructional exposition (textbooks, tutorial papers, etc.)
00-02 Research exposition (monographs, survey articles)
00Axx General and miscellaneous specific topics
00A05 General mathematics
00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.)
00A07 Problem books
00A08 Recreational mathematics
00A15 Bibliographies
00A20 Dictionaries and other general reference works
00A22 Formularies
00A30 Philosophy of mathematics, See also {03A05}
00A35 Methodology of mathematics, didactics
00A69 General applied mathematics, {For physics, See 00A79 and Sections 70 through 86}
00A71 Theory of mathematical modeling
00A72 General methods of simulation
00A73 Dimensional analysis
00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
00A99 Miscellaneous topics
00Bxx Conference proceedings and collections of papers
00B05 Collections of abstracts of lectures
00B10 Collections of articles of general interest
00B15 Collections of articles of miscellaneous specific content
00B20 Proceedings of conferences of general interest
00B25 Proceedings of conferences of miscellaneous specific interest
00B30 Festschriften
00B50 Volumes of selected translations
00B55 Miscellaneous volumes of translations
00B60 Collections of reprinted articles, See also {01A75}
* 01-XX History and biography {See also the classification number --03 in the other sections}
01-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
01-01 Instructional exposition (textbooks, tutorial papers, etc.)
01-02 Research exposition (monographs, survey articles)
01-06 Proceedings, conferences, collections, etc.
01-08 Computational methods
01Axx History of mathematics and mathematicians
01A05 General histories, source books
01A07 Ethnomathematics, general
01A10 Paleolithic, Neolithic
01A12 Indigenous cultures of the Americas
01A13 Other indigenous cultures (non-European)
01A15 Indigenous European cultures (pre-Greek, etc.)
01A16 Egyptian
01A17 Babylonian
01A20 Greek, Roman
01A25 China
01A27 Japan
01A29 Southeast Asia
01A30 Islam (Medieval)
01A32 India
01A35 Medieval
01A40 15th and 16th centuries, Renaissance
01A45 17th century
01A50 18th century
01A55 19th century
01A60 20th century
01A65 Contemporary
01A67 Future prospectives
01A70 Biographies, obituaries, personalia, bibliographies
01A72 Schools of mathematics
01A73 Universities
01A74 Other institutions and academies
01A75 Collected or selected works; reprintings or translations of classics, See also {00B60}
01A80 Sociology (and profession) of mathematics
01A99 Miscellaneous topics
* 03-XX Mathematical logic and foundations
03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
03-01 Instructional exposition (textbooks, tutorial papers, etc.)
03-02 Research exposition (monographs, survey articles)
03-03 Historical (must be assigned at least one Dclassification number from 01-XX)
03-04 Explicit machine computation and programs (not the theory of computation or programming)
03-06 Proceedings, conferences, collections, etc.
03A05 Philosophical and critical, {For philosophy of mathematics, See 00A30}
03Bxx General logic
03B05 Classical propositional logic
03B10 Classical first-order logic
03B15 Higher-order logic and type-theory
03B20 Subsystems of classical logic (including intuitionistic logic)
03B22 Abstract deductive systems
03B25 Decidability of theories and sets of sentences, See also {11U05, 12L05, 20F10}
03B30 Foundations and axiomatics of classical theories
03B35 Mechanization of proofs and logical operations, See also {68T15}
03B40 Combinatory logic and $lambda$-calculus
03B45 Modal and tense logic, {For provability logics, See also 03F40}
03B46 Relevance and entailment
03B48 Probability and inductive logic, See also {60A05}
03B50 Many-valued logic
03B52 Fuzzy logic, See also {94D05}
03B53 Paraconsistent logic
03B55 Intermediate logics
03B60 Other nonclassical logic
03B65 Logic of natural languages, See also {68S05, 92K20}
03B70 Logic of programming, See also {68Q55, 68Q60}
03B80 Other applications of logic
03B99 None of the above but in this section
03Cxx Model theory
03C05 Equational classes, universal algebra, See also {08Axx}
03C07 Basic properties of first-order languages and structures
03C10 Quantifier elimination and related topics
03C13 Finite structures
03C15 Denumerable structures
03C20 Ultraproducts and related constructions
03C25 Model-theoretic forcing
03C30 Other model constructions
03C35 Categoricity and completeness of theories
03C40 Interpolation, preservation, definability
03C45 Stability and related concepts
03C50 Models with special properties (saturated, rigid, etc.)
03C52 Properties of classes of models
03C55 Set-theoretic model theory
03C57 Recursion-theoretic model theory, See also {03D45}
03C60 Model-theoretic algebra, See also {08C10, 12Lxx, 13L05}
03C62 Models of arithmetic and set theory, See also {03Hxx}
03C65 Models of other mathematical theories
03C68 Other classical first-order model theory
03C70 Logic on admissible sets
03C75 Other infinitary logic
03C80 Logic with extra quantifiers and operators, See also {03B45}
03C85 Second- and higher-order model theory
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)
03C95 Abstract model theory
03C99 None of the above but in this section
03Dxx Recursion theory
03D03 Thue and Post systems, etc.
03D05 Automata and formal grammars in connection with logical questions, See also {68Qxx}
03D10 Turing machines and related notions, See also {68Q05}
03D15 Complexity of computation, See also {68Q15}
03D20 Recursive functions and relations, subrecursive hierarchies
03D25 Recursively enumerable sets and degrees
03D30 Other degrees; reducibilities
03D35 Undecidability and degrees of sets of sentences
03D40 Word problems, etc., See also {06B25, 08A50, 20F10}
03D45 Theory of numerations, effectively presented structures, See also {03C57}
03D50 Recursive equivalence types of sets and structures, isols
03D55 Hierarchies
03D60 Recursion theory on ordinals, admissible sets, etc.
03D65 Higher-type and set recursion theory
03D70 Inductive definability
03D75 Abstract and axiomatic recursion theory
03D80 Applications of recursion theory
03D99 None of the above but in this section
03Exx Set theory, see also {04-XX}
03E05 Combinatorial set theory, See also {04A20}
03E10 Ordinal and cardinal numbers, See also {04A10}
03E15 Descriptive set theory, See also {04A15, 28A05, 54H05}
03E20 Other classical set theory
03E25 Axiom of choice and related propositions, See also {04A25}
03E30 Axiomatics of classical set theory and its fragments
03E35 Consistency and independence results
03E40 Other aspects of forcing and Boolean-valued models
03E45 Constructibility, ordinal definability, and related notions
03E47 Other notions of set-theoretic definability
03E50 Continuum hypothesis and Martin's axiom, See also {04A30, 54A25}
03E55 Large cardinals
03E60 Determinacy and related principles which contradict the axiom of choice
03E65 Other hypotheses and axioms
03E70 Nonclassical and second-order set theories
03E72 Fuzzy sets See mainly{04A72}
03E75 Applications
03E99 None of the above but in this section
03Fxx Proof theory and constructive mathematics
03F03 Proof theory, general
03F05 Cut-elimination and normal-form theorems
03F07 Structure of proofs
03F10 Functionals in proof theory
03F15 Recursive ordinals and ordinal notations
03F20 Complexity of proofs
03F25 Relative consistency and interpretations
03F30 First-order arithmetic and fragments
03F35 Second- and higher-order arithmetic and fragments, See also {03E30, 03E70}
03F40 Godel numberings in proof theory
03F50 Metamathematics of constructive systems
03F55 Intuitionistic mathematics
03F60 Constructive and recursive analysis, See also {26E40, 46S30, 47S30}
03F65 Other constructive mathematics, See also {26E40, 46S30, 47S30}
03F99 None of the above but in this section
03Gxx Algebraic logic
03G05 Boolean algebras, See also {06Exx}
03G10 Lattices and related structures, See also {06Bxx}
03G12 Quantum logic, See also {81P10}
03G15 Cylindric and polyadic algebras; relation algebras
03G20 Lukasiewicz and Post algebras, See also {06D25, 06D30}
03G25 Other algebras related to logic, See also {06F35}
03G30 Categorical logic, topoi, See also {18B25}
03G99 None of the above but in this section
03Hxx Nonstandard models, see also {03C62}
03H05 Nonstandard models in mathematics, See also {26E35, 28E05, 30G06, 46S20, 47S20, 54J05}
03H10 Other applications of nonstandard models (economics, physics, etc.)
03H15 Nonstandard models of arithmetic, See also {11U10, 12L15, 13L05}
03H99 None of the above but in this section
* 04-XX Set theory, See also {03Exx}
04-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
04-01 Instructional exposition (textbooks, tutorial papers, etc.)
04-02 Research exposition (monographs, survey articles)
04-03 Historical (must be assigned at least one classification number from 01-XX)
04-04 Explicit machine computation and programs (not the theory of computation or programming)
04-06 Proceedings, conferences, collections, etc.
04A03 Set algebra
04A05 Relations, functions, See also {08A02}
04A10 Ordinal and cardinal numbers; generalizations, See Also {03E10}
04A15 Descriptive set theory; Borel classifications, Suslin schemes, etc., See also {03E15, 26A21, 28A05, 54H05}
04A20 Combinatorial set theory, See also {03E05, 05A05}; filters
04A25 Axiom of choice and equivalent propositions (Zorn's lemma, etc.), See also {03E25}
04A30 Continuum hypothesis, generalized continuum hypothesis, See also {03E50, 54A25}
04A72 Fuzzy sets, fuzzy relations, See also {03E72, 94D05}, {For fuzzy versions, See specific sections}
04A99 Miscellaneous topics
* 05-XX Combinatorics, {For finite fields, See 11Txx}
05-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
05-01 Instructional exposition (textbooks, tutorial papers, etc.)
05-02 Research exposition (monographs, survey articles)
05-03 Historical (must be assigned at least one classification number from 01-XX)
05-04 Explicit machine computation and programs (not the theory of computation or programming)
05-06 Proceedings, conferences, collections, etc.
05Axx Classical combinatorial problems
05A05 Combinatorial choice problems (subsets, representatives, permutations)
05A10 Factorials, binomial coefficients, combinatorial functions, See also {11B65, 33Cxx}
05A15 Exact enumeration problems, generating functions, See Also {33Cxx, 33Dxx}
05A16 Asymptotic enumeration
05A17 Partitions of integers, See also {11P81, 11P82, 11P83}
05A18 Partitions of sets
05A19 Combinatorial identities
05A20 Combinatorial inequalities
05A30 $q$-calculus and related topics, See also {03Dxx}
05A40 Umbral calculus
05A99 None of the above but in this section
05Bxx Designs and configurations, {For applications of design theory, see 94C30}
05B05 Block designs, See also {51E05, 62K10}
05B07 Triple systems
05B10 Difference sets (number-theoretic, group-theoretic, etc.), See also {11B13}
05B15 Orthogonal arrays, Latin squares, Room squares
05B20 Matrices (incidence, Hadamard, etc.)
05B25 Finite geometries, See also {51D20, 51Exx}
05B30 Other designs, configurations, See also {51E30}
05B35 Matroids, geometric lattices, See also {52B40, 90C27}
05B40 Packing and covering, See also {11H31, 52C15, 52C17}
05B45 Tessellation and tiling problems, See also {52C20, 52C22}
05B50 Polyominoes
05B99 None of the above but in this section
05Cxx Graph theory, {For applications of graphs, see 68Q90, 68R10, 90C35, 94C15}
05C05 Trees
05C10 Topological graph theory, imbedding, See also {57M15, 57M25}
05C12 Distance in graphs
05C15 Chromatic theory of graphs and maps
05C20 Directed graphs (digraphs), tournaments
05C25 Graphs and groups, See also {20F32}
05C30 Enumeration of graphs and maps
05C35 Extremal problems, See also {90C35}
05C38 Paths and cycles, See also {90B10}
05C40 Connectivity
05C45 Eulerian and Hamiltonian graphs
05C50 Graphs and matrices
05C55 Generalized Ramsey theory
05C60 Isomorphism problems (reconstruction conjecture, perfect graphs, etc.)
05C65 Hypergraphs
05C70 Factorization, matching, covering and packing
05C75 Structural characterization of types of graphs
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C80 Random graphs
05C85 Graph algorithms, See also {68Q20, 68R10}
05C90 Applications
05C99 None of the above but in this section
05Dxx Extremal combinatorics
05D05 Extremal set theory
05D10 Ramsey theory
05D15 Transversal (matching) theory
05D99 None of the above but in this section
05Exx Algebraic combinatorics
05E05 Symmetric functions
05E10 Tableaux, representations of the symmetric group, See also {20C30}
05E15 Combinatorial problems concerning the classical groups, See also {22E45, 33C80}
05E20 Group actions on designs, geometries and codes
05E25 Group actions on posets and homology groups of posets, See also {06A09}
05E30 Association schemes, strongly regular graphs
05E35 Orthogonal polynomials, See also {33C45, 33C50, 33D45}
05E99 None of the above but in this section
* 06-XX Order, lattices, ordered algebraic structures, See also {18B35}
06-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
06-01 Instructional exposition (textbooks, tutorial papers, etc.)
06-02 Research exposition (monographs, survey articles)
06-03 Historical (must be assigned at least one classification number from 01-XX)
06-04 Explicit machine computation and programs (not the theory of computation or programming)
06-06 Proceedings, conferences, collections, etc.
06Axx Ordered sets
06A05 Total order
06A06 Partial order, general
06A07 Combinatorics of partially ordered sets
06A08 Shellable posets, Cohen-Macaulay posets, See also {52B20}
06A09 Cohomology of posets, See also {05E25}
06A12 Semilattices, See also {20M10}
06A15 Galois correspondences, closure operators
06A23 Complete lattices, completions
06A99 None of the above but in this section
06Bxx Lattices, see also {03G10}
06B05 Structure theory
06B10 Ideals, congruence relations
06B15 Representation theory
06B20 Varieties of lattices
06B25 Free lattices, projective lattices, word problems, See also {03D40, 08A50, 20F10}
06B30 Topological lattices, order topologies, See also {06F30, 22A26, 54F05, 54H12}
06B35 Continuous lattices, generalizations, applications, See also {06B30, 06D10, 06F30, 18B35, 22A26, 68Q55}
06B99 None of the above but in this section
06Cxx Modular lattices, complemented lattices
06C05 Modular lattices, Desarguesian lattices
06C10 Semimodular lattices, geometric lattices
06C15 Complemented lattices, orthocomplemented lattices
06C20 Complemented modular lattices, continuous geometries
06C99 None of the above but in this section
06Dxx Distributive lattices
06D05 Structure and representation theory
06D10 Complete distributivity
06D15 Pseudocomplemented lattices
06D20 Heyting algebras, See also {03Gxx}
06D25 Post algebras, See also {03G20}
06D30 De Morgan algebras, Lukasiewicz algebras, See also {03G20}
06D99 None of the above but in this section
06Exx Boolean algebras (Boolean rings), see also {03G05}
06E05 Structure theory
06E10 Chain conditions, complete algebras
06E15 Stone space and related constructions
06E20 Ring-theoretic properties, See also {16E50, 16G30}
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
06E30 Boolean functions, See also {94C10}
06E99 None of the above but in this section
06Fxx Ordered structures
06F05 Ordered semigroups, See also {20Mxx}
06F10 Noether lattices
06F15 Ordered groups, See also {20F60}
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces, See also {46A40}
06F25 Ordered rings, algebras, modules, {For ordered fields, See 12J15; See also 13J25, 16W80}
06F30 Topological lattices, order topologies, See also {06B30, 22A26, 54F05, 54H12}
06F35 BCK-algebras, BCI-algebras, See also {03G25}
06F99 None of the above but in this section
* 08-XX General algebraic systems
08-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
08-01 Instructional exposition (textbooks, tutorial papers, etc.)
08-02 Research exposition (monographs, survey articles)
08-03 Historical (must be assigned at least one classification number from 01-XX)
08-04 Explicit machine computation and programs (not the theory of computation or programming)
08-06 Proceedings, conferences, collections, etc.
08Axx Algebraic structures, see also {03C05}
08A02 Relational systems, laws of composition
08A05 Structure theory
08A30 Subalgebras, congruence relations
08A35 Automorphisms, endomorphisms
08A40 Operations, polynomials, primal algebras
08A45 Equational compactness
08A50 Word problems, See also {03D40, 06B25, 20F10, 68R15}
08A55 Partial algebras
08A60 Unary algebras
08A62 Finitary algebras
08A65 Infinitary algebras
08A70 Applications of universal algebra in computer science
08A99 None of the above but in this section
08Bxx Varieties
08B05 Equational logic, Malcev (Maltsev) conditions
08B10 Congruence modularity, congruence distributivity
08B15 Lattices of varieties
08B20 Free algebras
08B25 Products, amalgamated products, and other kinds of limits and colimits, See also {18A30}
08B26 Subdirect products and subdirect irreducibility
08B30 Injectives, projectives
08B99 None of the above but in this section
08Cxx Other classes of algebras
08C05 Categories of algebras, See also {18C05}
08C10 Axiomatic model classes, See also {03Cxx, in particular 03C60}
08C15 Quasivarieties
08C99 None of the above but in this section
* 11-XX Number theory
11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
11-01 Instructional exposition (textbooks, tutorial papers, etc.)
11-02 Research exposition (monographs, survey articles)
11-03 Historical (must be assigned at least one classification number from 01-XX)
11-04 Explicit machine computation and programs (not the theory of computation or programming)
11-06 Proceedings, conferences, collections, etc.
11Axx Elementary number theory, {For analogues in number fields, see 11R04}
11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors
11A07 Congruences; primitive roots; residue systems
11A15 Power residues, reciprocity
11A25 Arithmetic functions; related numbers; inversion formulas
11A41 Primes
11A51 Factorization; primality
11A55 Continued fractions, {For approximation results, See 11J70; See also 11K50, 30B70, 40A15}
11A63 Radix representation; digital problems, {For metric results, See 11K16}
11A67 Other representations
11A99 None of the above but in this section
11Bxx Sequences and sets
11B05 Density, gaps, topology
11B13 Additive bases, See also {05B10}
11B25 Arithmetic progressions, See also {11N13}
11B34 Representation functions
11B37 Recurrences, {For applications to special functions, See 33-XX}
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B50 Sequences (mod m)
11B57 Farey sequences; the sequences ${1^k, 2^k, ... }$
11B65 Binomial coefficients; factorials; $q$-identities, See also {05A10, 05A30}
11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
11B75 Other combinatorial number theory
11B83 Special sequences and polynomials
11B85 Automata sequences
11B99 None of the above but in this section
11Cxx Polynomials and matrices
11C08 Polynomials, See also {13F20}
11C20 Matrices, determinants, See also {15A36}
11C99 None of the above but in this section
11Dxx Diophantine equations, see also {11Gxx, 14Gxx}
11D04 Linear equations
11D09 Quadratic and bilinear equations
11D25 Cubic and quartic equations
11D41 Higher degree equations; Fermat's equation
11D57 Multiplicative and norm form equations
11D61 Exponential equations
11D68 Rational numbers as sums of fractions
11D72 Equations in many variables, See also {11P55}
11D75 Diophantine inequalities, See also {11J25}
11D79 Congruences in many variables
11D85 Representation problems, See also {11P55}
11D88 $p$-adic and power series fields
11D99 None of the above but in this section
11Exx Forms and linear algebraic groups, see also {19Gxx}, {For quadratic forms in linear algebra, See 15A63}
11E04 Quadratic forms over general fields
11E08 Quadratic forms over local rings and fields
11E10 Forms over real fields
11E12 Quadratic forms over global rings and fields
11E16 General binary quadratic forms
11E20 General ternary and quaternary quadratic forms; forms of more than two variables
11E25 Sums of squares and representations by other particular quadratic forms
11E39 Bilinear and Hermitian forms
11E41 Class numbers of quadratic and Hermitian forms
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
11E57 Classical groups, See also {14Lxx, 20Gxx}
11E70 $K$-theory of quadratic and Hermitian forms
11E72 Galois cohomology of linear algebraic groups, See also {20G10}
11E76 Forms of degree higher than two
11E81 Algebraic theory of quadratic forms; Witt groups and rings, See also {19G12, 19G24}
11E88 Quadratic spaces; Clifford algebras, See also {15A63, 15A66}
11E95 $p$-adic theory
11E99 None of the above but in this section
11Fxx Discontinuous groups and automorphic forms, see also {11R39, 11S37, {14-XX, 22Exx} {14Gxx, 14Kxx, 22E50, 22E55}, 30F35, 32Nxx; for relations with quadratic forms, See 11E45}
11F03 Modular and automorphic functions
11F06 Structure of modular groups and generalizations; arithmetic groups, See also {20H05, 20H10, 22E40}
11F11 Modular forms, one variable
11F12 Automorphic forms, one variable
11F20 Dedekind eta function, Dedekind sums
11F22 Relationship to Lie algebras and finite simple groups
11F25 Hecke-Petersson operators, differential operators (one variable)
11F27 Theta series; Weil representation
11F30 Fourier coefficients of automorphic forms
11F32 Modular correspondences, etc.
11F33 Congruences for modular and $p$-adic modular forms, See also {14G20, 22E50}
11F37 Forms of half-integer weight; nonholomorphic modular forms
11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, See also {14J20}
11F46 Siegel modular groups and their modular and automorphic forms
11F55 Other groups and their modular and automorphic forms (several variables)
11F60 Hecke-Petersson operators, differential operators (several variables)
11F66 Dirichlet series and functional equations in connection with modular forms
11F67 Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F72 Spectral theory; Selberg trace formula
11F75 Cohomology of arithmetic groups
11F80 Galois properties
11F85 $p$-adic theory, local fields, See also {14G20, 22E50}
11F99 None of the above but in this section
11Gxx Arithmetic algebraic geometry (Diophantine geometry), see also {11Dxx, {14-XX} {14Gxx, 14Kxx}}
11G05 Elliptic curves over global fields, See also {14H52}
11G07 Elliptic curves over local fields, See also {14G20, 14H52}
11G09 Drinfeld modules; higher-dimensional motives, etc., See also {14L05}
11G10 Abelian varieties of dimension $\gtr 1$, See also {14Kxx}
11G15 Complex multiplication and moduli of abelian varieties, See also {14K22}
11G16 Elliptic and modular units, See also {11R27}
11G18 Arithmetic aspects of modular and Shimura varieties, See also {14G35}
11G20 Curves over finite and local fields, See also {14H25}
11G25 Varieties over finite and local fields, See also {14G15, 14G20}
11G30 Curves of arbitrary genus or genus $\ne 1$ over global fields, See also {14H25}
11G35 Varieties over global fields, See also {14G25}
11G40 $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, See also {14G10}
11G45 Geometric class field theory, See also {11R37, 14C35, 19F05}
11G99 None of the above but in this section
11Hxx Geometry of numbers, {For applications in coding theory, see 94B75}
11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}
11H16 Nonconvex bodies
11H31 Lattice packing and covering, See also {05B40, 52C15, 52C17}
11H46 Products of linear forms
11H50 Minima of forms
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
11H56 Automorphism groups of lattices
11H60 Mean value and transfer theorems
11H99 None of the above but in this section
11Jxx Diophantine approximation, transcendental number theory, see also {11K60}
11J04 Homogeneous approximation to one number
11J06 Markov and Lagrange spectra and generalizations
11J13 Simultaneous homogeneous approximation, linear forms
11J17 Approximation by numbers from a fixed field
11J20 Inhomogeneous linear forms
11J25 Diophantine inequalities, See also {11D75}
11J54 Small fractional parts of polynomials and generalizations
11J61 Approximation in non-Archimedean valuations
11J68 Approximation to algebraic numbers
11J70 Continued fractions and generalizations, See also {11A55, 11K50}
11J71 Distribution modulo one, See also {11K06}
11J72 Irrationality; linear independence over a field
11J81 Transcendence (general theory)
11J82 Measures of irrationality and of transcendence
11J83 Metric theory
11J85 Algebraic independence; Gelfond's method
11J86 Linear forms in logarithms; Baker's method
11J89 Transcendence theory of elliptic and abelian functions
11J91 Transcendence theory of other special functions
11J99 None of the above but in this section
11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms
11K06 General theory of distribution modulo $1$, See also {11J71}
11K16 Normal numbers, radix expansions, etc., See also {11A63}
11K31 Special sequences
11K36 Well-distributed sequences and other variations
11K38 Irregularities of distribution, discrepancy, See also {11Nxx}
11K41 Continuous, $p$-adic and abstract analogues
11K45 Pseudo-random numbers; Monte Carlo methods
11K50 Metric theory of continued fractions, See also {11A55, 11J70}
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension, See also {11N99, 28Dxx}
11K60 Diophantine approximation, See also {11Jxx}
11K65 Arithmetic functions, See also {11Nxx}
11K70 Harmonic analysis and almost periodicity
11K99 None of the above but in this section
11Lxx Exponential sums and character sums, {For finite fields, see 11Txx}
11L03 Trigonometric and exponential sums, general
11L05 Gauss and Kloosterman sums; generalizations
11L07 Estimates on exponential sums
11L10 Jacobsthal and Brewer sums; other complete character sums
11L15 Weyl sums
11L20 Sums over primes
11L26 Sums over arbitrary intervals
11L40 Estimates on character sums
11L99 None of the above but in this section
11Mxx Zeta and $L$-functions: analytic theory
11M06 $zeta (s)$ and $L(s, chi)$
11M20 Real zeros of $L(s, chi)$; results on $L(1, chi)$
11M26 Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
11M35 Hurwitz and Lerch zeta functions
11M41 Other 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}
11M45 Tauberian theorems, See also {40E05}
11M99 None of the above but in this section
11Nxx Multiplicative number theory
11N05 Distribution of primes
11N13 Primes in progressions, See also {11B25}
11N25 Distribution of integers with specified multiplicative constraints
11N30 Turan theory, See also {30Bxx}
11N32 Primes represented by polynomials; other multiplicative structure of polynomial values
11N35 Sieves
11N36 Applications of sieve methods
11N37 Asymptotic results on arithmetic functions
11N45 Asymptotic results on counting functions for algebraic and topological structures
11N56 Rate of growth of arithmetic functions
11N60 Distribution functions associated with additive and positive multiplicative functions
11N64 Other results on the distribution of values or the characterization of arithmetic functions
11N69 Distribution of integers in special residue classes
11N75 Applications of automorphic functions and forms to multiplicative problems, See also {11Fxx}
11N80 Generalized primes and integers
11N99 None of the above but in this section
11Pxx Additive number theory; partitions
11P05 Waring's problem and variants
11P21 Lattice points in specified regions
11P32 Goldbach-type theorems; other additive questions involving primes
11P55 Applications of the Hardy-Littlewood method, See also {11D85}
11P81 Elementary theory of partitions, See also {05A17}
11P82 Analytic theory of partitions
11P83 Partitions; congruences and congruential restrictions
11P99 None of the above but in this section
11Rxx Algebraic number theory: global fields, {For complex multiplication, see 11G15}
11R04 Algebraic numbers; rings of algebraic integers
11R06 PV-numbers and generalizations; other special algebraic numbers
11R09 Polynomials (irreducibility, etc.)
11R11 Quadratic extensions
11R16 Cubic and quartic extensions
11R18 Cyclotomic extensions
11R20 Other abelian and metabelian extensions
11R21 Other number fields
11R23 Iwasawa theory
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants
11R32 Galois theory
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers, See Also {20C10}
11R34 Galois cohomology, See also {12Gxx, 16H05, 19A31}
11R37 Class field theory
11R39 Langlands-Weil conjectures, nonabelian class field theory, See also {11Fxx, 22E55}
11R42 Zeta functions and $L$-functions of number fields, See also {11M41, 19F27}
11R44 Distribution of prime ideals, See also {11N05}
11R45 Density theorems
11R47 Other analytic theory, See also {11Nxx}
11R52 Quaternion and other division algebras: arithmetic, zeta functions
11R54 Other algebras and orders, and their zeta and $L$-functions, See also {11S45, 16H05, 16Kxx}
11R56 Adele rings and groups
11R58 Arithmetic theory of algebraic function fields, See also {14-XX}
11R65 Class groups and Picard groups of orders
11R70 $K$-theory of global fields, See also {19Fxx}
11R80 Totally real and totally positive fields, See also {12J15}
11R99 None of the above but in this section
11Sxx Algebraic number theory: local and $p$-adic fields
11S05 Polynomials
11S15 Ramification and extension theory
11S20 Galois theory
11S23 Integral representations
11S25 Galois cohomology, See also {12Gxx, 16H05}
11S31 Class field theory; $p$-adic formal groups, See also {14L05}
11S37 Langlands-Weil conjectures, nonabelian class field theory, See also {11Fxx, 22E50}
11S40 Zeta functions and $L$-functions, See also {11M41, 19F27}
11S45 Algebras and orders, and their zeta functions, See Also {11R52, 11R54, 16H05, 16Kxx}
11S70 $K$-theory of local fields, See also {19Fxx}
11S80 Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
11S85 Other nonanalytic theory
11S99 None of the above but in this section
11Txx Finite fields and commutative rings (number-theoretic aspects)
11T06 Polynomials
11T22 Cyclotomy
11T23 Exponential sums
11T24 Other character sums and Gauss sums
11T30 Structure theory
11T55 Arithmetic theory of polynomial rings over finite fields
11T71 Algebraic coding theory; cryptography
11T99 None of the above but in this section
11Uxx Connections with logic
11U05 Decidability, See also {03B25}
11U07 Ultraproducts, See also {03C20}
11U09 Model theory, See also {03Cxx}
11U10 Nonstandard arithmetic, See also {03H15}
11U99 None of the above but in this section
11Yxx Computational number theory, see also {11-04}
11Y05 Factorization
11Y11 Primality
11Y16 Algorithms; complexity, See also {68Q25}
11Y35 Analytic computations
11Y40 Algebraic number theory computations
11Y50 Computer solution of Diophantine equations
11Y55 Calculation of integer sequences
11Y60 Evaluation of constants
11Y65 Continued fraction calculations
11Y70 Values of arithmetic functions; tables
11Y99 None of the above but in this section
11Z50 Miscellaneous applications of number theory
* 12-XX Field theory and polynomials
12-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
12-01 Instructional exposition (textbooks, tutorial papers, etc.)
12-02 Research exposition (monographs, survey articles)
12-03 Historical (must be assigned at least one classification number from 01-XX)
12-04 Explicit machine computation and programs (not the theory of computation or programming)
12-06 Proceedings, conferences, collections, etc.
12Dxx Real and complex fields
12D05 Polynomials: factorization
12D10 Polynomials: location of zeros (algebraic theorems), {For the analytic theory, See 26C10, 30C15}
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.), See also {11Exx}
12D99 None of the above but in this section
12Exx General field theory
12E05 Polynomials (irreducibility, etc.)
12E10 Special polynomials
12E12 Equations
12E15 Skew fields, division rings, See also {11R52, 11R54, 11S45, 16Kxx}
12E20 Finite fields (field-theoretic aspects)
12E25 Hilbertian fields; Hilbert's irreducibility theorem
12E99 None of the above but in this section
12Fxx Field extensions
12F05 Algebraic extensions
12F10 Separable extensions, Galois theory
12F12 Inverse Galois theory
12F15 Inseparable extensions
12F20 Transcendental extensions
12F99 None of the above but in this section
12Gxx Homological methods (field theory)
12G05 Galois cohomology, See also {13A20, 16H05}
12G10 Cohomological dimension
12G99 None of the above but in this section
12Hxx Differential and difference algebra
12H05 Differential algebra, See also {13Nxx}
12H10 Difference algebra, See also {39Axx}
12H20 Abstract differential equations, See also {34Gxx}
12H25 $p$-adic differential equations, See also {11S80, 14G20, 34Gxx}
12H99 None of the above but in this section
12Jxx Topological fields
12J05 Normed fields
12J10 Valued fields
12J12 Formally $p$-adic fields
12J15 Ordered fields
12J17 Topological semifields
12J20 General valuation theory
12J25 Non-Archimedean valued fields, See also {30G06, 32P05, 46S10, 47S10}
12J27 Krasner-Tate algebras See mainly{32P05; See also 46S10, 47S10}
12J99 None of the above but in this section
12Kxx Generalizations of fields
12K05 Near-fields, See also {16Y30}
12K10 Semifields, See also {16Y60}
12K99 None of the above but in this section
12Lxx Connections with logic
12L05 Decidability, See also {03B25}
12L10 Ultraproducts, See also {03C20}
12L12 Model theory, See also {03C60}
12L15 Nonstandard arithmetic, See also {03H15}
12L99 None of the above but in this section
12Y05 Computational aspects of field theory and polynomials
* 13-XX Commutative rings and algebras
13-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
13-01 Instructional exposition (textbooks, tutorial papers, etc.)
13-02 Research exposition (monographs, survey articles)
13-03 Historical (must be assigned at least one classification number from 01-XX)
13-04 Explicit machine computation and programs (not the theory of computation or programming)
13-06 Proceedings, conferences, collections, etc.
13Axx General commutative ring theory
13A02 Graded rings, See also {16W50}
13A05 Divisibility
13A10 Radical theory
13A15 Ideals; multiplicative ideal theory
13A18 Valuations and their generalizations
13A20 Brauer groups, See also {12Gxx, 16H05}
13A30 Associated graded rings of ideals (Rees ring, form ring) and related topics
13A35 Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$, See also {13Mxx}
13A50 Invariant theory, See also {14D25}
13A99 None of the above but in this section
13Bxx Ring extensions and related topics
13B02 Extension theory
13B05 Galois theory (commutative rings)
13B10 Morphisms and derivations
13B15 Ramification theory
13B21 Integral dependence
13B22 Integral closure; integrally closed rings, related rings (Japanese, etc.)
13B24 Going up; going down; going between
13B25 Polynomials over commutative rings
13B30 Quotients and localization
13B35 Completion, See also {13J10}
13B40 Etale extensions and Henselization; Artin approximation, See also {13J15, 14B12}
13B99 None of the above but in this section
13Cxx Theory of modules and ideals
13C05 Structure, classification theorems
13C10 Projective and free modules and ideals, See also {18G05, 19A13}
13C11 Injective and flat modules and ideals, See also {18G05}
13C12 Torsion modules and ideals
13C13 Other special types
13C14 Cohen-Macaulay modules, See also {13H10}
13C15 Dimension theory, depth, related rings (catenary, etc.)
13C20 Class groups
13C40 Linkage, complete intersections and determinantal ideals, See also {14M12}
13C99 None of the above but in this section
13Dxx (Co)homological methods
13D02 Syzygies
13D03 (Co)homology of commutative rings and algebras
13D05 (Co)homological dimension, See also {18G20}
13D10 Deformations and infinitesimal methods, See also {14B12, 14D15, 16S80, 32Gxx}
13D15 Grothendieck groups, $K$-theory, See also {14C35, 18F30, 19-XX}
13D25 Complexes
13D30 Torsion theory, See also {13C12, 18E40}
13D40 Hilbert-Samuel functions and Poincare series
13D45 Local cohomology, See also {14B15}
13D99 None of the above but in this section
13Exx Chain conditions, finiteness conditions
13E05 Noetherian rings and modules
13E10 Artinian rings and modules, finite-dimensional algebras
13E15 Rings and modules of finite generation or presentation
13E99 None of the above but in this section
13Fxx Arithmetic rings and other special rings, see also {12-XX}
13F05 Dedekind and Prufer rings and their generalizations
13F07 Euclidean rings and generalizations
13F10 Principal ideal rings
13F15 Factorial rings, unique factorization domains, See Also { 14M05}
13F20 Polynomial rings and ideals, See also {11C08}
13F25 Formal power series rings, See also {13J05}
13F30 Valuation rings
13F40 Excellent rings
13F45 Seminormal rings
13F50 Rings with straightening laws, Hodge algebras
13F99 None of the above but in this section
13G05 Integral domains
13Hxx Local rings and semilocal rings
13H05 Regular local rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), See also {14M05}
13H15 Multiplicity theory and related topies
13H99 None of the above but in this section
13Jxx Topological rings and modules, see also {16W60, 16W80}
13J05 Power series rings, See also {13F25}
13J07 Analytical algebras and rings, See also {32B05}
13J10 Complete rings, completion, See also {13B35}
13J15 Henselian rings, See also {13B40}
13J20 Global topological rings
13J25 Ordered rings, See also {06F25}
13J99 None of the above but in this section
13K05 Witt vectors and related rings
13L05 Applications of logic to commutative algebra, See Also {03Cxx, 03Hxx}
13Mxx Finite commutative rings, {For number-theoretic aspects, see 11Txx}
13M05 Structure
13M10 Polynomials (commutative rings)
13M99 None of the above but in this section
13Nxx Differential algebra, see also {12H05, 14F10}
13N05 Modules of differentials, See also {16S32}
13N10 Rings of differential operators, See also {16S32, 32C38}
13N99 None of the above but in this section
13Pxx Computational aspects of commutative algebra, see Also { 68Q40}
13P05 Polynomials, factorization, See also {12Y05}
13P10 Polynomial ideals, Grobner bases
13P99 None of the above but in this section
* 14-XX Algebraic geometry
14-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
14-01 Instructional exposition (textbooks, tutorial papers, etc.)
14-02 Research exposition (monographs, survey articles)
14-03 Historical (must be assigned at least one classification number from 01-XX)
14-04 Explicit machine computation and programs (not the theory of computation or programming)
14-06 Proceedings, conferences, collections, etc.
14Axx Foundations
14A05 Relevant commutative algebra, See also {13-XX}
14A10 Varieties
14A15 Schemes
14A20 Generalizations (algebraic spaces, motifs)
14A22 Noncommutative algebraic geometry; algebraic supervarieties, See also {14M30, 32C11, 58A50}
14A25 Elementary questions
14A99 None of the above but in this section
14Bxx Local theory, see also {32Sxx}
14B05 Singularities, See also {14E15, 14H20, 32Sxx, 58C27}
14B07 Deformations of singularities, See also {14D15, 32Sxx}
14B10 Infinitesimal methods, See also {13D10}
14B12 Local deformation theory, Artin approximation, etc., See also {13B40, 13D10}
14B15 Local cohomology, See also {13D45, 32C36}
14B20 Formal neighborhoods
14B99 None of the above but in this section
14Cxx Cycles and subschemes
14C05 Parametrization (Chow and Hilbert schemes)
14C10 Equivalence relations
14C15 Rational equivalence rings
14C17 Intersection theory
14C20 Divisors, linear systems, invertible sheaves
14C21 Pencils, nets, webs, See also {53A60}
14C22 Picard groups
14C25 Algebraic cycles
14C30 Transcendental methods, Hodge theory, See also {14D07, 32G20, 32J25, 32S35}, Hodge conjecture
14C34 Torelli problem, See also {32G20}
14C35 Applications of methods of algebraic $K$-theory, See Also {14F05, 19Exx}
14C40 Riemann-Roch theorems, See also {19E20, 19L10}
14C99 None of the above but in this section
14Dxx Families, fibrations
14D05 Structure of families (Picard-Lefschetz, Picard-Fuchs theory, etc.)
14D07 Variation of Hodge structures
14D10 Arithmetic ground fields (finite, local, global)
14D15 Formal methods; deformations, See also {13D10, 14B07, 16S80 32Gxx}
14D20 Algebraic moduli problems, moduli of vector bundles, {For analytic moduli problems, See 32G13}
14D22 Fine and coarse moduli spaces
14D25 Geometric invariants, See also {14L30}
14D99 None of the above but in this section
14Exx Mappings and correspondences
14E05 Rational maps, birational correspondences
14E07 Birational automorphisms, Cremona group and generalizations, See also {32G20}
14E09 Automorphisms, See also {14J50, 14L27}
14E10 General correspondences
14E15 Global theory of singularities, resolution, See Also {14B05, 32S20, 32S45}
14E20 Coverings, fundamental group (mappings)
14E22 Ramification problems, See also {11S15}
14E25 Imbeddings
14E30 Minimal models
14E35 Results in dimension $\leq 3$
14E40 Local structure of maps: etale, flat, etc., See Also {13-XX, 14F20}
14E99 None of the above but in this section
14Fxx (Co)homology theory, see also {13Dxx}
14F05 Vector bundles, sheaves, related construction, See Also {18F20, 32Lxx, 46M20}
14F10 Differentials and other special sheaves, See also {32C38}
14F17 Vanishing theorems, See also {32L20}
14F20 Etale and other Grothendieck topologies and cohomologies
14F25 Classical real and complex cohomology
14F30 $p$-adic cohomology, crystalline cohomology
14F32 Intersection (co)homology, See also {32S60}
14F35 Homotopy theory; fundamental groups, See also {14E20, 14H30}
14F40 de Rham cohomology, See also {14C30, 32C35, 32L10}
14F45 Topological properties
14F99 None of the above but in this section
14Gxx Arithmetic problems. Diophantine geometry, see also {11Dxx, 11Gxx}
14G05 Rationality questions, rational points
14G10 Zeta-functions and related questions, See also {11G40} (Birch-Swinnerton-Dyer conjecture)
14G15 Finite ground fields
14G20 $p$-adic ground fields
14G25 Global ground fields
14G27 Nonalgebraically closed ground fields
14G35 Modular and Shimura varieties, See also {11F41, 11F46, 11G18}
14G40 Arithmetic varieties and schemes; Arakelov theory
14G99 None of the above but in this section
14Hxx Curves
14H05 Algebraic functions; function fields, See also {11R58}
14H10 Families, moduli (algebraic)
14H15 Families, moduli (analytic), See also {30F10, 32Gxx}
14H20 Singularities, local rings, See also {13Hxx}
14H25 Arithmetic ground fields, See also {11Dxx, 11G05, 14Gxx}
14H30 Coverings, fundamental group, See also {14E20, 14F35}
14H35 Correspondences, See also {14Exx}
14H40 Jacobians, See also {32G20}
14H42 Theta functions; Schottky problem, See also {14K25, 32G20}
14H45 Special curves and curves of low genus
14H50 Space curves
14H52 Elliptic curves, See also {11G05, 11G07, 14Kxx}
14H55 Riemann surfaces; Weierstrass points; gap sequences, See also {30Fxx}
14H60 Vector bundles on curves, See also {14F05}
14H99 None of the above but in this section
14Jxx Surfaces and higher-dimensional varieties, {For analytic theory, see 32Jxx}
14J05 Picard group, See also {14C22, 19A49, 32L05}
14J10 Families, moduli, classification: algebraic theory
14J15 Moduli, classification: analytic theory, See also {32G13, 32J15}
14J17 Singularities of surfaces
14J20 Arithmetic ground fields, See also {11Dxx, 11G25, 11G35, 14Gxx}
14J25 Special surfaces, {For Hilbert modular surfaces, See 14G35}
14J26 Rational and ruled surfaces
14J27 Elliptic surfaces
14J28 $K3$ surfaces and Enriques surfaces
14J29 Surfaces of general type
14J30 Special $3$-folds, See also {14E05}
14J35 Special $4$-folds, See also {14E05}
14J40 Special $n$-folds
14J45 Fano varieties
14J50 Automorphisms of surfaces and higher-dimensional varieties, See also {14E09}
14J60 Vector bundles on surfaces and higher-dimensional varieties, See also {14F05, 32Lxx}
14J70 Hypersurfaces
14J99 None of the above but in this section
14Kxx Abelian varieties and schemes
14K02 Isogeny
14K05 Algebraic theory
14K10 Algebraic moduli, classification
14K15 Arithmetic ground fields, See also {11Dxx, 11Fxx, 11Gxx, 14Gxx}
14K20 Analytic theory; abelian integrals and differentials
14K22 Complex multiplication, See also {11G15}
14K25 Theta functions
14K30 Picard schemes, higher Jacobians, See also {14H40, 32G20}
14K99 None of the above but in this section
14Lxx Group schemes, {For linear algebraic groups, see 20Gxx. For Lie algebras, See 17B45}
14L05 Formal groups, $p$-divisible groups, See also {55N22}
14L10 Group varieties
14L15 Group schemes
14L17 Affine algebraic groups, hyperalgebra constructions, See also {17B45, 18D35}
14L27 Automorphism groups, See also {14E09}
14L30 Group actions on varieties or schemes (quotients), See also {14D25}
14L35 Classical groups (geometric aspects), See also {20Gxx, 51N30}
14L40 Other algebraic groups (geometric aspects)
14L99 None of the above but in this section
14Mxx Special varieties
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), See also {13C14, 13F45, 13H10}
14M06 Linkage, See also {13C40}
14M07 Low codimension problems, See also {14Cxx}
14M10 Complete intersections, See also {13C40}
14M12 Determinantal varieties, See also {13C40}
14M15 Grassmannians, Schubert varieties, flag manifolds, See also {32M10, 51M35}
14M17 Homogeneous spaces and generalizations, See also {32M10, 53C30, 57T15}
14M20 Rational varieties
14M25 Toric varieties, Newton polyhedra
14M30 Supervarieties, See also {14A22, 32C11, 58A50}
14M99 None of the above but in this section
14Nxx Classical methods and problems, see also {51-XX}
14N05 Projective techniques, See also {51N35}
14N10 Enumerative problems (combinatorial problems)
14N99 None of the above but in this section
14Pxx Real algebraic and real analytic geometry
14P05 Real algebraic sets, See also {12Dxx}
14P10 Semialgebraic sets and related spaces
14P15 Real analytic and semianalytic sets, See also {32B20, 32C05}
14P20 Nash functions and manifolds, See also {32C07, 58A07}
14P25 Topology of real algebraic varieties
14P99 None of the above but in this section
14Qxx Computational aspects in algebraic geometry, see also {12-04, 68Q40}
14Q05 Curves
14Q10 Surfaces, hypersurfaces
14Q15 Higher-dimensional varieties
14Q20 Effectivity
14Q99 None of the above but in this section
* 15-XX Linear and multilinear algebra; matrix theory {(finite and infinite)}
15-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
15-01 Instructional exposition (textbooks, tutorial papers, etc.)
15-02 Research exposition (monographs, survey articles)
15-03 Historical (must be assigned at least one classification number from 01-XX)
15-04 Explicit machine computation and programs (not the theory of computation or programming)
15-06 Proceedings, conferences, collections, etc.
15A03 Vector spaces, linear dependence, rank
15A04 Linear transformations, semilinear transformations
15A06 Linear equations
15A09 Matrix inversion, generalized inverses
15A12 Conditioning of matrices, See also {65F35}
15A15 Determinants, permanents, other special matrix functions, See also {19B10, 19B14}
15A18 Eigenvalues, singular values, and eigenvectors
15A21 Canonical forms, reductions, classification
15A22 Matrix pencils, See also {47A56}
15A23 Factorization of matrices
15A24 Matrix equations and identities
15A27 Commutativity
15A30 Algebraic systems of matrices, See also {16S50, 20Gxx, 20Hxx}
15A33 Matrices over special rings (quaternions, finite fields, etc.)
15A36 Matrices of integers, See also {11C20}
15A39 Linear inequalities
15A42 Inequalities involving eigenvalues and eigenvectors
15A45 Miscellaneous inequalities involving matrices
15A48 Positive matrices and their generalizations; cones of matrices
15A51 Stochastic matrices
15A52 Random matrices
15A54 Matrices over function rings in one or more variables
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory, See also {65F35, 65J05}
15A63 Quadratic and bilinear forms, inner products See mainly{ 11Exx}
15A66 Clifford algebras, spinors
15A69 Multilinear algebra, tensor products
15A72 Vector and tensor algebra, theory of invariants, See Also {13A50, 14D25}
15A75 Exterior algebra, Grassmann algebras
15A78 Other algebras built from modules
15A90 Applications of matrix theory to physics
15A99 Miscellaneous topics
* 16-XX Associative rings and algebras, {For the commutative case, See 13-XX}
16-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
16-01 Instructional exposition (textbooks, tutorial papers, etc.)
16-02 Research exposition (monographs, survey articles)
16-03 Historical (must be assigned at least one classification number from 01-XX)
16-04 Explicit machine computation and programs (not the theory of computation or programming)
16-06 Proceedings, conferences, collections, etc.
16Bxx General and miscellaneous
16B50 Category-theoretic methods and results (except as in 16D90, 16E10), See also {18-XX}
16B70 Applications of logic, See also {03Cxx}
16B99 None of the above but in this section
16Dxx Modules, bimodules and ideals
16D10 General module theory
16D15 1-sided ideals
16D20 Bimodules
16D25 2-sided ideals
16D30 Maximal and prime 2-sided ideals, See also {16N60, 16D60}, simple rings (except as in 16Kxx)
16D40 Free, projective, and flat modules and ideals, See Also {18G05, 19A13}
16D50 Injective modules, self-injective rings, See also {16L60, 18G05}
16D60 Simple and semisimple modules, primitive rings and ideals
16D70 Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
16D80 Other classes of modules and ideals, See also {16G60}
16D90 Module categories, See also {16Exx, 16Gxx, 16S90}; module theory in a category-theoretic context; Morita equivalence and duality
16D99 None of the above but in this section
16Exx Homological methods and results, see also {18Gxx}
16E10 Homological dimension
16E20 Grothendieck groups, $K$-theory, etc., See also {18F30, 19-XX}
16E30 Homological functors on modules
16E40 Hochschild and other homology and cohomology theories for rings
16E50 von Neumann regular rings and generalizations
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16E70 Other rings of low global or flat dimension
16E99 None of the above but in this section
16Gxx Representation theory of rings and algebras
16G10 Representations of Artinian rings
16G20 Representations of quivers and partially ordered sets
16G30 Representations of orders, lattices, algebras over commutative rings, See also {16H05}
16G50 Cohen-Macaulay modules
16G60 Representation type (finite, tame, wild, etc.)
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G99 None of the above but in this section
16H05 Orders and arithmetic, separable algebras, Azumaya algebras, See also {11R52, 11R54, 11S45, 13A20}
16Kxx Division rings and semisimple Artin rings, see also {12E15, 15A30}
16K20 Finite-dimensional, {For Brauer group theory, See 12Gxx, 13A20; for crossed products, See 16S35}
16K40 Infinite-dimensional and general
16K99 None of the above but in this section
16Lxx Local rings and generalizations
16L30 Noncommutative local and semilocal rings, perfect rings
16L60 Quasi-Frobenius rings, See also {16D50}
16L99 None of the above but in this section
16Nxx Radicals and radical properties of rings
16N20 Jacobson radical, quasimultiplication
16N40 Nil and nilpotent radicals, sets, ideals, rings
16N60 Prime and semiprime rings, See also {16D30, 16D60, 16U10}
16N80 General radicals and rings, {For radicals in module categories, See 16S90}
16N99 None of the above but in this section
16Pxx Chain conditions, growth conditions, and other forms of finiteness
16P10 Finite rings and finite-dimensional algebras, {For semisimple, See 16K20; for commutative, See 11Txx, 13Mxx}
16P20 Artinian rings and modules
16P40 Noetherian rings and modules
16P50 Localization and Noetherian rings, See also {16U20}
16P60 Chain conditions on annihilators and summands: Goldie type conditions, See also {16U20}, Krull dimension
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
16P90 Growth rate, Gelfand-Kirillov dimension
16P99 None of the above but in this section
16Rxx Rings with polynomial identity
16R10 $T$-ideals, identities, varieties of rings and algebras
16R20 Semiprime p.i. rings, rings embeddable in matrices over commutative rings
16R30 Trace rings and invariant theory
16R40 Identities other than those of matrices over commutative rings
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16R99 None of the above but in this section
16Sxx Rings and algebras arising under various constructions
16S10 Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
16S20 Centralizing and normalizing extensions
16S30 Universal enveloping algebras of Lie algebras See mainly{ 17B35}
16S32 Rings of differential operators, See also {13N10, 32C38}
16S34 Group rings, See also {20C05, 20C07}, Laurent polynomial rings
16S35 Twisted and skew group rings, crossed products
16S36 Ordinary and skew polynomial rings and semigroup rings, See also {20M25}
16S40 Smash products of general Hopf actions, See also {16W30}
16S50 Endomorphism rings: matrix rings, See also {15-XX}
16S60 Rings of functions, subdirect products, sheaves of rings
16S70 Extensions of rings by ideals
16S80 Deformations of rings, See also {14D15}
16S90 Maximal ring of quotients, torsion theories, radicals on module categories, See also {13D30, 18E40}, {For radicals of rings, See {16Nxx}}
16S99 None of the above but in this section
16Uxx Conditions on elements (including elements of matrix rings, etc.)
16U10 Integral domains
16U20 Ore rings, multiplicative sets, Ore localization
16U30 Divisibility, noncommutative UFDs
16U50 Algebraicity and local finiteness, See also {16N40}
16U60 Units, groups of units, general linear groups
16U70 Center, normalizer (invariant elements)
16U80 Generalizations of commutativity
16U99 None of the above but in this section
16Wxx Rings and algebras with additional structure
16W10 Rings with involution: Lie, Jordan and other nonassociative structures, See also {17B60, 17C50, 46Kxx}
16W20 Automorphisms and endomorphisms, actions of groups and semigroups and their fixed rings
16W25 Derivations, actions of Lie algebras
16W30 Coalgebras, bialgebras, Hopf algebras, See also {57T05, 16S30-- 16S40}; rings, modules, etc. on which these act
16W50 Graded rings and modules
16W55 ``Super'' (or ``skew'') structure, See also {17A70, 17B70, 17C70}, {For exterior algebras, See {15A75}; for Clifford algebras, See 11E88, 15A66}
16W60 Filtrations and valuations, generalizations of Euclidean algorithm, completions, formal power series and related constructions, See also {13Jxx}
16W80 Topological and ordered rings and modules, See also {13Jxx}
16W99 None of the above but in this section
16Yxx Generalizations, {For nonassociative rings, see 17-XX}
16Y30 Near-rings, See also {12K05}
16Y60 Semirings, See also {12K10}
16Y99 None of the above but in this section
* 17-XX Nonassociative rings and algebras
17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
17-01 Instructional exposition (textbooks, tutorial papers, etc.)
17-02 Research exposition (monographs, survey articles)
17-03 Historical (must be assigned at least one classification number from 01-XX)
17-04 Explicit machine computation and programs (not the theory of computation or programming)
17-06 Proceedings, conferences, collections, etc.
17-08 Computational methods
17Axx General nonassociative rings
17A01 General theory
17A05 Power-associative
17A10 Commutative power-associative
17A15 Noncommutative Jordan algebras
17A20 Flexible algebras
17A25 Nodal algebras
17A30 Algebras satisfying other identities
17A35 Division algebras
17A36 Automorphisms, derivatives, other operators
17A40 Ternary compositions
17A42 Other $n$-ary compositions
17A45 Quadratic algebras (but not quadratic Jordan algebras)
17A50 Free algebras
17A60 Structure theory
17A65 Radical theory
17A70 Superalgebras
17A75 Composition algebras
17A80 Valued algebras
17A99 None of the above but in this section
17Bxx Lie algebras, {For Lie groups, see 22Exx}
17B01 Identities, free Lie algebras
17B05 Structure theory
17B10 Representations, algebraic theory (weights)
17B15 Representations, analytic theory
17B20 Simple, semisimple, reductive algebras (roots)
17B25 Exceptional algebras
17B30 Solvable, nilpotent algebras
17B35 Universal enveloping algebras, See also {16S30}
17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}
17B40 Automorphisms, derivations, other operators
17B45 Lie algebras of linear algebraic groups, See also {14Lxx and 20Gxx}
17B50 Modular Lie algebras
17B55 Homological methods in Lie algebras
17B56 Cohomology of Lie algebras
17B60 Lie rings associated with other structures (associative, Jordan, etc.), See also {15A30, 16W10, 17C40, 17C50}
17B65 Infinite-dimensional Lie algebras, See also {22E65}
17B66 Lie algebras of vector fields and related algebras
17B67 Kac-Moody algebras (structure and representation theory)
17B68 Virasoro and related algebras
17B70 Graded Lie algebras
17B81 Applications to physics
17B99 None of the above but in this section
17Cxx Jordan algebras (algebras, triples and pairs)
17C05 Identities and free Jordan structures
17C10 Structure theory
17C17 Radicals
17C20 Simple, semisimple algebras
17C27 Idempotents, Peirce decompositions
17C30 Associated groups, automorphisms
17C36 Associated manifolds
17C37 Associated geometries
17C40 Exceptional Jordan structures
17C50 Jordan structures associated with other structures, See also {16W10}
17C55 Finite-dimensional structures
17C60 Division algebras
17C65 Jordan structures on Banach spaces and algebras, See Also {46H70, 46L70}
17C70 Super structures
17C90 Applications to physics
17C99 None of the above but in this section
17Dxx Other nonassociative rings and algebras
17D05 Alternative rings
17D10 Malcev (Maltsev) rings and algebras
17D15 Right alternative rings
17D20 $(gamma, delta)$-rings, including $(1,-1)$-rings
17D25 Lie-admissible algebras
17D92 Genetic algebras
17D99 None of the above but in this section
* 18-XX Category theory, homological algebra
18-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
18-01 Instructional exposition (textbooks, tutorial papers, etc.)
18-02 Research exposition (monographs, survey articles)
18-03 Historical (must be assigned at least one classification number from 01-XX)
18-04 Explicit machine computation and programs (not the theory of computation or programming)
18-06 Proceedings, conferences, collections, etc.
18Axx General theory of categories and functors
18A05 Definitions, generalizations
18A10 Graphs, diagram schemes, precategories, neocategories, See also {20Lxx}
18A15 Foundations, relations to logic and deductive systems, See also {03-XX}
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms, factorization (bicategories)
18A22 Special properties of functors (faithful, full, etc.)
18A23 Natural morphisms, dinatural morphisms
18A25 Functor categories, comma categories
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18A32 Factorization of morphisms (via images, coimages, dominions, codominions), substructures, quotient structures, congruences, amalgams
18A35 Categories admitting limits (complete categories), functors commuting with limits, continuous functors, completions
18A40 Adjoint functors (representable functors, universal constructions, reflective subcategories, reflections, etc.), constructions of adjoints (Kan extensions, etc.)
18A99 None of the above but in this section
18Bxx Special categories
18B05 Category of sets, characterizations, See also {03-XX}
18B10 Category of relations, additive relations
18B15 Embedding theorems, universal categories, See also {18E20}
18B20 Categories of machines, automata, operative categories, See also {03D05, 68Qxx}
18B25 Topoi, See also {03G30}
18B30 Categories of topological spaces and continuous mappings, See also {54-XX}
18B35 Preorders, orders and lattices (viewed as categories), See also {06-XX}
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories), See also {20Axx, 20Lxx, 20Mxx}
18B99 None of the above but in this section
18Cxx Categories and algebraic theories
18C05 Equational categories, See also {03C05, 08C05}
18C10 Theories (e.g. algebraic theories), structure, and semantics, See also {03G30}
18C15 Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples, See also {18Gxx}
18C20 Algebras and Kleisli categories associated with monads
18C99 None of the above but in this section
18Dxx Categories with structure
18D05 Double categories, $2$-categories, bicategories, hypercategories
18D10 Monoidal categories (= multiplicative categories), See also {19D23}
18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
18D20 Enriched categories (over closed or monoidal categories)
18D25 Strong functors, strong adjunctions
18D30 Fibered categories
18D35 Structured objects in a category (group objects, etc.)
18D99 None of the above but in this section
18Exx Abelian categories
18E05 Preadditive, additive categories
18E10 Exact categories, abelian categories
18E15 Grothendieck categories
18E20 Embedding theorems, See also {18B15}
18E25 Derived functors and satellites
18E30 Derived categories, triangulated categories
18E35 Localization of categories
18E40 Torsion theories, radicals, See also {13D30, 16S90}
18E99 None of the above but in this section
18Fxx Categories and geometry
18F05 Local categories and functors
18F10 Grothendieck topologies, See also {14F20}
18F15 Abstract manifolds and fiber bundles, See also {55Rxx, 57Pxx}
18F20 Presheaves and sheaves, See also {14F05, 32C35, 32L10, 54B40, 55N30}
18F25 Algebraic $K$-theory and $L$-theory, See also {11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67}
18F30 Grothendieck groups, See also {13D15, 16E20, 19Axx}
18F99 None of the above but in this section
18Gxx Homological algebra, see also {13Dxx, 16Exx, 55Uxx}
18G05 Projectives and injectives, See also {13C10, 13C11, 16D40, 16D50}
18G10 Resolutions; derived functors, See also {18E25}
18G15 Ext and Tor, generalizations, Kunneth formula, See Also { 55U25}
18G20 Homological dimension, See also {13D05, 16E10}
18G25 Relative homological algebra, projective classes
18G30 Simplicial sets, simplicial objects (in a category), See also {55U10}
18G35 Chain complexes, See also {18E30, 55U15}
18G40 Spectral sequences, hypercohomology, See also {55Txx}
18G50 Nonabelian homological algebra
18G55 Nonabelian homotopical algebra
18G60 Other (co)homology theories (cyclic, dihedral, etc.), See also {19D55, 46L80, 58B30, 58G12}
18G99 None of the above but in this section
* 19-XX $K$-theory, See also {16E20, 18F25}
19-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
19-01 Instructional exposition (textbooks, tutorial papers, etc.)
19-02 Research exposition (monographs, survey articles)
19-03 Historical (must be assigned at least one classification number from 01-XX)
19-04 Explicit machine computation and programs (not the theory of computation or programming)
19-06 Proceedings, conferences, collections, etc.
19Axx Grothendieck groups and $K_0$, see also {13D15, 18F30}
19A13 Stability for projective modules, See also {13C10}
19A15 Efficient generation
19A22 Frobenius induction, Burnside and representation rings
19A31 $K_0$ of group rings and orders
19A49 $K_0$ of other rings
19A99 None of the above but in this section
19Bxx Whitehead groups and $K_1$
19B10 Stable range conditions
19B14 Stability for linear groups
19B28 $K_1$ of group rings and orders, See also {57Q10}
19B37 Congruence subgroup problems, See also {20H05}
19B99 None of the above but in this section
19Cxx Steinberg groups and $K_2$
19C09 Central extensions and Schur multipliers
19C20 Symbols, presentations and stability of $K_2$
19C30 $K_2$ and the Brauer group
19C40 Excision for $K_2$
19C99 None of the above but in this section
19Dxx Higher algebraic $K$-theory
19D06 $Q$- and plus-constructions
19D10 Algebraic $K$-theory of spaces
19D23 Symmetric monoidal categories, See also {18D10}
19D25 Karoubi-Villamayor-Gersten $K$-theory
19D35 Negative $K$-theory, NK and Nil
19D45 Higher symbols, Milnor $K$-theory
19D50 Computations of higher $K$-theory of rings, See Also {13D15, 16E20}
19D55 $K$-theory and homology; cyclic homology and cohomology, See also {18G60}
19D99 None of the above but in this section
19Exx $K$-theory in geometry
19E08 $K$-theory of schemes, See also {14C35}
19E15 Algebraic cycles, See also {14C25, 14C35}
19E20 Relations with cohomology theories, See also {14Fxx}
19E99 None of the above but in this section
19Fxx $K$-theory in number theory, see also {11R70, 11S70}
19F05 Generalized class field theory, See also {11G45}
19F15 Symbols and arithmetic, See also {11R37}
19F27 Etale cohomology, higher regulators, zeta and $L$-functions, See also {11G40, 11R42, 11S40, 14F20, 14G10}
19F99 None of the above but in this section
19Gxx $K$-theory of forms, see also {11Exx}
19G05 Stability for quadratic modules
19G12 Witt groups of rings, See also {11E81}
19G24 $L$-theory of group rings, See also {11E81}
19G38 Hermitian $K$-theory, relations with $K$-theory of rings
19G99 None of the above but in this section
19Jxx Obstructions from topology
19J05 Finiteness and other obstructions in $K_0$
19J10 Whitehead (and related) torsion
19J25 Surgery obstructions, See also {57R67}
19J35 Obstructions to group actions
19J99 None of the above but in this section
19Kxx $K$-theory and operator algebras See mainly{46L80, and also 46M20}
19K14 $K_0$ as an ordered group, traces
19K33 EXT and $K$-homology, See also {55N22}
19K35 Kasparov theory ($KK$-theory), See also {58G12}
19K56 Index theory, See also {58G12}
19K99 None of the above but in this section
19Lxx Topological $K$-theory, see also {55N15, 55R50, 55S25}
19L10 Riemann-Roch theorems, Chern characters
19L20 $J$-homomorphism, Adams operations, See also {55Q50}
19L41 Connective $K$-theory, cobordism, See also {55N22}
19L47 Equivariant $K$-theory, See also {55N91, 55P91, 55Q91, 55R91, 55S91}
19L64 Computations, geometric applications
19L99 None of the above but in this section
19M05 Miscellaneous applications of $K$-theory
* 20-XX Group theory and generalizations
20-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
20-01 Instructional exposition (textbooks, tutorial papers, etc.)
20-02 Research exposition (monographs, survey articles)
20-03 Historical (must be assigned at least one classification number from 01-XX)
20-04 Explicit machine computation and programs (not the theory of computation or programming)
20-06 Proceedings, conferences, collections, etc.
20Axx Foundations
20A05 Axiomatics and elementary properties
20A10 Metamathematical considerations, {For word problems, See 20F10}
20A15 Applications of logic to group theory
20A99 None of the above but in this section
20Bxx Permutation groups
20B05 General theory for finite groups
20B07 General theory for infinite groups
20B10 Characterization theorems
20B15 Primitive groups
20B20 Multiply transitive finite groups
20B22 Multiply transitive infinite groups
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures, See also {05Bxx, 12F10, 20G40, 20H30, 51-XX}
20B27 Infinite automorphism groups, See also {12F10}
20B30 Symmetric groups
20B35 Subgroups of symmetric groups
20B40 Computational methods
20B99 None of the above but in this section
20Cxx Representation theory of groups, see also {19A22 (for representation rings and Burnside rings)}
20C05 Group rings of finite groups and their modules, See Also { 16S34}
20C07 Group rings of infinite groups and their modules, See Also { 16S34}
20C10 Integral representations of finite groups
20C11 $p$-adic representations of finite groups
20C12 Integral representations of infinite groups
20C15 Ordinary representations and characters
20C20 Modular representations and characters
20C25 Projective representations and multipliers
20C30 Representations of finite symmetric groups
20C32 Representations of infinite symmetric groups
20C33 Representations of finite groups of Lie type
20C34 Representations of sporadic groups
20C35 Applications of group representations to physics
20C40 Computational methods
20C99 None of the above but in this section
20Dxx Abstract finite groups
20D05 Classification of simple and nonsolvable groups
20D06 Simple groups: alternating groups and groups of Lie type, See also {20Gxx, 22Exx}
20D08 Simple groups: sporadic groups
20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks, See also {20F17}
20D15 Nilpotent groups, $p$-groups
20D20 Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure
20D25 Special subgroups (Frattini, Fitting, etc.)
20D30 Series and lattices of subgroups
20D35 Subnormal subgroups
20D40 Products of subgroups
20D45 Automorphisms
20D50 Covering of subgroups
20D60 Arithmetic and combinatorial problems
20D99 None of the above but in this section
20Exx Structure and classification of infinite or finite groups
20E05 Free nonabelian groups
20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E07 Subgroup theorems
20E08 Groups acting on trees
20E10 Quasivarieties and varieties of groups
20E15 Chains and lattices of subgroups, subnormal subgroups, See also {20F22}
20E18 Limits, profinite groups
20E22 Extensions, wreath products, and other compositions, See also {20J05}
20E25 Local properties
20E26 Residual properties and generalizations
20E28 Maximal subgroups
20E32 Simple groups, See also {20D05}
20E34 General structure theorems
20E36 General theorems concerning automorphisms of groups
20E42 Groups with a $BN$-pair; buildings, See also {51E24}
20E99 None of the above but in this section
20Fxx Special aspects of infinite or finite groups
20F05 Generators, relations, and presentations
20F06 Cancellation theory; application of van Kampen diagrams, See also {57M05}
20F10 Word problems, other decision problems, connections with logic and automata, See also {03B25, 03D05, 03D40, 06B25, 08A50, 68Qxx}
20F12 Commutator calculus
20F14 Derived series, central series, and generalizations
20F16 Solvable groups, supersolvable groups
20F17 Formations of groups, Fitting classes, See also {20D10}
20F18 Nilpotent groups
20F19 Generalizations of solvable and nilpotent groups
20F22 Other classes of groups defined by subgroup chains
20F24 FC-groups and their generalizations
20F28 Automorphism groups of groups, See also {20E36}
20F29 Representations of groups as automorphism groups of algebraic systems
20F32 Geometric group theory, See also {05C25, 20Exx, 20Gxx}
20F34 Fundamental groups and their automorphisms, See Also {57M05, 57Sxx, 22E40}
20F36 Braid groups; Artin groups
20F38 Other groups related to topology or analysis
20F40 Associated Lie structures
20F45 Engel conditions
20F50 Periodic groups; locally finite groups
20F55 Coxeter groups, See also {22E40}
20F60 Ordered groups See mainly{06F15}
20F99 None of the above but in this section
20Gxx Linear algebraic groups (classical groups), {For arithmetic theory, see 11E57, 11H06; for geometric theory, See 14Lxx, 22Exx; for other methods in representation theory, See {15AQ30, 22Exx} {15A30, 22E45, 22E46, 22E47, 22E50, 22E55}}
20G05 Representation theory
20G10 Cohomology theory
20G15 Linear algebraic groups over arbitrary fields
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20G25 Linear algebraic groups over local fields and their integers
20G30 Linear algebraic groups over global fields and their integers
20G35 Linear algebraic groups over adeles and other rings and schemes
20G40 Linear algebraic groups over finite fields
20G45 Applications to physics; explicit representations
20G99 None of the above but in this section
20Hxx Other groups of matrices, see also {15A30}
20H05 Unimodular groups, congruence subgroups, See also {11F06, 19B37, 22E40, 51F20}
20H10 Fuchsian groups and their generalizations, See also {11F06, 22E40, 30F35, 32Nxx}
20H15 Other geometric groups, including crystallographic groups, See also {51-XX, especially 51F15, and 82D25}
20H20 Other matrix groups over fields
20H25 Other matrix groups over rings
20H30 Other matrix groups over finite fields
20H99 None of the above but in this section
20Jxx Connections with homological algebra and category theory
20J05 Homological methods in group theory
20J06 Cohomology of finite groups
20J10 Groups arising as cohomology groups
20J15 Category of groups
20J99 None of the above but in this section
20Kxx Abelian groups
20K01 Finite abelian groups
20K05 Finitely generated groups
20K10 Torsion groups, primary groups and generalized primary groups
20K12 Ulm sequences
20K15 Torsion free groups, finite rank
20K20 Torsion free groups, infinite rank
20K21 Mixed groups
20K25 Direct sums, direct products, etc.
20K26 Indecomposable groups
20K27 Subgroups
20K30 Automorphisms, homomorphisms, endomorphisms, etc.
20K35 Extensions
20K40 Homological and categorical methods
20K45 Topological methods, See also {22A05, 22B05}
20K99 None of the above but in this section
20Lxx Groupoids (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}
20L05 General theory
20L10 Connections with group theory
20L13 Mappings of groupoids
20L15 Connections with topology
20L17 Connections with category theory
20L99 None of the above but in this section
20Mxx Semigroups
20M05 Free semigroups, generators and relations, word problems
20M07 Varieties of semigroups
20M10 General structure theory
20M11 Radical theory
20M12 Ideal theory
20M14 Commutative semigroups
20M15 Mappings of semigroups
20M17 Regular semigroups
20M18 Inverse semigroups
20M19 Orthodox semigroups
20M20 Semigroups of transformations, etc., See also {47D03, 47H20, 54H15}
20M25 Semigroup rings, multiplicative semigroups of rings, See also {16S36, 16Y60}
20M30 Representation of semigroups
20M35 Semigroups in automata theory, linguistics, etc., See Also {03D05, 68Qxx, 68S05}
20M50 Connections of semigroups with homological algebra and category theory
20M99 None of the above but in this section
20Nxx Other generalizations of groups
20N02 Sets with a single binary operation (groupoids)
20N05 Loops, quasigroups, See also {05Bxx}
20N07 Mappings of loops
20N10 Ternary systems (heaps, semiheaps, heapoids, etc.)
20N15 $n$-ary systems
20N20 Hypergroups
20N25 Fuzzy groups, See also {04A72}
20N99 None of the above but in this section
20P05 Probabilistic methods in group theory
* 22-XX Topological groups, Lie groups, {For transformation groups, See 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, See 43-XX}
22-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
22-01 Instructional exposition (textbooks, tutorial papers, etc.)
22-02 Research exposition (monographs, survey articles)
22-03 Historical (must be assigned at least one classification number from 01-XX)
22-04 Explicit machine computation and programs (not the theory of computation or programming)
22-06 Proceedings, conferences, collections, etc.
22Axx Topological and differentiable algebraic systems, {For topological rings and fields, see 12Jxx, 13Jxx, 16W80; for dual spaces of operator algebras and topological groups, See 47D35}
22A05 Structure of general topological groups
22A10 Analysis on general topological groups
22A15 Structure of topological semigroups
22A20 Analysis on topological semigroups
22A22 Topological groupoids (including differentiable and Lie groupoids)
22A25 Representations of general topological groups and semigroups
22A26 Topological semilattices, lattices and applications, See also {06B30, 06B35, 06F30}
22A30 Other topological algebraic systems and their representations
22A99 None of the above but in this section
22Bxx Locally compact abelian groups (LCA groups)
22B05 General properties and structure of LCA groups
22B10 Structure of group algebras of LCA groups
22B99 None of the above but in this section
22C05 Compact groups
22Dxx Locally compact groups and their algebras
22D05 General properties and structure of locally compact groups
22D10 Unitary representations of locally compact groups
22D12 Other representations of locally compact groups
22D15 Group algebras of locally compact groups
22D20 Representations of group algebras
22D25 $C$*-algebras and $W$*-algebras arising from group representations, See also {46Lxx}
22D30 Induced representations
22D35 Duality theorems
22D40 Ergodic theory on groups, See also {28Dxx, 43A60}
22D45 Automorphism groups of locally compact groups
22D99 None of the above but in this section
22Exx Lie groups, {For the topology of Lie groups and homogeneous spaces, see {57-XX, 57Sxx, 57Txx}; for analysis thereon, See {43-XX, 43A80, 43A85, 43A90}
22E05 Local Lie groups, See also {34-XX, 35-XX, 58H05}
22E10 General properties and structure of complex Lie groups, See also {32M05}
22E15 General properties and structure of real Lie groups
22E20 General properties and structure of other Lie groups
22E25 Nilpotent and solvable Lie groups
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
22E30 Analysis on real and complex Lie groups, See also {33C80, 43-XX}
22E35 Analysis on $p$-adic Lie groups, See also {11R56}
22E40 Discrete subgroups of Lie groups, See also {20Hxx, 32Nxx}
22E41 Continuous cohomology, See also {57R32, 57Txx, 58H10}
22E43 Structure and representation of the Lorentz group
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods, {For the purely algebraic theory, See 20G05}
22E46 Semisimple Lie groups and their representations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), See also {17B35}
22E50 Representations of Lie and linear algebraic groups over local fields
22E55 Representations of Lie and linear algebraic groups over global fields and adele rings, See also {20G05}
22E60 Lie algebras of Lie groups, {For the algebraic theory of Lie algebras, See 17Bxx}
22E65 Infinite-dimensional Lie groups and their Lie algebras, See also {17B65, 58B25, 58H05}
22E67 Loop groups and related constructions, group-theoretic treatment, See also {58D05}
22E70 Applications of Lie groups to physics; explicit representations, See also {81R05, 81R10}
22E99 None of the above but in this section
* 26-XX Real functions, See also {54C30}
26-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
26-01 Instructional exposition (textbooks, tutorial papers, etc.)
26-02 Research exposition (monographs, survey articles)
26-03 Historical (must be assigned at least one classification number from 01-XX)
26-04 Explicit machine computation and programs (not the theory of computation or programming)
26-06 Proceedings, conferences, collections, etc.
26Axx Functions of one variable
26A03 Foundations: limits and generalizations, elementary topology of the line
26A06 One-variable calculus
26A09 Elementary functions
26A12 Rate of growth of functions, orders of infinity, slowly varying functions, See also {26A48}
26A15 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}
26A16 Lipschitz (Holder) classes
26A18 Iteration, See also {39B12, 47H10, 54H25, 58F08, 58F13}
26A21 Classification of real functions; Baire classification of sets and functions, See also {04A15, 28A05, 54C50}
26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems, See also {28A15}
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
26A30 Singular functions, Cantor functions, functions with other special properties
26A33 Fractional derivatives and integrals
26A36 Antidifferentiation
26A39 Denjoy and Perron integrals, other special integrals
26A42 Integrals of Riemann, Stieltjes and Lebesgue type, See also {28-XX}
26A45 Functions of bounded variation, generalizations
26A46 Absolutely continuous functions
26A48 Monotonic functions, generalizations
26A51 Convexity, generalizations
26A99 None of the above but in this section
26Bxx Functions of several variables
26B05 Continuity and differentiation questions
26B10 Implicit function theorems, Jacobians, transformations with several variables
26B12 Calculus of vector functions
26B15 Integration: length, area, volume, See also {28A75, 51M25}
26B20 Integral formulas (Stokes, Gauss, Green, etc.)
26B25 Convexity, generalizations
26B30 Absolutely continuous functions, functions of bounded variation
26B35 Special properties of functions of several variables, Holder conditions, etc.
26B40 Representation and superposition of functions
26B99 None of the above but in this section
26Cxx Polynomials, rational functions
26C05 Polynomials: analytic properties, etc., See also {12Dxx, 12Exx}
26C10 Polynomials: location of zeros, See also {12D10, 30C15, 65H05}
26C15 Rational functions, See also {14Pxx}
26C99 None of the above but in this section
26Dxx Inequalities, {For maximal function inequalities, see 42B25; for functional inequalities, See 39B72; for probabilistic inequalities, See 60E15}
26D05 Inequalities for trigonometric functions and polynomials
26D07 Inequalities involving other types of functions
26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
26D20 Other analytical inequalities
26D99 None of the above but in this section
26Exx Miscellaneous topics, see also {58Cxx}
26E05 Real-analytic functions, See also {32B05, 32C05}
26E10 $C^\infty$-functions, quasi-analytic functions, See also {58C25}
26E15 Calculus of functions on infinite-dimensional spaces, See also {46G05, 58Cxx}
26E20 Calculus of functions taking values in infinite-dimensional spaces, See also {46E40, 46G10, 58Cxx}
26E25 Set-valued functions, See also {28B20, 54C60}, {For nonsmooth analysis, See 49J52, 58Cxx, 90Cxx}
26E30 Non-Archimedean analysis, See also {12J25}
26E35 Nonstandard analysis, See also {03H05, 28E05, 54J05}
26E40 Constructive real analysis, See also {03F60, 03F65}
26E50 Fuzzy real analysis, See also {04A72, 28E10}
26E99 None of the above but in this section
* 28-XX Measure and integration, {For analysis on manifolds, See 58-XX}
28-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
28-01 Instructional exposition (textbooks, tutorial papers, etc.)
28-02 Research exposition (monographs, survey articles)
28-03 Historical (must be assigned at least one classification number from 01-XX)
28-04 Explicit machine computation and programs (not the theory of computation or programming)
28-06 Proceedings, conferences, collections, etc.
28Axx Classical measure theory
28A05 Classes of sets (Borel fields, $sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets, See Also {03E15, 04A15, 26A21, 54H05}
28A10 Real- or complex-valued set functions
28A12 Contents, measures, outer measures, capacities
28A15 Abstract differentiation theory, differentiation of set functions, See also {26A24}
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A25 Integration with respect to measures and other set functions
28A33 Spaces of measures, convergence of measures, See Also {46E27, 60Bxx}
28A35 Measures and integrals in product spaces
28A50 Integration and disintegration of measures
28A51 Lifting theory, See also {46G15}
28A60 Measures on Boolean rings, measure algebras, See Also { 54H10}
28A75 Length, area, volume, other geometric measure theory, See also {26B15, 49Q15}
28A78 Hausdorff measures
28A80 Fractals, See also {58Fxx}
28A99 None of the above but in this section
28Bxx Set functions, measures and integrals with values in abstract spaces
28B05 Vector-valued set functions, measures and integrals, See also {46G10}
28B10 Group- or semigroup-valued set functions, measures and integrals
28B15 Set functions, measures and integrals with values in ordered spaces
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections, See Also {26E25, 54C60, 54C65, 90A14}
28B99 None of the above but in this section
28Cxx Set functions and measures on spaces with additional structure, see also {46G12, 58C35, 58D20}
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
28C10 Set functions and measures on topological groups, Haar measures, invariant measures, See also {22Axx, 43A05}
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), See also {46G12, 58C35, 58D20, 60B11}
28C99 None of the above but in this section
28Dxx Measure-theoretic ergodic theory, see also {11K50, 11K55, 22D40, 47A35, 54H20, 58Fxx, 60Fxx, 60G10}
60A99 None of the above but in this section(28Dxx and 60Fxx)
28Exx Miscellaneous topics in measure theory
28E05 Nonstandard measure theory, See also {03H05, 26E35}
28E10 Fuzzy measure theory, See also {04A72, 26E50, 94D05}
28E15 Other connections with logic and set theory
28E99 None of the above but in this section
* 30-XX Functions of a complex variable, {For analysis on manifolds, See 58-XX}
30-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
30-01 Instructional exposition (textbooks, tutorial papers, etc.)
30-02 Research exposition (monographs, survey articles)
30-03 Historical (must be assigned at least one classification number from 01-XX)
30-04 Explicit machine computation and programs (not the theory of computation or programming)
30-06 Proceedings, conferences, collections, etc.
30Axx General properties
30A05 Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
30A10 Inequalities in the complex domain
30A99 None of the above but in this section
30Bxx Series expansions
30B10 Power series (including lacunary series)
30B20 Random power series
30B30 Boundary behavior of power series, over-convergence
30B40 Analytic continuation
30B50 Dirichlet series and other series expansions, exponential series, See also {11M41, 42-XX}
30B60 Completeness problems, closure of a system of functions
30B70 Continued fractions, See also {11A55, 40A15}
30B99 None of the above but in this section
30Cxx Geometric function theory
30C10 Polynomials
30C15 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}
30C20 Conformal mappings of special domains
30C25 Covering theorems in conformal mapping theory
30C30 Numerical methods in conformal mapping theory, See Also { 65E05}
30C35 General theory of conformal mappings
30C40 Kernel functions and applications
30C45 Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions
30C55 General theory of univalent and multivalent functions
30C62 Quasiconformal mappings in the plane
30C65 Quasiconformal mappings in $R^n$, other generalizations
30C70 Extremal problems for conformal and quasiconformal mappings, variational methods
30C75 Extremal problems for conformal and quasiconformal mappings, other methods
30C80 Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination
30C85 Capacity and harmonic measure in the complex plane, See also {31A15}
30C99 None of the above but in this section
30Dxx Entire and meromorphic functions, and related topics
30D05 Functional equations in the complex domain, iteration and composition of analytic functions, See also {34A20, 39-XX, 58F08, 58F23}
30D10 Representations of entire functions by series and integrals
30D15 Special classes of entire functions and growth estimates
30D20 Entire functions, general theory
30D30 Meromorphic functions, general theory
30D35 Distribution of values, Nevanlinna theory
30D40 Cluster sets, prime ends, boundary behavior
30D45 Bloch functions, normal functions, normal families
30D50 Blashke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part
30D55 ${H}^p$-classes
30D60 Quasi-analytic and other classes of functions
30D99 None of the above but in this section
30Exx Miscellaneous topics of analysis in the complex domain
30E05 Moment problems, interpolation problems
30E10 Approximation in the complex domain
30E15 Asymptotic representations in the complex domain
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions, See also {45Exx}
30E25 Boundary value problems, See also {45Exx}
30E99 None of the above but in this section
30Fxx Riemann surfaces
30F10 Compact Riemann surfaces and uniformization, See Also {14H15, 32G15}
30F15 Harmonic functions on Riemann surfaces
30F20 Classification theory of Riemann surfaces
30F25 Ideal boundary theory
30F30 Differentials on Riemann surfaces
30F35 Fuchsian groups and automorphic functions, See also {11Fxx, 20H10, 22E40, 32Gxx, 32Nxx}
30F40 Kleinian groups, See also {20H10}
30F45 Conformal metrics (hyperbolic, Poincare, distance functions)
30F50 Klein surfaces
30F60 Teichmuller theory, See also {32G15}
30F99 None of the above but in this section
30Gxx Generalized function theory
30G06 Non-Archimedean function theory, See also {12J25}; nonstandard function theory, See also {03H05}
30G12 Finely holomorphic functions and topological function theory
30G15 Topological function theory
30G20 Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)
30G25 Discrete analytic functions
30G30 Other generalizations of analytic functions (including abstract-valued functions)
30G35 Functions of hypercomplex variables and generalized variables
30G99 None of the above but in this section
30H05 Spaces and algebras of analytic functions, See also {32E25, 46Exx, 46J15}
* 31-XX Potential theory, {For probabilistic potential theory, See 60J45}
31-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
31-01 Instructional exposition (textbooks, tutorial papers, etc.)
31-02 Research exposition (monographs, survey articles)
31-03 Historical (must be assigned at least one classification number from 01-XX)
31-04 Explicit machine computation and programs (not the theory of computation or programming)
31-06 Proceedings, conferences, collections, etc.
31Axx Two-dimensional theory
31A05 Harmonic, subharmonic, superharmonic functions
31A10 Integral representations, integral operators, integral equations methods
31A15 Potentials and capacity, harmonic measure, extremal length, See also {30C85}
31A20 Boundary behavior (theorems of Fatou type, etc.)
31A25 Boundary value and inverse problems
31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
31A35 Connections with differential equations
31A99 None of the above but in this section
31Bxx Higher-dimensional theory
31B05 Harmonic, subharmonic, superharmonic functions
31B10 Integral representations, integral operators, integral equations methods
31B15 Potentials and capacities, extremal length
31B20 Boundary value and inverse problems
31B25 Boundary behavior
31B30 Biharmonic and polyharmonic equations and functions
31B35 Connections with differential equations
31B99 None of the above but in this section
31Cxx Other generalizations
31C05 Harmonic, subharmonic, superharmonic functions
31C10 Pluriharmonic and plurisubharmonic functions, See Also { 32F05}
31C12 Potential theory on Riemannian manifolds, See also {53C20; for Hodge theory, See 58A14}
31C15 Potentials and capacities
31C20 Discrete potential theory and numerical methods
31C25 Dirichlet spaces
31C35 Martin boundary theory, See also {60J50}
31C40 Fine potential theory
31C45 Other generalizations (nonlinear potential theory, etc.)
31C99 None of the above but in this section
31D05 Axiomatic potential theory
* 32-XX Several complex variables and analytic spaces, {For infinite-dimensional holomorphy, See also 46G20, 58B12}
32-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
32-01 Instructional exposition (textbooks, tutorial papers, etc.)
32-02 Research exposition (monographs, survey articles)
32-03 Historical (must be assigned at least one classification number from 01-XX)
32-04 Explicit machine computation and programs (not the theory of computation or programming)
32-06 Proceedings, conferences, collections, etc.
32Axx Holomorphic functions of several complex variables
32A05 Power series, series of functions
32A07 Special domains (Reinhardt, Hartogs, tube domains, etc.)
32A10 Holomorphic functions
32A15 Entire functions
32A17 Special families of functions (e.g. normal families)
32A20 Meromorphic functions
32A22 Nevanlinna theory (local); growth estimates; other inequalities, {For geometric theory, See 32H25, 32H30}
32A25 Integral representation
32A27 Local theory of residues, See also {32C30}
32A30 Other 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}
32A35 ${H}^p$-spaces, See also {32M15, 42B30, 43A85, 46J15}
32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) in $n$ dimensions), See also {46Exx}
32A40 Boundary behavior
32A45 Hyperfunctions, See also {46F15}
32A99 None of the above but in this section
32Bxx Local analytic geometry, see also {13-XX and 14-XX}
32B05 Analytic algebras and generalizations, preparation theorems
32B10 Germs of analytic sets
32B15 Analytic subsets of affine space
32B20 Semi-analytic sets and subanalytic sets, See also {14P15}
32B25 Triangulation and related questions
32B99 None of the above but in this section
32Cxx General theory of analytic spaces
32C05 Real-analytic manifolds, real-analytic spaces, See Also {14Pxx, 58A07}
32C07 Real-analytic sets, complex Nash functions, See Also {14P15, 14P20}
32C10 Complex manifolds, {For almost complex manifolds, See 53C15}
32C11 Complex supergeometry, See also {14A22, 14M30, 58A50}
32C15 Complex spaces
32C16 CR-manifolds
32C17 Kahler geometry, {For differential-geometric methods, See 53C55}
32C18 Topology of analytic spaces
32C20 Normal analytic spaces
32C25 Analytic subsets and submanifolds
32C30 Integration on analytic sets and spaces, currents, {For local theory, See 32A25 or 32A27}
32C35 Analytic sheaves and cohomology groups, See also {14Fxx, 18F20, 55N30}
32C36 Local cohomology of analytic spaces
32C37 Duality theorems
32C38 Sheaves of differential operators and their modules, See also {14F10, 16S32, 35A27, 58G07}
32C81 Applications to physics
32C99 None of the above but in this section
32Dxx Analytic continuation
32D05 Domains of holomorphy
32D10 Envelopes of holomorphy
32D15 Continuation of analytic objects
32D20 Removable singularities
32D99 None of the above but in this section
32Exx Holomorphic convexity
32E05 Holomorphically convex complex spaces, reduction theory
32E10 Stein spaces, Stein manifolds
32E20 Polynomial convexity
32E25 Algebras of holomorphic functions, See also {30H05, 46J10, 46J15}
32E30 Holomorphic and polynomial approximation, Runge pairs, interpolation
32E35 Global boundary behavior of holomorphic functions
32E99 None of the above but in this section
32Fxx Geometric convexity, partial differential operators
32F05 Plurisubharmonic functions and generalizations, See Also { 31C10}
32F07 Complex Monge-Ampere operator
32F10 $q$-convexity, $q$-concavity
32F15 Pseudoconvex domains
32F20 $\overline\partial$- and $\overline\partial_b$-Neumann problems, See also {35N15}
32F25 Real submanifolds in complex manifolds
32F30 Pseudoconvex manifolds
32F40 CR structures, (tangential) CR operators and generalizations
32F99 None of the above but in this section
32Gxx Deformations of analytic structures
32G05 Deformations of complex structures, See also {13D10, 16S80, 58H10, 58H15}
32G07 Deformations of special (e.g. CR) structures
32G08 Deformations of fiber bundles
32G10 Deformations of submanifolds and subspaces
32G13 Analytic moduli problems, {For algebraic moduli problems, See 14D20, 14D22, 14H10, 14J10}, See also {14H15, 14J15}
32G15 Moduli of Riemann surfaces, Teichmuller theory, See Also {14H15, 30Fxx}
32G20 Period matrices, variation of Hodge structure; degenerations, See also {14D05, 14D07, 14K30}
32G34 Moduli and deformations for ordinary differential equations, See also {34A20}
32G81 Applications to physics
32G99 None of the above but in this section
32Hxx Holomorphic mappings and correspondences
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions
32H04 Meromorphic mappings
32H10 Bergman kernel function, representative domains
32H15 Invariant metrics and pseudodistances
32H20 Hyperbolic complex manifolds
32H25 Picard-type theorems and generalizations, {For function-theoretic properties, See 32A22}
32H30 Value distribution theory in higher dimensions, {For function-theoretic properties, See 32A22}
32H35 Proper mappings, finiteness theorems
32H40 Boundary regularity of holomorphic maps
32H50 Iteration problems
32H99 None of the above but in this section
32Jxx Compact analytic spaces, {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, See 14Jxx}
32J05 Compactification of analytic spaces
32J10 Algebraic dependence theorems
32J15 Compact surfaces
32J17 Compact $3$-folds
32J18 Compact $n$-folds $(n \ge 4)$
32J20 Algebraicity criteria
32J25 Transcendental methods of algebraic geometry, See Also { 14C30}
32J27 Compact Kahler manifolds: generalizations, classification
32J81 Applications to physics
32J99 None of the above but in this section
32Kxx Generalizations of analytic spaces {(should also be assigned at least one other classification number in this section)}
32K05 Banach analytic spaces, See also {58Bxx}
32K07 Formal and graded complex spaces, See also {58C50}
32K15 Differentiable functions on analytic spaces, differentiable spaces, See also {58C25}
32K99 None of the above but in this section
32Lxx Holomorphic fiber spaces, see also {55Rxx}
32L05 Holomorphic fiber bundles and generalizations
32L07 Hermite-Einstein bundles; Kahler-Einstein bundles, See also {53C07}
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results, See also {14F05, 18F20, 55N30}
32L15 Bundle convexity, See also {32F10}
32L20 Vanishing theorems
32L25 Twistor theory, double fibrations
32L30 Holomorphic foliations, See also {58F18}
32L81 Applications to physics
32L99 None of the above but in this section
32Mxx Complex spaces with a group of automorphisms
32M05 Complex Lie groups, automorphism groups of complex spaces, See also {22E10}
32M10 Homogeneous complex manifolds, See also {14M17, 57T15}
32M12 Almost homogeneous manifolds and spaces, See also {14M17}
32M15 Hermitian symmetric spaces, bounded symmetric domains, See also {22E10, 22E40, 53C35, 57T15}
32M99 None of the above but in this section
32Nxx Automorphic functions, see also {11Fxx, 20H10, 22E40, 30F35}
32N05 General theory of automorphic functions of several complex variables
32N10 Automorphic forms
32N15 Automorphic functions in symmetric domains
32N99 None of the above but in this section
32P05 Non-Archimedean complex analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
32Sxx Singularities
32S05 Local singularities, See also {14B05}
32S10 Invariants of analytic local rings
32S15 Equisingularity (topological and analytic), See Also { 14E15}
32S20 Global theory of singularities; cohomological properties, See also {14E15}
32S25 (Hyper-) surface singularities, See also {14J17}
32S30 Deformations of singularities; vanishing cycles, See Also { 14B07}
32S35 Mixed Hodge theory of singular varieties, See also {14C30, 14D07}
32S40 Monodromy; relations with differential equations and $D$-modules
32S45 Modifications; resolution of singularities, See Also { 14E15}
32S50 Topological aspects: Lefschetz theorems, topological classification, invariants
32S55 Milnor fibration; relations with knot theory, See Also {57M25, 57Q45}
32S60 Stratifications; constructible sheaves; intersection cohomology, See also {58C27}
32S65 Singularities of holomorphic vector fields
32S70 Other operations on singularities
* 33-XX Special functions, {33-XX deals with the properties of functions as functions. For orthogonal functions, See also 42Cxx; for aspects of combinatorics, See 05Axx; for number-theoretic aspects, See 11-XX; for representation theory, See 22Exx}
33-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
33-01 Instructional exposition (textbooks, tutorial papers, etc.)
33-02 Research exposition (monographs, survey articles)
33-03 Historical (must be assigned at least one classification number from 01-XX)
33-04 Explicit machine computation and programs (not the theory of computation or programming)
33-06 Proceedings, conferences, collections, etc.
33Bxx Elementary classical functions
33B10 Exponential and trigonometric functions
33B15 Gamma, beta and polygamma functions
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
33B99 None of the above but in this section
33Cxx Hypergeometric functions
33C05 Classical hypergeometric functions, $_2F_1$
33C10 Bessel and Airy functions, cylinder functions, $_0F_1$
33C15 Confluent hypergeometric functions, Whittaker functions, $_1F_1$
33C20 Generalized hypergeometric series, $_pF_q$
33C45 Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)
33C50 Orthogonal polynomials and functions in several variables
33C55 Spherical functions, spherical harmonics, ultraspherical polynomials
33C60 Hypergeometric integrals and functions defined by them ($E$, $G$ and ${H}$ functions)
33C65 Appell, Horn and Lauricella functions
33C70 Other hypergeometric functions and integrals in several variables
33C75 Elliptic integrals as hypergeometric functions
33C80 Connections with groups, algebras, root systems and related topics
33C90 Applications
33C99 None of the above but in this section
33Dxx Basic hypergeometric functions
33D05 $q$-gamma functions, $q$-beta functions and integrals
33D10 Basic theta functions
33D15 Basic hypergeometric functions in one variable
33D20 Generalized basic hypergeometric series
33D45 Basic orthogonal polynomials and functions in one and several variables
33D55 Basic spherical functions, spherical harmonics (continuous and discrete)
33D60 Basic hypergeometric integrals and functions defined by them
33D65 Bibasic functions and multiple bases
33D70 Other basic hypergeometric functions and integrals in several variables
33D80 Connections with groups, algebras, and related topics
33D90 Applications
33D99 None of the above but in this section
33Exx Other special functions
33E05 Elliptic functions and integrals
33E10 Lame, Mathieu, and spheroidal wave functions
33E15 Other wave functions
33E20 Other functions defined by series and integrals
33E30 Other functions coming from differential, difference and integral equations
33E99 None of the above but in this section
* 34-XX Ordinary differential equations
34-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
34-01 Instructional exposition (textbooks, tutorial papers, etc.)
34-02 Research exposition (monographs, survey articles)
34-03 Historical (must be assigned at least one classification number from 01-XX)
34-04 Explicit machine computation and programs (not the theory of computation or programming)
34-06 Proceedings, conferences, collections, etc.
34Axx General theory
34A05 Explicit solutions and reductions
34A09 Implicit equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
34A20 Differential equations in the complex domain, See Also {30D05, 32G34}
34A25 Analytical theory: series, transformations, transforms, operational calculus, etc., See also {44-XX, 47E05}
34A26 Geometric methods in differential equations
34A30 Linear equations and systems
34A34 Nonlinear equations and systems, general
34A35 Differential equations of infinite order
34A37 Differential equations with impulses
34A40 Differential inequalities
34A45 Theoretical approximation of solutions
34A46 Theoretical solution methods other than approximations
34A47 Bifurcation
34A50 Numerical approximation of solutions, {For numerical analysis, See 65Lxx}
34A55 Inverse problems
34A60 Equations with multivalued right-hand sides, See Also {49J24, 49K24}
34A65 Stiff equations
34A99 None of the above but in this section
34Bxx Boundary value problems, {For ordinary differential operators, see 34Lxx}
34B05 Linear equations
34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems
34B20 Weyl theory and its generalizations
34B24 Sturm-Liouville theory, See also {34Lxx}
34B27 Green functions
34B30 Special equations (Mathieu, Hill, Bessel, etc.)
34B99 None of the above but in this section
34Cxx Qualitative theory, see also {58Fxx}
34C05 Location of integral curves, singular points, limit cycles
34C10 Oscillation theory, zeros, disconjugacy and comparison theory
34C11 Growth, boundedness, comparison of solutions
34C15 Nonlinear oscillations
34C20 Transformation and reduction of equations and systems, normal forms
34C23 Bifurcation See mainly{58F14}
34C25 Periodic solutions
34C27 Almost-periodic solutions
34C28 Other types of ``recurrent'' solutions
34C29 Averaging method
34C30 Manifolds of solutions
34C35 Dynamical systems, See also {54H20, 58Fxx, 70-XX}
34C37 Homoclinic and heteroclinic solutions, See also {58F15}
34C40 Equations and systems on manifolds See mainly{58Fxx, 58Gxx}
34C45 Method of integral manifolds
34C50 Method of accelerated convergence
34C99 None of the above but in this section
34Dxx Stability theory, see also {58F10, 93Dxx}
34D05 Asymptotic properties
34D08 Lyapunov exponents
34D10 Perturbations
34D15 Singular perturbations
34D20 Lyapunov stability
34D25 Popov-type stability
34D30 Structural stability and analogous concepts , See Also {58F10, 58F12}
34D35 Stability of manifolds of solutions
34D40 Ultimate boundedness
34D45 Attractors
34D99 None of the above but in this section
34Exx Asymptotic theory
34E05 Asymptotic expansions
34E10 Perturbations, asymptotics
34E15 Singular perturbations, general theory
34E20 Singular perturbations, turning point theory, WKB methods
34E99 None of the above but in this section
34F05 Equations and systems with randomness, See also {34K50, 60H10, 93E03}
34Gxx Differential equations in abstract spaces, see also {58D25}
34G10 Linear equations, See also {47Axx, 47Bxx, 47D06, 47D09}
34G20 Nonlinear equations, See also {47Hxx}
34G99 None of the above but in this section
34H05 Control problems, See also {49J25, 49K25, 93C15}
34Kxx Functional-differential and differential-difference equations with or without deviating arguments
34K05 General theory
34K10 Boundary value problems
34K15 Qualitative theory
34K20 Stability theory
34K25 Asymptotic theory
34K30 Equations in abstract spaces, See also {34Gxx}
34K35 Control problems, See also {49J25, 49K25, 93C15}
34K40 Neutral equations
34K50 Stochastic delay equations, See also {34F05, 60Hxx}
34K99 None of the above but in this section
34Lxx Ordinary differential operators, see also {47E05}
34L05 General spectral theory
34L10 Eigenfunction expansions, completeness of eigenfunctions
34L15 Estimation of eigenvalues, upper and lower bounds
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
34L25 Scattering theory
34L30 Nonlinear ordinary differential operators
34L40 Particular operators (Dirac, one-dimensional Schrodinger, etc.)
34L99 None of the above but in this section
* 35-XX Partial differential equations
35-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
35-01 Instructional exposition (textbooks, tutorial papers, etc.)
35-02 Research exposition (monographs, survey articles)
35-03 Historical (must be assigned at least one classification number from 01-XX)
35-04 Explicit machine computation and programs (not the theory of computation or programming)
35-06 Proceedings, conferences, collections, etc.
35Axx General theory
35A05 General existence and uniqueness theorems
35A07 Local existence and uniqueness theorems, See also {35H05, 35Sxx}
35A08 Fundamental solutions
35A10 Cauchy-Kovalevskaya theorems
35A15 Variational methods
35A20 Analytic methods, singularities
35A22 Transform methods (e.g. integral transforms)
35A25 Other special methods
35A27 Microlocal methods; methods of sheaf theory and homological algebra in PDE, See also {32C38, 58G07}
35A30 Geometric theory, characteristics, transformations, See also {58G35, 58G37}
35A35 Theoretical approximation to solutions
35A40 Numerical approximation to solutions, {For numerical analysis, See 65Mxx, 65Nxx, 65P05}
35A99 None of the above but in this section
35Bxx Qualitative properties of solutions
35B05 General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)
35B10 Periodic solutions
35B15 Almost periodic solutions
35B20 Perturbations
35B25 Singular perturbations
35B27 Homogenization; partial differential equations in media with periodic structure, See also {73B27, 76D30}
35B30 Dependence of solutions of PDE on initial and boundary data, parameters, See also {58F14}
35B32 Bifurcation, See also {58F14}
35B35 Stability, boundedness
35B37 PDE in connection with control problems, See also {49J20, 49K20, 93C20}
35B40 Asymptotic behavior of solutions
35B45 A priori estimates
35B50 Maximum principles
35B60 Continuation and prolongation of solutions of PDE, See also {58A15, 58A17, 58Hxx}
35B65 Smoothness/regularity of solutions of PDE
35B99 None of the above but in this section
35Cxx Representations of solutions
35C05 Solutions in closed form
35C10 Series solutions, expansion theorems
35C15 Integral representations of solutions of PDE
35C20 Asymptotic expansions
35C99 None of the above but in this section
35Dxx Generalized solutions of partial differential equations
35D05 Existence of generalized solutions
35D10 Regularity of generalized solutions
35D99 None of the above but in this section
35Exx Equations and systems with constant coefficients, see Also { 35N05}
35E05 Fundamental solutions
35E10 Convexity properties
35E15 Initial value problems
35E20 General theory
35E99 None of the above but in this section
35Fxx General first-order equations and systems
35F05 General theory of linear first-order PDE
35F10 Initial value problems for linear first-order PDE, linear evolution equations
35F15 Boundary value problems for linear first-order PDE
35F20 General theory of nonlinear first-order PDE
35F25 Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
35F30 Boundary value problems for nonlinear first-order PDE
35F99 None of the above but in this section
35Gxx General higher-order equations and systems
35G05 General theory of linear higher-order PDE
35G10 Initial value problems for linear higher-order PDE, linear evolution equations
35G15 Boundary value problems for linear higher-order PDE
35G20 General theory of nonlinear higher-order PDE
35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
35G30 Boundary value problems for nonlinear higher-order PDE
35G99 None of the above but in this section
35H05 Hypoelliptic equations and systems, See also {58Gxx}
35Jxx Partial differential equations of elliptic type, see also {{ 58Gxx} {58G05, 58G10}}
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation, See also {31Axx, 31Bxx}
35J10 Schrodinger operator, See also {35Pxx}
35J15 General theory of second-order, elliptic equations
35J20 Variational methods for second-order, elliptic equations
35J25 Boundary value problems for second-order, elliptic equations
35J30 General theory of higher-order, elliptic equations , See also {31A30, 31B30}
35J35 Variational methods for higher-order, elliptic equations
35J40 Boundary value problems for higher-order, elliptic equations
35J45 General theory of elliptic systems of PDE
35J50 Variational methods for elliptic systems
35J55 Boundary value problems for elliptic systems
35J60 Nonlinear PDE of elliptic type
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
35J67 Boundary values of solutions to elliptic PDE
35J70 Elliptic partial differential equations of degenerate type
35J85 Unilateral problems and variational inequalities for elliptic PDE, See also {35R35, 49J40}
35J99 None of the above but in this section
35Kxx Parabolic equations and systems, see also {35Bxx, 35Dxx, 35R30, 35R35, 58G11}
35K05 Heat equation
35K10 General theory of second-order, parabolic equations
35K15 Initial value problems for second-order, parabolic equations
35K20 Boundary value problems for second-order, parabolic equations
35K22 Evolution equations (any order in the spatial derivatives), See also {58D25}
35K25 General theory of higher-order, parabolic equations
35K30 Initial value problems for higher-order, parabolic equations
35K35 Boundary value problems for higher-order, parabolic equations
35K40 General theory of parabolic systems of PDE
35K45 Initial value problems for pararabolic systems
35K50 Boundary value problems for parabolic systems
35K55 Nonlinear PDE of parabolic type
35K57 Reaction-diffusion equations
35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
35K65 Parabolic partial differential equations of degenerate type
35K70 Ultraparabolic, pseudoparabolic PDE, etc.
35K85 Unilateral problems and variational inequalities for parabolic PDE, See also {35R35, 49J40}
35K99 None of the above but in this section
35Lxx Partial differential equations of hyperbolic type, see Also { 58G16}
35L05 Wave equation
35L10 General theory of second-order, hyperbolic equations
35L15 Initial value problems for second-order, hyperbolic equations
35L20 Boundary value problems for second-order, hyperbolic equations
35L25 General theory of higher-order, hyperbolic equations
35L30 Initial value problems for higher-order, hyperbolic equations
35L35 Boundary value problems for higher-order, hyperbolic equations
35L40 General theory of hyperbolic systems of first-order PDE
35L45 Initial value problems for hyperbolic systems of first-order PDE
35L50 Boundary value problems for hyperbolic systems of first-order PDE
35L55 Hyperbolic systems of higher-order PDE
35L60 Nonlinear first-order PDE of hyperbolic type
35L65 Conservation laws
35L67 Shocks and singularities, See also {58C27, 76L05}
35L70 Nonlinear second-order PDE of hyperbolic type
35L75 Nonlinear hyperabolic PDE of higher ($\gtr 2$) order
35L80 Hyperbolic PDE of degenerate type
35L85 Unilateral problems; variational inequalities for hyperbolic PDE, See also {35R35, 49J40}
35L99 None of the above but in this section
35Mxx Partial differential equations of special type (mixed, composite, etc.), {For degenerate types, see 35J70, 35K65, 35L80}
35M10 PDE of mixed type
35M20 PDE of composite type
35M99 None of the above but in this section
35Nxx Overdetermined systems, see also {{58Gxx} {58G05, 58G07, 58Hxx}}
35N05 Overdetermined systems with constant coefficients
35N10 Overdetermined systems with variable coefficients (general)
35N15 $\overline\partial$-Neumann problem and generalizations; formal complexes, See also {32F20 and 58G05}
35N99 None of the above but in this section
35Pxx Spectral theory and eigenvalue problems for partial differential operators, see also {47Axx, 47Bxx, 47F05}
35P05 General spectral theory of PDE
35P10 Completeness of eigenfunctions, eigenfunction expansions for PDO
35P15 Estimation of eigenvalues, upper and lower bounds
35P20 Asymptotic distribution of eigenvalues and eigenfunctions for PDO
35P25 Scattering theory for PDE, See also {47A40}
35P30 Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
35P99 None of the above but in this section
35Qxx Equations of mathematical physics and other areas of application, see also {35J05, 35J10, 35K05, 35L05}
35Q05 Euler-Poisson-Darboux equation and generalizations
35Q15 Riemann-Hilbert problems, See also {30E25, 31A25, 31B20}
35Q30 Stokes and Navier-Stokes equations, See also {76D05, 76D07, 76N10}
35Q35 Other equations arising in fluid mechanics
35Q40 Equations from quantum mechanics
35Q51 Solitons, See also {58F07}
35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.), See also {58F07}
35Q55 NLS-like (nonlinear Schrodinger) equations, See Also { 58F07}
35Q58 Other completely integrable equations, See also {58F07}
35Q60 Equations of electromagnetic theory and optics
35Q72 Other equations from mechanics
35Q75 PDE in relativity
35Q80 Applications of PDE in areas other than physics
35Q99 None of the above but in this section
35Rxx Miscellaneous topics involving partial differential equations, {For equations on manifolds, see 58Gxx; for manifolds of solutions, See 58Bxx; for stochastic PDEs, See also 60H15}
35R05 PDE with discontinuous coefficients or data
35R10 Partial functional-differential or differential-difference equations, with or without deviating arguments
35R15 Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables), See also {46Gxx, 58D25}
35R20 Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions), See also {34Gxx, 47A50, 47D03, 47D06, 47D09, 47H15, 47H20}
35R25 Improperly posed problems for PDE
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
35R35 Free boundary problems for PDE
35R45 Partial differential inequalities
35R50 Partial differential equations of infinite order
35R60 Partial differential equations with randomness, See Also { 60H15}
35R70 PDE with multivalued right-hand sides
35R99 None of the above but in this section
35Sxx Pseudodifferential operators and other generalizations of partial differential operators, see also {47G30, 58G15}
35S05 General theory of $\Psi$DO
35S10 Initial value problems for $\Psi$DO
35S15 Boundary value problems for $\Psi$DO
35S30 Fourier integral operators
35S35 Topological aspects: intersection cohomology, stratified sets, etc., See also {32C38, 32S40, 32S60, 58G07}
35S50 Paradifferential operators
35S99 None of the above but in this section
* 39-XX Finite differences and functional equations
39-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
39-01 Instructional exposition (textbooks, tutorial papers, etc.)
39-02 Research exposition (monographs, survey articles)
39-03 Historical (must be assigned at least one classification number from 01-XX)
39-04 Explicit machine computation and programs (not the theory of computation or programming)
39-06 Proceedings, conferences, collections, etc.
39Axx Difference equations, {For dynamical systems, see 58Fxx}
39A05 General
39A10 Difference equations, See also {33Dxx}
39A11 Stability of difference equations
39A12 Discrete version of topics in analysis
39A70 Difference operators, See also {47B39}
39A99 None of the above but in this section
39Bxx Functional equations, see also {30D05}
39B05 General
39B12 Iteration theory, iterative and composite equations, See also {26A18, 30D05, 58F08}
39B22 Equations for real functions
39B32 Equations for complex functions, See also {30D05}
39B42 Matrix and operator equations
39B52 Equations for functions with more general domains and/or ranges
39B62 Systems of functional equations
39B72 Inequalities involving unknown functions, See also {26A51, 26Dxx}
39B99 None of the above but in this section
* 40-XX Sequences, series, summability
40-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
40-01 Instructional exposition (textbooks, tutorial papers, etc.)
40-02 Research exposition (monographs, survey articles)
40-03 Historical (must be assigned at least one classification number from 01-XX)
40-04 Explicit machine computation and programs (not the theory of computation or programming)
40-06 Proceedings, conferences, collections, etc.
40Axx Convergence and divergence of infinite limiting processes
40A05 Convergence and divergence of series and sequences
40A10 Convergence and divergence of integrals
40A15 Convergence and divergence of continued fractions, See also {30B70}
40A20 Convergence and divergence of infinite products
40A25 Approximation to limiting values (summation of series, etc.), {For the Euler-Maclaurin summation formula, See 65B15}
40A30 Convergence and divergence of series and sequences of functions
40A99 None of the above but in this section
40B05 Multiple sequences and series {(should also be assigned at least one other classification number in this section)}
40Cxx General summability methods
40C05 Matrix methods
40C10 Integral methods
40C15 Function-theoretic methods (including power series methods and semicontinuous methods)
40C99 None of the above but in this section
40Dxx Direct theorems on summability
40D05 General theorems
40D09 Structure of summability fields
40D10 Tauberian constants and oscillation limits
40D15 Convergence factors and summability factors
40D20 Summability and bounded fields of methods
40D25 Inclusion and equivalence theorems
40D99 None of the above but in this section
40Exx Inversion theorems
40E05 Tauberian theorems, general
40E10 Growth estimates
40E15 Lacunary inversion theorems
40E20 Tauberian constants
40E99 None of the above but in this section
40F05 Absolute and strong summability
40Gxx Special methods of summability
40G05 Cesaro, Euler, Norlund and Hausdorff methods
40G10 Abel, Borel and power series methods
40G99 None of the above but in this section
40H05 Functional analytic methods in summability
40J05 Summability in abstract structures, See also {43A55, 46A35, 46B15}
* 41-XX Approximations 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}
41-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
41-01 Instructional exposition (textbooks, tutorial papers, etc.)
41-02 Research exposition (monographs, survey articles)
41-03 Historical (must be assigned at least one classification number from 01-XX)
41-04 Explicit machine computation and programs (not the theory of computation or programming)
41-06 Proceedings, conferences, collections, etc.
41A05 Interpolation, See also {42A15 and 65D05}
41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}
41A15 Spline approximation
41A17 Inequalities in approximation (Bernstein, Jackson, Nikolskiui type inequalities)
41A20 Approximation by rational functions
41A21 Pade approximation
41A25 Rate of convergence, degree of approximation
41A27 Inverse theorems
41A28 Simultaneous approximation
41A29 Approximation with constraints
41A30 Approximation by other special function classes
41A35 Approximation by operators (in particular, by integral operators)
41A36 Approximation by positive operators
41A40 Saturation
41A44 Best constants
41A45 Approximation by arbitrary linear expressions
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
41A55 Approximate quadratures
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.), See also {30E15}
41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A80 Remainders in approximation formulas
41A99 Miscellaneous topics
* 42-XX Fourier analysis
42-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
42-01 Instructional exposition (textbooks, tutorial papers, etc.)
42-02 Research exposition (monographs, survey articles)
42-03 Historical (must be assigned at least one classification number from 01-XX)
42-04 Explicit machine computation and programs (not the theory of computation or programming)
42-06 Proceedings, conferences, collections, etc.
42Axx Fourier analysis in one variable
42A05 Trigonometric polynomials, inequalities, extremal problems
42A10 Trigonometric approximation
42A15 Trigonometric interpolation
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series, {For automorphic theory, See mainly 11F30}
42A20 Convergence of Fourier and trigonometric series
42A24 Summability of Fourier and trigonometric series
42A28 Absolute convergence, absolute summability
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A45 Multipliers
42A50 Conjugate functions, conjugate series, singular integrals
42A55 Lacunary series of trigonometric and other functions; Riesz products
42A61 Probabilistic methods
42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A65 Completeness of sets of functions
42A70 Trigonometric moment problems
42A75 Classical almost periodic functions, mean periodic functions, See also {43A60}
42A82 Positive definite functions
42A85 Convolution, factorization
42A99 None of the above but in this section
42Bxx Fourier analysis in several variables, {For automorphic theory, see mainly 11F30}
42B05 Fourier series and coefficients
42B08 Summability
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B15 Multipliers
42B20 Singular integrals (Calderon-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
42B30 $H^p$-spaces
42B99 None of the above but in this section
42Cxx Nontrigonometric Fourier analysis
42C05 Orthogonal functions and polynomials, general theory, See also {33A65, 33C45, 33C50, 33D45}
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
42C20 Rearrangements and other transformations of Fourier and other orthogonal series
42C25 Uniqueness and localization for orthogonal series
42C30 Completeness of sets of functions
42C99 None of the above but in this section
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