MSC Classification Codes
MSC Classification Codes
The Mathematics Subject
Classification (MSC) is an alphanumerical
classification scheme formulated by the American Mathematical Society
based on the coverage of two major reviewing databases Mathematical
Reviews and Zentralblatt MATH. It is used by many mathematics journals,
which ask authors of research papers and expository articles to list
subject codes from the Mathematics Subject Classification in their
papers.
(Taken from
Wikipedia .)
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
00A17: External book reviews
00A20: Dictionaries and other general reference works
00A22: Formularies
00A30: Philosophy of mathematics
00A35: Methodology of mathematics, didactics
00A69: General applied mathematics
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 01-xx : History and biography
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
01A61: Twenty-first 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
01A80: Sociology (and profession) of mathematics
01A85: Historiography
01A90: Bibliographic studies
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 also be assigned at least one classification number from Section 01)
03-04: Explicit machine computation and programs (not the theory of computation or programming)
03-06: Proceedings, conferences, collections, etc.
03A05: Philosophical and critical
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
03B30: Foundations of classical theories (including reverse mathematics)
03B35: Mechanization of proofs and logical operations
03B40: Combinatory logic and lambda-calculus
03B42: Logic of knowledge and belief
03B44: Temporal logic
03B45: Modal logic
03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B48: Probability and inductive logic
03B50: Many-valued logic
03B52: Fuzzy logic; logic of vagueness
03B53: Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
03B55: Intermediate logics
03B60: Other nonclassical logic
03B65: Logic of natural languages
03B70: Logic in computer science
03B80: Other applications of logic
03B99: None of the above, but in this section 03Cxx : Model theory
03C05: Equational classes, universal algebra
03C07: Basic properties of first-order languages and structures
03C10: Quantifier elimination, model completeness 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: Classification theory, stability and related concepts
03C50: Models with special properties (saturated, rigid, etc.)
03C52: Properties of classes of models
03C55: Set-theoretic model theory
03C57: Effective and recursion-theoretic model theory
03C60: Model-theoretic algebra
03C62: Models of arithmetic and set theory
03C64: Model theory of ordered structures; o-minimality
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
03C85: Second- and higher-order model theory
03C90: Nonclassical models (Boolean-valued, sheaf, etc.)
03C95: Abstract model theory
03C98: Applications of model theory
03C99: None of the above, but in this section 03Dxx : Computability and recursion theory
03D03: Thue and Post systems, etc.
03D05: Automata and formal grammars in connection with logical questions
03D10: Turing machines and related notions
03D15: Complexity of computation
03D20: Recursive functions and relations, subrecursive hierarchies
03D25: Recursively (computably) enumerable sets and degrees
03D28: Other Turing degree structures
03D30: Other degrees and reducibilities
03D35: Undecidability and degrees of sets of sentences
03D40: Word problems, etc.
03D45: Theory of numerations, effectively presented structures
03D50: Recursive equivalence types of sets and structures, isols
03D55: Hierarchies
03D60: Computability and recursion theory on ordinals, admissible sets, etc.
03D65: Higher-type and set recursion theory
03D70: Inductive definability
03D75: Abstract and axiomatic computability and recursion theory
03D80: Applications of computability and recursion theory
03D99: None of the above, but in this section 03Exx : Set theory
03E02: Partition relations
03E04: Ordered sets and their cofinalities; pcf theory
03E05: Other combinatorial set theory
03E10: Ordinal and cardinal numbers
03E15: Descriptive set theory
03E17: Cardinal characteristics of the continuum
03E20: Other classical set theory (including functions, relations, and set algebra)
03E25: Axiom of choice and related propositions
03E30: Axiomatics of classical set theory and its fragments
03E35: Consistency and independence results
03E40: Other aspects of forcing and Boolean-valued models
03E45: Inner models, including constructibility, ordinal definability, and core models
03E47: Other notions of set-theoretic definability
03E50: Continuum hypothesis and Martin's axiom
03E55: Large cardinals
03E60: Determinacy principles
03E65: Other hypotheses and axioms
03E70: Nonclassical and second-order set theories
03E72: Fuzzy set theory
03E75: Applications of set theory
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
03F40: Gödel numberings in proof theory
03F45: Provability logics and related algebras (e.g., diagonalizable algebras)
03F50: Metamathematics of constructive systems
03F52: Linear logic and other substructural logics
03F55: Intuitionistic mathematics
03F60: Constructive and recursive analysis
03F65: Other constructive mathematics
03F99: None of the above, but in this section 03Gxx : Algebraic logic
03G05: Boolean algebras
03G10: Lattices and related structures
03G12: Quantum logic
03G15: Cylindric and polyadic algebras; relation algebras
03G20: Lukasiewicz and Post algebras
03G25: Other algebras related to logic
03G30: Categorical logic, topoi
03G99: None of the above, but in this section 03Hxx : Nonstandard models
03H05: Nonstandard models in mathematics
03H10: Other applications of nonstandard models (economics, physics, etc.)
03H15: Nonstandard models of arithmetic
03H99: None of the above, but in this section 05-xx : Combinatorics
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 also be assigned at least one classification number from Section 01)
05-04: Explicit machine computation and programs (not the theory of computation or programming)
05-06: Proceedings, conferences, collections, etc.
05Axx : Enumerative combinatorics
05A05: Combinatorial choice problems (subsets, representatives, permutations)
05A10: Factorials, binomial coefficients, combinatorial functions
05A15: Exact enumeration problems, generating functions
05A16: Asymptotic enumeration
05A17: Partitions of integers
05A18: Partitions of sets
05A19: Combinatorial identities
05A20: Combinatorial inequalities
05A30: $q$-calculus and related topics
05A40: Umbral calculus
05A99: None of the above, but in this section 05Bxx : Designs and configurations
05B05: Block designs
05B07: Triple systems
05B10: Difference sets (number-theoretic, group-theoretic, etc.)
05B15: Orthogonal arrays, Latin squares, Room squares
05B20: Matrices (incidence, Hadamard, etc.)
05B25: Finite geometries
05B30: Other designs, configurations
05B35: Matroids, geometric lattices
05B40: Packing and covering
05B45: Tessellation and tiling problems
05B50: Polyominoes
05B99: None of the above, but in this section 05Cxx : Graph theory
05C05: Trees
05C07: Degree sequences
05C10: Topological graph theory, imbedding
05C12: Distance in graphs
05C15: Coloring of graphs and hypergraphs
05C17: Perfect graphs
05C20: Directed graphs (digraphs), tournaments
05C22: Signed, gain and biased graphs
05C25: Graphs and groups
05C30: Enumeration of graphs and maps
05C35: Extremal problems
05C38: Paths and cycles
05C40: Connectivity
05C45: Eulerian and Hamiltonian graphs
05C50: Graphs and matrices
05C55: Generalized Ramsey theory
05C60: Isomorphism problems (reconstruction conjecture, etc.)
05C62: Graph representations (geometric and intersection representations, etc.)
05C65: Hypergraphs
05C69: Dominating sets, independent sets, cliques
05C70: Factorization, matching, covering and packing
05C75: Structural characterization of types of graphs
05C78: Graph labelling (graceful graphs, bandwidth, etc.)
05C80: Random graphs
05C83: Graph minors
05C85: Graph algorithms
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
05D40: Probabilistic methods
05D99: None of the above, but in this section 05Exx : Algebraic combinatorics
05E05: Symmetric functions
05E10: Tableaux, representations of the symmetric group
05E15: Combinatorial problems concerning the classical groups
05E20: Group actions on designs, geometries and codes
05E25: Group actions on posets and homology groups of posets
05E30: Association schemes, strongly regular graphs
05E35: Orthogonal polynomials
05E99: None of the above, but in this section 06-xx : Order, lattices, ordered algebraic structures
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 also be assigned at least one classification number from Section 01)
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
06A11: Algebraic aspects of posets
06A12: Semilattices
06A15: Galois correspondences, closure operators
06A99: None of the above, but in this section 06Bxx : Lattices
06B05: Structure theory
06B10: Ideals, congruence relations
06B15: Representation theory
06B20: Varieties of lattices
06B23: Complete lattices, completions
06B25: Free lattices, projective lattices, word problems
06B30: Topological lattices, order topologies
06B35: Continuous lattices and posets, applications
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 and posets
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
06D22: Frames, locales
06D25: Post algebras
06D30: De Morgan algebras, Lukasiewicz algebras
06D35: MV-algebras
06D50: Lattices and duality
06D72: Fuzzy lattices (soft algebras) and related topics
06D99: None of the above, but in this section 06Exx : Boolean algebras (Boolean rings)
06E05: Structure theory
06E10: Chain conditions, complete algebras
06E15: Stone space and related constructions
06E20: Ring-theoretic properties
06E25: Boolean algebras with additional operations (diagonalizable algebras, etc.)
06E30: Boolean functions
06E99: None of the above, but in this section 06Fxx : Ordered structures
06F05: Ordered semigroups and monoids
06F07: Quantales
06F10: Noether lattices
06F15: Ordered groups
06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
06F25: Ordered rings, algebras, modules
06F30: Topological lattices, order topologies
06F35: BCK-algebras, BCI-algebras
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 also be assigned at least one classification number from Section 01)
08-04: Explicit machine computation and programs (not the theory of computation or programming)
08-06: Proceedings, conferences, collections, etc.
08Axx : Algebraic structures
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
08A55: Partial algebras
08A60: Unary algebras
08A62: Finitary algebras
08A65: Infinitary algebras
08A68: Heterogeneous algebras
08A70: Applications of universal algebra in computer science
08A72: Fuzzy algebraic structures
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
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
08C10: Axiomatic model classes
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 also be assigned at least one classification number from Section 01)
11-04: Explicit machine computation and programs (not the theory of computation or programming)
11-06: Proceedings, conferences, collections, etc.
11Axx : Elementary number theory
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
11A63: Radix representation; digital problems
11A67: Other representations
11A99: None of the above, but in this section 11Bxx : Sequences and sets
11B05: Density, gaps, topology
11B13: Additive bases
11B25: Arithmetic progressions
11B34: Representation functions
11B37: Recurrences
11B39: Fibonacci and Lucas numbers and polynomials and generalizations
11B50: Sequences (mod $m$)
11B57: Farey sequences; the sequences ${1^k, 2^k, \cdots]$
11B65: Binomial coefficients; factorials; $q$-identities
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
11C20: Matrices, determinants
11C99: None of the above, but in this section 11Dxx : Diophantine equations
11D04: Linear equations
11D09: Quadratic and bilinear equations
11D25: Cubic and quartic equations
11D41: Higher degree equations; Fermat's equation
11D45: Counting solutions of Diophantine equations
11D57: Multiplicative and norm form equations
11D59: Thue-Mahler equations
11D61: Exponential equations
11D68: Rational numbers as sums of fractions
11D72: Equations in many variables
11D75: Diophantine inequalities
11D79: Congruences in many variables
11D85: Representation problems
11D88: $p$-adic and power series fields
11D99: None of the above, but in this section 11Exx : Forms and linear algebraic groups
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
11E70: $K$-theory of quadratic and Hermitian forms
11E72: Galois cohomology of linear algebraic groups
11E76: Forms of degree higher than two
11E81: Algebraic theory of quadratic forms; Witt groups and rings
11E88: Quadratic spaces; Clifford algebras
11E95: $p$-adic theory
11E99: None of the above, but in this section 11Fxx : Discontinuous groups and automorphic forms
11F03: Modular and automorphic functions
11F06: Structure of modular groups and generalizations; arithmetic groups
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
11F23: Relations with algebraic geometry and topology
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
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
11F46: Siegel modular groups and their modular and automorphic forms
11F50: Jacobi forms
11F52: Modular forms associated to Drinfel'd modules
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 representations
11F85: $p$-adic theory, local fields
11F99: None of the above, but in this section 11Gxx : Arithmetic algebraic geometry (Diophantine geometry)
11G05: Elliptic curves over global fields
11G07: Elliptic curves over local fields
11G09: Drinfeld modules; higher-dimensional motives, etc.
11G10: Abelian varieties of dimension $\gtr 1$
11G15: Complex multiplication and moduli of abelian varieties
11G16: Elliptic and modular units
11G18: Arithmetic aspects of modular and Shimura varieties
11G20: Curves over finite and local fields
11G25: Varieties over finite and local fields
11G30: Curves of arbitrary genus or genus $\ne 1$ over global fields
11G35: Varieties over global fields
11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11G45: Geometric class field theory
11G50: Heights
11G55: Polylogarithms and relations with $K$-theory
11G99: None of the above, but in this section 11Hxx : Geometry of numbers
11H06: Lattices and convex bodies
11H16: Nonconvex bodies
11H31: Lattice packing and covering
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
11H71: Relations with coding theory
11H99: None of the above, but in this section 11Jxx : Diophantine approximation, transcendental number theory
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
11J54: Small fractional parts of polynomials and generalizations
11J61: Approximation in non-Archimedean valuations
11J68: Approximation to algebraic numbers
11J70: Continued fractions and generalizations
11J71: Distribution modulo one
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
11J93: Transcendence theory of Drinfel'd and $t$-modules
11J95: Results involving abelian varieties
11J97: Analogues of methods in Nevanlinna theory (work of Vojta et al.)
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 $1$
11K16: Normal numbers, radix expansions, etc.
11K31: Special sequences
11K36: Well-distributed sequences and other variations
11K38: Irregularities of distribution, discrepancy
11K41: Continuous, $p$-adic and abstract analogues
11K45: Pseudo-random numbers; Monte Carlo methods
11K50: Metric theory of continued fractions
11K55: Metric theory of other algorithms and expansions; measure and Hausdorff dimension
11K60: Diophantine approximation
11K65: Arithmetic functions
11K70: Harmonic analysis and almost periodicity
11K99: None of the above, but in this section 11Lxx : Exponential sums and character sums
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
11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
11M38: Zeta and $L$-functions in characteristic $p$
11M41: Other Dirichlet series and zeta functions
11M45: Tauberian theorems
11M99: None of the above, but in this section 11Nxx : Multiplicative number theory
11N05: Distribution of primes
11N13: Primes in progressions
11N25: Distribution of integers with specified multiplicative constraints
11N30: Turán theory
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
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
11P70: Inverse problems of additive number theory
11P81: Elementary theory of partitions
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
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
11R34: Galois cohomology
11R37: Class field theory
11R39: Langlands-Weil conjectures, nonabelian class field theory
11R42: Zeta functions and $L$-functions of number fields
11R44: Distribution of prime ideals
11R45: Density theorems
11R47: Other analytic theory
11R52: Quaternion and other division algebras: arithmetic, zeta functions
11R54: Other algebras and orders, and their zeta and $L$-functions
11R56: Adèle rings and groups
11R58: Arithmetic theory of algebraic function fields
11R60: Cyclotomic function fields (class groups, Bernoulli objects, etc.)
11R65: Class groups and Picard groups of orders
11R70: $K$-theory of global fields
11R80: Totally real and totally positive fields
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
11S31: Class field theory; $p$-adic formal groups
11S37: Langlands-Weil conjectures, nonabelian class field theory
11S40: Zeta functions and $L$-functions
11S45: Algebras and orders, and their zeta functions
11S70: $K$-theory of local fields
11S80: Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)
11S85: Other nonanalytic theory
11S90: Prehomogeneous vector spaces
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
11T60: Finite upper half-planes
11T71: Algebraic coding theory; cryptography
11T99: None of the above, but in this section 11Uxx : Connections with logic
11U05: Decidability
11U07: Ultraproducts
11U09: Model theory
11U10: Nonstandard arithmetic
11U99: None of the above, but in this section 11Yxx : Computational number theory
11Y05: Factorization
11Y11: Primality
11Y16: Algorithms; complexity
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
11Z05: 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 also be assigned at least one classification number from Section 01)
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)
12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
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
12E20: Finite fields (field-theoretic aspects)
12E25: Hilbertian fields; Hilbert's irreducibility theorem
12E30: Field arithmetic
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
12G10: Cohomological dimension
12G99: None of the above, but in this section 12Hxx : Differential and difference algebra
12H05: Differential algebra
12H10: Difference algebra
12H20: Abstract differential equations
12H25: $p$-adic differential equations
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
12J27: Krasner-Tate algebras
12J99: None of the above, but in this section 12Kxx : Generalizations of fields
12K05: Near-fields
12K10: Semifields
12K99: None of the above, but in this section 12Lxx : Connections with logic
12L05: Decidability
12L10: Ultraproducts
12L12: Model theory
12L15: Nonstandard arithmetic
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 also be assigned at least one classification number from Section 01)
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
13A05: Divisibility
13A10: Radical theory
13A15: Ideals; multiplicative ideal theory
13A18: Valuations and their generalizations
13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure
13A50: Actions of groups on commutative rings; invariant theory
13A99: None of the above, but in this section 13Bxx : Ring extensions and related topics
13B02: Extension theory
13B05: Galois theory
13B10: Morphisms
13B21: Integral dependence
13B22: Integral closure of rings and ideals; 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
13B40: Étale and flat extensions; Henselization; Artin approximation
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
13C11: Injective and flat modules and ideals
13C12: Torsion modules and ideals
13C13: Other special types
13C14: Cohen-Macaulay modules
13C15: Dimension theory, depth, related rings (catenary, etc.)
13C20: Class groups
13C40: Linkage, complete intersections and determinantal ideals
13C99: None of the above, but in this section 13Dxx : Homological methods
13D02: Syzygies and resolutions
13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D05: Homological dimension
13D07: Homological functors on modules (Tor, Ext, etc.)
13D10: Deformations and infinitesimal methods
13D15: Grothendieck groups, $K$-theory
13D22: Homological conjectures (intersection theorems)
13D25: Complexes
13D30: Torsion theory
13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
13D45: Local cohomology
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; number of generators
13E99: None of the above, but in this section 13Fxx : Arithmetic rings and other special rings
13F05: Dedekind, Prüfer and Krull rings and their generalizations
13F07: Euclidean rings and generalizations
13F10: Principal ideal rings
13F15: Factorial rings, unique factorization domains
13F20: Polynomial rings and ideals; rings of integer-valued polynomials
13F25: Formal power series rings
13F30: Valuation rings
13F40: Excellent rings
13F45: Seminormal rings
13F50: Rings with straightening laws, Hodge algebras
13F55: Face and Stanley-Reisner rings; simplicial complexes
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.)
13H15: Multiplicity theory and related topics
13H99: None of the above, but in this section 13Jxx : Topological rings and modules
13J05: Power series rings
13J07: Analytical algebras and rings
13J10: Complete rings, completion
13J15: Henselian rings
13J20: Global topological rings
13J25: Ordered rings
13J30: Real algebra
13J99: None of the above, but in this section
13K05: Witt vectors and related rings
13L05: Applications of logic to commutative algebra 13Mxx : Finite commutative rings
13M05: Structure
13M10: Polynomials
13M99: None of the above, but in this section 13Nxx : Differential algebra
13N05: Modules of differentials
13N10: Rings of differential operators and their modules
13N15: Derivations
13N99: None of the above, but in this section 13Pxx : Computational aspects of commutative algebra
13P05: Polynomials, factorization
13P10: Polynomial ideals, Gröbner 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 also be assigned at least one classification number from Section 01)
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
14A10: Varieties and morphisms
14A15: Schemes and morphisms
14A20: Generalizations (algebraic spaces, stacks)
14A22: Noncommutative algebraic geometry
14A25: Elementary questions
14A99: None of the above, but in this section 14Bxx : Local theory
14B05: Singularities
14B07: Deformations of singularities
14B10: Infinitesimal methods
14B12: Local deformation theory, Artin approximation, etc.
14B15: Local cohomology
14B20: Formal neighborhoods
14B25: Local structure of morphisms: étale, flat, etc.
14B99: None of the above, but in this section 14Cxx : Cycles and subschemes
14C05: Parametrization (Chow and Hilbert schemes)
14C15: Chow groups and rings
14C17: Intersection theory, characteristic classes, intersection multiplicities
14C20: Divisors, linear systems, invertible sheaves
14C21: Pencils, nets, webs
14C22: Picard groups
14C25: Algebraic cycles
14C30: Transcendental methods, Hodge theory, Hodge conjecture
14C34: Torelli problem
14C35: Applications of methods of algebraic $K$-theory
14C40: Riemann-Roch theorems
14C99: None of the above, but in this section 14Dxx : Families, fibrations
14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
14D06: Fibrations, degenerations
14D07: Variation of Hodge structures
14D10: Arithmetic ground fields (finite, local, global)
14D15: Formal methods; deformations
14D20: Algebraic moduli problems, moduli of vector bundles
14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14D22: Fine and coarse moduli spaces
14D99: None of the above, but in this section 14Exx : Birational geometry
14E05: Rational and birational maps
14E07: Birational automorphisms, Cremona group and generalizations
14E08: Rationality questions
14E15: Global theory and resolution of singularities
14E20: Coverings
14E22: Ramification problems
14E25: Embeddings
14E30: Minimal model program (Mori theory, extremal rays)
14E99: None of the above, but in this section 14Fxx : (Co)homology theory
14F05: Vector bundles, sheaves, related constructions
14F10: Differentials and other special sheaves
14F17: Vanishing theorems
14F20: Étale and other Grothendieck topologies and cohomologies
14F22: Brauer groups of schemes
14F25: Classical real and complex cohomology
14F30: $p$-adic cohomology, crystalline cohomology
14F35: Homotopy theory; fundamental groups
14F40: de Rham cohomology
14F42: Motivic cohomology
14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14F45: Topological properties
14F99: None of the above, but in this section 14Gxx : Arithmetic problems. Diophantine geometry
14G05: Rational points
14G10: Zeta-functions and related questions(Birch-Swinnerton-Dyer conjecture)
14G15: Finite ground fields
14G20: Local ground fields
14G22: Rigid analytic geometry
14G25: Global ground fields
14G27: Other nonalgebraically closed ground fields
14G32: Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
14G35: Modular and Shimura varieties
14G40: Arithmetic varieties and schemes; Arakelov theory; heights
14G50: Applications to coding theory and cryptography
14G99: None of the above, but in this section 14Hxx : Curves
14H05: Algebraic functions; function fields
14H10: Families, moduli (algebraic)
14H15: Families, moduli (analytic)
14H20: Singularities, local rings
14H25: Arithmetic ground fields
14H30: Coverings, fundamental group
14H37: Automorphisms
14H40: Jacobians, Prym varieties
14H42: Theta functions; Schottky problem
14H45: Special curves and curves of low genus
14H50: Plane and space curves
14H51: Special divisors (gonality, Brill-Noether theory)
14H52: Elliptic curves
14H55: Riemann surfaces; Weierstrass points; gap sequences
14H60: Vector bundles on curves and their moduli
14H70: Relationships with integrable systems
14H81: Relationships with physics
14H99: None of the above, but in this section 14Jxx : Surfaces and higher-dimensional varieties
14J10: Families, moduli, classification: algebraic theory
14J15: Moduli, classification: analytic theory; relations with modular forms
14J17: Singularities
14J20: Arithmetic ground fields
14J25: Special surfaces
14J26: Rational and ruled surfaces
14J27: Elliptic surfaces
14J28: $K3$ surfaces and Enriques surfaces
14J29: Surfaces of general type
14J30: $3$-folds
14J32: Calabi-Yau manifolds, mirror symmetry
14J35: $4$-folds
14J40: $n$-folds ($n>4$)
14J45: Fano varieties
14J50: Automorphisms of surfaces and higher-dimensional varieties
14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J70: Hypersurfaces
14J80: Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
14J81: Relationships with physics
14J99: None of the above, but in this section 14Kxx : Abelian varieties and schemes
14K02: Isogeny
14K05: Algebraic theory
14K10: Algebraic moduli, classification
14K12: Subvarieties
14K15: Arithmetic ground fields
14K20: Analytic theory; abelian integrals and differentials
14K22: Complex multiplication
14K25: Theta functions
14K30: Picard schemes, higher Jacobians
14K99: None of the above, but in this section 14Lxx : Algebraic groups
14L05: Formal groups, $p$-divisible groups
14L10: Group varieties
14L15: Group schemes
14L17: Affine algebraic groups, hyperalgebra constructions
14L24: Geometric invariant theory
14L30: Group actions on varieties or schemes (quotients)
14L35: Classical groups (geometric aspects)
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)
14M06: Linkage
14M07: Low codimension problems
14M10: Complete intersections
14M12: Determinantal varieties
14M15: Grassmannians, Schubert varieties, flag manifolds
14M17: Homogeneous spaces and generalizations
14M20: Rational and unirational varieties
14M25: Toric varieties, Newton polyhedra
14M30: Supervarieties
14M99: None of the above, but in this section 14Nxx : Projective and enumerative geometry
14N05: Projective techniques
14N10: Enumerative problems (combinatorial problems)
14N15: Classical problems, Schubert calculus
14N20: Configurations of linear subspaces
14N25: Varieties of low degree
14N30: Adjunction problems
14N35: Gromov-Witten invariants, quantum cohomology
14N99: None of the above, but in this section 14Pxx : Real algebraic and real analytic geometry
14P05: Real algebraic sets
14P10: Semialgebraic sets and related spaces
14P15: Real analytic and semianalytic sets
14P20: Nash functions and manifolds
14P25: Topology of real algebraic varieties
14P99: None of the above, but in this section 14Qxx : Computational aspects in algebraic geometry
14Q05: Curves
14Q10: Surfaces, hypersurfaces
14Q15: Higher-dimensional varieties
14Q20: Effectivity
14Q99: None of the above, but in this section 14Rxx : Affine geometry
14R05: Classification of affine varieties
14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
14R15: Jacobian problem
14R20: Group actions on affine varieties
14R25: Affine fibrations
14R99: None of the above, but in this section 15-xx : Linear and multilinear algebra; matrix theory
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 also be assigned at least one classification number from Section 01)
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
15A15: Determinants, permanents, other special matrix functions
15A18: Eigenvalues, singular values, and eigenvectors
15A21: Canonical forms, reductions, classification
15A22: Matrix pencils
15A23: Factorization of matrices
15A24: Matrix equations and identities
15A27: Commutativity
15A29: Inverse problems
15A30: Algebraic systems of matrices
15A33: Matrices over special rings (quaternions, finite fields, etc.)
15A36: Matrices of integers
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
15A63: Quadratic and bilinear forms, inner products
15A66: Clifford algebras, spinors
15A69: Multilinear algebra, tensor products
15A72: Vector and tensor algebra, theory of invariants
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
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 also be assigned at least one classification number from Section 01)
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)
16B70: Applications of logic
16B99: None of the above, but in this section 16Dxx : Modules, bimodules and ideals
16D10: General module theory
16D20: Bimodules
16D25: Ideals
16D30: Infinite-dimensional simple rings (except as in 16Kxx)
16D40: Free, projective, and flat modules and ideals
16D50: Injective modules, self-injective rings
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
16D90: Module categories; module theory in a category-theoretic context; Morita equivalence and duality
16D99: None of the above, but in this section 16Exx : Homological methods
16E05: Syzygies, resolutions, complexes
16E10: Homological dimension
16E20: Grothendieck groups, $K$-theory, etc.
16E30: Homological functors on modules (Tor, Ext, etc.)
16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
16E45: Differential graded algebras and applications
16E50: von Neumann regular rings and generalizations
16E60: Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
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
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 16Kxx : Division rings and semisimple Artin rings
16K20: Finite-dimensional
16K40: Infinite-dimensional and general
16K50: Brauer groups
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
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
16N80: General radicals and rings
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
16P20: Artinian rings and modules
16P40: Noetherian rings and modules
16P50: Localization and Noetherian rings
16P60: Chain conditions on annihilators and summands: Goldie-type conditions, 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
16S32: Rings of differential operators
16S34: Group rings, Laurent polynomial rings
16S35: Twisted and skew group rings, crossed products
16S36: Ordinary and skew polynomial rings and semigroup rings
16S37: Quadratic and Koszul algebras
16S38: Rings arising from non-commutative algebraic geometry
16S40: Smash products of general Hopf actions
16S50: Endomorphism rings; matrix rings
16S60: Rings of functions, subdirect products, sheaves of rings
16S70: Extensions of rings by ideals
16S80: Deformations of rings
16S90: Maximal ring of quotients, torsion theories, radicals on module categories
16S99: None of the above, but in this section 16Uxx : Conditions on elements
16U10: Integral domains
16U20: Ore rings, multiplicative sets, Ore localization
16U30: Divisibility, noncommutative UFDs
16U60: Units, groups of units
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
16W20: Automorphisms and endomorphisms
16W22: Actions of groups and semigroups; invariant theory
16W25: Derivations, actions of Lie algebras
16W30: Coalgebras, bialgebras, Hopf algebras; rings, modules, etc. on which these act
16W35: Ring-theoretic aspects of quantum groups
16W50: Graded rings and modules
16W55: ``Super'' (or ``skew'') structure
16W60: Valuations, completions, formal power series and related constructions
16W70: Filtered rings; filtrational and graded techniques
16W80: Topological and ordered rings and modules
16W99: None of the above, but in this section 16Yxx : Generalizations
16Y30: Near-rings
16Y60: Semirings
16Y99: None of the above, but in this section
16Z05: Computational aspects of associative rings 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 also be assigned at least one classification number from Section 01)
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 rings
17A15: Noncommutative Jordan algebras
17A20: Flexible algebras
17A30: Algebras satisfying other identities
17A32: Leibniz algebras
17A35: Division algebras
17A36: Automorphisms, derivations, other operators
17A40: Ternary compositions
17A42: Other $n$-ary compositions $(n \ge 3)$
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 and Lie superalgebras
17B01: Identities, free Lie (super)algebras
17B05: Structure theory
17B10: Representations, algebraic theory (weights)
17B15: Representations, analytic theory
17B20: Simple, semisimple, reductive (super)algebras (roots)
17B25: Exceptional (super)algebras
17B30: Solvable, nilpotent (super)algebras
17B35: Universal enveloping (super)algebras
17B37: Quantum groups (quantized enveloping algebras) and related deformations
17B40: Automorphisms, derivations, other operators
17B45: Lie algebras of linear algebraic groups
17B50: Modular Lie (super)algebras
17B55: Homological methods in Lie (super)algebras
17B56: Cohomology of Lie (super)algebras
17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.)
17B62: Lie bialgebras
17B63: Poisson algebras
17B65: Infinite-dimensional Lie (super)algebras
17B66: Lie algebras of vector fields and related (super) algebras
17B67: Kac-Moody (super)algebras (structure and representation theory)
17B68: Virasoro and related algebras
17B69: Vertex operators; vertex operator algebras and related structures
17B70: Graded Lie (super)algebras
17B75: Color Lie (super)algebras
17B80: Applications to integrable systems
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
17C55: Finite-dimensional structures
17C60: Division algebras
17C65: Jordan structures on Banach spaces and algebras
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 also be assigned at least one classification number from Section 01)
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
18A15: Foundations, relations to logic and deductive systems
18A20: Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
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, substructures, quotient structures, congruences, amalgams
18A35: Categories admitting limits (complete categories), functors preserving limits, completions
18A40: Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A99: None of the above, but in this section 18Bxx : Special categories
18B05: Category of sets, characterizations
18B10: Category of relations, additive relations
18B15: Embedding theorems, universal categories
18B20: Categories of machines, automata, operative categories
18B25: Topoi
18B30: Categories of topological spaces and continuous mappings
18B35: Preorders, orders and lattices (viewed as categories)
18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories)
18B99: None of the above, but in this section 18Cxx : Categories and theories
18C05: Equational categories
18C10: Theories (e.g. algebraic theories), structure, and semantics
18C15: Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples
18C20: Algebras and Kleisli categories associated with monads
18C30: Sketches and generalizations
18C35: Accessible and locally presentable categories
18C50: Categorical semantics of formal languages
18C99: None of the above, but in this section 18Dxx : Categories with structure
18D05: Double categories, $2$-categories, bicategories and generalizations
18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories
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.)
18D50: Operads
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
18E25: Derived functors and satellites
18E30: Derived categories, triangulated categories
18E35: Localization of categories
18E40: Torsion theories, radicals
18E99: None of the above, but in this section 18Fxx : Categories and geometry
18F05: Local categories and functors
18F10: Grothendieck topologies
18F15: Abstract manifolds and fiber bundles
18F20: Presheaves and sheaves
18F25: Algebraic $K$-theory and $L$-theory
18F30: Grothendieck groups
18F99: None of the above, but in this section 18Gxx : Homological algebra
18G05: Projectives and injectives
18G10: Resolutions; derived functors
18G15: Ext and Tor, generalizations, Künneth formula
18G20: Homological dimension
18G25: Relative homological algebra, projective classes
18G30: Simplicial sets, simplicial objects (in a category)
18G35: Chain complexes
18G40: Spectral sequences, hypercohomology
18G50: Nonabelian homological algebra
18G55: Homotopical algebra
18G60: Other (co)homology theories
18G99: None of the above, but in this section 19-xx : $K$-theory
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 also be assigned at least one classification number from Section 01)
19-04: Explicit machine computation and programs (not the theory of computation or programming)
19-06: Proceedings, conferences, collections, etc.
19Axx : Grothendieck groups and $K_0$
19A13: Stability for projective modules
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
19B37: Congruence subgroup problems
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
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
19D55: $K$-theory and homology; cyclic homology and cohomology
19D99: None of the above, but in this section 19Exx : $K$-theory in geometry
19E08: $K$-theory of schemes
19E15: Algebraic cycles and motivic cohomology
19E20: Relations with cohomology theories
19E99: None of the above, but in this section 19Fxx : $K$-theory in number theory
19F05: Generalized class field theory
19F15: Symbols and arithmetic
19F27: Étale cohomology, higher regulators, zeta and $L$-functions
19F99: None of the above, but in this section 19Gxx : $K$-theory of forms
19G05: Stability for quadratic modules
19G12: Witt groups of rings
19G24: $L$-theory of group rings
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
19J35: Obstructions to group actions
19J99: None of the above, but in this section 19Kxx : $K$-theory and operator algebras
19K14: $K_0$ as an ordered group, traces
19K33: EXT and $K$-homology
19K35: Kasparov theory ($KK$-theory)
19K56: Index theory
19K99: None of the above, but in this section 19Lxx : Topological $K$-theory
19L10: Riemann-Roch theorems, Chern characters
19L20: $J$-homomorphism, Adams operations
19L41: Connective $K$-theory, cobordism
19L47: Equivariant $K$-theory
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 also be assigned at least one classification number from Section 01)
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
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
20B27: Infinite automorphism groups
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
20C05: Group rings of finite groups and their modules
20C07: Group rings of infinite groups and their modules
20C08: Hecke algebras and their representations
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
20D08: Simple groups: sporadic groups
20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks
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
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; subgroup growth
20E08: Groups acting on trees
20E10: Quasivarieties and varieties of groups
20E15: Chains and lattices of subgroups, subnormal subgroups
20E18: Limits, profinite groups
20E22: Extensions, wreath products, and other compositions
20E25: Local properties
20E26: Residual properties and generalizations
20E28: Maximal subgroups
20E32: Simple groups
20E34: General structure theorems
20E36: General theorems concerning automorphisms of groups
20E42: Groups with a $BN$-pair; buildings
20E45: Conjugacy classes
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
20F10: Word problems, other decision problems, connections with logic and automata
20F12: Commutator calculus
20F14: Derived series, central series, and generalizations
20F16: Solvable groups, supersolvable groups
20F17: Formations of groups, Fitting classes
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
20F29: Representations of groups as automorphism groups of algebraic systems
20F34: Fundamental groups and their automorphisms
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: Reflection and Coxeter groups
20F60: Ordered groups
20F65: Geometric group theory
20F67: Hyperbolic groups and nonpositively curved groups
20F69: Asymptotic properties of groups
20F99: None of the above, but in this section 20Gxx : Linear algebraic groups (classical groups)
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 adèles and other rings and schemes
20G40: Linear algebraic groups over finite fields
20G42: Quantum groups (quantized function algebras) and their representations
20G45: Applications to physics
20G99: None of the above, but in this section 20Hxx : Other groups of matrices
20H05: Unimodular groups, congruence subgroups
20H10: Fuchsian groups and their generalizations
20H15: Other geometric groups, including crystallographic groups
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 groups
20J15: Category of groups
20J99: None of the above, but in this section 20Kxx : Abelian groups
20K01: Finite abelian groups
20K10: Torsion groups, primary groups and generalized primary groups
20K15: Torsion-free groups, finite rank
20K20: Torsion-free groups, infinite rank
20K21: Mixed groups
20K25: Direct sums, direct products, etc.
20K27: Subgroups
20K30: Automorphisms, homomorphisms, endomorphisms, etc.
20K35: Extensions
20K40: Homological and categorical methods
20K45: Topological methods
20K99: None of the above, but in this section
20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms) 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.
20M25: Semigroup rings, multiplicative semigroups of rings
20M30: Representation of semigroups; actions of semigroups on sets
20M35: Semigroups in automata theory, linguistics, etc.
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
20N10: Ternary systems (heaps, semiheaps, heapoids, etc.)
20N15: $n$-ary systems $(n\ge 3)$
20N20: Hypergroups
20N25: Fuzzy groups
20N99: None of the above, but in this section
20P05: Probabilistic methods in group theory 22-xx : Topological groups, Lie groups
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 also be assigned at least one classification number from Section 01)
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
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
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 in relation to group representations
22D30: Induced representations
22D35: Duality theorems
22D40: Ergodic theory on groups
22D45: Automorphism groups of locally compact groups
22D99: None of the above, but in this section 22Exx : Lie groups
22E05: Local Lie groups
22E10: General properties and structure of complex Lie groups
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
22E35: Analysis on $p$-adic Lie groups
22E40: Discrete subgroups of Lie groups
22E41: Continuous cohomology
22E43: Structure and representation of the Lorentz group
22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods
22E46: Semisimple Lie groups and their representations
22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
22E50: Representations of Lie and linear algebraic groups over local fields
22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
22E60: Lie algebras of Lie groups
22E65: Infinite-dimensional Lie groups and their Lie algebras
22E67: Loop groups and related constructions, group-theoretic treatment
22E70: Applications of Lie groups to physics; explicit representations
22E99: None of the above, but in this section 22Fxx : Noncompact transformation groups
22F05: General theory of group and pseudogroup actions
22F10: Measurable group actions
22F30: Homogeneous spaces
22F50: Groups as automorphisms of other structures 26-xx : Real functions
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 also be assigned at least one classification number from Section 01)
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
26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
26A16: Lipschitz (Hölder) classes
26A18: Iteration
26A21: Classification of real functions; Baire classification of sets and functions
26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
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
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
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, Hölder 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.
26C10: Polynomials: location of zeros
26C15: Rational functions
26C99: None of the above, but in this section 26Dxx : Inequalities
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
26E05: Real-analytic functions
26E10: $C^\infty$-functions, quasi-analytic functions
26E15: Calculus of functions on infinite-dimensional spaces
26E20: Calculus of functions taking values in infinite-dimensional spaces
26E25: Set-valued functions
26E30: Non-Archimedean analysis
26E35: Nonstandard analysis
26E40: Constructive real analysis
26E50: Fuzzy real analysis
26E60: Means
26E99: None of the above, but in this section 28-xx : Measure and integration
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 also be assigned at least one classification number from Section 01)
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
28A10: Real- or complex-valued set functions
28A12: Contents, measures, outer measures, capacities
28A15: Abstract differentiation theory, differentiation of set functions
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
28A35: Measures and integrals in product spaces
28A50: Integration and disintegration of measures
28A51: Lifting theory
28A60: Measures on Boolean rings, measure algebras
28A75: Length, area, volume, other geometric measure theory
28A78: Hausdorff and packing measures
28A80: Fractals
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
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
28B99: None of the above, but in this section 28Cxx : Set functions and measures on spaces with additional structure
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
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.)
28C99: None of the above, but in this section 28Dxx : Measure-theoretic ergodic theory
28D05: Measure-preserving transformations
28D10: One-parameter continuous families of measure-preserving transformations
28D15: General groups of measure-preserving transformations
28D20: Entropy and other invariants
28D99: None of the above, but in this section 28Exx : Miscellaneous topics in measure theory
28E05: Nonstandard measure theory
28E10: Fuzzy measure theory
28E15: Other connections with logic and set theory
28E99: None of the above, but in this section 30-xx : Functions of a complex variable
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 also be assigned at least one classification number from Section 01)
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
30B60: Completeness problems, closure of a system of functions
30B70: Continued fractions
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)
30C20: Conformal mappings of special domains
30C25: Covering theorems in conformal mapping theory
30C30: Numerical methods in conformal mapping theory
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 $<B>R</B>^n$, 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, Lindelöf principle, analogues and generalizations; subordination
30C85: Capacity and harmonic measure in the complex plane
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
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: Blaschke 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
30E25: Boundary value problems
30E99: None of the above, but in this section 30Fxx : Riemann surfaces
30F10: Compact Riemann surfaces and uniformization
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
30F40: Kleinian groups
30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
30F50: Klein surfaces
30F60: Teichmüller theory
30F99: None of the above, but in this section 30Gxx : Generalized function theory
30G06: Non-Archimedean function theory; nonstandard function theory
30G12: Finely holomorphic functions and 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 31-xx : Potential theory
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 also be assigned at least one classification number from Section 01)
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
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
31C12: Potential theory on Riemannian manifolds
31C15: Potentials and capacities
31C20: Discrete potential theory and numerical methods
31C25: Dirichlet spaces
31C35: Martin boundary theory
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
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 also be assigned at least one classification number from Section 01)
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, circular, tube)
32A10: Holomorphic functions
32A12: Multifunctions
32A15: Entire functions
32A17: Special families of functions
32A18: Bloch functions, normal functions
32A19: Normal families of functions, mappings
32A20: Meromorphic functions
32A22: Nevanlinna theory (local); growth estimates; other inequalities
32A25: Integral representations; canonical kernels (Szegó, Bergman, etc.)
32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
32A27: Local theory of residues
32A30: Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30)
32A35: ${H]^p$-spaces, Nevanlinna spaces
32A36: Bergman spaces
32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
32A38: Algebras of holomorphic functions
32A40: Boundary behavior of holomorphic functions
32A45: Hyperfunctions
32A50: Harmonic analysis of several complex variables
32A55: Singular integrals
32A60: Zero sets of holomorphic functions
32A65: Banach algebra techniques
32A70: Functional analysis techniques
32A99: None of the above, but in this section 32Bxx : Local analytic geometry
32B05: Analytic algebras and generalizations, preparation theorems
32B10: Germs of analytic sets, local parametrization
32B15: Analytic subsets of affine space
32B20: Semi-analytic sets and subanalytic sets
32B25: Triangulation and related questions
32B99: None of the above, but in this section 32Cxx : Analytic spaces
32C05: Real-analytic manifolds, real-analytic spaces
32C07: Real-analytic sets, complex Nash functions
32C09: Embedding of real analytic manifolds
32C11: Complex supergeometry
32C15: Complex spaces
32C18: Topology of analytic spaces
32C20: Normal analytic spaces
32C22: Embedding of analytic spaces
32C25: Analytic subsets and submanifolds
32C30: Integration on analytic sets and spaces, currents
32C35: Analytic sheaves and cohomology groups
32C36: Local cohomology of analytic spaces
32C37: Duality theorems
32C38: Sheaves of differential operators and their modules, $D$-modules
32C55: The Levi problem in complex spaces; generalizations
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
32D26: Riemann domains
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
32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation
32E35: Global boundary behavior of holomorphic functions
32E40: The Levi problem
32E99: None of the above, but in this section 32Fxx : Geometric convexity
32F10: $q$-convexity, $q$-concavity
32F17: Other notions of convexity
32F18: Finite-type conditions
32F27: Topological consequences of geometric convexity
32F32: Analytical consequences of geometric convexity (vanishing theorems, etc.)
32F45: Invariant metrics and pseudodistances
32F99: None of the above, but in this section 32Gxx : Deformations of analytic structures
32G05: Deformations of complex structures
32G07: Deformations of special (e.g. CR) structures
32G08: Deformations of fiber bundles
32G10: Deformations of submanifolds and subspaces
32G13: Analytic moduli problems
32G15: Moduli of Riemann surfaces, Teichmüller theory
32G20: Period matrices, variation of Hodge structure; degenerations
32G34: Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation)
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
32H12: Boundary uniqueness of mappings
32H25: Picard-type theorems and generalizations
32H30: Value distribution theory in higher dimensions
32H35: Proper mappings, finiteness theorems
32H40: Boundary regularity of mappings
32H50: Iteration problems
32H99: None of the above, but in this section 32Jxx : Compact analytic spaces
32J05: Compactification of analytic spaces
32J10: Algebraic dependence theorems
32J15: Compact surfaces
32J17: Compact $3$-folds
32J18: Compact $n$-folds
32J25: Transcendental methods of algebraic geometry
32J27: Compact Kähler 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 from Section 32 describing the type of problem)
32K05: Banach analytic spaces
32K07: Formal and graded complex spaces
32K15: Differentiable functions on analytic spaces, differentiable spaces
32K99: None of the above, but in this section 32Lxx : Holomorphic fiber spaces
32L05: Holomorphic bundles and generalizations
32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results
32L15: Bundle convexity
32L20: Vanishing theorems
32L25: Twistor theory, double fibrations
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 acting on complex spaces
32M10: Homogeneous complex manifolds
32M12: Almost homogeneous manifolds and spaces
32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras
32M17: Automorphism groups of ${\bf C]^n$ and affine manifolds
32M25: Complex vector fields
32M99: None of the above, but in this section 32Nxx : Automorphic functions
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) 32Qxx : Complex manifolds
32Q05: Negative curvature manifolds
32Q10: Positive curvature manifolds
32Q15: Kähler manifolds
32Q20: Kähler-Einstein manifolds
32Q25: Calabi-Yau theory
32Q28: Stein manifolds
32Q30: Uniformization
32Q35: Complex manifolds as subdomains of Euclidean space
32Q40: Embedding theorems
32Q45: Hyperbolic and Kobayashi hyperbolic manifolds
32Q55: Topological aspects of complex manifolds
32Q57: Classification theorems
32Q60: Almost complex manifolds
32Q65: Pseudoholomorphic curves
32Q99: None of the above, but in this section 32Sxx : Singularities
32S05: Local singularities
32S10: Invariants of analytic local rings
32S15: Equisingularity (topological and analytic)
32S20: Global theory of singularities; cohomological properties
32S22: Relations with arrangements of hyperplanes
32S25: Surface and hypersurface singularities
32S30: Deformations of singularities; vanishing cycles
32S35: Mixed Hodge theory of singular varieties
32S40: Monodromy; relations with differential equations and $D$-modules
32S45: Modifications; resolution of singularities
32S50: Topological aspects: Lefschetz theorems, topological classification, invariants
32S55: Milnor fibration; relations with knot theory
32S60: Stratifications; constructible sheaves; intersection cohomology
32S65: Singularities of holomorphic vector fields and foliations
32S70: Other operations on singularities
32S99: None of the above, but in this section 32Txx : Pseudoconvex domains
32T05: Domains of holomorphy
32T15: Strongly pseudoconvex domains
32T20: Worm domains
32T25: Finite type domains
32T27: Geometric and analytic invariants on weakly pseudoconvex boundaries
32T35: Exhaustion functions
32T40: Peak functions
32T99: None of the above, but in this section 32Uxx : Pluripotential theory
32U05: Plurisubharmonic functions and generalizations
32U10: Plurisubharmonic exhaustion functions
32U15: General pluripotential theory
32U20: Capacity theory and generalizations
32U25: Lelong numbers
32U30: Removable sets
32U35: Pluricomplex Green functions
32U40: Currents
32U99: None of the above, but in this section 32Vxx : CR manifolds
32V05: CR structures, CR operators, and generalizations
32V10: CR functions
32V15: CR manifolds as boundaries of domains
32V20: Analysis on CR manifolds
32V25: Extension of functions and other analytic objects from CR manifolds
32V30: Embeddings of CR manifolds
32V35: Finite type conditions on CR manifolds
32V40: Real submanifolds in complex manifolds
32V99: None of the above, but in this section 32Wxx : Differential operators in several variables
32W05: $\overline\partial$ and $\overline\partial$-Neumann operators
32W10: $\overline\partial_b$ and $\overline\partial_b$-Neumann operators
32W20: Complex Monge-Ampère operators
32W25: Pseudodifferential operators in several complex variables
32W30: Heat kernels in several complex variables
32W50: Other partial differential equations of complex analysis
32W99: None of the above, but in this section 33-xx : Special functions (33-XX deals with the properties of functions as functions)
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 also be assigned at least one classification number from Section 01)
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)
33B30: Higher logarithm functions
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 of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C47: Other special orthogonal polynomials and functions
33C50: Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
33C52: Orthogonal polynomials and functions associated with root systems
33C55: Spherical harmonics
33C60: Hypergeometric integrals and functions defined by them ($E$, $G$ and ${H]$ functions)
33C65: Appell, Horn and Lauricella functions
33C67: Hypergeometric functions associated with root systems
33C70: Other hypergeometric functions and integrals in several variables
33C75: Elliptic integrals as hypergeometric functions
33C80: Connections with groups and algebras, 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
33D15: Basic hypergeometric functions in one variable, ${]_r\phi_s$
33D45: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33D50: Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
33D52: Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
33D60: Basic hypergeometric integrals and functions defined by them
33D65: Bibasic functions and multiple bases
33D67: Basic hypergeometric functions associated with root systems
33D70: Other basic hypergeometric functions and integrals in several variables
33D80: Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke 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: Lamé, Mathieu, and spheroidal wave functions
33E12: Mittag-Leffler functions and generalizations
33E15: Other wave functions
33E17: Painlevé-type functions
33E20: Other functions defined by series and integrals
33E30: Other functions coming from differential, difference and integral equations
33E50: Special functions in characteristic $p$ (gamma functions, etc.)
33E99: None of the above, but in this section 33Fxx : Computational aspects
33F05: Numerical approximation
33F10: Symbolic computation (Gosper and Zeilberger algorithms, etc.)
33F99: 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 also be assigned at least one classification number from Section 01)
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, differential-algebraic equations
34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
34A25: Analytical theory: series, transformations, transforms, operational calculus, etc.
34A26: Geometric methods in differential equations
34A30: Linear equations and systems, general
34A34: Nonlinear equations and systems, general
34A35: Differential equations of infinite order
34A36: Discontinuous equations
34A37: Differential equations with impulses
34A40: Differential inequalities
34A45: Theoretical approximation of solutions
34A55: Inverse problems
34A60: Differential inclusions
34A99: None of the above, but in this section 34Bxx : Boundary value problems
34B05: Linear boundary value problems
34B07: Linear boundary value problems with nonlinear dependence on the spectral parameter
34B08: Multi-parameter boundary value problems
34B09: Boundary value problems with an indefinite weight
34B10: Multipoint boundary value problems
34B15: Nonlinear boundary value problems
34B16: Singular nonlinear boundary value problems
34B18: Positive solutions of nonlinear boundary value problems
34B20: Weyl theory and its generalizations
34B24: Sturm-Liouville theory
34B27: Green functions
34B30: Special equations (Mathieu, Hill, Bessel, etc.)
34B37: Boundary value problems with impulses
34B40: Boundary value problems on infinite intervals
34B45: Boundary value problems on graphs and networks
34B60: Applications
34B99: None of the above, but in this section 34Cxx : Qualitative theory
34C05: Location of integral curves, singular points, limit cycles
34C07: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)
34C08: Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
34C10: Oscillation theory, zeros, disconjugacy and comparison theory
34C11: Growth, boundedness, comparison of solutions
34C12: Monotone systems
34C14: Symmetries, invariants
34C15: Nonlinear oscillations, coupled oscillators
34C20: Transformation and reduction of equations and systems, normal forms
34C23: Bifurcation
34C25: Periodic solutions
34C26: Relaxation oscillations
34C27: Almost periodic solutions
34C28: Complex behavior, chaotic systems
34C29: Averaging method
34C30: Manifolds of solutions
34C37: Homoclinic and heteroclinic solutions
34C40: Equations and systems on manifolds
34C41: Equivalence, asymptotic equivalence
34C45: Method of integral manifolds
34C55: Hysteresis
34C60: Applications
34C99: None of the above, but in this section 34Dxx : Stability theory
34D05: Asymptotic properties
34D08: Characteristic and Lyapunov exponents
34D09: Dichotomy, trichotomy
34D10: Perturbations
34D15: Singular perturbations
34D20: Lyapunov stability
34D23: Global stability
34D30: Structural stability and analogous concepts
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
34E13: Multiple scale methods
34E15: Singular perturbations, general theory
34E18: Methods of nonstandard analysis
34E20: Singular perturbations, turning point theory, WKB methods
34E99: None of the above, but in this section
34F05: Equations and systems with randomness 34Gxx : Differential equations in abstract spaces
34G10: Linear equations
34G20: Nonlinear equations
34G25: Evolution inclusions
34G99: None of the above, but in this section
34H05: Control problems 34Kxx : Functional-differential and differential-difference equations
34K05: General theory
34K06: Linear functional-differential equations
34K07: Theoretical approximation of solutions
34K10: Boundary value problems
34K11: Oscillation theory
34K12: Growth, boundedness, comparison of solutions
34K13: Periodic solutions
34K14: Almost periodic solutions
34K17: Transformation and reduction of equations and systems, normal forms
34K18: Bifurcation theory
34K19: Invariant manifolds
34K20: Stability theory
34K23: Complex (chaotic) behavior of solutions
34K25: Asymptotic theory
34K26: Singular perturbations
34K28: Numerical approximation of solutions
34K29: Inverse problems
34K30: Equations in abstract spaces
34K35: Control problems
34K40: Neutral equations
34K45: Equations with impulses
34K50: Stochastic delay equations
34K60: Applications
34K99: None of the above, but in this section 34Lxx : Ordinary differential operators
34L05: General spectral theory
34L10: Eigenfunction expansions, completeness of eigenfunctions
34L15: Estimation of eigenvalues, upper and lower bounds
34L16: Numerical approximation of eigenvalues and of other parts of the spectrum
34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
34L25: Scattering theory
34L30: Nonlinear ordinary differential operators
34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.)
34L99: None of the above, but in this section 34Mxx : Differential equations in the complex domain
34M05: Entire and meromorphic solutions
34M10: Oscillation, growth of solutions
34M15: Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
34M20: Nonanalytic aspects
34M25: Formal solutions, transform techniques
34M30: Asymptotics, summation methods
34M35: Singularities, monodromy, local behavior of solutions, normal forms
34M37: Resurgence phenomena
34M40: Stokes phenomena and connection problems (linear and nonlinear)
34M45: Differential equations on complex manifolds
34M50: Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
34M55: Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
34M60: Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent)
34M99: 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 also be assigned at least one classification number from Section 01)
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
35A08: Fundamental solutions
35A10: Cauchy-Kovalevskaya theorems
35A15: Variational methods
35A17: Parametrices
35A18: Wave front sets
35A20: Analytic methods, singularities
35A21: Propagation of singularities
35A22: Transform methods (e.g. integral transforms)
35A25: Other special methods
35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE
35A30: Geometric theory, characteristics, transformations
35A35: Theoretical approximation to solutions
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
35B30: Dependence of solutions of PDE on initial and boundary data, parameters
35B32: Bifurcation
35B33: Critical exponents
35B34: Resonances
35B35: Stability, boundedness
35B37: PDE in connection with control problems
35B38: Critical points
35B40: Asymptotic behavior of solutions
35B41: Attractors
35B42: Inertial manifolds
35B45: A priori estimates
35B50: Maximum principles
35B60: Continuation and prolongation of solutions of PDE
35B65: Smoothness and 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
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 35Hxx : Close-to-elliptic equations
35H10: Hypoelliptic equations
35H20: Subelliptic equations
35H30: Quasi-elliptic equations
35H99: None of the above, but in this section 35Jxx : Partial differential equations of elliptic type
35J05: Laplace equation, reduced wave equation (Helmholtz), Poisson equation
35J10: Schrödinger operator
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
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
35J99: None of the above, but in this section 35Kxx : Parabolic equations and systems
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
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 parabolic 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
35K90: Abstract parabolic evolution equations
35K99: None of the above, but in this section 35Lxx : Partial differential equations of hyperbolic type
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
35L70: Nonlinear second-order PDE of hyperbolic type
35L75: Nonlinear hyperbolic PDE of higher ($\gtr 2$) order
35L80: Hyperbolic PDE of degenerate type
35L82: Pseudohyperbolic equations
35L85: Unilateral problems; variational inequalities for hyperbolic PDE
35L90: Abstract hyperbolic evolution equations
35L99: None of the above, but in this section 35Mxx : Partial differential equations of special type (mixed, composite, etc.)
35M10: PDE of mixed type
35M20: PDE of composite type
35M99: None of the above, but in this section 35Nxx : Overdetermined systems
35N05: Overdetermined systems with constant coefficients
35N10: Overdetermined systems with variable coefficients (general)
35N15: $\overline\partial$-Neumann problem and generalizations; formal complexes
35N99: None of the above, but in this section 35Pxx : Spectral theory and eigenvalue problems for partial differential operators
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
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
35Q05: Euler-Poisson-Darboux equation and generalizations
35Q15: Riemann-Hilbert problems
35Q30: Stokes and Navier-Stokes equations
35Q35: Other equations arising in fluid mechanics
35Q40: Equations from quantum mechanics
35Q51: Solitons
35Q53: KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.)
35Q55: NLS-like (nonlinear Schrödinger) equations
35Q58: Other completely integrable equations
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
35R05: PDE with discontinuous coefficients or data
35R10: Partial functional-differential or differential-difference equations, with or without deviating arguments
35R12: Impulsive partial differential equations
35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)
35R20: Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions)
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
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
35S05: General theory of PsDO
35S10: Initial value problems for PsDO
35S15: Boundary value problems for PsDO
35S30: Fourier integral operators
35S35: Topological aspects: intersection cohomology, stratified sets, etc.
35S50: Paradifferential operators
35S99: None of the above, but in this section 37-xx : Dynamical systems and ergodic theory
37-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
37-01: Instructional exposition (textbooks, tutorial papers, etc.)
37-02: Research exposition (monographs, survey articles)
37-03: Historical (must also be assigned at least one classification number from Section 01)
37-04: Explicit machine computation and programs (not the theory of computation or programming)
37-06: Proceedings, conferences, collections, etc.
37Axx : Ergodic theory
37A05: Measure-preserving transformations
37A10: One-parameter continuous families of measure-preserving transformations
37A15: General groups of measure-preserving transformations
37A17: Homogeneous flows
37A20: Orbit equivalence, cocycles, ergodic equivalence relations
37A25: Ergodicity, mixing, rates of mixing
37A30: Ergodic theorems, spectral theory, Markov operators
37A35: Entropy and other invariants, isomorphism, classification
37A40: Nonsingular (and infinite-measure preserving) transformations
37A45: Relations with number theory and harmonic analysis
37A50: Relations with probability theory and stochastic processes
37A55: Relations with the theory of $C^*$-algebras
37A60: Dynamical systems in statistical mechanics
37A99: None of the above, but in this section 37Bxx : Topological dynamics
37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B10: Symbolic dynamics
37B15: Cellular automata
37B20: Notions of recurrence
37B25: Lyapunov functions and stability; attractors, repellers
37B30: Index theory, Morse-Conley indices
37B35: Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
37B40: Topological entropy
37B45: Continua theory in dynamics
37B50: Multi-dimensional shifts of finite type, tiling dynamics
37B55: Nonautonomous dynamical systems
37B99: None of the above, but in this section 37Cxx : Smooth dynamical systems: general theory
37C05: Smooth mappings and diffeomorphisms
37C10: Vector fields, flows, ordinary differential equations
37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37C20: Generic properties, structural stability
37C25: Fixed points, periodic points, fixed-point index theory
37C27: Periodic orbits of vector fields and flows
37C29: Homoclinic and heteroclinic orbits
37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37C35: Orbit growth
37C40: Smooth ergodic theory, invariant measures
37C45: Dimension theory of dynamical systems
37C50: Approximate trajectories (pseudotrajectories, shadowing, etc.)
37C55: Periodic and quasiperiodic flows and diffeomorphisms
37C60: Nonautonomous smooth dynamical systems
37C65: Monotone flows
37C70: Attractors and repellers, topological structure
37C75: Stability theory
37C80: Symmetries, equivariant dynamical systems
37C85: Dynamics of group actions other than <B>Z</B> and <B>R</B>, and foliations
37C99: None of the above, but in this section 37Dxx : Dynamical systems with hyperbolic behavior
37D05: Hyperbolic orbits and sets
37D10: Invariant manifold theory
37D15: Morse-Smale systems
37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D25: Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D30: Partially hyperbolic systems and dominated splittings
37D35: Thermodynamic formalism, variational principles, equilibrium states
37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37D45: Strange attractors, chaotic dynamics
37D50: Hyperbolic systems with singularities (billiards, etc.)
37D99: None of the above, but in this section 37Exx : Low-dimensional dynamical systems
37E05: Maps of the interval (piecewise continuous, continuous, smooth)
37E10: Maps of the circle
37E15: Combinatorial dynamics (types of periodic orbits)
37E20: Universality, renormalization
37E25: Maps of trees and graphs
37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
37E35: Flows on surfaces
37E40: Twist maps
37E45: Rotation numbers and vectors
37E99: None of the above, but in this section 37Fxx : Complex dynamical systems
37F05: Relations and correspondences
37F10: Polynomials; rational maps; entire and meromorphic functions
37F15: Expanding maps; hyperbolicity; structural stability
37F20: Combinatorics and topology
37F25: Renormalization
37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
37F35: Conformal densities and Hausdorff dimension
37F40: Geometric limits
37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets
37F75: Holomorphic foliations and vector fields
37F99: None of the above, but in this section 37Gxx : Local and nonlocal bifurcation theory
37G05: Normal forms
37G10: Bifurcations of singular points
37G15: Bifurcations of limit cycles and periodic orbits
37G20: Hyperbolic singular points with homoclinic trajectories
37G25: Bifurcations connected with nontransversal intersection
37G30: Infinite nonwandering sets arising in bifurcations
37G35: Attractors and their bifurcations
37G40: Symmetries, equivariant bifurcation theory
37G99: None of the above, but in this section 37Hxx : Random dynamical systems
37H05: Foundations, general theory of cocycles, algebraic ergodic theory
37H10: Generation, random and stochastic difference and differential equations
37H15: Multiplicative ergodic theory, Lyapunov exponents
37H20: Bifurcation theory
37H99: None of the above, but in this section 37Jxx : Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
37J05: General theory, relations with symplectic geometry and topology
37J10: Symplectic mappings, fixed points
37J15: Symmetries, invariants, invariant manifolds, momentum maps, reduction
37J20: Bifurcation problems
37J25: Stability problems
37J30: Obstructions to integrability (nonintegrability criteria)
37J35: Completely integrable systems, topological structure of phase space, integration methods
37J40: Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion
37J45: Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37J50: Action-minimizing orbits and measures
37J55: Contact systems
37J60: Nonholonomic dynamical systems
37J99: None of the above, but in this section 37Kxx : Infinite-dimensional Hamiltonian systems
37K05: Hamiltonian structures, symmetries, variational principles, conservation laws
37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
37K15: Integration of completely integrable systems by inverse spectral and scattering methods
37K20: Relations with algebraic geometry, complex analysis, special functions
37K25: Relations with differential geometry
37K30: Relations with infinite-dimensional Lie algebras and other algebraic structures
37K35: Lie-Bäcklund and other transformations
37K40: Soliton theory, asymptotic behavior of solutions
37K45: Stability problems
37K50: Bifurcation problems
37K55: Perturbations, KAM for infinite-dimensional systems
37K60: Lattice dynamics
37K65: Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
37K99: None of the above, but in this section 37Lxx : Infinite-dimensional dissipative dynamical systems
37L05: General theory, nonlinear semigroups, evolution equations
37L10: Normal forms, center manifold theory, bifurcation theory
37L15: Stability problems
37L20: Symmetries
37L25: Inertial manifolds and other invariant attracting sets
37L30: Attractors and their dimensions, Lyapunov exponents
37L40: Invariant measures
37L45: Hyperbolicity; Lyapunov functions
37L50: Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
37L55: Infinite-dimensional random dynamical systems; stochastic equations
37L60: Lattice dynamics
37L65: Special approximation methods (nonlinear Galerkin, etc.)
37L99: None of the above, but in this section 37Mxx : Approximation methods and numerical treatment of dynamical systems
37M05: Simulation
37M10: Time series analysis
37M15: Symplectic integrators
37M20: Computational methods for bifurcation problems
37M25: Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
37M99: None of the above, but in this section 37Nxx : Applications
37N05: Dynamical systems in classical and celestial mechanics
37N10: Dynamical systems in fluid mechanics, oceanography and meteorology
37N15: Dynamical systems in solid mechanics
37N20: Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37N25: Dynamical systems in biology
37N30: Dynamical systems in numerical analysis
37N35: Dynamical systems in control
37N40: Dynamical systems in optimization and economics
37N99: None of the above, but in this section 39-xx : Difference 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 also be assigned at least one classification number from Section 01)
39-04: Explicit machine computation and programs (not the theory of computation or programming)
39-06: Proceedings, conferences, collections, etc.
39Axx : Difference equations
39A05: General
39A10: Difference equations, additive
39A11: Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc.
39A12: Discrete version of topics in analysis
39A13: Difference equations, scaling ($q$-differences)
39A20: Multiplicative and other generalized difference equations, e.g. of Lyness type
39A70: Difference operators
39A99: None of the above, but in this section 39Bxx : Functional equations and inequalities
39B05: General
39B12: Iteration theory, iterative and composite equations
39B22: Equations for real functions
39B32: Equations for complex functions
39B42: Matrix and operator equations
39B52: Equations for functions with more general domains and/or ranges
39B55: Orthogonal additivity and other conditional equations
39B62: Functional inequalities, including subadditivity, convexity, etc.
39B72: Systems of functional equations and inequalities
39B82: Stability, separation, extension, and related topics
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 also be assigned at least one classification number from Section 01)
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
40A20: Convergence and divergence of infinite products
40A25: Approximation to limiting values (summation of series, etc.)
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: Cesàro, Euler, Nörlund 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 41-xx : Approximations and expansions
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 also be assigned at least one classification number from Section 01)
41-04: Explicit machine computation and programs (not the theory of computation or programming)
41-06: Proceedings, conferences, collections, etc.
41A05: Interpolation
41A10: Approximation by polynomials
41A15: Spline approximation
41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski\u\i-type inequalities)
41A20: Approximation by rational functions
41A21: Padé 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.)
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 also be assigned at least one classification number from Section 01)
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
42A20: Convergence and absolute convergence of Fourier and trigonometric series
42A24: Summability and absolute summability of Fourier and trigonometric series
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
42A82: Positive definite functions
42A85: Convolution, factorization
42A99: None of the above, but in this section 42Bxx : Fourier analysis in several variables
42B05: Fourier series and coefficients
42B08: Summability
42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B15: Multipliers
42B20: Singular integrals (Calderón-Zygmund, etc.)
42B25: Maximal functions, Littlewood-Paley theory
42B30: $H^p$-spaces
42B35: Function spaces arising in harmonic analysis
42B99: None of the above, but in this section 42Cxx : Nontrigonometric Fourier analysis
42C05: Orthogonal functions and polynomials, general theory
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
42C40: Wavelets
42C99: None of the above, but in this section 43-xx : Abstract harmonic analysis
43-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
43-01: Instructional exposition (textbooks, tutorial papers, etc.)
43-02: Research exposition (monographs, survey articles)
43-03: Historical (must also be assigned at least one classification number from Section 01)
43-04: Explicit machine computation and programs (not the theory of computation or programming)
43-06: Proceedings, conferences, collections, etc.
43A05: Measures on groups and semigroups, etc.
43A07: Means on groups, semigroups, etc.; amenable groups
43A10: Measure algebras on groups, semigroups, etc.
43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
43A17: Analysis on ordered groups, ${H]^p$-theory
43A20: $L^1$-algebras on groups, semigroups, etc.
43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A25: Fourier and Fourier-Stieltjes transforms on locally compact abelian groups
43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A32: Other transforms and operators of Fourier type
43A35: Positive definite functions on groups, semigroups, etc.
43A40: Character groups and dual objects
43A45: Spectral synthesis on groups, semigroups, etc.
43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
43A50: Convergence of Fourier series and of inverse transforms
43A55: Summability methods on groups, semigroups, etc.
43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
43A62: Hypergroups
43A65: Representations of groups, semigroups, etc.
43A70: Analysis on specific locally compact abelian groups
43A75: Analysis on specific compact groups
43A77: Analysis on general compact groups
43A80: Analysis on other specific Lie groups
43A85: Analysis on homogeneous spaces
43A90: Spherical functions
43A95: Categorical methods
43A99: Miscellaneous topics 44-xx : Integral transforms, operational calculus
44-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
44-01: Instructional exposition (textbooks, tutorial papers, etc.)
44-02: Research exposition (monographs, survey articles)
44-03: Historical (must also be assigned at least one classification number from Section 01)
44-04: Explicit machine computation and programs (not the theory of computation or programming)
44-06: Proceedings, conferences, collections, etc.
44A05: General transforms
44A10: Laplace transform
44A12: Radon transform
44A15: Special transforms (Legendre, Hilbert, etc.)
44A20: Transforms of special functions
44A30: Multiple transforms
44A35: Convolution
44A40: Calculus of Mikusi\'nski and other operational calculi
44A45: Classical operational calculus
44A55: Discrete operational calculus
44A60: Moment problems
44A99: Miscellaneous topics 45-xx : Integral equations
45-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
45-01: Instructional exposition (textbooks, tutorial papers, etc.)
45-02: Research exposition (monographs, survey articles)
45-03: Historical (must also be assigned at least one classification number from Section 01)
45-04: Explicit machine computation and programs (not the theory of computation or programming)
45-06: Proceedings, conferences, collections, etc.
45A05: Linear integral equations
45B05: Fredholm integral equations
45C05: Eigenvalue problems
45D05: Volterra integral equations
45Exx : Singular integral equations
45E05: Integral equations with kernels of Cauchy type
45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45E99: None of the above, but in this section 45Fxx : Systems of linear integral equations
45F05: Systems of nonsingular linear integral equations
45F10: Dual, triple, etc., integral and series equations
45F15: Systems of singular linear integral equations
45F99: None of the above, but in this section 45Gxx : Nonlinear integral equations
45G05: Singular nonlinear integral equations
45G10: Other nonlinear integral equations
45G15: Systems of nonlinear integral equations
45H05: Miscellaneous special kernels
45J05: Integro-ordinary differential equations
45K05: Integro-partial differential equations
45L05: Theoretical approximation of solutions 45Mxx : Qualitative behavior
45M05: Asymptotics
45M10: Stability theory
45M15: Periodic solutions
45M20: Positive solutions
45M99: None of the above, but in this section
45N05: Abstract integral equations, integral equations in abstract spaces
45P05: Integral operators
45Q05: Inverse problems
45R05: Random integral equations 46-xx : Functional analysis
46-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
46-01: Instructional exposition (textbooks, tutorial papers, etc.)
46-02: Research exposition (monographs, survey articles)
46-03: Historical (must also be assigned at least one classification number from Section 01)
46-04: Explicit machine computation and programs (not the theory of computation or programming)
46-06: Proceedings, conferences, collections, etc.
46Axx : Topological linear spaces and related structures
46A03: General theory of locally convex spaces
46A04: Locally convex Fréchet spaces and (DF)-spaces
46A08: Barrelled spaces, bornological spaces
46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A17: Bornologies and related structures; Mackey convergence, etc.
46A19: Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\bf R]$, etc.)
46A20: Duality theory
46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46A25: Reflexivity and semi-reflexivity
46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)
46A32: Spaces of linear operators; topological tensor products; approximation properties
46A35: Summability and bases
46A40: Ordered topological linear spaces, vector lattices
46A45: Sequence spaces (including Köthe sequence spaces)
46A50: Compactness in topological linear spaces; angelic spaces, etc.
46A55: Convex sets in topological linear spaces; Choquet theory
46A61: Graded Fréchet spaces and tame operators
46A63: Topological invariants ((DN), ($\Omega$), etc.)
46A70: Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
46A80: Modular spaces
46A99: None of the above, but in this section 46Bxx : Normed linear spaces and Banach spaces; Banach lattices
46B03: Isomorphic theory (including renorming) of Banach spaces
46B04: Isometric theory of Banach spaces
46B07: Local theory of Banach spaces
46B08: Ultraproduct techniques in Banach space theory
46B09: Probabilistic methods in Banach space theory
46B10: Duality and reflexivity
46B15: Summability and bases
46B20: Geometry and structure of normed linear spaces
46B22: Radon-Nikodym, Krein-Milman and related properties
46B25: Classical Banach spaces in the general theory
46B26: Nonseparable Banach spaces
46B28: Spaces of operators; tensor products; approximation properties
46B40: Ordered normed spaces
46B42: Banach lattices
46B45: Banach sequence spaces
46B50: Compactness in Banach (or normed) spaces
46B70: Interpolation between normed linear spaces
46B99: None of the above, but in this section 46Cxx : Inner product spaces and their generalizations, Hilbert spaces
46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46C07: Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.)
46C15: Characterizations of Hilbert spaces
46C20: Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.)
46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.)
46C99: None of the above, but in this section 46Exx : Linear function spaces and their duals
46E05: Lattices of continuous, differentiable or analytic functions
46E10: Topological linear spaces of continuous, differentiable or analytic functions
46E15: Banach spaces of continuous, differentiable or analytic functions
46E20: Hilbert spaces of continuous, differentiable or analytic functions
46E22: Hilbert spaces with reproducing kernels (= proper functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
46E25: Rings and algebras of continuous, differentiable or analytic functions
46E27: Spaces of measures
46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
46E39: Sobolev (and similar kinds of) spaces of functions of discrete variables
46E40: Spaces of vector- and operator-valued functions
46E50: Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
46E99: None of the above, but in this section 46Fxx : Distributions, generalized functions, distribution spaces
46F05: Topological linear spaces of test functions, distributions and ultradistributions
46F10: Operations with distributions
46F12: Integral transforms in distribution spaces
46F15: Hyperfunctions, analytic functionals
46F20: Distributions and ultradistributions as boundary values of analytic functions
46F25: Distributions on infinite-dimensional spaces
46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
46F99: None of the above, but in this section 46Gxx : Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
46G05: Derivatives
46G10: Vector-valued measures and integration
46G12: Measures and integration on abstract linear spaces
46G15: Functional analytic lifting theory
46G20: Infinite-dimensional holomorphy
46G25: (Spaces of) multilinear mappings, polynomials
46G99: None of the above, but in this section 46Hxx : Topological algebras, normed rings and algebras, Banach algebras
46H05: General theory of topological algebras
46H10: Ideals and subalgebras
46H15: Representations of topological algebras
46H20: Structure, classification of topological algebras
46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H30: Functional calculus in topological algebras
46H35: Topological algebras of operators
46H40: Automatic continuity
46H70: Nonassociative topological algebras
46H99: None of the above, but in this section 46Jxx : Commutative Banach algebras and commutative topological algebras
46J05: General theory of commutative topological algebras
46J10: Banach algebras of continuous functions, function algebras
46J15: Banach algebras of differentiable or analytic functions, ${H]^p$-spaces
46J20: Ideals, maximal ideals, boundaries
46J25: Representations of commutative topological algebras
46J30: Subalgebras
46J40: Structure, classification of commutative topological algebras
46J45: Radical Banach algebras
46J99: None of the above, but in this section 46Kxx : Topological (rings and) algebras with an involution
46K05: General theory of topological algebras with involution
46K10: Representations of topological algebras with involution
46K15: Hilbert algebras
46K50: Nonselfadjoint (sub)algebras in algebras with involution
46K70: Nonassociative topological algebras with an involution
46K99: None of the above, but in this section 46Lxx : Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W$*-) algebras, etc.)
46L05: General theory of $C^*$-algebras
46L06: Tensor products of $C^*$-algebras
46L07: Operator spaces and completely bounded maps
46L08: $C^*$-modules
46L09: Free products of $C^*$-algebras
46L10: General theory of von Neumann algebras
46L30: States
46L35: Classifications of $C^*$-algebras, factors
46L37: Subfactors and their classification
46L40: Automorphisms
46L45: Decomposition theory for $C^*$-algebras
46L51: Noncommutative measure and integration
46L52: Noncommutative function spaces
46L53: Noncommutative probability and statistics
46L54: Free probability and free operator algebras
46L55: Noncommutative dynamical systems
46L57: Derivations, dissipations and positive semigroups in $C^*$-algebras
46L60: Applications of selfadjoint operator algebras to physics
46L65: Quantizations, deformations
46L70: Nonassociative selfadjoint operator algebras
46L80: $K$-theory and operator algebras (including cyclic theory)
46L85: Noncommutative topology
46L87: Noncommutative differential geometry
46L89: Other ``noncommutative'' mathematics based on $C^*$-algebra theory
46L99: None of the above, but in this section 46Mxx : Methods of category theory in functional analysis
46M05: Tensor products
46M07: Ultraproducts
46M10: Projective and injective objects
46M15: Categories, functors
46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
46M20: Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.)
46M35: Abstract interpolation of topological vector spaces
46M40: Inductive and projective limits
46M99: None of the above, but in this section 46Nxx : Miscellaneous applications of functional analysis
46N10: Applications in optimization, convex analysis, mathematical programming, economics
46N20: Applications to differential and integral equations
46N30: Applications in probability theory and statistics
46N40: Applications in numerical analysis
46N50: Applications in quantum physics
46N55: Applications in statistical physics
46N60: Applications in biology and other sciences
46N99: None of the above, but in this section 46Sxx : Other (nonclassical) types of functional analysis
46S10: Functional analysis over fields other than <B>R</B> or <B>C</B> or the quaternions; non-Archimedean functional analysis
46S20: Nonstandard functional analysis
46S30: Constructive functional analysis
46S40: Fuzzy functional analysis
46S50: Functional analysis in probabilistic metric linear spaces
46S60: Functional analysis on superspaces (supermanifolds) or graded spaces
46S99: None of the above, but in this section 46Txx : Nonlinear functional analysis
46T05: Infinite-dimensional manifolds
46T10: Manifolds of mappings
46T12: Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds
46T20: Continuous and differentiable maps
46T25: Holomorphic maps
46T30: Distributions and generalized functions on nonlinear spaces
46T99: None of the above, but in this section 47-xx : Operator theory
47-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
47-01: Instructional exposition (textbooks, tutorial papers, etc.)
47-02: Research exposition (monographs, survey articles)
47-03: Historical (must also be assigned at least one classification number from Section 01)
47-04: Explicit machine computation and programs (not the theory of computation or programming)
47-06: Proceedings, conferences, collections, etc.
47Axx : General theory of linear operators
47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A06: Linear relations (multivalued linear operators)
47A07: Forms (bilinear, sesquilinear, multilinear)
47A10: Spectrum, resolvent
47A11: Local spectral properties
47A12: Numerical range, numerical radius
47A13: Several-variable operator theory (spectral, Fredholm, etc.)
47A15: Invariant subspaces
47A16: Cyclic and hypercyclic vectors
47A20: Dilations, extensions, compressions
47A25: Spectral sets
47A30: Norms (inequalities, more than one norm, etc.)
47A35: Ergodic theory
47A40: Scattering theory
47A45: Canonical models for contractions and nonselfadjoint operators
47A46: Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
47A48: Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
47A50: Equations and inequalities involving linear operators, with vector unknowns
47A52: Ill-posed problems, regularization
47A53: (Semi-) Fredholm operators; index theories
47A55: Perturbation theory
47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
47A57: Operator methods in interpolation, moment and extension problems
47A58: Operator approximation theory
47A60: Functional calculus
47A62: Equations involving linear operators, with operator unknowns
47A63: Operator inequalities
47A64: Operator means, shorted operators, etc.
47A65: Structure theory
47A66: Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
47A67: Representation theory
47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
47A70: (Generalized) eigenfunction expansions; rigged Hilbert spaces
47A75: Eigenvalue problems
47A80: Tensor products of operators
47A99: None of the above, but in this section 47Bxx : Special classes of linear operators
47B06: Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47B07: Operators defined by compactness properties
47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B20: Subnormal operators, hyponormal operators, etc.
47B25: Symmetric and selfadjoint operators (unbounded)
47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
47B33: Composition operators
47B34: Kernel operators
47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
47B36: Jacobi (tridiagonal) operators (matrices) and generalizations
47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B38: Operators on function spaces (general)
47B39: Difference operators
47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
47B44: Accretive operators, dissipative operators, etc.
47B47: Commutators, derivations, elementary operators, etc.
47B48: Operators on Banach algebras
47B49: Transformers (= operators on spaces of operators)
47B50: Operators on spaces with an indefinite metric
47B60: Operators on ordered spaces
47B65: Positive operators and order-bounded operators
47B80: Random operators
47B99: None of the above, but in this section 47Cxx : Individual linear operators as elements of algebraic systems
47C05: Operators in algebras
47C10: Operators in $^*$-algebras
47C15: Operators in $C^*$- or von Neumann algebras
47C99: None of the above, but in this section 47Dxx : Groups and semigroups of linear operators, their generalizations and applications
47D03: Groups and semigroups of linear operators
47D06: One-parameter semigroups and linear evolution equations
47D07: Markov semigroups and applications to diffusion processes
47D08: Schrödinger and Feynman-Kac semigroups
47D09: Operator sine and cosine functions and higher-order Cauchy problems
47D60: $C$-semigroups
47D62: Integrated semigroups
47D99: None of the above, but in this section
47E05: Ordinary differential operators
47F05: Partial differential operators 47Gxx : Integral, integro-differential, and pseudodifferential operators
47G10: Integral operators
47G20: Integro-differential operators
47G30: Pseudodifferential operators
47G99: None of the above, but in this section 47Hxx : Nonlinear operators and their properties
47H04: Set-valued operators
47H05: Monotone operators (with respect to duality)
47H06: Accretive operators, dissipative operators, etc.
47H07: Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H09: Nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-set contractions, etc.)
47H10: Fixed-point theorems
47H11: Degree theory
47H14: Perturbations of nonlinear operators
47H20: Semigroups of nonlinear operators
47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskii, Uryson, etc.)
47H40: Random operators
47H50: Potential operators
47H60: Multilinear and polynomial operators
47H99: None of the above, but in this section 47Jxx : Equations and inequalities involving nonlinear operators
47J05: Equations involving nonlinear operators (general)
47J06: Nonlinear ill-posed problems
47J07: Abstract inverse mapping and implicit function theorems
47J10: Nonlinear eigenvalue problems
47J15: Abstract bifurcation theory
47J20: Variational and other types of inequalities involving nonlinear operators (general)
47J25: Methods for solving nonlinear operator equations (general)
47J30: Variational methods
47J35: Nonlinear evolution equations
47J40: Equations with hysteresis operators
47J99: None of the above, but in this section 47Lxx : Linear spaces and algebras of operators
47L05: Linear spaces of operators
47L07: Convex sets and cones of operators
47L10: Algebras of operators on Banach spaces and other topological linear spaces
47L15: Operator algebras with symbol structure
47L20: Operator ideals
47L25: Operator spaces (= matricially normed spaces)
47L30: Abstract operator algebras on Hilbert spaces
47L35: Nest algebras, CSL algebras
47L40: Limit algebras, subalgebras of $C^*$-algebras
47L45: Dual algebras; weakly closed singly generated operator algebras
47L50: Dual spaces of operator algebras
47L55: Representations of (nonselfadjoint) operator algebras
47L60: Algebras of unbounded operators; partial algebras of operators
47L65: Crossed product algebras (analytic crossed products)
47L70: Nonassociative nonselfadjoint operator algebras
47L75: Other nonselfadjoint operator algebras
47L80: Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
47L90: Applications of operator algebras to physics
47L99: None of the above, but in this section 47Nxx : Miscellaneous applications of operator theory
47N10: Applications in optimization, convex analysis, mathematical programming, economics
47N20: Applications to differential and integral equations
47N30: Applications in probability theory and statistics
47N40: Applications in numerical analysis
47N50: Applications in quantum physics
47N55: Applications in statistical physics
47N60: Applications in biology and other sciences
47N70: Applications in systems theory, circuits, etc.
47N99: None of the above, but in this section 47Sxx : Other (nonclassical) types of operator theory
47S10: Operator theory over fields other than <B>R</B>, <B>C</B> or the quaternions; non-Archimedean operator theory
47S20: Nonstandard operator theory
47S30: Constructive operator theory
47S40: Fuzzy operator theory
47S50: Operator theory in probabilistic metric linear spaces
47S99: None of the above, but in this section 49-xx : Calculus of variations and optimal control; optimization
49-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
49-01: Instructional exposition (textbooks, tutorial papers, etc.)
49-02: Research exposition (monographs, survey articles)
49-03: Historical (must also be assigned at least one classification number from Section 01)
49-04: Explicit machine computation and programs (not the theory of computation or programming)
49-06: Proceedings, conferences, collections, etc.
49Jxx : Existence theories
49J05: Free problems in one independent variable
49J10: Free problems in two or more independent variables
49J15: Optimal control problems involving ordinary differential equations
49J20: Optimal control problems involving partial differential equations
49J22: Optimal control problems involving integral equations
49J24: Optimal control problems involving differential inclusions
49J25: Optimal control problems involving equations with retarded arguments
49J27: Problems in abstract spaces
49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49J35: Minimax problems
49J40: Variational methods including variational inequalities
49J45: Methods involving semicontinuity and convergence; relaxation
49J50: Fréchet and Gateaux differentiability
49J52: Nonsmooth analysis
49J53: Set-valued and variational analysis
49J55: Problems involving randomness
49J99: None of the above, but in this section 49Kxx : Necessary conditions and sufficient conditions for optimality
49K05: Free problems in one independent variable
49K10: Free problems in two or more independent variables
49K15: Problems involving ordinary differential equations
49K20: Problems involving partial differential equations
49K22: Problems involving integral equations
49K24: Problems involving differential inclusions
49K25: Problems involving equations with retarded arguments
49K27: Problems in abstract spaces
49K30: Optimal solutions belonging to restricted classes
49K35: Minimax problems
49K40: Sensitivity, stability, well-posedness
49K45: Problems involving randomness
49K99: None of the above, but in this section 49Lxx : Hamilton-Jacobi theories, including dynamic programming
49L20: Dynamic programming method
49L25: Viscosity solutions
49L99: None of the above, but in this section 49Mxx : Methods of successive approximations
49M05: Methods based on necessary conditions
49M15: Methods of Newton-Raphson, Galerkin and Ritz types
49M20: Methods of relaxation type
49M25: Discrete approximations
49M27: Decomposition methods
49M29: Methods involving duality
49M30: Other methods, not based on necessary conditions (penalty function, etc.)
49M37: Methods of nonlinear programming type
49M99: None of the above, but in this section 49Nxx : Miscellaneous topics
49N05: Linear optimal control problems
49N10: Linear-quadratic problems
49N15: Duality theory
49N20: Periodic optimization
49N25: Impulsive optimal control problems
49N30: Problems with incomplete information
49N35: Optimal feedback synthesis
49N45: Inverse problems
49N60: Regularity of solutions
49N70: Differential games
49N75: Pursuit and evasion games
49N90: Applications of optimal control and differential games
49N99: None of the above, but in this section 49Qxx : Manifolds
49Q05: Minimal surfaces
49Q10: Optimization of shapes other than minimal surfaces
49Q12: Sensitivity analysis
49Q15: Geometric measure and integration theory, integral and normal currents
49Q20: Variational problems in a geometric measure-theoretic setting
49Q99: None of the above, but in this section
49R50: Variational methods for eigenvalues of operators
49S05: Variational principles of physics 51-xx : Geometry
51-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
51-01: Instructional exposition (textbooks, tutorial papers, etc.)
51-02: Research exposition (monographs, survey articles)
51-03: Historical (must also be assigned at least one classification number from Section 01)
51-04: Explicit machine computation and programs (not the theory of computation or programming)
51-06: Proceedings, conferences, collections, etc.
51Axx : Linear incidence geometry
51A05: General theory and projective geometries
51A10: Homomorphism, automorphism and dualities
51A15: Structures with parallelism
51A20: Configuration theorems
51A25: Algebraization
51A30: Desarguesian and Pappian geometries
51A35: Non-Desarguesian affine and projective planes
51A40: Translation planes and spreads
51A45: Incidence structures imbeddable into projective geometries
51A50: Polar geometry, symplectic spaces, orthogonal spaces
51A99: None of the above, but in this section 51Bxx : Nonlinear incidence geometry
51B05: General theory
51B10: Möbius geometries
51B15: Laguerre geometries
51B20: Minkowski geometries
51B25: Lie geometries
51B99: None of the above, but in this section
51C05: Ring geometry (Hjelmslev, Barbilian, etc.) 51Dxx : Geometric closure systems
51D05: Abstract (Maeda) geometries
51D10: Abstract geometries with exchange axiom
51D15: Abstract geometries with parallelism
51D20: Combinatorial geometries
51D25: Lattices of subspaces
51D30: Continuous geometries and related topics
51D99: None of the above, but in this section 51Exx : Finite geometry and special incidence structures
51E05: General block designs
51E10: Steiner systems
51E12: Generalized quadrangles, generalized polygons
51E14: Finite partial geometries (general), nets, partial spreads
51E15: Affine and projective planes
51E20: Combinatorial structures in finite projective spaces
51E21: Blocking sets, ovals, $k$-arcs
51E22: Linear codes and caps in Galois spaces
51E23: Spreads and packing problems
51E24: Buildings and the geometry of diagrams
51E25: Other finite nonlinear geometries
51E26: Other finite linear geometries
51E30: Other finite incidence structures
51E99: None of the above, but in this section 51Fxx : Metric geometry
51F05: Absolute planes
51F10: Absolute spaces
51F15: Reflection groups, reflection geometries
51F20: Congruence and orthogonality
51F25: Orthogonal and unitary groups
51F99: None of the above, but in this section
51G05: Ordered geometries (ordered incidence structures, etc.) 51Hxx : Topological geometry
51H05: General theory
51H10: Topological linear incidence structures
51H15: Topological nonlinear incidence structures
51H20: Topological geometries on manifolds
51H25: Geometries with differentiable structure
51H30: Geometries with algebraic manifold structure
51H99: None of the above, but in this section 51Jxx : Incidence groups
51J05: General theory
51J10: Projective incidence groups
51J15: Kinematic spaces
51J20: Representation by near-fields and near-algebras
51J99: None of the above, but in this section 51Kxx : Distance geometry
51K05: General theory
51K10: Synthetic differential geometry
51K99: None of the above, but in this section 51Lxx : Geometric order structures
51L05: Geometry of orders of nondifferentiable curves
51L10: Directly differentiable curves
51L15: $n$-vertex theorems via direct methods
51L20: Geometry of orders of surfaces
51L99: None of the above, but in this section 51Mxx : Real and complex geometry
51M04: Elementary problems in Euclidean geometries
51M05: Euclidean geometries (general) and generalizations
51M09: Elementary problems in hyperbolic and elliptic geometries
51M10: Hyperbolic and elliptic geometries (general) and generalizations
51M15: Geometric constructions
51M16: Inequalities and extremum problems
51M20: Polyhedra and polytopes; regular figures, division of spaces
51M25: Length, area and volume
51M30: Line geometries and their generalizations
51M35: Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
51M99: None of the above, but in this section 51Nxx : Analytic and descriptive geometry
51N05: Descriptive geometry
51N10: Affine analytic geometry
51N15: Projective analytic geometry
51N20: Euclidean analytic geometry
51N25: Analytic geometry with other transformation groups
51N30: Geometry of classical groups
51N35: Questions of classical algebraic geometry
51N99: None of the above, but in this section
51P05: Geometry and physics (should also be assigned at least one other classification number from Sections 70--86) 52-xx : Convex and discrete geometry
52-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
52-01: Instructional exposition (textbooks, tutorial papers, etc.)
52-02: Research exposition (monographs, survey articles)
52-03: Historical (must also be assigned at least one classification number from Section 01)
52-04: Explicit machine computation and programs (not the theory of computation or programming)
52-06: Proceedings, conferences, collections, etc.
52Axx : General convexity
52A01: Axiomatic and generalized convexity
52A05: Convex sets without dimension restrictions
52A07: Convex sets in topological vector spaces
52A10: Convex sets in $2$ dimensions (including convex curves)
52A15: Convex sets in $3$ dimensions (including convex surfaces)
52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
52A22: Random convex sets and integral geometry
52A27: Approximation by convex sets
52A30: Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
52A35: Helly-type theorems and geometric transversal theory
52A37: Other problems of combinatorial convexity
52A38: Length, area, volume
52A39: Mixed volumes and related topics
52A40: Inequalities and extremum problems
52A41: Convex functions and convex programs
52A55: Spherical and hyperbolic convexity
52A99: None of the above, but in this section 52Bxx : Polytopes and polyhedra
52B05: Combinatorial properties (number of faces, shortest paths, etc.)
52B10: Three-dimensional polytopes
52B11: $n$-dimensional polytopes
52B12: Special polytopes (linear programming, centrally symmetric, etc.)
52B15: Symmetry properties of polytopes
52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
52B22: Shellability
52B35: Gale and other diagrams
52B40: Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
52B45: Dissections and valuations (Hilbert's third problem, etc.)
52B55: Computational aspects related to convexity
52B60: Isoperimetric problems for polytopes
52B70: Polyhedral manifolds
52B99: None of the above, but in this section 52Cxx : Discrete geometry
52C05: Lattices and convex bodies in $2$ dimensions
52C07: Lattices and convex bodies in $n$ dimensions
52C10: Erdös problems and related topics of discrete geometry
52C15: Packing and covering in $2$ dimensions
52C17: Packing and covering in $n$ dimensions
52C20: Tilings in $2$ dimensions
52C22: Tilings in $n$ dimensions
52C23: Quasicrystals, aperiodic tilings
52C25: Rigidity and flexibility of structures
52C26: Circle packings and discrete conformal geometry
52C30: Planar arrangements of lines and pseudolines
52C35: Arrangements of points, flats, hyperplanes
52C40: Oriented matroids
52C45: Combinatorial complexity of geometric structures
52C99: None of the above, but in this section 53-xx : Differential geometry
53-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
53-01: Instructional exposition (textbooks, tutorial papers, etc.)
53-02: Research exposition (monographs, survey articles)
53-03: Historical (must also be assigned at least one classification number from Section 01)
53-04: Explicit machine computation and programs (not the theory of computation or programming)
53-06: Proceedings, conferences, collections, etc.
53Axx : Classical differential geometry
53A04: Curves in Euclidean space
53A05: Surfaces in Euclidean space
53A07: Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
53A10: Minimal surfaces, surfaces with prescribed mean curvature
53A15: Affine differential geometry
53A17: Kinematics
53A20: Projective differential geometry
53A25: Differential line geometry
53A30: Conformal differential geometry
53A35: Non-Euclidean differential geometry
53A40: Other special differential geometries
53A45: Vector and tensor analysis
53A55: Differential invariants (local theory), geometric objects
53A60: Geometry of webs
53A99: None of the above, but in this section 53Bxx : Local differential geometry
53B05: Linear and affine connections
53B10: Projective connections
53B15: Other connections
53B20: Local Riemannian geometry
53B21: Methods of Riemannian geometry
53B25: Local submanifolds
53B30: Lorentz metrics, indefinite metrics
53B35: Hermitian and Kählerian structures
53B40: Finsler spaces and generalizations (areal metrics)
53B50: Applications to physics
53B99: None of the above, but in this section 53Cxx : Global differential geometry
53C05: Connections, general theory
53C07: Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills)
53C10: $G$-structures
53C12: Foliations (differential geometric aspects)
53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C17: Sub-Riemannian geometry
53C20: Global Riemannian geometry, including pinching
53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
53C22: Geodesics
53C23: Global topological methods (à la Gromov)
53C24: Rigidity results
53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C26: Hyper-Kähler and quaternionic Kähler geometry, ``special'' geometry
53C27: Spin and Spin$^c$ geometry
53C28: Twistor methods
53C29: Issues of holonomy
53C30: Homogeneous manifolds
53C35: Symmetric spaces
53C38: Calibrations and calibrated geometries
53C40: Global submanifolds
53C42: Immersions (minimal, prescribed curvature, tight, etc.)
53C43: Differential geometric aspects of harmonic maps
53C44: Geometric evolution equations (mean curvature flow)
53C45: Global surface theory (convex surfaces à la A. D. Aleksandrov)
53C50: Lorentz manifolds, manifolds with indefinite metrics
53C55: Hermitian and Kählerian manifolds
53C56: Other complex differential geometry
53C60: Finsler spaces and generalizations (areal metrics)
53C65: Integral geometry; differential forms, currents, etc.
53C70: Direct methods ($G$-spaces of Busemann, etc.)
53C75: Geometric orders, order geometry
53C80: Applications to physics
53C99: None of the above, but in this section 53Dxx : Symplectic geometry, contact geometry
53D05: Symplectic manifolds, general
53D10: Contact manifolds, general
53D12: Lagrangian submanifolds; Maslov index
53D15: Almost contact and almost symplectic manifolds
53D17: Poisson manifolds
53D20: Momentum maps; symplectic reduction
53D22: Canonical transformations
53D25: Geodesic flows
53D30: Symplectic structures of moduli spaces
53D35: Global theory of symplectic and contact manifolds
53D40: Floer homology and cohomology, symplectic aspects
53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
53D50: Geometric quantization
53D55: Deformation quantization, star products
53D99: None of the above, but in this section
53Z05: Applications to physics 54-xx : General topology
54-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
54-01: Instructional exposition (textbooks, tutorial papers, etc.)
54-02: Research exposition (monographs, survey articles)
54-03: Historical (must also be assigned at least one classification number from Section 01)
54-04: Explicit machine computation and programs (not the theory of computation or programming)
54-06: Proceedings, conferences, collections, etc.
54Axx : Generalities
54A05: Topological spaces and generalizations (closure spaces, etc.)
54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54A15: Syntopogeneous structures
54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
54A35: Consistency and independence results
54A40: Fuzzy topology
54A99: None of the above, but in this section 54Bxx : Basic constructions
54B05: Subspaces
54B10: Product spaces
54B15: Quotient spaces, decompositions
54B17: Adjunction spaces and similar constructions
54B20: Hyperspaces
54B30: Categorical methods
54B35: Spectra
54B40: Presheaves and sheaves
54B99: None of the above, but in this section 54Cxx : Maps and general types of spaces defined by maps
54C05: Continuous maps
54C08: Weak and generalized continuity
54C10: Special maps on topological spaces (open, closed, perfect, etc.)
54C15: Retraction
54C20: Extension of maps
54C25: Embedding
54C30: Real-valued functions
54C35: Function spaces
54C40: Algebraic properties of function spaces
54C45: $C$- and $C^*$-embedding
54C50: Special sets defined by functions
54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
54C56: Shape theory
54C60: Set-valued maps
54C65: Selections
54C70: Entropy
54C99: None of the above, but in this section 54Dxx : Fairly general properties
54D05: Connected and locally connected spaces (general aspects)
54D10: Lower separation axioms ($T_0$--$T_3$, etc.)
54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D20: Noncompact covering properties (paracompact, Lindelöf, etc.)
54D25: ``$P$-minimal'' and ``$P$-closed'' spaces
54D30: Compactness
54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D40: Remainders
54D45: Local compactness, $\sigma$-compactness
54D50: $k$-spaces
54D55: Sequential spaces
54D60: Realcompactness and realcompactification
54D65: Separability
54D70: Base properties
54D80: Special constructions of spaces (spaces of ultrafilters, etc.)
54D99: None of the above, but in this section 54Exx : Spaces with richer structures
54E05: Proximity structures and generalizations
54E15: Uniform structures and generalizations
54E17: Nearness spaces
54E18: $p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
54E20: Stratifiable spaces, cosmic spaces, etc.
54E25: Semimetric spaces
54E30: Moore spaces
54E35: Metric spaces, metrizability
54E40: Special maps on metric spaces
54E45: Compact (locally compact) metric spaces
54E50: Complete metric spaces
54E52: Baire category, Baire spaces
54E55: Bitopologies
54E70: Probabilistic metric spaces
54E99: None of the above, but in this section 54Fxx : Special properties
54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
54F15: Continua and generalizations
54F35: Higher-dimensional local connectedness
54F45: Dimension theory
54F50: Spaces of dimension $\leq 1$; curves, dendrites
54F55: Unicoherence, multicoherence
54F65: Topological characterizations of particular spaces
54F99: None of the above, but in this section 54Gxx : Peculiar spaces
54G05: Extremally disconnected spaces, $F$-spaces, etc.
54G10: $P$-spaces
54G12: Scattered spaces
54G15: Pathological spaces
54G20: Counterexamples
54G99: None of the above, but in this section 54Hxx : Connections with other structures, applications
54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
54H10: Topological representations of algebraic systems
54H11: Topological groups
54H12: Topological lattices, etc.
54H13: Topological fields, rings, etc.
54H15: Transformation groups and semigroups
54H20: Topological dynamics
54H25: Fixed-point and coincidence theorems
54H99: None of the above, but in this section
54J05: Nonstandard topology 55-xx : Algebraic topology
55-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
55-01: Instructional exposition (textbooks, tutorial papers, etc.)
55-02: Research exposition (monographs, survey articles)
55-03: Historical (must also be assigned at least one classification number from Section 01)
55-04: Explicit machine computation and programs (not the theory of computation or programming)
55-06: Proceedings, conferences, collections, etc.
55Mxx : Classical topics
55M05: Duality
55M10: Dimension theory
55M15: Absolute neighborhood retracts
55M20: Fixed points and coincidences
55M25: Degree, winding number
55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
55M35: Finite groups of transformations (including Smith theory)
55M99: None of the above, but in this section 55Nxx : Homology and cohomology theories
55N05: Cech types
55N07: Steenrod-Sitnikov homologies
55N10: Singular theory
55N15: $K$-theory
55N20: Generalized (extraordinary) homology and cohomology theories
55N22: Bordism and cobordism theories, formal group laws
55N25: Homology with local coefficients, equivariant cohomology
55N30: Sheaf cohomology
55N33: Intersection homology and cohomology
55N34: Elliptic cohomology
55N35: Other homology theories
55N40: Axioms for homology theory and uniqueness theorems
55N45: Products and intersections
55N91: Equivariant homology and cohomology
55N99: None of the above, but in this section 55Pxx : Homotopy theory
55P05: Homotopy extension properties, cofibrations
55P10: Homotopy equivalences
55P15: Classification of homotopy type
55P20: Eilenberg-Mac Lane spaces
55P25: Spanier-Whitehead duality
55P30: Eckmann-Hilton duality
55P35: Loop spaces
55P40: Suspensions
55P42: Stable homotopy theory, spectra
55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
55P45: ${H]$-spaces and duals
55P47: Infinite loop spaces
55P48: Loop space machines, operads
55P55: Shape theory
55P57: Proper homotopy theory
55P60: Localization and completion
55P62: Rational homotopy theory
55P65: Homotopy functors
55P91: Equivariant homotopy theory
55P92: Relations between equivariant and nonequivariant homotopy theory
55P99: None of the above, but in this section 55Qxx : Homotopy groups
55Q05: Homotopy groups, general; sets of homotopy classes
55Q07: Shape groups
55Q10: Stable homotopy groups
55Q15: Whitehead products and generalizations
55Q20: Homotopy groups of wedges, joins, and simple spaces
55Q25: Hopf invariants
55Q35: Operations in homotopy groups
55Q40: Homotopy groups of spheres
55Q45: Stable homotopy of spheres
55Q50: $J$-morphism
55Q51: $v_n$-periodicity
55Q52: Homotopy groups of special spaces
55Q55: Cohomotopy groups
55Q70: Homotopy groups of special types
55Q91: Equivariant homotopy groups
55Q99: None of the above, but in this section 55Rxx : Fiber spaces and bundles
55R05: Fiber spaces
55R10: Fiber bundles
55R12: Transfer
55R15: Classification
55R20: Spectral sequences and homology of fiber spaces
55R25: Sphere bundles and vector bundles
55R35: Classifying spaces of groups and ${H]$-spaces
55R37: Maps between classifying spaces
55R40: Homology of classifying spaces, characteristic classes
55R45: Homology and homotopy of $B{\rm O]$ and $B{\rm U]$; Bott periodicity
55R50: Stable classes of vector space bundles, $K$-theory
55R55: Fiberings with singularities
55R60: Microbundles and block bundles
55R65: Generalizations of fiber spaces and bundles
55R70: Fibrewise topology
55R80: Discriminantal varieties, configuration spaces
55R91: Equivariant fiber spaces and bundles
55R99: None of the above, but in this section 55Sxx : Operations and obstructions
55S05: Primary cohomology operations
55S10: Steenrod algebra
55S12: Dyer-Lashof operations
55S15: Symmetric products, cyclic products
55S20: Secondary and higher cohomology operations
55S25: $K$-theory operations and generalized cohomology operations
55S30: Massey products
55S35: Obstruction theory
55S36: Extension and compression of mappings
55S37: Classification of mappings
55S40: Sectioning fiber spaces and bundles
55S45: Postnikov systems, $k$-invariants
55S91: Equivariant operations and obstructions
55S99: None of the above, but in this section 55Txx : Spectral sequences
55T05: General
55T10: Serre spectral sequences
55T15: Adams spectral sequences
55T20: Eilenberg-Moore spectral sequences
55T25: Generalized cohomology
55T99: None of the above, but in this section 55Uxx : Applied homological algebra and category theory
55U05: Abstract complexes
55U10: Simplicial sets and complexes
55U15: Chain complexes
55U20: Universal coefficient theorems, Bockstein operator
55U25: Homology of a product, Künneth formula
55U30: Duality
55U35: Abstract and axiomatic homotopy theory
55U40: Topological categories, foundations of homotopy theory
55U99: None of the above, but in this section 57-xx : Manifolds and cell complexes
57-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
57-01: Instructional exposition (textbooks, tutorial papers, etc.)
57-02: Research exposition (monographs, survey articles)
57-03: Historical (must also be assigned at least one classification number from Section 01)
57-04: Explicit machine computation and programs (not the theory of computation or programming)
57-06: Proceedings, conferences, collections, etc.
57Mxx : Low-dimensional topology
57M05: Fundamental group, presentations, free differential calculus
57M07: Topological methods in group theory
57M10: Covering spaces
57M12: Special coverings, e.g. branched
57M15: Relations with graph theory
57M20: Two-dimensional complexes
57M25: Knots and links in $S^3$
57M27: Invariants of knots and 3-manifolds
57M30: Wild knots and surfaces, etc., wild embeddings
57M35: Dehn's lemma, sphere theorem, loop theorem, asphericity
57M40: Characterizations of $E^3$ and $S^3$ (Poincaré conjecture)
57M50: Geometric structures on low-dimensional manifolds
57M60: Group actions in low dimensions
57M99: None of the above, but in this section 57Nxx : Topological manifolds
57N05: Topology of $E^2$, $2$-manifolds
57N10: Topology of general $3$-manifolds
57N12: Topology of $E^3$ and $S^3$
57N13: Topology of $E^4$, $4$-manifolds
57N15: Topology of $E^n$, $n$-manifolds ($4 < n < \infty$)
57N16: Geometric structures on manifolds
57N17: Topology of topological vector spaces
57N20: Topology of infinite-dimensional manifolds
57N25: Shapes
57N30: Engulfing
57N35: Embeddings and immersions
57N37: Isotopy and pseudo-isotopy
57N40: Neighborhoods of submanifolds
57N45: Flatness and tameness
57N50: $S^{n-1]\subset E^n$, Schoenflies problem
57N55: Microbundles and block bundles
57N60: Cellularity
57N65: Algebraic topology of manifolds
57N70: Cobordism and concordance
57N75: General position and transversality
57N80: Stratifications
57N99: None of the above, but in this section 57Pxx : Generalized manifolds
57P05: Local properties of generalized manifolds
57P10: Poincaré duality spaces
57P99: None of the above, but in this section 57Qxx : PL-topology
57Q05: General topology of complexes
57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57Q12: Wall finiteness obstruction for CW-complexes
57Q15: Triangulating manifolds
57Q20: Cobordism
57Q25: Comparison of PL-structures: classification, Hauptvermutung
57Q30: Engulfing
57Q35: Embeddings and immersions
57Q37: Isotopy
57Q40: Regular neighborhoods
57Q45: Knots and links (in high dimensions)
57Q50: Microbundles and block bundles
57Q55: Approximations
57Q60: Cobordism and concordance
57Q65: General position and transversality
57Q91: Equivariant PL-topology
57Q99: None of the above, but in this section 57Rxx : Differential topology
57R05: Triangulating
57R10: Smoothing
57R12: Smooth approximations
57R15: Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R17: Symplectic and contact topology
57R19: Algebraic topology on manifolds
57R20: Characteristic classes and numbers
57R22: Topology of vector bundles and fiber bundles
57R25: Vector fields, frame fields
57R27: Controllability of vector fields on $C^\infty$ and real-analytic manifolds
57R30: Foliations; geometric theory
57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology
57R35: Differentiable mappings
57R40: Embeddings
57R42: Immersions
57R45: Singularities of differentiable mappings
57R50: Diffeomorphisms
57R52: Isotopy
57R55: Differentiable structures
57R56: Topological quantum field theories
57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants
57R58: Floer homology
57R60: Homotopy spheres, Poincaré conjecture
57R65: Surgery and handlebodies
57R67: Surgery obstructions, Wall groups
57R70: Critical points and critical submanifolds
57R75: O- and SO-cobordism
57R77: Complex cobordism (U- and SU-cobordism)
57R80: $h$- and $s$-cobordism
57R85: Equivariant cobordism
57R90: Other types of cobordism
57R91: Equivariant algebraic topology of manifolds
57R95: Realizing cycles by submanifolds
57R99: None of the above, but in this section 57Sxx : Topological transformation groups
57S05: Topological properties of groups of homeomorphisms or diffeomorphisms
57S10: Compact groups of homeomorphisms
57S15: Compact Lie groups of differentiable transformations
57S17: Finite transformation groups
57S20: Noncompact Lie groups of transformations
57S25: Groups acting on specific manifolds
57S30: Discontinuous groups of transformations
57S99: None of the above, but in this section 57Txx : Homology and homotopy of topological groups and related structures
57T05: Hopf algebras
57T10: Homology and cohomology of Lie groups
57T15: Homology and cohomology of homogeneous spaces of Lie groups
57T20: Homotopy groups of topological groups and homogeneous spaces
57T25: Homology and cohomology of ${H]$-spaces
57T30: Bar and cobar constructions
57T35: Applications of Eilenberg-Moore spectral sequences
57T99: None of the above, but in this section 58-xx : Global analysis, analysis on manifolds
58-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
58-01: Instructional exposition (textbooks, tutorial papers, etc.)
58-02: Research exposition (monographs, survey articles)
58-03: Historical (must also be assigned at least one classification number from Section 01)
58-04: Explicit machine computation and programs (not the theory of computation or programming)
58-06: Proceedings, conferences, collections, etc.
58Axx : General theory of differentiable manifolds
58A03: Topos-theoretic approach to differentiable manifolds
58A05: Differentiable manifolds, foundations
58A07: Real-analytic and Nash manifolds
58A10: Differential forms
58A12: de Rham theory
58A14: Hodge theory
58A15: Exterior differential systems (Cartan theory)
58A17: Pfaffian systems
58A20: Jets
58A25: Currents
58A30: Vector distributions (subbundles of the tangent bundles)
58A32: Natural bundles
58A35: Stratified sets
58A40: Differential spaces
58A50: Supermanifolds and graded manifolds
58A99: None of the above, but in this section 58Bxx : Infinite-dimensional manifolds
58B05: Homotopy and topological questions
58B10: Differentiability questions
58B12: Questions of holomorphy
58B15: Fredholm structures
58B20: Riemannian, Finsler and other geometric structures
58B25: Group structures and generalizations on infinite-dimensional manifolds
58B32: Geometry of quantum groups
58B34: Noncommutative geometry (à la Connes)
58B99: None of the above, but in this section 58Cxx : Calculus on manifolds; nonlinear operators
58C05: Real-valued functions
58C06: Set valued and function-space valued mappings
58C07: Continuity properties of mappings
58C10: Holomorphic maps
58C15: Implicit function theorems; global Newton methods
58C20: Differentiation theory (Gateaux, Fréchet, etc.)
58C25: Differentiable maps
58C30: Fixed point theorems on manifolds
58C35: Integration on manifolds; measures on manifolds
58C40: Spectral theory; eigenvalue problems
58C50: Analysis on supermanifolds or graded manifolds
58C99: None of the above, but in this section 58Dxx : Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
58D05: Groups of diffeomorphisms and homeomorphisms as manifolds
58D07: Groups and semigroups of nonlinear operators
58D10: Spaces of imbeddings and immersions
58D15: Manifolds of mappings
58D17: Manifolds of metrics (esp. Riemannian)
58D19: Group actions and symmetry properties
58D20: Measures (Gaussian, cylindrical, etc.) on manifolds of maps
58D25: Equations in function spaces; evolution equations
58D27: Moduli problems for differential geometric structures
58D29: Moduli problems for topological structures
58D30: Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
58D99: None of the above, but in this section 58Exx : Variational problems in infinite-dimensional spaces
58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
58E07: Abstract bifurcation theory
58E09: Group-invariant bifurcation theory
58E10: Applications to the theory of geodesics (problems in one independent variable)
58E11: Critical metrics
58E12: Applications to minimal surfaces (problems in two independent variables)
58E15: Application to extremal problems in several variables; Yang-Mills functionals, etc.
58E17: Pareto optimality, etc., applications to economics
58E20: Harmonic maps, etc.
58E25: Applications to control theory
58E30: Variational principles
58E35: Variational inequalities (global problems)
58E40: Group actions
58E50: Applications
58E99: None of the above, but in this section 58Hxx : Pseudogroups, differentiable groupoids and general structures on manifolds
58H05: Pseudogroups and differentiable groupoids
58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
58H15: Deformations of structures
58H99: None of the above, but in this section 58Jxx : Partial differential equations on manifolds; differential operators
58J05: Elliptic equations on manifolds, general theory
58J10: Differential complexes; elliptic complexes
58J15: Relations with hyperfunctions
58J20: Index theory and related fixed point theorems
58J22: Exotic index theories
58J26: Elliptic genera
58J28: Eta-invariants, Chern-Simons invariants
58J30: Spectral flows
58J32: Boundary value problems on manifolds
58J35: Heat and other parabolic equation methods
58J37: Perturbations; asymptotics
58J40: Pseudodifferential and Fourier integral operators on manifolds
58J42: Noncommutative global analysis, noncommutative residues
58J45: Hyperbolic equations
58J47: Propagation of singularities; initial value problems
58J50: Spectral problems; spectral geometry; scattering theory
58J52: Determinants and determinant bundles, analytic torsion
58J53: Isospectrality
58J55: Bifurcation
58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)
58J65: Diffusion processes and stochastic analysis on manifolds
58J70: Invariance and symmetry properties
58J72: Correspondences and other transformation methods (e.g. Lie-Bäcklund)
58J90: Applications
58J99: None of the above, but in this section 58Kxx : Theory of singularities and catastrophe theory
58K05: Critical points of functions and mappings
58K10: Monodromy
58K15: Topological properties of mappings
58K20: Algebraic and analytic properties of mappings
58K25: Stability
58K30: Global theory
58K35: Catastrophe theory
58K40: Classification; finite determinacy of map germs
58K45: Singularities of vector fields, topological aspects
58K50: Normal forms
58K55: Asymptotic behavior
58K60: Deformation of singularities
58K65: Topological invariants
58K70: Symmetries, equivariance
58K99: None of the above, but in this section
58Z05: Applications to physics 60-xx : Probability theory and stochastic processes
60-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
60-01: Instructional exposition (textbooks, tutorial papers, etc.)
60-02: Research exposition (monographs, survey articles)
60-03: Historical (must also be assigned at least one classification number from Section 01)
60-04: Explicit machine computation and programs (not the theory of computation or programming)
60-06: Proceedings, conferences, collections, etc.
60-08: Computational methods (not classified at a more specific level)
60Axx : Foundations of probability theory
60A05: Axioms; other general questions
60A10: Probabilistic measure theory
60A99: None of the above, but in this section 60Bxx : Probability theory on algebraic and topological structures
60B05: Probability measures on topological spaces
60B10: Convergence of probability measures
60B11: Probability theory on linear topological spaces
60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)
60B15: Probability measures on groups, Fourier transforms, factorization
60B99: None of the above, but in this section
60C05: Combinatorial probability
60D05: Geometric probability, stochastic geometry, random sets 60Exx : Distribution theory
60E05: Distributions: general theory
60E07: Infinitely divisible distributions; stable distributions
60E10: Characteristic functions; other transforms
60E15: Inequalities; stochastic orderings
60E99: None of the above, but in this section 60Fxx : Limit theorems
60F05: Central limit and other weak theorems
60F10: Large deviations
60F15: Strong theorems
60F17: Functional limit theorems; invariance principles
60F20: Zero-one laws
60F25: $L^p$-limit theorems
60F99: None of the above, but in this section 60Gxx : Stochastic processes
60G05: Foundations of stochastic processes
60G07: General theory of processes
60G09: Exchangeability
60G10: Stationary processes
60G12: General second-order processes
60G15: Gaussian processes
60G17: Sample path properties
60G18: Self-similar processes
60G20: Generalized stochastic processes
60G25: Prediction theory
60G30: Continuity and singularity of induced measures
60G35: Applications (signal detection, filtering, etc.)
60G40: Stopping times; optimal stopping problems; gambling theory
60G42: Martingales with discrete parameter
60G44: Martingales with continuous parameter
60G46: Martingales and classical analysis
60G48: Generalizations of martingales
60G50: Sums of independent random variables; random walks
60G51: Processes with independent increments
60G52: Stable processes
60G55: Point processes
60G57: Random measures
60G60: Random fields
60G70: Extreme value theory; extremal processes
60G99: None of the above, but in this section 60Hxx : Stochastic analysis
60H05: Stochastic integrals
60H07: Stochastic calculus of variations and the Malliavin calculus
60H10: Stochastic ordinary differential equations
60H15: Stochastic partial differential equations
60H20: Stochastic integral equations
60H25: Random operators and equations
60H30: Applications of stochastic analysis (to PDE, etc.)
60H35: Computational methods for stochastic equations
60H40: White noise theory
60H99: None of the above, but in this section 60Jxx : Markov processes
60J05: Markov processes with discrete parameter
60J10: Markov chains with discrete parameter
60J20: Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.)
60J22: Computational methods in Markov chains
60J25: Markov processes with continuous parameter
60J27: Markov chains with continuous parameter
60J35: Transition functions, generators and resolvents
60J40: Right processes
60J45: Probabilistic potential theory
60J50: Boundary theory
60J55: Local time and additive functionals
60J57: Multiplicative functionals
60J60: Diffusion processes
60J65: Brownian motion
60J70: Applications of diffusion theory (population genetics, absorption problems, etc.)
60J75: Jump processes
60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
60J85: Applications of branching processes
60J99: None of the above, but in this section 60Kxx : Special processes
60K05: Renewal theory
60K10: Applications (reliability, demand theory, etc.)
60K15: Markov renewal processes, semi-Markov processes
60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K25: Queueing theory
60K30: Applications (congestion, allocation, storage, traffic, etc.)
60K35: Interacting random processes; statistical mechanics type models; percolation theory
60K37: Processes in random environments
60K40: Other physical applications of random processes
60K99: None of the above, but in this section 62-xx : Statistics
62-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
62-01: Instructional exposition (textbooks, tutorial papers, etc.)
62-02: Research exposition (monographs, survey articles)
62-03: Historical (must also be assigned at least one classification number from Section 01)
62-04: Explicit machine computation and programs (not the theory of computation or programming)
62-06: Proceedings, conferences, collections, etc.
62-07: Data analysis
62-09: Graphical methods
62A01: Foundational and philosophical topics
62Bxx : Sufficiency and information
62B05: Sufficient statistics and fields
62B10: Information-theoretic topics
62B15: Theory of statistical experiments
62B99: None of the above, but in this section 62Cxx : Decision theory
62C05: General considerations
62C07: Complete class results
62C10: Bayesian problems; characterization of Bayes procedures
62C12: Empirical decision procedures; empirical Bayes procedures
62C15: Admissibility
62C20: Minimax procedures
62C25: Compound decision problems
62C99: None of the above, but in this section
62D05: Sampling theory, sample surveys 62Exx : Distribution theory
62E10: Characterization and structure theory
62E15: Exact distribution theory
62E17: Approximations to distributions (nonasymptotic)
62E20: Asymptotic distribution theory
62E99: None of the above, but in this section 62Fxx : Parametric inference
62F03: Hypothesis testing
62F05: Asymptotic properties of tests
62F07: Ranking and selection
62F10: Point estimation
62F12: Asymptotic properties of estimators
62F15: Bayesian inference
62F25: Tolerance and confidence regions
62F30: Inference under constraints
62F35: Robustness and adaptive procedures
62F40: Bootstrap, jackknife and other resampling methods
62F99: None of the above, but in this section 62Gxx : Nonparametric inference
62G05: Estimation
62G07: Density estimation
62G08: Nonparametric regression
62G09: Resampling methods
62G10: Hypothesis testing
62G15: Tolerance and confidence regions
62G20: Asymptotic properties
62G30: Order statistics; empirical distribution functions
62G32: Statistics of extreme values; tail inference
62G35: Robustness
62G99: None of the above, but in this section 62Hxx : Multivariate analysis
62H05: Characterization and structure theory
62H10: Distribution of statistics
62H11: Directional data; spatial statistics
62H12: Estimation
62H15: Hypothesis testing
62H17: Contingency tables
62H20: Measures of association (correlation, canonical correlation, etc.)
62H25: Factor analysis and principal components; correspondence analysis
62H30: Classification and discrimination; cluster analysis
62H35: Image analysis
62H99: None of the above, but in this section 62Jxx : Linear inference, regression
62J02: General nonlinear regression
62J05: Linear regression
62J07: Ridge regression; shrinkage estimators
62J10: Analysis of variance and covariance
62J12: Generalized linear models
62J15: Paired and multiple comparisons
62J20: Diagnostics
62J99: None of the above, but in this section 62Kxx : Design of experiments
62K05: Optimal designs
62K10: Block designs
62K15: Factorial designs
62K20: Response surface designs
62K25: Robust parameter designs
62K99: None of the above, but in this section 62Lxx : Sequential methods
62L05: Sequential design
62L10: Sequential analysis
62L12: Sequential estimation
62L15: Optimal stopping
62L20: Stochastic approximation
62L99: None of the above, but in this section 62Mxx : Inference from stochastic processes
62M02: Markov processes: hypothesis testing
62M05: Markov processes: estimation
62M07: Non-Markovian processes: hypothesis testing
62M09: Non-Markovian processes: estimation
62M10: Time series, auto-correlation, regression, etc.
62M15: Spectral analysis
62M20: Prediction; filtering
62M30: Spatial processes
62M40: Random fields; image analysis
62M45: Neural nets and related approaches
62M99: None of the above, but in this section 62Nxx : Survival analysis and censored data
62N01: Censored data models
62N02: Estimation
62N03: Testing
62N05: Reliability and life testing
62N99: None of the above, but in this section 62Pxx : Applications
62P05: Applications to actuarial sciences and financial mathematics
62P10: Applications to biology and medical sciences
62P12: Applications to environmental and related topics
62P15: Applications to psychology
62P20: Applications to economics
62P25: Applications to social sciences
62P30: Applications in engineering and industry
62P35: Applications to physics
62P99: None of the above, but in this section
62Q05: Statistical tables 65-xx : Numerical analysis
65-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
65-01: Instructional exposition (textbooks, tutorial papers, etc.)
65-02: Research exposition (monographs, survey articles)
65-03: Historical (must also be assigned at least one classification number from Section 01)
65-04: Explicit machine computation and programs (not the theory of computation or programming)
65-05: Experimental papers
65-06: Proceedings, conferences, collections, etc.
65Bxx : Acceleration of convergence
65B05: Extrapolation to the limit, deferred corrections
65B10: Summation of series
65B15: Euler-Maclaurin formula
65B99: None of the above, but in this section 65Cxx : Probabilistic methods, simulation and stochastic differential equations
65C05: Monte Carlo methods
65C10: Random number generation
65C20: Models, numerical methods
65C30: Stochastic differential and integral equations
65C35: Stochastic particle methods
65C40: Computational Markov chains
65C50: Other computational problems in probability
65C60: Computational problems in statistics
65C99: None of the above, but in this section 65Dxx : Numerical approximation and computational geometry {Primarily algorithms; for theory, see 41-XX and 68Uxx]
65D05: Interpolation
65D07: Splines
65D10: Smoothing, curve fitting
65D15: Algorithms for functional approximation
65D17: Computer aided design (modeling of curves and surfaces)
65D18: Computer graphics and computational geometry
65D20: Computation of special functions, construction of tables
65D25: Numerical differentiation
65D30: Numerical integration
65D32: Quadrature and cubature formulas
65D99: None of the above, but in this section
65E05: Numerical methods in complex analysis (potential theory, etc.) 65Fxx : Numerical linear algebra
65F05: Direct methods for linear systems and matrix inversion
65F10: Iterative methods for linear systems
65F15: Eigenvalues, eigenvectors
65F18: Inverse eigenvalue problems
65F20: Overdetermined systems, pseudoinverses
65F22: Ill-posedness, regularization
65F25: Orthogonalization
65F30: Other matrix algorithms
65F35: Matrix norms, conditioning, scaling
65F40: Determinants
65F50: Sparse matrices
65F99: None of the above, but in this section 65Gxx : Error analysis and interval analysis
65G20: Algorithms with automatic result verification
65G30: Interval and finite arithmetic
65G40: General methods in interval analysis
65G50: Roundoff error
65G99: None of the above, but in this section 65Hxx : Nonlinear algebraic or transcendental equations
65H05: Single equations
65H10: Systems of equations
65H17: Eigenvalues, eigenvectors
65H20: Global methods, including homotopy approaches
65H99: None of the above, but in this section 65Jxx : Numerical analysis in abstract spaces
65J05: General theory
65J10: Equations with linear operators (do not use 65Fxx)
65J15: Equations with nonlinear operators (do not use 65Hxx)
65J20: Improperly posed problems; regularization
65J22: Inverse problems
65J99: None of the above, but in this section 65Kxx : Mathematical programming, optimization and variational techniques
65K05: Mathematical programming {Algorithms; for theory see 90Cxx]
65K10: Optimization and variational techniques
65K99: None of the above, but in this section 65Lxx : Ordinary differential equations
65L05: Initial value problems
65L06: Multistep, Runge-Kutta and extrapolation methods
65L07: Numerical investigation of stability of solutions
65L08: Improperly posed problems
65L09: Inverse problems
65L10: Boundary value problems
65L12: Finite difference methods
65L15: Eigenvalue problems
65L20: Stability and convergence of numerical methods
65L50: Mesh generation and refinement
65L60: Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
65L70: Error bounds
65L80: Methods for differential-algebraic equations
65L99: None of the above, but in this section 65Mxx : Partial differential equations, initial value and time-dependent initial-boundary value problems
65M06: Finite difference methods
65M12: Stability and convergence of numerical methods
65M15: Error bounds
65M20: Method of lines
65M25: Method of characteristics
65M30: Improperly posed problems
65M32: Inverse problems
65M50: Mesh generation and refinement
65M55: Multigrid methods; domain decomposition
65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65M70: Spectral, collocation and related methods
65M99: None of the above, but in this section 65Nxx : Partial differential equations, boundary value problems
65N06: Finite difference methods
65N12: Stability and convergence of numerical methods
65N15: Error bounds
65N21: Inverse problems
65N22: Solution of discretized equations
65N25: Eigenvalue problems
65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65N35: Spectral, collocation and related methods
65N38: Boundary element methods
65N40: Method of lines
65N45: Method of contraction of the boundary
65N50: Mesh generation and refinement
65N55: Multigrid methods; domain decomposition
65N99: None of the above, but in this section 65Pxx : Numerical problems in dynamical systems
65P10: Hamiltonian systems including symplectic integrators
65P20: Numerical chaos
65P30: Bifurcation problems
65P40: Nonlinear stabilities
65P99: None of the above, but in this section
65Q05: Difference and functional equations, recurrence relations 65Rxx : Integral equations, integral transforms
65R10: Integral transforms
65R20: Integral equations
65R30: Improperly posed problems
65R32: Inverse problems
65R99: None of the above, but in this section
65S05: Graphical methods 65Txx : Numerical methods in Fourier analysis
65T40: Trigonometric approximation and interpolation
65T50: Discrete and fast Fourier transforms
65T60: Wavelets
65T99: None of the above, but in this section 65Yxx : Computer aspects of numerical algorithms
65Y05: Parallel computation
65Y10: Algorithms for specific classes of architectures
65Y15: Packaged methods
65Y20: Complexity and performance of numerical algorithms
65Y99: None of the above, but in this section
65Z05: Applications to physics 68-xx : Computer science
68-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
68-01: Instructional exposition (textbooks, tutorial papers, etc.)
68-02: Research exposition (monographs, survey articles)
68-03: Historical (must also be assigned at least one classification number from Section 01)
68-04: Explicit machine computation and programs (not the theory of computation or programming)
68-06: Proceedings, conferences, collections, etc.
68Mxx : Computer system organization
68M01: General
68M07: Mathematical problems of computer architecture
68M10: Network design and communication
68M12: Network protocols
68M14: Distributed systems
68M15: Reliability, testing and fault tolerance
68M20: Performance evaluation; queueing; scheduling
68M99: None of the above, but in this section 68Nxx : Software
68N01: General
68N15: Programming languages
68N17: Logic programming
68N18: Functional programming and lambda calculus
68N19: Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
68N20: Compilers and interpreters
68N25: Operating systems
68N30: Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
68N99: None of the above, but in this section 68Pxx : Theory of data
68P01: General
68P05: Data structures
68P10: Searching and sorting
68P15: Database theory
68P20: Information storage and retrieval
68P25: Data encryption
68P30: Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.)
68P99: None of the above, but in this section 68Qxx : Theory of computing
68Q01: General
68Q05: Models of computation (Turing machines, etc.)
68Q10: Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
68Q15: Complexity classes (hierarchies, relations among complexity classes, etc.)
68Q17: Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
68Q19: Descriptive complexity and finite models
68Q25: Analysis of algorithms and problem complexity
68Q30: Algorithmic information theory (Kolmogorov complexity, etc.)
68Q32: Computational learning theory
68Q42: Grammars and rewriting systems
68Q45: Formal languages and automata
68Q55: Semantics
68Q60: Specification and verification (program logics, model checking, etc.)
68Q65: Abstract data types; algebraic specification
68Q70: Algebraic theory of languages and automata
68Q80: Cellular automata
68Q85: Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q99: None of the above, but in this section 68Rxx : Discrete mathematics in relation to computer science
68R01: General
68R05: Combinatorics
68R10: Graph theory
68R15: Combinatorics on words
68R99: None of the above, but in this section 68Txx : Artificial intelligence
68T01: General
68T05: Learning and adaptive systems
68T10: Pattern recognition, speech recognition
68T15: Theorem proving (deduction, resolution, etc.)
68T20: Problem solving (heuristics, search strategies, etc.)
68T27: Logic in artificial intelligence
68T30: Knowledge representation
68T35: Languages and software systems (knowledge-based systems, expert systems, etc.)
68T37: Reasoning under uncertainty
68T40: Robotics
68T45: Machine vision and scene understanding
68T50: Natural language processing
68T99: None of the above, but in this section 68Uxx : Computing methodologies and applications
68U01: General
68U05: Computer graphics; computational geometry
68U07: Computer-aided design
68U10: Image processing
68U15: Text processing; mathematical typography
68U20: Simulation
68U35: Information systems (hypertext navigation, interfaces, decision support, etc.)
68U99: None of the above, but in this section 68Wxx : Algorithms
68W01: General
68W05: Nonnumerical algorithms
68W10: Parallel algorithms
68W15: Distributed algorithms
68W20: Randomized algorithms
68W25: Approximation algorithms
68W30: Symbolic computation and algebraic computation
68W35: VLSI algorithms
68W40: Analysis of algorithms
68W99: None of the above, but in this section 70-xx : Mechanics of particles and systems
70-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
70-01: Instructional exposition (textbooks, tutorial papers, etc.)
70-02: Research exposition (monographs, survey articles)
70-03: Historical (must also be assigned at least one classification number from Section 01)
70-04: Explicit machine computation and programs (not the theory of computation or programming)
70-05: Experimental work
70-06: Proceedings, conferences, collections, etc.
70-08: Computational methods
70A05: Axiomatics, foundations
70Bxx : Kinematics
70B05: Kinematics of a particle
70B10: Kinematics of a rigid body
70B15: Mechanisms, robots
70B99: None of the above, but in this section
70C20: Statics 70Exx : Dynamics of a rigid body and of multibody systems
70E05: Motion of the gyroscope
70E15: Free motion of a rigid body
70E17: Motion of a rigid body with a fixed point
70E18: Motion of a rigid body in contact with a solid surface
70E20: Perturbation methods for rigid body dynamics
70E40: Integrable cases of motion
70E45: Higher-dimensional generalizations
70E50: Stability problems
70E55: Dynamics of multibody systems
70E60: Robot dynamics and control
70E99: None of the above, but in this section 70Fxx : Dynamics of a system of particles, including celestial mechanics
70F05: Two-body problems
70F07: Three-body problems
70F10: $n$-body problems
70F15: Celestial mechanics
70F16: Collisions in celestial mechanics, regularization
70F17: Inverse problems
70F20: Holonomic systems
70F25: Nonholonomic systems
70F35: Collision of rigid or pseudo-rigid bodies
70F40: Problems with friction
70F45: Infinite particle systems
70F99: None of the above, but in this section 70Gxx : General models, approaches, and methods
70G10: Generalized coordinates; event, impulse-energy, configuration, state, or phase space
70G40: Topological and differential-topological methods
70G45: Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.)
70G55: Algebraic geometry methods
70G60: Dynamical systems methods
70G65: Symmetries, Lie-group and Lie-algebra methods
70G70: Functional-analytic methods
70G75: Variational methods
70G99: None of the above, but in this section 70Hxx : Hamiltonian and Lagrangian mechanics
70H03: Lagrange's equations
70H05: Hamilton's equations
70H06: Completely integrable systems and methods of integration
70H07: Nonintegrable systems
70H08: Nearly integrable Hamiltonian systems, KAM theory
70H09: Perturbation theories
70H11: Adiabatic invariants
70H12: Periodic and almost periodic solutions
70H14: Stability problems
70H15: Canonical and symplectic transformations
70H20: Hamilton-Jacobi equations
70H25: Hamilton's principle
70H30: Other variational principles
70H33: Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
70H40: Relativistic dynamics
70H45: Constrained dynamics, Dirac's theory of constraints
70H50: Higher-order theories
70H99: None of the above, but in this section 70Jxx : Linear vibration theory
70J10: Modal analysis
70J25: Stability
70J30: Free motions
70J35: Forced motions
70J40: Parametric resonances
70J50: Systems arising from the discretization of structural vibration problems
70J99: None of the above, but in this section 70Kxx : Nonlinear dynamics
70K05: Phase plane analysis, limit cycles
70K20: Stability
70K25: Free motions
70K28: Parametric resonances
70K30: Nonlinear resonances
70K40: Forced motions
70K42: Equilibria and periodic trajectories
70K43: Quasi-periodic motions and invariant tori
70K44: Homoclinic and heteroclinic trajectories
70K45: Normal forms
70K50: Bifurcations and instability
70K55: Transition to stochasticity (chaotic behavior)
70K60: General perturbation schemes
70K65: Averaging of perturbations
70K70: Systems with slow and fast motions
70K75: Nonlinear modes
70K99: None of the above, but in this section
70L05: Random vibrations
70M20: Orbital mechanics
70P05: Variable mass, rockets
70Q05: Control of mechanical systems 70Sxx : Classical field theories
70S05: Lagrangian formalism and Hamiltonian formalism
70S10: Symmetries and conservation laws
70S15: Yang-Mills and other gauge theories
70S20: More general nonquantum field theories
70S99: None of the above, but in this section 74-xx : Mechanics of deformable solids
74-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
74-01: Instructional exposition (textbooks, tutorial papers, etc.)
74-02: Research exposition (monographs, survey articles)
74-03: Historical (must also be assigned at least one classification number from Section 01)
74-04: Explicit machine computation and programs (not the theory of computation or programming)
74-05: Experimental work
74-06: Proceedings, conferences, collections, etc.
74Axx : Generalities, axiomatics, foundations of continuum mechanics of solids
74A05: Kinematics of deformation
74A10: Stress
74A15: Thermodynamics
74A20: Theory of constitutive functions
74A25: Molecular, statistical, and kinetic theories
74A30: Nonsimple materials
74A35: Polar materials
74A40: Random materials and composite materials
74A45: Theories of fracture and damage
74A50: Structured surfaces and interfaces, coexistent phases
74A55: Theories of friction (tribology)
74A60: Micromechanical theories
74A65: Reactive materials
74A99: None of the above, but in this section 74Bxx : Elastic materials
74B05: Classical linear elasticity
74B10: Linear elasticity with initial stresses
74B15: Equations linearized about a deformed state (small deformations superposed on large)
74B20: Nonlinear elasticity
74B99: None of the above, but in this section 74Cxx : Plastic materials, materials of stress-rate and internal-variable type
74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74C10: Small-strain, rate-dependent theories (including theories of viscoplasticity)
74C15: Large-strain, rate-independent theories (including nonlinear plasticity)
74C20: Large-strain, rate-dependent theories
74C99: None of the above, but in this section 74Dxx : Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74D05: Linear constitutive equations
74D10: Nonlinear constitutive equations
74D99: None of the above, but in this section 74Exx : Material properties given special treatment
74E05: Inhomogeneity
74E10: Anisotropy
74E15: Crystalline structure
74E20: Granularity
74E25: Texture
74E30: Composite and mixture properties
74E35: Random structure
74E40: Chemical structure
74E99: None of the above, but in this section 74Fxx : Coupling of solid mechanics with other effects
74F05: Thermal effects
74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F15: Electromagnetic effects
74F20: Mixture effects
74F25: Chemical and reactive effects
74F99: None of the above, but in this section 74Gxx : Equilibrium (steady-state) problems
74G05: Explicit solutions
74G10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
74G15: Numerical approximation of solutions
74G20: Local existence of solutions (near a given solution)
74G25: Global existence of solutions
74G30: Uniqueness of solutions
74G35: Multiplicity of solutions
74G40: Regularity of solutions
74G45: Bounds for solutions
74G50: Saint-Venant's principle
74G55: Qualitative behavior of solutions
74G60: Bifurcation and buckling
74G65: Energy minimization
74G70: Stress concentrations, singularities
74G75: Inverse problems
74G99: None of the above, but in this section 74Hxx : Dynamical problems
74H05: Explicit solutions
74H10: Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
74H15: Numerical approximation of solutions
74H20: Existence of solutions
74H25: Uniqueness of solutions
74H30: Regularity of solutions
74H35: Singularities, blowup, stress concentrations
74H40: Long-time behavior of solutions
74H45: Vibrations
74H50: Random vibrations
74H55: Stability
74H60: Dynamical bifurcation
74H65: Chaotic behavior
74H99: None of the above, but in this section 74Jxx : Waves
74J05: Linear waves
74J10: Bulk waves
74J15: Surface waves
74J20: Wave scattering
74J25: Inverse problems
74J30: Nonlinear waves
74J35: Solitary waves
74J40: Shocks and related discontinuities
74J99: None of the above, but in this section 74Kxx : Thin bodies, structures
74K05: Strings
74K10: Rods (beams, columns, shafts, arches, rings, etc.)
74K15: Membranes
74K20: Plates
74K25: Shells
74K30: Junctions
74K35: Thin films
74K99: None of the above, but in this section 74Lxx : Special subfields of solid mechanics
74L05: Geophysical solid mechanics
74L10: Soil and rock mechanics
74L15: Biomechanical solid mechanics
74L99: None of the above, but in this section 74Mxx : Special kinds of problems
74M05: Control, switches and devices (``smart materials'')
74M10: Friction
74M15: Contact
74M20: Impact
74M25: Micromechanics
74M99: None of the above, but in this section 74Nxx : Phase transformations in solids
74N05: Crystals
74N10: Displacive transformations
74N15: Analysis of microstructure
74N20: Dynamics of phase boundaries
74N25: Transformations involving diffusion
74N30: Problems involving hysteresis
74N99: None of the above, but in this section 74Pxx : Optimization
74P05: Compliance or weight optimization
74P10: Optimization of other properties
74P15: Topological methods
74P20: Geometrical methods
74P99: None of the above, but in this section 74Qxx : Homogenization, determination of effective properties
74Q05: Homogenization in equilibrium problems
74Q10: Homogenization and oscillations in dynamical problems
74Q15: Effective constitutive equations
74Q20: Bounds on effective properties
74Q99: None of the above, but in this section 74Rxx : Fracture and damage
74R05: Brittle damage
74R10: Brittle fracture
74R15: High-velocity fracture
74R20: Anelastic fracture and damage
74R99: None of the above, but in this section 74Sxx : Numerical methods
74S05: Finite element methods
74S10: Finite volume methods
74S15: Boundary element methods
74S20: Finite difference methods
74S25: Spectral and related methods
74S30: Other numerical methods
74S99: None of the above, but in this section 76-xx : Fluid mechanics
76-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
76-01: Instructional exposition (textbooks, tutorial papers, etc.)
76-02: Research exposition (monographs, survey articles)
76-03: Historical (must also be assigned at least one classification number from Section 01)
76-04: Explicit machine computation and programs (not the theory of computation or programming)
76-05: Experimental work
76-06: Proceedings, conferences, collections, etc.
76Axx : Foundations, constitutive equations, rheology
76A02: Foundations of fluid mechanics
76A05: Non-Newtonian fluids
76A10: Viscoelastic fluids
76A15: Liquid crystals
76A20: Thin fluid films
76A25: Superfluids (classical aspects)
76A99: None of the above, but in this section 76Bxx : Incompressible inviscid fluids
76B03: Existence, uniqueness, and regularity theory
76B07: Free-surface potential flows
76B10: Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B20: Ship waves
76B25: Solitary waves
76B45: Capillarity (surface tension)
76B47: Vortex flows
76B55: Internal waves
76B60: Atmospheric waves
76B65: Rossby waves
76B70: Stratification effects in inviscid fluids
76B75: Flow control and optimization
76B99: None of the above, but in this section 76Dxx : Incompressible viscous fluids
76D03: Existence, uniqueness, and regularity theory
76D05: Navier-Stokes equations
76D06: Statistical solutions of Navier-Stokes and related equations
76D07: Stokes and related (Oseen, etc.) flows
76D08: Lubrication theory
76D09: Viscous-inviscid interaction
76D10: Boundary-layer theory, separation and reattachment, higher-order effects
76D17: Viscous vortex flows
76D25: Wakes and jets
76D27: Other free-boundary flows; Hele-Shaw flows
76D33: Waves
76D45: Capillarity (surface tension)
76D50: Stratification effects in viscous fluids
76D55: Flow control and optimization
76D99: None of the above, but in this section 76Exx : Hydrodynamic stability
76E05: Parallel shear flows
76E06: Convection
76E07: Rotation
76E09: Stability and instability of nonparallel flows
76E15: Absolute and convective instability and stability
76E17: Interfacial stability and instability
76E19: Compressibility effects
76E20: Stability and instability of geophysical and astrophysical flows
76E25: Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30: Nonlinear effects
76E99: None of the above, but in this section 76Fxx : Turbulence
76F02: Fundamentals
76F05: Isotropic turbulence; homogeneous turbulence
76F06: Transition to turbulence
76F10: Shear flows
76F20: Dynamical systems approach to turbulence
76F25: Turbulent transport, mixing
76F30: Renormalization and other field-theoretical methods
76F35: Convective turbulence
76F40: Turbulent boundary layers
76F45: Stratification effects
76F50: Compressibility effects
76F55: Statistical turbulence modeling
76F60: $k$-$\varepsilon$ modeling
76F65: Direct numerical and large eddy simulation of turbulence
76F70: Control of turbulent flows
76F99: None of the above, but in this section
76G25: General aerodynamics and subsonic flows
76H05: Transonic flows
76J20: Supersonic flows
76K05: Hypersonic flows
76L05: Shock waves and blast waves 76Mxx : Basic methods in fluid mechanics
76M10: Finite element methods
76M12: Finite volume methods
76M15: Boundary element methods
76M20: Finite difference methods
76M22: Spectral methods
76M23: Vortex methods
76M25: Other numerical methods
76M27: Visualization algorithms
76M28: Particle methods and lattice-gas methods
76M30: Variational methods
76M35: Stochastic analysis
76M40: Complex-variables methods
76M45: Asymptotic methods, singular perturbations
76M50: Homogenization
76M55: Dimensional analysis and similarity
76M60: Symmetry analysis, Lie group and algebra methods
76M99: None of the above, but in this section 76Nxx : Compressible fluids and gas dynamics, general
76N10: Existence, uniqueness, and regularity theory
76N15: Gas dynamics, general
76N17: Viscous-inviscid interaction
76N20: Boundary-layer theory
76N25: Flow control and optimization
76N99: None of the above, but in this section
76P05: Rarefied gas flows, Boltzmann equation
76Q05: Hydro- and aero-acoustics 76Rxx : Diffusion and convection
76R05: Forced convection
76R10: Free convection
76R50: Diffusion
76R99: None of the above, but in this section
76S05: Flows in porous media; filtration; seepage 76Txx : Two-phase and multiphase flows
76T10: Liquid-gas two-phase flows, bubbly flows
76T15: Dusty-gas two-phase flows
76T20: Suspensions
76T25: Granular flows
76T30: Three or more component flows
76T99: None of the above, but in this section
76U05: Rotating fluids
76V05: Reaction effects in flows
76W05: Magnetohydrodynamics and electrohydrodynamics
76X05: Ionized gas flow in electromagnetic fields; plasmic flow
76Y05: Quantum hydrodynamics and relativistic hydrodynamics 76Zxx : Biological fluid mechanics
76Z05: Physiological flows
76Z10: Biopropulsion in water and in air
76Z99: None of the above, but in this section 78-xx : Optics, electromagnetic theory
78-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
78-01: Instructional exposition (textbooks, tutorial papers, etc.)
78-02: Research exposition (monographs, survey articles)
78-03: Historical (must also be assigned at least one classification number from Section 01)
78-04: Explicit machine computation and programs (not the theory of computation or programming)
78-05: Experimental work
78-06: Proceedings, conferences, collections, etc.
78Axx : General
78A02: Foundations
78A05: Geometric optics
78A10: Physical optics
78A15: Electron optics
78A20: Space charge waves
78A25: Electromagnetic theory, general
78A30: Electro- and magnetostatics
78A35: Motion of charged particles
78A40: Waves and radiation
78A45: Diffraction, scattering
78A46: Inverse scattering problems
78A48: Composite media; random media
78A50: Antennas, wave-guides
78A55: Technical applications
78A60: Lasers, masers, optical bistability, nonlinear optics
78A70: Biological applications
78A97: Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
78A99: Miscellaneous topics 78Mxx : Basic methods
78M05: Method of moments
78M10: Finite element methods
78M15: Boundary element methods
78M20: Finite difference methods
78M25: Other numerical methods
78M30: Variational methods
78M35: Asymptotic analysis
78M40: Homogenization
78M50: Optimization
78M99: None of the above, but in this section 80-xx : Classical thermodynamics, heat transfer
80-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
80-01: Instructional exposition (textbooks, tutorial papers, etc.)
80-02: Research exposition (monographs, survey articles)
80-03: Historical (must also be assigned at least one classification number from Section 01)
80-04: Explicit machine computation and programs (not the theory of computation or programming)
80-05: Experimental work
80-06: Proceedings, conferences, collections, etc.
80Axx : Thermodynamics and heat transfer
80A05: Foundations
80A10: Classical thermodynamics, including relativistic
80A17: Thermodynamics of continua
80A20: Heat and mass transfer, heat flow
80A22: Stefan problems, phase changes, etc.
80A23: Inverse problems
80A25: Combustion
80A30: Chemical kinetics
80A32: Chemically reacting flows
80A50: Chemistry (general)
80A99: None of the above, but in this section 80Mxx : Basic methods
80M10: Finite element methods
80M15: Boundary element methods
80M20: Finite difference methods
80M25: Other numerical methods
80M30: Variational methods
80M35: Asymptotic analysis
80M40: Homogenization
80M50: Optimization
80M99: None of the above, but in this section 81-xx : Quantum theory
81-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
81-01: Instructional exposition (textbooks, tutorial papers, etc.)
81-02: Research exposition (monographs, survey articles)
81-03: Historical (must also be assigned at least one classification number from Section 01)
81-04: Explicit machine computation and programs (not the theory of computation or programming)
81-05: Experimental papers
81-06: Proceedings, conferences, collections, etc.
81-08: Computational methods
81Pxx : Axiomatics, foundations, philosophy
81P05: General and philosophical
81P10: Logical foundations of quantum mechanics; quantum logic
81P15: Quantum measurement theory
81P20: Stochastic mechanics (including stochastic electrodynamics)
81P68: Quantum computation and quantum cryptography
81P99: None of the above, but in this section 81Qxx : General mathematical topics and methods in quantum theory
81Q05: Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations
81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
81Q15: Perturbation theories for operators and differential equations
81Q20: Semiclassical techniques including WKB and Maslov methods
81Q30: Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81Q40: Bethe-Salpeter and other integral equations
81Q50: Quantum chaos
81Q60: Supersymmetric quantum mechanics
81Q70: Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
81Q99: None of the above, but in this section 81Rxx : Groups and algebras in quantum theory
81R05: Finite-dimensional groups and algebras motivated by physics and their representations
81R10: Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations
81R12: Relations with integrable systems
81R15: Operator algebra methods
81R20: Covariant wave equations
81R25: Spinor and twistor methods
81R30: Coherent states; squeezed states
81R40: Symmetry breaking
81R50: Quantum groups and related algebraic methods
81R60: Noncommutative geometry
81R99: None of the above, but in this section 81Sxx : General quantum mechanics and problems of quantization
81S05: Commutation relations and statistics
81S10: Geometry and quantization, symplectic methods
81S20: Stochastic quantization
81S25: Quantum stochastic calculus
81S30: Phase space methods including Wigner distributions, etc.
81S40: Path integrals
81S99: None of the above, but in this section 81Txx : Quantum field theory; related classical field theories
81T05: Axiomatic quantum field theory; operator algebras
81T08: Constructive quantum field theory
81T10: Model quantum field theories
81T13: Yang-Mills and other gauge theories
81T15: Perturbative methods of renormalization
81T16: Nonperturbative methods of renormalization
81T17: Renormalization group methods
81T18: Feynman diagrams
81T20: Quantum field theory on curved space backgrounds
81T25: Quantum field theory on lattices
81T27: Continuum limits
81T30: String and superstring theories; other extended objects (e.g., branes)
81T40: Two-dimensional field theories, conformal field theories, etc.
81T45: Topological field theories
81T50: Anomalies
81T60: Supersymmetric field theories
81T70: Quantization in field theory; cohomological methods
81T75: Noncommutative geometry methods
81T80: Simulation and numerical modeling
81T99: None of the above, but in this section 81Uxx : Scattering theory
81U05: $2$-body potential scattering theory
81U10: $n$-body potential scattering theory
81U15: Exactly and quasi-solvable systems
81U20: $S$-matrix theory, etc.
81U30: Dispersion theory, dispersion relations
81U40: Inverse scattering problems
81U99: None of the above, but in this section 81Vxx : Applications to specific physical systems
81V05: Strong interaction, including quantum chromodynamics
81V10: Electromagnetic interaction; quantum electrodynamics
81V15: Weak interaction
81V17: Gravitational interaction
81V19: Other fundamental interactions
81V22: Unified theories
81V25: Other elementary particle theory
81V35: Nuclear physics
81V45: Atomic physics
81V55: Molecular physics
81V70: Many-body theory; quantum Hall effect
81V80: Quantum optics
81V99: None of the above, but in this section 82-xx : Statistical mechanics, structure of matter
82-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
82-01: Instructional exposition (textbooks, tutorial papers, etc.)
82-02: Research exposition (monographs, survey articles)
82-03: Historical (must also be assigned at least one classification number from Section 01)
82-04: Explicit machine computation and programs (not the theory of computation or programming)
82-05: Experimental papers
82-06: Proceedings, conferences, collections, etc.
82-08: Computational methods
82Bxx : Equilibrium statistical mechanics
82B03: Foundations
82B05: Classical equilibrium statistical mechanics (general)
82B10: Quantum equilibrium statistical mechanics (general)
82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B21: Continuum models (systems of particles, etc.)
82B23: Exactly solvable models; Bethe ansatz
82B24: Interface problems; diffusion-limited aggregation
82B26: Phase transitions (general)
82B27: Critical phenomena
82B28: Renormalization group methods
82B30: Statistical thermodynamics
82B31: Stochastic methods
82B35: Irreversible thermodynamics, including Onsager-Machlup theory
82B40: Kinetic theory of gases
82B41: Random walks, random surfaces, lattice animals, etc.
82B43: Percolation
82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
82B80: Numerical methods (Monte Carlo, series resummation, etc.)
82B99: None of the above, but in this section 82Cxx : Time-dependent statistical mechanics (dynamic and nonequilibrium)
82C03: Foundations
82C05: Classical dynamic and nonequilibrium statistical mechanics (general)
82C10: Quantum dynamics and nonequilibrium statistical mechanics (general)
82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
82C21: Dynamic continuum models (systems of particles, etc.)
82C22: Interacting particle systems
82C23: Exactly solvable dynamic models
82C24: Interface problems; diffusion-limited aggregation
82C26: Dynamic and nonequilibrium phase transitions (general)
82C27: Dynamic critical phenomena
82C28: Dynamic renormalization group methods
82C31: Stochastic methods (Fokker-Planck, Langevin, etc.)
82C32: Neural nets
82C35: Irreversible thermodynamics, including Onsager-Machlup theory
82C40: Kinetic theory of gases
82C41: Dynamics of random walks, random surfaces, lattice animals, etc.
82C43: Time-dependent percolation
82C44: Dynamics of disordered systems (random Ising systems, etc.)
82C70: Transport processes
82C80: Numerical methods (Monte Carlo, series resummation, etc.)
82C99: None of the above, but in this section 82Dxx : Applications to specific types of physical systems
82D05: Gases
82D10: Plasmas
82D15: Liquids
82D20: Solids
82D25: Crystals
82D30: Random media, disordered materials (including liquid crystals and spin glasses)
82D35: Metals
82D37: Semiconductors
82D40: Magnetic materials
82D45: Ferroelectrics
82D50: Superfluids
82D55: Superconductors
82D60: Polymers
82D75: Nuclear reactor theory; neutron transport
82D99: None of the above, but in this section 83-xx : Relativity and gravitational theory
83-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
83-01: Instructional exposition (textbooks, tutorial papers, etc.)
83-02: Research exposition (monographs, survey articles)
83-03: Historical (must also be assigned at least one classification number from Section 01)
83-04: Explicit machine computation and programs (not the theory of computation or programming)
83-05: Experimental work
83-06: Proceedings, conferences, collections, etc.
83-08: Computational methods
83A05: Special relativity
83B05: Observational and experimental questions
83Cxx : General relativity
83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)
83C10: Equations of motion
83C15: Exact solutions
83C20: Classes of solutions; algebraically special solutions, metrics with symmetries
83C22: Einstein-Maxwell equations
83C25: Approximation procedures, weak fields
83C27: Lattice gravity, Regge calculus and other discrete methods
83C30: Asymptotic procedures (radiation, news functions, {\scr H]-spaces, etc.)
83C35: Gravitational waves
83C40: Gravitational energy and conservation laws; groups of motions
83C45: Quantization of the gravitational field
83C47: Methods of quantum field theory
83C50: Electromagnetic fields
83C55: Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C57: Black holes
83C60: Spinor and twistor methods; Newman-Penrose formalism
83C65: Methods of noncommutative geometry
83C75: Space-time singularities, cosmic censorship, etc.
83C80: Analogues in lower dimensions
83C99: None of the above, but in this section
83D05: Relativistic gravitational theories other than Einstein's, including asymmetric field theories 83Exx : Unified, higher-dimensional and super field theories
83E05: Geometrodynamics
83E15: Kaluza-Klein and other higher-dimensional theories
83E30: String and superstring theories
83E50: Supergravity
83E99: None of the above, but in this section
83F05: Cosmology 85-xx : Astronomy and astrophysics
85-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
85-01: Instructional exposition (textbooks, tutorial papers, etc.)
85-02: Research exposition (monographs, survey articles)
85-03: Historical (must also be assigned at least one classification number from Section 01)
85-04: Explicit machine computation and programs (not the theory of computation or programming)
85-05: Experimental work
85-06: Proceedings, conferences, collections, etc.
85-08: Computational methods
85A04: General
85A05: Galactic and stellar dynamics
85A15: Galactic and stellar structure
85A20: Planetary atmospheres
85A25: Radiative transfer
85A30: Hydrodynamic and hydromagnetic problems
85A35: Statistical astronomy
85A40: Cosmology
85A99: Miscellaneous topics 86-xx : Geophysics
86-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
86-01: Instructional exposition (textbooks, tutorial papers, etc.)
86-02: Research exposition (monographs, survey articles)
86-03: Historical (must also be assigned at least one classification number from Section 01)
86-04: Explicit machine computation and programs (not the theory of computation or programming)
86-05: Experimental work
86-06: Proceedings, conferences, collections, etc.
86-08: Computational methods
86A04: General
86A05: Hydrology, hydrography, oceanography
86A10: Meteorology and atmospheric physics
86A15: Seismology
86A17: Global dynamics, earthquake problems
86A20: Potentials, prospecting
86A22: Inverse problems
86A25: Geo-electricity and geomagnetism
86A30: Geodesy, mapping problems
86A32: Geostatistics
86A40: Glaciology
86A60: Geological problems
86A99: Miscellaneous topics 90-xx : Operations research, mathematical programming
90-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
90-01: Instructional exposition (textbooks, tutorial papers, etc.)
90-02: Research exposition (monographs, survey articles)
90-03: Historical (must also be assigned at least one classification number from Section 01)
90-04: Explicit machine computation and programs (not the theory of computation or programming)
90-06: Proceedings, conferences, collections, etc.
90-08: Computational methods
90Bxx : Operations research and management science
90B05: Inventory, storage, reservoirs
90B06: Transportation, logistics
90B10: Network models, deterministic
90B15: Network models, stochastic
90B18: Communication networks
90B20: Traffic problems
90B22: Queues and service
90B25: Reliability, availability, maintenance, inspection
90B30: Production models
90B35: Scheduling theory, deterministic
90B36: Scheduling theory, stochastic
90B40: Search theory
90B50: Management decision making, including multiple objectives
90B60: Marketing, advertising
90B70: Theory of organizations, manpower planning
90B80: Discrete location and assignment
90B85: Continuous location
90B90: Case-oriented studies
90B99: None of the above, but in this section 90Cxx : Mathematical programming
90C05: Linear programming
90C06: Large-scale problems
90C08: Special problems of linear programming (transportation, multi-index, etc.)
90C09: Boolean programming
90C10: Integer programming
90C11: Mixed integer programming
90C15: Stochastic programming
90C20: Quadratic programming
90C22: Semidefinite programming
90C25: Convex programming
90C26: Nonconvex programming
90C27: Combinatorial optimization
90C29: Multi-objective and goal programming
90C30: Nonlinear programming
90C31: Sensitivity, stability, parametric optimization
90C32: Fractional programming
90C33: Complementarity problems
90C34: Semi-infinite programming
90C35: Programming involving graphs or networks
90C39: Dynamic programming
90C40: Markov and semi-Markov decision processes
90C46: Optimality conditions, duality
90C47: Minimax problems
90C48: Programming in abstract spaces
90C49: Extreme-point and pivoting methods
90C51: Interior-point methods
90C52: Methods of reduced gradient type
90C53: Methods of quasi-Newton type
90C55: Methods of successive quadratic programming type
90C56: Derivative-free methods
90C57: Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C59: Approximation methods and heuristics
90C60: Abstract computational complexity for mathematical programming problems
90C70: Fuzzy programming
90C90: Applications of mathematical programming
90C99: None of the above, but in this section 91-xx : Game theory, economics, social and behavioral sciences
91-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
91-01: Instructional exposition (textbooks, tutorial papers, etc.)
91-02: Research exposition (monographs, survey articles)
91-03: Historical (must also be assigned at least one classification number from section 01)
91-04: Explicit machine computation and programs (not the theory of computation or programming)
91-06: Proceedings, conferences, collections, etc.
91-08: Computational methods
91Axx : Game theory
91A05: 2-person games
91A06: $n$-person games, $n>2$
91A10: Noncooperative games
91A12: Cooperative games
91A13: Games with infinitely many players
91A15: Stochastic games
91A18: Games in extensive form
91A20: Multistage and repeated games
91A22: Evolutionary games
91A23: Differential games
91A24: Positional games (pursuit and evasion, etc.)
91A25: Dynamic games
91A26: Rationality, learning
91A28: Signaling, communication
91A30: Utility theory for games
91A35: Decision theory for games
91A40: Game-theoretic models
91A43: Games involving graphs
91A44: Games involving topology or set theory
91A46: Combinatorial games
91A50: Discrete-time games
91A55: Games of timing
91A60: Probabilistic games; gambling
91A65: Hierarchical games
91A70: Spaces of games
91A80: Applications of game theory
91A90: Experimental studies
91A99: None of the above, but in this section 91Bxx : Mathematical economics
91B02: Fundamental topics (basic mathematics, methodology; applicable to economics in general)
91B06: Decision theory
91B08: Individual preferences
91B10: Group preferences
91B12: Voting theory
91B14: Social choice
91B16: Utility theory
91B18: Public goods
91B24: Price theory and market structure
91B26: Market models (auctions, bargaining, bidding, selling, etc.)
91B28: Finance, portfolios, investment
91B30: Risk theory, insurance
91B32: Resource and cost allocation
91B38: Production theory, theory of the firm
91B40: Labor market, contracts
91B42: Consumer behavior, demand theory
91B44: Informational economics
91B50: Equilibrium: general theory
91B52: Special types of equilibria
91B54: Special types of economies
91B60: General economic models, trade models
91B62: Dynamic economic models, growth models
91B64: Macro-economic models (monetary models, models of taxation)
91B66: Multisectoral models
91B68: Matching models
91B70: Stochastic models
91B72: Spatial models
91B74: Models of real-world systems
91B76: Environmental economics (natural resource models, harvesting, pollution, etc.)
91B82: Statistical methods; economic indices and measures
91B84: Economic time series analysis
91B99: None of the above, but in this section 91Cxx : Social and behavioral sciences: general topics
91C05: Measurement theory
91C15: One- and multidimensional scaling
91C20: Clustering
91C99: None of the above, but in this section 91Dxx : Mathematical sociology (including anthropology)
91D10: Models of societies, social and urban evolution
91D20: Mathematical geography and demography
91D25: Spatial models
91D30: Social networks
91D35: Manpower systems
91D99: None of the above, but in this section 91Exx : Mathematical psychology
91E10: Cognitive psychology
91E30: Psychophysics and psychophysiology; perception
91E40: Memory and learning
91E45: Measurement and performance
91E99: None of the above, but in this section 91Fxx : Other social and behavioral sciences (mathematical treatment)
91F10: History, political science
91F20: Linguistics
91F99: None of the above, but in this section 92-xx : Biology and other natural sciences
92-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
92-01: Instructional exposition (textbooks, tutorial papers, etc.)
92-02: Research exposition (monographs, survey articles)
92-03: Historical (must also be assigned at least one classification number from Section 01)
92-04: Explicit machine computation and programs (not the theory of computation or programming)
92-06: Proceedings, conferences, collections, etc.
92-08: Computational methods
92Bxx : Mathematical biology in general
92B05: General biology and biomathematics
92B10: Taxonomy, statistics
92B15: General biostatistics
92B20: Neural networks, artificial life and related topics
92B99: None of the above, but in this section 92Cxx : Physiological, cellular and medical topics
92C05: Biophysics
92C10: Biomechanics
92C15: Developmental biology, pattern formation
92C17: Cell movement (chemotaxis, etc.)
92C20: Neural biology
92C30: Physiology (general)
92C35: Physiological flow
92C37: Cell biology
92C40: Biochemistry, molecular biology
92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C50: Medical applications (general)
92C55: Biomedical imaging and signal processing
92C60: Medical epidemiology
92C80: Plant biology
92C99: None of the above, but in this section 92Dxx : Genetics and population dynamics
92D10: Genetics
92D15: Problems related to evolution
92D20: Protein sequences, DNA sequences
92D25: Population dynamics (general)
92D30: Epidemiology
92D40: Ecology
92D50: Animal behavior
92D99: None of the above, but in this section 92Exx : Chemistry
92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
92E20: Classical flows, reactions, etc.
92E99: None of the above, but in this section
92F05: Other natural sciences 93-xx : Systems theory; control
93-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
93-01: Instructional exposition (textbooks, tutorial papers, etc.)
93-02: Research exposition (monographs, survey articles)
93-03: Historical (must also be assigned at least one classification number from Section 01)
93-04: Explicit machine computation and programs (not the theory of computation or programming)
93-06: Proceedings, conferences, collections, etc.
93Axx : General
93A05: Axiomatic system theory
93A10: General systems
93A13: Hierarchical systems
93A14: Decentralized systems
93A15: Large scale systems
93A30: Mathematical modeling (models of systems, model-matching, etc.)
93A99: None of the above, but in this section 93Bxx : Controllability, observability, and system structure
93B03: Attainable sets
93B05: Controllability
93B07: Observability
93B10: Canonical structure
93B11: System structure simplification
93B12: Variable structure systems
93B15: Realizations from input-output data
93B17: Transformations
93B18: Linearizations
93B20: Minimal systems representations
93B25: Algebraic methods
93B27: Geometric methods (including algebro-geometric)
93B28: Operator-theoretic methods
93B29: Differential-geometric methods
93B30: System identification
93B35: Sensitivity (robustness)
93B36: ${H]^\infty$-control
93B40: Computational methods
93B50: Synthesis problems
93B51: Design techniques (robust design, computer-aided design, etc.)
93B52: Feedback control
93B55: Pole and zero placement problems
93B60: Eigenvalue problems
93B99: None of the above, but in this section 93Cxx : Control systems, guided systems
93C05: Linear systems
93C10: Nonlinear systems
93C15: Systems governed by ordinary differential equations
93C20: Systems governed by partial differential equations
93C23: Systems governed by functional-differential equations
93C25: Systems in abstract spaces
93C30: Systems governed by functional relations other than differential equations
93C35: Multivariable systems
93C40: Adaptive control
93C41: Problems with incomplete information
93C42: Fuzzy control
93C55: Discrete-time systems
93C57: Sampled-data systems
93C62: Digital systems
93C65: Discrete event systems
93C70: Time-scale analysis and singular perturbations
93C73: Perturbations
93C80: Frequency-response methods
93C83: Control problems involving computers (process control, etc.)
93C85: Automated systems (robots, etc.)
93C95: Applications
93C99: None of the above, but in this section 93Dxx : Stability
93D05: Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)
93D09: Robust stability
93D10: Popov-type stability of feedback systems
93D15: Stabilization of systems by feedback
93D20: Asymptotic stability
93D21: Adaptive or robust stabilization
93D25: Input-output approaches
93D30: Scalar and vector Lyapunov functions
93D99: None of the above, but in this section 93Exx : Stochastic systems and control
93E03: Stochastic systems, general
93E10: Estimation and detection
93E11: Filtering
93E12: System identification
93E14: Data smoothing
93E15: Stochastic stability
93E20: Optimal stochastic control
93E24: Least squares and related methods
93E25: Other computational methods
93E35: Stochastic learning and adaptive control
93E99: None of the above, but in this section 94-xx : Information and communication, circuits
94-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
94-01: Instructional exposition (textbooks, tutorial papers, etc.)
94-02: Research exposition (monographs, survey articles)
94-03: Historical (must also be assigned at least one classification number from Section 01)
94-04: Explicit machine computation and programs (not the theory of computation or programming)
94-06: Proceedings, conferences, collections, etc.
94Axx : Communication, information
94A05: Communication theory
94A08: Image processing (compression, reconstruction, etc.)
94A11: Application of orthogonal functions in communication
94A12: Signal theory (characterization, reconstruction, etc.)
94A13: Detection theory
94A14: Modulation and demodulation
94A15: Information theory, general
94A17: Measures of information, entropy
94A20: Sampling theory
94A24: Coding theorems (Shannon theory)
94A29: Source coding
94A34: Rate-distortion theory
94A40: Channel models
94A45: Prefix, length-variable, comma-free codes
94A50: Theory of questionnaires
94A55: Shift register sequences and sequences over finite alphabets
94A60: Cryptography
94A62: Authentication and secret sharing
94A99: None of the above, but in this section 94Bxx : Theory of error-correcting codes and error-detecting codes
94B05: Linear codes, general
94B10: Convolutional codes
94B12: Combined modulation schemes (including trellis codes)
94B15: Cyclic codes
94B20: Burst-correcting codes
94B25: Combinatorial codes
94B27: Geometric methods (including applications of algebraic geometry)
94B30: Majority codes
94B35: Decoding
94B40: Arithmetic codes
94B50: Synchronization error-correcting codes
94B60: Other types of codes
94B65: Bounds on codes
94B70: Error probability
94B75: Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
94B99: None of the above, but in this section 94Cxx : Circuits, networks
94C05: Analytic circuit theory
94C10: Switching theory, application of Boolean algebra; Boolean functions
94C12: Fault detection; testing
94C15: Applications of graph theory
94C30: Applications of design theory
94C99: None of the above, but in this section
94D05: Fuzzy sets and logic (in connection with questions of Section 94) 97-xx : Mathematics education
97-00: General reference works (handbooks, dictionaries, bibliographies, etc.)
97-01: Instructional exposition (textbooks, tutorial papers, etc.)
97-02: Research exposition (monographs, survey articles)
97-03: Historical (must also be assigned at least one classification number from Section 01)
97-04: Explicit machine computation and programs (not the theory of computation or programming)
97-06: Proceedings, conferences, collections, etc.
97Axx : General
97A20: Recreational mathematics
97A40: Sociological issues
97A80: Standards
97A90: Fiction and games 97Bxx : Educational policy and educational systems
97B10: Educational research and planning
97B20: General education
97B30: Vocational education
97B40: Higher education
97B50: Teacher education
97B60: Out-of-school education. Adult and further education
97B70: Syllabuses. Curriculum guides, official documents
97B99: None of the above, but in this section 97Cxx : Psychology of and research in mathematics education
97C20: Affective aspects (motivation, anxiety, persistence, etc.)
97C30: Student learning and thinking (misconceptions, cognitive development, problem solving, etc.)
97C40: Assessment (large scale assessment, validity, reliability, etc.)
97C50: Theoretical perspectives (learning theories, epistemology, philosophies of teaching and learning, etc.)
97C60: Sociological aspects of learning (culture, group interactions, equity issues, etc.)
97C70: Teachers, and research on teacher education (teacher development, etc.)
97C80: Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.)
97C90: Teaching and curriculum (innovations, teaching practices, studies of curriculum materials, effective teaching, etc. )
97C99: None of the above, but in this section 97Dxx : Education and instruction in mathematics
97D10: Comparative studies on mathematics education
97D20: Philosophical and theoretical contributions to mathematical education
97D30: Goals of mathematics teaching. Curriculum development
97D40: Teaching methods and classroom techniques. Lesson preparation. Educational principles
97D50: Teaching problem solving and heuristic strategies
97D60: Achievement control and rating
97D70: Diagnosis, analysis and remediation of learning difficulties and student errors
97D80: Teaching units, draft lessons and master lessons
97D99: None of the above, but in this section 97Uxx : Educational material and media. Educational technology
97U20: Analysis of textbooks, development and evaluation of textbooks. Textbook use in the classroom
97U30: Teacher manuals and planning aids
97U40: Problem books; student competitions, examination questions
97U50: Computer assisted instruction and programmed instruction
97U60: Manipulative materials and their use in the classroom
97U70: Technological tools (computers, calculators, software, etc.) and their use in the classroom
97U80: Audiovisual media and their use in instruction
97U99: None of the above, but in this section