MSC Classification Codes

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 non-mathematicians (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: G�del 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 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 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 $e 1$ 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 $mod 1$; 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: Tur�n 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: Ad�le 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: �tale 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, Andr�-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; Poincar� 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, Pr�fer 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, Gr�bner 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: �tale, 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: �tale 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, K�nneth 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: �tale 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 ad�les 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 ad�le 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 (H�lder) 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, H�lder 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, Lindel�f 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: -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, Poincar�, distance functions) 30F50: Klein surfaces 30F60: Teichm�ller 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 (Szeg�, Bergman, etc.) 32A26: Integral representations, constructed kernels (e.g. Cauchy, Fantappi�-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: -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, Teichm�ller 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 K�hler 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 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: K�hler manifolds 32Q20: K�hler-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-Amp�re 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 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, 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: Lam�, Mathieu, and spheroidal wave functions 33E12: Mittag-Leffler functions and generalizations 33E15: Other wave functions 33E17: Painlev�-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 Schr�dinger, 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: Painlev� 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: Schr�dinger 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 () 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 Schr�dinger) 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 Z and R, 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 Teichm�ller 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-B�cklund 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: Ces�ro, Euler, N�rlund 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: Pad� 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 (Calder�n-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, -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 Fr�chet 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 , 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 K�the sequence spaces) 46A50: Compactness in topological linear spaces; angelic spaces, etc. 46A55: Convex sets in topological linear spaces; Choquet theory 46A61: Graded Fr�chet 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, K�the 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, -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 R or C 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: Schr�dinger 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 R, C 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: Fr�chet 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: M�bius 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: Erd�s 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 K�hlerian 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 (� la Gromov) 53C24: Rigidity results 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C26: Hyper-K�hler and quaternionic K�hler 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 � la A. D. Aleksandrov) 53C50: Lorentz manifolds, manifolds with indefinite metrics 53C55: Hermitian and K�hlerian 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, Lindel�f, 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: -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 -spaces 55R37: Maps between classifying spaces 55R40: Homology of classifying spaces, characteristic classes 55R45: Homology and homotopy of and ; 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, K�nneth 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 $S^3$ (Poincar� 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 () 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: , 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: Poincar� 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, Poincar� 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 -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 (� 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, Fr�chet, 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-B�cklund) 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. 65A05: Tables 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 Schr�dinger, 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 Schr�dinger 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: -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