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**▼****General mathematics****▼****00-XX General mathematics (8)****▼****00Axx General and miscellaneous specific topics (1)**- 00A05 General mathematics (11)
- 00A07 Problem books (11)
- 00A08 Recreational mathematics (14)
- 00A17 External book reviews (1)
- 00A20 Dictionaries and other general reference works (2)
- 00A22 Formularies (3)
- 00A30 Philosophy of mathematics (67)
- 00A35 Methodology of mathematics, didactics (110)
- 00A69 General applied mathematics (1)
- 00A79 Physics (1)
- 00A99 Miscellaneous topics (10)

**▼****00Bxx Conference proceedings and collections of papers**- 00B30 Festschriften (14)

**▼****History and Foundations****▼****01-XX History and biography**- 01-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 01-01 Instructional exposition (textbooks, tutorial papers, etc.) (4)
- 01-02 Research exposition (monographs, survey articles) (7)
- 01-08 Computational methods (1)
- 01-99 History and biography (3)
**▼****01Axx History of mathematics and mathematicians**- 01A05 General histories, source books (5)
- 01A07 Ethnomathematics, general (1)
- 01A17 Babylonian (2)
- 01A20 Greek, Roman (18)
- 01A25 China (3)
- 01A30 Islam (Medieval) (1)
- 01A35 Medieval (7)
- 01A40 15th and 16th centuries, Renaissance (6)
- 01A45 17th century (12)
- 01A50 18th century (10)
- 01A55 19th century (61)
- 01A70 Biographies, obituaries, personalia, bibliographies (1)
- 01A73 Universities (2)
- 01A75 Collected or selected works; reprintings or translations of classics (5)
- 01A80 Sociology (and profession) of mathematics (1)
- 01A99 Miscellaneous topics (12)

**▼****03-XX Mathematical logic and foundations**- 03-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
- 03-02 Research exposition (monographs, survey articles) (2)
- 03-03 Historical (5)
- 03-99 Mathematical logic and foundations (4)
- 03A05 Philosophical and critical (100)
**▼****03Bxx General logic****▼****03Cxx Model theory****▼****03Dxx Computability and recursion theory****▼****03Exx Set theory****▼****03Fxx Proof theory and constructive mathematics****▼****03Gxx Algebraic logic****▼****03Hxx Nonstandard models**

**▼****05-XX Combinatorics**- 05-01 Instructional exposition (textbooks, tutorial papers, etc.) (2)
- 05-02 Research exposition (monographs, survey articles) (3)
**▼****05Axx Enumerative combinatorics**- 05A05 Combinatorial choice problems (subsets, representatives, permutations) (68)
- 05A10 Factorials, binomial coefficients, combinatorial functions (26)
- 05A15 Exact enumeration problems, generating functions (22)
- 05A16 Asymptotic enumeration (2)
- 05A17 Partitions of integers (49)
- 05A18 Partitions of sets (7)
- 05A19 Combinatorial identities (21)
- 05A30 q-calculus and related topics (1)
- 05A99 None of the above, but in this section (13)

**▼****05Bxx Designs and configurations****▼****05Cxx Graph theory**- 05C15 Coloring of graphs and hypergraphs (2)
- 05C25 Graphs and groups (1)
- 05C35 Extremal problems (1)
- 05C38 Paths and cycles (3)
- 05C45 Eulerian and Hamiltonian graphs (7)
- 05C50 Graphs and matrices (1)
- 05C60 Isomorphism problems (reconstruction conjecture, etc.) (2)
- 05C62 Graph representations (geometric and intersection representations, etc.) (1)
- 05C70 Factorization, matching, covering and packing (1)
- 05C90 Applications (1)
- 05C99 None of the above, but in this section (1)

- 05Dxx Extremal combinatorics
**▼****05Exx Algebraic combinatorics**

**▼****Algebra****▼****06-XX Order, lattices, ordered algebraic structures****▼****08-XX General algebraic systems**- 08-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
**▼****08A00 xx Algebraic structures****▼****08Axx Algebraic structures**

**▼****08Bxx Varieties**- 08Cxx Other classes of algebras

**▼****11-XX Number theory**- 11-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (5)
- 11-01 Instructional exposition (textbooks, tutorial papers, etc.) (60)
- 11-02 Research exposition (monographs, survey articles) (30)
- 11-03 Historical (16)
- 11-04 Explicit machine computation and programs (2)
- 11-99 Number theory (12)
**▼****11Axx Elementary number theory**- 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors (144)
- 11A07 Congruences; primitive roots; residue systems (261)
- 11A15 Power residues, reciprocity (209)
- 11A25 Arithmetic functions; related numbers; inversion formulas (202)
- 11A41 Primes (140)
- 11A51 Factorization; primality (159)
- 11A55 Continued fractions (226)
- 11A63 Radix representation; digital problems (126)
- 11A67 Other representations (12)
- 11A99 None of the above, but in this section (123)
- 11Axx Elementary number theory (2)

**▼****11Bxx Sequences and sets**- 11B13 Additive bases (8)
- 11B25 Arithmetic progressions (38)
- 11B34 Representation functions (5)
- 11B37 Recurrences (28)
- 11B39 Fibonacci and Lucas numbers and polynomials and generalizations (20)
- 11B57 Farey sequences; the sequences 1k, 2k, …} (27)
- 11B65 Binomial coefficients; factorials; q-identities (89)
- 11B68 Bernoulli and Euler numbers and polynomials (107)
- 11B73 Bell and Stirling numbers (1)
- 11B75 Other combinatorial number theory (26)
- 11B83 Special sequences and polynomials (60)
- 11B99 None of the above, but in this section (13)

**▼****11Cxx Polynomials and matrices****▼****11Dxx Diophantine equations**- 11D04 Linear equations (61)
- 11D09 Quadratic and bilinear equations (202)
- 11D25 Cubic and quartic equations (112)
- 11D45 Counting solutions of Diophantine equations (4)
- 11D57 Multiplicative and norm form equations (12)
- 11D61 Exponential equations (8)
- 11D68 Rational numbers as sums of fractions (3)
- 11D72 Equations in many variables (7)
- 11D75 Diophantine inequalities (3)
- 11D79 Congruences in many variables (4)
- 11D85 Representation problems (15)
- 11D99 None of the above, but in this section (26)
- 11Dxx Diophantine equations (3)

**▼****11Exx Forms and linear algebraic groups**- 11E04 Quadratic forms over general fields (15)
- 11E10 Forms over real fields (15)
- 11E12 Quadratic forms over global rings and fields (62)
- 11E16 General binary quadratic forms (82)
- 11E20 General ternary and quaternary quadratic forms; forms of more than two variables (68)
- 11E25 Sums of squares and representations by other particular quadratic forms (131)
- 11E39 Bilinear and Hermitian forms (14)
- 11E41 Class numbers of quadratic and Hermitian forms (90)
- 11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (31)
- 11E57 Classical groups (6)
- 11E76 Forms of degree higher than two (67)
- 11E81 Algebraic theory of quadratic forms; Witt groups and rings (1)
- 11E88 Quadratic spaces; Clifford algebras (1)
- 11E99 None of the above, but in this section (22)

**▼****11Fxx Discontinuous groups and automorphic forms**- 11F03 Modular and automorphic functions (11)
- 11F06 Structure of modular groups and generalizations; arithmetic groups (13)
- 11F11 Modular forms, one variable (51)
- 11F12 Automorphic forms, one variable (1)
- 11F20 Dedekind eta function, Dedekind sums (1)
- 11F27 Theta series; Weil representation (27)
- 11F32 Modular correspondences, etc. (20)
- 11F41 Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (2)
- 11F50 Jacobi forms (10)
- 11F55 Other groups and their modular and automorphic forms (several variables) (3)
- 11F99 None of the above, but in this section (4)

**▼****11Gxx Arithmetic algebraic geometry (Diophantine geometry)**- 11G05 Elliptic curves over global fields (39)
- 11G15 Complex multiplication and moduli of abelian varieties (25)
- 11G20 Curves over finite and local fields (1)
- 11G30 Curves of arbitrary genus or genus ≠ 1 over global fields (1)
- 11G35 Varieties over global fields (1)
- 11G99 None of the above, but in this section (2)

**▼****11Hxx Geometry of numbers**- 11H06 Lattices and convex bodies (8)
- 11H16 Nonconvex bodies (1)
- 11H31 Lattice packing and covering (1)
- 11H46 Products of linear forms (6)
- 11H50 Minima of forms (15)
- 11H55 Quadratic forms (reduction theory, extreme forms, etc.) (27)
- 11H60 Mean value and transfer theorems (1)
- 11H99 None of the above, but in this section (8)
- 11Hxx Geometry of numbers (1)

**▼****11Jxx Diophantine approximation, transcendental number theory**- 11J04 Homogeneous approximation to one number (1)
- 11J06 Markov and Lagrange spectra and generalizations (1)
- 11J13 Simultaneous homogeneous approximation, linear forms (3)
- 11J17 Approximation by numbers from a fixed field (2)
- 11J20 Inhomogeneous linear forms (4)
- 11J25 Diophantine inequalities (2)
- 11J68 Approximation to algebraic numbers (5)
- 11J70 Continued fractions and generalizations (16)
- 11J71 Distribution modulo one (1)
- 11J72 Irrationality; linear independence over a field (11)
- 11J81 Transcendence (general theory) (16)
- 11J91 Transcendence theory of other special functions (2)
- 11J99 None of the above, but in this section (11)

**▼****11Kxx Probabilistic theory: distribution modulo 1; metric theory of algorithms****▼****11Lxx Exponential sums and character sums****▼****11Mxx Zeta and L-functions: analytic theory**- 11M06 ζ(s) and L(s, χ) (32)
- 11M20 Real zeros of L(s, χ); results on L(1, χ) (5)
- 11M26 Nonreal zeros of ζ(s) and L(s, χ); Riemann and other hypotheses (21)
- 11M35 Hurwitz and Lerch zeta functions (1)
- 11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas (1)
- 11M41 Other Dirichlet series and zeta functions (12)
- 11M99 None of the above, but in this section (3)

**▼****11Nxx Multiplicative number theory**- 11N05 Distribution of primes (78)
- 11N13 Primes in progressions (39)
- 11N25 Distribution of integers with specified multiplicative constraints (9)
- 11N32 Primes represented by polynomials; other multiplicative structure of polynomial values (16)
- 11N35 Sieves (12)
- 11N36 Applications of sieve methods (1)
- 11N37 Asymptotic results on arithmetic functions (37)
- 11N45 Asymptotic results on counting functions for algebraic and topological structures (1)
- 11N60 Distribution functions associated with additive and positive multiplicative functions (1)
- 11N64 Other results on the distribution of values or the characterization of arithmetic functions (3)
- 11N69 Distribution of integers in special residue classes (1)
- 11N75 Applications of automorphic functions and forms to multiplicative problems (2)
- 11N99 None of the above, but in this section (5)

**▼****11Pxx Additive number theory; partitions**- 11P05 Waring's problem and variants (18)
- 11P21 Lattice points in specified regions (3)
- 11P32 Goldbach-type theorems; other additive questions involving primes (9)
- 11P81 Elementary theory of partitions (58)
- 11P82 Analytic theory of partitions (6)
- 11P83 Partitions; congruences and congruential restrictions (7)
- 11P99 None of the above, but in this section (10)

**▼****11Rxx Algebraic number theory: global fields**- 11R04 Algebraic numbers; rings of algebraic integers (51)
- 11R06 PV-numbers and generalizations; other special algebraic numbers (1)
- 11R09 Polynomials (irreducibility, etc.) (11)
- 11R11 Quadratic extensions (31)
- 11R16 Cubic and quartic extensions (21)
- 11R18 Cyclotomic extensions (33)
- 11R20 Other abelian and metabelian extensions (10)
- 11R21 Other number fields (5)
- 11R27 Units and factorization (22)
- 11R29 Class numbers, class groups, discriminants (26)
- 11R32 Galois theory (4)
- 11R37 Class field theory (12)
- 11R42 Zeta functions and L-functions of number fields (3)
- 11R44 Distribution of prime ideals (3)
- 11R45 Density theorems (3)
- 11R52 Quaternion and other division algebras: arithmetic, zeta functions (3)
- 11R54 Other algebras and orders, and their zeta and L-functions (1)
- 11R58 Arithmetic theory of algebraic function fields (2)
- 11R65 Class groups and Picard groups of orders (1)
- 11R99 None of the above, but in this section (10)

**▼****11Sxx Algebraic number theory: local and p-adic fields****▼****11Txx Finite fields and commutative rings (number-theoretic aspects)**- 11Uxx Connections with logic
**▼****11Yxx Computational number theory**- 11Zxx Miscellaneous applications of number theory

**▼****12-XX Field theory and polynomials**- 12-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (3)
- 12-01 Instructional exposition (textbooks, tutorial papers, etc.) (13)
- 12-02 Research exposition (monographs, survey articles) (4)
- 12-03 Historical (1)
- 12-99 Algebraic number theory, field theory and polynomials (2)
**▼****12Dxx Real and complex fields****▼****12Exx General field theory****▼****12Fxx Field extensions**- 12Gxx Homological methods (field theory)
**▼****12Hxx Differential and difference algebra**- 12Jxx Topological fields
- 12Kxx Generalizations of fields
- 12Lxx Connections with logic

**▼****13-XX Commutative rings and algebras**- 13-99 Commutative rings and algebras (2)
**▼****13Axx General commutative ring theory****▼****13Bxx Ring extensions and related topics****▼****13Cxx Theory of modules and ideals****▼****13Dxx Homological methods**- 13Exx Chain conditions, finiteness conditions
**▼****13Fxx Arithmetic rings and other special rings****▼****13Hxx Local rings and semilocal rings****▼****13Jxx Topological rings and modules****▼****13Mxx Finite commutative rings**- 13Nxx Differential algebra
**▼****13Pxx Computational aspects of commutative algebra**

**▼****14-XX Algebraic geometry (1)**- 14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 14-01 Instructional exposition (textbooks, tutorial papers, etc.) (5)
- 14-02 Research exposition (monographs, survey articles) (2)
- 14-03 Historical (3)
- 14-99 Algebraic geometry (6)
**▼****14Axx Foundations****▼****14Bxx Local theory****▼****14Cxx Cycles and subschemes****▼****14Dxx Families, fibrations****▼****14Exx Birational geometry****▼****14Fxx (Co)homology theory****▼****14Gxx Arithmetic problems. Diophantine geometry****▼****14Hxx Curves**- 14H05 Algebraic functions; function fields (73)
- 14H10 Families, moduli (algebraic) (8)
- 14H15 Families, moduli (analytic) (3)
- 14H20 Singularities, local rings (26)
- 14H25 Arithmetic ground fields (2)
- 14H37 Automorphisms (15)
- 14H40 Jacobians, Prym varieties (14)
- 14H42 Theta functions; Schottky problem (76)
- 14H45 Special curves and curves of low genus (132)
- 14H50 Plane and space curves (257)
- 14H51 Special divisors (gonality, Brill-Noether theory) (2)
- 14H52 Elliptic curves (56)
- 14H55 Riemann surfaces; Weierstrass points; gap sequences (24)
- 14H60 Vector bundles on curves and their moduli (1)
- 14H99 None of the above, but in this section (73)
- 14Hxx Curves (78)

**▼****14Jxx Surfaces and higher-dimensional varieties**- 14J10 Families, moduli, classification: algebraic theory (10)
- 14J17 Singularities (15)
- 14J20 Arithmetic ground fields (1)
- 14J25 Special surfaces (69)
- 14J26 Rational and ruled surfaces (36)
- 14J28 K3 surfaces and Enriques surfaces (7)
- 14J29 Surfaces of general type (4)
- 14J30 3-folds (4)
- 14J70 Hypersurfaces (12)
- 14J99 None of the above, but in this section (10)
- 14Jxx Surfaces and higher-dimensional varieties (10)

**▼****14Kxx Abelian varieties and schemes****▼****14Lxx Algebraic groups****▼****14Mxx Special varieties****▼****14Nxx Projective and enumerative geometry****▼****14Pxx Real algebraic and real analytic geometry****▼****14Qxx Computational aspects in algebraic geometry****▼****14Rxx Affine geometry****▼****15-XX Linear and multilinear algebra; matrix theory**- 15-01 Instructional exposition (textbooks, tutorial papers, etc.) (13)
- 15-02 Research exposition (monographs, survey articles) (12)
- 15-03 Historical (5)
- 15-99 Linear and multilinear algebra; matrix theory (finite and infinite) (15)
**▼****15Axx Basic linear algebra**- 15A03 Vector spaces, linear dependence, rank (15)
- 15A04 Linear transformations, semilinear transformations (31)
- 15A06 Linear equations (40)
- 15A09 Matrix inversion, generalized inverses (2)
- 15A15 Determinants, permanents, other special matrix functions (164)
- 15A18 Eigenvalues, singular values, and eigenvectors (5)
- 15A21 Canonical forms, reductions, classification (3)
- 15A23 Factorization of matrices (2)
- 15A24 Matrix equations and identities (2)
- 15A33 Matrices over special rings (quaternions, finite fields, etc.) (2)
- 15A36 Matrices of integers (2)
- 15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.) (8)
- 15A63 Quadratic and bilinear forms, inner products (16)
- 15A66 Clifford algebras, spinors (1)
- 15A69 Multilinear algebra, tensor products (2)
- 15A72 Vector and tensor algebra, theory of invariants (26)
- 15A75 Exterior algebra, Grassmann algebras (4)
- 15A99 Miscellaneous topics (7)

**▼****16-XX Associative rings and algebras**- 16-01 Instructional exposition (textbooks, tutorial papers, etc.) (3)
- 16-99 Associative rings and algebras (15)
**▼****16Bxx General and miscellaneous**- 16Dxx Modules, bimodules and ideals
- 16Exx Homological methods
**▼****16Gxx Representation theory of rings and algebras****▼****16Kxx Division rings and semisimple Artin rings**- 16Lxx Local rings and generalizations
- 16Nxx Radicals and radical properties of rings
**▼****16Pxx Chain conditions, growth conditions, and other forms of finiteness****▼****16Rxx Rings with polynomial identity****▼****16Sxx Rings and algebras arising under various constructions**- 16Uxx Conditions on elements
**▼****16Wxx Rings and algebras with additional structure**- 16Yxx Generalizations

**▼****17-XX Nonassociative rings and algebras**- 17-08 Computational methods (1)
**▼****17Axx General nonassociative rings**- 17A35 Division algebras (2)
- 17A40 Ternary compositions (2)
- 17Bxx Lie algebras and Lie superalgebras
- 17Cxx Jordan algebras (algebras, triples and pairs)
- 17Dxx Other nonassociative rings and algebras

**▼****18-XX Category theory, homological algebra**- 18Axx General theory of categories and functors
- 18Bxx Special categories
- 18Cxx Categories and theories
- 18Dxx Categories with structure
- 18Exx Abelian categories
- 18Fxx Categories and geometry
- 18Gxx Homological algebra

**▼****19-XX K-theory**- 19Axx Grothendieck groups and K0
- 19Bxx Whitehead groups and K1
- 19Cxx Steinberg groups and K2
- 19Dxx Higher algebraic K-theory
- 19Exx K-theory in geometry
**▼****19Fxx K-theory in number theory**- 19Gxx K-theory of forms
- 19Jxx Obstructions from topology
- 19Kxx K-theory and operator algebras
- 19Lxx Topological K-theory

**▼****20-XX Group theory and generalizations**- 20-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 20-01 Instructional exposition (textbooks, tutorial papers, etc.) (2)
- 20-02 Research exposition (monographs, survey articles) (1)
- 20-99 Group theory and generalizations (3)
**▼****20Axx Foundations****▼****20Bxx Permutation groups**- 20B05 General theory for finite groups (27)
- 20B15 Primitive groups (12)
- 20B20 Multiply transitive finite groups (16)
- 20B22 Multiply transitive infinite groups (1)
- 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures (18)
- 20B30 Symmetric groups (4)
- 20B35 Subgroups of symmetric groups (4)
- 20B99 None of the above, but in this section (3)

**▼****20Cxx Representation theory of groups****▼****20Dxx Abstract finite groups**- 20D06 Simple groups: alternating groups and groups of Lie type (2)
- 20D08 Simple groups: sporadic groups (10)
- 20D10 Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks (2)
- 20D15 Nilpotent groups, p-groups (11)
- 20D20 Sylow subgroups, Sylow properties, π-groups, π-structure (5)
- 20D25 Special subgroups (Frattini, Fitting, etc.) (2)
- 20D30 Series and lattices of subgroups (1)
- 20D45 Automorphisms (5)
- 20D99 None of the above, but in this section (4)

**▼****20Exx Structure and classification of infinite or finite groups****▼****20Fxx Special aspects of infinite or finite groups**- 20F05 Generators, relations, and presentations (2)
- 20F17 Formations of groups, Fitting classes (1)
- 20F29 Representations of groups as automorphism groups of algebraic systems (1)
- 20F40 Associated Lie structures (1)
- 20F55 Reflection and Coxeter groups (1)
- 20F65 Geometric group theory (2)
- 20F99 None of the above, but in this section (1)

**▼****20Gxx Linear algebraic groups (classical groups)****▼****20Hxx Other groups of matrices**- 20Jxx Connections with homological algebra and category theory
**▼****20Kxx Abelian groups**- 20Mxx Semigroups
**▼****20Nxx Other generalizations of groups**

**▼****22-XX Topological groups, Lie groups**

**▼****Analysis****▼****26-XX Real functions**- 26-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 26-01 Instructional exposition (textbooks, tutorial papers, etc.) (49)
- 26-02 Research exposition (monographs, survey articles) (3)
- 26-03 Historical (5)
- 26-99 Real functions (2)
**▼****26Axx Functions of one variable**- 26A03 Foundations: limits and generalizations, elementary topology of the line (21)
- 26A06 One-variable calculus (101)
- 26A09 Elementary functions (28)
- 26A12 Rate of growth of functions, orders of infinity, slowly varying functions (6)
- 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) (13)
- 26A18 Iteration (3)
- 26A21 Classification of real functions; Baire classification of sets and functions (2)
- 26A24 Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems (229)
- 26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (17)
- 26A30 Singular functions, Cantor functions, functions with other special properties (3)
- 26A33 Fractional derivatives and integrals (2)
- 26A36 Antidifferentiation (2)
- 26A42 Integrals of Riemann, Stieltjes and Lebesgue type (382)
- 26A45 Functions of bounded variation, generalizations (3)
- 26A51 Convexity, generalizations (1)
- 26A99 None of the above, but in this section (37)

**▼****26Bxx Functions of several variables**- 26B05 Continuity and differentiation questions (23)
- 26B10 Implicit function theorems, Jacobians, transformations with several variables (42)
- 26B12 Calculus of vector functions (4)
- 26B15 Integration: length, area, volume (24)
- 26B20 Integral formulas (Stokes, Gauss, Green, etc.) (10)
- 26B99 None of the above, but in this section (25)

**▼****26Cxx Polynomials, rational functions****▼****26Dxx Inequalities****▼****26Exx Miscellaneous topics**

**▼****28-XX Measure and integration**- 28-99 Measure and integration (1)
**▼****28Axx Classical measure theory****▼****28Bxx Set functions, measures and integrals with values in abstract spaces****▼****28Cxx Set functions and measures on spaces with additional structure**- 28Dxx Measure-theoretic ergodic theory
- 28Exx Miscellaneous topics in measure theory

**▼****30-XX Functions of a complex variable**- 30-01 Instructional exposition (textbooks, tutorial papers, etc.) (32)
- 30-02 Research exposition (monographs, survey articles) (8)
- 30-03 Historical (4)
- 30-99 Functions of a complex variable (39)
**▼****30Axx General properties****▼****30Bxx Series expansions**- 30B10 Power series (including lacunary series) (61)
- 30B30 Boundary behavior of power series, over-convergence (12)
- 30B40 Analytic continuation (16)
- 30B50 Dirichlet series and other series expansions, exponential series (7)
- 30B70 Continued fractions (79)
- 30B99 None of the above, but in this section (46)

**▼****30Cxx Geometric function theory**- 30C10 Polynomials (3)
- 30C15 Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) (34)
- 30C20 Conformal mappings of special domains (12)
- 30C35 General theory of conformal mappings (5)
- 30C50 Coefficient problems for univalent and multivalent functions (1)
- 30C65 Quasiconformal mappings in Rn, other generalizations (1)
- 30C70 Extremal problems for conformal and quasiconformal mappings, variational methods (1)
- 30C99 None of the above, but in this section (7)

**▼****30Dxx Entire and meromorphic functions, and related topics**- 30D05 Functional equations in the complex domain, iteration and composition of analytic functions (20)
- 30D10 Representations of entire functions by series and integrals (12)
- 30D15 Special classes of entire functions and growth estimates (1)
- 30D20 Entire functions, general theory (24)
- 30D30 Meromorphic functions, general theory (20)
- 30D35 Distribution of values, Nevanlinna theory (3)
- 30D55 Hp-classes (1)
- 30D99 None of the above, but in this section (21)

**▼****30Exx Miscellaneous topics of analysis in the complex domain**- 30E05 Moment problems, interpolation problems (1)
- 30E10 Approximation in the complex domain (7)
- 30E15 Asymptotic representations in the complex domain (2)
- 30E20 Integration, integrals of Cauchy type, integral representations of analytic functions (14)
- 30E25 Boundary value problems (3)
- 30E99 None of the above, but in this section (14)

**▼****30Fxx Riemann surfaces**- 30F10 Compact Riemann surfaces and uniformization (26)
- 30F15 Harmonic functions on Riemann surfaces (2)
- 30F20 Classification theory of Riemann surfaces (6)
- 30F30 Differentials on Riemann surfaces (39)
- 30F35 Fuchsian groups and automorphic functions (55)
- 30F40 Kleinian groups (9)
- 30F50 Klein surfaces (2)
- 30F60 TeichmÃ¼ller theory (2)
- 30F99 None of the above, but in this section (45)
- 30Fxx Riemann surfaces (1)

**▼****30Gxx Generalized function theory**

**▼****31-XX Potential theory**- 31-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
- 31-99 Potential theory (4)
**▼****31Axx Two-dimensional theory**- 31A05 Harmonic, subharmonic, superharmonic functions (15)
- 31A10 Integral representations, integral operators, integral equations methods (3)
- 31A15 Potentials and capacity, harmonic measure, extremal length (2)
- 31A20 Boundary behavior (theorems of Fatou type, etc.) (1)
- 31A25 Boundary value and inverse problems (4)
- 31A35 Connections with differential equations (1)
- 31A99 None of the above, but in this section (8)

**▼****31Bxx Higher-dimensional theory****▼****31Cxx Other generalizations**

**▼****32-XX Several complex variables and analytic spaces**- 32-99 Several complex variables and analytic spaces (6)
**▼****32Axx Holomorphic functions of several complex variables****▼****32Bxx Local analytic geometry****▼****32Cxx Analytic spaces**- 32Dxx Analytic continuation
**▼****32Exx Holomorphic convexity**- 32Fxx Geometric convexity
- 32Gxx Deformations of analytic structures
**▼****32Hxx Holomorphic mappings and correspondences****▼****32Jxx Compact analytic spaces**- 32Kxx Generalizations of analytic spaces
- 32Lxx Holomorphic fiber spaces
- 32Mxx Complex spaces with a group of automorphisms
**▼****32Nxx Automorphic functions****▼****32Qxx Complex manifolds**- 32Rxx Local dynamics around a fixed point
- 32Sxx Singularities
- 32Txx Pseudoconvex domains
- 32Uxx Pluripotential theory
- 32Vxx CR manifolds
- 32Wxx Differential operators in several variables

**▼****33-XX Special functions**- 33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 33-01 Instructional exposition (textbooks, tutorial papers, etc.) (4)
- 33-02 Research exposition (monographs, survey articles) (5)
- 33-03 Historical (5)
- 33-04 Explicit machine computation and programs (1)
- 33-99 Special functions (14)
**▼****33Bxx Elementary classical functions****▼****33Cxx Hypergeometric functions**- 33C05 Classical hypergeometric functions, 2F1 (54)
- 33C10 Bessel and Airy functions, cylinder functions, 0F1 (68)
- 33C15 Confluent hypergeometric functions, Whittaker functions, 1F1 (1)
- 33C20 Generalized hypergeometric series, pFq (11)
- 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (28)
- 33C47 Other special orthogonal polynomials and functions (4)
- 33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (2)
- 33C55 Spherical harmonics (77)
- 33C60 Hypergeometric integrals and functions defined by them (E, G and H functions) (11)
- 33C65 Appell, Horn and Lauricella functions (1)
- 33C70 Other hypergeometric functions and integrals in several variables (4)
- 33C75 Elliptic integrals as hypergeometric functions (6)
- 33C80 Connections with groups and algebras, and related topics (2)
- 33C99 None of the above, but in this section (37)
- 33Cxx Hypergeometric functions (1)

**▼****33Dxx Basic hypergeometric functions****▼****33Exx Other special functions****▼****33Fxx Computational aspects**

**▼****34-XX Ordinary differential equations (1)**- 34-01 Instructional exposition (textbooks, tutorial papers, etc.) (5)
- 34-02 Research exposition (monographs, survey articles) (1)
- 34-99 Ordinary differential equations (11)
**▼****34Axx General theory**- 34A05 Explicit solutions and reductions (220)
- 34A09 Implicit equations, differential-algebraic equations (25)
- 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions (2)
- 34A25 Analytical theory: series, transformations, transforms, operational calculus, etc. (72)
- 34A26 Geometric methods in differential equations (16)
- 34A30 Linear equations and systems, general (329)
- 34A34 Nonlinear equations and systems, general (24)
- 34A40 Differential inequalities (1)
- 34A45 Theoretical approximation of solutions (2)
- 34A99 None of the above, but in this section (35)
- 34Axx General theory (1)

**▼****34Bxx Boundary value problems****▼****34Cxx Qualitative theory**- 34C05 Location of integral curves, singular points, limit cycles (21)
- 34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.) (2)
- 34C10 Oscillation theory, zeros, disconjugacy and comparison theory (2)
- 34C11 Growth, boundedness, comparison of solutions (2)
- 34C20 Transformation and reduction of equations and systems, normal forms (5)
- 34C99 None of the above, but in this section (2)

**▼****34Dxx Stability theory**- 34Exx Asymptotic theory
**▼****34Gxx Differential equations in abstract spaces****▼****34Kxx Functional-differential and differential-difference equations****▼****34Lxx Ordinary differential operators****▼****34Mxx Differential equations in the complex domain**- 34M05 Entire and meromorphic solutions (3)
- 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) (8)
- 34M25 Formal solutions, transform techniques (6)
- 34M30 Asymptotics, summation methods (1)
- 34M35 Singularities, monodromy, local behavior of solutions, normal forms (5)
- 34M99 None of the above, but in this section (14)
- 34Mxx Differential equations in the complex domain (1)

**▼****35-XX Partial differential equations (10)**- 35-01 Instructional exposition (textbooks, tutorial papers, etc.) (3)
- 35-02 Research exposition (monographs, survey articles) (1)
- 35-03 Historical (1)
**▼****35Axx General theory****▼****35Bxx Qualitative properties of solutions****▼****35Cxx Representations of solutions**- 35Dxx Generalized solutions of partial differential equations
**▼****35Exx Equations and systems with constant coefficients****▼****35Fxx General first-order equations and systems****▼****35Gxx General higher-order equations and systems**- 35Hxx Close-to-elliptic equations
**▼****35Jxx Partial differential equations of elliptic type**- 35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (7)
- 35J15 General theory of second-order, elliptic equations (2)
- 35J40 Boundary value problems for higher-order, elliptic equations (1)
- 35J99 None of the above, but in this section (2)
- 35Jxx Partial differential equations of elliptic type (2)

**▼****35Kxx Parabolic equations and systems****▼****35Lxx Partial differential equations of hyperbolic type**- 35Mxx Partial differential equations of special type (mixed, composite, etc.)
**▼****35Nxx Overdetermined systems**- 35Pxx Spectral theory and eigenvalue problems for partial differential operators
**▼****35Qxx Equations of mathematical physics and other areas of application**- 35Rxx Miscellaneous topics involving partial differential equations
- 35Sxx Pseudodifferential operators and other generalizations of partial differential operators

**▼****37-XX Dynamical systems and ergodic theory**- 37Axx Ergodic theory
- 37Bxx Topological dynamics
**▼****37Cxx Smooth dynamical systems: general theory**- 37Dxx Dynamical systems with hyperbolic behavior
- 37Exx Low-dimensional dynamical systems
**▼****37Fxx Complex dynamical systems**- 37Gxx Local and nonlocal bifurcation theory
- 37Hxx Random dynamical systems
- 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
- 37Kxx Infinite-dimensional Hamiltonian systems
- 37Lxx Infinite-dimensional dissipative dynamical systems
- 37Mxx Approximation methods and numerical treatment of dynamical systems
- 37Nxx Applications

**▼****39-XX Difference and functional equations**- 39-99 Difference and functional equations (3)
**▼****39Axx Difference equations****▼****39Bxx Functional equations and inequalities**

**▼****40-XX Sequences, series, summability**- 40-01 Instructional exposition (textbooks, tutorial papers, etc.) (3)
- 40-99 Sequences, series, summability (6)
**▼****40Axx Convergence and divergence of infinite limiting processes**- 40A05 Convergence and divergence of series and sequences (142)
- 40A10 Convergence and divergence of integrals (1)
- 40A15 Convergence and divergence of continued fractions (65)
- 40A20 Convergence and divergence of infinite products (18)
- 40A25 Approximation to limiting values (summation of series, etc.) (114)
- 40A30 Convergence and divergence of series and sequences of functions (28)
- 40A99 None of the above, but in this section (20)
- 40B05 Multiple sequences and series (1)

**▼****40Cxx General summability methods****▼****40Dxx Direct theorems on summability****▼****40Exx Inversion theorems****▼****40Gxx Special methods of summability**

**▼****41-XX Approximation and expansions**- 41-01 Instructional exposition (textbooks, tutorial papers, etc.) (4)
- 41-02 Research exposition (monographs, survey articles) (2)
- 41-99 Approximations and expansions (15)
**▼****41Axx Approximations and expansions**- 41A05 Interpolation (38)
- 41A10 Approximation by polynomials (26)
- 41A17 Inequalities in approximation (Bernstein, Jackson, Nikolcprime skiui-type inequalities) (1)
- 41A20 Approximation by rational functions (8)
- 41A21 PadÃ© approximation (7)
- 41A25 Rate of convergence, degree of approximation (2)
- 41A28 Simultaneous approximation (3)
- 41A29 Approximation with constraints (2)
- 41A30 Approximation by other special function classes (2)
- 41A44 Best constants (1)
- 41A45 Approximation by arbitrary linear expressions (1)
- 41A50 Best approximation, Chebyshev systems (2)
- 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (98)
- 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (9)
- 41A80 Remainders in approximation formulas (2)
- 41A99 Miscellaneous topics (12)

**▼****42-XX Harmonic analysis on Euclidean spaces**- 42-01 Instructional exposition (textbooks, tutorial papers, etc.) (4)
- 42-03 Historical (6)
**▼****42Axx Fourier analysis in one variable**- 42A05 Trigonometric polynomials, inequalities, extremal problems (6)
- 42A10 Trigonometric approximation (8)
- 42A15 Trigonometric interpolation (3)
- 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series (48)
- 42A20 Convergence and absolute convergence of Fourier and trigonometric series (27)
- 42A24 Summability and absolute summability of Fourier and trigonometric series (1)
- 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (4)
- 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (2)
- 42A50 Conjugate functions, conjugate series, singular integrals (1)
- 42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization (5)
- 42A70 Trigonometric moment problems (13)
- 42A99 None of the above, but in this section (5)
- 42Axx Fourier analysis in one variable (1)

**▼****42Bxx Fourier analysis in several variables****▼****42Cxx Nontrigonometric Fourier analysis**- 42C05 Orthogonal functions and polynomials, general theory (4)
- 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (10)
- 42C99 None of the above, but in this section (1)
- 44-99 Integral transforms, operational calculus (1)
- 44A05 General transforms (3)
- 44A10 Laplace transform (1)
- 44A12 Radon transform (2)
- 44A15 Special transforms (Legendre, Hilbert, etc.) (1)
- 44A60 Moment problems (1)
- 44A99 Miscellaneous topics (1)

- 43-XX Abstract harmonic analysis
- 44-XX Integral transforms, operational calculus
**▼****45-XX Integral equations****▼****45Exx Singular integral equations**- 45Fxx Systems of linear integral equations
- 45Gxx Nonlinear integral equations
- 45Mxx Qualitative behavior

**▼****46-XX Functional analysis**- 46-99 Functional analysis (6)
- 46Axx Topological linear spaces and related structures
**▼****46Bxx Normed linear spaces and Banach spaces; Banach lattices**- 46Cxx Inner product spaces and their generalizations, Hilbert spaces
**▼****46Exx Linear function spaces and their duals**- 46Fxx Distributions, generalized functions, distribution spaces
- 46Gxx Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces)
- 46Hxx Topological algebras, normed rings and algebras, Banach algebras
- 46Jxx Commutative Banach algebras and commutative topological algebras
- 46Kxx Topological (rings and) algebras with an involution
- 46Lxx Selfadjoint operator algebras (C*-algebras, von Neumann (W*-) algebras, etc.)
- 46Mxx Methods of category theory in functional analysis
- 46Nxx Miscellaneous applications of functional analysis
- 46Sxx Other (nonclassical) types of functional analysis
**▼****46Txx Nonlinear functional analysis**

**▼****47-XX Operator theory****▼****47Axx General theory of linear operators****▼****47Bxx Special classes of linear operators**- 47Cxx Individual linear operators as elements of algebraic systems
**▼****47Dxx Groups and semigroups of linear operators, their generalizations and applications****▼****47Gxx Integral, integro-differential, and pseudodifferential operators****▼****47Hxx Nonlinear operators and their properties**- 47Jxx Equations and inequalities involving nonlinear operators
- 47Lxx Linear spaces and algebras of operators
- 47Nxx Miscellaneous applications of operator theory
- 47Sxx Other (nonclassical) types of operator theory

**▼****49-XX Calculus of variations and optimal control; optimization (2)**- 49-01 Instructional exposition (textbooks, tutorial papers, etc.) (7)
- 49-03 Historical (3)
**▼****49Jxx Existence theories****▼****49Kxx Necessary conditions and sufficient conditions for optimality**- 49K05 Free problems in one independent variable (73)
- 49K10 Free problems in two or more independent variables (20)
- 49K15 Problems involving ordinary differential equations (8)
- 49K20 Problems involving partial differential equations (1)
- 49K35 Minimax problems (1)
- 49K99 None of the above, but in this section (1)

**▼****49Lxx Hamilton-Jacobi theories, including dynamic programming**- 49Mxx Methods of successive approximations
**▼****49Nxx Miscellaneous topics****▼****49Qxx Manifolds**

**▼****Geometry****▼****51-XX Geometry (3)**- 51-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (10)
- 51-01 Instructional exposition (textbooks, tutorial papers, etc.) (156)
- 51-02 Research exposition (monographs, survey articles) (7)
- 51-03 Historical (29)
- 51-04 Explicit machine computation and programs (2)
- 51-99 Geometry (57)
**▼****51Axx Linear incidence geometry**- 51A05 General theory and projective geometries (37)
- 51A10 Homomorphism, automorphism and dualities (3)
- 51A15 Structures with parallelism (12)
- 51A20 Configuration theorems (20)
- 51A25 Algebraization (1)
- 51A30 Desarguesian and Pappian geometries (7)
- 51A45 Incidence structures imbeddable into projective geometries (2)
- 51A50 Polar geometry, symplectic spaces, orthogonal spaces (10)
- 51A99 None of the above, but in this section (5)
- 51Axx Linear incidence geometry (5)

**▼****51Bxx Nonlinear incidence geometry****▼****51Exx Finite geometry and special incidence structures**- 51E10 Steiner systems (8)
- 51E12 Generalized quadrangles, generalized polygons (10)
- 51E15 Affine and projective planes (16)
- 51E20 Combinatorial structures in finite projective spaces (3)
- 51E24 Buildings and the geometry of diagrams (8)
- 51E30 Other finite incidence structures (1)
- 51E99 None of the above, but in this section (1)

**▼****51Fxx Metric geometry****▼****51Hxx Topological geometry****▼****51Jxx Incidence groups****▼****51Kxx Distance geometry****▼****51Lxx Geometric order structures****▼****51Mxx Real and complex geometry**- 51M04 Elementary problems in Euclidean geometries (520)
- 51M05 Euclidean geometries (general) and generalizations (60)
- 51M09 Elementary problems in hyperbolic and elliptic geometries (82)
- 51M10 Hyperbolic and elliptic geometries (general) and generalizations (39)
- 51M15 Geometric constructions (367)
- 51M16 Inequalities and extremum problems (16)
- 51M20 Polyhedra and polytopes; regular figures, division of spaces (276)
- 51M25 Length, area and volume (85)
- 51M30 Line geometries and their generalizations (63)
- 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (49)
- 51M99 None of the above, but in this section (24)

**▼****51Nxx Analytic and descriptive geometry**- 51N05 Descriptive geometry (75)
- 51N10 Affine analytic geometry (96)
- 51N15 Projective analytic geometry (143)
- 51N20 Euclidean analytic geometry (860)
- 51N25 Analytic geometry with other transformation groups (11)
- 51N30 Geometry of classical groups (1)
- 51N35 Questions of classical algebraic geometry (437)
- 51N99 None of the above, but in this section (33)
- 51Nxx Analytic and descriptive geometry (4)
- 51P05 Geometry and physics (12)

**▼****52-XX Convex and discrete geometry**- 52-99 Convex and discrete geometry (4)
**▼****52Axx General convexity**- 52A05 Convex sets without dimension restrictions (1)
- 52A10 Convex sets in 2 dimensions (including convex curves) (7)
- 52A15 Convex sets in 3 dimensions (including convex surfaces) (4)
- 52A20 Convex sets in n dimensions (including convex hypersurfaces) (2)
- 52A22 Random convex sets and integral geometry (3)
- 52A38 Length, area, volume (2)
- 52A40 Inequalities and extremum problems (9)
- 52A55 Spherical and hyperbolic convexity (7)

**▼****52Bxx Polytopes and polyhedra**- 52B05 Combinatorial properties (number of faces, shortest paths, etc.) (7)
- 52B10 Three-dimensional polytopes (55)
- 52B11 n-dimensional polytopes (18)
- 52B12 Special polytopes (linear programming, centrally symmetric, etc.) (9)
- 52B15 Symmetry properties of polytopes (4)
- 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (1)
- 52B55 Computational aspects related to convexity (1)
- 52B60 Isoperimetric problems for polytopes (2)
- 52Bxx Polytopes and polyhedra (2)

**▼****52Cxx Discrete geometry****▼****53Axx Classical differential geometry**- 53A04 Curves in Euclidean space (264)
- 53A05 Surfaces in Euclidean space (368)
- 53A07 Higher-dimensional and -codimensional surfaces in Euclidean n-space (6)
- 53A10 Minimal surfaces, surfaces with prescribed mean curvature (37)
- 53A15 Affine differential geometry (1)
- 53A17 Kinematics (3)
- 53A20 Projective differential geometry (5)
- 53A25 Differential line geometry (13)
- 53A30 Conformal differential geometry (1)
- 53A35 Non-Euclidean differential geometry (4)
- 53A40 Other special differential geometries (2)
- 53A45 Vector and tensor analysis (2)
- 53A55 Differential invariants (local theory), geometric objects (3)
- 53A60 Geometry of webs (2)
- 53A99 None of the above, but in this section (13)
- 53Axx Classical differential geometry (1)

**▼****53Bxx Local differential geometry****▼****53Cxx Global differential geometry**- 53C05 Connections, general theory (4)
- 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions (8)
- 53C22 Geodesics (25)
- 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) (1)
- 53C42 Immersions (minimal, prescribed curvature, tight, etc.) (2)
- 53C45 Global surface theory (convex surfaces Ã la A. D. Aleksandrov) (1)
- 53C56 Other complex differential geometry (1)
- 53C65 Integral geometry (3)
- 53C75 Geometric orders, order geometry (14)
- 53C99 None of the above, but in this section (1)

**▼****53Dxx Symplectic geometry, contact geometry****▼****54Axx Generalities****▼****54Bxx Basic constructions****▼****54Cxx Maps and general types of spaces defined by maps****▼****54Dxx Fairly general properties**- 54Exx Spaces with richer structures
**▼****54Fxx Special properties**- 54Gxx Peculiar spaces
- 54Hxx Connections with other structures, applications
**▼****55Mxx Classical topics**- 55Nxx Homology and cohomology theories
**▼****55Pxx Homotopy theory**- 55Qxx Homotopy groups
- 55Rxx Fiber spaces and bundles
- 55Sxx Operations and obstructions
- 55Txx Spectral sequences
**▼****55Uxx Applied homological algebra and category theory****▼****57Mxx Low-dimensional topology****▼****57Nxx Topological manifolds**- 57N05 Topology of E2, 2-manifolds (4)
- 57N12 Topology of E3 and S3 (1)
- 57N13 Topology of E4, 4-manifolds (1)
- 57N15 Topology of En, n-manifolds (4 < n < ∞) (2)
- 57N16 Geometric structures on manifolds (8)
- 57N20 Topology of infinite-dimensional manifolds (1)
- 57N35 Embeddings and immersions (1)
- 57N37 Isotopy and pseudo-isotopy (1)
- 57N65 Algebraic topology of manifolds (2)
- 57N99 None of the above, but in this section (3)

- 57Pxx Generalized manifolds
**▼****57Qxx PL-topology****▼****57Rxx Differential topology****▼****57Sxx Topological transformation groups****▼****57Txx Homology and homotopy of topological groups and related structures**- 58-03 Historical (1)

**▼****58Axx General theory of differentiable manifolds****▼****58Bxx Infinite-dimensional manifolds****▼****58Cxx Calculus on manifolds; nonlinear operators****▼****58Dxx Spaces and manifolds of mappings****▼****58Exx Variational problems in infinite-dimensional spaces**- 58Hxx Pseudogroups, differentiable groupoids and general structures on manifolds
**▼****58Jxx Partial differential equations on manifolds; differential operators**- 58Kxx Theory of singularities and catastrophe theory

**▼****Statistics****▼****60-XX Probability theory and stochastic processes (4)**- 60-01 Instructional exposition (textbooks, tutorial papers, etc.) (19)
- 60-02 Research exposition (monographs, survey articles) (1)
- 60-03 Historical (10)
- 60-99 Probability theory and stochastic processes (12)
**▼****60Axx Foundations of probability theory****▼****60Bxx Probability theory on algebraic and topological structures****▼****60Exx Distribution theory****▼****60Fxx Limit theorems****▼****60Gxx Stochastic processes**- 60Hxx Stochastic analysis
**▼****60Jxx Markov processes****▼****60Kxx Special processes**

**▼****62-XX Statistics**- 62Axx Foundational and philosophical topics
**▼****62Bxx Sufficiency and information****▼****62Cxx Decision theory****▼****62Exx Distribution theory****▼****62Fxx Parametric inference****▼****62Gxx Nonparametric inference**- 62G05 Estimation (2)

**▼****62Hxx Multivariate analysis**- 62H12 Estimation (1)

**▼****62Jxx Linear inference, regression**- 62Kxx Design of experiments
- 62Lxx Sequential methods
- 62Mxx Inference from stochastic processes
**▼****62Nxx Survival analysis and censored data****▼****62Pxx Applications**- 62P05 Applications to actuarial sciences and financial mathematics (36)
- 62P10 Applications to biology and medical sciences (2)
- 62P12 Applications to environmental and related topics (1)
- 62P20 Applications to economics (1)
- 62P25 Applications to social sciences (2)
- 62P99 None of the above, but in this section (2)

**▼****65-XX Numerical analysis**- 65-01 Instructional exposition (textbooks, tutorial papers, etc.) (1)
- 65-04 Explicit machine computation and programs (1)
- 65-99 Numerical analysis (2)
**▼****65Axx Tables**- 65A05 Tables (4)

**▼****65Bxx Acceleration of convergence****▼****65Cxx Probabilistic methods, simulation and stochastic differential equations****▼****65Dxx Numerical approximation and computational geometry**- 65D05 Interpolation (6)
- 65D10 Smoothing, curve fitting (11)
- 65D15 Algorithms for functional approximation (1)
- 65D20 Computation of special functions, construction of tables (1)
- 65D25 Numerical differentiation (1)
- 65D30 Numerical integration (13)
- 65D32 Quadrature and cubature formulas (11)
- 65D99 None of the above, but in this section (3)

**▼****65Fxx Numerical linear algebra****▼****65Gxx Error analysis and interval analysis****▼****65Hxx Nonlinear algebraic or transcendental equations**- 65Jxx Numerical analysis in abstract spaces
- 65Kxx Mathematical programming, optimization and variational techniques
**▼****65Lxx Ordinary differential equations**- 65Mxx Partial differential equations, initial value and time-dependent initial-boundary value problems
- 65Nxx Partial differential equations, boundary value problems
**▼****65Pxx Numerical problems in dynamical systems****▼****65Rxx Integral equations, integral transforms**- 65Txx Numerical methods in Fourier analysis
- 65Yxx Computer aspects of numerical algorithms

**▼****Applied Mathematics****▼****68-XX Computer science****▼****70-XX Mechanics of particles and systems**- 70-01 Instructional exposition (textbooks, tutorial papers, etc.) (5)
- 70-03 Historical (4)
- 70-99 Mechanics of particles and systems (6)
- 70-XX Mechanics of particles and systems (5)
**▼****70A05 Axiomatics, foundations****▼****70Bxx Kinematics****▼****70Exx Dynamics of a rigid body and of multibody systems****▼****70Fxx Dynamics of a system of particles, including celestial mechanics**- 70F05 Two-body problems (9)
- 70F07 Three-body problems (30)
- 70F10 n-body problems (5)
- 70F15 Celestial mechanics (238)
- 70F17 Inverse problems (1)
- 70F20 Holonomic systems (4)
- 70F25 Nonholonomic systems (1)
- 70F40 Problems with friction (4)
- 70F99 None of the above, but in this section (7)
- 70Fxx Dynamics of a system of particles, including celestial mechanics (14)

- 70Gxx General models, approaches, and methods
**▼****70Hxx Hamiltonian and Lagrangian mechanics****▼****70Jxx Linear vibration theory****▼****70Kxx Nonlinear dynamics**- 70Sxx Classical field theories

**▼****74-XX Mechanics of deformable solids**- 74-01 Instructional exposition (textbooks, tutorial papers, etc.) (5)
- 74-99 Mechanics of deformable solids (1)
- 74-XX Mechanics of deformable solids (2)
**▼****74Axx Generalities, axiomatics, foundations of continuum mechanics of solids****▼****74Bxx Elastic materials**- 74Cxx Plastic materials, materials of stress-rate and internal-variable type
- 74Dxx Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
**▼****74Exx Material properties given special treatment**- 74Fxx Coupling of solid mechanics with other effects
**▼****74Gxx Equilibrium (steady-state) problems****▼****74Hxx Dynamical problems**- 74H45 Vibrations (6)
- 74H55 Stability (1)
- 74Hxx Dynamical problems (4)

**▼****74Jxx Waves****▼****74Kxx Thin bodies, structures**- 74Lxx Special subfields of solid mechanics
- 74Mxx Special kinds of problems
- 74Nxx Phase transformations in solids
- 74Pxx Optimization
- 74Qxx Homogenization, determination of effective properties
- 74Rxx Fracture and damage
**▼****74Sxx Numerical methods**

**▼****76-XX Fluid mechanics (22)**- 76-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (1)
- 76-03 Historical (2)
- 76-99 Fluid mechanics (6)
**▼****76Axx Foundations, constitutive equations, rheology****▼****76Bxx Incompressible inviscid fluids****▼****76Dxx Incompressible viscous fluids**- 76Exx Hydrodynamic stability
**▼****76Fxx Turbulence**- 76Mxx Basic methods in fluid mechanics
**▼****76Nxx Compressible fluids and gas dynamics, general**- 76Rxx Diffusion and convection
**▼****76Txx Two-phase and multiphase flows**- 76Zxx Biological fluid mechanics

**▼****78-XX Optics, electromagnetic theory (12)**- 78-01 Instructional exposition (textbooks, tutorial papers, etc.) (3)
- 78-03 Historical (1)
- 78-05 Experimental work (2)
- 78-99 Optics, electromagnetic theory (1)
**▼****78Axx General**- 78A02 Foundations (2)
- 78A05 Geometric optics (108)
- 78A10 Physical optics (39)
- 78A25 Electromagnetic theory, general (28)
- 78A30 Electro- and magnetostatics (33)
- 78A40 Waves and radiation (27)
- 78A45 Diffraction, scattering (18)
- 78A55 Technical applications (19)
- 78A99 Miscellaneous topics (1)
- 78Axx General (15)

**▼****78Mxx Basic methods**

**▼****80-XX Classical thermodynamics, heat transfer (1)**- 80-03 Historical (4)
- 80-05 Experimental work (2)
- 80-99 Classical thermodynamics, heat transfer (2)
**▼****80Axx Thermodynamics and heat transfer**- 80Mxx Basic methods

**▼****81-XX Quantum theory**- 81Qxx General mathematical topics and methods in quantum theory
- 81Rxx Groups and algebras in quantum theory
**▼****81Sxx General quantum mechanics and problems of quantization**- 81Txx Quantum field theory; related classical field theories
- 81Uxx Scattering theory
**▼****81Vxx Applications to specific physical systems**

**▼****82-XX Statistical mechanics, structure of matter****▼****82Bxx Equilibrium statistical mechanics****▼****82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium)****▼****82Dxx Applications to specific types of physical systems**- 82D05 Gases (10)
- 82D15 Liquids (1)
- 82D25 Crystals (5)

- 83Cxx General relativity
- 83Exx Unified, higher-dimensional and super field theories

**▼****85-XX Astronomy and astrophysics**- 85-00 General reference works (handbooks, dictionaries, bibliographies, etc.) (7)
- 85-01 Instructional exposition (textbooks, tutorial papers, etc.) (18)
- 85-02 Research exposition (monographs, survey articles) (4)
- 85-03 Historical (3)
- 85-05 Experimental work (37)
- 85-08 Computational methods (51)
- 85-99 Astronomy and astrophysics (11)
**▼****85Axx Astronomy and astrophysics**

**▼****86-XX Geophysics (3)**- 86-01 Instructional exposition (textbooks, tutorial papers, etc.) (2)
- 86-03 Historical (1)
- 86-99 Geophysics (8)
**▼****86Axx Geophysics**

**▼****90-XX Operations research, mathematical programming (1)**- 90-99 Operations research, programming (1)
- 90Bxx Operations research and management science
- 90Cxx Mathematical programming

**▼****91-XX Game theory, economics, social and behavioral sciences**- 91-02 Research exposition (monographs, survey articles) (1)
**▼****91Axx Game theory****▼****91Bxx Mathematical economics**- 91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in general) (2)
- 91B12 Voting theory (1)
- 91B24 Price theory and market structure (2)
- 91B28 Finance, portfolios, investment (6)
- 91B30 Risk theory, insurance (36)
- 91B40 Labor market, contracts (1)
- 91B82 Statistical methods; economic indices and measures (1)
- 91B99 None of the above, but in this section (5)

- 91Cxx Social and behavioral sciences: general topics
- 91Dxx Mathematical sociology (including anthropology)
- 91Exx Mathematical psychology
- 91Fxx Other social and behavioral sciences (mathematical treatment)

**▼****92-XX Biology and other natural sciences**- 92Bxx Mathematical biology in general
**▼****92Cxx Physiological, cellular and medical topics****▼****92Dxx Genetics and population dynamics**- 92D10 Genetics (3)

**▼****92Exx Chemistry**- 92Exx Chemistry (1)

**▼****93-XX Systems theory; control****▼****94-XX Information and communication, circuits**- 94Axx Communication, information
- 94Bxx Theory of error-correcting codes and error-detecting codes
- 94Cxx Circuits, networks

**▼****97-XX Mathematics education**- 97-01 Instructional exposition (textbooks, tutorial papers, etc.) (18)
- 97-99 Mathematics education (22)
**▼****97Axx General****▼****97Bxx Educational policy and educational systems**- 97Cxx Psychology of and research in mathematics education
**▼****97Dxx Education and instruction in mathematics**- 97D20 Philosophical and theoretical contributions to mathematical education (1)
- 97D40 Teaching methods and classroom techniques. Lesson preparation. Educational principles (9)
- 97D70 Diagnosis, analysis and remediation of learning difficulties and student errors (1)
- 97D80 Teaching units, draft lessons and master lessons (2)
- 97D99 None of the above, but in this section (6)

**▼****97Uxx Educational material and media. Educational technology**

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