MSC2010 Classification Codes --> MSC2000 Classification CodesUpdate Date: 14 October 2009
MSC2010DescriptionMSC2000
00-XX General _
00A09 Popularization of mathematics 00A06 00A08
00A65 Mathematics and music 00A06 00A69
00A66 Mathematics and visual arts, visualization 00A06 00A08
00A67 Mathematics and architecture 00A06 00A08
00B99 None of the above, but in this section 00Bxx
01-XX History and biography [See also the classification number –03 in the other sections] _
03-XX Mathematical logic and foundations _
03Axx Philosophical aspects of logic and foundations 03A05
03A10 Logic in the philosophy of science 03A05
03A99 None of the above, but in this section 03A05
03B62 Combined logics 03B60 68T27
03C48 Abstract elementary classes and related topics [See also 03C45] 03C45
03D32 Algorithmic randomness and dimension [See also 68Q30] 03D80 68Q30
03D78 Computation over the reals For constructive aspects, see 03F60 03F60 68Q05
03E57 Generic absoluteness and forcing axioms [See also 03E50] 03E40 03E50 03E65
03G27 Abstract algebraic logic 03G25
05-XX Combinatorics For finite fields, see 11Txx _
05C21 Flows in graphs 05C15 05C20
05C31 Graph polynomials 05C15 05C50
05C42 Density (toughness, etc.) 05C40
05C51 Graph designs and isomomorphic decomposition [See also 05B30] 05B30 05B05
05C57 Games on graphs [See also 91A43, 91A46] 91A43 05C90
05C63 Infinite graphs 05C99 05C25
05C72 Fractional graph theory, fuzzy graph theory 05C99 05C15 05C69 05C70
05C76 Graph operations (line graphs, products, etc.) 05C62
05C81 Random walks on graphs 05C80
05C82 Small world graphs, complex networks [See also 90Bxx, 91D30] 05C80 05C90 91D30
05E18 Group actions on combinatorial structures 05E20
05E40 Combinatorial aspects of commutative algebra 05E15 05E20 05E25
05E45 Combinatorial aspects of simplicial complexes 05E25 05C25 05E99
06-XX Order, lattices, ordered algebraic structures [See also 18B35] _
06A75 Generalizations of ordered sets 06A06
06B75 Generalizations of lattices 06B05 06B99
06D75 Other generalizations of distributive lattices 06D05 06D99
06E75 Generalizations of Boolean algebras 06E05 06E99
08-XX General algebraic systems _
08C20 Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30] 08C05 08C99
11-XX Number theory _
11B30 Arithmetic combinatorics; higher degree uniformity 11B13 11B75 11P70
11D07 The Frobenius problem 11D04 11D45
11F68 Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series 11F66 11F67
11G32 Dessins d'enfants, Belyĭ theory 11G99 14G32
11G42 Arithmetic mirror symmetry [See also 14J33] 11G40 14J32
11J87 Schmidt Subspace Theorem and applications 11D75 11J25
11M32 Multiple Dirichlet series and zeta functions and multizeta values 11M41
11M50 Relations with random matrices 11M26
11M55 Relations with noncommutative geometry 11R56 58B34
11P84 Partition identities; identities of Rogers-Ramanujan type 11P81 11P82
11S82 Non-Archimedean dynamical systems [See mainly 37Pxx] 11S99 37Fxx
11Zxx Miscellaneous applications of number theory 11Z05
11Z99 None of the above, but in this section 11Z05
12-XX Field theory and polynomials _
12Yxx Computational aspects of field theory and polynomials 12Y05
12Y99 None of the above, but in this section 12Y05
13-XX Commutative rings and algebras _
13C60 Module categories 13C99
13D09 Derived categories 13C99
13F35 Witt vectors and related rings 13K05
13F60 Cluster algebras 13A99
13Gxx Integral domains 13G05
13G99 None of the above, but in this section 13G05
13Lxx Applications of logic to commutative algebra [See also 03Cxx, 03Hxx] 13L05
13L99 None of the above, but in this section 13L05
13P15 Solving polynomial systems; resultants 13P99
13P20 Computational homological algebra [See also 13Dxx] 13P99
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) 13P99
14-XX Algebraic geometry _
14D23 Stacks and moduli problems 14A20 14D20
14D24 Geometric Langlands program: algebro-geometric aspects [See also 22E57] 14L99
14E16 McKay correspondence 14B05
14E18 Arcs and motivic integration 14B05
14F18 Multiplier ideals 14F99 14C20
14G17 Positive characteristic ground fields 14G99
14H57 Dessins d'enfants theory For arithmetic aspects, see 11G32 14H55 14G99 14H30
14J33 Mirror symmetry [See also 11G42, 53D37] 14J32
14M22 Rationally connected varieties 14M99
14M27 Compactifications; symmetric and spherical varieties 14M99
14Txx Tropical geometry [See also 12K10, 14M25, 14N10, 52B20] 14P99
14T99 None of the above, but in this section 14P99
15-XX Linear and multilinear algebra; matrix theory _
15Axx Basic linear algebra 15-XX
15A16 Matrix exponential and similar functions of matrices 15A99
15A80 Max-plus and related algebras 15A99
15A83 Matrix completion problems 15A99
15A86 Linear preserver problems 15A04
15Bxx Special matrices 15A57
15B05 Toeplitz, Cauchy, and related matrices 15A57
15B10 Orthogonal matrices 15A57
15B15 Fuzzy matrices 15A57
15B33 Matrices over special rings (quaternions, finite fields, etc.) 15A33
15B34 Boolean and Hadamard matrices 15A36
15B35 Sign pattern matrices 15A99
15B36 Matrices of integers [See also 11C20] 15A36
15B48 Positive matrices and their generalizations; cones of matrices 15A48
15B51 Stochastic matrices 15A51
15B52 Random matrices 15A52
15B57 Hermitian, skew-Hermitian, and related matrices 15A57
15B99 None of the above, but in this section 15A99
16-XX Associative rings and algebras For the commutative case, see 13-XX _
16E35 Derived categories 16E99
16Hxx Algebras and orders For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30 16H05
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) _
16H10 Orders in separable algebras 16H05
16H15 Commutative orders 16H05
16H20 Lattices over orders 16H05
16H99 None of the above, but in this section 16H05
16R60 Functional identities 16R99
16S85 Rings of fractions and localizations [See also 13B30] 16S90
16Txx Hopf algebras, quantum groups and related topics 16W30 16W35
16T05 Hopf algebras and their applications [See also 16S40, 57T05] 16W30
16T10 Bialgebras 16W30
16T15 Coalgebras and comodules; corings 16W30
16T20 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] 16W35
16T25 Yang-Baxter equations 16W30
16T30 Connections with combinatorics 16W30
16T99 None of the above, but in this section 16W30
16Zxx Computational aspects of associative rings 16Z05
16Z99 None of the above, but in this section 16Z05
17-XX Nonassociative rings and algebras _
17B08 Coadjoint orbits; nilpotent varieties 14L30 17B20
17B22 Root systems 17B20
18-XX Category theory; homological algebra For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also for algebraic topology _
19-XX $K$-theory [See also 16E20, 18F25] _
19L50 Twisted $K$-theory; differential $K$-theory 19L64 19L99
19Mxx Miscellaneous applications of $K$-theory 19M05
19M99 None of the above, but in this section 19M05
20-XX Group theory and generalizations _
20F11 Groups of finite Morley rank [See also 03C45, 03C60] 20E32
20F70 Algebraic geometry over groups; equations over groups 20F99
20G07 Structure theory 20G99
20G41 Exceptional groups 20G99
20G43 Schur and $q$-Schur algebras 16S99 20G99
20G44 Kac-Moody groups 20G99
20Lxx Groupoids (i.e. small categories in which all morphisms are isomorphisms) For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05 20L05
20L99 None of the above, but in this section 20L05
20M13 Arithmetic theory of monoids 20M99
20M32 Algebraic monoids 20M99
20Pxx Probabilistic methods in group theory [See also 60Bxx] 20P05
20P99 None of the above, but in this section 20P05
22-XX Topological groups, Lie groups For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX _
22Cxx Compact groups 22C05
22C99 None of the above, but in this section 22C05
22E57 Geometric Langlands program: representation-theoretic aspects [See also 14D24] 11R39 14D20 22E55
22E66 Analysis on and representations of infinite-dimensional Lie groups 22E65
22F99 None of the above, but in this section 22Fxx
26-XX Real functions [See also 54C30] _
26E70 Real analysis on time scales or measure chains For dynamic equations on time scales or measure chains see 34N05 39A10
28-XX Measure and integration For analysis on manifolds, see 58-XX _
30-XX Functions of a complex variable For analysis on manifolds, see 58-XX _
30Hxx Spaces and algebras of analytic functions 30H05 46Exx 46Jxx
30H05 Bounded analytic functions 30D50 46Exx 46Jxx
30H10 Hardy spaces 30D55 46E15 46E20 46E22 46E40 46J15 46J20
30H15 Nevanlinna class and Smirnov class 30D15 46E99
30H20 Bergman spaces, Fock spaces 30D60 46E20 46E22 46E40
30H25 Besov spaces and $Q_p$-spaces 30D60 46E15 46E20 46E22 46E35
30H30 Bloch spaces 30D45 46E15
30H35 BMO-spaces 30D60 46E15
30H50 Algebras of analytic functions 30H05 46J15 46J20
30H80 Corona theorems 30H05 46J15
30H99 None of the above, but in this section 30D99
30Jxx Function theory on the disc 30D50
30J05 Inner functions 30D50
30J10 Blaschke products 30D50
30J15 Singular inner functions 30D50
30J99 None of the above, but in this section 30D99
30Kxx Universal holomorphic functions 30B99
30K05 Universal Taylor series 30B99 30B10
30K10 Universal Dirichlet series 30B99 30B50
30K15 Bounded universal functions 30B99
30K20 Compositional universality 30B99
30K99 None of the above, but in this section 30B99
30Lxx Analysis on metric spaces 30C65 46E35
30L05 Geometric embeddings of metric spaces 30C65 46B20
30L10 Quasiconformal mappings in metric spaces 30C65
30L99 None of the above, but in this section 30C99
31-XX Potential theory For probabilistic potential theory, see 60J45 _
31Dxx Axiomatic potential theory 31D05
31D99 None of the above, but in this section 31D05
31Exx Potential theory on metric spaces 31Cxx 46E35
31E05 Potential theory on metric spaces 31C05 46E35
31E99 None of the above, but in this section 31C99 46E35
32-XX Several complex variables and analytic spaces For infinite-dimensional holomorphy, see 46G20, 58B12 _
32Pxx Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32P05
32P99 None of the above, but in this section 32P05
32Q26 Notions of stability 32Q15 32Q20
33-XX Special functions [(33-XX deals with the properties of functions as functions)} For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx] _
34-XX Ordinary differential equations _
34A07 Fuzzy differential equations 34A12 34A60 34G25
34A08 Fractional differential equations 34A12 34Bxx 26A33
34A33 Lattice differential equations 34A12 34B45 34C15 34A35 37K60 37L60
34A38 Hybrid systems 34A12 93C23
34C46 Multifrequency systems 34C15 34C29 70K43
34D06 Synchronization 34Dxx 34K20 34K05
34E17 Canard solutions 34C05 34E15 34C26
34Fxx Equations and systems with randomness [See also 34K50, 60H10, 93E03] 34F05 37H10
34F10 Bifurcation 34C23 34F05 34K18 37H20
34F15 Resonance phenomena 34F05 37J40 70J40 70K28 70K30 37H10 70L05
34F99 None of the above, but in this section 34F05 37H10
34Hxx Control problems [See also 49J15, 49K15, 93C15] 34H05
34H10 Chaos control 34C28 37D45 37N35
34H15 Stabilization 34Dxx 93Dxx
34H20 Bifurcation control 34C23 34K18
34H99 None of the above, but in this section 34H05 34C23
34K08 Spectral theory of functional-differential operators 34Lxx 47E05 47G20
34K09 Functional-differential inclusions 34A60 34G25 34K05
34K21 Stationary solutions 34Dxx 34K20
34K27 Perturbations 34D10 34E10
34K31 Lattice functional-differential equations 34C15 34B45 37K60 37L60
34K32 Implicit equations 34A09 34K05
34K33 Averaging 34C29 37J40 70K65
34K34 Hybrid systems 34A12 93C23
34K36 Fuzzy functional-differential equations 34K05 34K06 34A60 34G25
34K37 Functional-differential equations with fractional derivatives 34K05 34K06
34K38 Functional-differential inequalities 34A40 34K05
34M03 Linear equations and systems 34Mxx
34M56 Isomonodromic deformations 34M55 37J35
34Nxx Dynamic equations on time scales or measure chains For real analysis on time scales see 26E70 39A10 39A11
34N05 Dynamic equations on time scales or measure chains For real analysis on time scales or measure chains, see 26E70 39A10 39A11
34N99 None of the above, but in this section 39A10 39A11
35-XX Partial differential equations _
35A01 Existence problems: global existence, local existence, non-existence 35A05
35A02 Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness 35A05
35A09 Classical solutions 35A05
35A16 Topological and monotonicity methods 35A25
35A23 Inequalities involving derivatives and differential and integral operators, inequalities for integrals 35A25 26D10
35A24 Methods of ordinary differential equations 35A25
35B06 Symmetries, invariants, etc. 35B05 58J70
35B07 Axially symmetric solutions 35B05
35B08 Entire solutions 35B05
35B09 Positive solutions 35B05
35B36 Pattern formation 35B34
35B44 Blow-up 35B40
35B51 Comparison principles 35B05
35B53 Liouville theorems, Phragmén-Lindelöf theorems 35B40
35C06 Self-similar solutions 35C05
35C07 Traveling wave solutions 35C05
35C08 Soliton solutions 35Q51
35C09 Trigonometric solutions 35C05
35C11 Polynomial solutions 35C05
35D30 Weak solutions 35D05
35D35 Strong solutions 35D05
35D40 Viscosity solutions 35D05
35F16 Initial-boundary value problems for linear first-order equations 35F15
35F21 Hamilton-Jacobi equations 35F20
35F31 Initial-boundary value problems for nonlinear first-order equations 35F30
35F35 Linear first-order systems 35F05
35F40 Initial value problems for linear first-order systems 35F10
35F45 Boundary value problems for linear first-order systems 35F15
35F46 Initial-boundary value problems for linear first-order systems 35F15
35F50 Nonlinear first-order systems 35F20
35F55 Initial value problems for nonlinear first-order systems 35F25
35F60 Boundary value problems for nonlinear first-order systems 35F30
35F61 Initial-boundary value problems for nonlinear first-order systems 35F30
35G16 Initial-boundary value problems for linear higher-order equations 35G05
35G31 Initial-boundary value problems for nonlinear higher-order equations 35G30
35G35 Linear higher-order systems 35G05
35G40 Initial value problems for linear higher-order systems 35G10
35G45 Boundary value problems for linear higher-order systems 35G15
35G46 Initial-boundary value problems for linear higher-order systems 35G15
35G50 Nonlinear higher-order systems 35G20
35G55 Initial value problems for nonlinear higher-order systems 35G25
35G60 Boundary value problems for nonlinear higher-order systems 35G30
35G61 Initial-boundary value problems for nonlinear higher-order systems 35G30
35J08 Green's functions 35A08
35J46 First-order elliptic systems 35F05
35J47 Second-order elliptic systems 35J15 35J45
35J48 Higher-order elliptic systems 35J30 35J45
35J56 Boundary value problems for first-order elliptic systems 35F15 35J55
35J57 Boundary value problems for second-order elliptic systems 35J25 35J55
35J58 Boundary value problems for higher-order elliptic systems 35J40 35J55
35J61 Semilinear elliptic equations 35J60
35J62 Quasilinear elliptic equations 35J60
35J66 Nonlinear boundary value problems for nonlinear elliptic equations 35J65
35J75 Singular elliptic equations 35J60
35J86 Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40] 35J85
35J87 Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40] 35J85
35J88 Systems of elliptic variational inequalities [See also 35R35, 49J40] 35J85
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 35J60
35J92 Quasilinear elliptic equations with $p$-Laplacian 35J60
35J93 Quasilinear elliptic equations with mean curvature operator 35J60
35J96 Elliptic Monge-Ampère equations 35J60
35K08 Heat kernel 35K05
35K41 Higher-order parabolic systems 35K25 35K40
35K46 Initial value problems for higher-order parabolic systems 35K45 35K30
35K51 Initial-boundary value problems for second-order parabolic systems 35K20 35K35
35K52 Initial-boundary value problems for higher-order parabolic systems 35K35
35K58 Semilinear parabolic equations 35K55
35K59 Quasilinear parabolic equations 35K55
35K61 Nonlinear initial-boundary value problems for nonlinear parabolic equations 35K60
35K67 Singular parabolic equations 35K55
35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40] 35K85
35K87 Systems of parabolic variational inequalities [See also 35R35, 49J40] 35K85
35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian 35K55
35K92 Quasilinear parabolic equations with $p$-Laplacian 35K55
35K93 Quasilinear parabolic equations with mean curvature operator 35K55 53C44
35K96 Parabolic Monge-Ampère equations 35K55
35L02 First-order hyperbolic equations 35L40
35L03 Initial value problems for first-order hyperbolic equations 35L45
35L04 Initial-boundary value problems for first-order hyperbolic equations 35L50
35L51 Second-order hyperbolic systems 35L10
35L52 Initial value problems for second-order hyperbolic systems 35L15
35L53 Initial-boundary value problems for second-order hyperbolic systems 35L20
35L56 Initial value problems for higher-order hyperbolic systems 35L30
35L57 Initial-boundary value problems for higher-order hyperbolic systems 35L35
35L71 Semilinear second-order hyperbolic equations 35L70
35L72 Quasilinear second-order hyperbolic equations 35L70
35L76 Semilinear higher-order hyperbolic equations 35L75
35L77 Quasilinear higher-order hyperbolic equations 35L75
35L81 Singular hyperbolic equations 35L70
35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40] 35L85
35L87 Unilateral problems and variational inequalities for hyperbolic systems [See also 35R35, 49J40] 35L85
35M11 Initial value problems for equations of mixed type 35M10
35M12 Boundary value problems for equations of mixed type 35M10
35M13 Initial-boundary value problems for equations of mixed type 35M10
35M30 Systems of mixed type 35M10
35M31 Initial value problems for systems of mixed type 35M10
35M32 Boundary value problems for systems of mixed type 35M10
35M33 Initial-boundary value problems for systems of mixed type 35M10
35M85 Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40] 35M10
35M86 Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40] 35M10
35M87 Systems of variational inequalities of mixed type [See also 35R35, 49J40] 35M10
35N20 Overdetermined initial value problems 35N05
35N25 Overdetermined boundary value problems 35N05
35N30 Overdetermined initial-boundary value problems 35N05
35Q20 Boltzmann equations 35F20 76P05 82C40
35Q31 Euler equations [See also 76D05, 76D07, 76N10] 35Q35
35Q41 Time-dependent Schrödinger equations, Dirac equations 35Q40
35Q56 Ginzburg-Landau equations 35Q60
35Q61 Maxwell equations 35Q60
35Q62 PDEs in connection with statistics 35Q80
35Q68 PDEs in connection with computer science 35Q80
35Q70 PDEs in connection with mechanics of particles and systems 35Q72
35Q74 PDEs in connection with mechanics of deformable solids 35Q72
35Q76 Einstein equations 35Q75
35Q79 PDEs in connection with classical thermodynamics and heat transfer 35K05 35K55
35Q82 PDEs in connection with statistical mechanics 35Q99
35Q83 Vlasov-like equations 35F20
35Q84 Fokker-Planck equations 35K55
35Q85 PDEs in connection with astronomy and astrophysics 35Q99
35Q86 PDEs in connection with geophysics 35Q99
35Q90 PDEs in connection with mathematical programming 35Q80
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences 35Q80
35Q92 PDEs in connection with biology and other natural sciences 35Q80
35Q93 PDEs in connection with control and optimization 35B37
35Q94 PDEs in connection with information and communication 35Q80
35R01 Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx] 35R99 31C12 58Jxx
35R02 Partial differential equations on graphs and networks (ramified or polygonal spaces) 35R99 31C20
35R03 Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc. 35R99
35R06 Partial differential equations with measure 35R05
35R09 Integro-partial differential equations [See also 45Kxx] 35R10
35R11 Fractional partial differential equations 35R10 26A33
35R13 Fuzzy partial differential equations 35R99
35R37 Moving boundary problems 35R35
35S11 Initial-boundary value problems for pseudodifferential operators 35S15
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] _
37Pxx Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45] 11S99 37A45 37B10 37B99 37F10
37P05 Polynomial and rational maps 11S99 37A45 37B10 37B99 37F10
37P10 Analytic and meromorphic maps 11S99 37A45 37B10 37B99 37F10
37P15 Global ground fields 11S99 37A45 37B10 37B99 37F10
37P20 Non-Archimedean local ground fields 11S99 37A45 37B10 37B99 37F10
37P25 Finite ground fields 11S99 37A45 37B10 37B99 37F10
37P30 Height functions; Green functions; invariant measures [See also 11G50, 14G40] 11S99 37A45 37B10 37B99 37F10
37P35 Arithmetic properties of periodic points 11S99 37A45 37B10 37B99 37F10
37P40 Non-Archimedean Fatou and Julia sets 37F50
37P45 Families and moduli spaces 11S99 37A45 37B10 37B99 37F10
37P50 Dynamical systems on Berkovich spaces 11S99 37A45 37B10 37B99 37F10
37P55 Arithmetic dynamics on general algebraic varieties 11S99 37A45 37B10 37B99 37F10
37P99 None of the above, but in this section 11S99 37A45 37B10 37B99 37F10
39-XX Difference and functional equations _
39A06 Linear equations 39A10 39A11
39A14 Partial difference equations 39A10 39A11 39A20
39A21 Oscillation theory 39A10 39A11
39A22 Growth, boundedness, comparison of solutions 39A10 39A11
39A23 Periodic solutions 39A10 39A11 37C25 37E05
39A24 Almost periodic solutions 39A10 39A11
39A28 Bifurcation theory 39A10 39A11 37E05 37Gxx
39A30 Stability theory 39A10 39A11 37B25 37C75
39A33 Complex (chaotic) behavior of solutions 39A10 39A11 37E05 37D45
39A45 Equations in the complex domain 39A10 39A11
39A50 Stochastic difference equations 39A10 39A11 37H10
39A60 Applications 39Axx
40-XX Sequences, series, summability _
40A35 Ideal and statistical convergence [See also 40G15] 40G99
40Bxx Multiple sequences and series 40B05
40B99 None of the above, but in this section 40B05
40Fxx Absolute and strong summability (should also be assigned at least one other classification number in Section 40) 40F05
40F99 None of the above, but in this section 40F05
40G15 Summability methods using statistical convergence [See also 40A35] 40G99
40Hxx Functional analytic methods in summability 46A35 46A45 46B15 46B45
40H99 None of the above, but in this section 40H05
40Jxx Summability in abstract structures [See also 43A55, 46A35, 46B15] 40J05
40J99 None of the above, but in this section 40J05
41-XX Approximations and expansions For all approximation theory in the complex domain, see~; for numerical approximation, see~65Dxx _
41Axx Approximations and expansions For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx 41-XX
42-XX Fourier analysis _
42B37 Harmonic analysis and PDE [See also 35-XX] 32D50 35A25 35S30 43A85
43-XX Abstract harmonic analysis For other analysis on topological and Lie groups, see 22Exx _
43Axx Abstract harmonic analysis For other analysis on topological and Lie groups, see 22Exx 43-XX
44-XX Integral transforms, operational calculus For fractional derivatives and integrals, see 26A33. For Fourier transforms, see . For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10 _
44Axx Integral transforms, operational calculus For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10 44-XX
45-XX Integral equations _
45Axx Linear integral equations 45-XX
45A99 None of the above, but in this section 45A05
45Bxx Fredholm integral equations 45B05
45B99 None of the above, but in this section 45B05
45Cxx Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75] 47A75 47G10 47N20
45C99 None of the above, but in this section 45C05
45Dxx Volterra integral equations [See also 34A12] 45D05
45D99 None of the above, but in this section 45D05
45G99 None of the above, but in this section 45G15
45Hxx Miscellaneous special kernels [See also 44A15] 45H05
45H99 None of the above, but in this section 45H05
45Jxx Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] 47G20
45J99 None of the above, but in this section 45J05
45Kxx Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 45K05
45K99 None of the above, but in this section 45K05
45Lxx Theoretical approximation of solutions For numerical analysis, see 65Rxx 45L05
45L99 None of the above, but in this section 45L05
45Nxx Abstract integral equations, integral equations in abstract spaces 47N20
45N99 None of the above, but in this section 45N05 47N20
45Pxx Integral operators [See also 47B38, 47G10] 45P05 47G10
45P99 None of the above, but in this section 45P05 47G10
45Qxx Inverse problems 45Q05
45Q99 None of the above, but in this section 45Q05
45Rxx Random integral equations [See also 60H20] 45R05
45R99 None of the above, but in this section 45R05
46-XX Functional analysis For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx _
46B06 Asymptotic theory of Banach spaces [See also 52A23] 46B07 46B20 46B99
46B80 Nonlinear classification of Banach spaces; nonlinear quotients 46B03 46B20 46B99 46T99
46B85 Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx] 46B07 46B20
46L36 Classification of factors 46L10 46L35
47-XX Operator theory _
47Exx Ordinary differential operators [See also 34Bxx, 34Lxx] 47E05
47E99 None of the above, but in this section 47E05
47Fxx Partial differential operators [See also 35Pxx, 58Jxx] 47F05
47F99 None of the above, but in this section 47F05
47G40 Potential operators [See also 31-XX] 47H50
47H08 Measures of noncompactness and condensing mappings, $K$-set contractions, etc. 46A50 46B50 47H09
47H25 Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35] 47A35 47H09 47H10 47H20
47J22 Variational and other types of inclusions [See also 34A60, 49J21, 49K21] 47J20 49J40
47L22 Ideals of polynomials and of multilinear mappings 46G25 47H60
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] _
49J21 Optimal control problems involving relations other than differential equations 49J22 49J24
49K21 Problems involving relations other than differential equations 49K22 49K24
49Rxx Variational methods for eigenvalues of operators [See also 47A75] 49R50
49R99 None of the above, but in this section 49R50
49Sxx Variational principles of physics 49S05
49S99 None of the above, but in this section 49S05
51-XX Geometry For algebraic geometry, see 14-XX _
51Cxx Ring geometry (Hjelmslev, Barbilian, etc.) 51C05
51C99 None of the above, but in this section 51C05
51Gxx Ordered geometries (ordered incidence structures, etc.) 51G05
51G99 None of the above, but in this section 51G05
51Pxx Geometry and physics (should also be assigned at least one other classification number from Sections 70–86) 51P05
51P99 None of the above, but in this section 51P05
52-XX Convex and discrete geometry _
52A23 Asymptotic theory of convex bodies [See also 46B06] 52A20 52A27 52A40 46B07 46B20
53-XX Differential geometry For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx _
53C08 Gerbes, differential characters: differential geometric aspects 53C05 55R65
53D18 Generalized geometries (à la Hitchin) 53C26 53D17
53D37 Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33] 14J32 53D35 53D45
53D42 Symplectic field theory; contact homology 53D35
53Zxx Applications to physics 53Z05
53Z99 None of the above, but in this section 53Z05
54-XX General topology For the topology of manifolds of all dimensions, see 57Nxx _
54Jxx Nonstandard topology [See also 03H05] 54J05
54J99 None of the above, but in this section 54J05
55-XX Algebraic topology _
55N32 Orbifold cohomology 55N35 57R19
55P50 String topology 55P35 57R19
57-XX Manifolds and cell complexes For complex manifolds, see 32Qxx _
57R18 Topology and geometry of orbifolds 57R19
58-XX Global analysis, analysis on manifolds [See also \FullScheme49Q15] _
58J51 Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity 37A25 58J50
58Zxx Applications to physics 58Z05
58Z99 None of the above, but in this section 58Z05
60-XX Probability theory and stochastic processes For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX _
60A86 Fuzzy probability 03E72 28E10 60A05 60A10 60F99
60B20 Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 15A52 46L53 60B11 82B44 82C44
60Cxx Combinatorial probability 60C05
60C99 None of the above, but in this section 60C05
60Dxx Geometric probability and stochastic geometry [See also 52A22, 53C65] 60D05
60D99 None of the above, but in this section 60D05
60G22 Fractional processes, including fractional Brownian motion 60G15 60G18
60J28 Applications of continuous-time Markov processes on discrete state spaces 60J27 60J20
60J67 Stochastic (Schramm-)Loewner evolution (SLE) 60J65 60K35 82B31 82C31
60J68 Superprocesses 60J80 60G57 60J55 60J25
62-XX Statistics _
62Axx Foundational and philosophical topics 62A01
62A86 Fuzzy analysis in statistics 28A99 62A01 94D05
62A99 None of the above, but in this section 62A01
62B86 Fuzziness, sufficiency, and information 62B05 62B10 62B15 62B99 94D05
62C86 Decision theory and fuzziness 62C05 62C99
62Dxx Sampling theory, sample surveys 62D05
62D99 None of the above, but in this section 62D05
62E86 Fuzziness in connection with the topics on distributions in this section 62E15 62E99
62F86 Parametric inference and fuzziness 62F03 62F10 62F12 62F15 62F99
62G86 Nonparametric inference and fuzziness 62G99 62G05 62G07 62G08 62G09 62G10 62G20
62H86 Multivariate analysis and fuzziness 03E72 60E05 62H05 62H20 62H25 62H30 68T10
62J86 Fuzziness, and linear inference and regression 03E72 62J02 62J05 62J99
62K86 Fuzziness and design of experiments 62K99
62L86 Fuzziness and sequential methods 62L99
62M86 Inference from stochastic processes and fuzziness 03E72 26E50 62M10 62M30 62M45 62M99
62N86 Fuzziness, and survival analysis and censored data 62N01 62N02 62N03 62N99
62Qxx Statistical tables 62Q05
62Q99 None of the above, but in this section 62Q05
65-XX Numerical analysis _
65Axx Tables 65A05
65A99 None of the above, but in this section 65A05
65D19 Computational issues in computer and robotic vision 65D18 68T45
65Exx Numerical methods in complex analysis (potential theory, etc.) For numerical methods in conformal mapping, see also 30C30 65E05
65E99 None of the above, but in this section 65E05
65F08 Preconditioners for iterative methods 65F10
65F60 Matrix exponential and similar matrix functions 65F30
65H04 Roots of polynomial equations 65H05
65J08 Abstract evolution equations 65J10
65K15 Numerical methods for variational inequalities and related problems 65K10
65L03 Functional-differential equations 65L05
65L04 Stiff equations 65L05
65L11 Singularly perturbed problems 65L10
65M08 Finite volume methods 65M06
65M22 Solution of discretized equations [See also 65Fxx, 65Hxx] 65M99
65M38 Boundary element methods 65M99
65M75 Probabilistic methods, particle methods, etc. 65M99
65M80 Fundamental solutions, Green's function methods, etc. 65M99
65M85 Fictitious domain methods 65M99
65N08 Finite volume methods 65N06
65N20 Ill-posed problems 65J20
65N75 Probabilistic methods, particle methods, etc. 65N99
65N80 Fundamental solutions, Green's function methods, etc. 65N99
65N85 Fictitious domain methods 65N99
65Qxx Difference and functional equations, recurrence relations 65Q05
65Q10 Difference equations 65Q05
65Q20 Functional equations 65Q05
65Q30 Recurrence relations 65Q05
65Q99 None of the above, but in this section 65Q05
65Sxx Graphical methods 65S05
65S99 None of the above, but in this section 65S05
65Y04 Algorithms for computer arithmetic, etc. [See also 68M07] 65Y99
65Zxx Applications to physics 65Z05
65Z99 None of the above, but in this section 65Z05
68-XX Computer science For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area _
68M11 Internet topics [See also 68U35] 68M10 68U35
68Q12 Quantum algorithms and complexity [See also 68Q05, 81P68] 68Q05 68Q15 81P68 68Q10
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40] 68Q25 68W20 68W40
68T42 Agent technology 68T20 68T99
68W27 Online algorithms 68Q10 68W40 68W05
68W32 Algorithms on strings 68W05
70-XX Mechanics of particles and systems For relativistic mechanics, see~; for statistical mechanics, see~82-XX _
70Axx Axiomatics, foundations 70A05
70A99 None of the above, but in this section 70A05
70Cxx Statics 70C20
70C99 None of the above, but in this section 70C20
70Lxx Random vibrations [See also 74H50] 70L05
70L99 None of the above, but in this section 70L05
70Mxx Orbital mechanics 70M20
70M99 None of the above, but in this section 70M20
70Pxx Variable mass, rockets 70P05
70P99 None of the above, but in this section 70P05
70Qxx Control of mechanical systems [See also 60Gxx, 60Jxx] 70Q05
70Q99 None of the above, but in this section 70Q05
74-XX Mechanics of deformable solids _
74S60 Stochastic methods 74G15 74H15 74S30
74S70 Complex variable methods 74G05 74G15 74H05 74H15 74S30
76-XX Fluid mechanics For general continuum mechanics, see 74Axx, or other parts of 74-XX _
76Gxx General aerodynamics and subsonic flows 76G25
76G99 None of the above, but in this section 76G25
76Hxx Transonic flows 76H05
76H99 None of the above, but in this section 76H05
76Jxx Supersonic flows 76J20
76J99 None of the above, but in this section 76J20
76Kxx Hypersonic flows 76K05
76K99 None of the above, but in this section 76K05
76Lxx Shock waves and blast waves [See also 35L67] 76L05
76L99 None of the above, but in this section 76L05
76Pxx Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05] 76P05
76P99 None of the above, but in this section 76P05
76Qxx Hydro- and aero-acoustics 76Q05
76Q99 None of the above, but in this section 76Q05
76Sxx Flows in porous media; filtration; seepage 76S05
76S99 None of the above, but in this section 76S05
76Uxx Rotating fluids 76U05
76U99 None of the above, but in this section 76U05
76Vxx Reaction effects in flows [See also 80A32] 76V05
76V99 None of the above, but in this section 76V05
76Wxx Magnetohydrodynamics and electrohydrodynamics 76W05
76W99 None of the above, but in this section 76W05
76Xxx Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10] 76X05
76X99 None of the above, but in this section 76X05
76Yxx Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30] 76Y05
76Y99 None of the above, but in this section 76Y05
78-XX Optics, electromagnetic theory For quantum optics, see 81V80 _
78A37 Ion traps 78A55
78A57 Electrochemistry 92E10 92E99
78M12 Finite volume methods, finite integration techniques 78M25
78M16 Multipole methods 78M25
78M22 Spectral methods 78M25
78M31 Monte Carlo methods 78M25
78M32 Neural and heuristic methods 78M25
78M34 Model reduction 78M25 78M99
80-XX Classical thermodynamics, heat transfer For thermodynamics of solids, see 74A15 _
81-XX Quantum theory _
81P13 Contextuality 81P15
81P16 Quantum state spaces, operational and probabilistic concepts 81P15 81S25
81P40 Quantum coherence, entanglement, quantum correlations 81P15
81P45 Quantum information, communication, networks [See also 94A15, 94A17] 81P68
81P50 Quantum state estimation, approximate cloning 46L60 46N50 81P15
81P70 Quantum coding (general) 81P68 94B60
81P94 Quantum cryptography [See also 94A60] 81P68 94A60
81Q12 Non-selfadjoint operator theory in quantum theory 47N50
81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 34B45
81Q37 Quantum dots, waveguides, ratchets, etc. 81Q50 81Q99
81Q65 Alternative quantum mechanics 81Q05 81Q99
81Q80 Special quantum systems, such as solvable systems 81Q05 81Q10
81Q93 Quantum control 81Q99
81S22 Open systems, reduced dynamics, master equations, decoherence [See also 82C31] 82C10
81T28 Thermal quantum field theory [See also 82B30] 81T99
81T55 Casimir effect 81T10 81T99
81U35 Inelastic and multichannel scattering 81U10 81U99
81V65 Quantum dots [See also 82D20] 81Q99
82-XX Statistical mechanics, structure of matter _
82D77 Quantum wave guides, quantum wires [See also 78A50] 81Q99 82B10 82D20
82D80 Nanostructures and nanoparticles 74A25 74A60 74A99
83-XX Relativity and gravitational theory _
83Axx Special relativity 70H40 83A05
83A99 None of the above, but in this section 70H40 83A05
83Bxx Observational and experimental questions 83B05
83B99 None of the above, but in this section 83B05
83Dxx Relativistic gravitational theories other than Einstein's, including asymmetric field theories 83D05
83D99 None of the above, but in this section 83D05
83Fxx Cosmology 83F05
83F99 None of the above, but in this section 83F05
85-XX Astronomy and astrophysics For celestial mechanics, see 70F15 _
85Axx Astronomy and astrophysics For celestial mechanics, see 70F15 85-XX
86-XX Geophysics [See also 76U05, 76V05] _
86Axx Geophysics [See also 76U05, 76V05] 86-XX
90-XX Operations research, mathematical programming _
91-XX Game theory, economics, social and behavioral sciences _
91B15 Welfare economics 91B14 91B18
91B25 Asset pricing models 91B28
91B51 Dynamic stochastic general equilibrium theory 91B50 91B52 91A15
91B55 Economic dynamics 91B62 91B64 91A25
91B69 Heterogeneous agent models 91B28 91B62 91B64
91B80 Applications of statistical and quantum mechanics to economics (econophysics) 91B99 91B82
91Gxx Mathematical finance 91B28
91G10 Portfolio theory 91B28
91G20 Derivative securities 91B28
91G30 Interest rates (stochastic models) 91B28 91B70
91G40 Credit risk 91B30 91B28
91G50 Corporate finance 91B28
91G60 Numerical methods (including Monte Carlo methods) 91B28
91G70 Statistical methods, econometrics 91B82 91B84
91G80 Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 91B28
91G99 None of the above, but in this section 91B28 91B99
92-XX Biology and other natural sciences _
92B25 Biological rhythms and synchronization 92C20 92C30
92C42 Systems biology, networks 92B05 92B20
92Fxx Other natural sciences (should also be assigned at least one other classification number in this section) 92F05
92F99 None of the above, but in this section 92F05
93-XX Systems theory; control For optimal control, see 49-XX _
94-XX Information and communication, circuits _
94Dxx Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10] 94D05
94D99 None of the above, but in this section 94D05
97-XX Mathematics education _
97A10 Comprehensive works, reference books 97-99
97A30 History of mathematics and mathematics education [See also 01-XX] 01-XX
97A50 Bibliographies [See also 01-00] 01A70
97A70 Theses and postdoctoral theses 97-02
97A99 None of the above, but in this section 97-99
97C10 Comprehensive works 97-99
97Exx Foundations of mathematics 03A05 03Bxx 03Exx
97E10 Comprehensive works 97-99
97E20 Philosophy and mathematics 03A05
97E30 Logic 03Bxx
97E40 Language of mathematics 97-99
97E50 Reasoning and proving in the mathematics classroom 97-99
97E60 Sets, relations, set theory 03Exx
97E99 None of the above, but in this section 97-99
97Fxx Arithmetic, number theory 11-XX
97F10 Comprehensive works 97-99
97F20 Pre-numerical stage, concept of numbers 97-99
97F30 Natural numbers 97-99
97F40 Integers, rational numbers 97-99
97F50 Real numbers, complex numbers 97-99
97F60 Number theory 11Axx
97F70 Measures and units 97-99
97F80 Ratio and proportion, percentages 97-99
97F90 Real life mathematics, practical arithmetic 00A69
97F99 None of the above, but in this section 97-99
97Gxx Geometry 97-99
97G10 Comprehensive works 97-99
97G20 Informal geometry 97-99
97G30 Areas and volumes 97-99
97G40 Plane and solid geometry 97-99
97G50 Transformation geometry 97-99
97G60 Plane and spherical trigonometry 97-99
97G70 Analytic geometry. Vector algebra 15-XX
97G80 Descriptive geometry 97-99
97G99 None of the above, but in this section 97-99
97Hxx Algebra 15-XX
97H10 Comprehensive works 97-99
97H20 Elementary algebra 97-99
97H30 Equations and inequalities 97-99
97H40 Groups, rings, fields 20-XX
97H50 Ordered algebraic structures 97-99
97H60 Linear algebra 15-XX
97H99 None of the above, but in this section 97-99
97Ixx Analysis 97-99
97I10 Comprehensive works 97-99
97I20 Mappings and functions 97-99
97I30 Sequences and series 11Bxx 40Axx
97I40 Differential calculus 26A24
97I50 Integral calculus 26B15
97I60 Functions of several variables 26Bxx
97I70 Functional equations 39Bxx
97I80 Complex analysis 30-XX
97I99 None of the above, but in this section 97-99
97Kxx Combinatorics, graph theory, probability theory, statistics 05-XX 60-XX 62-XX
97K10 Comprehensive works 97-99
97K20 Combinatorics 05-XX
97K30 Graph theory 05Cxx
97K40 Descriptive statistics 62-XX
97K50 Probability theory 60-XX
97K60 Distributions and stochastic processes 60Exx 60Gxx
97K70 Foundations and methodology of statistics 62-XX
97K80 Applied statistics 62Pxx
97K99 None of the above, but in this section 97-99
97Mxx Mathematical modeling, applications of mathematics 93A30 00A69
97M10 Modeling and interdisciplinarity 97-99
97M20 Mathematics in vocational training and career education 97-99
97M30 Financial and insurance mathematics 91Bxx
97M40 Operations research, economics 91Bxx
97M50 Physics, astronomy, technology, engineering 70-XX 74-XX 76-XX 78-XX 80-XX 81-XX 83-XX 85-XX 86-XX 90-XX 93-XX
97M60 Biology, chemistry, medicine 92-XX
97M70 Behavioral and social sciences 91-XX
97M80 Arts, music, language, architecture 00A06 00A69
97M99 None of the above, but in this section 07-99
97Nxx Numerical mathematics 65Nxx
97N10 Comprehensive works 97-99
97N20 Rounding, estimation, theory of errors 97-99
97N30 Numerical algebra 97-99
97N40 Numerical analysis 65Nxx
97N50 Interpolation and approximation 65Dxx
97N60 Mathematical programming 90Cxx
97N70 Discrete mathematics 05Cxx 68Rxx
97N80 Mathematical software, computer programs 90Cxx
97N99 None of the above, but in this section 97-99
97Pxx Computer science 68-XX
97P10 Comprehensive works 97-99
97P20 Theory of computer science 68Pxx 68Qxx
97P30 System software 68Nxx
97P40 Programming languages 68N15
97P50 Programming techniques 68N17 68N18 68N19
97P60 Hardware 68Mxx
97P70 Computer science and society 68-99
97P99 None of the above, but in this section 68-99
97Qxx Computer science education 68-99
97Q10 Comprehensive works 68-99
97Q20 Affective aspects in teaching computer science 68-99
97Q30 Cognitive processes 68-99
97Q40 Sociological aspects 68-99
97Q50 Objectives 68-99
97Q60 Teaching methods and classroom techniques 68-99
97Q70 Student assessment 68-99
97Q80 Teaching units 68-99
97Q99 None of the above, but in this section 68-99
97Rxx Computer science applications 68Uxx
97R10 Comprehensive works, collections of programs 97-99
97R20 Applications in mathematics 68U99
97R30 Applications in sciences 68U99
97R40 Artificial intelligence 68Txx
97R50 Data bases, information systems 68U35
97R60 Computer graphics 68U05
97R70 User programs, administrative applications 97-99
97R80 Recreational computing 97-99
97R99 None of the above, but in this section 97-99
MSC2010DescriptionMSC2000
 
 
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