MSC2000 Classification Codes --> MSC2010 Classification CodesUpdate Date: 29 January 2010
00-XX General _
01-XX History and biography [See also the classification number –03 in the other sections] _
03-XX Mathematical logic and foundations _
05-XX Combinatorics {For finite fields, see 11Txx} _
05E20 Group actions on designs, geometries and codes 05E18
05E25 Group actions on posets and homology groups of posets [See also 06A11] 05E40 05E18
05E35 Orthogonal polynomials [See also 33C45, 33C50, 33D45] 05E30 33C45 33C50 33D45
06-XX Order, lattices, ordered algebraic structures [See also 18B35] _
08-XX General algebraic systems _
11-XX Number theory _
12-XX Field theory and polynomials _
13-XX Commutative rings and algebras _
13A10 Radical theory 13A15
13B24 Going up; going down; going between 13B21
13D25 Complexes 13D02
13K05 Witt vectors and related rings 13F35
14-XX Algebraic geometry _
15-XX Linear and multilinear algebra; matrix theory _
15A33 Matrices over special rings (quaternions, finite fields, etc.) 15B33
15A36 Matrices of integers [See also 11C20] 15B36
15A48 Positive matrices and their generalizations; cones of matrices 15B48
15A51 Stochastic matrices 15B51
15A52 Random matrices 15B52
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.) 15B57
15A90 Applications of matrix theory to physics 15Axx 15Bxx 81R05
16-XX Associative rings and algebras {For the commutative case, see 13-XX} _
16H05 Orders and arithmetic, separable algebras, Azumaya algebras [See also 11R52, 11R54, 11S45] 16Hxx
16W30 Coalgebras, bialgebras, Hopf algebras [See also 16S40, 57T05]; rings, modules, etc. on which these act 16Txx
16W35 Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50] 16Txx
17-XX Nonassociative rings and algebras _
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] _
20-XX Group theory and generalizations _
22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} _
26-XX Real functions [See also 54C30] _
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} _
30D50 Blaschke products, bounded mean oscillation, bounded characteristic, bounded functions, functions with positive real part 30J10
30D55 ${H}^p$-classes 30H10
31-XX Potential theory {For probabilistic potential theory, see 60J45} _
32-XX Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12} _
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 _
34C30 Manifolds of solutions 34Cxx
34D40 Ultimate boundedness 34C11 34D05 34K12
34M20 Nonanalytic aspects 37Fxx 30Dxx 34Mxx
34M37 Resurgence phenomena 30Dxx 34Mxx 37Fxx
35-XX Partial differential equations _
35A05 General existence and uniqueness theorems 35A01 35A02
35A07 Local existence and uniqueness theorems [See also 35Hxx, 35Sxx] 35A01 35A02
35B37 PDE in connection with control problems [See also 49J20, 49K20, 93C20] 35Q93
35D05 Existence of generalized solutions 35Dxx
35D10 Regularity of generalized solutions 35Dxx
35J45 General theory of elliptic systems of PDE 35J46 35J47 35J48
35J55 Boundary value problems for elliptic systems 35J57 35J58 35J56
35J85 Unilateral problems and variational inequalities for elliptic PDE [See also 35R35, 49J40] 35J86 35J87
35K50 Boundary value problems for parabolic systems 35K51 35K52
35M20 PDE of composite type 35M10
35Q58 Other completely integrable equations [See also 37J35, 37K10] 35C05
35Q72 Other equations from mechanics 35Q74 35Q70
35Q80 Applications of PDE in areas other than physics 35Q92 35Q93 35Q94 35Q90 35Q91 35Q68 35Q62
37-XX Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] _
39-XX Difference and functional equations _
39A11 Stability and asymptotics of difference equations; oscillatory and periodic solutions, etc. 39A24 39A45 39A22 39A50 39A14 39A30 39A21 39A28 39A23
40-XX Sequences, series, summability _
41-XX Approximations and expansions {For all approximation theory in the complex domain, see~; for numerical approximation, see~65Dxx} _
42-XX Fourier analysis _
43-XX Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx} _
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} _
45-XX Integral equations _
46-XX Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} _
47-XX Operator theory _
47H50 Potential operators 47G40
47N55 Applications in statistical physics 47N50
49-XX Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] _
49J22 Optimal control problems involving integral equations 49J21
49J24 Optimal control problems involving differential inclusions [See also 34A60] 49J21
49J25 Optimal control problems involving equations with retarded arguments [See also 34K35] 49J21
49K22 Problems involving integral equations 49K21
49K24 Problems involving differential inclusions [See also 34A60] 49K21
49K25 Problems involving equations with retarded arguments [See also 34K35] 49K21
51-XX Geometry {For algebraic geometry, see 14-XX} _
52-XX Convex and discrete geometry _
53-XX Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} _
54-XX General topology {For the topology of manifolds of all dimensions, see 57Nxx} _
55-XX Algebraic topology _
57-XX Manifolds and cell complexes {For complex manifolds, see 32Qxx} _
58-XX Global analysis, analysis on manifolds [See also \FullScheme{49Q15]} _
60-XX Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} _
62-XX Statistics _
65-XX Numerical analysis _
65Q05 Difference and functional equations, recurrence relations 65Q20 65Q10 65Q30
68-XX Computer science For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area _
70-XX Mechanics of particles and systems {For relativistic mechanics, see~; for statistical mechanics, see~82-XX} _
74-XX Mechanics of deformable solids _
76-XX Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX} _
78-XX Optics, electromagnetic theory {For quantum optics, see 81V80} _
80-XX Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15} _
81-XX Quantum theory _
82-XX Statistical mechanics, structure of matter _
83-XX Relativity and gravitational theory _
85-XX Astronomy and astrophysics {For celestial mechanics, see 70F15} _
86-XX Geophysics [See also 76U05, 76V05] _
90-XX Operations research, mathematical programming _
91-XX Game theory, economics, social and behavioral sciences _
91B28 Finance, portfolios, investment 91Gxx
92-XX Biology and other natural sciences _
93-XX Systems theory; control {For optimal control, see 49-XX} _
93B29 Differential-geometric methods 93B27
94-XX Information and communication, circuits _
97-XX Mathematics education _
97C80 Technological tools and other materials in teaching and learning (research on innovations, role in student learning, use of tools by teachers, etc.) 97U70
American Mathematical Society