MSC2000 | Description | MSC2010 |
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00-XX | General and overarching topics; collections | _ |
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 | Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | 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, see 16Exx; for groups, see 20Jxx; for topological groups and related structures, see 57Txx; for algebraic topology, see also 55Nxx, 55Uxx} | _ |
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 | _ | ||
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-\newline dimensional holomorphy, see also 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 approximation theory in the complex domain, see 30E05, 30E10; for trigonometric approximation and interpolation, see 42A10, 42A15; for numerical approximation, see 65Dxx} | _ |
42-XX | Harmonic analysis on Euclidean spaces | _ |
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 42A38, 42B10; 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; for differential geometry, see 53-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\newline 32Qxx} | _ |
58-XX | Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 53Cxx] {For nonlinear operators, see 47Hxx; for geometric integration theory, see 49Q15} | _ |
60-XX | Probability theory and stochastic processes {For additional applications, see 05Cxx, 11Kxx, 34-XX, 35-XX, 62-XX, 76-XX, 81-XX, 82-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 containing software, source code, etc. in a specific mathematical area, see the classification number –04 in that area} | _ |
70-XX | Mechanics of particles and systems {For relativistic mechanics, see 83A05, 83C10; 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, finance, and other 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 theory, 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 |
MSC2000 | Description | MSC2010 |
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