MSC2000 | Description | MSC2010 |
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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 |

MSC2000 | Description | MSC2010 |
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