| Section |
P |
S |
| 00? |
General |
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|
|
| 01? |
History and biography |
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|
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| 03 |
Mathematical logic and foundations |
|
67 |
2 |
| 05 |
Combinatorics |
For finite fields, see 11Txx |
6 |
|
| 06 |
Order, lattices, ordered algebraic structures |
See also 18B35 |
19 |
|
| 08? |
General algebraic systems |
|
|
|
| 11 |
Number theory |
|
11 |
|
| 12 |
Field theory and polynomials |
|
6 |
|
| 13 |
Commutative rings and algebras |
|
1 |
|
| 14? |
Algebraic geometry |
|
|
|
| 15 |
Linear and multilinear algebra; matrix theory |
|
16 |
1 |
| 16 |
Associative rings and algebras |
For the commutative case, see 13-xx |
13 |
|
| 17? |
Nonassociative rings and algebras |
|
|
|
| 18 |
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 55Nxx and 55Uxx for algebraic topology |
9 |
|
| 19? |
$K$-theory |
See also 16E20, 18F25 |
|
|
| 20 |
Group theory and generalizations |
|
7 |
|
| 22? |
Topological groups, Lie groups |
For transformation groups, see 54H15, 57Sxx, 58-xx. For abstract harmonic analysis, see 43-xx |
|
|
| 26 |
Real functions |
See also 54C30 |
31 |
|
| 28 |
Measure and integration |
For analysis on manifolds, see 58-xx |
13 |
|
| 30? |
Functions of a complex variable |
For analysis on manifolds, see 58-xx |
|
|
| 31? |
Potential theory |
For probabilistic potential theory, see 60J45 |
|
|
| 32? |
Several complex variables and analytic spaces |
For infinite-dimensional holomorphy, see 46G20, 58B12 |
|
|
| 33 |
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 |
8 |
|
| 34? |
Ordinary differential equations |
|
|
|
| 35? |
Partial differential equations |
|
|
|
| 37? |
Dynamical systems and ergodic theory |
See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-xx |
|
|
| 39? |
Difference and functional equations |
|
|
|
| 40 |
Sequences, series, summability |
|
6 |
|
| 41? |
Approximations and expansions |
For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx |
|
|
| 42? |
Fourier analysis |
|
|
|
| 43? |
Abstract harmonic analysis |
For other analysis on topological and Lie groups, see 22Exx |
|
|
| 44? |
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? |
Integral equations |
|
|
|
| 46 |
Functional analysis |
For manifolds modeled on topological linear spaces, see 57N20, 58Bxx |
9 |
|
| 47? |
Operator theory |
|
|
|
| 49? |
Calculus of variations and optimal control; optimization |
See also 34H05, 34K35, 65Kxx, 90Cxx, 93-xx |
|
|
| 51? |
Geometry |
For algebraic geometry, see 14-xx |
|
|
| 52? |
Convex and discrete geometry |
|
|
|
| 53? |
Differential geometry |
For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx |
|
|
| 54 |
General topology |
For the topology of manifolds of all dimensions, see 57Nxx |
3 |
|
| 55? |
Algebraic topology |
|
|
|
| 57? |
Manifolds and cell complexes |
For complex manifolds, see 32Qxx |
|
|
| 58? |
Global analysis, analysis on manifolds |
See also 32Cxx, 32Fxx, 32Wxx, 46-xx, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15 |
|
|
| 60? |
Probability theory and stochastic processes |
For additional applications, see 11Kxx, 62-xx, 90-xx, 91-xx,92-xx, 93-xx, 94-xx |
|
|
| 62? |
Statistics |
|
|
|
| 65? |
Numerical analysis |
|
|
|
| 68 |
Computer science |
For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area |
43 |
|
| 70? |
Mechanics of particles and systems |
For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-xx |
|
|
| 74? |
Mechanics of deformable solids |
|
|
|
| 76? |
Fluid mechanics |
For general continuum mechanics, see 74Axx, or other parts of 74-xx |
|
|
| 78? |
Optics, electromagnetic theory |
For quantum optics, see 81V80 |
|
|
| 80? |
Classical thermodynamics, heat transfer |
For thermodynamics of solids, see 74A15 |
|
|
| 81? |
Quantum theory |
|
|
|
| 82? |
Statistical mechanics, structure of matter |
|
|
|
| 83? |
Relativity and gravitational theory |
|
|
|
| 85? |
Astronomy and astrophysics |
For celestial mechanics, see 70F15 |
|
|
| 86? |
Geophysics |
See also 76U05, 76V05 |
|
|
| 90? |
Operations research, mathematical programming |
|
|
|
| 91? |
Game theory, economics, social and behavioral sciences |
|
|
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| 92? |
Biology and other natural sciences |
|
|
|
| 93? |
Systems theory; control |
For optimal control, see 49-xx |
|
|
| 94 |
Information and communication, circuits |
|
5 |
|
| 97? |
Mathematics education |
|
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