TheBestLinks.com:Classifications of mathematics topics

From TheBestLinks.com

Perhaps this page should be deleted. I seems to have been superceded by list of lists of mathematical topics (not to be confused with list of mathematical topics), and at any rate would take an enormous amount of work to bring up to date.

Here is a place to propose classifications of mathematical topics

The arXiv's organization of mathematical subjects can be found at the Front [1] (http://front.math.ucdavis.edu/). This is considered (at least by me) to be a more modern classification than the AMS classification, given below. The MSC does poorly when confronted with fields which are combinations of things. For examples see the way it treats representation theory, commutative algebra, and geometric topology.

Also the Library of Congress Classification for Mathematics (QAxxx) is not to be sneered at, I think... I am not exactly sure how it is arranged (but see [2] (http://lcweb.loc.gov/catdir/cpso/lcco/lcco.html)) but at least it is exhaustive. User:Sam_nead

here is the American Mathematical Society (http://www.ams.org)'s one, called MSC2000 (http://www.ams.org/msc/) which is the standard (posted by Mark). It may look difficult at a first glance but is well structured. Second level links will follow.

00-xx General
01-xx History and biography [See also the classification number -03 in the other sections]
03-xx Mathematical logic and foundations
04-xx This section has been deleted {For set theory see 03Exx}
05-xx Combinatorics {For finite fields, see 11Txx}
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
14-xx Algebraic geometry
15-xx Linear and multilinear algebra; matrix theory
16-xx Associative rings and algebras {For the commutative case, see 13-xx}
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 55Nxx and55Uxx 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, see54H15, 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}
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
35-xx Partial differential equations
37-xx Dynamical systems and ergodic theory [See also 26A18, 28Dxx, *34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-xx]
39-xx Difference and functional equations
40-xx Sequences, series, summability
41-xx 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-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 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 57N20, 58Bxx}
47-xx Operator theory
49-xx Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-xx]
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 32Cxx, 32Fxx, 32Wxx, 46-xx, 47Hxx, 53Cxx] {For geometric integration theory, see 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
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 *83A05 and 83C10; for statistical mechanics, see 82-xx}
73-xx This section has been deleted {For mechanics of solids, see 74-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
92-xx Biology and other natural sciences
93-xx Systems theory; control {For optimal control, see 49-xx}
94-xx Information and communication, circuits
97-xx Mathematics education