I found only one Mathematics Subject Classification, are there more?
Yes, there are more ways of classifying the subject areas of mathematics; classification schemes are merely human constructs that attempt to impose some sort of organization or structure to the domains of mathematics in a manner that is useful and that makes sense:
The MSC (*Mathematical Subject Classificatio*n) is a fairly standard scheme. Here is a little history and overview of the MSC.
And what follows are some suggestions for
- $(1)$ different representations of the MSC, AND
- $(2)$ different (alternative) classification schemes of organizing the different branches of math.
$(1)$ See the Mathematical Atlas (www.math-atlas.org), for a "Math Map" of subject areas in mathematics which depicts the interconnections of the various branches in math.
The webpage with the "Math Map" is searchable, and you'll find the linked page "Subject Index". (Click here: "Browse: list of subject headings", or you can click that same link at the bottom Math Map* webpage linked above.)
Top-level subject areas in the MSC, each of which is "searchable" through the Mathematical Atlas, if you want to explore "sub-levels" encompassed by "top-level" subjects:
00: General material including elementary mathematics 01: History and biography 03: Mathematical logic and foundations 05: Combinatorics and graph theory 06: Order, lattices, ordered algebraic structures 08: General algebraic systems 11: Number theory 12: Field theory and polynomials 13: Commutative rings and algebras 14: Algebraic geometry 15: Linear and multilinear algebra; matrix theory 16: Associative rings and algebras 17: Nonassociative rings and algebras 18: Category theory, homological algebra 19: K-theory 20: Group theory and generalizations 22: Topological groups, Lie groups 26: Real functions and elementary calculus 28: Measure and integration 30: Functions of a complex variable 31: Potential theory 32: Several complex variables and analytic spaces 33: Special functions including trigonometric functions 34: Ordinary differential equations 35: Partial differential equations 37: Dynamical systems and ergodic theory 39: Difference and functional equations 40: Sequences, series, summability 41: Approximations and expansions 42: Fourier analysis 43: Abstract harmonic analysis 44: Integral transforms, operational calculus 45: Integral equations 46: Functional analysis 47: Operator theory 49: Calculus of variations and optimal control; optimization 51: Geometry, including classic Euclidean geometry 52: Convex and discrete geometry 53: Differential geometry 54: General topology 55: Algebraic topology 57: Manifolds and cell complexes 58: Global analysis, analysis on manifolds 60: Probability theory and stochastic processes 62: Statistics 65: Numerical analysis 68: Computer science 70: Mechanics of particles and systems 74: Mechanics of deformable solids 76: Fluid mechanics 78: Optics, electromagnetic theory 80: Classical thermodynamics, heat transfer 81: Quantum Theory 82: Statistical mechanics, structure of matter 83: Relativity and gravitational theory 85: Astronomy and astrophysics 86: Geophysics 90: Operations research, mathematical programming 91: Game theory, economics, social and behavioral sciences 92: Biology and other natural sciences 93: Systems theory; control 94: Information and communication, circuits 97: Mathematics education
$(2)$ And for Alternate classifications of mathematical subjects, see:
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