> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/900-index/980-hierarchy/classification/ccs-top-levels.md).

# Math hierarchy

General/foundations 01: History and biography 00: General

* recreational mathematics
* philosophy of mathematics
* mathematical modeling 03: **Mathematical logic and foundations**
* model theory
* computability theory
* set theory
* proof theory
* algebraic logic

**Discrete math/algebra**: Study of structure of math abstractions 05: Combinatorics 06: Order, lattices, ordered *algebraic structures* 08: General algebraic systems 11: Number theory 12: *Field* theory and polynomials 13: Commutative algebra (Commutative rings and algebras) 14: Algebraic geometry 15: Linear and multilinear algebra; matrix theory 16: Associative *rings* and (associative) algebras 17: Non-associative rings and (non-associative) algebras 18: *Category theory*; homological algebra 19: K-theory 20: *Group* theory and generalizations 22: Topological groups, Lie groups (and analysis upon them)

**Analysis**: Study of change and quantity 26: Real functions (including derivatives and integrals) 28: Measure and integration 30: Functions of a complex variable (including approximation theory in the complex domain) 31: Potential theory 32: Several complex variables and analytic spaces 33: Special functions 34: Ordinary differential equations 35: Partial differential equations 37: Dynamical systems and ergodic theory 39: Difference (equations) and functional equations 40: Sequences, series, summability 41: Approximations and expansions 42: Harmonic analysis on Euclidean spaces (including Fourier analysis, Fourier transforms, trigonometric approximation, trigonometric interpolation, and orthogonal functions) 43: Abstract harmonic analysis 44: Integral transforms, operational calculus 45: Integral equations 46: Functional analysis (including infinite-dimensional holomorphy, integral transforms in distribution spaces) 47: Operator theory 49: Calculus of variations and optimal control; optimization (including geometric integration theory)

**Geometry and topology** \[Study of space] 51: *Geometry* 52: Convex (geometry) and discrete geometry 53: Differential geometry 54: General topology 55: Algebraic topology 57: Manifolds and cell complexes 58: Global analysis, analysis on manifolds (including infinite-dimensional holomorphy)

**Applied mathematics** / other \[Study of applications of mathematical abstractions] 60: *Probability theory and stochastic processes* 62: *Statistics* 65: Numerical analysis 68: *Computer science* 70: Mechanics of particles and systems (including particle mechanics) 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 (including relativistic mechanics) 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 (including optimal control) 94: Information and communication, circuits 97: Mathematics education