> 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/corr-taxonomy.md). # Taxonomy: Mathematics Computing Research Repository (CoRR) style math.AG - `Algebraic Geometry` * Algebraic varieties * stacks * sheaves * schemes * moduli spaces * complex geometry * quantum cohomology (subsumes `alg-geom`) math.AT - `Algebraic Topology` * Homotopy theory * homological algebra * algebraic treatments of manifolds math.AP - `Analysis of Partial Differential Equations (PDE)` * Existence and uniqueness * boundary conditions * linear and non-linear operators * stability * soliton theory * integrable PDE's * conservation laws * qualitative dynamics math.CT - `Category Theory` * Enriched categories * topoi * abelian categories * monoidal categories * homological algebra math.CA - `Classical Analysis and ODEs` * Special functions * orthogonal polynomials * harmonic analysis * ODE's * differential relations * calculus of variations * approximations * expansions * asymptotics math.CO - `Combinatorics` * Discrete mathematics * graph theory * enumeration * combinatorial optimization * Ramsey theory * combinatorial game theory math.AC - `Commutative Algebra` * Commutative rings * modules * ideals * homological algebra * computational aspects * invariant theory * connections to algebraic geometry and combinatorics math.CV - `Complex Variables` * Holomorphic functions * automorphic group actions and forms * pseudoconvexity * complex geometry * analytic spaces * analytic sheaves math.DG - `Differential Geometry` * Complex * contact * Riemannian * pseudo-Riemannian and Finsler geometry * relativity * gauge theory * global analysis (subsumes dg-ga) math.DS - `Dynamical Systems` * Dynamics of differential equations and flows * mechanics * classical few-body problems * iterations * complex dynamics * delayed differential equations math.FA - `Functional Analysis` * Banach spaces * function spaces * real functions * integral transforms * theory of distributions * measure theory (subsumes funct-an) math.GM - `General Mathematics` * Mathematical material of general interest * topics not covered elsewhere math.GN - `General Topology` * Continuum theory * point-set topology * spaces with algebraic structure * foundations * dimension theory * local and global properties math.GT - `Geometric Topology` * Manifolds * orbifolds * polyhedra * cell complexes * foliations * geometric structures math.GR - `Group Theory` * Finite groups * topological groups * representation theory * cohomology * classification and structure math.HO - `History and Overview` * Biographies * philosophy of mathematics * mathematics education * recreational mathematics * communication of mathematics math.IT - `Information Theory` math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding. math.KT - `K-Theory and Homology` * Algebraic and topological K-theory * relations with topology * commutative algebra * and operator algebras math.LO - `Logic` * Logic * set theory * point-set topology * formal mathematics math.MP - `Mathematical Physics` * Mathematical methods in quantum field theory * quantum mechanics * statistical mechanics * condensed matter * nuclear and atomic physics math.MG - `Metric Geometry` * Euclidean * hyperbolic * discrete * convex * coarse geometry * comparisons in Riemannian geometry * symmetric spaces math.NT - `Number Theory` * Prime numbers * Diophantine equations * Analytic number theory * Algebraic number theory * Arithmetic geometry * Galois theory math.NA - `Numerical Analysis` * Numerical algorithms for problems in analysis and algebra * Scientific computation math.OA - `Operator Algebras` * Algebras of operators on Hilbert space * C^\*-algebras * von Neumann algebras * non-commutative geometry math.OC - `Optimization and Control` * Operations research * linear programming * control theory * systems theory * optimal control * game theory math.PR - `Probability` * theory and applications of probability and stochastic processes: e.g. central limit theorems * large deviations * stochastic differential equations * models from statistical mechanics * queuing theory math.QA - `Quantum Algebra` * Quantum groups * skein theories * operadic and diagrammatic algebra * quantum field theory (subsumes q-alg) math.RT - `Representation Theory` * Linear representations of algebras and groups * Lie theory * associative algebras * multilinear algebra math.RA - `Rings and Algebras` * Non-commutative rings and algebras * non-associative algebras * universal algebra and lattice theory * linear algebra * semigroups math.SP - `Spectral Theory` * Schrodinger operators * operators on manifolds * general differential operators * numerical studies * integral operators * discrete models * resonances * non-self-adjoint operators * random operators/matrices math.ST - `Statistics Theory` math.ST is an alias for `stat.TH` * Applied * computational and theoretical statistics: e.g. statistical inference * regression * time series * multivariate analysis * data analysis * Markov chain Monte Carlo * design of experiments * case studies math.SG - `Symplectic Geometry` * Hamiltonian systems * symplectic flows * classical integrable systems