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	Index using Los Alamos Preprint-Server Classifications

Here are the subdivisions of mathematics classified according to the system used at the Los Alamos preprint-server. The LANL archive is largely an amalgam of independently-founded specialty archives, and thus is not necessarily comprehensive in scope nor non-duplicative nor arranged according to any single system. (Other specialty preprint servers are mentioned on the corresponding index pages at this site.) We provide links here to what appear to be the best-matching index pages at this site to each of the 31 subject classes at LANL. You can go directly back to the index arranged according to the AMS/Zbl Mathematics Subject Classification system used to organize materials at this site.

There are also separate categories at LANL for Computer Science, Physics, and "Nonlinear Sciences" [Adaptation, Noise, and Self-Organizing Systems / Chaotic Dynamics / Cellular Automata and Lattice Gases / Nonlinear Sciences / Pattern Formation and Solitons / Exactly Solvable and Integrable Systems ]

The remainder of this page is taken nearly verbatim from http://xxx.lanl.gov/new/math.html.

Why not the Math Subject Classification?

The categories (or subject classes) of the xxx math archive bear some resemblance to the top-level sections of the Math Subject Classification (MSC) used by Math Reviews and Zentralblatt für Mathematik. The two classifications, however, differ in their intent and history, and the math archive advisory committee decided that strictly following the MSC was unworkable. For example, Quantum Algebra, the most popular category in the math archive, has no counterpart in the MSC. It would be impractical, perhaps even counterproductive, to reorganize this category into MSC sections. Each category of the math archive must maintain a self-sustaining stream of new submissions in order to be useful; the committee decided that the MSC sections are in places too specific or too dated for this purpose.

Finally, all authors are encouraged as well to use the optional MSC-class: field when submitting new e-prints, since some readers may wish to search for e-prints by their MSC classification.

(Important areas may have been overlooked and the best names may not have been chosen. These oversights can be corrected.)

(The existing archives alg-geom, dg-ga, funct-an, and q-alg are included as subject classifications. Old papers will be available as always, but new papers will be routed automatically to the math archive with the appropriate Subj-class.)

The subject classes of the LANL math archives are:

• AG - Algebraic Geometry (subsumes alg-geom)
  

  Real and complex algebraic geometry, schemes, stacks, commutative rings, local rings

• AP - Analysis of PDEs
  

  Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics

• AT - Algebraic Topology
  

  Homotopy theory, homological algebra, algebraic treatments of manifolds

• CA - Classical Analysis
  

  Special functions, orthogonal polynomials, harmonic analysis, ODEs, differential relations, calculus of variations, approximations, expansions, asymptotics

• CO - Combinatorics
  

  Discrete mathematics, graph theory, enumeration, lattice theory

• CT - Category Theory
  

  Enriched categories, topoi, abelian categories, monoidal categories, homological algebra

• CV - Complex variables
  

  Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves

• DG - Differential geometry (subsumes dg-ga)
  

  Complex, contact, Riemannian, pseudo-Riemannian geometry, relativity, gauge theory, global analysis

• DS - Dynamical Systems
  

  Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations

• FA - Functional analysis
  

  Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory

• GN - General Topology
  

  Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties

• GR - Group theory
  

  Finite groups, topological groups, representation theory, cohomology, classification and structure

• GT - Geometric Topology
  

  Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures

• HO - History and Overview
  

  Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics

• IG - Infinite Group Theory
  

  Combinatorial and geometric group theory, presentations, hyperbolic and automatic groups, related topics

• KT - K-Theory and Homology
  

  Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

• LA - Linear Algebra
  

  Analytic, combinatorial, and algebraic matrix analysis, numerical and computational linear algebra, applications to science and engineering, multilinear algebra

• LO - Logic
  

  Logic, set theory, point-set topology, formal mathematics

• MG - Metric Geometry
  

  Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces

• MP - Mathematical Physics
  

  Rigorous results in all areas of theoretical physics, and physically motivated mathematics

• NA - Numerical Analysis
  

  Numerical algorithms for problems in analysis and algebra

• NT - Number Theory
  

  Prime numbers, Diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory

• OA - Operator Algebras (subsumes funct-an)
  

  Algebras of operators on Hilbert space, C*-algebras, von Neumann algebras, non-commutative geometry

• OC - Optimization and Control
  

  Operations research, linear programming, Control theory, systems , optimal control

• PR - Probability Theory
  

  Stochastic processes, ergodic theory, martingale theory

• QA - Quantum algebra (subsumes q-alg)
  

  Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory

• RA - Rings and Algebras
  

  Commutative and non-commutative rings and algebras, non-associative algebras, universal algebra, semigroups

• RT - Representation Theory
  

  Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra

• SC - Scientific Computation
  

  Scientific and industrial simulations and algorithms, fluid mechanics, models of solids, geophysics, mathematical biology, economic models

• SG - Symplectic Geometry
  

  Hamiltonian systems, symplectic flows, classical integrable systems

• SP - Spectral Theory
  

  Schrödinger operators, Operators on manifolds, General differential operators, Numerical studies, Integral operators, Discrete models, Resonances, Non-self-adjoint operators, Random operators/matrices