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University Library, University of Illinois at Urbana-Champaign

Using MathSciNet: Mathematics Subject Classification

How to Use Mathematics Subject Classification (MSC)

The main purpose of the classification of items in the mathematical literature using the Mathematics Subject Classification scheme is to help users find the items of present or potential interest to them as readily as possible---in products derived from the Mathematical Reviews Database (MRDB), in Zentralblatt MATH, or anywhere else where this classification scheme is used. An item in the mathematical literature should be classified so as to attract the attention of all those possibly interested in it. The item may be something which falls squarely within one clear area of the MSC, or it may involve several areas. Ideally, the MSC codes attached to an item should represent the subjects to which the item contains a contribution. The classification should serve both those closely concerned with specific subject areas, and those familiar enough with subjects to apply their results and methods elsewhere, inside or outside of mathematics. It will be extremely useful for both users and classifiers to familiarize themselves with the entire classification system and thus to become aware of all the classifications of possible interest to them.

Every item in the MRDB receives precisely one primary classification, which is simply the MSC code that describes its principal contribution. When an item contains several principal contributions to different areas, the primary classification should cover the most important among them. A paper or book may be assigned one or several secondary classification numbers to cover any remaining principal contributions, ancillary results, motivation or origin of the matters discussed, intended or potential field of application, or other significant aspects worthy of notice.

The principal contribution is meant to be the one including the most important part of the work actually done in the item. For example, a paper whose main overall content is the solution of a problem in graph theory, which arose in computer science and whose solution is (perhaps) at present only of interest to computer scientists, would have a primary classification in 05C (Graph Theory) with one or more secondary classifications in 68 (Computer Science); conversely, a paper whose overall content lies mainly in computer science should receive a primary classification in 68, even if it makes heavy use of graph theory and proves several new graph-theoretic results along the way.

There are two types of cross-references given at the end of many of the entries in the MSC. The first type is in braces: ``{For A, see X}''; if this appears in section Y, it means that contributions described by A should usually be assigned the classification code X, not Y. The other type of cross-reference merely points out related classifications; it is in brackets: ``[See also ...]'', ``[See mainly ...]'', etc., and the classification codes listed in the brackets may, but need not, be included in the classification codes of a paper, or they may be used in place of the classification where the cross-reference is given. The classifier must judge which classification is the most appropriate for the paper at hand.

- From MathSciNet "How to use the MSC"

Subject Classification Numbers for Department of Mathematics Focus Areas

Actuarial Science

  • 62 (Statistics)

  • 91 (Game theory, economics, social and behavioral sciences)

Algebra

  • 06 (Order, lattices, ordered algebraic structures)

  • 12 (Field theory and polynomials)

  • 13 (Commutative algebra)

  • 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)

  • 55 (Algebraic topology)

Algebraic Geometry

  • 14 (Algebraic Geometry)

Analysis

  • 28 (Measure and integration)

  • 32 (Several complex variables and analytic spaces)

  • 34 (Ordinary differential equations)

  • 35 (Partial differential equations)

  • 37 (Dynamical systems and ergodic theory)

  • 46 (Functional analysis)

  • 65 (Numerical analysis)

Combinatorics

  • 05 (Combinatorics)

  • 49 (Calculus of variations and optimal control; optimization)

Differential Equations and Applied Mathematics

  • 34 (Ordinary differential equations)

  • 35 (Partial differential equations)

Geometry and Topology

  • 51 (Geometry)

  • 52 (Convex and discrete geometry)

  • 53 (Differential geometry)

  • 54 (General topology)

  • 55 (Algebraic topology)

  • 58 (Global analysis, analysis on manifolds)

 Logic

  • 03 (Mathematical logic and foundations)

Mathematical Physics

  • 35Qxx  (Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] )

  • 81 Quantum theory

Number Theory

  • 11 (Number theory)

Probability

  • 60 (Probability theory and stochastic processes)

Statistics

  • 62 (Statistics)

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