Some topics don't seem to fit into just one category of the Mathematics Subject Classification scheme. This page will be a home for them, although right now it's just sort of garbage file. If you know what you're looking for but couldn't find any good matches in the Layman's Guide, try scanning this file for some keywords that seem appropriate for your needs.

There are some areas of mathematics (?) which fall outside the MSC altogether; it's unclear what to offer as a good site for these. For example, one might mention

- mathematics education (try the NCTM: National Council for Teachers of Mathematics). Note that there is a new section 97-XX of the MSC for just this topic, but it is likely to focus on research in mathematics education rather than teaching tips or classroom modules.
- mathematical modeling (but see some topics in applications of mathematics)
- actuarial science (but see some topics in Statistics -- 62P05)
- finance (but see some topics in Economics -- 90A09 or Statistics -- 62P05.)

The sphere FAQ and (division) ring FAQ written some time ago do not seem to fit so neatly into these area boundaries, but we have tried to give them appropriate cross-links as well.

There are some topics which are discussed in several areas of the MSC. We try in such cases to provide crosslinks. See for example the division of material on polynomials, mentioned in the page for 12F: Galois theory.

It looks like there should be multi-heading pages for some parts of mathematics with greatly overlapping resources. For the most part these seem to coincide with the broad-area classifications the AMS used in the MSC until 1972 (see below for defunct MSC codes):

- abstract algebra (areas 12 through 18, surely, and usually 11: number theory and some other allied topics.)
- analysis (areas 26 through 47, certainly -- even more in the broader sense of "analysis".)
- topology (areas 54, 55, 57, and the more analytical 58 and geometric 53, perhaps.)
- mathematical physics (areas 70 through 86, at least!); there is a newsgroup sci.physics.research (moderated) and unmoderated groups sci.physics and sci.physics.particle.

There are many closely allied *pairs* of fields, too:
Probability(60)/Statistics(62), Logic(03)/Set Theory(04), Geometry(51)/Convex Geometry(52),
etc.; but pairs of pages are probably easily crosslinked, that is, there's
probably no need to set up "parent" pages for these pairs.

There are some subjects which, based on reports in the popular press and the presentations in the undergraduate curriculum, one might expect to be major portions of the subject classification system. Did you look for these in vain? Here are a few pointers:

- Trigonometry: Mathematically there's nothing very interesting here, but the trig functions are a major component of Special Functions
- Vectors and Matrices: Nominally the content of Linear Algebra, the topics there are rather beyond questions of determining normal lines to planes and so on.
- Calculus: Elementary calculus is considered in Real functions. Vector calculus (Stokes' theorem and so on) may be in Calculus on manifolds. Specific derivatives and integrals may be discussed in Special functions; the general theory is more likely in Measure and integration. Topics in Approximations and expansions and Sequences and series are usually also included in calculus courses.
- Differential equations: Beside Ordinary Differential Equations, the material treated in an introductory course may include Integral transforms (Laplace, Fourier).
- "Discrete mathematics" is, if not an elementary course, likely to be mostly Combinatorics and Graph Theory.
- Chaos, catastrophe theory, dynamical systems: Try Global analysis
- Fractals: Try Measure theory or General topology
- Inverse problems: try 65J; 35R
- p-adic numbers: some material is in section 11S; areas 43, 54E are also reasonable places to look.

There are some topics which just aren't mathematics! It's always possible, perhaps, that a person lands at this web site completely by mistake. What non-mathematical query might have brought you here?:

- Group Therapy -- try Psychiatry
- Numerology -- see Fortune-telling
- Arithmonancy -- see Fortune-telling
- Manifolds, automotive
- Lucky numbers and the lottery
- [Real or imagined mistakes welcome for this list!]

Perhaps it's also appropriate to show the nearest cognates with other classification systems. e.g. Computing Reviews? AIP? See the page for 00-XX. [Computing reviews: http://www.acm.org/class]

One might envision other ways to break up the discipline and see how even they are. Sample topics: distribution of SIAM members' fields of interest; distribution of Fields medalists; division of math fields in AMS's annual list of recent PhDs; etc.

What about the defunct parts of the MSC? A few fields were discarded
after a reorganization: 02 (became 03), 10 (became 11), 21 (became
22), 50 (became 51); A few fields were for papers unclassifiable
except for broad field: 09(algebra), 27(analysis), 36 (differential
equations), 48(geometry), 56(topology), 69(applied math), 99(misc).
Some numbers were *apparently* never used: 7,23-25,29,37-38,
59,61,63-64,66-67,74-75,77,87-89,95-98

For more detail on old classifications, see URL: http://www.ams.org/msnmain?screen=Classification

09 (40-72) Classical algebra

09-XX (40-72) Classical algebra 09.0X (40-58) Algebra 09.00 (59-72) Classical algebra 09.1X (40-58) Abstract algebra 09.2X (40-58) Elementary algebra 09.3X (40-58) Rings, fields and algebras

21 (40-58) Topological algebraic structures

21-XX (40-58) Topological algebraic structures 21.0X (40-58) Topological algebraic structures

27 (40-58) Analysis

27-XX (40-58) Analysis 27.0X (40-58) Analysis 27.1X (40-58) Foundations of analysis 27.2X (40-58) Theory of sets, theory of functions of real variables 27.3X (40-58) Theory of functions of real variables, theory of measure and integration 27.4X (40-58) Geometrical analysis 27.5X (40-58) Functions with particular properties

36 (40-58) Differential equations, operational calculus

36-XX (40-58) Differential equations, operational calculus 36.0X (40-58) Differential equations 36.1X (40-58) Differential equations, operational calculus

48 (40-58) Geometry

48-XX (40-58) Geometry 48.0X (40-58) Geometry

56 (40-58) Topology

56-XX (40-58) Topology 56.0X (40-58) Topology

69 (40-72) General applied mathematics

69-XX (40-72) General applied mathematics 69.00 (59-79) General Applied Mathematics

71 (40-58) Mechanics

71-XX (1940-1958) Mechanics 71.0X (1940-1958) Mechanics

79 (40-58) Mathematical physics, physical applications

79-XX (1940-1958) Mathematical physics, physical applications 79.0X (1940-1958) Mathematical physics, physical applications

84 (40-58) Relativity, astronomy

84-XX (1940-1958) Relativity, astronomy 84.0X (1940-1958) Relativity, astronomy

91 (40-58) Other applications

91-XX (1940-1958) Other applications 91.0X (1940-1958) Other applications

99 (40-58) Miscellaneous

99-XX (40-58) Miscellaneous 99.0X (40-58) Miscellaneous

Like we said, this is still sort of a garbage file...

Last modified 1999/06/12 by Dave Rusin. Mail: feedback@math-atlas.org