Mathematics Subject Classification

This is intended to be a guide to the Mathematics Subject Classification (MSC) scheme generally used to classify newly-released mathematics resources. This page is intended for a person with approximately the training of an undergraduate mathematics student; links lead to pages assuming greater familiarity with the sub-disciplines. The MSC does not include classifications for elementary material. Since there are some materials at this site which border on the elementary (e.g. plane geometry and elementary calculus), I have made the best fit I could, but this implies a slight extension of the MSC system. There is a short page of topics which do not fit neatly into the MSC , including a couple of topics (rings; spheres) on which I have written detailed summary articles. (Also included there are links to a few subjects which do fall within a MSC heading but whose position there may be hard for a newcomer to find.) The major divisions of the MSC hardly provide an equal division of the current mathematics spectrum. Of course what really would be an "equal division" is open to interpretation. The welcome page for this collection shows an image of the areas of mathematics which shows the relative numbers of recent papers in each area (arranged so as to illustrate the affinities among related areas). [The MSC is updated at the turn of a decade; the changes for the year 2000 are mentioned only briefly below. The total will be 63 major headings, not 61.] Warning: this is a single-author document and thus reflects the opinions and deficiencies of that author [Dave Rusin]. (I'm particularly unsatisfied with the descriptions of applications to the physical sciences and other allied disciplines.) Helpful suggestions are always solicited. Any attempt to distinguish the parts of mathematics must begin with a decision about what constitutes mathematics in the first place! I have tried to keep the broad definition here, that mathematics includes all the related areas which touch on quantitative, geometric, and logical themes. This includes Statistics, Computer Science, Logic, Applied Mathematics, and other fields which are frequently considered distinct from mathematics. We draw the line only at experimental sciences, philosophy, and computer applications. Personal perspectives vary widely, of course! Contrary to common perception, mathematics does not consist of "crunching numbers" or "solving equations". As we shall see there are branches of mathematics concerned with setting up equations, or analyzing their solutions, and there are parts of mathematics devoted to creating methods for doing computations. But there are also parts of mathematics which have nothing at all to do with numbers and equations. One way to divide the mathematics literature is to decide which books and articles are designed to reveal the structure of mathematics itself, and which are intended to apply mathematics to closely allied areas. Foundations considers questions in logic or set theory -- the very language of mathematics. Algebra is principally concerned with symmetry, patterns, discrete sets, and the rules for manipulating arithmetic operations; one might think of this as the outgrowth of arithmetic and algebra classes in primary and secondary school. Geometry is concerned with shapes and sets, and the properties of them which are preserved under various kinds of motions. Naturally this is related to elementary geometry and analytic geometry. Analysis studies functions, the real number line, and the ideas of continuity and limit; this is perhaps the natural successor to courses in graphing, trigonometry, and calculus. (This is a very large area; I subdivide it below.) The second broad part of the mathematics literature includes those areas which could be considered either independent disciplines or central parts of mathematics, as well as those areas which clearly use mathematics but are interested in non-mathematical ideas too. It is important to note t