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Index Pages for topics outside the Mathematics Subject Classification |
The index pages at this site are organized according to the Mathematics Subject Classification (MSC) scheme. (This is the scheme developed by the American Mathematical Society and Zentralblatt für Mathematik. Here's the original.) But some topics don't seem to fit into just one category of the Mathematics Subject Classification scheme, or are outside the scope of the MSC. We provide pages for a few of these which are similar are spirit to the ordinary MSC index pages. In general they refer to the ordinary pages whenever appropriate.
| These pages will be identifiable by their | green | backgrounds; |
| standard MSC-area pages are marked with the | blue | backgrounds. |
Some topics in mathematics are quite broad, consisting of several (usually a more or less well-defined set of) MSC major headings. There are many books and internet materials which treat these as cohesive units. Many of these seem to coincide with the broad-area classifications the AMS used in the MSC until 1972 (see below for defunct MSC codes):
One way to identify "legitimate" topics in mathematics is to look for subject headings used by other classification schemes. Here are a few other classification systems which have seen significant use:
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.
Some areas of mathematics cut across boundaries of the MSC. It is actually quite frequently the case that a topic fits equally well in more than one classification; in these cases the two (or more) subfields are usually marked quite clearly by cross-reference (e.g. arithmetic questions in algebraic geometry are just as naturally classified as 11G as well as within section 14). Occasionally however we find topics which are arguably cohesive branches of mathematics, but which have over the last few decades not been accorded an MSC heading of their own. Here are a few which have been suggested:
What about the defunct parts of the MSC itself? A few fields were discarded after a reorganization: 02 (became 03), 04 (folded into 03), 10 (became 11), 21 (became 22), 50 (became 51), 73 (became 74). 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: 7,23-25,29,38, 59,61,63-64,66-67,75,77,87-89,95-96,98
For more detail on old classifications, see this AMS page
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
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:
Mathematics is frequently presented to target audiences, with the theory selected, and the examples configured, to match the practical needs of the audience. In some cases (e.g. "woodshop mathematics") the mathematics used is actually quite elementary (see above). In other cases, some more or less sophisticated mathematics is used, gathered together irrespective of the mathematical basis of the tools. We mention in particular
We next consider some topics in mathematics which are too elementary for inclusion in the MSC. (Recall that the MSC is designed to classify only new research work. Occasionally expository articles on these topics, or work discussing the teaching of these topics, will be included in the most appropriate subject headings.)
Next we mention some topics often associated with mathematics, but whose primary content is rather free of mathematical ideas -- in particular, these are topics about which a mathematician is unlikely to offer the best surveys. The nearest match to topics within the purvey of the MSC are shown
Finally, 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?: