User:Tom Hundred Percent/Mathematics Subject Classification

The Mathematics Subject Classification (MSC) is an alphanumerical classification scheme formulated by the American Mathematical Society based on the coverage of two major reviewing databases Mathematical Reviews and Zentralblatt MATH. It is used by many mathematics journals, which ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers.

Structure
The MSC is a heierachical scheme, with three levels of structure. A classification can be two, three or five digits long, depending on how many levels of the classification scheme are used.

The first level is represented by a two digit number, the second by a letter, and the third by another two digit number. For example:


 * 53 is the classification for Differential Geometry
 * 53A is the classification for Classical Differential Geometry
 * 53A45 is the classification for Vector and Tensor Analysis

First Level
At the top level 64 mathematical disciplines are labeled with a unique 2 digit number. As well as the typical areas of mathematical research, there are top level categories for "History and Biography", "Mathematics Education", and for the overlap with different sciences. Physics is particularly well represented in the classification scheme with a number of different categories including:
 * Fluid Mechanics
 * Quantum theory
 * Geophysics
 * Optics and electromagnetic theory

All valid MSC classification codes must have at least the first level identifier.

Second Level
The second level codes are a single letter from the Latin alphabet. These represent specific areas covered by the first level discipline. The second level codes very from discipline to discipline.

For example, for Differential Geometry the top level code is 53, and the second level codes are:
 * A for Classical Differential Geometry
 * B for Local Differential Geometry
 * C for Global Differential Geometry
 * D for Sympletic Geometry and Contact Geometry

In addition the special second level code "-" is used for specific kinds of materials. These codes are of the form:


 * 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
 * 53-01 Instructional exposition (textbooks, tutorial papers, etc.)
 * 53-02 Research exposition (monographs, survey articles)
 * 53-03 Historical (must also be assigned at least one classification number from Section 01)
 * 53-04 Explicit machine computation and programs (not the theory of computation or programming)
 * 53-06 Proceedings, conferences, collections, etc.

The second and third level of these codes are always the same - only the first level changes. It is not valid to put 53- as a classification, either 53 on it's own, or better yet a more specific code should be used.

Third Level
Third level codes are the most specific, usually corresponding to a specific kind of mathematical object or a well known problem or research area.

The third level code 99 exists in every category and means none of the above, but in this section

Using the scheme
The AMS recommends that papers submitted to it's journals for publication have one primary classification and one or more optional secondary classifications. A typical MSC subject class line on a research paper looks like

MSC Primary 03C90; Secondary 03-02;

Versions
There are two versions of the MSC, published in 1991 and in 2000. The 2000 version is now the most widely used.

The 2000 version combines and/or removes underused codes from the 1991 version, and introduces additional codes for areas of research which have opened up since 1991.

The AMS is currently revising the classification scheme in preparation for a new version in 2010.

Relation to other classification schemes
For papers on physics the Physics and Astronomy Classification Scheme is used instead. Due to the large overlap between Mathematics and Physics research is it quite common to see both PACS and MSC codes on research papers, particularly for multidisciplinary journals and repositories such as the arXiv.

The ACM Computing Classification System is a similar hierarchical classification scheme for Computer Science. There is some overlap between the AMS and ACM classification schemes, in subjects related to both mathematics and computer science, however the two schemes differ in the details of their organization of those topics.

The classification scheme used on the arXiv is chosen to reflect the papers submitted. As arXiv is multidisciplinary its classification scheme does not fit entirely with the MSC, ACM or PACS classification schemes. It is common to see codes from one or more of these schemes on individual papers.