Areas of Mathematics - Classification Systems

Classification Systems

• The Mathematics Subject Classification (MSC) is produced by the staff of the review databases Mathematical Reviews and Zentralblatt MATH. Many mathematics journals ask authors to label their papers with MSC subject codes. The MSC divides mathematics into over 60 areas, with further subdivisions within each area.
• In the Library of Congress Classification, mathematics is assigned the subclass QA within the class Q (Science). The LCC defines broad divisions, and individual subjects are assigned specific numerical values.
• The Dewey Decimal Classification assigns mathematics to division 510, with subdivisions for Algebra & number theory, Arithmetic, Topology, Analysis, Geometry, Numerical analysis, and Probabilities & applied mathematics.
• The Categories within Mathematics list is used by the Arxiv for categorising preprints. It is more modern than MSC and so includes things like quantum algebra.
• The IMU uses its programme structure for organizing the lectures at its four-yearly ICM. One of its top-level sections that MSC doesn't have is Lie theory.
• The ACM Computing Classification System includes a couple of mathematical categories F. Theory of Computation, and G. Mathematics of Computing.
• MathOverflow has a tag system.
• Mathematics book publishers such as Springer (subdisciplines), Cambridge (Browse Mathematics and statistics) and the AMS (subject area) use their own subject lists on their websites to enable customers to browse books or filter searches by subdiscipline, including topics such as mathematical biology and mathematical finance as top-level headings.
• Schools and other educational bodies have syllabuses.
• Research institutes and university mathematics departments often have sub-departments or study groups. e.g. SIAM has activity groups for its members.
• Wikipedia uses a Category:Mathematics system on its articles, and also has a list of mathematics lists.