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Mathematics has become a vastly diverse subject over history, and there is a corresponding need to categorize the different areas of mathematics (and the Langlands program has found unexpected connections between areas previously thought unconnected, at least Galois groups, Riemann surfaces and number theory). A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics continues to be developed, these classification schemes must change as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas. A traditional division of mathematics is into pure mathematics, mathematics studied for its intrinsic interest, and applied mathematics, mathematics which can be directly applied to real world problems.〔For example the Encyclopædia Britannica Eleventh Edition groups its mathematics articles as Pure, Applied, and Biographies. See: ().〕 This division is not always clear and many subjects have been developed as pure mathematics to find unexpected applications later on. Broad divisions, such as discrete mathematics and computational mathematics, have emerged more recently. ==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 differs form MSC; for example it 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 system on its articles, and also has a list of mathematics lists. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Areas of mathematics」の詳細全文を読む スポンサード リンク
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