Introduction to the Math Review 1991 Mathematics Subject Classification (MSC)

This is a completely revised version of the MSC, prepared in the editorial offices of Zbl and MR. It replaces the 1980 MSC and is effective (in MR) with the January 1991 issue.

While many areas in the MSC saw only very small changes, others (or parts of them) had to be expanded significantly, and in some areas there is an altogether new classification. The following paragraphs give a synopsis of the principal changes.

In Section 00, the entries for collections of papers (reviewed as a whole) were replaced by the new subsection 00Bxx. There is a new entry 04A72 for ``general'' papers involving fuzzy sets and relations. Section 05 has two new subsections: 05D Extremal combinatorics and 05E Algebraic combinatorics. Both Zbl and MR are now using Section 11 for number theory (and 12D--L for field theory). Section 13 contains significant changes throughout. Subsections 12Y, 13P and 14Q, on computational aspects, are new, and 14P Real algebraic and real analytic geometry is also new. The old one-chapter Section 16 has been replaced by a completely new classification (16B--Y) for associative rings. Section 19 on $K$-theory is now available for primary classifications (previously, for technical reasons, it could be used only for secondary classifications); subsection 19J Obstructions from topology is new.

In Section 32, the chapter 32S Singularities is new. The old one-chapter Section 33 has been replaced by a completely new classification for special functions. In Section 34, ordinary differential operators were taken out of 34B and given a more detailed description in 34L. Subsection 35Q was expanded and made much more detailed. There was some revision and expansion in 46A, 46B and 46C (with 46D05 moved to 46C20), and also in 46L. Subsection 46N05 was expanded, with 46N now citing different areas of application, while the list of ``nontraditional'' versions of functional analysis (46P--R) was extended and placed into a new subsection 46S; parallel to 46N and 46S, there are also new subsections 47N and 47S. The contents of Section 49 were rearranged significantly; the area is now divided into subsections 49J--N and 49Q--S; in particular, 49N is brand new. Section 52 has been expanded into three chapters: 52A General convexity, 52B Polytopes and polyhedra, 52C Discrete geometry. Subsection 65Y Computer aspects of numerical algorithms is new, replacing 65V05; 65W05 becomes 65Y05.

In mechanics (Sections 70, 73, 76) a few subsections were condensed into one line each (and some one-line subsections absorbed elsewhere). Subsection 73V on basic mathematical methods in solid mechanics is new. The line 76M05 was deleted, and its place taken by the new subsection 76M on basic mathematical methods in fluid mechanics. The material in Sections 81 and 82 was completely rearranged and expanded significantly to reflect the rapid changes and advances that have been occurring in these fields; there are subsections 81P--V and 82B--D in the new version.

Each chapter of Section 90 contains several new entries. The old one-chapter Section 92 has been replaced by a completely new classification for biology and other natural sciences (92B--F) and for social and behavioral sciences (92G--K).

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