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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been replaced by a completely new classification (16B--Y) for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one-chapter Section 33 has been replaced by a completely new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).
Instructions for using the
1991 Mathematics Subject Classification
These instructions apply uniformly to all fields listed. The main
purpose of the classification is to help readers to find the items of
present or potential interest to them as readily as possible---in MR,
in Zbl, or anywhere else where this classification system is used. The
review of a paper or book should be printed in the section where it
will receive the broadest attention from all readers possibly
interested in it---these include both people working in that area and
people who are familiar with that area and apply its results and
methods elsewhere (inside or outside of mathematics). It will be
extremely useful for both readers and classifiers to familiarize
themselves with the entire classification system and thus to become
aware of all the classifications of possible interest to them.
Every paper or book reviewed in MR receives precisely one ``primary''
classification number, which is simply the number of the section in
which the review of the item will be printed. This section should be
the one that covers the principal contribution. When a paper contains
several principal contributions in different areas, the primary
classification should cover the ``most important'' among them. A paper
or book may receive one or several ``secondary'' classification
numbers (or ``cross-references''), to cover any remaining principal
contributions, ancillary results, motivation or origin of the problems
discussed, intended or potential field of application, or other
significant aspects worthy of notice.
The ``primary'' principal contribution is meant to be the one
including the most important part of the work actually done in the
paper. For example, a paper whose main overall content is the solution
of a problem in graph theory, which arose in computer science and
whose solution is (perhaps) at present only of interest to computer
scientists, belongs primarily in 05C with a cross-reference in 68;
conversely, a paper whose overall content lies mainly in computer
science should receive a primary classification in 68, even if it
makes heavy use of graph theory and proves several new graph-theoretic
results along the way.
For an item with its primary classification in an ``applied'' section
(68 through 94), it is recommended that a cross-reference be given to
any ``pure'' mathematics section (00 through 65) to which the item
being classified makes a contribution.
There are two types of cross-references given after many
classifications in the list. The first type is of the form ``\{For A,
see X\}''; if this appears in section Y, it means that for
contributions described by A one should usually assign the
classification X, not Y. The other type of cross-reference merely
points out related classifications; it is of the form ``[See
also$\ldots$]'', ``[See mainly$\ldots$]'', etc., and the
classifications listed in the brackets may, but need not, be added to
the classification of a paper, or they may be used in place of the
classification where the cross-reference is given. The classifier
will have to judge which classification is the most appropriate for
the paper at hand.
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