Colección: La Educación
Número: (116) III
Año: 1993
7. Kiyosi ITO, ed. Encyclopedic Dictionary of Mathematics. 2nd Edition,
Vol. I, A-N. Cambridge: Massachusetts Institute of Technology, 1992. 1147
p., Vol. II, O-Z, 2148 p.
The second edition of the Encyclopedic Dictionary of Mathematics is basically
an English version of the third Japanese edition of the Dictionary, and is
presented in two volumes. The content of the Dictionary was prepared considering
21 topics including, among others: Logic and Foundations, General Topology
and Categories, Algebra, Group Theory, Number Theory, and Functional Analysis.
The included topics are organized in alphabetical order and are presented
through specialized articles produced under the supervision of an editorial
committee nominated by the Mathematical Society of Japan. The scope of the
Dictionary goes beyond the usual structure of an encyclopedic dictionary.
Each of the topics included in the 21 selected areas are a synthesis of the
principal research contributions in each specific case. The presentations
are organized in the form of academical articles, and are documented with
substantial references. Most of the included references are related to contributions
made during the period 1940-1980.
The Dictionary should be made available in libraries of higher education institutions,
providing formal training for mathematicians, scientists and engineers. It
includes articles related to some modern developments of applied mathematics,
such as Numerical Analysis, Computer Science and Combanitorics, and Mathematical
Programming and Operations Research. Language used is highly formal; therefore,
for comprehension of the majority of the articles, a mathematical education
beyond multivariate calculus and differential equations is required. Various
articles also require a basic knowledge of Abstract Algebras and Mathematical
Logic.
One of the main characteristics of the Dictionary is its dynamical conception
of mathematical development. It includes, for example, an interesting treatment
of recent developments such as Catastrophe Theory. It also includes new articles
in domains of growing importance such as Categories and Functors and K-theory.
This edition was concluded before the renewed interest in extreme non-linear
systems and randomness came about. This may explain the absence of specific
consideration of such topics as Fractal Geometry, Chaos Theory, Fuzzy Sets
and Bayesian Statistical Methods.