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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.

Leonel Zúñiga M.