Synopsis
When the first edition of the Encyclopedic Dictionary of Mathematics appeared in 1977, it was immediately hailed as a landmark contribution to mathematics: "The standard reference for anyone who wants to get acquainted with any part of the mathematics of our time" (Jean Dieudonné, American Mathematical Monthly). "A magnificent reference work that belongs in every college and university library" (Choice), "This unique and masterfully written encyclopedia is more than just a reference work: it is a carefully conceived course of study in graduate-level mathematics" (Library Journal).The new edition of the encyclopedia has been revised to bring it up to date and expanded to include more subjects in applied mathematics. There are 450 articles as compared to 436 in the first edition: 70 new articles have been added, whereas 56 have been incorporated into other articles and out-of-date material has been dropped. All the articles have been newly edited and revised to take account of recent work, and the extensive appendixes have been expanded to make them even more useful. The cross-referencing and indexing and the consistent set-theoretical orientation that characterized the first edition remain unchanged,The encyclopedia includes articles in the following areas: Logic and Foundations; Sets, General Topology, and Categories; Algebra; Group Theory; Number Theory; Euclidean and Projective Geometry; Differential Geometry; Algebraic Geometry; Topology; Analysis; Complex Analysis; Functional Analysis; Differential, Integral, and Functional Equations; Special Functions; Numerical Analysis; Computer Science and Combinatorics; Probability Theory; Statistics; Mathematical Programming and Operations Research; Mechanics and Theoretical Physics; History of Mathematics.Kiyosi Ito is professor emeritus of mathematics at Kyoto University.
Review
The Encyclopedic Dictionary of Mathematics, as put out by the Mathematical Society of Japan, is as complete and comprehensive an opus as one could wish for, concisely comprising in its two volumes all significant mathematical results, both pure and applied, elementary to advanced. This second edition is, basically, an English version of the acclaimed Japanese third edition. The EDM2, as it is known, succinctly but thoroughly covers math from A to Z, from Niels Henrik Abel and Abelian groups to Witt vectors and Zeta functions. Within its 2,000-plus pages are elegant explanations of diffusion processes, Fourier series, linear operators, and meromorphic functions. There are pages dedicated to quadratic fields and robust and nonparametric methods, and following each section, all the relevant references are listed. In addition, there are appendices with tables of formulas, numerical tables, and statistical tables, journals, publishers, and special notations, articles listed both systematically and alphabetically, plus a name index and an exhaustive subject index that's 231 pages long. It is a quality product--easily accessible, adhering to rigorous standards, and worth the investment for any school or personal math library. --Stephanie Gold
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