Product Description

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to 436 in the first edition: 70 new articles have been added, whereas 56 have been incorporated into other articles and out-of-date material has been dropped.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.

Product Details

• Amazon Sales Rank: #1768288 in Books
• Published on: 1987-06-08
• Number of items: 1
• Binding: Hardcover
• 2120 pages

Amazon.com
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

Language Notes
Text: English (translation)

Customer Reviews

Excellent reference for a math major
I am majoring in mathematics, and thus needed to search out a good reference book that covers most everything. Well, this is it, and I looked at all of them. The price for the softcover is reasonable, and I would only get the hardcover if it were to be used extensively (library or multiple users). The amazing amount of information is dictated in mathematical shorthand, so the beginner may have some difficulty, but then again, it is a reference (and a might good one too) and not a text.

PS, Do not buy the compilation of Eric Weisstein's work published by the CRC Press. The CONSTANTLY UPDATED work can be accessed for free from Wolfram Research. Reason: Greedy publishers. If you use his site regurlarly and wish to support his work, then just send the man $5 and buy these books instead.

Good way to start a math library
EDM2 is exceptional for the uniformly high quality of the writing. Each major field of mathematics is divided into subfields and treated in essay format. There are no synthesizing overview articles. It does a good job of referencing original results and notable texts as of around 1980.

To meet their goal of covering all fields of mathematics while keeping EDM2 to a reasonable size, the editors appear to have set two basic limits. First, there is no coverage of methods. You won't find any description of how to do something. The second restriction is on depth. The articles tend to cover about 80% of the terms you would find in an introductory graduate text on the same subject. Often, even those terms are just mentioned in passing. It's useless for help in reading research articles, because the coverage is not sufficiently deep or current.

I would recommend EDM2 to any math major. The articles give a good introduction to practically any field and the references are current enough to get you started in the library. There's a lot to be said for the security of having at least something on everything. Get the paperback version as an undergrad, take good care of it until your math library grows enough that you don't refer to it any more, and then pass it on to a younger student.

Indispensable. How did I ever get on without it?
If my house were on fire and I had only sufficient time to rescue four books, I would likely grab my four-volume Encyclopedic Dictionary of Mathematics, Second Edition (EDM2). Truly, this is one of the most useful books I own. As testimony to this fact one need only observe that there are more bookmarks protruding from my copy of EDM2 than there are pages (well, almost).

If you are a mathematician, or if mathematics is central to what you do, you will likely appreciate this collection as it contains wonderfully concise yet informative and authoritative entries on nearly every branch of modern mathematics. Need to refresh your memory on Radon-Nikodym derivatives and their properties? No problem. Are you up on Grassman algebras? If not, you can look it up in EDM2. Interested in game theory? It's in there. What about semi groups, elliptic integrals, perturbation theory, lattice theory, Hilbert spaces, projective geometry, integral geometry, measure theory, geometrical optics, and non-standard analysis? All there!

But simply listing the topics covered in EDM2 will not give you an adequate picture of its utility. What is amazing about the book is how much information it can pack into very few pages, yet manage to keep the discussion quite readable. Don't get me wrong; it doesn't read like a Stephen King novel (nor would you want it to). But the entries are self-contained and cogent enough that you can actually learn a good bit about topics that are totally new to you. Of course, you will want to avail yourself of the many cited references to gain a more complete understanding of any given topic, but you will be well on your way to getting acquainted with fundamental definitions and techniques of a hitherto unfamiliar branch of mathematics.

Here are several examples: If you look up "polynomial approximation" you will find a succinct discussion that rigorously defines such terms Bernstein polynomials, Chebyshev system, Haar's condition, degree of approximation, moduli of continuity, approximation by Fourier expansions, trigonometric interpolation, Lagrange interpolation, and orthogonal polynomials, and all in FOUR terse but readable pages, with plenty of references at the end. The entry on "geometric optics" covers Fermat's principle, Gauss mappings, Malus's theorem, and aberration, all in TWO pages. The succinct one-page biography of David Hilbert is followed by a one-page synopsis of Hilbert spaces. In a mere eight pages on function spaces it provides what amounts to a condensed survey of functional analysis, covering norms, dual spaces, Besov spaces, the Sobolev-Besov embedding theorem, Kothe spaces, etc.

Of course, what you will not find in this book is a single proof. Nor will you find up-to-the-minute esoteric theorems. But then I cannot imagine how such a reference could encompass such things; mathematics is far too vast. Nonetheless, EDM2 has amazing breadth and depth for a meager four-volume collection. And it is written with mathematicians in mind, so the discussions are crisp and rigorous. It's exceedingly well done.