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Encyclopedic Dictionary of Mathematics: The Mathematical Society of Japan (2 Vol. Set) 2nd Edition

4.9 out of 5 stars 9 customer reviews
ISBN-13: 978-0262590204
ISBN-10: 0262590204
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Editorial Reviews

Amazon.com 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

Language Notes

Text: English (translation)

Product Details

  • Paperback: 2168 pages
  • Publisher: The MIT Press; 2 edition (May 4, 1993)
  • Language: English
  • ISBN-10: 0262590204
  • ISBN-13: 978-0262590204
  • Product Dimensions: 12.6 x 6.3 x 4 inches
  • Shipping Weight: 9 pounds
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #2,386,849 in Books (See Top 100 in Books)

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Top Customer Reviews

The Encyclopedic Dictionary of Mathematics is an astonishing achievement. The result of an extraordinary, decades-long collaboration among literally hundreds of celebrated Japanese mathematicians, it will not only never be equalled but in all probability will never be challenged. In two massive volumes, the EDM surveys the whole of the mathematical sciences, both pure and applied, through a series of pithy articles containing the key definitions, methods, and results of every mathematical subdiscipline sufficiently coherent to have a name. It also tabulates vast amounts of information -- homotopy groups of spheres, symmetries of ordinary differential equations, characters of finite groups, class numbers of algebraic number fields, and so forth, seemingly, ad infinitum -- available, as far as I know, in no other single reference work.
Equipped with a detailed and extensive system of indexes, the EDM makes its myriad resources readily available even to the befuddled; the vaguest, most dimly remembered hint is generally enough to track down a topic or result quickly and easily. Each entry, too, offers its own references to the mathematical literature -- and these invariably include the seminal contributions to the particular area under discussion. But it is important to note that the EDM was written by the Japanese, for the Japanese: many of its references direct the reader to (untranslated, Japanese-language) works in (often inaccessible) Japanese mathematics journals.
It is likewise only fair to point out that the EDM is a tool for serious research mathematicians. To keep its component articles brief, it makes full, unapologetic use of a wide variety of notational and expositional economies.
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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.
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I've been using this book in my work as a mathematician since I bought the first english-language edition in 1984. The second english-language edition is not enormously different to the first, but it is an improvement. Both have been by far the most useful reference on my bookshelf for 18 years. I have always found that the coverage is in-depth and yet comprehensible (with a bit of pen-on-paper work). It's especially useful for accessing results from areas other than my own speciality. I've found the differential geometry coverage literally better than the dozen texts on DG which I have bought. It must be worth more than 100 books on the shelf. Indexing and cross-referencing are both excellent. Historical context is very good. I use this encyclopedia at least 10 times a week. Virtually every definition I need is here, and every important theorem is summarised.
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Prepared by the Mathematical Society of Japan, this two-volume set provides an outstanding reference of mathematics. It is considered by many to be the best available work that is both definitive and encompassing. Treatment is in depth, and presentations assume a solid mathematical background of the reader. This reference is excellent for the researcher working at the doctoral level. Cost of the paperback edition is very reasonable.
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I have found this survey of mathematics very useful both as research and teaching tool. It includes almost every topic you can imagine treated in a complete and concise way. It also gives a lot of valuable and difficult-to-find original references, of crucial importance when doing research.
I saw this dictionary for the first time in my Polythecnic Institute's library (Mexico City). I think every math library should own its.
Please read my other reviews in my member page (just click on my name above).
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