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Title: Encyclopedic Dictionary of Mathematics: The Mathematical Society of Japan by Kiyosi Ito ISBN: 0-262-59020-4 Publisher: MIT Press Pub. Date: 04 May, 1993 Format: Paperback Volumes: 2 List Price(USD): $105.00 |
Average Customer Rating: 5 (8 reviews)
Rating: 5
Summary: Indispensable. How did I ever get on without it?
Comment: 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.
Rating: 5
Summary: The Consumate Personal Mathematics Reference
Comment: 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.
Rating: 5
Summary: best all-round math book for the mathematician's bookshelf
Comment: 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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Title: CRC Concise Encyclopedia of Mathematics, Second Edition by Eric W. Weisstein ISBN: 1584883472 Publisher: CRC Press Pub. Date: December, 2002 List Price(USD): $119.95 |
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Title: Handbook of Physics by John W. Harris, Horst Stocker, Holger Lutz, Walter Benenson, Horst Stoecker ISBN: 0387952691 Publisher: Springer Verlag Pub. Date: April, 2002 List Price(USD): $49.95 |
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Title: Handbook of Mathematics and Computational Science by Horst Stocker, John W. Harris ISBN: 0387947469 Publisher: Springer Verlag Pub. Date: 17 July, 1998 List Price(USD): $39.95 |
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Title: Table of Integrals, Series, and Products by I. S. Gradshteyn, I. M. Ryzhik, Alan Jeffrey, Daniel Zwillinger ISBN: 0122947576 Publisher: Academic Press Pub. Date: 31 July, 2000 List Price(USD): $88.95 |
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Title: CRC Standard Mathematical Tables and Formulae, 31st Edition by Daniel Zwillinger ISBN: 1584882913 Publisher: CRC Press Pub. Date: 27 November, 2002 List Price(USD): $49.95 |
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