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

Encyclopedic Dictionary of Mathematics: The Mathematical Society of Japan (2 Vol. Set)
Kiyosi Ito | 1993-05-04 00:00:00 | The MIT Press | 2168 | Science
The second edition of the widely acclaimed Encyclopedic Dictionary of Mathematics was published in 1987 and is now available in paperback. It includes 70 new articles, particularly in applied mathematics, expanded explanations and appendices, coverage of recent work, and reorganization of older topics.
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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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.




Reviews
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.
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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.

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.
Reviews
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'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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Symmetries of Equations of Quantum Mechanics

Symmetries of Equations of Quantum Mechanics
Vilgelm Ilich Fushchich,A. G. Nikitin,W. I. Fushchich | 1900-01-01 00:00:00 | Allerton Pr | 465 | Science

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An Introduction to the Smarandache Function

An Introduction to the Smarandache Function
Charles Ashbacher | 1900-01-01 00:00:00 | Erhus Univ Pr | 60 | Science

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Chemical Crystallography - An Introduction To Optical And X Ray Methods.

Chemical Crystallography - An Introduction To Optical And X Ray Methods.
C.W. Bunn | 2007-03-15 00:00:00 | Bunn Press | 468 | Science
Text extracted from opening pages of book: CHEMICAL CBYSTALLOGRAPHY AN. INTRODUCTION TO OPTICAL AND X-RAY METHODS BY C. W. BUNN OXFORD AT THE CLARENDON PRESS Oxford University Press, Amen House, London E. G. 4 GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON BOMBAY CALCUTTA MADRAS CAPETOWN Geoffrey Cumberlege, Publisher to the University FIRST PUBLISHED 1045 REPRINTED WITH CORRECTIONS 1946 Reprinted lithographically in Great Britain at the UNIVERSITY PRESS, OXFORD, 1948, 1949, 1952, from corrected sheets of the second impression PREFACE CEYSTALLOGRAPHIC methods are used in chemistry for two main pur poses the identification of solid substances, and the determination of atomic configurations ; there are also other applications, most of which, as far as technique is concerned, may* be said to lie between the two main subjects. This baok is intended to be a guide to these methods. I have tried to explain the elementary principles involved, and to give as much practical information as will enable the reader to start using the methods described. I have not attempted to give a rigorous treat ment of the physical principles: the f approach is consistently from the chemist's point of view, and physical theory is included only in so far as it is necessary for the general comprehension of the principles and methods described. Nor have I attempted to give an exhaustive account of any subject ; the aim throughout has been to lay the founda tions, and to give sufficient references ( either to larger works or to original papers) to enable the reader to follow up any subject in greater detail if he so desires. The treatment of certain subjects is perhaps somewhat unorthodox. Crystal morphology, for instance, is described in terms of the concept of the unit cell ( rather than in terms of the axial ratios of the earlier morphologists), and is approached by way of the phenomena of crystal growth. The optical properties of crystals are described solely in terms of the phenomena observed in the polarizing microscope. X-ray diffrac tion is considered first in connexion with powder photographs; it is moj* e usual to start with the interpretation of the diffraction effects of single crystals. These methods of treatment are dictated by the form and scope of the book ; they also reflect the course of the writer's own experience in applying crystallographic methods to chemical problems. It is therefore hoped that they may at any rate seem natural to those to whom the book is addressed - students of chemistry who wish to acquire some knowledge of crystallographic methods, and research workers who wish to make practical use of such methods. If the book should come to the notice of a more philosophical reader, I can only hope that any qualms such a reader may feel about its avoidance of formal physical or mathematical treatment may be somewhat offset by the interest of a novel, if rather severely practical, viewpoint. The difficulties of three-dimensional thinking have, I hope, been lightened as much as possible by the provision of a large number of vi PREFACE diagrams ; but crystallography is emphatically not a subject which can be learnt solely from books: solid models should be used freely models of crystal shapes, of atomic . nd molecular configurations, of reciprocal lattices and of vectorial representations of optical and other physical properties. Most of the diagrams are original, but a few have been reproduced, by permission, from published books and journals: Figs. 197, 207-9, 215, and 222 from the Journal of the Chemical Society ; Figs. 199, 203, and 217 from the Proceedings of the Royal Society, Figs. 102-4 from the Journal of Scientific Instruments ; Fig. 229 from the Journal of the American Chemical Society, Fig. 161 from Inter nationale Tabetten ftir Bestimmung von Kristallstrukturen ( Berlin: Born traeger); Fig. 192 from the * Strnkturbericht ' of the Zeitschrift fttr Kristallographie\ and Figs. 212 and 216 from Bragg's The Crystalline State

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Inverse Scattering Papers, 1955-1963 (Lie groups : history, frontiers, and applications)

Inverse Scattering Papers, 1955-1963 (Lie groups : history, frontiers, and applications)
Irvin W. Kay | 1900-01-01 00:00:00 | Math Science Pr | 305 | Science

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From Polymers to Plastics

From Polymers to Plastics
A. K. van der Vegt | 2005-12-28 00:00:00 | VSSD | 268 | Science
Treatment of properties and structure of polymers and behaviour of plastics materials.

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Practical Ephemeris Calculations

Practical Ephemeris Calculations
Oliver Montenbruck | 1900-01-01 00:00:00 | Springer-Verlag | 146 | Science
The calculation of exact positions of stars, the Sun and the celestial bodies of the solar system is a prerequisite of successful practical work in astronomy. This text gives the necessary background of spherical astronomy and celestial mechanics from the practitioner's point of view, and collates all the formulae and numerical values needed to calculate precise ephemerides. The clear structure of the book allows easy use of the material in computer programs. Students, lecturers and amateurs in astronomy will find the book an invaluable reference in their daily work, lectures or lab courses.
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One of the better astronomical calculation books. It's a lot like Jean Meeus' books: a series of recipes for performing practical calculations, not much theory or background. It is assumed you already know the necessary astronomy to know more or less what you want to do. Montenbruck goes into a couple of areas which Meeus does not, or which Meeus treats incompletely:

- numerical integration, which is the modern method used by the astronomical almanacs to compute their accurate ephemerides. His treatment is very basic, but is a great jumping-off point for further study.

- physical ephemerides, which Meeus develops completely only for the Sun, Mars and the Moon, and partially for Jupiter.

That being said, Meeus' books are better for orbital positions of the Moon and planets, and satellites. Montenbruck gives only approximate planetary orbits, but gives very complete math for handling them, and he does not go into planetary satellites at all. Neither author's treatment of physical ephemerides gives planetographic coordinates (vs planetocentric), which are needed if you're trying to duplicate almanac data.
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Oliver Montenbruck is a great author. But that's not the main reason I bought this book.



I am really interested in planetary astronomy. And I do care very much about the motion of minor bodies orbiting the Sun. And sure, I care about the positions of the planets as well. This book is indeed useful for that. And, yes, you can put the equations on your computer or calculator or PDA. And there's an appendix that gives mean orbital elements for Mercury, Venus, Earth, and Mars as well as osculating orbital elements for Jupiter, Saturn, Uranus, Neptune, and Pluto for the years 1941 through 2049. That's useful too!



But I confess, the real reason I got this book, and the real use I put it to is simple. I can get really confused about how to go between geocentric ecliptic, geocentric equatorial, heliocentric, horizontal, and topocentric coordinates. And this book tells me how to transform my way into the one I want. It also explains the different definitions of time: TAI, ET, TDT, TDB, UT, UTC, AST, MST, GMST, LMST, GAST, LAST, and Julian Date.

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