Product Description

Hailed by The New York Times Book Review as "...nothing less than a major contribution to the scientific culture of this world," this major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 ed.

Product Details

• Amazon Sales Rank: #171415 in Books
• Published on: 1999-07-07
• Original language: English
• Number of items: 1
• Binding: Paperback
• 1120 pages

Features

• ISBN13: 9780486409160
• Condition: NEW
• Notes: Brand New from Publisher. No Remainder Mark.
• Click here to view our Condition Guide and Shipping Prices

Review
"An excellent reference set for bright high school students and beginning college students ... also of value to their teachers for lucid discussions and many good elementary examples in both familiar and unfamiliar branches. The intelligentsia of laymen who care to tackle more than today's popular magazine articles on mathematics will find many rewarding introductions to subjects of current interest."
— The Mathematics Teacher

"In effect, these volumes present a do-it-yourself course for the person who would like to know what the chief fields of modern mathematics are all about bit who does not aspire to be a professional mathematician or a professional user of mathematics. The coverage is extremely wide, including such important areas as linear algebra, group theory, functional analysis, ordinary and partial differential equations, the theory of functions of real and complex variables, and related subjects.... What makes these volumes so readable as compared with usual mathematics textbooks is the emphasis here upon basic concepts and results rather than upon the intricate and wearying proofs that make such demands in conventional textbooks and courses. There are proofs in these volumes, but usually they are presented only for the most important results, and even then to emphasize key areas and to illustrate the kind of methodology employed.... It is hard to imagine that any intelligent American with a curious mind and some good recollection of his high school and college mathematics would not find many entrancing discoveries in the intellectual gold mine that is this work."
— The New York Times Book Review

"Whether a physicist wishes to know what a Lie algebra is or how it is related to a Lie group, or an undergraduate would like to begin the study of homology, or a crystallographer is interested in Fedorov groups, or an engineer in probability, or any scientist in computing machines, he will find here a connected, lucid account."
— Science

Customer Reviews

Excellent introduction with lots of insights
Many mathematics and engineering books today require "relatively modest background and mathematical maturity," and the text goes with mathematical formalism and compact descriptions. However, this series (three books) is a collection of chapters on single topic, written by top Russian mathematicians in plain language and vivid illustrations. Bright high school students should be able to read them, but the material is no kids stuff, in a sense that every chapter gives at least some real feeling of the topic. I recommend this series only to those who are seriously interested in mathematics but looking for the friendly version of the real mathematics. I think the title describes this.

Among the three books, I like Volume 2 the best, because Chapter 10 is on prime numbers (Mardzanisvili and Postnikov), 11 on probability theory (Kolmogorov), 12 and 13 on approximation of functions and numerical aspects, and these match with my interests the best. This volume also includes differential equations, culculus, complex analysis, etc.

Volume 1 and 3 contain analysis, topology, algebra, geometry, etc. At this paper edition price, all three are worth keeping.

A small caveat is that my review and contents description is based on the original edition by MIT press in 1960s. I assumed that second edition did not reorganize the general construction of the books.

Additional comments to my previous review
In addition to my previous review, concerning the contents, here are a few additions on physical aspects.

This 1999 paperback edition has all three volumes in one binding. The paper is thinner so the book is less bulky. Page number resets at the beginning of volume 2 and 3. (not renumbered.) Thus the book content is not altered from the 2nd edition (three volumes set) from MIT Press in 1969.

One major change is that there is one index at the end of the book which covers all three volumes. The volume is indicated together with the page number. This improves the convenience.

Great book for math fans
I whole-heartedly agree with the other positive reviews offered here. There are only a few things I would like to add:

(1) Popular math and science has become quite popular lately. I'm sure that there are many pop-math/pop-sci readers who would like a more 'meatier' treatment of math that still has an accessible style. If you're in that group, then this book is for you.

It basically requires recollection of high school algebra and a willingness to wade through and learn some challenging material. I should add that the book looks intimidating in size but this is mostly due to the fact that Dover has bound 3 volumes as 1 (which is actually a great deal for readers).

(2) I can't think of too may books that can, with effort, take a novice through the bulk of a college/university level math curriculum.

(3) This book contains material by 2 of the greatest mathematicians/scientists of all time: Andrei Kolmogorov (famous for his work on probability and information theory as well as Kolmogorov Complexity/Algorithmic Information Theory) and I. M. Gelfand (for his work on mathematical physics). The book is worth buying for that reason alone.