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Mathematics: Its Content, Methods and Meaning [Paperback]

A. D. Aleksandrov , A. N. Kolmogorov , M. A. Lavrent’ev
5.0 out of 5 stars  See all reviews (4 customer reviews)
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Book Description

July 7 1999 Dover Books on Mathematics
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 edition.

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About the Author

The Russian Equation
Representative of the tremendous impact which Russian mathematicians have had on the Dover list since the Sputnik era is this outstanding book edited by A. D. Aleksandrov and others.

Critical Acclaim for Mathematics: Its Content, Methods and Meaning:
"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 but 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

"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

"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


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Front Cover | Table of Contents | Excerpt | Index | Back Cover
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Most helpful customer reviews
4 of 4 people found the following review helpful
5.0 out of 5 stars Great book for math fans Oct. 17 2002
By A Customer
Format:Paperback
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.
Was this review helpful to you?
4 of 4 people found the following review helpful
5.0 out of 5 stars Mathematics : Its Content, Methods and Meaning May 4 2000
Format:Paperback
It is a wonderful book. It reminds me of "The Feynman Lectures" in that it focuses on understanding, is (relatively) accessibly, has an incredible depth, and in that it covers an amazing amount. It includes "real" instruction, and you would be able to "do problems" after reading the book, although the real focus is more on understanding/ conceptual stuff.
Was this review helpful to you?
3 of 3 people found the following review helpful
5.0 out of 5 stars Wonderful Nov. 14 2003
Format:Paperback
This books is an amazing summary of almost all undergraduate math. It is definitely a mathematical masterpiece of all time, written by some of the most prominent mathematicians of all time.
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2 of 2 people found the following review helpful
5.0 out of 5 stars Additional comments to my previous review May 2 2000
Format:Paperback
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.
Was this review helpful to you?
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 4.8 out of 5 stars  18 reviews
60 of 60 people found the following review helpful
5.0 out of 5 stars Great book for math fans Oct. 17 2002
By A Customer - Published on Amazon.com
Format:Paperback
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.
55 of 56 people found the following review helpful
5.0 out of 5 stars Additional comments to my previous review May 2 2000
By Ryuji Suzuki - Published on Amazon.com
Format:Paperback
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.
37 of 37 people found the following review helpful
5.0 out of 5 stars Mathematics : Its Content, Methods and Meaning May 4 2000
By David Liu - Published on Amazon.com
Format:Paperback
It is a wonderful book. It reminds me of "The Feynman Lectures" in that it focuses on understanding, is (relatively) accessibly, has an incredible depth, and in that it covers an amazing amount. It includes "real" instruction, and you would be able to "do problems" after reading the book, although the real focus is more on understanding/ conceptual stuff.
27 of 28 people found the following review helpful
5.0 out of 5 stars Superb but BEWARE of what you buy Nov. 21 2008
By Ken Braithwaite - Published on Amazon.com
Format:Paperback|Verified Purchase
The Dover edition is 3 volumes in one. Many of the copies for sale here are just ONE of the 3 volumes. So be careful what you order!

This is a superb series of essays on major areas of math, by leading Russian mathematicians. They provide a splendid but SERIOUS introduction to each area. It is 50 years old but all this stuff is still central to any math related degree.

The book does a great job providing "motivation" and connecting the areas of math together. I wish I had had it when I did my degrees.

Suitable for those in math, physics, engineering. If you want a less ambitious, popular account of math then look for Ian Stewart's Concepts of Modern Mathematics, also from Dover.

Anf again, be careful about what you order.
18 of 18 people found the following review helpful
5.0 out of 5 stars A great text to have in your collection! March 23 2005
By From Detroit - Published on Amazon.com
Format:Paperback|Verified Purchase
This book gives a nice overview of the various fields of mathematics (no pun intended ;-)). Famous Russian authors have pooled their talents to come up with a book that summarizes the majority of the mathematics available the time. It's basically a dictionary for mathematicians! Covers topics from number theory, calculus, analysis, topology and even higher up subjects such as functional analysis and differential geometry. There are interesting theorems, and examples throughout.
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