Mathematics: Its Content, Methods and Meaning : Three Volumes Bound As One

Rating:
Summary: Great book for math fans
Review: 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.

Rating:
Summary: Additional comments to my previous review
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.

Rating:
Summary: Great book for math fans
Review: 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.

Rating:
Summary: Mathematics : Its Content, Methods and Meaning
Review: 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.

Rating:
Summary: Excellent introduction with lots of insights
Review: 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.

Rating:
Summary: Wonderful
Review: 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.