Princeton Companion to Mathematics (1 Viewer)

[tywebb]

What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity. More than 200 articles, organized thematically and written by many of the world's leading mathematicians, explain the major ideas and branches of mathematics in a clear, accessible style. Presenting not only definitions but also motivation and context for concepts, methods, theorems, and other topics of mathematical study, this is an indispensable resource for everyone with a serious interest in the field.

1. What is Mathematics?

Introduces the language and grammar of mathematics
fundamental definitions
general goals of mathematical research
the subject matter of mathematics

2. The Fundamental Ideas of Mathematics

Explores algebra
algorithms
geometry
how analysis became rigorous
numbers
the crisis in the foundations of mathematics
the development of the idea of proof

3. Mathematical Objects

Defines and explains more than 75 mathematical objects, concepts, and buzzwords, from axiom of choice to zeta function

4. Branches of Mathematics

Includes detailed coverage of algebra
algebraic geometry
analysis
combinatorics
computation
geometry
logic and set theory
number theory
probability

5. Mathematicians

Profiles 70 mathematicians, from Apollonius to Weyl, who influenced the field

6. Theorems and Problems

Discusses notable theorems and open problems, from the four-color theorem to the Reimann hypothesis

7. The Influence of Mathematics

Covers the intellectual and practical influence of mathematics on other disciplines such as analytic philosophy, art, biology, chemistry, economics, finance, and music

8. Miscellaneous

Advice to a Young Mathematician
Chronology of Mathematics
Computer Experiments in Mathematics
The Art of Problem Solving
and more

available for order at http://press.princeton.edu/titles/8350.html (publ. date: Oct. 5, 2008)

or http://www.amazon.com/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809

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[buchanan]

Timothy Gowers speaks about it in the following mp3 (18.3 MB, 19min 58sec):

http://www.press.princeton.edu/podcasts/Gowers/gowers.mp3

John Watkins from Colorado College calls it THE reference work in mathematics.

It's already available as a free torrent download on the internet - and looks great on the iphone (and also much lighter to carry than the huge book!). I will attempt to finish reading it by the end of the holidays - when I'm not trying to get past Level 5D on Space Invaders Extreme for the Nintendo DS, which I am finding very difficult (even with the Paddle Controller)