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On Numbers and Games (L.M.S. Monographs ; No. 6)

By John Horton Conway

Publisher: Academic Pr
Number Of Pages: 247
Publication Date: 1976-06
Sales Rank: 2965939
ISBN / ASIN: 0121863506
EAN: 9780121863500
Binding: Hardcover
Manufacturer: Academic Pr
Studio: Academic Pr
Average Rating: 5

ONAG, as the book is known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Still in high demand, it is being republished with some adjustments and corrections. The original motivation for writing the book was an attempt to understand the relation between the theories of transfinite numbers and mathematical games. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers (so named by Donald Knuth) that includes at the same time the real numbers and the ordinal numbers.

This new edition ends with an epilogue that sets the stage for further research on surreal numbers. The book is a must-have for all readers with a serious interest in the mathematical foundations of game strategies.

Review:

Mind-blowingly original, side-splittingly funny

This is not a book for mathematical beginners, even though it starts from literally nothing. But readers who have learned enough traditional math to understand the point of set theory and who have a solid grasp of the real number system are in for a wild ride, and will never look at numbers, or games, in the same way again.

Conway is the most original mathematician on the planet, as well as a remarkably witty and vivid writer, who combines wordplay and logic better than anyone since Lewis Carroll. The book is far too densely packed to summarize in a short review. All I can say is that it’s practically inexhaustible; like all good math books, what you get out is proportional to the effort you make while reading it, but the amount of effort it will repay is a hundred times as much as for an ordinary book.

This is an all-time classic, a “desert island book”. Even though this new edition differs from the old one in very minor ways, I bought it immediately because my 1978 copy was falling apart from extreme overuse. (My other “desert island math book” is Cohen’s “Set Theory and the Continuum Hypothesis”.)password: OR password:

File: Conway J.H. On numbers and games (AP, 1976)(T)(ISBN 0121863506)(243s)_MAc_.djvu

http://rapidshare.com/files/45825136/t00115.rar

http://rapidshare.com/files/3761877/Conway.djvu

http://mihd.net/ep8mdo

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