On Numbers and Games

by John H. Conway

Overview

Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.

Product Details

ISBN-13:	9781040053133
Publisher:	CRC Press
Publication date:	12/11/2000
Sold by:	Barnes & Noble
Format:	eBook
Pages:	256
File size:	2 MB

About the Author

John H. Conway- John von Neumann Professor of Mathematics, Princeton University

Table of Contents

Prologue, Preface, Zeroth Part . . . On Numbers Chapter 0: All Numbers Great and Small Chapter 1: The Class No is a Field Chapter 2: The Real and Ordinal Numbers Chapter 3: The Structure of the General Surreal Number Chapter 4: Algebra and Analysis of Numbers Chapter 5: Number Theory in the Land of Oz Chapter 6: The Curious Field On2 First Part... and Games Chapter 7: Playing Several Games at Once Chapter 8: Some Games are Already Numbers Chapter 9: On Games and Numbers Chapter 10: Simplifying Games Chapter 11: Impartial Games and the Game of Nim Chapter 12: How to Lose when you Must Chapter 13: Animating Functions, Welter’s Game and Hackenbush Unrestrained Chapter 14: How to Play Several Games at Once in a Dozen Different Ways Chapter 15: Ups, Downs and Bynumbers Chapter 16: The Long and the Short and the Small. Epilogue

Editorial Reviews

This book, defined, if not created, the field of mathematical game theory when it was introduced 25 years ago. In it Conway (mathematics, Princeton U.) explores the strengths of various positions in several games and arrives at a new class of numbers, called surreal numbers, which include both real numbers and ordinal numbers; these surreal numbers are applied in the author's mathematical analysis of game strategies. This new edition has been supplemented with new developments in game theory and a concentration on the additive theory of partizan games. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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