On Numbers and Games / Edition 2
  • On Numbers and Games / Edition 2
  • On Numbers and Games / Edition 2

On Numbers and Games / Edition 2

by John H. Conway
     
 

ONAG, as the book is commonly 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. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently

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Overview

ONAG, as the book is commonly 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. 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, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

Product Details

ISBN-13:
9781568811277
Publisher:
Taylor & Francis
Publication date:
12/01/2000
Edition description:
REVISED
Pages:
256
Sales rank:
385,753
Product dimensions:
6.18(w) x 9.25(h) x (d)

Table of Contents

Prologue
Preface
Ch. 0All Numbers Great and Small3
Ch. 1The Class No is a Field15
Ch. 2The Real and Ordinal Numbers23
Ch. 3The Structure of the Genral Surreal Number29
Ch. 4Algebra and Analysis of Numbers39
Ch. 5Number Theory in the Land of Oz45
Ch. 6The Curious Field On[subscript 2]50
Appendix to Part Zero64
Ch. 7Playing Several Games at Once71
Ch. 8Some Games are Already Numbers81
Ch. 9On Games and Numbers97
Ch. 10Simplifying Games109
Ch. 11Impartial Games and the Game of Nim122
Ch. 12How to Lose when you Must122
Ch. 13Animating Functions, Welter's Game and Hackenbush Unrestrained153
Ch. 14How to Play Several Games at Once in a Dozen Different Ways173
Ch. 15Ups, Downs and Bynumbers188
Ch. 16The Long and the Short and the Small205
Epilogue225
Appendix229
Index235

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