On Numbers and Games

John H. Conway

248 pages, parution le 01/01/2001 (2^eme édition)

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Résumé

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. 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.ContentsZeroth part: ...On numbers

Ch. 0 All Numbers Great and Small
Ch. 1 The Class No is a Field
Ch. 2 The Real and Ordinal Numbers
Ch. 3 The Structure of the Genral Surreal Number
Ch. 4 Algebra and Analysis of Numbers
Ch. 5 Number Theory in the Land of Oz
Ch. 6 The Curious Field On[subscript 2]

First part: ...on games

Ch. 7 Playing Several Games at Once
Ch. 8 Some Games are Already Numbers
Ch. 9 On Games and Numbers
Ch. 10 Simplifying Games
Ch. 11 Impartial Games and the Game of Nim
Ch. 12 How to Lose when you Must
Ch. 13 Animating Functions, Welter's Game and Hackenbush Unrestrained
Ch. 14 How to Play Several Games at Once in a Dozen Different Ways
Ch. 15 Ups, Downs and By numbers
Ch. 16 The Long and the Short and the Small

Caractéristiques techniques

	PAPIER
Éditeur(s)	AK Peters
Auteur(s)	John H. Conway
Parution	01/01/2001
Édition	2^eme édition
Nb. de pages	248
Format	15,7 x 23,5
Couverture	Relié
Poids	518g
Intérieur	Noir et Blanc
EAN13	9781568811277
ISBN13	978-1-56881-127-7