On Numbers and Games

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.

Informationen zum Autor John H. Conway- John von Neumann Professor of Mathematics, Princeton University Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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...

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

Klappentext

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.

Inhalt
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