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.

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

Science & Math

Conway, John Horton

Mathematics

Academic Pr

This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections

Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups

Reference

Atlases & Maps

Oxford University Press

World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular algebra, axiomatic questions, the strength of classical axioms, and logical problems. Complete solutions to problems appear at the end.

Regular algebra and finite machines, (Chapman and Hall mathematics series)

Chapman and Hall

World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians. His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include event classes and operator classes, some regulator algebras, context-free languages, communicative regular algebra, axiomatic questions, the strength of classical axioms, and logical problems. Complete solutions to problems appear at the end.

Regular Algebra and Finite Machines (Dover Books on Mathematics)

Dover Publications

The Sensual (Quadratic) Form (Carus Mathematical Monographs, Series Number 26)

The distinguished mathematician John Conway presents quadratic forms in a pictorial way that enables the reader to understand them mathematically without proving theorems in the traditional fashion. One learns to sense their properties. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of mathematical topics from algebra, number theory and geometry, including many new ideas and features.

The Mathematical Association of America

The Sensual Quadratic Form (Carus Mathematical Monographs, 26)

Amer Mathematical Society

Sphere packings, lattices, and groups (Grundlehren der mathematischen Wissenschaften)

Springer, Verlag

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