Winning Ways includes several theories for a wide range of different compounds which are described in detail in the first volume, Games in General. In this volume, Games in Particular, there is a dazzling presentation of the examples: any game which presents an opportunity for witty and original comment has been included. The analyses start with basic theory using simple examples, but progress to detailed case-studies of well-known games ranging from the elementary to the elaborate and including Tic-Tac-Toe, Dots-and-Boxes, Hackenbush, Peg Solitaire and the maddening Hungarian cube puzzle.

Winning Ways for Your Mathematical Plays: Games in Particular (Vol. 2)

Humor & Entertainment

John Horton Conway

Richard Guy

Elwyn Berlekamp

Puzzles & Games

Academic Press

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.

Literature & Fiction

Francis Y. C. Fung

British & Irish

The Mathematical Association of America

This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.

On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry

Science & Math

Derek, Smith

Mathematics

A K Peters/CRC Press

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Books by John Horton Conway