John H. Conway's Books

The Book of Numbers

By: John H. Conway,Richard Guy

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...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL

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Page Count

313

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461240727

ISBN 13

9781461240723

Winning Ways for Your Mathematical Plays

Volume 1

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

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Winning Ways for Your Mathematical Plays

Volume 1

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

This classic on games and how to play them intelligently is being re-issued in a new, four volume edition. This book has laid the foundation to a mathematical approach to playing games. The wise authors wield witty words, which wangle wonderfully winning ways. In Volume 1, the authors do the Spade Work, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies.

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Page Count

343

Publisher

CRC Press

Published Date

ISBN 10

0429945590

ISBN 13

9780429945595

On Numbers and Games

By: John H. Conway

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On Numbers and Games

By: John H. Conway

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.

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Page Count

253

Publisher

CRC Press

Published Date

ISBN 10

1439864152

ISBN 13

9781439864159

Sphere Packings, Lattices and Groups

By: John H. Conway,Neil J.A. Sloane

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Sphere Packings, Lattices and Groups

By: John H. Conway,Neil J.A. Sloane

The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.

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Page Count

690

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475720165

ISBN 13

9781475720167

On Quaternions and Octonions

By: John H. Conway,Derek A. Smith

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On Quaternions and Octonions

By: John H. Conway,Derek A. Smith

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 f

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Page Count

172

Publisher

CRC Press

Published Date

ISBN 10

1439864187

ISBN 13

9781439864180

The Symmetries of Things

By: John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss

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The Symmetries of Things

By: John H. Conway,Heidi Burgiel,Chaim Goodman-Strauss

Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

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Page Count

442

Publisher

CRC Press

Published Date

ISBN 10

1439864896

ISBN 13

9781439864890

Winning Ways for Your Mathematical Plays, Volume 2

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

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Winning Ways for Your Mathematical Plays, Volume 2

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 2, the authors have a Change of Heart, bending the rules established in Volume 1 to apply them to games such as Cut-cake and Loopy Hackenbush. From the Table of Contents: - If You Can't Beat 'Em, Join 'Em! - Hot Bottles Followed by Cold Wars - Games Infinite and Indefinite - Games Eternal--Games Entailed - Survival in the Lost World

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Page Count

252

Publisher

CRC Press

Published Date

ISBN 10

0429945604

ISBN 13

9780429945601

Winning Ways for Your Mathematical Plays, Volume 3

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

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Winning Ways for Your Mathematical Plays, Volume 3

By: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy

In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 3, the authors examine Games played in Clubs, giving case studies for coin and paper-and-pencil games, such as Dots-and-Boxes and Nimstring. From the Table of Contents: - Turn and Turn About - Chips and Strips - Dots-and-Boxes - Spots and Sprouts - The Emperor and His Money - The King and the Consumer - Fox and Geese; Hare and Hounds - Lines and Squares

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Page Count

426

Publisher

CRC Press

Published Date

ISBN 10

0429945612

ISBN 13

9780429945618

Exploring Mathematics

An Engaging Introduction to Proof

By: John Meier,Derek Smith

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Exploring Mathematics

An Engaging Introduction to Proof

By: John Meier,Derek Smith

Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

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Page Count

341

Publisher

Cambridge University Press

Published Date

ISBN 10

1108509282

ISBN 13

9781108509282

Book's by John H. Conway

The Book of Numbers

The Book of Numbers

Winning Ways for Your Mathematical Plays

Winning Ways for Your Mathematical Plays

On Numbers and Games

On Numbers and Games

Sphere Packings, Lattices and Groups

Sphere Packings, Lattices and Groups

On Quaternions and Octonions

On Quaternions and Octonions

The Symmetries of Things

The Symmetries of Things

Winning Ways for Your Mathematical Plays, Volume 2

Winning Ways for Your Mathematical Plays, Volume 2

Winning Ways for Your Mathematical Plays, Volume 3

Winning Ways for Your Mathematical Plays, Volume 3

Exploring Mathematics

Exploring Mathematics

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