John H. Conway

G. Polya

Outlines a method of solving mathematical problems for teachers and students based upon the four steps of understanding the problem, devising a plan, carrying out the plan, and checking the results.

A New Aspect of Mathematical Method

How to Solve It

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

Richard Guy

"...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

The Book of Numbers

Chaim Goodman-Strauss

Heidi Burgiel

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 Thursto

The Symmetries of Things

Richard K. Guy

Elwyn R. Berlekamp

This is a text on mathematical games and how to play them intelligently. In this volume, the authors present a Diamond of a find, cover one-player games such as Solitaire, and ponder questions like What is life?

Winning Ways for Your Mathematical Plays, Volume 4

This is a text on games and how to play them intelligently. In this volume, the authors examine games played in clubs, giving case studies for coin and paper-and-pencil games, such as Dots-and-Boxes and Nimstring.

Winning Ways for Your Mathematical Plays, Volume 3

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

John H. Conway

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