On Numbers and Games

Author: John H. Conway

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 256

View: 644

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

Author: John H. Conway

Publisher: CRC Press

ISBN:

Category: Mathematics

Page: 256

View: 758

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.

Combinatorial Game Theory

Surreal Number, Solved Game, Nim, Sprague-grundy Theorem, Nimber, Impartial Game, on Numbers and Games, Col

Author: Books, LLC

Publisher: Books LLC, Wiki Series

ISBN:

Category: Mathematics

Page: 177

View: 117

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 45. Chapters: Surreal number, Solved game, Nim, Sprague-Grundy theorem, Nimber, Impartial game, On Numbers and Games, Col, Shannon switching game, Game complexity, Go and mathematics, Angel problem, Jenga, Octal game, Domineering, Chomp, Genus theory, Map-coloring games, Shannon number, Game tree, Hackenbush, Kayles, Cram, Hot game, Subtract a square, Mis re, Pebble game, Toads and Frogs, Grundy's game, Star, Winning Ways for your Mathematical Plays, Maker-Breaker game, Sylver coinage, Sim, Tiny and miny, Variation, Indistinguishability quotient, Fuzzy game, Clobber, Disjunctive sum, Bulgarian solitaire, Branching factor, Positional game, Generalized game, Mex, Zero game, Partisan game, Null move, Sum of combinatorial games. Excerpt: In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. In a rigorous set theoretic sense, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed. The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the...

Winning Ways, for Your Mathematical Plays: Games in particular

Author: Elwyn R. Berlekamp

Publisher: Academic Pr

ISBN:

Category: Education

Page: 422

View: 563

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.

Computers and Games

5th International Conference, CG 2006, Turin, Italy, May 29-31, 2006, Revised Papers

Author: H. Jaap van den Herik

Publisher: Springer

ISBN:

Category: Computers

Page: 283

View: 954

This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Computers and Games, CG 2006, co-located with the 14th World Computer-Chess Championship and the 11th Computer Olympiad. The 24 revised papers cover all aspects of artificial intelligence in computer-game playing. Topics addressed are evaluation and learning, search, combinatorial games and theory opening and endgame databases, single-agent search and planning, and computer Go.

Badiou Dictionary

Author: Steven Corcoran

Publisher: Edinburgh University Press

ISBN:

Category: Philosophy

Page: 424

View: 282

From Antiphilosophy to Worlds and from Beckett to Wittgenstein, the 110 entries in this dictionary provide detailed explanations and engagements with Badious's key concepts and major interlocutors.

Numbers

Author: Heinz-Dieter Ebbinghaus

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 391

View: 987

A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.

The Book of Numbers

Author: John H. Conway

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 310

View: 712

"...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