Search Results for "on-numbers-and-games"

On Numbers and Games

On Numbers and Games

  • Author: John H. Conway
  • Publisher: CRC Press
  • ISBN: 9781568811277
  • Category: Mathematics
  • Page: 256
  • View: 8486
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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

On Numbers and Games

  • Author: John H. Conway
  • Publisher: CRC Press
  • ISBN: 1439864152
  • Category: Mathematics
  • Page: 256
  • View: 470
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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.

The Book of Numbers

The Book of Numbers

  • Author: John H. Conway,Richard Guy
  • Publisher: Springer Science & Business Media
  • ISBN: 1461240727
  • Category: Mathematics
  • Page: 310
  • View: 4910
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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

Numbers

Numbers

  • Author: Heinz-Dieter Ebbinghaus,Hans Hermes,Friedrich Hirzebruch,Max Koecher,Klaus Mainzer,Jürgen Neukirch,Alexander Prestel,Reinhold Remmert
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387974972
  • Category: Mathematics
  • Page: 391
  • View: 8963
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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.

Winning ways for your mathematical plays

Winning ways for your mathematical plays

Games in particular

  • Author: Elwyn R. Berlekamp,John Horton Conway,Richard K. Guy
  • Publisher: N.A
  • ISBN: 9780120911523
  • Category: Education
  • Page: 422
  • View: 571
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Badiou Dictionary

Badiou Dictionary

  • Author: Steven Corcoran
  • Publisher: Edinburgh University Press
  • ISBN: 0748669647
  • Category: Philosophy
  • Page: 424
  • View: 542
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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.

Surreal Numbers

Surreal Numbers

How Two Ex-students Turned on to Pure Mathematics and Found Total Happiness : a Mathematical Novelette

  • Author: Donald Ervin Knuth
  • Publisher: Addison-Wesley Professional
  • ISBN: 9780201038125
  • Category: Computers
  • Page: 119
  • View: 6560
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Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself...". It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created. 0201038129B04062001

Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum

Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum

  • Author: Peter Schuster,Ulrich Berger,Horst Osswald
  • Publisher: Springer Science & Business Media
  • ISBN: 9781402001529
  • Category: Mathematics
  • Page: 316
  • View: 6757
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Symposion Proceedings, San Servolo, Venice, Italy, May 16-22, 1999

More Games of No Chance

More Games of No Chance

  • Author: Richard Nowakowski,Silvio Levy
  • Publisher: Cambridge University Press
  • ISBN: 9780521808323
  • Category: Mathematics
  • Page: 535
  • View: 8796
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This 2003 book documents mathematical and computational advances in Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex, and more.