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

## On Numbers and Games

**Author**: John H. Conway**Publisher:**CRC Press**ISBN:**9781568811277**Category:**Mathematics**Page:**256**View:**3485

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:**1439864152**Category:**Mathematics**Page:**256**View:**2155

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.

## Über Zahlen und Spiele

**Author**: John H. Conway**Publisher:**Springer-Verlag**ISBN:**3322889971**Category:**Mathematics**Page:**205**View:**735

## Die Macht der Vier

*von der pythagoreischen Zahl zum modernen mathematischen Strukturbegriff in Jacques Roubauds oulipotischer Erzählung La Princesse Hoppy ou le conte du Labrador*

**Author**: Elvira Laskowski-Caujolle**Publisher:**Elvira Laskowski-Caujolle**ISBN:**9783631348727**Category:**Mathematics in literature**Page:**376**View:**2708

Im Mittelpunkt dieses Buches steht ein vergleichsweise kurzer zeitgenossischer Text des Dichters und Mathematikers Jacques Roubaud. Die Autorin weist nach, dass Roubaud Bahnbrechendes in der Aufarbeitung der Mathematikgeschichte und der Erforschung mathematischer Strukturen in der Dichtung geleistet hat. Die kunstlerische Gestaltung mathematischer Sachverhalte, die bisher in der Forschung meist unberucksichtigt blieben, steht in keinem Widerspruch zum asthetischen Anspruch des Textes. Die Fusion mathematischen und poetischen Denkens wird durch die Verbindung gruppentheoretischer mit autobiographischen Elementen, die Integration indianischer Erzahltradition und die Ruckkehr zur hofisch-mittelalterlichen Roman- bzw. Gestentradition moglich, wobei der Zahl "Vier" eine Schlusselfunktion zukommt."

## 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:**8000

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.

## 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:**4559

Symposion Proceedings, San Servolo, Venice, Italy, May 16-22, 1999

## Badiou Dictionary

**Author**: Steven Corcoran**Publisher:**Edinburgh University Press**ISBN:**0748669647**Category:**Philosophy**Page:**424**View:**8488

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.

## Gewinnen Strategien für mathematische Spiele

*Band 4 Solitairspiele*

**Author**: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy**Publisher:**Springer-Verlag**ISBN:**3322831736**Category:**Technology & Engineering**Page:**159**View:**3961

Der vierte Band ,,Solitairspiele" behandelt Ein-Personen-Spiele mit Ausnahme von Schach, Go etc. Ein Hauptteil ist dem berühmten ,,Game of Life" gewidmet.

## The Book of Numbers

**Author**: John H. Conway,Richard Guy**Publisher:**Springer Science & Business Media**ISBN:**1461240727**Category:**Mathematics**Page:**310**View:**4315

"...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

## Winning Ways for Your Mathematical Plays

*Games in General*

**Author**: Elwyn R. Berlekamp,John Horton Conway,Richard K. Guy**Publisher:**Academic Pr**ISBN:**9780120911011**Category:**Education**Page:**850**View:**7988

## Lessons in Play

*An Introduction to Combinatorial Game Theory*

**Author**: Michael Albert,Richard Nowakowski,David Wolfe**Publisher:**CRC Press**ISBN:**1439864373**Category:**Mathematics**Page:**304**View:**9541

Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and new games, several appearing for the first time in this book.

## Gewinnen Strategien für mathematische Spiele

*Band 3 Fallstudien*

**Author**: Elwyn R. Berlekamp,John H. Conway,Richard K. Guy**Publisher:**Springer-Verlag**ISBN:**3322831728**Category:**Technology & Engineering**Page:**274**View:**718

Der dritte Band ,,Fallstudien" bietet eine Fülle von speziellen Beispielen.

## Mathemagic

*Magic, Puzzles and Games with Numbers*

**Author**: Royal V. Heath**Publisher:**Courier Corporation**ISBN:**0486201104**Category:**Games & Activities**Page:**126**View:**8164

Includes elementary puzzles, number stunts, mental multiplication, interest rates, oddities, and more.

## 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:**5857

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

## The Mathematics of Games

**Author**: John D. Beasley**Publisher:**Courier Corporation**ISBN:**048615162X**Category:**Mathematics**Page:**176**View:**6092

Lucid, instructive, and full of surprises, this book examines how simple mathematical analysis can throw unexpected light on games of every type, from poker to golf to the Rubik's cube. 1989 edition.

## Combinatorial Games

**Author**: Richard K. Guy**Publisher:**American Mathematical Soc.**ISBN:**0821819259**Category:**Mathematics**Page:**233**View:**8271

Based on lectures presented at the AMS Short Course on Combinatorial Games, held at the Joint Mathematics Meetings in Columbus in August 1990, the ten papers in this volume will provide readers with insight into this exciting field. Because the book requires very little background, it will likely find a wide audience that includes the amateur interested in playing games, the undergraduate looking for a new area of study, instructors seeking a refreshing area in which to give new courses at both the undergraduate and graduate levels, and graduate students looking for a variety of research topics.In the opening paper, Guy contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. Conway introduces a new theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the theory of games. Guy describes impartial games, with the same options for both players, and the Sprague-Grundy theory. Conway discusses a variety of ways in which games can be played simultaneously. Berlekamp uses the theory of 'hot' games to make remarkable progress in the analysis of Go Endgames.Pless demonstrates the close connection between several impartial games and error-correcting codes. Fraenkel explains the way in which complexity theory is very well illustrated by combinatorial games, which supply a plethora of examples of harder problems than most of those which have been considered in the past. Nowakowski outlines the theory of three particular games - Welter's Game, Sylver Coinage, and Dots-and-Boxes. A list of three dozen open problems and a bibliography of 400 items are appended.

## Lingua Universalis vs. Calculus Ratiocinator:

*An Ultimate Presupposition of Twentieth-Century Philosophy*

**Author**: Jaakko Hintikka**Publisher:**Springer Science & Business Media**ISBN:**9401586012**Category:**Philosophy**Page:**270**View:**2487

R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

## Theoretical Aspects of Computing - ICTAC 2006

*Third International Colloquium, Tunis, Tunisia, November 20-24, 2006 Proceedings*

**Author**: Kamel Barkaoui,Ana Cavalcanti**Publisher:**Springer Science & Business Media**ISBN:**3540488154**Category:**Computers**Page:**370**View:**572

The International Colloquium on Theoretical Aspects of Computing (ICTAC) held in 2006 in Tunis, Tunisia, was the third of a series of events created by the InternationalInstituteforSoftwareTechnologyoftheUnitedNationsUniversity. The aim of the colloquium is to bring together researchers from academia, - dustry, and governmentto present their results, and exchange experience, ideas, and solutions for their problems in theoretical aspects of computing. The previous events were held in Guiyang, China (2004), and Hanoi, Vi- nam (2005). Beyond its scholarly goals, another main purpose of ICTAC is to promote cooperation in research and education between participants and their institutions, from developing and industrial countries, as in the mandate of the United Nations University. These proceedings record the contributions from the invited speakers and from the technical sessions. We present four invited papers, 21 technical papers, selected out of 78 submissions from 24 countries, and two extended abstracts of tutorials. The Programme Committee includes researchers from 27 countries. Each of the 78 papers was evaluated by at least three reviewers. After the evaluation, reports were returned to the Programme Committee for discussion and reso- tion of con?icts. Based on their recommendations, we concluded the consensus process, and selected the 21 papers that we present here. For the evaluation of the submitted tutorials, this year we had the help of a separate Programme Committee especially invited for that purpose.