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A carregar... On Numbers and Games (1976)por John Horton Conway
A carregar...
Adira ao LibraryThing para descobrir se irá gostar deste livro. Ainda não há conversas na Discussão sobre este livro. I read the first edition of this book as an undergraduate student of mathematics and, like many of my peers, was astonished at the effortless way in which an entire new class of numbers was defined, and then extended again to embrace the world of mathematical games. It's deep, yet playful (anything which deals with 'surreal numbers' is OK by me) and accessible, although not to someone without some knowledge of algebra. Conway is an inventive genius and nowhere is that more obvious than in this book. (The copy catalogued here is the second edition of 2001; the original dates from 1976, when I first read it.) This ranks with "Mathematics made difficult" and most of Martin Gardner's mathematical diversions as essential reading for enthusiasts of mathematics. It reminds you why it's fun. Cet ouvrage traite de l'aspect mathématique d'une démarche qui existait parallèlement dans les deux ouvrages, Winning Ways : tome 1 et 2 Knuth a voulu faire un récit autour d'une genèse de ces notions dans Surreal Numbers J'ai retrouvé dans la démarche de Conway la manière dont, dans les années 60, on m'avait présenté les réels à travers les coupures, avant la présentation par les suites de Cauchy On s'approche des réels dont je reste convaincu que nous n'avons, à l'heure actuelle, qu'une approche assez réduite. Comme un voyageur parcourant les océans le long de routes balisées. On peut s'en apercevoir à travers le peu de parcours possibles dans l'ensemble des transcendants (j'ai l'impression qu'on n'en connaît que quelques familles algébriques) ou dans l'émergence des nombres Ω sem críticas | adicionar uma crítica
"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."--Provided by publisher. Não foram encontradas descrições de bibliotecas. |
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Google Books — A carregar... GénerosSistema Decimal de Melvil (DDC)519.3Natural sciences and mathematics Mathematics Applied Mathematics, Probabilities Game TheoryClassificação da Biblioteca do Congresso dos EUA (LCC)AvaliaçãoMédia:
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"Preface" handler om ???
"Zeroth Part ... On Numbers" handler om ???
" Chapter 0: All Numbers Great and Small" handler om ???
" Chapter 1: The Class No is a Field" handler om ???
" Chapter 2: The Real and Ordinal Numbers" handler om ???
" Chapter 3: The Structure of the General Number" handler om ???
" Chapter 4: Algebra and Analysis of Numbers" handler om ???
" Chapter 5: Number Theory in the Land of Oz" handler om ???
" Chapter 6: The Curious Field On2" handler om ???
" Appendix to Part Zero" handler om ???
"First Part ... and Games" handler om ???
" Chapter 7: Playing Several Games at Once" handler om ???
" Chapter 8: Some Games are Already Numbers" handler om ???
" Chapter 9: On Games and Numbers" handler om ???
" Chapter 10: Simplifying Games" handler om ???
" Chapter 11: Impartial Games and the Game of Nim" handler om ???
" Chapter 12: How to Lose when you Must" handler om ???
" Chapter 13: Animated Functions, Welter's Game and Hackenbush Unrestrained" handler om ???
" Chapter 14: How to Play Several Games at Once in a Dozen Different Ways" handler om ???
" Chapter 15: Ups, Downs and Bynumbers" handler om ???
" Chapter 16: The Long and the Short and the Small" handler om ???
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Conway, alias J. H. Conway alias John Horton Conway, er genial. Denne gamle bog fra 1976 er historien om hvordan man kan definere tal på en måde, så snart sagt alle mulige udvidelser springer frem af panden af sig selv. Surreal Numbers er et forsøg fra Donald Knuth på at lave en lille roman ud af disse tal.
Theorem 100: This is the last theorem in this book. (The proof is obvious). ( )