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An Introduction To The Theory Of Surreal Numbers
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Book Synopsis An Introduction to the Theory of Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by Cambridge University Press. This book was released on 1986-09-18 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Book Synopsis An Introduction to the Theory of Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to Surreal Numbers written by Harry Gonshor and published by . This book was released on 2014-05-14 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Book Synopsis Surreal Numbers by : Donald Ervin Knuth
Download or read book Surreal Numbers written by Donald Ervin Knuth and published by Addison-Wesley Professional. This book was released on 1974 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis An Introduction to the Theory of Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by Cambridge University Press. This book was released on 1986-09-18 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.
Book Synopsis On Numbers and Games by : John H. Conway
Download or read book On Numbers and Games written by John H. Conway and published by CRC Press. This book was released on 2000-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.
Book Synopsis Contributions to the Founding of the Theory of Transfinite Numbers by : Georg Cantor
Download or read book Contributions to the Founding of the Theory of Transfinite Numbers written by Georg Cantor and published by . This book was released on 1915 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Number and Numbers by : Alain Badiou
Download or read book Number and Numbers written by Alain Badiou and published by John Wiley & Sons. This book was released on 2018-05-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosophically penetrating account with a powerful political subtext of the attempts that have been made over the last century to define the special status of number. Badiou argues that number cannot be defined by the multiform calculative uses to which numbers are put, nor is it exhausted by the various species described by number theory. Drawing on the mathematical theory of surreal numbers, he develops a unified theory of Number as a particular form of being, an infinite expanse to which our access remains limited. This understanding of Number as being harbours important philosophical truths about the structure of the world in which we live. In Badiou's view, only by rigorously thinking through Number can philosophy offer us some hope of breaking through the dense and apparently impenetrable capitalist fabric of numerical relations. For this will finally allow us to point to that which cannot be numbered: the possibility of an event that would deliver us from our unthinking subordination of number.
Book Synopsis Winning Ways for Your Mathematical Plays by : Elwyn R. Berlekamp
Download or read book Winning Ways for Your Mathematical Plays written by Elwyn R. Berlekamp and published by CRC Press. This book was released on 2018-05-08 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic on games and how to play them intelligently is being re-issued in a new, four volume edition. This book has laid the foundation to a mathematical approach to playing games. The wise authors wield witty words, which wangle wonderfully winning ways. In Volume 1, the authors do the Spade Work, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies.
Book Synopsis Real Numbers, Generalizations of the Reals, and Theories of Continua by : P. Ehrlich
Download or read book Real Numbers, Generalizations of the Reals, and Theories of Continua written by P. Ehrlich and published by Springer. This book was released on 2012-12-22 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
Book Synopsis Which Numbers Are Real? by : Michael Henle
Download or read book Which Numbers Are Real? written by Michael Henle and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.
Download or read book SURREAL NUMBERS written by and published by . This book was released on with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mathematics of Various Entertaining Subjects by : Jennifer Beineke
Download or read book The Mathematics of Various Entertaining Subjects written by Jennifer Beineke and published by Princeton University Press. This book was released on 2017-09-05 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic’s background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.
Book Synopsis Structure and Randomness by : Terence Tao
Download or read book Structure and Randomness written by Terence Tao and published by American Mathematical Soc.. This book was released on with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.
Book Synopsis Hypernumbers and Extrafunctions by : Mark Burgin
Download or read book Hypernumbers and Extrafunctions written by Mark Burgin and published by Springer Science & Business Media. This book was released on 2012-05-16 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.
Book Synopsis An Interpretive Introduction to Quantum Field Theory by : Paul Teller
Download or read book An Interpretive Introduction to Quantum Field Theory written by Paul Teller and published by Princeton University Press. This book was released on 2020-07-21 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of physics as well as students of philosophy. Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged.
Book Synopsis The Symmetries of Things by : John H. Conway
Download or read book The Symmetries of Things written by John H. Conway and published by CRC Press. This book was released on 2016-04-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.
