Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    This popular student textbook has been revised and updated in order to provide clear explanations of the subject matter, permitting more classroom time to be spent in problem solving, applications or explanations of the most difficult points.

    Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

      In this classic study, Caillois defines play as a free and voluntary activity that occurs in a pure space, isolated and protected from the rest of life. Play is uncertain, since the outcome may not be foreseen, and it is governed by rules that provide a level playing field for all participants. In its most basic form, play consists of finding a response to the opponent's action--or to the play situation--that is free within the limits set by the rules.   Caillois qualifies types of games-- according to whether competition, chance, simulation, or vertigo (being physically out of control) is dominant--and ways of playing, ranging from the unrestricted improvisation characteristic of children's play to the disciplined pursuit of solutions to gratuitously difficult puzzles. Caillois also examines the means by which games become part of daily life and ultimately contribute to various cultures their most characteristic customs and institutions.            Presented here in Meyer Barash's superb English translation, Man, Play and Games is a companion volume to Caillois's Man and the Sacred.

    Like civilization, play requires structure and participants willing to create within limits. Starting with Plato, Huizinga traces the contribution of Homo Ludens, or "Man the player" through Medieval Times, the Renaissance, and into our modern civilization. Huizinga defines play against a rich theoretical background, using cross-cultural examples from the humanities, business, and politics. Homo Ludens defines play for generations to come."A happier age than ours once made bold to call our species by the name of Homo Sapiens. In the course of time we have come to realize that we are not so reasonable after all as the Eighteenth Century with its worship of reason and naive optimism, though us; "hence moder fashion inclines to designate our species asHomo Faber Man the Maker. But though faber may not be quite so dubious as sapiens it is, as a name specific of the human being, even less appropriate, seeing that many animals too are makers. There is a third function, howver, applicable to both human and animal life, and just as important as reasoning and making--namely, playing. it seems to me that next to Homo Faber, and perhaps on the same level as Homo Sapiens, Homo Ludens, Man the Player, deserves a place in our nomenclature. "--from the Foreward, by Johan Huizinga

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

    Omaha has long been the most popular form of poker in Europe, and now it's spreading like wildfire throughout North America. The reason is simple: Omaha offers more action and bigger pots than Texas Hold'em. Isn't it time you got in on it? Whether you're a cash-game professional or poker hobbyist--and whether you play live or online--this book will arm you with a winning big-play strategy that's easy to master even if you've never played Omaha before. You'll discover the subtle distinctions that set Omaha above other games. Key topics include: The Big Play Objectives The Power of the Big DrawStraight Draws and Starting Hand ConstructionPlaying the Position GameLimit Omaha Hi/Lo and Pot-Limit Omaha Hi/LoComplete with practice situations and hand quizzes, this is the most comprehensive Omaha book available--and the only one you'll ever need. Jeff Hwang is a semi-professional poker player and an investment analyst who regularly writes about the gaming industry for the Motley Fool, a well known website about stocks and investing. A graduate of Washington University in St. Louis with a B.S./B.A. in both finance and management, Jeff has been an advantage player since 1999, when he took an interest in blackjack. After he graduated college, Jeff picked up poker, and he has been playing semi-professionally ever since. His regular lineup includes Pot-Limit Omaha and Omaha Hi/Lo, with the occasional No-Limit Hold'em game. The material in this book is the result of playing various Omaha games nearly exclusively for over eighteen months, both live and online. Jeff lives in St. Louis eight months of the year and spends time in Fort Lauderdale, Washington, D.C., and on the road the rest."

    The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems. With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.

    In Rules of Play Katie Salen and Eric Zimmerman present a much-needed primer for this emerging field. They offer a unified model for looking at all kinds of games, from board games and sports to computer and video games. As active participants in game culture, the authors have written Rules of Play as a catalyst for innovation, filled with new concepts, strategies, and methodologies for creating and understanding games. Building an aesthetics of interactive systems, Salen and Zimmerman define core concepts like play, design, and interactivity. They look at games through a series of eighteen game design schemas, or conceptual frameworks, including games as systems of emergence and information, as contexts for social play, as a storytelling medium, and as sites of cultural resistance.Written for game scholars, game developers, and interactive designers, Rules of Play is a textbook, reference book, and theoretical guide. It is the first comprehensive attempt to establish a solid theoretical framework for the emerging discipline of game design.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.