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A Beautiful Math John Nash, Game Theory, and the Modern Quest for a Code of Nature Tom Siegfried

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A Beautiful Math John Nash, Game Theory, and the Modern Quest for a Code of Nature Tom Siegfried National Academies Press (September 21, 2006) Summary: Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. 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. Language: English ISBN: 9780309101929 Category: History of Mathematics A Beautiful Mind A Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics, 1994 Sylvia Nasar Simon & Schuster (1998) Summary: In this dramatic and moving biography, Sylvia Nasar re-creates the life of a mathematical genius whose brilliant career was cut short by schizophrenia and who, after three decades of devastating mental illness, miraculously recovered and was honored with a Nobel Prize. "A Beautiful Mind" traces the meteoric rise of John Forbes Nash, Jr., from his lonely childhood in West Virginia to his student years at Princeton, where he encountered Albert Einstein, John von Neumann, and a host of other mathematical luminaries. At twenty-one, the handsome, ambitious, eccentric graduate student invented what would become the most influential theory of rational human behavior in modern social science. Nash's contribution to game theory would ultimately revolutionize the field of economics.As a young professor at MIT, still in his twenties, Nash dazzled the mathematical world by solving a series of deep problems deemed "impossible" by other mathematicians. As unconventional in his private life as in his mathematics, Nash fathered a child with a woman he did not marry. At the height of the McCarthy era, he was expelled as a security risk from the supersecret RAND Corporation -- the Cold War think tank where he was a consultant. At thirty, Nash was poised to take his dreamed-of place in the pantheon of history's greatest mathematicians. His associates included the most renowned mathematicians and economists of the era: Norbert Wiener, John Milnor, Alexandre Grothendieck, Kenneth Arrow, Robert Solow, and Paul Samuelson. He married an exotic and beautiful MIT physics student, Alicia Larde. They had a son. Then Nash suffered a catastrophic mental breakdown.Nasar details Nash's harrowing descent into insanity -- his bizarre delusions that he was the Prince of Peace; his resignation from MIT, flight to Europe, and attempt to renounce his American citizenship; his repeated hospitalizations, from the storied McLean, where he came to know the poet Robert Lowell, to the crowded wards of a state hospital; his "enforced interludes of rationality" during which he was able to return briefly to mathematical research. Nash and his wife were divorced in 1963, but Alicia Nash continued to care for him and for their mathematically gifted son, who was diagnosed with schizophrenia as a teenager. Saved from homelessness by his loyal ex-wife and protected by a handful of mathematical friends, Nash lived quietly in Princeton for many years, a dreamy, ghostlike figure who scrawled numerological messages on blackboards, all but forgotten by the outside world.His early achievements, however, fired the imagination of a new generation of scholars. At age sixty-six, twin miracles -- a spontaneous remission of his illness and the sudden decision of the Nobel Prize committee to honor his contributions to game theory -- restored the world to him. Nasar recounts the bitter behind-the-scenes battle in Stockholm over whether to grant the ultimate honor in science to a man thought to be "mad". She describes Nash's current ambition to pursue new mathematical breakthroughs and his efforts to be a loving father to his adult sons.Based on hundreds of interviews with Nash's family, friends, and colleagues and scores of letters and documents, "A Beautiful Mind" is a heartbreaking but inspiring story about the most remarkable mathematician of our time and his triumph over a tragic illness. Language: English ISBN: 9780684819068 Category: History of Mathematics A Course in Combinatorics J. H. van Lint, R. M. Wilson Cambridge University Press (November 22, 2001) Summary: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference. Language: English ISBN: 9780521006019 Category: Mathematics A Course in Game Theory Martin J. Osborne, Ariel Rubinstein MIT Press (July 12, 1994) Summary: A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises. Language: English ISBN: 9780262650403 Category: Mathematics A First Course in Differential Equations with Modeling Applications Dennis G. Zill Cengage Learning (March 15, 2012) Summary: A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 10th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven and accessible text speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects. Written in a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. Language: English ISBN: 9781285401102 Category: Mathematics A History of Mathematics Carl B. Boyer Wiley (March 20, 1991) Summary: "Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions to the subject." --J. W. Dauben The City University of New York "Both readable and scholarly, this book can serve as a fine introduction to the topic and also a reference book." --J. David Bolter University of North Carolina Author of Turing's Man Revised to make it more accessible to a general audience, A History of Mathematics paints a vivid picture of humankind's relationship with numbers. Updated and expanded, it now offers broadened coverage of twentieth century advances in probability and computers, and updated references to further reading. A feature that will be of interest to every reader is an appendix containing an extensive chronological table of mathematical and general historical developments. Language: English ISBN: 9780471543978 Category: History of Mathematics Abstract Algebra David S. Dummit, Richard M. Foote John Wiley & Sons (2004) Summary: Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics.
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