In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    The books published on the subject are so technical that only a person trained in pure physics and higher mathematics is able to fully understand them. In order to make a popular explanation of this far-reaching theory available, the present book is published.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Lemos, Teaching Philosophy'The single most comprehensive, reliable and economical collection ofRousseaus explicitly political writings.'--Michael Franz, Loyola College

    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

    Breathtaking in its range and erudition, it explores Shiite festivals and the English Civil war, the finger exercises of monkeys and the effects of inflation in Weimar Germany. In this study of the interplay of crowds, Canetti offers one of the most profound and startling portraits of the human condition.

    Written by a 12th- century thinker who was equally active as an original philosopher and as a Biblical and Talmudic scholar, it is both a classic of great historical importance and a work of living significance today.The Guide for the Perplexed was written for scholars who were bewildered by the conflict between religion and the scientific and philosophic thought of the day. It is concerned, basically, with finding a concord between the religion of the Old Testament and its commentaries, and Aristotelian philosophy. After analyzing the ideas of the Old Testament by means of "homonyms," Maimonides examines other reconciliations of religion and philosophy (the Moslem rationalists) and then proposes his own resolution with contemporary Aristotelianism. The Guide for the Perplexed was at once recognized as a masterwork, and it strongly influenced Jewish, Christian, and Moslem thought of the Middle Ages. It is necessary reading for any full comprehension of the thought of such scholastics as Aquinas and Scotus, and indispensable for everyone interested in the Middle Ages, Judaism, medieval philosophy, or the larger problems which Maimonides discusses.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    Psychology is the only branch of learning in which I am particularly versed. To the psychologist the religious propensities of man must be at least as interesting as any other of the facts pertaining to his mental constitution. It would seem, therefore, as a psychologist, the natural thing for me would be to invite you to a descriptive survey of those religious propensities." When William James went to the University of Edinburgh in 1901 to deliver a series of lectures on "natural religion," he defined religion as "the feelings, acts, and experiences of individual men in their solitude, so far as they apprehend themselves to stand in relation to whatever they may consider the divine." Considering religion, then, not as it is defined by--or takes place in--the churches, but as it is felt in everyday life, he undertook a project that, upon completion, stands not only as one of the most important texts on psychology ever written, not only as a vitally serious contemplation of spirituality, but for many critics one of the best works of nonfiction written in the 20th century. Reading The Varieties of Religious Experience, it is easy to see why. Applying his analytic clarity to religious accounts from a variety of sources, James elaborates a pluralistic framework in which "the divine can mean no single quality, it must mean a group of qualities, by being champions of which in alternation, different men may all find worthy missions." It's an intellectual call for serious religious tolerance--indeed, respect--the vitality of which has not diminished through the subsequent decades.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. This volume offers the reader access to one of the greatest discoveries in the history of physics and one of the outstanding intellectual achievements of the twentieth century.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    A simple, eloquent description of his 1856-1863 study of the inheritance of traits in pea plants--Mendel analyzed 29,000 of them--this is essential reading for biology students and readers of science history.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton