“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    The analytic material is accompanied by many applications, examples, and exercises. The theory of noncooperative games studies the behavior of agents in any situation where each agent's optimal choice may depend on a forecast of the opponents' choices. "Noncooperative" refers to choices that are based on the participant's perceived selfinterest. Although game theory has been applied to many fields, Fudenberg and Tirole focus on the kinds of game theory that have been most useful in the study of economic problems. They also include some applications to political science. The fourteen chapters are grouped in parts that cover static games of complete information, dynamic games of complete information, static games of incomplete information, dynamic games of incomplete information, and advanced topics.--mitpress.mit.edu

    Following on the success of Quadrivium and Sciencia, Trivium gathers six Wooden Books titles together into a beautiful six-color package that presents ancient wisdom in an accessible way. Trivium includes the books Euphonics, Grammar, Logic, Rhetoric,, Poetic Meter and Form, and Ethics.

    Explaining how such basic concepts as number and magnitude, space and force were developed, the great French mathematician refutes the skeptical position that modern scientific method and its results are wholly factitious. The places of rigorous logic and intuitive leaps are both established by an analysis of contrasting methods of idea-creation in individuals and in modern scientific traditions. The nature of hypothesis and the role of probability are investigated with all of Poincaré's usual fertility of insight.Partial contents: On the nature of mathematical reasoning. Magnitude and experiment. Space: non-Euclidean geometrics, space and geometry, experiment and geometry. Force: classical mechanics, relative and absolute motion, energy and thermodynamics. Nature: hypotheses in physics, the theories of modern physics, the calculus of probabilities, optics and electricity, electro-dynamics."Poincaré's was the last man to take practically all mathematics, both pure and applied as his province. Few mathematicians have had the breadth of philosophic vision that Poincaré's had, and none is his superior in the gift of clear exposition." — Men of Mathematics, Eric Temple Bell, Professor of Mathematics, University of Cambridge

    In De Cive (1642) and Leviathan (1651), the great political philosopher had developed an analytical framework for discussing sedition, rebellion, and the breakdown of authority. Behemoth, completed around 1668 and not published until after Hobbes's death, represents the systematic application of this framework to the English Civil War. In his insightful and substantial Introduction, Stephen Holmes examines the major themes and implications of Behemoth in Hobbes's system of thought. Holmes notes that a fresh consideration of Behemoth dispels persistent misreadings of Hobbes, including the idea that man is motivated solely by a desire for self-preservation. Behemoth, which is cast as a series of dialogues between a teacher and his pupil, locates the principal cause of the Civil War less in economic interests than in the stubborn irrationality of key actors. It also shows more vividly than any of Hobbes's other works the importance of religion in his theories of human nature and behavior. "The placing of Hobbes's political thought in its historical context--and specifically, viewing it as a direct response to and interpretation of the English Civil War--necessarily has the consequence of increasing the value of Behemoth, Hobbes's own analysis of that event. Students (and scholars) who wish to know not only how the Civil War shaped Hobbes's political thinking but also why it retained its central place in his thought nearly twenty years after he wrote Leviathan will have to turn to Behemoth for the answers." -- Richard Ashcraft

    This handsome new edition of Stanley Cavell's landmark text, first published 20 years ago, provides a new preface that discusses the reception and influence of his work, which occupies a unique niche between philosophy and literary studies.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    Johnson. It was the first book exclusively on the theory of NP-completeness and computational intractability. The book features an appendix providing a thorough compendium of NP-complete problems (which was updated in later printings of the book). The book is now outdated in some respects as it does not cover more recent development such as the PCP theorem. It is nevertheless still in print and is regarded as a classic: in a 2006 study, the CiteSeer search engine listed the book as the most cited reference in computer science literature.

    Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.

    Scientists have marveled at the beauty and elegance of his analysis, while ordinary programmers have successfully applied his "cookbook" solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books. "I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up.""--"Charles Long Primarily written as a reference, some people have nevertheless found it possible and interesting to read each volume from beginning to end. A programmer in China even compared the experience to reading a poem. "If you think you're a really good programmer... read Knuth's] "Art of Computer Programming.".. You should definitely send me a resume if you can read the whole thing.""--"Bill Gates Whatever your background, if you need to do any serious computer programming, you will find your own good reason to make each volume in this series a readily accessible part of your scholarly or professional library. "It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers.""--"Jonathan LaventholIn describing the new fourth volume, one reviewer listed the qualities that distinguish all of Knuth's work. In sum: ] "detailed coverage of the basics, illustrated with well-chosen examples; occasional forays into more esoteric topics and problems at the frontiers of research; impeccable writing peppered with occasional bits of humor; extensive collections of exercises, all with solutions or helpful hints; a careful attention to history; implementations of many of the algorithms in his classic step-by-step form."--Frank RuskeyThese four books comprise what easily could be the most important set of information on any serious programmer's bookshelf.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    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.

    Short-Cut Math is a concise, remarkably clear compendium of about 150 math short-cuts — timesaving tricks that provide faster, easier ways to add, subtract, multiply, and divide.By using the simple foolproof methods in this volume, you can double or triple your calculation speed — even if you always hated math in school. Here's a sampling of the amazingly effective techniques you will learn in minutes: Adding by 10 Groups; No-Carry Addition; Subtraction Without Borrowing; Multiplying by Aliquot Parts; Test for Divisibility by Odd and Even Numbers; Simplifying Dividends and Divisors; Fastest Way to Add or Subtract Any Pair of Fractions; Multiplying and Dividing with Mixed Numbers, and more.The short-cuts in this book require no special math ability. If you can do ordinary arithmetic, you will have no trouble with these methods. There are no complicated formulas or unfamiliar jargon — no long drills or exercises. For each problem, the author provides an explanation of the method and a step-by-step solution. Then the short-cut is applied, with a proof and an explanation of why it works.Students, teachers, businesspeople, accountants, bank tellers, check-out clerks — anyone who uses numbers and wishes to increase his or her speed and arithmetical agility, can benefit from the clear, easy-to-follow techniques given here.

    Course Lecture Titles (36 lectures, 30 minutes/lecture)1. Why We Study History 2. World War I and the Lessons of History 3. Hitler's Rise and the Lessons of History 4. World War II and the Lessons of History 5. Is Freedom a Universal Value? 6. Birth of Civilization in the Middle East 7. The Trojan War and the Middle East 8. Ancient Israel and the Middle East 9. Ancient Greece and the Middle East 10. Athenian Democracy and Empire 11. The Destiny of the Athenian Democracy 12. Alexander the Great and the Middle East 13. The Roman Republic as Superpower 14. Rome of the Caesars as Superpower 15. Rome and the Middle East 16. Why the Roman Empire Fell 17. Christianity 18. Islam 19. The Ottoman Empire and Turkey 20. The Spanish Empire and Latin America 21. Napoleon's Liberal Empire 22. The British Empire in India 23. Russia and Empire 24. China and Empire 25. The Empire of Genghis Khan 26. Britain's Legacy of Freedom 27. George Washington as Statesman 28. Thomas Jefferson as Statesman 29. America's Empire of LibertyLewis and Clark 30. America and Slavery 31. Abraham Lincoln as Statesman 32. The United States and Empire 33. Franklin Roosevelt as Statesman 34. A Superpower at the Crossroads 35. The Wisdom of History and the Citizen 36. The Wisdom of History and You Wisdom of History (36 lectures, 30 minutes/lecture)Course No. 4360 Taught by J. Rufus FearsUniversity of OklahomaPh.D., Harvard University

    It is also the focal point of current attempts to understand 18th-century philosophy. The Treatise first explains how we form such concepts as cause and effect, external existence, and personal identity, and to form compelling but unconfirmable beliefs in the entities represented by these concepts. It then offers a novel account of the passions, explains freedom and necessity as they apply to human choices and actions, and concludes with detailed explanations of how we distinguish between virtue and vice and of the different kinds of virtue. Hume's Abstract of the Treatise, also included in the volume, outlines his 'chief argument' regarding our conception of, and belief in, cause and effect. The texts printed in this volume are those of the critical edition of Hume's philosophical works now being published by the Clarendon Press. The volume includes a substantial introduction explaining the aims of the Treatise as a whole and of each of its ten parts, extensive annotations, a glossary of terms, a comprehensive index, and suggestions for further reading.