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.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    Burger teaches at Wiliams College; Starbird at The University of Texas at Austin. Here, they “reveal the hidden powers of deep understanding (earth), failure (fire), questions (air), the flow of ideas (water), and the quintessential element of change that brings all four elements together. By mastering and applying these practical and proven strategies, readers develop better thinking habits and learn how to create their own successes.”Brilliant people aren't a special breed--they just use their minds differently. By using the straightforward and thought-provoking techniques in "The 5 Elements of Effective Thinking," you will regularly find imaginative solutions to difficult challenges, and you will discover new ways of looking at your world and yourself--revealing previously hidden opportunities.The book offers real-life stories, explicit action items, and concrete methods that allow you to attain a deeper understanding of any issue, exploit the power of failure as a step toward success, develop a habit of creating probing questions, see the world of ideas as an ever-flowing stream of thought, and embrace the uplifting reality that we are all capable of change. No matter who you are, the practical mind-sets introduced in the book will empower you to realize any goal in a more creative, intelligent, and effective manner. Filled with engaging examples that unlock truths about thinking in every walk of life, "The 5 Elements of Effective Thinking" is written for all who want to reach their fullest potential--including students, parents, teachers, businesspeople, professionals, athletes, artists, leaders, and lifelong learners.Whenever you are stuck, need a new idea, or want to learn and grow, "The 5 Elements of Effective Thinking" will inspire and guide you on your way.

    Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.

    The Platonic-Pythagorean tradition looked on nature in geometric terms with the conviction that the cosmos was constructed according to the principles of mathematical order, while the mechanical philosophy conceived of nature as a huge machine and sought to explain the hidden mechanisms behind phenomena. Pursuing different goals, these two movements of thought tended to conflict with each other, and more than the obviously mathematical sciences were affected - the influence spread as far as chemistry and the life sciences. As this book demonstrates, the full fruition of the scientific revolution required a resolution of the tension between the two dominant trends.

    This gorgeous book features clear, entertaining, and enlightening commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties.  With its lush format and layflat dimensions that closely approximate the golden ratio, this is the ultimate coffee table book for math enthusiasts, architects, designers, and fans of sacred geometry.

    The work is powerful and has established a passionate following as well as harsh critics.

    That’s a mistake, Tim Harford says in The Data Detective. We shouldn’t be suspicious of statistics—we need to understand what they mean and how they can improve our lives: they are, at heart, human behavior seen through the prism of numbers and are often “the only way of grasping much of what is going on around us.” If we can toss aside our fears and learn to approach them clearly—understanding how our own preconceptions lead us astray—statistics can point to ways we can live better and work smarter.As “perhaps the best popular economics writer in the world” (New Statesman), Tim Harford is an expert at taking complicated ideas and untangling them for millions of readers. In The Data Detective, he uses new research in science and psychology to set out ten strategies for using statistics to erase our biases and replace them with new ideas that use virtues like patience, curiosity, and good sense to better understand ourselves and the world. As a result, The Data Detective is a big-idea book about statistics and human behavior that is fresh, unexpected, and insightful.

    Unlike party puzzles or brain teasers, many paradoxes are serious in that they raise serious philosophical problems, and are associated with crises of thought and revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but to come to grips with issues of real import. The second, revised edition of this intriguing book expands and updates the text to take account of new work on the subject. It provides a valuable and accessible introduction to a range of paradoxes and their possible solutions, with questions designed to engage the reader with the arguments and full bibliographical references to both classic and current literature on the topic.

     According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.

    Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    Yates traces the art of memory from its treatment by Greek orators, through its Gothic transformations in the Middle Ages, to the occult forms it took in the Renaissance, and finally to its use in the seventeenth century. This book, the first to relate the art of memory to the history of culture as a whole, was revolutionary when it first appeared and continues to mesmerize readers with its lucid and revelatory insights.

    At a summer tea party in Cambridge, England, a guest states that tea poured into milk tastes different from milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one man, Ronald Fisher, proposes to scientifically test the hypothesis. There is no better person to conduct such an experiment, for Fisher is a pioneer in the field of statistics.The Lady Tasting Tea spotlights not only Fisher's theories but also the revolutionary ideas of dozens of men and women which affect our modern everyday lives. Writing with verve and wit, David Salsburg traces breakthroughs ranging from the rise and fall of Karl Pearson's theories to the methods of quality control that rebuilt postwar Japan's economy, including a pivotal early study on the capacity of a small beer cask at the Guinness brewing factory. Brimming with intriguing tidbits and colorful characters, The Lady Tasting Tea salutes the spirit of those who dared to look at the world in a new way.

    Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton's calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians -- an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work's clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.