He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather.Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship.The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.'A wonderful book . . . Moving, sometimes comic, sometimes infinitely sad, and goes to the roots of what we mean by truth in science.' Lord Waldegrave, Daily Telegraph

    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    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.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.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 hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month.     But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough.     Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective.     An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.

    and now, The Fourth Dimension is this handy paperback. The result is a fantastic, enlightening, and mind-expanding reading experience. In text, pictures, and puzzles, master science and science fiction writer Rudy Rucker immerses his readers in an amazing exploration of a mysterious realm — a realm once seen only by mystics, physicists, and mathematicians. More accessible than Gödel, Escher, Bach and more playful than The Tao of Physics, Rucker's The Fourth Dimension is the most engaging tour of other dimensions since Flatland.David Povilaitis' 200 drawings illustrate Rucker's heady insights while dozens of puzzles and problems make the book a delight to the eye and mind. As Eileen Pollack has written in her rave review, The Fourth Dimension is "magical ... Its effects persist beyond its covers." That's because, like everything else in the fourth dimension, this is more than a book, it is a mental spaceship capable of grand tours of universes far beyond our own.

    From man's first act of counting to higher mathematics, from the smallest living creature to the dazzling reaches of outer space, Asimov is a master at "explaining complex material better than any other living person." (The New York Times) You'll learn: HOW to make a trillion seem small; WHY imaginary numbers are real; THE real size of the universe - in photons; WHY the zero isn't "good for nothing;" AND many other marvelous discoveries, in ASIMOV ON NUMBERS.

    Each chapter, or unit, is divided into easily comprehended small "bites" that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

    It offers a fine balance between abstraction/theory and computational skills, and gives readers an excellent opportunity to learn how to handle abstract concepts. Included in this comprehensive and easy-to-follow manual are these topics: linear equations and matrices; solving linear systems; real vector spaces; inner product spaces; linear transformations and matrices; determinants; eigenvalues and eigenvectors; differential equations; and MATLAB for linear algebra. Because this book gives real applications for linear algebraic basic ideas and computational techniques, it is useful as a reference work for mathematicians and those in field of computer science.

    The stories show that, as James Gleick puts it in the foreword, "inspiration strikes willy-nilly." One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a "bathroom sink epiphany" and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge."Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the "conspiracy" of the title); consider whether math is the universal language of nature (allowing for "a unified theory of randomness"); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question "Is mathematics good for you?"ContributorsAriel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie WolchoverCopublished with Quanta Magazine

    Amazingly, the story unveiled in it is true.In the world of math, the Poincaré Conjecture was a holy grail. Decade after decade the theorem that informs how we understand the shape of the universe defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of our time, earning the right to claim the first one-million-dollar Millennium math prize.George Szpiro begins his masterfully told story in 1904 when Frenchman Henri Poincaré formulated a conjecture about a seemingly simple problem. Imagine an ant crawling around on a large surface. How would it know whether the surface is a flat plane, a round sphere, or a bagel- shaped object? The ant would need to lift off into space to observe the object. How could you prove the shape was spherical without actually seeing it? Simply, this is what Poincaré sought to solve.In fact, Poincaré thought he had solved it back at the turn of the twentieth century, but soon realized his mistake. After four more years' work, he gave up. Across the generations from China to Texas, great minds stalked the solution in the wilds of higher dimensions. Among them was Grigory Perelman, a mysterious Russian who seems to have stepped out of a Dostoyevsky novel. Living in near poverty with his mother, he has refused all prizes and academic appointments, and rarely talks to anyone, including fellow mathematicians. It seemed he had lost the race in 2002, when the conjecture was widely but, again, falsely reported as solved. A year later, Perelman dropped three papers onto the Internet that not only proved the Poincaré Conjecture but enlightened the universe of higher dimensions, solving an array of even more mind-bending math with implications that will take an age to unravel. After years of review, his proof has just won him a Fields Medal--the 'Nobel of math'--awarded only once every four years. With no interest in fame, he refused to attend the ceremony, did not accept the medal, and stayed home to watch television.Perelman is a St. Petersburg hero, devoted to an ascetic life of the mind. The story of the enigma in the shape of space that he cracked is part history, part math, and a fascinating tale of the most abstract kind of creativity.

    It is the complex dynamics of flow that structures our atmosphere, land, and oceans.Part of a trilogy of books exploring the science of patterns in nature by acclaimed science writer Philip Ball, this volume explores the elusive rules that govern flow - the science of chaotic behavior.

    Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics -- the universal language of science -- keep the masterpieces of the subject hidden behind a veil?"The Universe in Zero Words" tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society -- from the elementary (1+1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc^2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called a "popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.(From the jacket copy.)Note: The Princeton University Press version (black cover) is for sale in the English-speaking world outside Australia. The Newsouth Press version (blue cover) is for sale in Australia. The two versions are identical except for the covers.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    He evokes the profound intellectual impact the infinite has exercised on the human mind--from the horror infiniti of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates.--Los Angeles Times [Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama.--Choice Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics.--Science