He revolutionized the field of topology, which studies properties of geometric configurations that are unchanged by stretching or twisting. The Poincare conjecture lies at the heart of modern geometry and topology, and even pertains to the possible shape of the universe. The conjecture states that there is only one shape possible for a finite universe in which every loop can be contracted to a single point.Poincare's conjecture is one of the seven "millennium problems" that bring a one-million-dollar award for a solution. Grigory Perelman, a Russian mathematician, has offered a proof that is likely to win the Fields Medal, the mathematical equivalent of a Nobel prize, in August 2006. He also will almost certainly share a Clay Institute millennium award.In telling the vibrant story of The Poincare Conjecture, Donal O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians whose work have led to Perelman's proof of this famous conjecture.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.

    Prize-winning novelist Cai Emmons praises Sterry by saying she really knows how to tell a story. Sterry grew up in a succession of isolated one-room schools in northern and central Montana, where her mother, a teacher, eked out a living. A must read for anyone who loves Montana and its rich history.

    Above all it fizzes with a dizzying mix of deliciously vital ideas. . . A staggering achievement' Tim HarfordThe smartphones in our pockets and computers like brains. The vagaries of game theory and evolutionary biology. Self-replicating moon bases and nuclear weapons. All bear the fingerprints of one remarkable man: John von Neumann.Born in Budapest at the turn of the century, von Neumann is one of the most influential scientists to have ever lived. His colleagues believed he had the fastest brain on the planet - bar none. He was instrumental in the Manhattan Project and helped formulate the bedrock of Cold War geopolitics and modern economic theory. He created the first ever programmable digital computer. He prophesied the potential of nanotechnology and, from his deathbed, expounded on the limits of brains and computers - and how they might be overcome.Taking us on an astonishing journey, Ananyo Bhattacharya explores how a combination of genius and unique historical circumstance allowed a single man to sweep through so many different fields of science, sparking revolutions wherever he went.Insightful and illuminating, The Man from the Future is a thrilling intellectual biography of the visionary thinker who shaped our century.

    Kennedy’s assassination has been the subject of public and cultural fascination (a film by Oliver Stone, a novel by Stephen King, endless conspiracy theories) for nearly 50 years. It’s time, this brief biography argues, to give equal consideration to Kennedy’s life.

    He continues to be a household name today and his velvety voice can be heard on Radio 2's The Bob Harris Show and Bob Harris Country. In this fully revised and updated autobiography, with a forward by Robert Plant, Bob tells his story of over 40 years of broadcasting with the BBC, from the young, passionate music fan who moved to London determined to make music his life, to being presented with an OBE for his services to music broadcasting. Much like his musical heroes, Bob's personal life has had somewhat of a rock 'n' roll vibe: he has been married three times, gone bankrupt, fought cancer, weathered a very public spat with a fellow DJ and has had to revamp his career four times. Throughout all these times, however, his love of music and talent for broadcasting has endured. The Whispering Years is a frank, vibrant and inspiring tale of one of the most influential names on the radio and reveals the story of the man behind the voice.

    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.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    Robert Oppenheimer, Freeman Dyson has composed an autobiography unlike any other. Dyson evocatively conveys the thrill of a deep engagement with the world-be it as scientist, citizen, student, or parent. Detailing a unique career not limited to his groundbreaking work in physics, Dyson discusses his interest in minimizing loss of life in war, in disarmament, and even in thought experiments on the expansion of our frontiers into the galaxies.

    A week passed. President Amin then summoned the minister and asked, 'Did you carry out my orders?' He replied saying that there was a problem. 'What problem?' the president inquired. 'Your Excellency, there is a country called Cyprus.The people are called Cypriots. If Uganda were to be called Idi, we would be called Idiots.' There are few leaders that K. Natwar Singh, in a diplomatic career spanning more than three decades, has not known -and fewer still about whom he has no story to tell. In Walking with Lions: Tales from a Diplomatic Past, Singh puts together fifty episodes that entertain, inform and illuminate.Featured here is Indira Gandhi as a statesman and friend, alongside other renowned figures such as Fidel Castro, Haile Selassie and Zia-ul-Haq. Singh analyses some personalities with disarming candour, among them Morarji Desai and Lord Mountbatten; at other times, his admiration for leaders like C. Rajagopalalchari and Nelson Mandela shines through. In these pages you will also find a rare, fascinating glimpse of Godman Chandraswami and his cohort Mamaji, and their interaction with a surprisingly submissive Iron Lady Margaret Thatcher. Besides, there are short tributes to artists, writers, cricketers and film stars, like M.F. Husain, Nadine Gordimer, Don Bradman and Dev Anand. Recounted with empathy and humour, this collection of stories from contemporary history is a warm, unaffected and reassuring reminder that the great too can be as fallible as the rest of us.

    Men like Andrew Carnegie built empires like Carnegie Steel, and financiers like J.P. Morgan merged and consolidated them. The era also made names like Astor, Cooke, and Vanderbilt instantly recognizable across the globe. Over time, the unfathomable wealth generated by the businesses made the individuals on top incredibly rich, and that in turn led to immense criticism and an infamous epithet used to rail against them: robber barons. Dozens of men were called “robber barons”, but few of them were as notorious as Cornelius Vanderbilt, who also happened to be one of the nation’s first business titans. Vanderbilt was a railroad and shipping magnate at a time that the industry was almost brand new, but he rode his success to become one of the richest and most powerful men in American history. When historians are asked to name the richest man in history, a name that often pops up is that of John D. Rockefeller, who co-founded Standard Oil and turned it into the first real trust in the United States. Rockefeller had been groomed ambitiously by a huckster father nicknamed “Devil Bill”, who was just as willing to cheat his son as an unsuspecting public, and John certainly chased his dreams of living long and large. Rockefeller forged his empire in the first few decades of his life and nearly worked himself to death by the time he was 50, which helped compel him to retire for the last several decades of his life. At one point, Rockefeller’s wealth was worth more than 1.5% of the entire country’s gross domestic product, and by adjusting for inflation, he is arguably the richest man in American history if not world history. When robber barons across America took the reins of vast industries, they needed financing, and many of them turned to the most famous banker of all: John Pierpont Morgan. It was J.P. Morgan who bankrolled the consolidation of behemoth corporations across various industries, including the merging of Edison General Electric and Thomson-Houston Electric Company, which subsequently became General Electric, still known simply as GE across the world today. Similarly, he financed Federal Steel Company and consolidated various other steel businesses to help form the United States Steel Corporation. While critics complained about the outsized influence that these gigantic businesses had, Morgan’s massive wealth also gave him unprecedented power in the financial sector and the ability to deal with politicians. In fact, Morgan played an important part in the Panic of 1907 and the subsequent decision to create the Federal Reserve as a monetary oversight. Ironically, one of America’s most famous robber barons, Andrew Carnegie, epitomized the American Dream, migrating with his poor family to America in the mid-19th century and rising to the top of the business world in his adopted country. A prodigious writer in addition to his keen sense of business, Carnegie was one of the most outspoken champions of capitalism at a time when there was pushback among lower social classes who witnessed the great disparities in wealth; as he once put it, “Upon the sacredness of property civilization itself depends—the right of the laborer to his hundred dollars in the savings bank, and equally the legal right of the millionaire to his millions.