. . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann--father of the modern computer and one of the sharpest minds of the century--to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery.Called the prisoner's dilemma, it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the preventive war movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy--alternately accused of justifying arms races and touted as the only hope of preventing them.A masterful work of science writing, Prisoner's Dilemma weaves together a biography of the brilliant and tragic von Neumann, a history of pivotal phases of the cold war, and an investigation of game theory's far-reaching influence on public policy today. Most important, Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    Their work has uncovered a number of the universe’s more surprising secrets, and many believe further wonders remain hidden within the theory’s tangle of equations, waiting to be exposed. In this sweeping narrative of science and culture, astrophysicist Pedro Ferreira brings general relativity to life through the story of the brilliant physicists, mathematicians, and astronomers who have taken up its challenge. For these scientists, the theory has been both a treasure trove and an enigma, fueling a century of intellectual struggle and triumph.. Einstein’s theory, which explains the relationships among gravity, space, and time, is possibly the most perfect intellectual achievement of modern physics, yet studying it has always been a controversial endeavor. Relativists were the target of persecution in Hitler’s Germany, hounded in Stalin’s Russia, and disdained in 1950s America. Even today, PhD students are warned that specializing in general relativity will make them unemployable. Despite these pitfalls, general relativity has flourished, delivering key insights into our understanding of the origin of time and the evolution of all the stars and galaxies in the cosmos. Its adherents have revealed what lies at the farthest reaches of the universe, shed light on the smallest scales of existence, and explained how the fabric of reality emerges. Dark matter, dark energy, black holes, and string theory are all progeny of Einstein’s theory. We are in the midst of a momentous transformation in modern physics. As scientists look farther and more clearly into space than ever before, The Perfect Theory reveals the greater relevance of general relativity, showing us where it started, where it has led, and where it can still take us.

    She conjures up early operating theaters--no place for the squeamish--and surgeons, working before anesthesia, who were lauded for their speed and brute strength. These medical pioneers knew that the aftermath of surgery was often more dangerous than their patients' afflictions, and they were baffled by the persistent infections that kept mortality rates stubbornly high. At a time when surgery couldn't have been more hazardous, an unlikely figure stepped forward: a young, melancholy Quaker surgeon named Joseph Lister, who would solve the deadly riddle and change the course of history.Fitzharris dramatically recounts Lister's discoveries in gripping detail, culminating in his audacious claim that germs were the source of all infection--and could be countered by antiseptics. Focusing on the tumultuous period from 1850 to 1875, she introduces us to Lister and his contemporaries--some of them brilliant, some outright criminal--and takes us through the grimy medical schools and dreary hospitals where they learned their art, the deadhouses where they studied anatomy, and the graveyards they occasionally ransacked for cadavers.Eerie and illuminating, The Butchering Art celebrates the triumph of a visionary surgeon whose quest to unite science and medicine delivered us into the modern world.

    In a "witty, erudite, and entertaining" (Esquire) style, Simon Garfield explains how the experimental mishap that produced an odd shade of purple revolutionized fashion, as well as industrial applications of chemistry research. Occasionally honored in certain colleges and chemistry clubs, Perkin until now has been a forgotten man.

    Can our world support that? What kind of world will it be? Those answering these questions generally fall into two deeply divided groups--Wizards and Prophets, as Charles Mann calls them in this balanced, authoritative, nonpolemical new book. The Prophets, he explains, follow William Vogt, a founding environmentalist who believed that in using more than our planet has to give, our prosperity will lead us to ruin. Cut back! was his mantra. Otherwise everyone will lose! The Wizards are the heirs of Norman Borlaug, whose research, in effect, wrangled the world in service to our species to produce modern high-yield crops that then saved millions from starvation. Innovate! was Borlaug's cry. Only in that way can everyone win! Mann delves into these diverging viewpoints to assess the four great challenges humanity faces--food, water, energy, climate change--grounding each in historical context and weighing the options for the future. With our civilization on the line, the author's insightful analysis is an essential addition to the urgent conversation about how our children will fare on an increasingly crowded Earth.

    Yet, despite the astonishing discoveries of science, we still have only the vaguest idea of how the brain works. In The Idea of the Brain, scientist and historian Matthew Cobb traces how our conception of the brain has evolved over the centuries. Although it might seem to be a story of ever-increasing knowledge of biology, Cobb shows how our ideas about the brain have been shaped by each era's most significant technologies. Today we might think the brain is like a supercomputer. In the past, it has been compared to a telegraph, a telephone exchange, or some kind of hydraulic system. What will we think the brain is like tomorrow, when new technology arises? The result is an essential read for anyone interested in the complex processes that drive science and the forces that have shaped our marvelous brains.

    Mass starvation, long predicted for the fast-growing population, was about to become a reality. A call went out to the world’s scientists to find a solution. This is the story of the two enormously gifted, fatally flawed men who found it: the brilliant, self-important Fritz Haber and the reclusive, alcoholic Carl Bosch. Together they discovered a way to make bread out of air, built city-sized factories, controlled world markets, and saved millions of lives. Their invention continues to feed us today; without it, more than two billion people would starve.But their epochal triumph came at a price we are still paying. The Haber-Bosch process was also used to make the gunpowder and high explosives that killed millions during the two world wars. Both men were vilified during their lives; both, disillusioned and disgraced, died tragically. Today we face the other un­intended consequences of their discovery—massive nitrogen pollution and a growing pandemic of obesity.The Alchemy of Air is the extraordinary, previously untold story of two master scientists who saved the world only to lose everything and of the unforseen results of a discovery that continues to shape our lives in the most fundamental and dramatic of ways.

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    Why do living things and physical phenomena take the forms they do? Analyzing the mathematical and physical aspects of biological processes, this historic work, first published in 1917, has become renowned as well for the poetry of is descriptions.

    A prize of one million dollars was offered to anyone who could unravel it, but Perelman declined the winnings, and in doing so inspired journalist Masha Gessen to tell his story. Drawing on interviews with Perelman’s teachers, classmates, coaches, teammates, and colleagues in Russia and the United States—and informed by her own background as a math whiz raised in Russia—Gessen uncovered a mind of unrivaled computational power, one that enabled Perelman to pursue mathematical concepts to their logical (sometimes distant) end. But she also discovered that this very strength turned out to be Perelman's undoing and the reason for his withdrawal, first from the world of mathematics and then, increasingly, from the world in general.

    But in the same way that the science of space travel transforms our everyday lives, so research into telepathy, fortune-telling and out-of-body experiences produces remarkable insights into our brains, behaviour and beliefs. Paranormality embarks on a wild ghost chase into this new science of the supernatural and is packed with activities that allow you to experience the impossible. So throw away your crystals, ditch your lucky charms and cancel your subscription to Reincarnation Weekly. It is time to discover the real secrets of the paranormal. Learn how to control your dreams -- and leave your body behind Convince complete strangers that you know all about them Unleash the power of your unconscious mind.

    It is the history of who you are and how you came to be. It is unique to you, as it is to each of the 100 billion modern humans who have ever drawn breath. But it is also our collective story, because in every one of our genomes we each carry the history of our species births, deaths, disease, war, famine, migration, and a lot of sex. Since scientists first read the human genome in 2001, it has been subject to all sorts of claims, counterclaims, and myths. In fact, as Adam Rutherford explains, our genomes should be read not as instruction manuals, but as epic poems. DNA determines far less than we have been led to believe about us as individuals, but vastly more about us as a species. In this captivating journey through the expanding landscape of genetics, Adam Rutherford reveals what our genes now tell us about history, and what history tells us about our genes. From Neanderthals to murder, from redheads to race, dead kings to plague, evolution to epigenetics, this is a demystifying and illuminating new portrait of who we are and how we came to be."

    Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity—his eccentricities, his brilliance, his fatal candor—and elegantly explains his work and its implications.