. . 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

    In Turing’s Cathedral, George Dyson focuses on a small group of men and women, led by John von Neumann at the Institute for Advanced Study in Princeton, New Jersey, who built one of the first computers to realize Alan Turing’s vision of a Universal Machine. Their work would break the distinction between numbers that mean things and numbers that do things—and our universe would never be the same. Using five kilobytes of memory (the amount allocated to displaying the cursor on a computer desktop of today), they achieved unprecedented success in both weather prediction and nuclear weapons design, while tackling, in their spare time, problems ranging from the evolution of viruses to the evolution of stars. Dyson’s account, both historic and prophetic, sheds important new light on how the digital universe exploded in the aftermath of World War II. The proliferation of both codes and machines was paralleled by two historic developments: the decoding of self-replicating sequences in biology and the invention of the hydrogen bomb. It’s no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time.  How did code take over the world? In retracing how Alan Turing’s one-dimensional model became John von Neumann’s two-dimensional implementation, Turing’s Cathedral offers a series of provocative suggestions as to where the digital universe, now fully three-dimensional, may be heading next.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    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.

    Darwin was only too aware of the storm his theory of evolution would provoke but he would surely have raised an incredulous eyebrow at the controversy still raging a century and a half later. Evolution is accepted as scientific fact by all reputable scientists and indeed theologians, yet millions of people continue to question its veracity.In The Greatest Show on Earth Richard Dawkins takes on creationists, including followers of ‘Intelligent Design’ and all those who question the fact of evolution through natural selection. Like a detective arriving on the scene of a crime, he sifts through fascinating layers of scientific facts and disciplines to build a cast-iron case: from the living examples of natural selection in birds and insects; the ‘time clocks’ of trees and radioactive dating that calibrate a timescale for evolution; the fossil record and the traces of our earliest ancestors; to confirmation from molecular biology and genetics. All of this, and much more, bears witness to the truth of evolution.The Greatest Show on Earth comes at a critical time: systematic opposition to the fact of evolution is now flourishing as never before, especially in America. In Britain and elsewhere in the world, teachers witness insidious attempts to undermine the status of science in their classrooms. Richard Dawkins provides unequivocal evidence that boldly and comprehensively rebuts such nonsense. At the same time he shares with us his palpable love of the natural world and the essential role that science plays in its interpretation. Written with elegance, wit and passion, it is hard-hitting, absorbing and totally convincing.

    Augustine equate nothingness with the Devil? What tortuous means did 17th-century scientists employ in their attempts to create a vacuum? And why do contemporary quantum physicists believe that the void is actually seething with subatomic activity? You’ll find the answers in this dizzyingly erudite and elegantly explained book by the English cosmologist John D. Barrow.Ranging through mathematics, theology, philosophy, literature, particle physics, and cosmology, The Book of Nothing explores the enduring hold that vacuity has exercised on the human imagination. Combining high-wire speculation with a wealth of reference that takes in Freddy Mercury and Shakespeare alongside Isaac Newton, Albert Einstein, and Stephen Hawking, the result is a fascinating excursion to the vanishing point of our knowledge.

    When temperatures drop below 56°F, tin crumbles into powder. Were the soldiers of the Grande Armée acutee fatally weakened by cold because the buttons of their uniforms fell apart? How different our world might be if tin did not disintegrate at low temperatures and the French had continued their eastward expansion! This fascinating book tells the stories of seventeen molecules that, like the tin of those buttons, greatly influenced the course of history. These molecules provided the impetus for early exploration and made possible the ensuing voyages of discovery. They resulted in grand feats of engineering and spurred advances in medicine; lie behind changes in gender roles, in law, and in the environment; and have determined what we today eat, drink, and wear. Showing how a change as small as the position of an atom can lead to enormous differences in the properties of a substance, the authors reveal the astonishing chemical connections among seemingly unrelated events. Napoleon's Buttons offers a novel way to understand how our contemporary world works and how our civilization has been shaped over time.

    From the first time mankind had an inkling of the vast space that surrounds us, those who study the universe have had to struggle against political and religious preconceptions. They have included some of the most charismatic, courageous, and idiosyncratic thinkers of all time. In Coming of Age in the Milky Way, Timothy Ferris uses his unique blend of rigorous research and captivating narrative skill to draw us into the lives and minds of these extraordinary figures, creating a landmark work of scientific history.

    Could she use quantum tunnelling to get through the neighbour's fence and chase bunnies? What about quantum teleportation to catch squirrels before they climb out of reach? In this witty and informative book, Orzel and Emmy - the talking dog - discuss the key theories of Quantum Physics and its fascinating history. From quarks and gluons to Heisenberg's uncertainty principle, this is the perfect introduction to the fundamental laws which govern the universe.

    It intersects with Darwin’s theory of evolution, and collides with the horrors of Nazi eugenics in the 1940s. The gene transforms post-war biology. It reorganizes our understanding of sexuality, temperament, choice and free will. This is a story driven by human ingenuity and obsessive minds – from Charles Darwin and Gregor Mendel to Francis Crick, James Watson and Rosalind Franklin, and the thousands of scientists still working to understand the code of codes.This is an epic, moving history of a scientific idea coming to life, by the author of The Emperor of All Maladies. But woven through The Gene, like a red line, is also an intimate history – the story of Mukherjee’s own family and its recurring pattern of mental illness, reminding us that genetics is vitally relevant to everyday lives. These concerns reverberate even more urgently today as we learn to “read” and “write” the human genome – unleashing the potential to change the fates and identities of our children.Majestic in its ambition, and unflinching in its honesty, The Gene gives us a definitive account of the fundamental unit of heredity – and a vision of both humanity’s past and future.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    Frizzle were a physics student of Stephen Hawking, she might have written THE UNIVERSE IN YOUR HAND, a wild tour through the reaches of time and space, from the interior of a proton to the Big Bang to the rough suburbs of a black hole. It's friendly, excitable, erudite, and cosmic."—Jordan Ellenberg, New York Times besteselling author of How Not To Be WrongQuantum physics, black holes, string theory, the Big Bang, dark matter, dark energy, parallel universes: even if we are interested in these fundamental concepts of our world, their language is the language of math. Which means that despite our best intentions of finally grasping, say, Einstein's Theory of General Relativity, most of us are quickly brought up short by a snarl of nasty equations or an incomprehensible graph.Christophe Galfard's mission in life is to spread modern scientific ideas to the general public in entertaining ways. Using his considerable skills as a brilliant theoretical physicist and successful young adult author, The Universe in Your Hand employs the immediacy of simple, direct language to show us, not explain to us, the theories that underpin everything we know about our universe. To understand what happens to a dying star, we are asked to picture ourselves floating in space in front of it. To get acquainted with the quantum world, we are shrunk to the size of an atom and then taken on a journey. Employing everyday similes and metaphors, addressing the reader directly, and writing stories rather than equations renders these astoundingly complex ideas in an immediate and visceral way.Utterly captivating and entirely unique, The Universe in Your Hand will find its place among other classics in the field.

    Annotation copyright Book News, Inc. Portland, Or.

    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.

    In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.