But almost everything about it, from the elements that forged stars, planets, and lifeforms, to the fundamental forces of physics, can be traced back to what happened in just the first three minutes of its life.In this book, Nobel Laureate Steven Weinberg describes in wonderful detail what happened in these first three minutes. It is an exhilarating journey that begins with the Planck Epoch - the earliest period of time in the history of the universe - and goes through Einstein's Theory of Relativity, the Hubble Red Shift, and the detection of the Cosmic Microwave Background. These incredible discoveries all form the foundation for what we now understand as the "standard model" of the origin of the universe. The First Three Minutes examines not only what this model looks like, but also tells the exciting story of the bold thinkers who put it together.Clearly and accessibly written, The First Three Minutes is a modern-day classic, an unsurpassed explanation of where it is we really come from.

    It would become the world's most baffling mathematical mystery. Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries. For some it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr. Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, "Fermat's Last Theorem" brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.

    In the hands of one of today’s hottest young physicists, that simple fact of breakfast becomes a doorway to understanding the Big Bang, the universe, and other universes, too. In From Eternity to Here, Sean Carroll argues that the arrow of time, pointing resolutely from the past to the future, owes its existence to conditions before the Big Bang itself, a period modern cosmology of which Einstein never dreamed. Increasingly, though, physicists are going out into realms that make the theory of relativity seem like child’s play. Carroll’s scenario is not only elegant, it’s laid out in the same easy-to- understand language that has made his group blog, Cosmic Variance, the most popular physics blog on the Net. From Eternity to Here uses ideas at the cutting edge of theoretical physics to explore how properties of spacetime before the Big Bang can explain the flow of time we experience in our everyday lives. Carroll suggests that we live in a baby universe, part of a large family of universes in which many of our siblings experience an arrow of time running in the opposite direction. It’s an ambitious, fascinating picture of the universe on an ultra-large scale, one that will captivate fans of popular physics blockbusters like Elegant Universe and A Brief History of Time.

    His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Gö's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Gö's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Gö's contributions to mathematics, philosophy, computer science, artificial intelligence -- even cosmology -- in an entertaining and accessible way.

    This title is intended for those who might enjoy an engaging dialogue on abstract mathematical ideas, and those who might wish to experience how new mathematics is created.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    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.

    “I walk with a new spring in my step and I look at life through physics-colored eyes,” wrote one such fan. When Lewin’s lectures were made available online, he became an instant YouTube celebrity, and The New York Times declared, “Walter Lewin delivers his lectures with the panache of Julia Child bringing French cooking to amateurs and the zany theatricality of YouTube’s greatest hits.” For more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.” Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions. Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes. “For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.

    It’s time we stand face-to-digital-face with the true powers and limitations of the algorithms that already automate important decisions in healthcare, transportation, crime, and commerce. Hello World is indispensable preparation for the moral quandaries of a world run by code, and with the unfailingly entertaining Hannah Fry as our guide, we’ll be discussing these issues long after the last page is turned.

    Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.

    Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. His personal encounters with Godel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

    The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    For mathematicians, physicists, engineers, and everyone else with an interest in mathematics' cutting edge, The Millennium Problems is the definitive account of a subject that will have a very long shelf life.

    There are deep connections between stars and atoms, between the cosmos and the microworld. Just six numbers, imprinted in the "big bang," determine the essential features of our entire physical world. Moreover, cosmic evolution is astonishingly sensitive to the values of these numbers. If any one of them were "untuned," there could be no stars and no life. This realization offers a radically new perspective on our universe, our place in it, and the nature of physical laws.