Over the next two decades, Copernicus expanded his theory through hundreds of observations, while compiling in secret a book-length manuscript that tantalized mathematicians and scientists throughout Europe. For fear of ridicule, he refused to publish.In 1539, a young German mathematician, Georg Joachim Rheticus, drawn by rumors of a revolution to rival the religious upheaval of Martin Luther's Reformation, traveled to Poland to seek out Copernicus. Two years later, the Protestant youth took leave of his aging Catholic mentor and arranged to have Copernicus's manuscript published, in 1543, as De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres)-the book that forever changed humankind's place in the universe.In her elegant, compelling style, Dava Sobel chronicles, as nobody has, the conflicting personalities and extraordinary discoveries that shaped the Copernican Revolution. At the heart of the book is her play And the Sun Stood Still, imagining Rheticus's struggle to convince Copernicus to let his manuscript see the light of day. As she achieved with her bestsellers Longitude and Galileo's Daughter, Sobel expands the bounds of narration, giving us an unforgettable portrait of scientific achievement, and of the ever-present tensions between science and faith.

    In The Irrationals , the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define--and why so many questions still surround them. That definition seems so simple: they are numbers that cannot be expressed as a ratio of two integers, or that have decimal expansions that are neither infinite nor recurring. But, as The Irrationals shows, these are the real "complex" numbers, and they have an equally complex and intriguing history, from Euclid's famous proof that the square root of 2 is irrational to Roger Apry's proof of the irrationality of a number called Zeta(3), one of the greatest results of the twentieth century. In between, Havil explains other important results, such as the irrationality of e and pi. He also discusses the distinction between "ordinary" irrationals and transcendentals, as well as the appealing question of whether the decimal expansion of irrationals is "random". Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.

    Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.

    New to this third edition are expanded coverage of such important topics as surface boundary interfaces, improved discussions of such physical and mathematical laws as the Law of Biot and Savart and the Euler Momentum Integral. A very important new section on Computational Fluid Dynamics has been added for the very first time to this edition. Expanded and improved end-of-chapter problems will facilitate the teaching experience for students and instrutors alike. This book remains one of the most comprehensive and useful texts on fluid mechanics available today, with applications going from engineering to geophysics, and beyond to biology and general science. * Ample, useful end-of-chapter problems.* Excellent Coverage of Computational Fluid Dynamics.* Coverage of Turbulent Flows.* Solutions Manual available.

    . . Nobel winner . . . bestselling author . . . safe-cracker. In this substantial graphic novel biography, First Second presents the larger-than-life exploits of Nobel-winning quantum physicist, adventurer, musician, world-class raconteur, and one of the greatest minds of the twentieth century: Richard Feynman. Written by nonfiction comics mainstay Jim Ottaviani and brilliantly illustrated by First Second author Leland Myrick, Feynman tells the story of the great man's life from his childhood in Long Island to his work on the Manhattan Project and the Challenger disaster. Ottaviani tackles the bad with the good, leaving the reader delighted by Feynman's exuberant life and staggered at the loss humanity suffered with his death. Anyone who ever wanted to know more about Richard P. Feynman, quantum electrodynamics, the fine art of the bongo drums, the outrageously obscure nation of Tuva, or the development and popularization of the field of physics in the United States need look no further than this rich and joyful work.• One of School Library Journal's Best Adult Books 4 Teens titles of 2011 • One of Horn Book's Best Nonfiction Books of 2011

    Since then, physicists have been placing new forces into ever-grander theories. But perhaps the ultimate challenge is achieving a monumental synthesis of the two remaining theories--relativity and the quantum theory. This would be the crowning achievement of science, a profound merging of all the forces of nature into one beautiful, magnificent equation to unlock the deepest mysteries in science: What happened before the Big Bang? What lies on the other side of a black hole? Are there other universes and dimensions? Is time travel possible? Why are we here? Kaku also explains the intense controversy swirling around this theory, with Nobel laureates taking opposite sides on this vital question.

    The calculus is not a hard subject and I prove this through an easy to read and obvious approach spanning only 100 pages. I have written this book with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.Show more Show less

    Here he tackles all the "big questions," including the biggest of them all: Why does the universe seem so well adapted for life? In his characteristically clear and elegant style, Davies shows how recent scientific discoveries point to a perplexing fact: many different aspects of the cosmos, from the properties of the humble carbon atom to the speed of light, seem tailor-made to produce life. A radical new theory says it's because our universe is just one of an infinite number of universes, each one slightly different. Our universe is bio-friendly by accident -- we just happened to win the cosmic jackpot. While this "multiverse" theory is compelling, it has bizarre implications, such as the existence of infinite copies of each of us and Matrix-like simulated universes. And it still leaves a lot unexplained. Davies believes there's a more satisfying solution to the problem of existence: the observations we make today could help shape the nature of reality in the remote past. If this is true, then life -- and, ultimately, consciousness -- aren't just incidental byproducts of nature, but central players in the evolution of the universe. Whether he's elucidating dark matter or dark energy, M-theory or the multiverse, Davies brings the leading edge of science into sharp focus, provoking us to think about the cosmos and our place within it in new and thrilling ways.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    New Proofs for the Existence of God responds to these glaring omissions. From universal space-time asymmetry to cosmic coincidences to the intelligibility of reality, Robert Spitzer tackles a wealth of evidence. He considers string theory, quantum cosmology, mathematical thoughts on infinity, and much more. This fascinating and stunning collection of evidence provides solid grounding for reasonable and responsible belief in a super-intelligent, transcendent, creative power standing at the origins of our universe.

    The neatly printed equations on the scrap of paper outlined his world-changing theory of general relativity, the first complete revision of our conception of the universe since Isaac Newton.Until then, Einstein's masterpiece of time and space had been trapped behind the physical and ideological lines of battle, unknown. Many Britons were rejecting anything German, but Eddington realized the importance of the letter: perhaps Einstein's esoteric theory could not only change the foundations of science but also lead to international co-operation in a time of brutal war.Few recognize how the Great War, the industrialized slaughter that bled Europe from 1914 to 1918, shaped Einstein's life and work. While Einstein never held a rifle, he formulated general relativity blockaded in Berlin, literally starving. His name is now synonymous with 'genius', but it was not an easy road.Einstein spent a decade creating relativity and his ascent to global celebrity owed much to against-the-odds international collaboration, including Eddington's globe-spanning expedition of 1919 - two years before they finally met - to catch a fleeting solar eclipse for a rare opportunity to confirm Einstein's bold prediction that light has weight.We usually think of scientific discovery as a flash of individual inspiration, but here we see it is the result of hard work, gambles and wrong turns. Einstein's War is a celebration of what science can offer when bigotry and nationalism are defeated. Using previously unknown sources and written like a thriller, it shows relativity being built brick-by-brick in front of us, as it happened 100 years ago.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    In the past, discoveries often had to wait for the rise of the next generation to see questions in a new light and let go of old truisms. Today, in a world that is defined by a rapid rate of change, staying on the cutting edge has as much to do with shedding outdated notions as adopting new ones. In this spirit, John Brockman, publisher of the online salon Edge.org ("the world's smartest website"—The Guardian), asked 175 of the world's most influential scientists, economists, artists, and philosophers: What scientific idea is ready for retirement?Jared Diamond explores the diverse ways that new ideas emerge * Nassim Nicholas Taleb takes down the standard deviation * Richard Thaler and novelist Ian McEwan reveal the usefulness of "bad" ideas * Steven Pinker dismantles the working theory of human behavior * Richard Dawkins renounces essentialism * Sherry Turkle reevaluates our expectations of artificial intelligence * Physicist Andrei Linde suggests that our universe and its laws may not be as unique as we think * Martin Rees explains why scientific understanding is a limitless goal * Alan Guth rethinks the origins of the universe * Sam Harris argues that our definition of science is too narrow * Nobel Prize winner Frank Wilczek disputes the division between mind and matter * Lawrence Krauss challenges the notion that the laws of physics were preordained * plus contributions from Daniel Goleman, Mihaly Csikszentmihalyi, Nicholas Carr, Rebecca Newberger Goldstein, Matt Ridley, Stewart Brand, Sean Carroll, Daniel C. Dennett, Helen Fisher, Douglas Rushkoff, Lee Smolin, Kevin Kelly, Freeman Dyson, and others.

    Everyday experience cannot prepare us for the sub-atomic world, where quantum effects become all-important. Here, particles can look like waves, and vice versa; electrons seem to lose their identity and instead take on a shifting, unpredictable appearance that depends on how they are being observed; and a single photon may sometimes behave as if it could be in two places at once. In the world of quantum mechanics, uncertainty and ambiguity become not just unavoidable, but essential ingredients of science -- a development so disturbing that to Einstein "it was as if God were playing dice with the universe." And there is no one better able to explain the quantum revolution as it approaches the century mark than David Lindley. He brings the quantum revolution full circle, showing how the familiar and trustworthy reality of the world around us is actually a consequence of the ineffable uncertainty of the subatomic quantum world -- the world we can't see.

    He shows that there are many ways of achieving happiness; for example, there is the inherent happiness that comes with the love of a child; the competitive happiness of triumphing over your opponents; the sensual happiness of the hedonist. Rather than preaching a particular behavior or way of life, Morris provides knowledge that we can use, if we wish, to make ourselves happier.