He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects.

    At the dawn of the Industrial Revolution in eighteenth-century England, standards of measurement were established, giving way to the development of machine tools—machines that make machines. Eventually, the application of precision tools and methods resulted in the creation and mass production of items from guns and glass to mirrors, lenses, and cameras—and eventually gave way to further breakthroughs, including gene splicing, microchips, and the Hadron Collider.Simon Winchester takes us back to origins of the Industrial Age, to England where he introduces the scientific minds that helped usher in modern production: John Wilkinson, Henry Maudslay, Joseph Bramah, Jesse Ramsden, and Joseph Whitworth. It was Thomas Jefferson who later exported their discoveries to the fledgling United States, setting the nation on its course to become a manufacturing titan. Winchester moves forward through time, to today’s cutting-edge developments occurring around the world, from America to Western Europe to Asia.As he introduces the minds and methods that have changed the modern world, Winchester explores fundamental questions. Why is precision important? What are the different tools we use to measure it? Who has invented and perfected it? Has the pursuit of the ultra-precise in so many facets of human life blinded us to other things of equal value, such as an appreciation for the age-old traditions of craftsmanship, art, and high culture? Are we missing something that reflects the world as it is, rather than the world as we think we would wish it to be? And can the precise and the natural co-exist in society?

    Yet as bestselling author and astrophysicist Jeffrey Bennett points out, black holes don't suck. With that simple idea in hand, Bennett begins an entertaining introduction to Einstein's theories, describing the amazing phenomena readers would actually experience if they took a trip through a black hole.The theory of relativity also gives us the cosmic speed limit of the speed of light, the mind-bending ideas of time dilation and curvature of spacetime, and what may be the most famous equation in history: e = mc2. Indeed, the theory of relativity shapes much of our modern understanding of the universe, and it is not "just a theory: " every major prediction of relativity has been tested to exquisite precision and its practical applications include the Global Positioning System (GPS). Bennett proves anyone can understand the basics of Einstein's ideas. His intuitive, nonmathematical approach gives a wide audience its first real taste of how relativity works and why it is so important not only to science but also to the way we view ourselves as human beings.

    “They are both brilliantly original and outsiders,” the narrator tells us. “They are both besotted with mathematics. But for all their devotion, mathematics is indifferent, unaltered by any of their dramas . . . Against indifference, I want to tell their stories.” Which she does in a haunting, incantatory voice, the two lives unfolding in parallel narratives that overlap in the magnitude of each man’s achievement and demise: Gödel, delusional and paranoid, would starve himself to death; Turing, arrested for homosexual activities, would be driven to suicide. And they meet as well in the narrator’s mind, where facts are interwoven with her desire and determination to find meaning in the maze of their stories: two men devoted to truth of the highest abstract nature, yet unable to grasp the mundane truths of their own lives.A unique amalgam of luminous imagination and richly evoked historic character and event—A Madman Dreams of Turing Machines is a story about the pursuit of truth and its effect on the lives of two men. A story of genius and madness, incredible yet true.

    Few episodes in the development of scientific theory show so clearly how the solution to a highly technical problem can alter our basic thought processes and attitudes. Understanding the processes which underlay the Revolution gives us a perspective, in this scientific age, from which to evaluate our own beliefs more intelligently. With a constant keen awareness of the inseparable mixture of its technical, philosophical, and humanistic elements, Thomas S. Kuhn displays the full scope of the Copernican Revolution as simultaneously an episode in the internal development of astronomy, a critical turning point in the evolution of scientific thought, and a crisis in Western man's concept of his relation to the universe and to God.The book begins with a description of the first scientific cosmology developed by the Greeks. Mr. Kuhn thus prepares the way for a continuing analysis of the relation between theory and observation and belief. He describes the many functions--astronomical, scientific, and nonscientific--of the Greek concept of the universe, concentrating especially on the religious implications. He then treats the intellectual, social, and economic developments which nurtured Copernicus' break with traditional astronomy. Although many of these developments, including scholastic criticism of Aristotle's theory of motion and the Renaissance revival of Neoplatonism, lie entirely outside of astronomy, they increased the flexibility of the astronomer's imagination. That new flexibility is apparent in the work of Copernicus, whose De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) is discussed in detail both for its own significance and as a representative scientific innovation.With a final analysis of Copernicus' life work--its reception and its contribution to a new scientific concept of the universe--Mr. Kuhn illuminates both the researches that finally made the heliocentric arrangement work, and the achievements in physics and metaphysics that made the planetary earth an integral part of Newtonian science. These are the developments that once again provided man with a coherent and self-consistent conception of the universe and of his own place in it.This is a book for any reader interested in the evolution of ideas and, in particular, in the curious interplay of hypothesis and experiment which is the essence of modern science. Says James Bryant Conant in his Foreword: "Professor Kuhn's handling of the subject merits attention, for...he points the way to the road which must be followed if science is to be assimilated into the culture of our times."

    His public advocacy of the Copernican over the Aristotelian system of the universe flew directly in the face of biblical authority and ecclesiastical tradition. Condemned and placed under house arrest by the Inquisition, Galileo nonetheless devoted his last years to the completion of his Dialogues Concerning Two New Sciences, which deals with motion and the resistance of solids. The Two New Sciences, which Galileo called his most important work, may be regarded as the summary statement of a life devoted to scientific experimentation and free inquiry untrammeled by tradition and authority.

    Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

    Tie Knots unravels the history of ties, the story of the discovery of the new knots and some very elegant mathematics in action. If Einstein had been left alone in Tie Rack for long enough perhaps he would have worked it out : why do people tie their ties in only 4 ways? And how many other possibilities are there? Two Cambridge University physicists, research fellows working from the Cavendish laboratories, have discovered via a recherche branch of mathematics - knot theory - that although only four knots are traditionally used in tying neck ties another 81 exist. This is the story of their discovery, of the history of neck ties and of the equations that express whether a tie is handsome or not. Of the 81 new knots, 6 are practical and elegant. We now have somewhere else to go after the Pratt, the Four-in-Hand, the Full and Half Windsor. Sartorial stylishness is wrapped effortlessly around popular mathematics. A concept developed to describe the movement of gas molecules - the notion of persistent walks around a triangular lattice - also describes the options for tie tying. Pure maths becomes pure fashion in a delightfully designed little package from Fourth Estate.

    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.

    On board were: writers, artists, honeymooners, sportsmen, priests, reverends, fashion designers, aristocrats, millionaires, children, crew and emigrants looking for a better life.This book tells of their lives, and shines the spotlight on: Some of the great ship’s surprising treasures Her fêted voyage from Belfast’s Harland & Wolff shipyard The fascinating museums devoted to her memory, including Titanic Belfast The iconic music and movies Her winged and four-legged passengers The sister ships of Olympic and Britannic Tales of heroism Theories surrounding Titanic’s fatal collision The lifeboats and just how close the SS Californian was on that tragic night How Arctic explorer Ernest Shackleton and the inquiries viewed events These stories and much more lie inside.

    Next, he examines the three critiques that currently challenge this classic Darwinian edifice: that selection operates on multiple levels, from the gene to the group; that evolution proceeds by a variety of mechanisms, not just natural selection; and that causes operating at broader scales, including catastrophes, have figured prominently in the course of evolution.Then, in a stunning tour de force that will likely stimulate discussion and debate for decades, Gould proposes his own system for integrating these classical commitments and contemporary critiques into a new structure of evolutionary thought.In 2001 the Library of Congress named Stephen Jay Gould one of America's eighty-three Living Legends--people who embody the quintessentially American ideal of individual creativity, conviction, dedication, and exuberance. Each of these qualities finds full expression in this peerless work, the likes of which the scientific world has not seen--and may not see again--for well over a century.

    --Karen Joy FowlerMandelbrot the Magnificent is a stunning, magical pseudo-biography of Benoit Mandelbrot as he flees into deep mathematics to escape the rise of HitlerBorn in Warsaw and growing up in France during the rise of Hitler, Benoit Mandelbrot found escape from the cruelties of the world around him through mathematics. Logic sometimes makes monsters, and Mandelbrot began hunting monsters at an early age. Drawn into the infinite promulgations of formulae, he sinks into secret dimensions and unknown wonders.His gifts do not make his life easier, however. As the Nazis give up the pretense of puppet government in Vichy France, the jealousy of Mandelbrot's classmates leads to denunciation and disaster. The young mathematician must save his family with the secret spaces he's discovered, or his genius will destroy them.

    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.