In this Very Short Introduction, Peter M. Higgins, a renowned popular-science writer, unravels the world of numbers, demonstrating its richness and providing an overview of all the number types that feature in modern science and mathematics. Indeed, Higgins paints a crystal-clear picture of the number world, showing how the modern number system matured over many centuries, and introducing key concepts such as integers, fractions, real and imaginary numbers, and complex numbers. Higgins sheds light on such fascinating topics as the series of primes, describing how primes are now used to encrypt confidential data on the internet. He also explores the infinite nature of number collections and explains how the so-called real numbers knit together to form the continuum of the number line. Written in the fashion of Higgins' highly popular science paperbacks, Numbers accurately explains the nature of numbers and how so-called complex numbers and number systems are used in calculations that arise in real problems.

    Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.

    Designed for the junior- level astrophysics course, each topic is approached in the context of the major unresolved questions in astrophysics. The core chapters have been designed for a course in stellar structure and evolution, while the extended chapters provide additional coverage of the solar system, galactic structure, dynamics, evolution, and cosmology. * Two versions of this text are available: An Introduction to Modern Stellar Astrophysics, (Chapters 1-17), and An Introduction to Modern Astrophysics, (Chapters 1-28). * Computer programs included with the text allow students to explore the physics of stars and galaxies. * In designing a curriculum, instructors can combine core and extended chapters with the optional advanced sections so as to meet their individual goals. * Up-to-date coverage of current astrophysical discoveries are included. * This text emphasizes computational physics, including computer problems and on-line programs. * This text also includes a selection of over 500 problems. For additional information and computer codes to be used

    Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, computation, and knowledge with quantum physics. Considered jointly, these four strands of explanation reveal a unified fabric of reality that is both objective and comprehensible, the subject of this daring, challenging book. The Fabric of Reality explains and connects many topics at the leading edge of current research and thinking, such as quantum computers (which work by effectively collaborating with their counterparts in other universes), the physics of time travel, the comprehensibility of nature and the physical limits of virtual reality, the significance of human life, and the ultimate fate of the universe. Here, for scientist and layperson alike, for philosopher, science-fiction reader, biologist, and computer expert, is a startlingly complete and rational synthesis of disciplines, and a new, optimistic message about existence.

    These assorted merchants, gardeners, barber-surgeons, midwives, instrument makers, mathematics teachers, engineers, alchemists, and other experimenters, she contends, formed a patchwork scientific community whose practices set the stage for the Scientific Revolution. While Francis Bacon has been widely regarded as the father of modern science, scores of his London contemporaries also deserve a share in this distinction. It was their collaborative, yet often contentious, ethos that helped to develop the ideals of modern scientific research.The book examines six particularly fascinating episodes of scientific inquiry and dispute in sixteenth-century London, bringing to life the individuals involved and the challenges they faced. These men and women experimented and invented, argued and competed, waged wars in the press, and struggled to understand the complexities of the natural world. Together their stories illuminate the blind alleys and surprising twists and turns taken as medieval philosophy gave way to the empirical, experimental culture that became a hallmark of the Scientific Revolution.

    In an era when women were rarely permitted any serious schooling, this twenty-seven-year-old’s nimble conversation and unusual brilliance led Voltaire, then in his late thirties, to wonder, “Why did you only reach me so late?” They fell immediately and passionately in love.Through the prism of their tumultuous fifteen-year relationship we see the crumbling of an ancient social order and the birth of the Enlightenment. Together the two lovers rebuilt a dilapidated and isolated rural chateau at Cirey where they conducted scientific experiments, entertained many of the leading thinkers of the burgeoning scientific revolution, and developed radical ideas about the monarchy, the nature of free will, the subordination of women, and the separation of church and state. But their time together was filled with far more than reading and intellectual conversation. There were frantic gallopings across France, sword fights in front of besieged German fortresses, and a deadly burning of Voltaire’s books by the public executioner at the base of the grand stairwell of the Palais de Justice in Paris. The pair survived court intrigues at Versailles, narrow escapes from agents of the king, a covert mission to the idyllic lakeside retreat of Frederick the Great of Prussia, forays to the royal gambling tables (where Emilie put her mathematical acumen to lucrative use), and intense affairs that bent but did not break their bond.Along with its riveting portrait of Voltaire as a vulnerable romantic, Passionate Minds at last does justice to the supremely unconventional life and remarkable achievements of Emilie du Châtelet—including her work on the science of fire and the nature of light. Long overlooked, her story tells us much about women’s lives at the time of the Enlightenment. Equally important, it demonstrates how this graceful, quick-witted, and attractive woman worked out the concepts that would lead directly to the “squared” part of Einstein’s revolutionary equation: E=mc2.Based on a rich array of personal letters, as well as writings from houseguests, neighbors, scientists, and even police reports, Passionate Minds is both panoramic and intimate in feeling. It is an unforgettable love story and a vivid rendering of the birth of modern ideas.

     The eternal questions of science and religion were profoundly recast by Einstein's theory of relativity and its implications that time can be warped by motion and gravitation, and that it cannot be meaningfully divided into past, present, and future. In About Time, Paul Davies discusses the big bang theory, chaos theory, and the recent discovery that the universe appears to be younger than some of the objects in it, concluding that Einstein's theory provides only an incomplete understanding of the nature of time. Davies explores unanswered questions such as: * Does the universe have a beginning and an end? * Is the passage of time merely an illusion? * Is it possible to travel backward -- or forward -- in time? About Time weaves physics and metaphysics in a provocative contemplation of time and the universe.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    He was twenty-two. Soon recognized as a cryptographer of genius, he became head of communications at the Special Operations Executive (SOE), where he revolutionized the codemaking techniques of the Allies and trained some of the most famous agents dropped into occupied Europe, including "the White Rabbit" and Violette Szabo. As a top codemaker, Marks had a unique perspective on one of the most fascinating and, until now, little-known aspects of the Second World War. Writing with the narrative flair and vivid characterization of his famous screenplays, Marks gives free rein to his keen sense of the absurd and his wry wit, resulting in a thrilling and poignant memoir that celebrates individual courage and endeavor, without losing sight of the human cost and horror of war.

    Now, two of the world's most eminent thinkers -- University of London physicists David Bohm, a former protege of Einstein's and one of the world's most respected quantum physicists, and Stanford neurophysiologist Karl Pribram, one of the architects of our modern understanding of the brain -- believe that the universe itself may be a giant hologram, quite literally a kind of image or construct created, at least in part, by the human mind. This remarkable new way of looking at the universe explains not only many of the unsolved puzzles of physics, but also such mysterious occurrences as telepathy, out-of-body and near death experiences, "lucid" dreams, and even religious and mystical experiences such as feelings of cosmic unity and miraculous healings.

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

    "What They Did There: Profiles From the Battle of Gettysburg" offers a unique view of its subject, telling the story of the battle not through convention narrative but via 170 mini-bios of not only combatants blue and gray, but of civilians, doctors, nurses, artists, photographers, Samaritans; saints, sinners and the moral terrain in-between.

    This is how engineers calculate your quality of living, how corporations determine your needs, and how politicians estimate your opinions. These are the numbers you never think about-even though they play a crucial role in every single aspect of your life.What you learn may surprise you, amuse you, or even enrage you. But there's one thing you won't be able to deny: Numbers Rule Your World...An easy read with a big benefit. --Fareed Zakaria, CNNFor those who have anxiety about how organization data-mining is impacting their world, Kaiser Fung pulls back the curtain to reveal the good and the bad of predictive analytics. --Ian Ayres, Yale professor and author of Super Crunchers: Why Thinking By Numbers is the New Way to Be Smart A book that engages us with stories that a journalist would write, the compelling stories behind the stories as illuminated by the numbers, and the dynamics that the numbers reveal. --John Sall, Executive Vice President, SAS InstituteLittle did I suspect, when I picked up Kaiser Fung's book, that I would become so entranced by it - an illuminating and accessible exploration of the power of statistical analysis for those of us who have no prior training in a field that he explores so ably. --Peter Clarke, author of Keynes: The Rise, Fall, and Return of the 20th Century's Most Influential EconomistA tremendous book. . . . If you want to understand how to use statistics, how to think with numbers and yet to do this without getting lost in equations, if you've been looking for the book to unlock the door to logical thinking about problems, well, you will be pleased to know that you are holding that book in your hands. --Daniel Finkelstein, Executive Editor, The Times of LondonI thoroughly enjoyed this accessible book and enthusiastically recommend it to anyone looking to understand and appreciate the role of statistics and data analysis in solving problems and in creating a better world. --Michael Sherman, Texas A&M University, American Statistician

    Based on her work at the Santa Fe Institute and drawing on its interdisciplinary strategies, Mitchell brings clarity to the workings of complexity across a broad range of biological, technological, and social phenomena, seeking out the general principles or laws that apply to all of them. Richly illustrated, Complexity: A Guided Tour--winner of the 2010 Phi Beta Kappa Book Award in Science--offers a wide-ranging overview of the ideas underlying complex systems science, the current research at the forefront of this field, and the prospects for its contribution to solving some of the most important scientific questions of our time.

    The perceived distances between objects in the sky mirrored (and were mirrored by) the spaces between notes forming chords and scales. The smooth operation of the cosmos created a divine harmony that composers sought to capture and express. Jamie James allows readers to see how this scientific philosophy emerged, how it was shattered by changing views of the universe and the rise of Romanticism, and to what extent it survives today - if at all. From Pythagoras to Newton, Bach to Beethoven, and on to the twentieth century of Einstein, Schoenberg, Stravinsky, Cage and Glass. A spellbinding examination of the interwoven fates of science and music throughout history.