More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Relates the life of the remarkable man who made major contributions in such fields as physics, languages, and music, describing how he proposed the light-wave theory and the three-color theory of vision, and was instrumental in the deciphering of the Rosetta Stone.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

    Indeed, many physicists today believe that there are other dimensions beyond the four of our space-time, and that a unified vision of the various forces of nature can be achieved, if we consider that everything we see around us, from the trees to the stars are nothing but vibrations in hyperspace. Hyperspace theory - and its more recent derivation, superstring theory - is the eye of this revolution. In this book, Michio Kaku shows us a fascinating panorama, which completely changes our view of the cosmos, and takes us on a dazzling journey through new dimensions: wormholes connecting parallel universes, time machines, "baby universes" and more. Similar wonders are emerging in some pages in which everything is explained with elegant simplicity and where the mathematical formulation is replaced by imaginative illustrations that allow the problems to be visualized. The result is a very entertaining and surprising book, which even leaves behind the greatest fantasies of the old science fiction authors.

    The Story of Western Science shows us the joy and importance of reading groundbreaking science writing for ourselves and guides us back to the masterpieces that have changed the way we think about our world, our cosmos, and ourselves.Able to be referenced individually, or read together as the narrative of Western scientific development, the book's twenty-eight succinct chapters lead readers from the first science texts by Hippocrates, Plato, and Aristotle through twentieth-century classics in biology, physics, and cosmology. The Story of Western Science illuminates everything from mankind's earliest inquiries to the butterfly effect, from the birth of the scientific method to the rise of earth science and the flowering of modern biology.Each chapter recommends one or more classic books and provides entertaining accounts of crucial contributions to science, vivid sketches of the scientist-writers, and clear explanations of the mechanics underlying each concept. The Story of Western Science reveals science to be a dramatic undertaking practiced by some of history's most memorable characters. It reminds us that scientific inquiry is a human pursuit—an essential, often deeply personal, sometimes flawed, frequently brilliant way of understanding the world.In the tradition of her perennial bestseller The-Well Educated Mind, Susan Wise Bauer delivers an accessible, entertaining, and illuminating springboard into the scientific education you never had.

    No, hang on, let's make this interesting. Between zero and infinity. Even if you stick to the whole numbers, there are a lot to choose from - an infinite number in fact. Throw in decimal fractions and infinity suddenly gets an awful lot bigger (is that even possible?) And then there are the negative numbers, the imaginary numbers, the irrational numbers like pi which never end. It literally never ends.The world of numbers is indeed strange and beautiful. Among its inhabitants are some really notable characters - pi, e, the "imaginary" number i and the famous golden ratio to name just a few. Prime numbers occupy a special status. Zero is very odd indeed: is it a number, or isn't it?How Numbers Work takes a tour of this mind-blowing but beautiful realm of numbers and the mathematical rules that connect them. Not only that, but take a crash course on the biggest unsolved problems that keep mathematicians up at night, find out about the strange and unexpected ways mathematics influences our everyday lives, and discover the incredible connection between numbers and reality itself. ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    Designed for two-semester, beginning graduate courses in Mathematical Statistics, and for senior undergraduate Mathematics, Statistics, and Actuarial Science majors, this text retains its ongoing features and continues to provide students with background material.

    What happened during those years and what has happened since to refine the understanding of this phenomenon is the fascinating story told here.We move from a coffee shop in Zurich, where Einstein and Max von Laue discuss the madness of quantum theory, to a bar in Brazil, as David Bohm and Richard Feynman chat over cervejas. We travel to the campuses of American universities—from J. Robert Oppenheimer’s Berkeley to the Princeton of Einstein and Bohm to Bell’s Stanford sabbatical—and we visit centers of European physics: Copenhagen, home to Bohr’s famous institute, and Munich, where Werner Heisenberg and Wolfgang Pauli picnic on cheese and heady discussions of electron orbits.Drawing on the papers, letters, and memoirs of the twentieth century’s greatest physicists, Louisa Gilder both humanizes and dramatizes the story by employing their own words in imagined face-to-face dialogues. Here are Bohr and Einstein clashing, and Heisenberg and Pauli deciding which mysteries to pursue. We see Schrödinger and Louis de Broglie pave the way for Bell, whose work is here given a long-overdue revisiting. And with his characteristic matter-of-fact eloquence, Richard Feynman challenges his contemporaries to make something of this entanglement.

    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.

    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

    Hofstadter's collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

    The manuscript was a palimpsest-a book made from an earlier codex whose script had been scraped off and the pages used again. Behind the script of the thirteenth-century monk's prayer book, the palimpsest revealed the faint writing of a much older, tenth-century manuscript. Part archaeological detective story, part science, and part history, The Archimedes Codex tells the extraordinary story of this lost manuscript, from its tenth-century creation in Constantinople to the auction block at Christie's, and how a team of scholars used the latest imaging technology to reveal and decipher the original text. What they found was the earliest surviving manuscript by Archimedes (287 b.c.-212 b.c.), the greatest mathematician of antiquity-a manuscript that revealed, for the first time, the full range of his mathematical genius, which was two thousand years ahead of modern science.

    In The Beginnings of Western Science, David C. Lindberg provides a rich chronicle of the development of scientific ideas, practices, and institutions from the pre-Socratic Greek philosophers to the late-medieval scholastics.Lindberg surveys all the most important themes in the history of ancient and medieval science, including developments in cosmology, astronomy, mechanics, optics, alchemy, natural history, and medicine. He synthesizes a wealth of information in superbly organized, clearly written chapters designed to serve students, scholars, and nonspecialists alike. In addition, Lindberg offers an illuminating account of the transmission of Greek science to medieval Islam and subsequently to medieval Europe. And throughout the book he pays close attention to the cultural and institutional contexts within which scientific knowledge was created and disseminated and to the ways in which the content and practice of science were influenced by interaction with philosophy and religion. Carefully selected maps, drawings, and photographs complement the text.Lindberg's story rests on a large body of important scholarship produced by historians of science, philosophy, and religion over the past few decades. However, Lindberg does not hesitate to offer new interpretations and to hazard fresh judgments aimed at resolving long-standing historical disputes. Addressed to the general educated reader as well as to students, his book will also appeal to any scholar whose interests touch on the history of the scientific enterprise.