Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    With his trademark elegant prose, eye for lively detail, and gift for lucid explanation, Professor von Baeyer turns the contemplation of a cooling coffee cup into a beguiling portrait of the birth of a science with relevance to almost every aspect of our lives.

     Tim accepted, and after extensive meetings with Elon and his staff, he wrote four blog posts that Vox’s David Roberts called “the meatiest, most fascinating, most satisfying posts I've read in ages.” Here is the whole series, in one ebook.

    Join one of the greatest contemporary philosophers on a breathtaking tour of time and the Kosmos--from the Big Bang right up to the eve of the twenty-first century. This accessible and entertaining summary of Ken Wilber's great ideas has been expanding minds now for two decades, providing a kind of unified field theory of the universe and, along the way, treating a host of issues related to that universe, from gender roles, to multiculturalism, to environmentalism, and even the meaning of the Internet. This special anniversary edition contains as an afterword a dialogue between the author and Lana Wachowski, the award-winning writer-director of the Matrix film trilogy, in which we're offered an intimate glimpse into the evolution of Ken's thinking and where he stands today. A Brief History of Everything may well be the best introduction to the thought of this man who has been called the -Einstein of Consciousness- (John White).

    Taking as territory everything from the Big Bang to the rise of civilization, Bryson seeks to understand how we got from there being nothing at all to there being us. To that end, he has attached himself to a host of the world’s most advanced (and often obsessed) archaeologists, anthropologists, and mathematicians, travelling to their offices, laboratories, and field camps. He has read (or tried to read) their books, pestered them with questions, apprenticed himself to their powerful minds. A Short History of Nearly Everything is the record of this quest, and it is a sometimes profound, sometimes funny, and always supremely clear and entertaining adventure in the realms of human knowledge, as only Bill Bryson can render it. Science has never been more involving or entertaining.

    Drawing on recent work in literary criticism, the authors study how the social world of the laboratory produces papers and other “texts,”’ and how the scientific vision of reality becomes that set of statements considered, for the time being, too expensive to change. The book is based on field work done by Bruno Latour in Roger Guillemin’s laboratory at the Salk Institute and provides an important link between the sociology of modern sciences and laboratory studies in the history of science.

    Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    The authors move deftly across a dazzling array of topics—from the dynamics of the bacterial realm, to the connection between sex and death, to theories of spirit and matter. They delve into the origins of life, offering the startling suggestion that life—not just human life—is free to act and has played an unexpectedly large part in its own evolution. Transcending the various formal concepts of life, this captivating book offers a unique overview of life’s history, essences, and future.Supplementing the text are stunning illustrations that range from the smallest known organism (Mycoplasma bacteria) to the largest (the biosphere itself). Creatures both strange and familiar enhance the pages of What Is Life? Their existence prompts readers to reconsider preconceptions not only about life but also about their own part in it.

    D. Landau and his distinguished colleague G. B. Rumer, employ a simple and straightforward manner to illuminate relativity theory's more subtle and elusive aspects. Using such familiar objects as trains, rulers, and clocks, the authors explain the reasoning behind seemingly self-contradictory ideas in which the relative seems absolute, but the absolute proves to be relative. A series of playful cartoons highlights the authors' witty observations on the laws governing inertia, the speed of light, the relationship of work and mass, and other relativistic concepts."The exposition is masterful . . . a superb book." — New York Times Book Review.

    In it, Socrates tries to determine the definition of virtue, or rather arete, meaning virtue in general, rather than particular virtues, such as justice or temperance. The first part of the work is written in the Socratic dialectical style, and depicts Meno as being reduced to confusion or aporia. In response to Meno's paradox (or the learner's paradox), however, Socrates introduces positive ideas: the immortality of the soul, the theory of knowledge as a recollection (anamnesis), which Socrates demonstrates by posing a mathematical puzzle to one of Meno's slaves, the method of hypothesis, and, in the final lines, the distinction between knowledge and true belief.

    The Will to Power, compiled from the notebooks, is one of the most famous books of the past hundred years, but few have studied it. Here, at last, is the first critical edition in any language.Down through the Nazi period The Will to Power was often mistakenly considered to be Nietzsche's crowning systematic labor; since World War II it has frequently been denigrated, just as fallaciously, as being not worth reading. In fact, it represents a stunning selection from Nietzsche's notebooks, in a topical arrangement that enables the reader to find what Nietzsche wrote on nihilism, art, morality, religion, the theory of knowledge, and whatever else interested him. But no previous edition—even in the original German—shows which notes Nietzsche utilized subsequently in his works, and which sections are not paralleled in the finished books. Nor has any previous edition furnished a commentary or index.Walter Kauffman, in collaboration with R.J. Hollingdale, brings to this volume his unsurpassed skills as a Nietzsche translator and scholar. Professor Kauffman has included the approximate date of each note. His running footnote commentary offers the information needed to follow Nietzsche's train of thought, and indicates, among other things, which notes were eventually superseded by later formulations, and where all German editions, including the very latest, depart from the manuscripts. The comprehensive index serves to guide the reader to the extraordinary riches of this book.

    It is a ‘ must’ book for those in every branch of science . . . in addition, economists, politicians, statesmen, and businessmen cannot afford to overlook cybernetics and its tremendous, even terrifying implications. "It is a beautifully written book, lucid, direct, and despite its complexity, as readable by the layman as the trained scientist." -- John B. Thurston, "The Saturday Review of Literature" Acclaimed one of the "seminal books . . . comparable in ultimate importance to . . . Galileo or Malthus or Rousseau or Mill," "Cybernetics" was judged by twenty-seven historians, economists, educators, and philosophers to be one of those books published during the "past four decades", which may have a substantial impact on public thought and action in the years ahead." -- Saturday Review

    It is also a lucid exposition of the nature and methods of genuine science. The book begins with a concise introduction to evolutionary theory for non-scientists and closes with a rebuttal of the charge that this theory undermines religious and moral values. It will astonish many readers that this case must still be made in the 1980s, but since it must, Philip Kitcher makes it irresistibly and forcefully.Not long ago, a federal court struck down an Arkansas law requiring that scientific Creationism be taught in high school science classes. Contemporary Creationists may have lost one legal battle, but their cause continues to thrive. Their efforts are directed not only at state legislatures but at local school boards and textbook publishers. As Kitcher argues in this rigorous but highly readable book, the integrity of science is under attack. The methods of inquiry used in evolutionary biology are those which are used throughout the sciences. Moreover, modern biology is intertwined with other fields of science--physics, chemistry, astronomy, and geology. Creationists hope to persuade the public that education in science should be torn apart to make room for a literal reading of Genesis.Abusing Science refutes the popular complaint that the scientific establishment is dogmatic and intolerant, denying academic freedom to the unorthodox. It examines Creationist claims seriously and systematically, one by one, showing clearly just why they are at best misguided, at worst ludicrous.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    In this masterfully written and brilliantly informed work of scientific history and explanation, Dr. Thorne, the Feynman Professor of Theoretical Physics at Caltech, leads his readers through an elegant, always human, tapestry of interlocking themes, coming finally to a uniquely informed answer to the great question: what principles control our universe and why do physicists think they know the things they think they know? Stephen Hawking's A Brief History of Time has been one of the greatest best-sellers in publishing history. Anyone who struggled with that book will find here a more slowly paced but equally mind-stretching experience, with the added fascination of a rich historical and human component.