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.

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    Combine this with thoughtful and thorough apparatus, and Philosophy of Science: The Central Issues is the most flexible and comprehensive collection ever created for undergraduate courses.

    A simple web search picks out a handful of relevant needles from the world's biggest haystack: the billions of pages on the World Wide Web. Uploading a photo to Facebook transmits millions of pieces of information over numerous error-prone network links, yet somehow a perfect copy of the photo arrives intact. Without even knowing it, we use public-key cryptography to transmit secret information like credit card numbers; and we use digital signatures to verify the identity of the websites we visit. How do our computers perform these tasks with such ease? This is the first book to answer that question in language anyone can understand, revealing the extraordinary ideas that power our PCs, laptops, and smartphones. Using vivid examples, John MacCormick explains the fundamental "tricks" behind nine types of computer algorithms, including artificial intelligence (where we learn about the "nearest neighbor trick" and "twenty questions trick"), Google's famous PageRank algorithm (which uses the "random surfer trick"), data compression, error correction, and much more. These revolutionary algorithms have changed our world: this book unlocks their secrets, and lays bare the incredible ideas that our computers use every day.

    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.

    Like you, the elements have lives: personalities and attitudes, talents and shortcomings, stories rich with meaning. You may think of them as the inscrutable letters of the periodic table but you know them much better than you realise. Welcome to a dazzling tour through history and literature, science and art. Here you'll meet iron that rains from the heavens and noble gases that light the way to vice. You'll learn how lead can tell your future while zinc may one day line your coffin. You'll discover what connects the bones in your body with the Whitehouse in Washington, the glow of a streetlamp with the salt on your dinner table. From ancient civilisations to contemporary culture, from the oxygen of publicity to the phosphorus in your pee, the elements are near and far and all around us. Unlocking their astonishing secrets and colourful pasts, Periodic Tales will take you on a voyage of wonder and discovery, excitement and novelty, beauty and truth. Along the way, you'll find that their stories are our stories, and their lives are inextricable from our own.

    Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.

    It would become the world's most baffling mathematical mystery. Simple, elegant, and utterly impossible to prove, Fermat's Last Theorem captured the imaginations of amateur and professional mathematicians for over three centuries. For some it became a wonderful passion. For others it was an obsession that led to deceit, intrigue, or insanity. In a volume filled with the clues, red herrings, and suspense of a mystery novel, Dr. Amir Aczel reveals the previously untold story of the people, the history, and the cultures that lie behind this scientific triumph. From formulas devised for the farmers of ancient Babylonia to the dramatic proof of Fermat's theorem in 1993, this extraordinary work takes us along on an exhilarating intellectual treasure hunt. Revealing the hidden mathematical order of the natural world in everything from stars to sunflowers, "Fermat's Last Theorem" brilliantly combines philosophy and hard science with investigative journalism. The result: a real-life detective story of the intellect, at once intriguing, thought-provoking, and impossible to put down.

    The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).

    Readers will find excerpts from bestsellers such as Douglas R. Hofstadter's Gödel, Escher, Bach, Francis Crick's Life Itself, Loren Eiseley's The Immense Journey, Daniel Dennett's Darwin's Dangerous Idea, and Rachel Carson's The Sea Around Us. There are classic essays ranging from J.B.S. Haldane's "On Being the Right Size" and Garrett Hardin's "The Tragedy of the Commons" to Alan Turing's "Computing Machinery and Intelligence" and Albert Einstein's famed New York Times article on "Relativity." And readers will also discover lesser-known but engaging pieces such as Lewis Thomas's "Seven Wonders of Science," J. Robert Oppenheimer on "War and Physicists," and Freeman Dyson's memoir of studying under Hans Bethe.A must-read volume for all science buffs, The Oxford Book of Modern Science Writing is a rich and vibrant anthology that captures the poetry and excitement of scientific thought and discovery.One of New Scientist's Editor's Picks for 2008.

    This groundbreaking book by the most influential philosopher since Sartre compels us to reevaluate our assumptions about all the ensuing reforms in the penal institutions of the West. For as he examines innovations that range from the abolition of torture to the institution of forced labor and the appearance of the modern penitentiary, Michel Foucault suggests that punishment has shifted its focus from the prisoner's body to the soul — and that our very concern with rehabilitation encourages and refines criminal activity.Lucidly reasoned and deftly marshaling a vast body of research, Discipline and Punish is a genuinely revolutionary book, whose implications extend beyond the prison to the minute power relations of our society.

    An astonishing synthesis of literary criticism, philosophy, theology, the theory of law and classical scholarship, it is undoubtedly one of the most important texts in twentieth century philosophy. Looking behind the self-consciousness of science, he discusses the tense relationship between truth and methodology. In examining the different experiences of truth, he aims to "present the hermeneutic phenomenon in its fullest extent."

    Monk's life of Wittgenstein is such a one."--"The Christian Science Monitor."

    With problems and solutions. Includes 99 illustrations.