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.

    The Structure of Scientific Revolutions is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty years later, it still has many lessons to teach. With The Structure of Scientific Revolutions, Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context.  Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    This elegant, humane, and engaging book "captures what we know of the development of what makes us human" (Nature).Visit Armand Marie Leroi on the web: http: //armandleroi.com/index.htmlStepping effortlessly from myth to cutting-edge science,

    Clearly, geeks know something about life in the 21st century that other folks don’t—something we all can learn from. Geek Wisdom takes as gospel some 200 of the most powerful and oft-cited quotes from movies (“Where we’re going, we don’t need roads”), television (“Now we know—and knowing is half the battle”), literature (“All that is gold does not glitter”), games, science, the Internet, and more. Now these beloved pearls of modern-day culture have been painstakingly interpreted by a diverse team of hardcore nerds with their imaginations turned up to 11. Yes, this collection of mini-essays is by, for, and about geeks—but it’s just so surprisingly profound, the rest of us would have to be dorks not to read it. So say we all.

    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.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    From the first lesson to the last, each chapter introduces games of increasing complexity and then teaches the game theoretical tools necessary to solve them. Inside, you will find: All the basics fully explained, including pure strategy Nash equilibrium, mixed strategy Nash equilibrium, the mixed strategy algorithm, how to calculate payoffs, strict dominance, weak dominance, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, and more! Dozens of games solved, including the prisoner's dilemma, stag hunt, matching pennies, zero sum games, battle of the sexes/Bach or Stravinsky, chicken/snowdrift, pure coordination, deadlock, and safety in numbers! Crystal clear, line-by-line calculations of every step, with more than 200 images so you don't miss a thing! Tons of applications: war, trade, game shows, and duopolistic competition. Quick, efficient, and to the point, Game Theory 101: The Basics is perfect for introductory game theory, intermediate microeconomics, and political science.

    Little did she know at the time that those simple markings would become the basis of a years-long, life-changing exploration into a mysterious group known only as The Wander Society, as well as the subject of this book.Within these pages, you’ll find the results of Smith’s research: A guide to the Wander Society, a secretive group that holds up the act of wandering, or unplanned exploring, as a way of life. You’ll learn about the group’s mysterious origins, meet fellow wanderers through time, discover how wandering feeds the creative mind, and learn how to best practice the art of wandering, should you choose to accept the mission.

    He demonstrates how hero stories continue to shape our world – arguing that we need them now more than ever.From the Stone Age to the Greek Tragedies, from Shakespeare to Robin Hood, we have always had our heroes. The hero is at the centre of formative myths in every culture and persists to this day in world-conquering books, films and TV shows. But why do these characters continue to inspire us, and why are they so central to storytelling?Scalpel-sharp on the roots of storytelling and enlightening on the history and science of myth, The Hero is essential reading for anyone trying to write or understand fiction. Child teaches us how these stories still shape our minds and behaviour in an increasingly confusing modern world, and with his trademark concision and wit, demonstrates that however civilised we get, we’ll always need heroes.

    The great psychologist dreamed that his work was understood by a wide public, rather than just by psychiatrists, and therefore he agreed to write and edit this fascinating book. Here, Jung examines the full world of the unconscious, whose language he believed to be the symbols constantly revealed in dreams. Convinced that dreams offer practical advice, sent from the unconscious to the conscious self, Jung felt that self-understanding would lead to a full and productive life. Thus, the reader will gain new insights into himself from this thoughtful volume, which also illustrates symbols throughout history. Completed just before his death by Jung and his associates, it is clearly addressed to the general reader.

    These were the concerns of Socrates, who spent his days in the ancient Athenian marketplace asking awkward questions, disconcerting the people he met by showing them how little they genuinely understood. This engaging book introduces the great thinkers in Western philosophy and explores their most compelling ideas about the world and how best to live in it.In forty brief chapters, Nigel Warburton guides us on a chronological tour of the major ideas in the history of philosophy. He provides interesting and often quirky stories of the lives and deaths of thought-provoking philosophers from Socrates, who chose to die by hemlock poisoning rather than live on without the freedom to think for himself, to Peter Singer, who asks the disquieting philosophical and ethical questions that haunt our own times.Warburton not only makes philosophy accessible, he offers inspiration to think, argue, reason, and ask in the tradition of Socrates. A Little History of Philosophy presents the grand sweep of humanity's search for philosophical understanding and invites all to join in the discussion.

    Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on* the relationship between mathematical knots and DNA* how computers based on quantum logic can significantly speed up the factoring of large composite numbers* the relationship between four-dimensional geometry and physical theories of the nature of matter* the application of cellular automata models to social questions and the peregrinations of virtual ants* a novel mathematical model of quasicrystals based on decagon-shaped tilesBlazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.

    In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time.Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.