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.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    ASIN: 0312295170

    Role of the unconscious in invention; the medium of ideas — do they come to mind in words? in pictures? in mathematical terms? Much more. "It is essential for the mathematician, and the layman will find it good reading." — Library Journal.

    He explores the new paradigm (replacing the centuries-old Newtonian view of the universe) that recognizes the collective and holistic properties of physical systems and the power of self-organization. He casts the laws in physics in the role of a "blueprint," embodying a grand cosmic scheme that progressively unfolds as the universe develops.Challenging the viewpoint that the physical universe is a meaningless collection particles, he finds overwhelming evidence for an underlying purpose: "Science may explain all the processes whereby the universe evolves its own destiny, but that still leaves room for there to be a meaning behind existence."

    Linear algebra is tightly integrated into the text.

    Through the introduction of MTV and the alternative rock revolution, it's been many things. Rude. Brilliant. Soulful. Snotty. Angry. Delirious. In the past two decades, genres have spawned like mad, from goth, indie rock, and gangsta rap to emo and the garage rock revival. This twentieth-anniversary tribute celebrates the passion and fury of the music, with original essays, quotes, and photographs by contributors who are as hopelessly obsessed with it as you are. SPIN: 20 Years of Alternative Music features: Alan Light on Beastie Boys, Ann Powers on U2, Charles Aaron on R.E.M., Dave Eggers on The Smiths + Morrissey, Marc Spitz on Goth, Simon Reynolds on Depeche Mode + Synth-pop, Dave Itzkoff on ’80s Teen Movies, Chuck Klosterman on Weezer, Will Hermes on Radiohead, Neil Strauss on Nine Inch Nails + Industrial, Sacha Jenkins on Public Enemy, Andy Greenwald on Emo, RJ Smith on Gangsta Rap, Jon Dolan on The White Stripes, Chris Norris on Nirvana, Doug Brod on Oasis + Britpop, Jim DeRogatis on Smashing Pumpkins, Laura Sinagra on Courtney Love, Ta-Nehisi Coates on Tupac

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    This brilliant account celebrates the incredible range of Greek achievement: the architectural marvels of the Athenian Acropolis; the birth of drama and the timeless tragedies of Aeschylus, Euripides, and Sophocles; Homer's epics; the philosophical revolutions of Plato and Aristotle; and the conquests of Alexander the Great. Lavishly illustrated with photographs and maps, The Greek Achievement paints a sweeping panorama of the ancient Greeks' world and provides a rich, contemporary overview of their enduring contribution to world civilization.

    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.

    He was 19 years old when he won the 2005 French Open in his very first appearance at the event. A left-hander with a booming forehand, Nadal had been known as a clay-court specialist since playing his first pro tournaments in 2001. His aggressive style, flowing hair, and muscular build have made him a fan favorite as well. He won his first singles title in 2004, and had a breakout season in 2005, winning at Monte Carlo, Rome, Barcelona, and Stuttgart as well as at Roland Garros. He won the French Open again in 2006, 2007, and 2008, defeating rival Roger Federer in the final each time. In 2008 he broke through at Wimbledon, beating Federer to win the men's singles title in a spectacular fashion. No Nadal fan will want to be without this comprehensive biography.

    How to make sense of them? The answer lies in mathematical modeling, a science with applications in a host of biological systems. Soccermatics brings the two together in a fascinating, mind-bending synthesis.What's the similarity between an ant colony and Total Football, Dutch style? How is the Barcelona midfield linked geometrically? And how can we relate the mechanics of a Mexican Wave to the singing of cicadas in an Australian valley? Welcome to the world of mathematical modeling, expressed brilliantly by David Sumpter through the prism of soccer. Soccer is indeed more than a game and this book is packed with game theory. After reading it, you will forever watch the game with new eyes.

    As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Françoise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

    Dealing with measure theory and Lebesque integration, this is an introductory graduate text.

    Hofstadter has been grappling with the mysteries of human thought for over thirty years. Now, with his trademark wit and special talent for making complex ideas vivid, he has partnered with Sander to put forth a highly novel perspective on cognition.We are constantly faced with a swirling and intermingling multitude of ill-defined situations. Our brain’s job is to try to make sense of this unpredictable, swarming chaos of stimuli. How does it do so? The ceaseless hail of input triggers analogies galore, helping us to pinpoint the essence of what is going on. Often this means the spontaneous evocation of words, sometimes idioms, sometimes the triggering of nameless, long-buried memories.Why did two-year-old Camille proudly exclaim, “I undressed the banana!”? Why do people who hear a story often blurt out, “Exactly the same thing happened to me!” when it was a completely different event? How do we recognize an aggressive driver from a split-second glance in our rearview mirror? What in a friend’s remark triggers the offhand reply, “That’s just sour grapes”? What did Albert Einstein see that made him suspect that light consists of particles when a century of research had driven the final nail in the coffin of that long-dead idea?The answer to all these questions, of course, is analogy-making—the meat and potatoes, the heart and soul, the fuel and fire, the gist and the crux, the lifeblood and the wellsprings of thought. Analogy-making, far from happening at rare intervals, occurs at all moments, defining thinking from top to toe, from the tiniest and most fleeting thoughts to the most creative scientific insights.Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core—the incessant, unconscious quest for strong analogical links to past experiences—this book puts forth a radical and deeply surprising new vision of the act of thinking.