In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Clear explanations are detailed with many current examples.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    

    Some mammoths were smaller than children. Owls are the dumbest birds in the world. Very few people with Tourette's syndrome swear. You can't get a six-pack from doing sit-ups. King Arthur's sword wasn't called Excalibur. Milk doesn't make your bones strong. There's no bones in your fingers. The Bible states that humans can't become angels. Humans have more than two nostrils. It's impossible to slide down a bannister. At a wedding, the bride doesn't walk down the aisle. Ties were invented for war, not fashion. Most Disney classics made almost no money. Slavery has only been illegal in the UK since 2010. George Washington wasn't the first American President. Velcro doesn’t exist. Nobody knows why we sleep.

    

    It has also often required oppressive and incomprehensible mathematics. Game Theory at Work steers around math and pedagogy to make this innovative tool accessible to a larger audience and allow all levels of business to use it to both improve decision-making skills and eliminate potentially lethal uncertainty.This proven tool requires everyone in an organization to look at the competition, guage his or her own responses to their actions, and then establish an appropriate strategy. Game Theory at Work will help business leaders at all levels improve their overall performance in:NegotiatingDecision makingEstablishing strategic alliancesMarketingPositioningBrandingPricing

    Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's mostamazing accomplishments. Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. RobynArianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a newand radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of theradio wave, teasing it out of the mathematical language itself. Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    This gorgeous book features clear, entertaining, and enlightening commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties.  With its lush format and layflat dimensions that closely approximate the golden ratio, this is the ultimate coffee table book for math enthusiasts, architects, designers, and fans of sacred geometry.

    The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology.Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings.

    Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.

    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.

    Rare Book