The book gives more than it promises, the text as well as the extensive bibliography including contributions of the analysts."-Hibbert Journal

    A brilliantly clear and penetrating exposition of developments in physical science and mathematics brought about by the advent of non-Euclidean geometries, including in-depth coverage of the foundations of geometry, the theory of time, Einstein's theory of relativity and its consequences, other key topics.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    Quantum physics is an antidote to the moral sterility and mechanistic approach of scientific materialism and is the best and clearest approach to understanding our universe. In short, quantum physics is indeed the theory of everything.Here in 17 chapters, Dr. Goswami and his friends and colleagues discuss, among other things, how quantum physics affects our understanding of:ZenThoughts, feelings, and intuitionsDreamsKarma, death, and reincarnationGod's will, evolution, and purposeThe meaning of dreamsThe spiritualization of economics and business, politics and education, and society itselfThis fascinating new book will appeal to a wide array of readers, ranging from those interested in the new physics to those captivated by the spiritual implications of the latest scientific breakthroughs.

    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 well-established two-book course is designed for class teaching and private study leading to GCSE examinations in mathematics and further Mathematics at A Level.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    Fully stocked with solved problemsN950 of themNit shows you how to solve problems that may not have been fully explained in class. Plus you ge"

    'Paul,' he said, 'you have such strange ideas. Why don't you write them down? I shall write a reply, we publish the whole thing and I promise you—we shall have a lot of fun.' " Although Lakatos died before he could write his reply, For and Against Method reconstructs his original counter-arguments from lectures and correspondence previously unpublished in English, allowing us to enjoy the "fun" two of this century's most eminent philosophers had, matching their wits and ideas on the subject of the scientific method.For and Against Method opens with an imaginary dialogue between Lakatos and Feyerabend, which Matteo Motterlini has constructed, based on their published works, to synthesize their positions and arguments. Part one presents the transcripts of the last lectures on method that Lakatos delivered. Part two, Feyerabend's response, consists of a previously published essay on anarchism, which began the attack on Lakatos's position that Feyerabend later continued in Against Method. The third and longest section consists of the correspondence Lakatos and Feyerabend exchanged on method and many other issues and ideas, as well as the events of their daily lives, between 1968 and Lakatos's death in 1974.The delight Lakatos and Feyerabend took in philosophical debate, and the relish with which they sparred, come to life again in For and Against Method, making it essential and lively reading for anyone interested in these two fascinating and controversial thinkers and their immense contributions to philosophy of science."The writings in this volume are of considerable intellectual importance, and will be of great interest to anyone concerned with the development of the philosophical views of Lakatos and Feyerabend, or indeed with the development of philosophy of science in general during this crucial period."—Donald Gillies, British Journal for the Philosophy of Science (on the Italian edition)"A stimulating exchange of letters between two philosophical entertainers."—Tariq Ali, The IndependentImre Lakatos (1922-1974) was professor of logic at the London School of Economics. He was the author of Proofs and Refutations and the two-volume Philosophical Papers. Paul Feyerabend (1924-1994) was educated in Europe and held numerous teaching posts throughout his career. Among his books are Against Method; Science in a Free Society; Farewell to Reason; and Killing Time: The Autobiography of Paul Feyerabend, the last published by the University of Chicago Press.

    

    This is done in a way that is not only easy to understand, but is actually fun! Professors and engineers, with high school and college students following closely, comprise the largest percentage of our readers. It is a must-have for anyone interested in music, mathematics, physics, engineering, or complex science. Dr. Yoichiro Nambu, 2008 Nobel Prize Winner in Physics, served as a senior adviser to the English version of Who is Fourier? A Mathematical Adventure.

    Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.

    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.