Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.

    Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    Tolkien is "the most influential author of the century," and The Lord of the Rings is "the book of the century." In support of these claims, the prominent medievalist and scholar of fantasy Professor Tom Shippey now presents us with a fascinating companion to the works of J.R.R. Tolkien, focusing in particular on The Hobbit, The Lord of the Rings, and The Silmarillion. The core of the book examines The Lord of the Rings as a linguistic and cultural map and as a response to the meaning of myth. It presents a unique argument to explain the nature of evil and also gives the reader a compelling insight into the unparalleled level of skill necessary to construct such a rich and complex story. Shippey also examines The Hobbit, explaining the hobbits' anachronistic relationship to the heroic world of Middle-earth, and shows the fundamental importance of The Silmarillion to the canon of Tolkien's work. He offers as well an illuminating look at other, lesser-known works in their connection to Tolkien's life.

    Forster's Aspects of the Novel is an innovative and effusive treatise on a literary form that, at the time of publication, had only recently begun to enjoy serious academic consideration. This Penguin Classics edition is edited with an introduction by Oliver Stallybrass, and features a new preface by Frank Kermode.First given as a series of lectures at Cambridge University, Aspects of the Novel is Forster's analysis of this great literary form. Here he rejects the 'pseudoscholarship' of historical criticism - 'that great demon of chronology' - that considers writers in terms of the period in which they wrote and instead asks us to imagine the great novelists working together in a single room. He discusses aspects of people, plot, fantasy and rhythm, making illuminating comparisons between novelists such as Proust and James, Dickens and Thackeray, Eliot and Dostoyevsky - the features shared by their books and the ways in which they differ. Written in a wonderfully engaging and conversational manner, this penetrating work of criticism is full of Forster's habitual irreverence, wit and wisdom.In his new introduction, Frank Kermode discusses the ways in which Forster's perspective as a novelist inspired his lectures. This edition also includes the original introduction by Oliver Stallybrass, a chronology, further reading and appendices.E. M. Forster (1879-1970) was a noted English author and critic and a member of the Bloomsbury group. His first novel, Where Angels Fear To Tread appeared in 1905. The Longest Journey appeared in 1907, followed by A Room With A View (1908), based partly on the material from extended holidays in Italy with his mother. Howards End (1910) was a story that centered on an English country house and dealt with the clash between two families, one interested in art and literature, the other only in business. Maurice was revised several times during his life, and finally published posthumously in 1971.If you enjoyed Aspects of the Novel, you might like Forster's A Room with a View, also available in Penguin Classics.

    Originally published in 1966, it has never gone out of print and has influenced generations of readers all over the world. It includes the famous essays "Notes on Camp" and "Against Interpretation," as well as her impassioned discussions of Sartre, Camus, Simone Weil, Godard, Beckett, Lévi-Strauss, science-fiction movies, psychoanalysis, and contemporary religious thought.This edition has a new afterword, "Thirty Years Later," in which Sontag restates the terms of her battle against philistinism and against ethical shallowness and indifference.

    Now a distinguished scholar offers the first comprehensive account of the evolutionary origins of art and storytelling. Brian Boyd explains why we tell stories, how our minds are shaped to understand them, and what difference an evolutionary understanding of human nature makes to stories we love.Art is a specifically human adaptation, Boyd argues. It offers tangible advantages for human survival, and it derives from play, itself an adaptation widespread among more intelligent animals. More particularly, our fondness for storytelling has sharpened social cognition, encouraged cooperation, and fostered creativity.After considering art as adaptation, Boyd examines Homer's "Odyssey" and Dr. Seuss's "Horton Hears a Who!" demonstrating how an evolutionary lens can offer new understanding and appreciation of specific works. What triggers our emotional engagement with these works? What patterns facilitate our responses? The need to hold an audience's attention, Boyd underscores, is the fundamental problem facing all storytellers. Enduring artists arrive at solutions that appeal to cognitive universals: an insight out of step with contemporary criticism, which obscures both the individual and universal. Published for the bicentenary of Darwin's birth and the 150th anniversary of the publication of "Origin of Species, " Boyd's study embraces a Darwinian view of human nature and art, and offers a credo for a new humanism.

    In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    The Weird and the Eerie are closely related but distinct modes, each possessing its own distinct properties. Both have often been associated with Horror, yet this emphasis overlooks the aching fascination that such texts can exercise. The Weird and the Eerie both fundamentally concern the outside and the unknown, which are not intrinsically horrifying, even if they are always unsettling. Perhaps a proper understanding of the human condition requires examination of liminal concepts such as the weird and the eerie. These two modes will be analysed with reference to the work of authors such as H.P. Lovecraft, H.G. Wells, M.R. James, Christopher Priest, Joan Lindsay, Nigel Kneale, Daphne Du Maurier, Alan Garner and Margaret Atwood, and films by Stanley Kubrick, Jonathan Glazer and Christoper Nolan.

    Throughout, Chabon energetically argues for a return to the thrilling, chilling origins of storytelling, rejecting the false walls around "serious" literature in favor of a wide-ranging affection.Cover art by Jordan Crane.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    This new and expanded third edition continues to offer students and readers the best one-volume introduction to the field.The bewildering variety of approaches, theorists and technical language is lucidly and expertly unraveled. Unlike many books which assume certain positions about the critics and the theories they represent, Peter Barry allows readers to develop their own ideas once first principles and concepts have been grasped.

    Brian Greene, one of the world's leading string theorists, peels away the layers of mystery surrounding string theory to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy.Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years. Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom. In this brilliantly articulated and refreshingly clear book, Greene relates the scientific story and the human struggle behind twentieth-century physics' search for a theory of everything.Through the masterful use of metaphor and analogy, The Elegant Universe makes some of the most sophisticated concepts ever contemplated viscerally accessible and thoroughly entertaining, bringing us closer than ever to understanding how the universe works.