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.

    For the first time in history, the secrets of the living brain are being revealed by a battery of high tech brain scans devised by physicists. Now what was once solely the province of science fiction has become a startling reality. Recording memories, telepathy, videotaping our dreams, mind control, avatars, and telekinesis are not only possible; they already exist. The Future of the Mind gives us an authoritative and compelling look at the astonishing research being done in top laboratories around the world—all based on the latest advancements in neuroscience and physics. One day we might have a "smart pill" that can enhance our cognition; be able to upload our brain to a computer, neuron for neuron; send thoughts and emotions around the world on a "brain-net"; control computers and robots with our mind; push the very limits of immortality; and perhaps even send our consciousness across the universe. Dr. Kaku takes us on a grand tour of what the future might hold, giving us not only a solid sense of how the brain functions but also how these technologies will change our daily lives. He even presents a radically new way to think about "consciousness" and applies it to provide fresh insight into mental illness, artificial intelligence and alien consciousness. With Dr. Kaku's deep understanding of modern science and keen eye for future developments, The Future of the Mind is a scientific tour de force--an extraordinary, mind-boggling exploration of the frontiers of neuroscience.

    Russolo calls for an infinite expansion of musical vocabulary and sensibility in coordination with that of industrial machinery—“We must enlarge and enrich more and more the domain of musical sounds”—envisioning a machine-based music that would dispense entirely with inherited forms. This publication made the text widely available in English for the first time. Also included is a description of the “First Concert of Futurist Noise Instruments” in Modena, Italy on June 2, 1913.

    But in Art & Physics, Leonard Shlain tracks their breakthroughs side by side throughout history to reveal an astonishing correlation of visions.From teh classical Greek sculptors to Andy Warhol and Jasper Johns, and from Aristotle to Einstein, aritsts have foreshadowed the discoveries of scientists, such as when Money and Cezanne intuited the coming upheaval in physics that Einstein would initiate. In this lively and colorful narrative, Leonard Shlain explores how artistic breakthroughs could have prefigured the visionary insights of physicists on so many occasions throughtout history.Provacative and original, Art & Physics is a seamless integration of the romance of art and the drama of science...and exhilarating history of ideas.

    Every concert-goer and lover of music will take keen pleasure in his notes about the essential features of music, the process of musical composition, inspiration, musical types, and musical execution. Throughout the volume are to he found trenchant comments on such subjects as Wagnerism, the operas of Verdi, musical taste, musical snobbery, the influence of political ideas on Russian music under the Soviets, musical improvisation as opposed to musical construction, the nature of melody, and the function of the critic of music. Musical people of every sort will welcome this first presentation in English of an unusually interesting book.

    Music. Through manifestos, scores, interviews, notes and critical papers, contributors to this in-depth anthology address composing, playing, improvising, teaching, and thinking in and through music. Rather than attempting to distill or define musician's work, ARCANA illuminates it with personal vision and experience.

    Appearing as goddess and demon, gate and pillar, garden and tree, hovering sky and containing vessel, the Feminine is seen as an essential factor in the dialectical relation of individual consciousness, symbolized by the child, to the ungraspable matrix, symbolized by the Great Mother.

    This edition provides increased coverage of taste and smell, circadian rhythms, brain development, and developmental disorders and includes new information on molecular mechanisms and functional brain imaging. Path of Discovery boxes, written by leading researchers, highlight major current discoveries. In addition, readers will be able to assess their knowledge of neuroanatomy with the Illustrated Guide to Human Neuroanatomy, which includes a perforated self-testing workbook.This edition's robust ancillary package includes a bound-in student CD-ROM, an Instructor's Resource CD-ROM, and resources online.

    The Intellectual Devotional is a secular version of the same—a collection of 365 short lessons that will inspire and invigorate the reader every day of the year. Each daily digest of wisdom is drawn from one of seven fields of knowledge: history, literature, philosophy, mathematics and science, religion, fine arts, and music.Impress your friends by explaining Plato's Cave Allegory, pepper your cocktail party conversation with opera terms, and unlock the mystery of how batteries work. Daily readings range from important passages in literature to basic principles of physics, from pivotal events in history to images of famous paintings with accompanying analysis. The book's goal is to refresh knowledge we've forgotten, make new discoveries, and exercise modes of thinking that are ordinarily neglected once our school days are behind us. Offering an escape from the daily grind to contemplate higher things, The Intellectual Devotional is a great way to awaken in the morning or to revitalize one's mind before retiring in the evening.

    With 116 million albums sold worldwide and 25 years on the pop charts to their credit, Pink Floyd is one of the most successful rock groups in history, yet their storyuntil nowis one of the least known. The only continuous member of the band through its entire 40-year history, Nick Mason has witnessed every twist, turn, and sommersault from behind his drum kit. The journey begins with the band's origins as the darlings of London's late 1960s underground and the creation of the classic Pink Floyd sound, all the way through to The Wall and those legendary stadium shows. Here are the players who shaped the band's history and the story behind the storythe inside perspective on, for example, the deterioration and departure of Syd Barrett; the overwhelming success of The Dark Side of the Moon and the resulting pressures and conflicts within the band, including the rift with Roger Waters; and Nick and David Gilmour's decision to put their reputations on the line and continue as Pink Floyd. Packed with rare photographs and vintage Floyd graphics from Nick Mason's extensive private archive, Inside Out is an eye-opener for both veteran fans and those just discovering the group. And, in keeping with the classic Floyd style, the book's cover was designed by Storm Thorgerson, creator of such iconic images as the Dark Side pyramid. Always candid, by turns poignant and funny, Nick's own memories are augmented with extensive research and interviews, making Inside Out a comprehensive history of one of the most brilliant and imaginative bands the world has knownand a masterly memoir of rock and roll.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    Focusing on Europe in the first half of the century and the United States in the postwar years, Douglas Kahn explores aural activities in literature, music, visual arts, theater, and film. Placing aurality at the center of the history of the arts, he revisits key artistic questions, listening to the sounds that drown out the politics and poetics that generated them. Artists discussed include Antonin Artaud, George Brecht, William Burroughs, John Cage, Sergei Eisenstein, Fluxus, Allan Kaprow, Michael McClure, Yoko Ono, Jackson Pollock, Luigi Russolo, and Dziga Vertov.

    The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and Reality covers logical positivism; the problems of induction and confirmation; Karl Popper's theory of science; Thomas Kuhn and "scientific revolutions"; the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend; and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student; a glossary of terms explains key concepts; and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years.Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow.

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    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.