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.

    She draws on conversations with hundreds of the world's top scientists and on her own work as a Pulitzer Prize-winning writer for the New York Times to create a thoroughly entertaining guide to scientific literacy. Angier's gifts are on full display in The Canon, an ebullient celebration of science that stands to become a classic. The Canon is vital reading for anyone who wants to understand the great issues of our time -- from stem cells and bird flu to evolution and global warming. And it's for every parent who has ever panicked when a child asked how the earth was formed or what electricity is. Angier's sparkling prose and memorable metaphors bring the science to life, reigniting our own childhood delight in discovering how the world works. "Of course you should know about science," writes Angier, "for the same reason Dr. Seuss counsels his readers to sing with a Ying or play Ring the Gack: These things are fun and fun is good." The Canon is a joyride through the major scientific disciplines: physics, chemistry, biology, geology, and astronomy. Along the way, we learn what is actually happening when our ice cream melts or our coffee gets cold, what our liver cells do when we eat a caramel, why the horse is an example of evolution at work, and how we're all really made of stardust. It's Lewis Carroll meets Lewis Thomas -- a book that will enrapture, inspire, and enlighten.

    This is the sky as it has never been presented before: the realm of stars and planets, but also of gods, devils, weather wizards, flying sailors, medieval aliens, mythological animals and rampaging spirits. The reader is taken on a tour of star-obsessed cultures around the world, learning about Tibetan sky burials, star-covered Inuit dancing coats, Mongolian astral prophets and Sir William Herschel's 1781 discovery of Uranus, the first planet to be found since antiquity. Even stranger are the forgotten stories from European history, like the English belief of the Middle Ages in ships that sailed a sea above the clouds, 16th-century German UFO sightings and the Edwardian aristocrat who mistakenly mapped alien-made canals on the surface of Mars.As the intricacies of our universe are today being revealed with unprecedented clarity, there has never been a better time for a highly readable book as beautiful as the night sky to contextualise the scale of these achievements for the general reader.

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    It defines our experience of the world; it echoes through our every waking hour. Time is the very foundation of conscious experience. Yet as familiar as it is, time is also deeply mysterious. We cannot see, hear, smell, taste, or touch it. Yet we do "feel" it--or at least we "think" we feel it. No wonder poets, writers, philosophers, and scientists have grappled with time for centuries.In his latest book, award-winning science writer Dan Falk chronicles the story of how humans have come to understand time over the millennia, and by drawing from the latest research in physics, psychology, and other fields, Falk shows how that understanding continues to evolve. "In Search of Time" begins with our earliest ancestors' perception of time and the discoveries that led--with much effort--to the Gregorian calendar, atomic clocks, and "leap seconds." Falk examines the workings of memory, the brain's remarkable "bridge across time," and asks whether humans are unique in their ability to recall the past and imagine the future. He explores the possibility of time travel, and the paradoxes it seems to entail. Falk looks at the quest to comprehend the beginning of time and how time--and the universe--may end. Finally, he examines the puzzle of time's "flow," and the remarkable possibility that the passage of time may be an illusion.Entertaining, illuminating, and ultimately thought provoking, "In Search of Time "reveals what some of our most insightful thinkers have had to say about time, from Aristotle to Kant, from Newton to Einstein, and continuing with the brightest minds of today.

    

    Why don't facts work? Why, that is, did the obviously intelligent man beside him sincerely believe in Adam and Eve, the Garden of Eden and a six-thousand-year-old Earth, in spite of the evidence against them? It was the start of a journey that would lead Storr all over the world--from Texas to Warsaw to the Outer Hebrides--meeting an extraordinary cast of modern heretics whom he tries his best to understand. He goes on a tour of Holocaust sites with David Irving and a band of neo-Nazis; experiences his own murder during past-life regression hypnosis; discusses the looming One World Government with iconic climate skeptic Lord Monckton; and investigates the tragic life and death of a woman who believed her parents were high priests in a baby-eating cult. Using a unique mix of highly personal memoir, investigative journalism, and the latest research from neuroscience and experimental psychology, Storr reveals how the stories we tell ourselves about the world invisibly shape our beliefs, and how the neurological "hero maker" inside us all can so easily lead to self-deception, toxic partisanship, and science denial.

    Conceived as a handbook and teaching aid for artists, instructors, and students, this timeless book presents Albers’s unique ideas of color experimentation in a way that is valuable to specialists as well as to a larger audience.Originally published by Yale University Press in 1963 as a limited silkscreen edition with 150 color plates, Interaction of Color first appeared in paperback in 1971, featuring ten representative color studies chosen by Albers. The paperback has remained in print ever since and is one of the most influential resources on color for countless readers.This new paperback edition presents a significantly expanded selection of more than thirty color studies alongside Albers’s original unabridged text, demonstrating such principles as color relativity, intensity, and temperature; vibrating and vanishing boundaries; and the illusions of transparency and reversed grounds. Now available in a larger format and with enhanced production values, this expanded edition celebrates the unique authority of Albers’s contribution to color theory and brings the artist’s iconic study to an eager new generation of readers.

    Ask them the meaning of 'relativity' and few of them will be able to tell you what it is.The basic principles of relativity have not changed since Russell first published his lucid guide for the general reader. The ABC of Relativity is Bertrand Russell's most brilliant work of scientific popularisation. With marvellous lucidity he steers the reader who has no knowledge of maths or physics through the subtleties of Einstein's thinking. In easy, assimilable steps, he explains the theories of special and general relativity and describes their practical application to, amongst much else, discoveries about gravitation and the invention of the hydrogen bomb.

    Now Pollan turns his sharp insight to the craft of building, as he recounts the process of designing and constructing a small one-room structure on his rural Connecticut property--a place in which he hoped to read, write and daydream, built with his two own unhandy hands.Invoking the titans of architecture, literature and philosophy, from Vitrivius to Thoreau, from the Chinese masters of feng shui to the revolutionary Frank Lloyd Wright, Pollan brilliantly chronicles a realm of blueprints, joints and trusses as he peers into the ephemeral nature of "houseness" itself. From the spark of an idea to the search for a perfect site to the raising of a ridgepole, Pollan revels in the infinitely detailed, complex process of creating a finished structure. At once superbly written, informative and enormously entertaining, A Place of My Own is for anyone who has ever wondered how the walls around us take shape--and how we might shape them ourselves.A Place of My Own recounts his two-and-a-half-year journey of discovery in an absorbing narrative that deftly weaves the day-to-day work of design and building--from siting to blueprint, from the pouring of foundations to finish carpentry--with reflections on everything form the power of place to shape our lives to the question of what constitutes "real work" in a technological society.A book about craft that is itself beautifully crafted, linking the world of the body and material things with the realm of mind, heart, and spirit, A Place of My Own has received extraordinary praise.

    Science should be on our daily conversation menu, along with topics like politics, books, sports, or the latest prestige cable drama. Conversations about science, he tells us, shouldn't be left to the experts. In The Dialogues, Johnson invites us to eavesdrop on a series of nine conversations, in graphic-novel form--written and drawn by Johnson--about "the nature of the universe." The conversations take place all over the world, in museums, on trains, in restaurants, in what may or may not be Freud's favorite coffeehouse. The conversationalists are men, women, children, experts, and amateur science buffs. The topics of their conversations range from the science of cooking to the multiverse and string theory. The graphic form is especially suited for physics; one drawing can show what it would take many words to explain.In the first conversation, a couple meets at a costume party; they speculate about a scientist with superhero powers who doesn't use them to fight crime but to do more science, and they discuss what it means to have a "beautiful equation" in science. Their conversation spills into another chapter ("Hold on, you haven't told me about light yet"), and in a third chapter they exchange phone numbers. Another couple meets on a train and discusses immortality, time, black holes, and religion. A brother and sister experiment with a grain of rice. Two women sit in a sunny courtyard and discuss the multiverse, quantum gravity, and the anthropic principle. After reading these conversations, we are ready to start our own.

    Tolkien.When J.R.R. Tolkien wrote The Hobbit, he was already an accomplished amateur artist, and drew illustrations for his book while it was still in manuscript. The Hobbit as first printed had ten black and white pictures, two maps, and binding and dust-jacket designs by its author. Later, Tolkien also painted five scenes for colour plates which are some of his best work. His illustrations for The Hobbit add an extra dimension to that remarkable book, and have long influenced how readers imagine Bilbo Baggins and his world.To celebrate the 75th anniversary of the publication of The Hobbit, the complete artwork created by the author for his story has been collected in The Art of The Hobbit by J.R.R. Tolkien. Including related pictures, more than one hundred sketches, drawings, paintings, maps, and plans are presented here, preliminary and alternate versions and experimental designs as well as finished art. Some of these images are now published for the first time, and others for the first time in colour. Fresh digital scans from the Bodleian Libraries in Oxford and Marquette University in Wisconsin allow Tolkien’s Hobbit pictures to be seen more vividly than ever before.The Art of The Hobbit by J.R.R. Tolkien has been written and edited by Wayne G. Hammond and Christina Scull, two of the leading experts on Tolkien and authors of the acclaimed J.R.R. Tolkien: Artist and Illustrator, The Lord of the Rings: A Reader’s Companion, and The J.R.R. Tolkien Companion and Guide.

    Vivid photos capture these historically important machinesincluding the Eniac, Crays 13, Apple I and IIwhile authoritative text profiles each, telling the stories of their innovations and peculiarities. Thirty-five machines are profiled in over 100 extraordinary color photographs, making Core Memory a surprising addition to the library of photography collectors and the ultimate geek-chic gift.

    Finding patterns and making meaningful connections inside complex data networks has emerged as one of the biggest challenges of the twenty-first century. In recent years, designers, researchers, and scientists have begun employing an innovative mix of colors, symbols, graphics, algorithms, and interactivity to clarify, and often beautify, the clutter. From representing networks of friends on Facebook to depicting interactions among proteins in a human cell, Visual Complexity presents one hundred of the most interesting examples of information-visualization by the field's leading practitioners.

    This XXL-format comprehensive survey is the most complete book ever made on the subject of this Italian painter, sculptor, architect, engineer, scientist and all-around genius. With huge, full-bleed details of Leonardo's masterworks, this highly original publication allows the reader to inspect the subtlest facets of his brushstrokes. * Part I explores Leonardo's life and work in ten chapters. All of his paintings are interpreted in depth, with The Annunciation and The Last Supper featured on large double-spreads. * Part II comprises a catalogue raisonn? of Leonardo's paintings, which covers all of his surviving and lost painted works and includes texts describing their states of preservation. * Part III contains an extensive catalogue of his drawings (numbering in the thousands, they cannot all be reproduced in one book); 663 are presented, arranged by category (architecture, technical, anatomical, figures, proportion, cartography, etc). This sumptuous TASCHEN offering is the most thorough and beautifully produced Leonardo book ever published, and this special edition offers it for a third of the usual price.