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.

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    From the first time mankind had an inkling of the vast space that surrounds us, those who study the universe have had to struggle against political and religious preconceptions. They have included some of the most charismatic, courageous, and idiosyncratic thinkers of all time. In Coming of Age in the Milky Way, Timothy Ferris uses his unique blend of rigorous research and captivating narrative skill to draw us into the lives and minds of these extraordinary figures, creating a landmark work of scientific history.

    Readers will find excerpts from bestsellers such as Douglas R. Hofstadter's Gödel, Escher, Bach, Francis Crick's Life Itself, Loren Eiseley's The Immense Journey, Daniel Dennett's Darwin's Dangerous Idea, and Rachel Carson's The Sea Around Us. There are classic essays ranging from J.B.S. Haldane's "On Being the Right Size" and Garrett Hardin's "The Tragedy of the Commons" to Alan Turing's "Computing Machinery and Intelligence" and Albert Einstein's famed New York Times article on "Relativity." And readers will also discover lesser-known but engaging pieces such as Lewis Thomas's "Seven Wonders of Science," J. Robert Oppenheimer on "War and Physicists," and Freeman Dyson's memoir of studying under Hans Bethe.A must-read volume for all science buffs, The Oxford Book of Modern Science Writing is a rich and vibrant anthology that captures the poetry and excitement of scientific thought and discovery.One of New Scientist's Editor's Picks for 2008.

    No one can stop him--but he walks away. A miracle? No...dysentery. Microbes saved the Roman Empire. Nearly a millennium later, the microbes of the Black Death ended the Middle Ages, making possible the Renaissance, western democracy, and the scientific revolution. Soon after, microbes ravaged the Americas, paving the way for their European conquest. Again and again, microbes have shaped our health, our genetics, our history, our culture, our politics, even our religion and ethics. This book reveals much that scientists and cultural historians have learned about the pervasive interconnections between infectious microbes and humans. It also considers what our ongoing fundamental relationship with infectious microbes might mean for the future of the human species. The "good side" of history's worst epidemics The surprising debt we owe to killer diseases Where diseases came from... ...and where they may be going Children of pestilence: disease and civilization From Egypt to Mexico, the Romans to Attila the Hun STDs, sexual behavior, and culture How microbes may shape cultural cycles of puritanism and promiscuity

    All of those organisms are rooted in a single origin, with a common code that underwrites our existence. This paradox - that our biology is indistinct from all life, yet we consider ourselves to be special - lies at the heart of who we are.In this original and entertaining tour of life on Earth, Adam Rutherford explores how many of the things once considered to be exclusively human are not: we are not the only species that communicates, makes tools, utilises fire, or has sex for reasons other than to make new versions of ourselves. Evolution has, however, allowed us to develop our culture to a level of complexity that outstrips any other observed in nature.THE BOOK OF HUMANS tells the story of how we became the creatures we are today, bestowed with the unique ability to investigate what makes us who we are. Illuminated by the latest scientific discoveries, it is a thrilling compendium of what unequivocally fixes us as animals, and reveals how we are extraordinary among them.

    This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. The main text makes no use of equations, but there is a Mathematical Appendix for those desiring stronger fare. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed. This volume offers the reader access to one of the greatest discoveries in the history of physics and one of the outstanding intellectual achievements of the twentieth century.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.

    Along the way he provides an engaging and witty commentary while introducing the lay reader to both classic and cutting-edge concepts in physics, including:What Superman's strength can tell us about the Newtonian physics of force, mass, and accelerationHow Iceman's and Storm's powers illustrate the principles of thermal dynamicsThe physics behind the death of Spider-Man's girlfriend Gwen StacyWhy physics professors gone bad are the most dangerous evil geniuses!

    You’ve had a martini or three, and you mingle through the crowd, wondering how long you need to stay before going out for pizza. Suddenly you’re introduced to someone new, Dr. Nice Tomeetya. You forget the pizza. Now is the perfect time to bring up all those strange questions you’d like to ask during an office visit with your own doctor but haven’t had the guts (or more likely the time) to do so. You’re filled with liquid courage . . . now is your chance! If you’ve ever wanted to ask a doctor . . .•How do people in wheelchairs have sex?•Why do I get a killer headache when I suck down my milkshake too fast?•Can I lose my contact lens inside my head forever?•Why does asparagus make my pee smell?•Why do old people grow hair on their ears?•Is the old adage “beer before liquor, never sicker, liquor before beer . . .” really true? . . . then Why Do Men Have Nipples? is the book for you.Compiled by Billy Goldberg, an emergency medicine physician, and Mark Leyner, bestselling author and well-known satirist, Why Do Men Have Nipples? offers real factual and really funny answers to some of the big questions about the oddities of our bodies.

    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    Could she use quantum tunnelling to get through the neighbour's fence and chase bunnies? What about quantum teleportation to catch squirrels before they climb out of reach? In this witty and informative book, Orzel and Emmy - the talking dog - discuss the key theories of Quantum Physics and its fascinating history. From quarks and gluons to Heisenberg's uncertainty principle, this is the perfect introduction to the fundamental laws which govern the universe.

    Thus began one of the boldest scientific projects in history, the Search for Extraterrestrial Intelligence (SETI). But after a half century of scanning the skies, astronomers have little to report but an eerie silence—eerie because many scientists are convinced that the universe is teeming with life. The problem, argues the leading physicist-astrobiologist Paul Davies, is that we’ve been looking in the wrong place, at the wrong time & in the wrong way. Davies should know. For more than three decades, he's been closely involved with SETI & now chairs its Post-Detection Taskgroup, charged with deciding what to do if we’re confronted with evidence of alien intelligence. In this extraordinary book, he shows how SETI has lost its edge & offers a new exciting road map for the future. Davies believes our search so far has been overly anthropocentric: we tend to assume an alien species will look, think & behave like us. He argues that we need to be far more expansive in our efforts, & in this book he completely redefines the search, challenging existing ideas of what form an alien intelligence might take, how it might try to communicate with us & how we should respond if it does. A provocative & mind-expanding journey, The Eerie Silence will thrill fans of science & science fiction alike.

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.

    Here is the Naked Ape at his most primal in love, at work, at war. Meet man as he really is: relative to the apes, stripped of his veneer as we see him courting, making love, sleeping, socializing, grooming, playing. The Naked Ape takes its place alongside Darwin’s Origin of the Species, presenting man not as a fallen angel, but as a risen ape, remarkable in his resilience, energy and imagination, yet an animal nonetheless, in danger of forgetting his origins. With its penetrating insights on man's beginnings, sex life, habits and our astonishing bonds to the animal kingdom, The Naked Ape is a landmark, at once provocative, compelling and timeless.

    Patrick Smith, airline pilot and author of the web's popular Ask the Pilot feature, separates the fact from fallacy and tells you everything you need to know...-How planes fly, and a revealing look at the men and women who fly them-Straight talk on turbulence, pilot training, and safety-The real story on congestion, delays, and the dysfunction of the modern airport-The myths and misconceptions of cabin air and cockpit automation-Terrorism in perspective, and a provocative look at security-Airfares, seating woes, and the pitfalls of airline customer service-The colors and cultures of the airlines we love to hateCockpit Confidential covers not only the nuts and bolts of flying, but also the grand theater of air travel, from airport architecture to inflight service to the excitement of travel abroad. It's a thoughtful, funny, at times deeply personal look into the strange and misunderstood world of commercial flying.It's the ideal book for frequent flyers, nervous passengers, and global travelers.Refreshed and vastly expanded from the original Ask the Pilot, with approximately 75 percent new material.