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.

    Through the astonishing combined achievements of natural scientists worldwide, we now have a detailed account of how galaxies and stars, planets and living organisms, human beings and human consciousness came to be. And yet . . . we thirst for answers to questions that have haunted humanity from the very beginning. What is our place in the 14-billion-year history of the universe? What roles do we play in Earth's history? How do we connect with the intricate web of life on Earth?In Journey of the Universe Brian Thomas Swimme and Mary Evelyn Tucker tell the epic story of the universe from an inspired new perspective, weaving the findings of modern science together with enduring wisdom found in the humanistic traditions of the West, China, India, and indigenous peoples. The authors explore cosmic evolution as a profoundly wondrous process based on creativity, connection, and interdependence, and they envision an unprecedented opportunity for the world's people to address the daunting ecological and social challenges of our times.Journey of the Universe transforms how we understand our origins and envision our future. Though a little book, it tells a big story—one that inspires hope for a way in which Earth and its human civilizations could flourish together.This book is part of a larger project that includes a documentary film, an educational DVD series, and a website. For more information, please consult the website, journeyoftheuniverse.org.

    Frizzle were a physics student of Stephen Hawking, she might have written THE UNIVERSE IN YOUR HAND, a wild tour through the reaches of time and space, from the interior of a proton to the Big Bang to the rough suburbs of a black hole. It's friendly, excitable, erudite, and cosmic."—Jordan Ellenberg, New York Times besteselling author of How Not To Be WrongQuantum physics, black holes, string theory, the Big Bang, dark matter, dark energy, parallel universes: even if we are interested in these fundamental concepts of our world, their language is the language of math. Which means that despite our best intentions of finally grasping, say, Einstein's Theory of General Relativity, most of us are quickly brought up short by a snarl of nasty equations or an incomprehensible graph.Christophe Galfard's mission in life is to spread modern scientific ideas to the general public in entertaining ways. Using his considerable skills as a brilliant theoretical physicist and successful young adult author, The Universe in Your Hand employs the immediacy of simple, direct language to show us, not explain to us, the theories that underpin everything we know about our universe. To understand what happens to a dying star, we are asked to picture ourselves floating in space in front of it. To get acquainted with the quantum world, we are shrunk to the size of an atom and then taken on a journey. Employing everyday similes and metaphors, addressing the reader directly, and writing stories rather than equations renders these astoundingly complex ideas in an immediate and visceral way.Utterly captivating and entirely unique, The Universe in Your Hand will find its place among other classics in the field.

    A meld of history and science, this book is a group portrait of some of the greatest minds who ever lived as they wrestled with nature’s most sweeping mysteries. The answers they uncovered still hold the key to how we understand the world.At the end of the seventeenth century—an age of religious wars, plague, and the Great Fire of London—when most people saw the world as falling apart, these earliest scientists saw a world of perfect order. They declared that, chaotic as it looked, the universe was in fact as intricate and perfectly regulated as a clock. This was the tail end of Shakespeare’s century, when the natural land the supernatural still twined around each other. Disease was a punishment ordained by God, astronomy had not yet broken free from astrology, and the sky was filled with omens. It was a time when little was known and everything was new. These brilliant, ambitious, curious men believed in angels, alchemy, and the devil, and they also believed that the universe followed precise, mathematical laws—-a contradiction that tormented them and changed the course of history.The Clockwork Universe is the fascinating and compelling story of the bewildered geniuses of the Royal Society, the men who made the modern world.

    Three ever widening domains are presented--the planets, the stars, and the large scale universe itself--each including the ones before it and extending outward''--..Title: .Space Atlas..Author: .Trefil, James/ Aldrin, Buzz (FRW)..Publisher: .Random House Inc..Publication Date: .2012/11/06..Number of Pages: .335..Binding Type: .HARDCOVER..Library of Congress: .2012020000

    The sixteenth and seventeenth centuries witnessed the Copernican Revolution, which bodychecked the Earth as the pivot point of creation and joined us with the rest of the cosmos as one planet among many orbiting the Sun. Three centuries later came the second great scientific revolution: the Darwinian Revolution. It removed us from a distinct, divine biological status to place us wholly in the ebb and flow of all terrestrial life. This book describes how we’re in the midst of a third great scientific revolution, five centuries in the making: the Stardust Revolution. It is the merging of the once-disparate realms of astronomy and evolutionary biology, and of the Copernican and Darwinian Revolutions, placing life in a cosmic context. This book takes readers on a grand journey that begins on the summit of California’s Mount Wilson, where astronomers first realized that the universe is both expanding and evolving, to a radio telescope used to identify how organic molecules—the building blocks of life—are made by stars. It’s an epic story told through a scientific cast that includes some of the twentieth century’s greatest minds—including Nobel laureate Charles Townes, who discovered cosmic water—as well as the most ambitious scientific explorers of the twenty-first century, those racing to find another living planet. Today, an entirely new breed of scientists—astrobiologists and astrochemists—are taking the study of life into the space age. Astrobiologists study the origins, evolution, and distribution of life, not just on Earth, but in the universe. Stardust science is filling in the missing links in our evolutionary story, ones that extend our family tree back to the stars.

    "A masterpiece of science."—Werner von Braun.

    

    In the oceans, though, living space has both vertical and horizontal dimensions: with an average depth of 3800 meters, the oceans offer 99% of the space on Earth where life can develop. And the deep sea, which has been immersed in total darkness since the dawn of time, occupies 85% of ocean space, forming the planet’s largest habitat.  Yet these depths abound with mystery. The deep sea is mostly uncharted—only about 5 percent of the seafloor has been mapped with any reasonable degree of detail—and we know very little about the creatures that call it home. Current estimates about the number of species yet to be found vary between ten and thirty million.  The deep sea no longer has anything to prove; it is without doubt Earth’s largest reservoir of life.Combining the latest scientific discoveries with astonishing color imagery, The Deep takes readers on a voyage into the darkest realms of the ocean. Revealing nature’s oddest and most mesmerizing creatures in crystalline detail, The Deep features more than two hundred color photographs of terrifying sea monsters, living fossils, and ethereal bioluminescent creatures, some photographed here for the very first time. Accompanying these breathtaking photographs are contributions from some of the world’s most respected researchers that examine the biology of deep-sea organisms, the ecology of deep-sea habitats, and the history of deep-sea exploration.An unforgettable visual and scientific tour of the teeming abyss, The Deep celebrates the incredible diversity of life on Earth and will captivate anyone intrigued by the unseen—and unimaginable—creatures of the deep sea.

    His influential work spans many practices over a 23-year period, from music packaging to installation work to printmaking. Here, he reveals his personal notebooks, photographs, sketches, and abandoned routes to iconic Radiohead artworks. Arranged chronologically, each chapter is dedicated to a major work—whether an album cover, promotional piece, or a personal project—and is presented as a step-by-step working case study. Featuring commentary by Thom Yorke and never-before-seen archival material, this is the first deep dive into Donwood’s creative practice and the artistic freedom afforded to him by working for a major music act. It is a must-have for fans of the band and anyone interested in graphic design and popular culture.

    In doing so, the authors synthesize information from astronomy, biology, and paleontology, and apply it to what we know about the rise of life on Earth and to what could possibly happen elsewhere in the universe. Everyone who has been thrilled by the recent discoveries of extrasolar planets and the indications of life on Mars and the Jovian moon Europa will be fascinated by Rare Earth, and its implications for those who look to the heavens for companionship.

    But are there limits to what we can discover about our physical universe?In this very personal journey to the edges of knowledge, Marcus du Sautoy investigates how leading experts in fields from quantum physics and cosmology, to sensory perception and neuroscience, have articulated the current lie of the land. In doing so, he travels to the very boundaries of understanding, questioning contradictory stories and consulting cutting edge data.Is it possible that we will one day know everything? Or are there fields of research that will always lie beyond the bounds of human comprehension? And if so, how do we cope with living in a universe where there are things that will forever transcend our understanding?In What We Cannot Know, Marcus du Sautoy leads us on a thought-provoking expedition to the furthest reaches of modern science. Prepare to be taken to the edge of knowledge to find out if there’s anything we truly cannot know.

    But there remains a critical gap in our knowledge: we still know very little about what happened in the first seconds after the Big Bang. At the Edge of Time focuses on what we have recently learned and are still striving to understand about this most essential and mysterious period of time at the beginning of cosmic history.Delving into the remarkable science of cosmology, Dan Hooper describes many of the extraordinary and perplexing questions that scientists are asking about the origin and nature of our world. Hooper examines how we are using the Large Hadron Collider and other experiments to re-create the conditions of the Big Bang and test promising theories for how and why our universe came to contain so much matter and so little antimatter. We may be poised to finally discover how dark matter was formed during our universe's first moments, and, with new telescopes, we are also lifting the veil on the era of cosmic inflation, which led to the creation of our world as we know it.Wrestling with the mysteries surrounding the initial moments that followed the Big Bang, At the Edge of Time presents an accessible investigation of our universe and its origin.

    While they're at it, they helpfully demystify many complicated things we do know about, from quarks and neutrinos to gravitational waves and exploding black holes. With equal doses of humor and delight, they invite us to see the universe as a vast expanse of mostly uncharted territory that's still ours to explore.This entertaining illustrated science primer is the perfect book for anyone who's curious about all the big questions physicists are still trying to answer.

    A total eclipse of the Sun will be visible from within a narrow corridor that traverses the United States. The path of the Moon's umbral shadow will begin in the northern Pacific and cross the USA from west to east from Oregon to South Carolina. The Moon's penumbral shadow will produce a partial eclipse visible from most of North America. In fact, the 2017 full eclipse is such an important sky event that sky watchers in Europe are already planning trips to view it. 2017 Guide to the Night Sky provides all of the information needed to view this exciting eclipse and track its path. The time zones and transit of the eclipse will be noted inside the book's jacket for quick and easy reference.The night sky makes for exciting viewing any time of the year, and 2017 Guide to the Night Sky is the ideal guide to help amateur astronomers find their way for the entire 12 months. With monthly charts and other diagrams set for a latitude of 40 degrees North, it shows how the visible stars change from month to month and includes the many sky events that occur throughout the year. It is highly practical for beginning sky gazers because the objects and events may be observed with the naked eye, or nothing more complicated than a pair of binoculars.The month-by-month guides include sky activity charts and moon calendars; meteors (with dates of showers, including hourly rate of radiants); the Planets; ecliptic charts; diagrams of interesting events; plus sky and constellation maps throughout.An appendix includes a full glossary; the Greek Alphabet; the constellation genitives, abbreviations and English names; a table of common asterisms; further information; recommended astronomy journals, societies, institutions and organizations; software, and internet sources.Especially useful for beginning sky watchers, this guide will be fully updated to 2017. Its small and light format makes it the ideal portable reference for backyard astronomers.