In that spirit, Edge.org publisher and author of Know This, John Brockman, asks 206 of the world’s most brilliant minds the 2017 Edge Question: What scientific term or concept ought to be more widely known?Contributors include: author of The God Delusion RICHARD DAWKINS on using animals’ “Genetic Book of the Dead” to reconstruct ecological history; MacArthur Fellow REBECCA NEWBERGER GOLDSTEIN on “scientific realism,” the idea that scientific theories explain phenomena beyond what we can see and touch; author of Seven Brief Lessons on Physics CARLO ROVELLI on “relative information,” which governs the physical world around us; theoretical physicist LAWRENCE M. KRAUSS on the hidden blessings of “uncertainty”; cognitive scientist and author of The Language Instinct STEVEN PINKER on “The Second Law of Thermodynamics”; biogerontologist AUBREY DE GREY on why “maladaptive traits” have been conserved evolutionarily; musician BRIAN ENO on “confirmation bias” in the internet age; Man Booker-winning author of Atonement IAN MCEWAN on the “Navier-Stokes Equations,” which govern everything from weather prediction to aircraft design and blood flow; plus pieces from RICHARD THALER, JARED DIAMOND, NICHOLAS CARR, JANNA LEVIN, LISA RANDALL, KEVIN KELLY, DANIEL COLEMAN, FRANK WILCZEK, RORY SUTHERLAND, NINA JABLONSKI, MARTIN REES, ALISON GOPNIK, and many, many others.

    Your guide to a higher math score on standardized tests*SATACT(R)ASVABGMAT(R)GRE(R)CBEST(R)PRAXIS I(R)GED(R) And More!Why CliffsNotes?Go with the name you know and trustGet the information you need-fast!About the Contents:IntroductionHow to use this bookOverview of the examsPart I: Basic Skills ReviewArithmetic and Data AnalysisAlgebraPart II: Strategies and PracticeMathematical AbilityQuantitative ComparisonData SufficiencyEach section includes a diagnostic test, explanations of rules, concepts withexamples, practice problems with complete explanations, a review test, and aglossary!Test-Prep Essentials from the Experts at CliffsNotes(R)For more test-prep help, visit CliffsNotes.com(R)*SAT is a registered trademark of the College Board, which was not involved inthe production of, and does not endorse, this product.

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    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    Everything around us, including matter, is energy. A deep look into the mysteries of the subatomic world – the particles that make up the atom – provides answers to basic questions about how the universe works. To solve the future of mankind’s energy needs we need to understand the basic building blocks of the universe, including the atom and its parts. By exploring the subatomic world we’ll find more answers to our questions about time, forces like gravity and the matter that surrounds us. More importantly, we’ll find new ways to tap into the energy that exists around us to power our growing needs. In a new branch of particle physics, where tiny particles are thought of as energy waves, we find new answers that may help us in our quest to find alternative energy sources.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    Price begins with the mystery of the arrow of time. Why, for example, does disorder always increase, as required by the second law of thermodynamics? Price shows that, for over a century, most physicists have thought about these problems the wrong way. Misled by the human perspective from withintime, which distorts and exaggerates the differences between past and future, they have fallen victim to what Price calls the double standard fallacy: proposed explanations of the difference between the past and the future turn out to rely on a difference which has been slipped in at thebeginning, when the physicists themselves treat the past and future in different ways. To avoid this fallacy, Price argues, we need to overcome our natural tendency to think about the past and the future differently. We need to imagine a point outside time -- an Archimedean view from nowhen --from which to observe time in an unbiased way. Offering a lively criticism of many major modern physicists, including Richard Feynman and Stephen Hawking, Price shows that this fallacy remains common in physics today -- for example, when contemporary cosmologists theorize about the eventual fate of the universe. The big bang theory normallyassumes that the beginning and end of the universe will be very different. But if we are to avoid the double standard fallacy, we need to consider time symmetrically, and take seriously the possibility that the arrow of time may reverse when the universe recollapses into a big crunch. Price then turns to the greatest mystery of modern physics, the meaning of quantum theory. He argues that in missing the Archimedean viewpoint, modern physics has missed a radical and attractive solution to many of the apparent paradoxes of quantum physics. Many consequences of quantum theoryappear counterintuitive, such as Schrodinger's Cat, whose condition seems undetermined until observed, and Bell's Theorem, which suggests a spooky nonlocality, where events happening simultaneously in different places seem to affect each other directly. Price shows that these paradoxes can beavoided by allowing that at the quantum level the future does, indeed, affect the past. This demystifies nonlocality, and supports Einstein's unpopular intuition that quantum theory describes an objective world, existing independently of human observers: the Cat is alive or dead, even when nobodylooks. So interpreted, Price argues, quantum mechanics is simply the kind of theory we ought to have expected in microphysics -- from the symmetric standpoint.Time's Arrow and Archimedes' Point presents an innovative and controversial view of time and contemporary physics. In this exciting book, Price urges physicists, philosophers, and anyone who has ever pondered the mysteries of time to look at the world from the fresh perspective of Archimedes' Pointand gain a deeper understanding of ourselves, the universe around us, and our own place in time.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    . . Nobel winner . . . bestselling author . . . safe-cracker. In this substantial graphic novel biography, First Second presents the larger-than-life exploits of Nobel-winning quantum physicist, adventurer, musician, world-class raconteur, and one of the greatest minds of the twentieth century: Richard Feynman. Written by nonfiction comics mainstay Jim Ottaviani and brilliantly illustrated by First Second author Leland Myrick, Feynman tells the story of the great man's life from his childhood in Long Island to his work on the Manhattan Project and the Challenger disaster. Ottaviani tackles the bad with the good, leaving the reader delighted by Feynman's exuberant life and staggered at the loss humanity suffered with his death. Anyone who ever wanted to know more about Richard P. Feynman, quantum electrodynamics, the fine art of the bongo drums, the outrageously obscure nation of Tuva, or the development and popularization of the field of physics in the United States need look no further than this rich and joyful work.• One of School Library Journal's Best Adult Books 4 Teens titles of 2011 • One of Horn Book's Best Nonfiction Books of 2011

    Approaching science with a freshness unbound by convention or previous expectations, he produced some of the most original scientific thinking of the nineteenth century - and his discoveries went on to shape the twentieth century.

    Now Lawrence M. Krauss, an internationally known theoretical physicist and educator, has written the quintessential physics book for Trekkers and non-Trekkers alike.Anyone who has ever wondered, "Could this really happen?" will gain useful insights into the "Star Trek" universe (and, incidentally, the real universe) in this charming and accessible volume. Krauss boldly goes where "Star Trek" has gone -- and beyond. He uses the "Star Trek" future as a launching pad to discuss the forefront of modern physics. From Newton to Hawking, from Einstein to Feynman, from Kirk to Janeway, Krauss leads the reader on a voyage to the world of physics as we now know it and as it might one day be.Featuring the Top 10 biggest physics bloopers in "Star Trek," as selected by Nobel Prize-winning physicists and other dedicated Trekkers!"This book is fun, and Mr. Krauss has a nice touch with a tough subject...Readers drawn by frivolity will be treated to substance." "--New York Times Book Review""Today's science fiction is often tomorrow's science fact. The physics that underlies "Star Trek" is surely worth investigating. To confine our attention to terrestrial matters would be to limit the human spirit."--Stephen Hawking (in the foreword)A