Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity.Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology.Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

    Highlights of the book include realistic problems and examples from a wide range of application areas. New to this edition are: much sharper pedagogy; an increase in the number of examples; more thorough development of the concepts; a greater range of homework problems; a greater number and variety of worked out examples; expanded coverage of dynamics modelling and Laplace transform topics; and integration of MATLAB, including many examples that are formatted in MATLAB.

    Not until the nineteenth century would three men, armed with the best telescopes of their age, race to conquer this astronomical Everest. Parallax tells the fast-moving story of their contest, which ended in a dead heat. Against a sweeping backdrop filled with kidnappings, dramatic rescue, swordplay, madness, and bitter rivalry, Alan W. Hirshfeld brings to life the heroes -- and heroines -- of this remarkable chapter in history. Characters include the destitute boy plucked from a collapsed building who grew up to become the world's greatest telescope maker; the hot-tempered Dane whose nose was lopped off in a duel over mathematics; a merchant's apprentice forced to choose between the lure of money and his passion for astronomy; and the musician who astounded the world by discovering a new planet from his own backyard.Generously illustrated with period engravings and paintings, Parallax is an unforgettable ride through time and space.

    " Fox has inspired millions of people over the past forty years through his simple, practical guidelines. In Diagrams for Living he presents valuable keys to living a more fulfilled life drawn from the eloquent spiritual wisdom of the Bible.If we read the Bible literally, cautions Fox, we miss the eternal power and personal relevance found in its symbols, allegories, and parables. "Whether you realize it or not," he writes, "you are on every page from Genesis to Revelation." Fox shows how to read dramatic biblical stories as symbolic diagrams for living that can "show you how to overcome difficulties and problems, and how to give expression to the deep aspirations that lie hidden in your soul." This power to reveal, inspire, and guide makes the Bible's teachings adaptable to everyone at every stage of spiritual development.Sensible, contemporary, and full of reassurance, Diagrams for Living offers sage counsel from a gifted teacher.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    Topics include: Limits, Derivatives, and Integrations.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains.

    joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike."A positively joyful exploration of mathematics."-Publishers Weekly, starred review"Each [trick] is more dazzling than the last."-Physics World

    For even as she sets out to determine how big “really big” may be, Levin gives us an intimate look at the day-to-day life of a globe-trotting physicist, complete with jet lag and romantic disturbances.Nimbly synthesizing geometry, topology, chaos and string theories, Levin shows how the pattern of hot and cold spots left over from the big bang may one day reveal the size and shape of the cosmos. She does so with such originality, lucidity—and even poetry—that How the Universe Got Its Spots becomes a thrilling and deeply personal communication between a scientist and the lay reader.

    Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further."

    Their work has uncovered a number of the universe’s more surprising secrets, and many believe further wonders remain hidden within the theory’s tangle of equations, waiting to be exposed. In this sweeping narrative of science and culture, astrophysicist Pedro Ferreira brings general relativity to life through the story of the brilliant physicists, mathematicians, and astronomers who have taken up its challenge. For these scientists, the theory has been both a treasure trove and an enigma, fueling a century of intellectual struggle and triumph.. Einstein’s theory, which explains the relationships among gravity, space, and time, is possibly the most perfect intellectual achievement of modern physics, yet studying it has always been a controversial endeavor. Relativists were the target of persecution in Hitler’s Germany, hounded in Stalin’s Russia, and disdained in 1950s America. Even today, PhD students are warned that specializing in general relativity will make them unemployable. Despite these pitfalls, general relativity has flourished, delivering key insights into our understanding of the origin of time and the evolution of all the stars and galaxies in the cosmos. Its adherents have revealed what lies at the farthest reaches of the universe, shed light on the smallest scales of existence, and explained how the fabric of reality emerges. Dark matter, dark energy, black holes, and string theory are all progeny of Einstein’s theory. We are in the midst of a momentous transformation in modern physics. As scientists look farther and more clearly into space than ever before, The Perfect Theory reveals the greater relevance of general relativity, showing us where it started, where it has led, and where it can still take us.

    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.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index