This popular student textbook has been revised and updated in order to provide clear explanations of the subject matter, permitting more classroom time to be spent in problem solving, applications or explanations of the most difficult points.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. Students of literature read Shakespeare; students of music listen to Bach, he writes. But this tradition of studying the major works of the masters is, if not wholly absent, certainly uncommon in mathematics. This book seeks to redress that situation.Like a great museum, The Calculus Gallery is filled with masterpieces, among which are Bernoulli's early attack upon the harmonic series (1689), Euler's brilliant approximation of pi (1779), Cauchy's classic proof of the fundamental theorem of calculus (1823), Weierstrass's mind-boggling counterexample (1872), and Baire's original category theorem (1899). Collectively, these selections document the evolution of calculus from a powerful but logically chaotic subject into one whose foundations are thorough, rigorous, and unflinching--a story of genius triumphing over some of the toughest, most subtle problems imaginable.Anyone who has studied and enjoyed calculus will discover in these pages the sheer excitement each mathematician must have felt when pushing into the unknown. In touring The Calculus Gallery, we can see how it all came to be.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    From very simple beginnings he takes us on a thrilling journey to some deep mathematical ideas. On the way, via Kepler and Newton, he explains what calculus really means, gives a brief history of pi, and even takes us to chaos theory and imaginary numbers. Every short chapter is carefully crafted to ensure that no one will get lost on the journey. Packed with puzzles and illustrated by world famous cartoonists, this is one of the most readable and imaginative books on mathematics ever written.

    do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    Decades ago, astronauts brought back 850 pounds of rocks from their lunar journeys; the U.S. gave some away as “goodwill” gifts to the world’s nations. Over time, many of them disappeared, stolen or lost in the aftermath of political turmoil, and offered for millions on the black market. Gutheinz, first as a NASA investigator and then the leader of a intrepid group of students, has dedicated his life to getting them back. Author Joe Kloc tells a wild story of geopolitics, crime, science, and one man’s obsession with keeping the moon out of the wrong hands.

    Though the answers may seem simple, their profound implications make the prisoner's dilemma one of the great unifying concepts of science. Watching players bluff in a poker game inspired John von Neumann--father of the modern computer and one of the sharpest minds of the century--to construct game theory, a mathematical study of conflict and deception. Game theory was readily embraced at the RAND Corporation, the archetypical think tank charged with formulating military strategy for the atomic age, and in 1950 two RAND scientists made a momentous discovery.Called the prisoner's dilemma, it is a disturbing and mind-bending game where two or more people may betray the common good for individual gain. Introduced shortly after the Soviet Union acquired the atomic bomb, the prisoner's dilemma quickly became a popular allegory of the nuclear arms race. Intellectuals such as von Neumann and Bertrand Russell joined military and political leaders in rallying to the preventive war movement, which advocated a nuclear first strike against the Soviet Union. Though the Truman administration rejected preventive war the United States entered into an arms race with the Soviets and game theory developed into a controversial tool of public policy--alternately accused of justifying arms races and touted as the only hope of preventing them.A masterful work of science writing, Prisoner's Dilemma weaves together a biography of the brilliant and tragic von Neumann, a history of pivotal phases of the cold war, and an investigation of game theory's far-reaching influence on public policy today. Most important, Prisoner's Dilemma is the incisive story of a revolutionary idea that has been hailed as a landmark of twentieth-century thought.

    Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge.Diaconis and Graham tell the stories--and reveal the best tricks--of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick--and much more.

    Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    These stars allegedly use Illuminati and satanic symbolism in their music videos and on their clothes that goes unnoticed by those not “in the know.”Since these stars appear in our livings rooms on family friendly mainstream shows like Good Morning America, Ellen, and dozens of others—and are loved by virtually all the kids—they couldn’t possibly have anything to do with the infamous Illuminati or anything “satanic,” could they? Some famous musicians have even publicly denounced the Illuminati in interviews or songs.Illuminati in the Music Industry takes a close look at some of today’s hottest stars and decodes the secret symbols, song lyrics, and separates the facts from the fiction in this fascinating topic. You may never see your favorite musicians the same way ever again. Includes 50 photographs.Discover why so many artists are promoting the Illuminati as the secret to success. Why an aspiring rapper in Virginia shot his friend as an “Illuminati sacrifice” hoping it would help him become rich and famous. How and why the founder of BET Black Entertainment Television became the first African American billionaire.Why popular female pop stars like Rihanna, Christina Aguilera, Kesha and others are promoting Satanism as cool, something that was once only seen in heavy metal and rock and roll bands. Some musicians like Korn’s singer Jonathan Davis, rapper MC Hammer, Megadeth’s frontman Dave Mustaine and others, have all denounced the Illuminati and artists promoting them. Les Claypool, singer of Primus wrote a song about the Bohemian Grove.Muse singer Matt Bellamy recants his belief that 9/11 was an inside job after getting a taste of mainstream success with his album, The Resistance. Bono said he attended an Illuminati meeting with other celebrities. Was he joking or serious?Why rap and hip hop is filled with Illuminati puppets and wannabes more than other genres of music.Learn about media effects, the power of celebrity, what the externalization of the hierarchy means and how you can break free from the mental enslavement of mainstream media and music. By the author of The Illuminati: Facts & Fiction-About the Author-Mark Dice is a media analyst, author, and political activist who, in an entertaining and educational way, gets people to question our celebrity obsessed culture and the role the mainstream media and elite secret societies play in shaping our lives. Mark's YouTube channel has received over 150 million views and his viral videos have been mentioned on the Fox News Channel, CNN, the Drudge Report, TMZ, the New York Daily News, the New York Post, and other media outlets around the world.He has been featured on various television shows including the History Channel's Decoded and America's Book of Secrets, Conspiracy Theory with Jesse Ventura, Secret Societies of Hollywood on E! Channel, America Declassified on the Travel Channel, and is a frequent guest on Coast to Coast AM, The Alex Jones Show, and more.Mark Dice is the author of several popular books on secret societies and conspiracies, including The Illuminati in Hollywood, Big Brother: The Orwellian Nightmare Come True, The New World Order, Facts & Fiction, Inside the Illuminat

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.