With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    Written by the man who started the adventure, Behind Deep Blue reveals the inside story of what happened behind the scenes at the two historic Deep Blue vs. Kasparov matches. This is also the story behind the quest to create the mother of all chess machines. The book unveils how a modest student project eventually produced a multimillion dollar supercomputer, from the development of the scientific ideas through technical setbacks, rivalry in the race to develop the ultimate chess machine, and wild controversies to the final triumph over the world's greatest human player.In nontechnical, conversational prose, Feng-hsiung Hsu, the system architect of Deep Blue, tells us how he and a small team of fellow researchers forged ahead at IBM with a project they'd begun as students at Carnegie Mellon in the mid-1980s: the search for one of the oldest holy grails in artificial intelligence--a machine that could beat any human chess player in a bona fide match. Back in 1949 science had conceived the foundations of modern chess computers but not until almost fifty years later--until Deep Blue--would the quest be realized.Hsu refutes Kasparov's controversial claim that only human intervention could have allowed Deep Blue to make its decisive, "uncomputerlike" moves. In riveting detail he describes the heightening tension in this war of brains and nerves, the "smoldering fire" in Kasparov's eyes. Behind Deep Blue is not just another tale of man versus machine. This fascinating book tells us how man as genius was given an ultimate, unforgettable run for his mind, no, not by the genius of a computer, but of man as toolmaker.

    It describes how the laws and discoveries of information theory now support controversial revisions to Darwinian evolution, begin to unravel the mysteries of language, memory and dreams, and stimulate provocative ideas in psychology, philosophy, art, music, computers and even the structure of society. Perhaps its most fascinating and unexpected surprise is the suggestion the order and complexity may be as natural as disorder and disorganization. Contrary to the entropy principle, which implies that order is the exception and confusion the rule, information theory asserts that order and sense can indeed prevail against disorder and nonsense. From the simplest forms of organic life to the words used to express our most complex ideas, from our genes to our dreams, from microcomputers to telecommunications, virtually everything around us follows simple rules of information. Life and the material world, like language, remain "grammatical." Grammatical man inhabits a grammatical universe.

    . . a most valuable contribution." — Douglas R. Hofstadter, author of Gödel, Escher, BachThe foundations of game theory were laid by John von Neumann, who in 1928 proved the basic minimax theorem, and with the 1944 publication of the Theory of Games and Economic Behavior, the field was established. Since then, game theory has become an enormously important discipline because of its novel mathematical properties and its many applications to social, economic, and political problems.Game theory has been used to make investment decisions, pick jurors, commit tanks to battle, allocate business expenses equitably — even to measure a senator's power, among many other uses. In this revised edition of his highly regarded work, Morton Davis begins with an overview of game theory, then discusses the two-person zero-sum game with equilibrium points; the general, two-person zero-sum game; utility theory; the two-person, non-zero-sum game; and the n-person game.A number of problems are posed at the start of each chapter and readers are given a chance to solve them before moving on. (Unlike most mathematical problems, many problems in game theory are easily understood by the lay reader.) At the end of the chapter, where solutions are discussed, readers can compare their "common sense" solutions with those of the author. Brimming with applications to an enormous variety of everyday situations, this book offers readers a fascinating, accessible introduction to one of the most fruitful and interesting intellectual systems of our time.

    Devised in India in the 7th and 8th centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential.The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the "Book of Calculation," and the revolution that followed its publication was enormous. Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance.Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers--the Fibonacci sequence--used by some to predict the rise and fall of financial markets, and evident in myriad biological structures.One of the great math popularizers of our time, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives.

    He believes that we should investigate what makes some countries more capable than others. Complex products—from films to robots, apps to automobiles—are a physical distillation of an economy’s knowledge, a measurable embodiment of its education, infrastructure, and capability. Economic wealth accrues when applications of this knowledge turn ideas into tangible products; the more complex its products, the more economic growth a country will experience.A radical new interpretation of global economics, Why Information Grows overturns traditional assumptions about the development of economies and the origins of wealth and takes a crucial step toward making economics less the dismal science and more the insightful one.

    This title is intended for those who might enjoy an engaging dialogue on abstract mathematical ideas, and those who might wish to experience how new mathematics is created.

    Called the Pope by his peers, he was regarded as infallible in his instincts and research. His discoveries changed our world; they led to weapons of mass destruction and conversely to life-saving medical interventions.This unassuming man struggled with issues relevant today, such as the threat of nuclear annihilation and the relationship of science to politics. Fleeing Fascism and anti-Semitism, Fermi became a leading figure in America's most secret project: building the atomic bomb. The last physicist who mastered all branches of the discipline, Fermi was a rare mixture of theorist and experimentalist. His rich legacy encompasses key advances in fields as diverse as comic rays, nuclear technology, and early computers.In their revealing book, The Pope of Physics, Gino Segré and Bettina Hoerlin bring this scientific visionary to life. An examination of the human dramas that touched Fermi’s life as well as a thrilling history of scientific innovation in the twentieth century, this is the comprehensive biography that Fermi deserves.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    In this narrative, Walter Isaacson explains how his mind worked and the mysteries of the universe that he discovered.

    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

    In Empires of Light, historian Jill Jonnes portrays this extraordinary trio and their riveting and ruthless world of cutting-edge science, invention, intrigue, money, death, and hard-eyed Wall Street millionaires. At the heart of the story are Thomas Alva Edison, the nation’s most famous and folksy inventor, creator of the incandescent light bulb and mastermind of the world’s first direct current electrical light networks; the Serbian wizard of invention Nikola Tesla, elegant, highly eccentric, a dreamer who revolutionized the generation and delivery of electricity; and the charismatic George Westinghouse, Pittsburgh inventor and tough corporate entrepreneur, an industrial idealist who in the era of gaslight imagined a world powered by cheap and plentiful electricity and worked heart and soul to create it. Edison struggled to introduce his radical new direct current (DC) technology into the hurly-burly of New York City as Tesla and Westinghouse challenged his dominance with their alternating current (AC), thus setting the stage for one of the eeriest feuds in American corporate history, the War of the Electric Currents. The battlegrounds: Wall Street, the 1893 Chicago World’s Fair, Niagara Falls, and, finally, the death chamber - Jonnes takes us on the tense walk down a prison hallway and into the sunlit room where William Kemmler, convicted ax murderer, became the first man to die in the electric chair. Empires of Light is the gripping history of electricity, the “mysterious fluid,” and how the fateful collision of Edison, Tesla, and Westinghouse left the world utterly transformed.

    Called a madman by his enemies, a genius by others, and an enigma by nearly everyone, Nikola Tesla was, without a doubt, a trailblazing inventor who created astonishing, sometimes world-transforming devices that were virtually without theoretical precedent. Tesla not only discovered the rotating magnetic field -- the basis of most alternating-current machinery -- but also introduced us to the fundamentals of robotics, computers, and missile science. Almost supernaturally gifted, unfailingly flamboyant and neurotic, Tesla was troubled by an array of compulsions and phobias and was fond of extravagant, visionary experimentations. He was also a popular man-about-town, admired by men as diverse as Mark Twain and George Westinghouse, and adored by scores of society beauties. From Tesla's childhood in Yugoslavia to his death in New York in the 1940s, Cheney paints a compelling human portrait and chronicles a lifetime of discoveries that radically altered -- and continue to alter -- the world in which we live. Tesla: Man Out of Time is an in-depth look at the seminal accomplishments of a scientific wizard and a thoughtful examination of the obsessions and eccentricities of the man behind the science.