Using Everett's unpublished papers (recently discovered in his son's basement) and dozens of interviews with his friends, colleagues, and surviving family members, Byrne paints, for the general reader, a detailed portrait of the genius who invented an astonishing way of describing our complex universe from the inside. Everett's mathematical model (called the "universal wave function") treats all possible events as "equally real," and concludes that countless copies of every person and thing exist in all possible configurations spread over an infinity of universes: many worlds. Afflicted by depression and addictions, Everett strove to bring rational order to the professional realms in which he played historically significant roles. In addition to his famous interpretation of quantum mechanics, Everett wrote a classic paper in game theory; created computer algorithms that revolutionized military operations research; and performed pioneering work in artificial intelligence for top secret government projects. He wrote the original software for targeting cities in a nuclear hot war; and he was one of the first scientists to recognize the danger of nuclear winter. As a Cold Warrior, he designed logical systems that modeled "rational" human and machine behaviors, and yet he was largely oblivious to the emotional damage his irrational personal behavior inflicted upon his family, lovers, and business partners. He died young, but left behind a fascinating record of his life, including correspondence with such philosophically inclined physicists as Niels Bohr, Norbert Wiener, and John Wheeler. These remarkable letters illuminate the long and often bitter struggle to explain the paradox of measurement at the heart of quantum physics. In recent years, Everett's solution to this mysterious problem-the existence of a universe of universes-has gained considerable traction in scientific circles, not as science fiction, but as an explanation of physical reality.

    The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http: //ocw.mit.edu/ans7870/resources/Strang/....

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    The realistic content of its examples and exercises, the clarity and brevity of its presentation, and the soundness of its pedagogical approach have received the highest remarks from both students and instructors. Now this bestseller is available in a new 6th edition.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

    In Tammet's world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives. Inspired by the complexity of snowflakes, Anne Boleyn's eleven fingers, or his many siblings, Tammet explores questions such as why time seems to speed up as we age, whether there is such a thing as an average person, and how we can make sense of those we love. Thinking In Numbers will change the way you think about math and fire your imagination to see the world with fresh eyes.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    That they exist, Simon Singh reveals, underscores the brilliance of the shows' writers, many of whom have advanced degrees in mathematics in addition to their unparalleled sense of humor. While recounting memorable episodes such as “Bart the Genius” and “Homer3,” Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes. With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

    For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    These centuries gave birth to the basic concepts from which modern physics has evolved. In this first volume of his celebrated UNDERSTANDING PHYSICS, Isaac Asimov deals with this fascinating, momentous stage of scientific development with an authority and clarity that add further lustre to an eminent reputation. Demanding the minimum of specialized knowledge from his audience, he has produced a work that is the perfect supplement to the student’s formal textbook, as well as offering invaluable illumination to the general reader.

    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

    This discovery dramatically reshaped how humans understood their place in the cosmos, and once and for all laid to rest the idea that the Milky Way galaxy was alone in the universe. Six years later, continuing research by Hubble and others forced Albert Einstein to renounce his own cosmic model and finally accept the astonishing fact that the universe was not immobile but instead expanding. The fascinating story of these interwoven discoveries includes battles of will, clever insights, and wrong turns made by the early investigators in this great twentieth-century pursuit. It is a story of science in the making that shows how these discoveries were not the work of a lone genius but the combined efforts of many talented scientists and researchers toiling away behind the scenes. The intriguing characters include Henrietta Leavitt, who discovered the means to measure the vast dimensions of the cosmos . . . Vesto Slipher, the first and unheralded discoverer of the universe’s expansion . . . Georges Lemaître, the Jesuit priest who correctly interpreted Einstein’s theories in relation to the universe . . . Milton Humason, who, with only an eighth-grade education, became a world-renowned expert on galaxy motions . . . and Harlow Shapley, Hubble’s nemesis, whose flawed vision of the universe delayed the discovery of its true nature and startling size for more than a decade.Here is a watershed moment in the history of astronomy, brought about by the exceptional combination of human curiosity, intelligence, and enterprise, and vividly told by acclaimed science writer Marcia Bartusiak.