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."

    He is dead famous for: discovering gravity, being a right clever dick and getting hit on the head with an apple. But have you heard that Isaac: came bottom of the class at school, poked sticks in his eye and nearly blinded himself and nearly got himself executed?

    What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough.Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters.For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

    Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories.Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores what that implies and why some founders of the theory became the foremost objectors to it. Schr�dinger showed that it absurdly allowed a cat to be in a superposition simultaneously dead and alive. Einstein derided the theory's spooky interactions. With Bell's Theorem, we now know Schr�dinger's superpositions and Einstein's spooky interactions indeed exist.Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation.Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial.Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing.Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves.

    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.

    Whether they bind computers, economies, or terrorist organizations, networks are everywhere in the real world, yet only recently have scientists attempted to explain their mysterious workings.From epidemics of disease to outbreaks of market madness, from people searching for information to firms surviving crisis and change, from the structure of personal relationships to the technological and social choices of entire societies, Watts weaves together a network of discoveries across an array of disciplines to tell the story of an explosive new field of knowledge, the people who are building it, and his own peculiar path in forging this new science.

    Reveals the important contributions of mathematics to the physical and social sciences, philosophy, religion, literature, and art.

    As in his first trip with Alberto Granado, this second journey was an encounter with the roots of indigenous America, with the incipient people’s movements and all the beauty and suffering of a continent oppressed for centuries.“The name of the sidekick has changed from Alberto to Calica, but the trip is the same: two free-spirits spanning out over South America without knowing exactly what they're looking for or which way is north,” wrote Guevara in his travel diary.The two friends explore Bolivia, Perú and Ecuador, alternating their enthusiasm for travel and youthful antics with revealing discoveries about social and political reality in Latin America, in the end turning the trip into a profound journey of self-discovery that would change them forever.The book presents previously unpublished photos from Calica’s personal album that portray the childhood and youth of the two friends in the town of Alta Gracia in the Province of Córdoba, Argentina, as well as their trip together.Alberto Granado, friend of both Ernesto and Calica, prologues the book and finishes with these words:“Thank you, Calica, for having brought this breath of fresh air and showing us our friend just as he was, is and always will be: a man of flesh and blood.”

    Turing’s openness about his homosexuality at a time when it was an imprisonable offense ultimately led to his untimely lo death at the age of only forty-one. In Alan Turing: Unlocking the Enigma, David Boyle reveals the mysteries behind the man and his remarkable career. Aged just 22, Turing was elected a fellow at King's College, Cambridge on the strength of a dissertation in which he proved the central limit theorem. By the age of 33, he had been awarded the OBE by King George VI for his wartime services: Turing was instrumental in cracking the Nazi Enigma machines at the top secret code breaking establishment at Bletchley Park during the Second World War.But his achievements were to be tragically overshadowed by the paranoia of the post-War years. Hounded for his supposedly subversive views and for his sexuality, Turing was prosecuted in 1952, and forced to accept the humiliation of hormone treatment to avoid a prison sentence. Just two years later, at the age of 41 he was dead. The verdict: cyanide poisoning.Was Turing’s death accidental as his mother always claimed? Or did persistent persecution drive him to take him own life?Alan Turing: Unlocking the Enigma seeks to find the man behind the science, illuminating the life of a person who is still a shadowy presence behind his brilliant achievements.

    Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    What happened during those years and what has happened since to refine the understanding of this phenomenon is the fascinating story told here.We move from a coffee shop in Zurich, where Einstein and Max von Laue discuss the madness of quantum theory, to a bar in Brazil, as David Bohm and Richard Feynman chat over cervejas. We travel to the campuses of American universities—from J. Robert Oppenheimer’s Berkeley to the Princeton of Einstein and Bohm to Bell’s Stanford sabbatical—and we visit centers of European physics: Copenhagen, home to Bohr’s famous institute, and Munich, where Werner Heisenberg and Wolfgang Pauli picnic on cheese and heady discussions of electron orbits.Drawing on the papers, letters, and memoirs of the twentieth century’s greatest physicists, Louisa Gilder both humanizes and dramatizes the story by employing their own words in imagined face-to-face dialogues. Here are Bohr and Einstein clashing, and Heisenberg and Pauli deciding which mysteries to pursue. We see Schrödinger and Louis de Broglie pave the way for Bell, whose work is here given a long-overdue revisiting. And with his characteristic matter-of-fact eloquence, Richard Feynman challenges his contemporaries to make something of this entanglement.

    From the early Greek influences to the Middle Ages and the Renaissance to the end of the 19th century, trace the fascinating foundation of mathematics as it developed through the ages. Aristotle, Galileo, Kepler, Newton: you know the names. Now here's what they really did, and the effect their discoveries had on our culture, all explained in a way the layperson can understand. Begin with the basis of arithmetic (Plato and the introduction of geometry), and discover why the use of Arabic numerals was critical to the development of both commerce and science. The development of calculus made space travel a reality, while the abacus prefigured the computer. The greats examined in depth include Leonardo da Vinci, a brilliant mathematician as well as artist; Pascal, who laid out the theory of probabilities; and Fermat, whose intriguing theory has only recently been solved.

    Illustrations.

    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.