But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Captioned cartoon drawings offering an overview of universal order as they deal with various phenomena are combined with scientific commentary

    Based on the experience of the authors in teaching Mathematics Courses for almost four decades at the Institute of Technology, New Delhi, this text book rather than a guide/problem book, lays emphasis on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner.

    

    Gerard 't Hooft was closely involved in many of the advances in modern theoretical physics that led to improved understanding of elementary particles, and this is a first-hand account of one of the most creative and exciting periods of discovery in the history of physics. Using language a layperson can understand, this narrative touches on many central topics and ideas, such as quarks and quantum physics; supergravity, superstrings and superconductivity; the Standard Model and grand unification; eleven-dimensional space time and black holes. This fascinating personal account of the past thirty years in one of the most dramatic areas in twentieth-century physics will be of interest to professional physicists and physics students, as well as the educated general reader with an interest in one of the most exciting scientific detective stories ever.

    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.

    By tracking a pendulum's path as it swung repeatedly across the interior of the large ceremonial hall, Foucault offered the first definitive proof -- before an audience that comprised the cream of Parisian society, including the future emperor, Napoleon III -- that the earth revolves on its axis.Through careful, primary research, world-renowned author Amir Aczel has revealed the life of a gifted physicist who had almost no formal education in science, and yet managed to succeed despite the adversity he suffered at the hands of his peers. The range and breadth of Foucault's discoveries is astonishing: He gave us the modern electric compass, devised an electric microscope, invented photographic technology, and made remarkable deductions about color theory, heat waves, and the speed of light. Yet until now so little has been known about his life.Richly detailed and evocative, Pendulum tells of the illustrious period in France during the Second Empire; of Foucault's relationship with Napoleon III, a colorful character in his own right; and -- most notably -- of the crucial triumph of science over religion.Dr. Aczel has crafted a fascinating narrative based on the life of this most astonishing and largely unrecognized scientist, whose findings answered many age-old scientific questions and posed new ones that are still relevant today.

    Such a device would operate under a different set of physical laws: The laws of quantum mechanics. Johnson gently leads the curious outsider through the surprisingly simple ideas needed to understand this dream, discussing the current state of the revolution, and ultimately assessing the awesome power these machines could have to change our world.

      In the constellation of Eridanus, there lurks a cosmic mystery: It’s as if something has taken a huge bite out of the universe. But what is the culprit? The hole in the universe is just one of many puzzles keeping cosmologists busy. Supermassive black holes, bubbles of nothingness gobbling up space, monster universes swallowing others—these and many other bizarre ideas are being pursued by scientists. Due to breathtaking progress in astronomy, the history of our universe is now better understood than the history of our own planet. But these advances have uncovered some startling riddles. In this electrifying new book, renowned cosmologist and author Paul Davies lucidly explains what we know about the cosmos and its enigmas, exploring the tantalizing—and sometimes terrifying—possibilities that lie before us. As Davies guides us through the audacious research offering mind-bending solutions to these and other mysteries, he leads us up to the greatest outstanding conundrum of all: Why does the universe even exist in the first place? And how did a system of mindless, purposeless particles manage to bring forth conscious, thinking beings? Filled with wit and wonder, What’s Eating the Universe? is a dazzling tour of cosmic questions, sure to entertain, enchant, and inspire us all.

    He asks how today's scientists can claim to predict future climate events when even three-day forecasts prove a serious challenge. Can we predict and control epidemics? Can we accurately foresee our financial future? Or will we only find out about tomorrow when tomorrow arrives?

    He spent two years gathering information that demonstrates this and along the way interviewed more than a hundred experts in a number of different fields. Among them were parapsychologists, medical doctors, psychologists, psychiatrists, quantum physicists, and researchers into the true nature of reality. Specific examples are presented that indicate what happens when we die, for example that memories can be formed and retained despite a subject’s brain having been shutdown and the blood drained from it. Questions such as whether or not you will be able to communicate with living loved ones after death are addressed, if it is possible to be reborn, and what might be missing from reproductive theory to explain the various phenomena indicated in the many case histories and scientific investigations presented. All of us will someday cross the border to what Shakespeare called "The undiscovered country." As long as we must make that trip, wouldn’t it be smart to find out where we are going and what to expect when we get there?

    It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

    In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.

    It reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

    The Kingfisher Science Encyclopedia is the one reference that includes all of the information students need to know in today's fast-paced world. Clearly written and illustrated articles provide in-depth insight and concise authoritative information. An impressive reference section at the end of the book contains minibiographies of famous scientists, plus an illustrated time line of key inventions and discoveries. Arranged thematically into ten chapters, with reference summaries at the end of each chapter and a full index, the encyclopedia does more than merely provide facts about science and technology—it helps the reader think for him or herself, develop an enquiring mind, pose challenging questions, and explore new topics.