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.

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    Includes expert coverage of new topics: Turbocodes, Turboequalization, Antenna Arrays, Digital Cellular Systems, and Iterative Detection. Convenient, sequential organization begins with a look at the historyo and classification of channel models and builds from there.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years.

    CONGRATULATIONS TO HERBERT KROEMER, 2000 NOBEL LAUREATE FOR PHYSICS For upper-division courses in thermodynamics or statistical mechanics, Kittel and Kroemer offers a modern approach to thermal physics that is based on the idea that all physical systems can be described in terms of their discrete quantum states, rather than drawing on 19th-century classical mechanics concepts.

    Topics include electrical work and energy in a system of conductors, mechanical action between two electrical systems, spherical harmonics, electric current, conduction and resistance, electrolysis, and other subjects. 1891 edition.

    Nobel laureate Murray Gell-Mann offers a uniquely personal and unifying vision of the relationship between the fundamental laws of physics and the complexity and diversity of the natural world.

    For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.

    This ninth edition covers both analytical and empirical approaches to the subject. The examples and templates provide students with resources for computer-numerical solutions.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

    is an American Board of Emergency Medicine certified ED doctor. His journey began in the mid-1970s, when he chose to pursue a career in medicine. In his youthful perspective, he came to regard doctors as the good guys, the ones who healed people and saved lives. He knew he’d be one of those good guys one day. Now, with a career spanning more than thirty years, he works as an emergency-room physician in North Carolina. In A License to Heal: Random Memories of an ER Doctor, Bentley describes the real world of emergency medicine from the viewpoint of a practicing physician. This memoir is filled with real-life stories of the ER, including life and death, triumph and tragedy. Meet a man named Solomon Darby, who spoke to long-dead relatives during his own near-death experience. Bentley also recalls the heartbreaking story of a young widow who desperately needed to understand and cope with the death of her husband. Amid the grief, there are also episodes of great humor and human comedy. In the dynamic world of emergency medicine, there is a great deal of pain, blood, and tragedy, but there is also hope, compassion, and excitement—for both the patients and the staff."

    This will let children know that there is a world out there they do not even know about. This will also make children wonder what goes on in these strange places. Some children will even develop the goal to visit some of these places when they get older. Most children do not know that there are strange places all over the earth.

    Where does this order and regularity come from? It creates itself. The patterns we see come from self-organization. Whether living or non-living, scientists have found that there is a pattern-forming tendency inherent in the basic structure and processes of nature, so that from a few simple themes, and the repetition of simple rules, endless beautiful variations can arise.Part of a trilogy of books exploring the science of patterns in nature, acclaimed science writer Philip Ball here looks at how shapes form. From soap bubbles to honeycombs, delicate shell patterns, and even the developing body parts of a complex animal like ourselves, he uncovers patterns in growth and form in all corners of the natural world, explains how these patterns are self-made, and why similar shapes and structures may be found in very different settings, orchestrated by nothing more than simple physical forces. This book will make you look at the world with fresh eyes, seeing order and form even in the places you'd least expect.

    No one seemed able to agree on a cause. (Dark matter? Tensor–vector–scalar gravity? Collisions with gravitons?) What did seem clear to those who became obsessed with it was that the Pioneer Anomaly had the potential to upend Einstein and Newton—to change everything we know about the universe.With riveting prose and the precision of an expert, Konstantin Kakaes gives us a scientific police procedural, tracking the steps of those who sought to unravel this high-stakes enigma. His thrilling account draws on extensive interviews and archival research, following the story from the Anomaly’s initial discovery, through decades of tireless investigation, to its ultimate conclusion. “The Pioneer Detectives” is a definitive account not just of the Pioneer Anomaly but of how scientific knowledge gets made and unmade, with scientists sometimes putting their livelihoods on the line in pursuit of cosmic truth. Perfect for fans of John McPhee, Thomas Kuhn, and Ed McBain, this is also an immensely enjoyable story accessible to anyone who loves brilliant, fascinating long-form journalism.* * * ABOUT THE AUTHOR: Konstantin Kakaes is a Bernard L. Schwartz fellow at the New America Foundation, writing about science and technology, and is the former Mexico City bureau chief for The Economist. His work has been published in The Wall Street Journal, Foreign Policy, and The Washington Post and appears frequently in Slate. Before becoming a journalist, he studied physics at Harvard University.