In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

    This book fills that need. Here, Philip E. Tetlock explores what constitutes good judgment in predicting future events, and looks at why experts are often wrong in their forecasts.Tetlock first discusses arguments about whether the world is too complex for people to find the tools to understand political phenomena, let alone predict the future. He evaluates predictions from experts in different fields, comparing them to predictions by well-informed laity or those based on simple extrapolation from current trends. He goes on to analyze which styles of thinking are more successful in forecasting. Classifying thinking styles using Isaiah Berlin's prototypes of the fox and the hedgehog, Tetlock contends that the fox--the thinker who knows many little things, draws from an eclectic array of traditions, and is better able to improvise in response to changing events--is more successful in predicting the future than the hedgehog, who knows one big thing, toils devotedly within one tradition, and imposes formulaic solutions on ill-defined problems. He notes a perversely inverse relationship between the best scientific indicators of good judgement and the qualities that the media most prizes in pundits--the single-minded determination required to prevail in ideological combat.Clearly written and impeccably researched, the book fills a huge void in the literature on evaluating expert opinion. It will appeal across many academic disciplines as well as to corporations seeking to develop standards for judging expert decision-making.

    The majority of solutions on offer, from using efficient light bulbs to biking to work, focus on individual lifestyle changes, yet the scale of the crisis requires far deeper adjustments. Ecology and Socialism argues that time still remains to save humanity and the planet, but only by building social movements for environmental justice that can demand qualitative changes in our economy, workplaces, and infrastructure."Williams adds a new and vigorous voice to the growing awareness that, yes, it is our capitalist system that is ruining the natural foundation of our civilization and threatening the very idea of a future. I am particularly impressed by the way he develops a clear and powerful argument for an ecological socialism directly from the actual ground of struggle, whetheragainst climate change, systematic poisoning from pollution, or the choking stream of garbage. Ecology and Socialism is a notable addition to the growing movement to save our planet from death-dealing capitalism.”—Joel Kovel, author of The Enemy of Nature�Finally, a book that bridges the best of the scholarly and activist literatures in socialist ecology! Sophisticated and compelling, eschewing academic jargons �postmodern’ and otherwise, Ecology and Socialism more than competently champions a Marxist approach to environmental crisis and the kind of economic democracy needed to achieve an ecologically friendly system of production and human development.”—Paul Burkett, author of Marxism and Ecological Economics�This book is more than essential reading—it is a powerful weapon in the fight to save our planet.”—Ian Angus, editor of climateandcapitalism.comChris Williams is a longtime environmental activist, professor of physics and chemistry at Pace University, and chair of the science department at Packer Collegiate Institute. He lives in New York City.

    Guth’s startling theory—widely regarded as one of the most important contributions to science during the twentieth century—states that the big bang was set into motion by a period of hyper-rapid “inflation,” lasting only a billion-trillion-billionth of a second. The Inflationary Universe is the passionate story of one leading scientist’s effort to look behind the cosmic veil and explain how the universe began.

    "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    The science of complexity studies how single elements, such as a species or a stock, spontaneously organize into complicated structures like ecosystems and economies; stars become galaxies, and snowflakes avalanches almost as if these systems were obeying a hidden yearning for order. Drawing from diverse fields, scientific luminaries such as Nobel Laureates Murray Gell-Mann and Kenneth Arrow are studying complexity at a think tank called The Santa Fe Institute. The revolutionary new discoveries researchers have made there could change the face of every science from biology to cosmology to economics. M. Mitchell Waldrop's groundbreaking bestseller takes readers into the hearts and minds of these scientists to tell the story behind this scientific revolution as it unfolds.

    From its inception, Margaret Wertheim shows, physics has been an overwhelmingly male-dominated activity; she argues that gender inequity in physics is a result of the religious origins of the enterprise.Pythagoras' Trousers is a highly original history of one of science's most powerful disciplines. It is also a passionate argument for the need to involve both women and men in the process of shaping the technologies from the next generation of physicists.

    Ecological writers propose a new worldview, but their very zeal to preserve the natural world leads them away from the "nature" they revere. The problem is a symptom of the ecological catastrophe in which we are living. Morton sets out a seeming paradox: to have a properly ecological view, we must relinquish the idea of nature once and for all."Ecology without Nature" investigates our ecological assumptions in a way that is provocative and deeply engaging. Ranging widely in eighteenth-century through contemporary philosophy, culture, and history, he explores the value of art in imagining environmental projects for the future. Morton develops a fresh vocabulary for reading "environmentality" in artistic form as well as content, and traces the contexts of ecological constructs through the history of capitalism. From John Clare to John Cage, from Kierkegaard to Kristeva, from "The Lord of the Rings" to electronic life forms, "Ecology without Nature" widens our view of ecological criticism, and deepens our understanding of ecology itself. Instead of trying to use an idea of nature to heal what society has damaged, Morton sets out a radical new form of ecological criticism: "dark ecology."

    . . 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.

    Chen draws on recent debates about sexuality, race, and affect to examine how matter that is considered insensate, immobile, or deathly, animates cultural lives. Toward that end, Chen investigates the blurry division between the living and the dead, or that which is beyond the human or animal. Within the field of linguistics, animacy has been described variously as a quality of agency, awareness, mobility, sentience, or liveness. Chen turns to cognitive linguistics to stress how language habitually differentiates the animate and the inanimate. Expanding this construct, Chen argues that animacy undergirds much that is pressing and indeed volatile in contemporary culture, from animal rights debates to biosecurity concerns.Chen's book is the first to bring the concept of animacy together with queer of color scholarship, critical animal studies, and disability theory. Through analyses of dehumanizing insults, the meanings of queerness, animal protagonists in recent Asian/American art and film, the lead toy panic in 2007, and the social lives of environmental illness, Animacies illuminates a hierarchical politics infused by race, sexuality, and ability. In this groundbreaking book, Chen rethinks the criteria governing agency and receptivity, health and toxicity, productivity and stillness—and demonstrates how attention to the affective charge of matter challenges commonsense orderings of the world.Mel Y. Chen is Assistant Professor of Gender and Women's Studies at the University of California, Berkeley."Animacies is a book about 'reworldings,' as Mel Y. Chen traces the myriad ways that objects and affects move through and reshape zones of possibility for political transformation and queer resistance to neoliberal biopolitics. At the same time, Animacies itself generates such transformations: grounded in a generous, expansive understanding of queer of color and disability/crip critique, Chen's study reworlds or reorients disability studies, gender and sexuality studies, critical race theory, animal studies, affect studies, and linguistics. In all of these critical spaces, Animacies might be described as the breathtaking and revivifying book we have been waiting for."—Robert McRuer, author of Crip Theory: Cultural Signs of Queerness and Disability"This ambitious transdisciplinary analysis of the relations between humans, nonhuman animals, and matter charts a compelling and innovative rethinking of the biopolitics of 'animacy.' Mel Y. Chen animates animacy, a concept of sentience hierarchy derived in linguistics, to offer a far-ranging critique that implicates disability studies, queer of color critique, and postcolonial theory. The generative result is a timely and crucial intervention that foregrounds the oft-occluded import of race and sex in the rapidly growing fields of posthumanist theory, new materialisms, and animal studies."—Jasbir K. Puar, author of Terrorist Assemblages: Homonationalism in Queer Times

    Here, Michael Tomasello proposes a complementary theory of human uniqueness, focused on development. Building on the seminal ideas of Vygotsky, his data-driven model explains how those things that make us most human are constructed during the first years of a child's life.Tomasello assembles nearly three decades of experimental work with chimpanzees, bonobos, and human children to propose a new framework for psychological growth between birth and seven years of age. He identifies eight pathways that starkly differentiate humans from their closest primate relatives: social cognition, communication, cultural learning, cooperative thinking, collaboration, prosociality, social norms, and moral identity. In each of these, great apes possess rudimentary abilities. But then, Tomasello argues, the maturation of humans' evolved capacities for shared intentionality transform these abilities--through the new forms of sociocultural interaction they enable--into uniquely human cognition and sociality. The first step occurs around nine months, with the emergence of joint intentionality, exercised mostly with caregiving adults. The second step occurs around three years, with the emergence of collective intentionality involving both authoritative adults, who convey cultural knowledge, and coequal peers, who elicit collaboration and communication. Finally, by age six or seven, children become responsible for self-regulating their beliefs and actions so that they comport with cultural norms.Becoming Human places human sociocultural activity within the framework of modern evolutionary theory, and shows how biology creates the conditions under which culture does its work.

    DLC: Quantum theory.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    A unique combination of authoritative content and stimulating applications. * Numerous improvements in the text, based on feedback from the many users of the sixth edition (both instructors and students) * Several thousand end-of-chapter problems have been rewritten to streamline both the presentations and answers * 'Chapter Puzzlers' open each chapter with an intriguing application or question that is explained or answered in the chapter * Problem-solving tactics are provided to help beginning Physics students solve problems and avoid common error * The first section in every chapter introduces the subject of the chapter by asking and answering, "What is Physics?" as the question pertains to the chapter * Numerous supplements available to aid teachers and students The extended edition provides coverage of developments in Physics in the last 100 years, including: Einstein and Relativity, Bohr and others and Quantum Theory, and the more recent theoretical developments like String Theory.