Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    The fifth edition preserves the lucid, lively and comprehensive qualities which marked the book in its earlier versions. Numerous student learning aids are provided.

    Writing in venues like the New Republic and Commentary, such intellectuals were always expected to opine on a broad array of topics, from foreign policy to literature to economics. Yet in recent years a new kind of thinker has supplanted that archetype: the thought leader. Equipped with one big idea, thought leaders focus their energies on TED talks rather than highbrow periodicals. How did this shift happen? In The Ideas Industry, Daniel W. Drezner points to the roles of political polarization, heightened inequality, and eroding trust in authority as ushering in the change. In contrast to public intellectuals, thought leaders gain fame as single-idea merchants. Their ideas are often laudable and highly ambitious: ending global poverty by 2025, for example. But instead of a class composed of university professors and freelance intellectuals debating in highbrow magazines, thought leaders often work through institutions that are closed to the public. They are more immune to criticism--and in this century, the criticism of public intellectuals also counts for less.Three equally important factors that have reshaped the world of ideas have been waning trust in expertise, increasing political polarization and plutocracy. The erosion of trust has lowered the barriers to entry in the marketplace of ideas. Thought leaders don't need doctorates or fellowships to advance their arguments. Polarization is hardly a new phenomenon in the world of ideas, but in contrast to their predecessors, today's intellectuals are more likely to enjoy the support of ideologically friendly private funders and be housed in ideologically-driven think tanks. Increasing inequality as a key driver of this shift: more than ever before, contemporary plutocrats fund intellectuals and idea factories that generate arguments that align with their own. But, while there are certainly some downsides to the contemporary ideas industry, Drezner argues that it is very good at broadcasting ideas widely and reaching large audiences of people hungry for new thinking. Both fair-minded and trenchant, The Ideas Industry will reshape our understanding of contemporary public intellectual life in America and the West.

    In this brilliant study (his best-known and most controversial), he opposes the Marxist concept of dialectical materialism and its view that change takes place through "the struggle of opposites." Instead, he relates the rise of a capitalist economy to the Puritan determination to work out anxiety over salvation or damnation by performing good deeds — an effort that ultimately discouraged belief in predestination and encouraged capitalism. Weber's classic study has long been required reading in college and advanced high school social studies classrooms.

    Its authors present a new view of cognition that has important social and ethical implications, for, they assert, the only world we humans can have is the one we create together through the actions of our coexistence. Written for a general audience as well as for students, scholars, and scientists and abundantly illustrated with examples from biology, linguistics, and new social and cultural phenomena, this revised edition includes a new afterword by Dr. Varela, in which he discusses the effect the book has had in the years since its first publication.

    Includes: Dance through Religion for the Hell of It; The Physics of Synchronicity; James Joyce and Finnegan's Wake; The Godfather and the Goddess; The Poet as Early Warning Radar; Mammary Metaphysics; and, The Married Catholic Priests Convention.

    The case study at the center of Direct Action is the organizing and events that led to the one of the most dramatic and militant mass protests in recent years—against the Summit of the Americas in Québec City. Written in a clear, accessible style (with a minimum of academic jargon), this study brings readers behind the scenes of a movement that has changed the terms of debate about world power relations. From informal conversations in coffee shops to large “spokescouncil” planning meetings and tear gas-drenched street actions, Graeber paints a vivid and fascinating picture.Along the way, he addresses matters of deep interest to anthropologists: meeting structure and process, language, symbolism and representation, the specific rituals of activist culture, and much more. Starting from the assumption that, when dealing with possibilities of global transformation and emerging political forms, a disinterested, “objective” perspective is impossible, Graeber writes as both scholar and activist. At the same time, his experiment in the application of ethnographic methods to important ongoing political events is a serious and unique contribution to the field of anthropology, as well as an inquiry into anthropology’s political implications.David Graeber is an anthropologist and activist who teaches at the University of London. Active in numerous direct-action political organizations, he has written for Harper’s Magazine and is the author of Fragments of an Anarchist Anthropology, Towards an Anthropological Theory of Value, and Possibilities.In Oakland, California on March 24, 2015 a fire destroyed the AK Press warehouse along with several other businesses. Please consider visiting the AK Press website to learn more about the fundraiser to help them and their neighbors.

    What happens when this rationality transposes the constituent elements of democracy into an economic register? In Undoing the Demos, Wendy Brown explains how democracy itself is imperiled. The demos disintegrates into bits of human capital; concerns with justice bow to the mandates of growth rates, credit ratings, and investment climates; liberty submits to the imperative of human capital appreciation; equality dissolves into market competition; and popular sovereignty grows incoherent. Liberal democratic practices may not survive these transformations. Radical democratic dreams may not either.In an original and compelling argument, Brown explains how and why neoliberal reason undoes the political form and political imaginary it falsely promises to secure and reinvigorate. Through meticulous analyses of neoliberalized law, political practices, governance, and education, she charts the new common sense. Undoing the Demos makes clear that for democracy to have a future, it must become an object of struggle and rethinking.

    The new edition, An Enduring Debate, continues the important discussion of nuclear proliferation and the dangers of a nuclear-armed world. With new chapters on the questions surrounding a nuclear North Korea, Iran, and Iraq and the potential for a world free of nuclear weapons, this Third Edition will continue to generate a lively classroom experience.

    Since Wallerstein first developed world-systems analysis, it has become a widely utilized methodology within the historical social sciences and a common point of reference in discussions of globalization. Now, for the first time in one volume, Wallerstein offers a succinct summary of world-systems analysis and a clear outline of the modern world-system, describing the structures of knowledge upon which it is based, its mechanisms, and its future.Wallerstein explains the defining characteristics of world-systems analysis: its emphasis on world-systems rather than nation-states, on the need to consider historical processes as they unfold over long periods of time, and on combining within a single analytical framework bodies of knowledge usually viewed as distinct from one another—such as history, political science, economics, and sociology. He describes the world-system as a social reality comprised of interconnected nations, firms, households, classes, and identity groups of all kinds. He identifies and highlights the significance of the key moments in the evolution of the modern world-system: the development of a capitalist world-economy in the sixteenth-century, the beginning of two centuries of liberal centrism in the French Revolution of 1789, and the undermining of that centrism in the global revolts of 1968. Intended for general readers, students, and experienced practitioners alike, this book presents a complete overview of world-systems analysis by its original architect.

    His analysis explains not only the deficiencies of the self-regulating market, but the potentially dire social consequences of untempered market capitalism. New introductory material reveals the renewed importance of Polanyi's seminal analysis in an era of globalization and free trade.

    He shows how the insights of modern evolutionary theory, particularly on the evolution of cooperation, can help the left attain its social and political goals.Singer explains why the left originally rejected Darwinian thought and why these reasons are no longer viable. He discusses how twentieth-century thinking has transformed our understanding of Darwinian evolution, showing that it is compatible with cooperation as well as competition, and that the left can draw on this modern understanding to foster cooperation for socially desirable ends. A Darwinian left, says Singer, would still be on the side of the weak, poor, and oppressed, but it would have a better understanding of what social and economic changes would really work to benefit them. It would also work toward a higher moral status for nonhuman animals and a less anthropocentric view of our dominance over nature.

    Mirroring his theory, Minsky boldly casts The Society of Mind as an intellectual puzzle whose pieces are assembled along the way. Each chapter -- on a self-contained page -- corresponds to a piece in the puzzle. As the pages turn, a unified theory of the mind emerges, like a mosaic. Ingenious, amusing, and easy to read, The Society of Mind is an adventure in imagination.

    Based on his life's research, the author of the bestseller The Psychology of Consciousness provides a provocative look at the evolution of the mind.In Evolution of Consciousness Robert Ornstein explains that we are not rational but adaptive, and that it is Darwin, not Freud, who is the central scientist of the brain.

    That transition is the basis of this book. In From Science to God, he blends physics, psychology, and philosophy to reach a new worldview in which consciousness is a fundamental quality of creation. Russell shows how all the ingredients for this worldview are in place; it remains only to put the pieces together and explore the new picture of reality that emerges. Integrating a deep knowledge of science with his own experiences of meditation, Russell arrives at a universe similar to that described by many mystics — one in which the inner and outer worlds no longer conflict. The bridge between them, he shows, is light, and this book invites readers to cross that bridge to find new meaning in God and a deeper significance in spiritual practice.