Against the backdrop of Archimedes's life and culture, the author discusses the man's work, his discoveries and the knowledge later based upon it. The simple, often humorous, illustrations and diagrams greatly enhance the text. Ages 10 and up.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    This reissue of a classic will reintroduce readers to Lévi-Strauss’s understanding of man and society in terms of individuals—kinship, social organization, religion, mythology, and art.

    His dissections of science, spiritual faith, legal systems, vanity, and love make him the undisputed master of social commentary.

    

    Also known as the Cyropaedia, this philosophical novel is loosely based on the accomplishments of Cyrus the Great, founder of the vast Persian Empire that later became the archrival of the Greeks in the classical age. It offers an extraordinary portrait of political ambition, talent, and their ultimate limits.The writings of Xenophon are increasingly recognized as important works of political philosophy. In The Education of Cyrus, Xenophon confronts the vexing problem of political instability by exploring the character and behavior of the ruler. Impressive though his successes are, however, Cyrus is also examined in the larger human context, in which love, honor, greed, revenge, folly, piety, and the search for wisdom all have important parts to play.Wayne Ambler's translation captures the charm and drama of the work while also achieving great accuracy. His introduction, annotations, and glossary help the reader to appreciate both the engaging story itself and the volume's contributions to philosophy.

    Written in short, carefully numbered paragraphs of extreme brilliance, it captured the imagination of a generation of philosophers. For Wittgenstein, logic was something we use to conquer a reality which is in itself both elusive and unobtainable. He famously summarized the book in the following words: 'What can be said at all can be said clearly; and what we cannot talk about we must pass over in silence.' David Pears and Brian McGuinness received the highest praise for their meticulous translation. The work is prefaced by Bertrand Russell's original introduction to the first English edition.

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    Mingling acute observation with often wild speculation, it offers a fascinating view of the world as it was understood in the first century AD, whether describing the danger of diving for sponges, the first water-clock, or the use of asses’ milk to remove wrinkles. Pliny himself died while investigating the volcanic eruption that destroyed Pompeii in AD 79, and the natural curiosity that brought about his death is also very much evident in the Natural History — a book that proved highly influential right up until the Renaissance and that his nephew, Pliny the younger, described ‘as full of variety as nature itself’. John F. Healy has made a fascinating and varied selection from the Natural History for this clear, modern translation. In his introduction, he discusses the book and its sources topic by topic. This edition also includes a full index and notes.

    It reveals the underlying radical coherency of his view of the world - from his enormously influential attacks on America's role in Vietnam to his perspective on Nicaragua and Central America Today. Chomsky's challenge to accepted wisdom about Israel and the Palestinians has caused a furore in America, as have his trenchant essays on the real nature of terrorism in our age. No one has dissected more graphically the character of the cold war consensus and the way it benefits the two superpowers, and argued more thoughtfully for a shared elitist ethos in liberalism and communism. No one has exposed more logically America's acclaimed freedoms as masking irresponsible power and unjustified privilege, or argued quite so insistently that the "free press" is part of a stultifying conformity that pervades all aspects of American intellectual life.

    But their enterprise was by no means limited to this proto-scientific task. Through, for instance, Heraclitus' enigmatic sayings, the poetry of Parmenides and Empedocles, and Zeno's paradoxes, the Western world was introduced to metaphysics, rationalist theology, ethics, and logic, by thinkers who often seem to be mystics or shamans as much as philosophers or scientists in the modern mould. And out of the Sophists' reflections on human beings and their place in the world arose and interest in language, and in political, moral, and social philosophy.This volume contains a translation of all the most important fragments of the Presocratics and Sophists, and of the most informative testimonia from ancient sources, supplemented by lucid commentary.