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.

    KEY TOPICS: This classic book enables readers to make connections between classical and modern physics - an indispensable part of a physicist's education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation, to reflect today's physics curriculum. They introduce readers to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help readers to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the book remains fully accessible to readers who have not had an intermediate course in classical mechanics. MARKET: For college instructors and students.

    A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on.Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena.Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments, while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory.Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    He holds that the universe is self-aware, and that consciousness creates the physical world.

    Provides a review of introductory noncalculus-based physics for those who do not have a strong background in mathematics.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    From verbalizing chimpanzees to scientific speculations involving machines with souls, from the mesmerizing, maze-like fiction of Borges to the tantalizing, dreamlike fiction of Lem and Princess Ineffable, her circuits glowing read and gold, The Mind's I opens the mind to the Black Box of fantasy, to the windfalls of reflection, to new dimensions of exciting possibilities."Ever since David Hume declared in the 18th century that the Self is only a heap of perceptions, the poor Ego has been in a shaky conditions indeed...Mind and consciousness becomes dispensable items in our accounts of reality, ghosts in the bodily machine...Yet there are indications here and there that the tide may be tuming...and the appearance of The Mind's I, edited by Douglas R. Hofstadter and Daniel C. Dennett, seems a welcome sign of change." William Barrett, The New York Times Book Review

    V. Quine presents logic as the product of two factors, truth and grammar--but argues against the doctrine that the logical truths are true because of grammar or language. Rather, in presenting a general theory of grammar and discussing the boundaries and possible extensions of logic, Quine argues that logic is not a mere matter of words.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    However, while physicists celebrated these momentous discoveries—which presaged the era of big science and nuclear bombs—Europe was moving inexorably toward totalitarianism and war. In April of that year, about forty of the world’s leading physicists—including Werner Heisenberg, Lise Meitner, and Paul Dirac—came to Niels Bohr’s Copenhagen Institute for their annual informal meeting about the frontiers of physics. Physicist Gino Segrè brings to life this historic gathering, which ended with a humorous skit based on Goethe’s Faust—a skit that eerily foreshadowed events that would soon unfold. Little did the scientists know the Faustian bargains they would face in the near future. Capturing the interplay between the great scientists as well as the discoveries they discussed and debated, Segrè evokes the moment when physics—and the world—was about to lose its innocence.

    Readers will find excerpts from bestsellers such as Douglas R. Hofstadter's Gödel, Escher, Bach, Francis Crick's Life Itself, Loren Eiseley's The Immense Journey, Daniel Dennett's Darwin's Dangerous Idea, and Rachel Carson's The Sea Around Us. There are classic essays ranging from J.B.S. Haldane's "On Being the Right Size" and Garrett Hardin's "The Tragedy of the Commons" to Alan Turing's "Computing Machinery and Intelligence" and Albert Einstein's famed New York Times article on "Relativity." And readers will also discover lesser-known but engaging pieces such as Lewis Thomas's "Seven Wonders of Science," J. Robert Oppenheimer on "War and Physicists," and Freeman Dyson's memoir of studying under Hans Bethe.A must-read volume for all science buffs, The Oxford Book of Modern Science Writing is a rich and vibrant anthology that captures the poetry and excitement of scientific thought and discovery.One of New Scientist's Editor's Picks for 2008.

    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.

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

    From Edward Lorenz’s discovery of the Butterfly Effect, to Mitchell Feigenbaum’s calculation of a universal constant, to Benoit Mandelbrot’s concept of fractals, which created a new geometry of nature, Gleick’s engaging narrative focuses on the key figures whose genius converged to chart an innovative direction for science. In Chaos, Gleick makes the story of chaos theory not only fascinating but also accessible to beginners, and opens our eyes to a surprising new view of the universe.