But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.

    More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field.

    In The Beginnings of Western Science, David C. Lindberg provides a rich chronicle of the development of scientific ideas, practices, and institutions from the pre-Socratic Greek philosophers to the late-medieval scholastics.Lindberg surveys all the most important themes in the history of ancient and medieval science, including developments in cosmology, astronomy, mechanics, optics, alchemy, natural history, and medicine. He synthesizes a wealth of information in superbly organized, clearly written chapters designed to serve students, scholars, and nonspecialists alike. In addition, Lindberg offers an illuminating account of the transmission of Greek science to medieval Islam and subsequently to medieval Europe. And throughout the book he pays close attention to the cultural and institutional contexts within which scientific knowledge was created and disseminated and to the ways in which the content and practice of science were influenced by interaction with philosophy and religion. Carefully selected maps, drawings, and photographs complement the text.Lindberg's story rests on a large body of important scholarship produced by historians of science, philosophy, and religion over the past few decades. However, Lindberg does not hesitate to offer new interpretations and to hazard fresh judgments aimed at resolving long-standing historical disputes. Addressed to the general educated reader as well as to students, his book will also appeal to any scholar whose interests touch on the history of the scientific enterprise.

    By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

    Like a Wu Li Master who would teach us wonder for the falling petal before speaking of gravity, Zukav writes in beautifully clear language—with no mathematical equations—opening our minds to the exciting new theories that are beginning to embrace the ultimate nature of our universe...Quantum mechanics, relativity, and beyond to the Einstein-Podolsky-Rosen effect and Bell's theorem.At an Esalen Institute meeting in 1976, tai chi master Al Huang said that the Chinese word for physics is Wu Li, "patterns of organic energy." Journalist Gary Zukav and the others present developed the idea of physics as the dance of the Wu Li Masters--the teachers of physical essence. Zukav explains the concept further: The Wu Li Master dances with his student. The Wu Li Master does not teach, but the student learns. The Wu Li Master always begins at the center, the heart of the matter.... This book deals not with knowledge, which is always past tense anyway, but with imagination, which is physics come alive, which is Wu Li.... Most people believe that physicists are explaining the world. Some physicists even believe that, but the Wu Li Masters know that they are only dancing with it. The "new physics" of Zukav's 1979 book comprises quantum theory, particle physics, and relativity. Even as these theories age they haven't percolated all that far into the collective consciousness; they're too far removed from mundane human experience not to need introduction. The Dancing Wu Li Masters remains an engaging, accessible way to meet the most profound and mind-altering insights of 20th-century science. --Mary Ellen Curtin

    This new edition, prepared by an acclaimed translator and scholar of Kant's practical philosophy, presents the first new translation of the work to appear for many years, together with a substantial and lucid introduction.

    In this new major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire oeuvre. This is the first book which deal comprehensively and in depth with Einstein's science, both the successes and the failures.Running through the book is a completely non-scientific biography (identified in the table of contents by italic type) including many letters which appear in English for the first time, as well as other information not published before.Throughout the preparation of this book, Pais has had complete access to the Einstein Archives (now in the possession of the Hebrew University) and the invaluable guidance of the late Helen Dukas--formerly Einstein's private secretary.

    Volume 1 was published in 1776, going thru six printings; 2-3 in 1781; 4-6 in 1788-89. It was a major literary achievement of the 18th century, adopted as a model for the methodologies of historians.The books cover the Roman Empire after Marcus Aurelius, from 180 to 1590. They take as their material the behavior & decisions that led to the eventual fall of the Empire in East & West, offering explanations.Gibbon is called the 1st modern historian of ancient Rome. By virtue of its mostly objective approach & accurate use of reference material, his work was adopted as a model for the methodologies of 19-20th century historians. His pessimism & detached irony was common to the historical genre of his era. Although he published other books, Gibbon devoted much of his life (1772-89) to this one work. His Memoirs of My Life & Writings is devoted largely to his reflections on how the book virtually became his life. He compared the publication of each succeeding volume to a newborn.Gibbon offers an explanation for why the Roman Empire fell, a task difficult because of few comprehensive written sources, tho he wasn't the only historian to tackle the subject. Most of his ideas are taken from what few relevant records were available: those of Roman moralists of the 4-5th centuries. According to Gibbon, the Empire succumbed to barbarian invasions because of lost of civic virtue. They'd become weak, outsourcing defence to barbarian mercenaries, who became so numerous & ingrained that they took over. Romans had become effeminate, incapable of tough military lifestyles. In addition, Christianity created belief that a better life existed after death, fostering indifference to the present, sapping patriotism. Its comparative pacifism tended to hamper martial spirit. Lastly, like other Enlightenment thinkers, he held in contempt the Middle Ages as a priest-ridden, superstitious, dark age. It wasn't until his age of reason that history could progress.

    Emerson offers timeless meditations on the value of individual greatness, reconnecting readers with the everyday virtues of his “Representative Men”: Plato, in whose writings are contained “the culture of nations”; Emanuel Swedenborg, a “rich discoverer” who strove to unite the scientific and spiritual planes; Michel de Montaigne, “the frankest and honestest of all writers”; William Shakespeare, who “wrote the text of modern life”; Napoleon Bonaparte, who had the “virtues and vices” of common men writ large; and Johann Wolfgang von Goethe, who “in conversation, in calamity…finds new materials.”This Modern Library Paperback Classic reflects the author’s corrections for an 1876 reprinting.

    Through the dramatic characterization of the famous physicist, Brecht examines the issues of scientific morality and the difficult relationship between the intellectual and authority. This version of the play is the famous one that was brought to completion by Brecht himself, working with Charles Laughton, who played Galileo in the first two American productions (Hollywood and New York, 1947). Since then the play has become a classic in the world repertoire. "The play which most strongly stamped on my mind a sense of Brecht's great stature as an artist of the modern theatre was Galileo." - Harold Clurman; "Thoughtful and profoundly sensitive." - Newsweek.

    Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    It begins with a Preface, created after the rest of the manuscript was completed, that explains the core of his method and what sets it apart from any preceding philosophy. The Introduction, written before the rest of the work, summarizes and completes Kant's ideas on skepticism by rendering it moot and encouraging idealism and self-realization. The body of the work is divided into six sections of varying length, entitled "Consciousness," "Self-Consciousness," "Reason," "Spirit," "Religion," and "Absolute Knowledge." A myriad of topics are discussed, and explained in such a harmoniously complex way that the method has been termed Hegelian dialectic. Ultimately, the work as a whole is a remarkable study of the mind's growth from its direct awareness to scientific philosophy, proving to be a difficult yet highly influential and enduring work.

    About The Author: Henry Gray, F.R.S., Fellow of the royal college of Surgeons: Lecturer on anatomy at St. George?s Hospital Medical School. Table Of Contents: Descriptive and Surgical Anatomy The Articulations Muscles and Fasclae The Blood-vascular system The Lymphatics The Nervous system The Organs of special sense The Organs of Digestion The Organs of voice and respiration The urinary organs The Male Organs of Generation The Female Organs of Generation The Surgical Anatomy of Hernia Surgical Anatomy of the Perinaeum General Anatomy or Histology Embryology