Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space -- in the living room or in some other galaxy -- have been the hidden engine of the highest achievements in science and technology. Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    A scholar, wit, lawyer and statesman, he wrote widely on politics, philosophy and science - declaring early in his career that 'I have taken all knowledge as my province'. In this, his most famous work, he considers a diverse range of subjects, such as death and marriage, ambition and atheism, in prose that is vibrant and rich in Renaissance learning. Bacon believed that rhetoric - the force of eloquence and persuasion - could lead the mind to the pure light of reason, and his own rhetorical genius is nowhere better expressed than in these vivid essays.

    Why do living things and physical phenomena take the forms they do? Analyzing the mathematical and physical aspects of biological processes, this historic work, first published in 1917, has become renowned as well for the poetry of is descriptions.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    His public advocacy of the Copernican over the Aristotelian system of the universe flew directly in the face of biblical authority and ecclesiastical tradition. Condemned and placed under house arrest by the Inquisition, Galileo nonetheless devoted his last years to the completion of his Dialogues Concerning Two New Sciences, which deals with motion and the resistance of solids. The Two New Sciences, which Galileo called his most important work, may be regarded as the summary statement of a life devoted to scientific experimentation and free inquiry untrammeled by tradition and authority.

    Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate-functor logic and the affinities between higher set theory and the elementary logic of terms, W. V. Quine's new edition will serve admirably for both classroom and independent use.

    The central work by one of the century's most influential thinkers, it altered the course of western philosophy. Its revolutionary approach challenged all previous assumptions about the individual's relationship with the world. Known as 'the Bible of existentialism', its impact on culture & literature was immediate & was felt worldwide, from the absurdist drama of Samuel Beckett to the soul-searching cries of the Beat poets.Being & Nothingness is one of those rare books whose influence has affected the mindset of subsequent generations. Seventy years after its 1st publication, its message remains as potent as ever--challenging readers to confront the fundamental dilemmas of human freedom, choice, responsibility & action.

    Louis are all intimately connected with the mysterious number e. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of e to mathematics and illuminates a golden era in the age of science.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    It furnishes us with a key to his main work, The Critique of Pure Reason; in fact, it is an extract containing all the salient ideas of Kant's system. It approaches the subject in the simplest and most direct way, and is therefore best adapted as an introduction into his philosophy.

    

    Unique in western philosophy for his affinity with Eastern thought, Schopenhauer influenced philosophers, writers, and composers including Nietzsche, Wittgenstein, Wagner, Tolstoy, Thomas Mann, and Samuel Beckett.The Work presented here appeals not only to the student of philosophy but everyone interested in psychology, literature and eastern and western religion. This paperback edition is the most comprehensive available and includes an introduction, bibliography, selected criticism, index and chronology of Schopenhauer's life and times.