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."

    This world of total human experience is the world that is (or at least ought to be) reflected and molded by the arts, above all by the art of literature. "What is the function of literature," Mr. Huxley asks, "what its psychology, what the nature of literary language? And how do its function, psychology and language differ from those of science? What in the past has been the relationship between literature and science? What is it now? What might it be in the future? And what would it be profitable, artistically speaking, for a twentieth-century man of letters to do about twentieth-century science?"Ours is the Age of Science; but from a study of the best contemporary literature one would find it difficult to infer this most obvious of facts. Contemporary poetry, drama and fiction contain remarkably few references to contemporary science—few references even to the metaphysical and ethical problems which contemporary science has raised. That this state of affairs should somehow be remedied is the theme of every recent discussion of "the Two Cultures." unfortunately most of these discussions have been carried on in abstract terms and with almost no citations of case histories, no references to the concrete problems of literary and scientific writing, no illustrative examples. Mr. Huxley has approached the subject in a different way. He deals with specific questions in the fields of immediate experience, of conceptualization, of philosophical interpretation and of verbal expression; and he illustrates these wide-ranging themes with copious quotations, drawn from a great variety of sources. He analyzes the nature of literary language and contrasts its many-meaninged richness with the simplified and jargonized language of science. He shows how the poets of earlier centuries made use of the scientific knowledge available to them. He gives examples of the ways in which modern science has modified and added to the traditional raw materials of literature. And he concludes with a speculative discussion of the ways in which future men of letters may work up the raw materials of brand new fact and revolutionary hypothesis provided by science, transfiguring them into a new kind of literature, capable of expression and at the same time coordinating and giving significance to the totality of an ever-widening human experience.

    Exploring issues that range from faith to prayer to evil to immortality, and far beyond, Garnder challenges the discerning reader with fundamental questions of classical philosophy and life's greater meanings.Recalling such philosophers was Wittgenstein and Arendt, The Whys of Philosophical Scrivener embodies Martin Garner's unceasing interest and joy in the impenetrable mysteries of life.

    His apothegm "Cogito, ergo sum" marked the birth of the mind-body problem, while his creation of so-called Cartesian coordinates have made our physical and intellectual conquest of physical space possible.But Descartes had a mysterious and mystical side, as well. Almost certainly a member of the occult brotherhood of the Rosicrucians, he kept a secret notebook, now lost, most of which was written in code. After Descartes's death, Gottfried Leibniz, inventor of calculus and one of the greatest mathematicians in history, moved to Paris in search of this notebook--and eventually found it in the possession of Claude Clerselier, a friend of Descartes. Leibniz called on Clerselier and was allowed to copy only a couple of pages--which, though written in code, he amazingly deciphered there on the spot. Leibniz's hastily scribbled notes are all we have today of Descartes's notebook, which has disappeared.Why did Descartes keep a secret notebook, and what were its contents? The answers to these questions lead Amir Aczel and the reader on an exciting, swashbuckling journey, and offer a fascinating look at one of the great figures of Western culture.

    

    The author rebuts all the major objections to this theory and shows that the alternative theories about the nature of ethics all face grave difficulties.

    Each chapter, or unit, is divided into easily comprehended small "bites" that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics. For individuals interested in the formal study of logic.

    Yet in the late twentieth century truth became suddenly rather unfashionable. The precedence given to assorted political and ideological agendas, along with the rise of relativism, postmodernism and pseudoscience in academia, led to a decline both of truth as a serious subject, and an intellectual tradition that began with the Enlightenment.Why Truth Matters is a timely, incisive and entertaining look at how and why modern thought and culture lost sight of the importance of truth. It is also an eloquent and inspiring argument for restoring truth to its rightful place. Jeremy Stangroom and Ophelia Benson, editors of the successful butterfliesandwheels website—itself established to "fight fashionable nonsense"—identify and debunk such senselessness, and the spurious claims made for it, in all its forms. Their account ranges over religious fundamentalism, Holocaust denial, the challenges of postmodernism and deconstruction, the wilful misinterpretation of evolutionary biology, identity politics and wishful thinking.Why Truth Matters is both a rallying cry for the Enlightenment vision and an essential read for anyone who's ever been bored, frustrated, bewildered or plain enraged by the worst excesses of the fashionable intelligentsia.

    This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

    Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

    Each section also includes quizzes, games, and mental exercises.

    It covers areas such as fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding.

    C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is a detailed and subtle exposition of concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself. In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.

    Each chapter opens with a surprising insight—not a mathematic formula, but a common observation. From there, the authors leapfrog over math and anecdote toward profound ideas about nature, art, and music. Coincidences is a book for lovers of puzzles and posers of outlandish questions, lapsed math aficionados and the formula-phobic alike.

    George Feuerstein has drawn short, memorable quotations from the key texts of this five-thousand-year-old legacy, with an emphasis on the wisdom of modern yoga masters.The quotations have been selected and arranged to address the needs of yoga practitioners in the twenty-first century.Among the many themes touched on in this treasure of a book: the process of inner growth; the value of silence; how to meditate; how to infuse everyday life with joy; universal kinship; overcoming suffering; dealing with grief, loss, anger, and jealousy; remembering and cultivating one’s true inner self; developing self-discipline; and bringing out the good in all you say and do.For both new and experienced yoga students alike, Yoga Gems is the perfect travel companion on the road to inner peace.