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.

    The selections range from his earliest days as a theoretical physicist to his death in 1955; from such subjects as relativity, nuclear war or peace, and religion and science, to human rights, economics, and government.

    His great book, On Nature, the world's first coherent philosophical treatise and touchstone for Plato, Aristotle, and Marcus Aurelius, has long been lost to history-but its surviving fragments have for thousands of years tantalized our greatest thinkers, from Montaigne to Nietzsche, Heidegger to Jung. Now, acclaimed poet Brooks Haxton presents a powerful free-verse translation of all 130 surviving fragments of the teachings of Heraclitus, with the ancient Greek originals beautifully reproduced en face.For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

    Leibniz' Monadology, one of the most important pieces of the Leibniz corpus, is at once one of the great classics of modern philosophy & one of its most puzzling productions. Because the essay is written in so compactly condensed a fashion, for almost three centuries it has baffled & beguiled those who read it for the first time. Nicholas Rescher accompanies the text of the Monadology section-by-section with relevant excerpts from some of Leibniz' widely scattered discussions of the matters at issue. The result serves a dual purpose of providing a commentary of the Monadology by Leibniz himself, while at the same time supplying an exposition of his philosophy using the Monadology as an outline. The book contains all the materials that even the most careful study of this text could require: a detailed overview of the philosophical background of the work & of its bibliographic ramifications; a presentation of the original French text together with a new, closely faithful English translation; a selection of other relevant Leibniz texts; & a detailed commentary. Rescher also provides a survey of Leibniz' use of analogies & three separate indices of key terms & expressions, Leibniz' French terminology, & citations. Rescher's edition of the Monadology presents Leibniz' ideas faithfully, accurately & accessibly, making it especially valuable to scholars & students alike.

    These provide the basis for a detailed critical study of the principal individual thinkers of the time. Besides serving as an essential text for undergraduate and graduate courses in Greek philosophy and in the history of science, this book will appeal to a wide range of readers with interests in philosophy, theology, the history of ideas and of the ancient world, and indeed to anyone who wants an authoritative account of the Presocratics.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    This unique selection of illustrations with commentaries and source texts guides us on a fascinating journey through the representations of the secret arts.

    But most residents of Denmark and Sweden, he found, don't worship any god at all, don't pray, and don't give much credence to religious dogma of any kind. Instead of being bastions of sin and corruption, however, as the Christian Right has suggested a godless society would be, these countries are filled with residents who score at the very top of the "happiness index" and enjoy their healthy societies, which boast some of the lowest rates of violent crime in the world (along with some of the lowest levels of corruption), excellent educational systems, strong economies, well-supported arts, free health care, egalitarian social policies, outstanding bike paths, and great beer.Zuckerman formally interviewed nearly 150 Danes and Swedes of all ages and educational backgrounds over the course of fourteen months. He was particularly interested in the worldviews of people who live their lives without religious orientation. How do they think about and cope with death? Are they worried about an afterlife? What he found is that nearly all of his interviewees live their lives without much fear of the Grim Reaper or worries about the hereafter. This led him to wonder how and why it is that certain societies are non-religious in a world that seems to be marked by increasing religiosity. Drawing on prominent sociological theories and his own extensive research, Zuckerman ventures some interesting answers.This fascinating approach directly counters the claims of outspoken, conservative American Christians who argue that a society without God would be hell on earth. It is crucial, Zuckerman believes, for Americans to know that "society without God is not only possible, but it can be quite civil and pleasant."

    Now available in a smaller, more convenient format, the astonishingly in-depth and widely praised Oxford History of the Classical World offers the general reader the definitive companion to the Graeco-Roman world.The first volume, Classical Greece and the Hellenistic World, covers the period from the eighth to the first centuries B.C., a period unparalleled in history for its brilliance in literature, philosophy, and the visual arts. It also treats the Hellenization of the Middle East by the monarchies established in the area conquested by Alexander the Great. The second volume, Classical Rome, covers early Rome and Italy, the expansion of the Roman republic, the foundation of the Roman Empire by Augustus, its consolidation in the first two centuries A.D., and the later Empire and its influence on Western civilization. The editors, John Boardman, Jasper Griffen, and Oswyn Murray—all eminent classicists—intersperse chapters on political and social history with sections on literature, philosophy, and the arts, and reinforce the historical framework with maps and historical charts. The two volumes also offer bibliographies and a full index, as well as black and white photographs integrated into the text. The contributors—thirty of the world's leading scholars—present the latest in modern scholarship through masterpieces of wit, brevity, and style. While concentrating on the aspects essential to the understanding of each period, they also focus on those elements of the classical world that remain of lasting importance and interest to readers today. Together, these volumes provide both a provocative and entertaining window into our classical heritage.

    From the Pulitzer Prize-winning author of The Denial of Death, a penetrating and insightful perspective on the source of evil in our world."A profound, nourishing book…absolutely essential to the understanding of our troubled times." —Anais Nin"An urgent essay that bears all the marks of a final philosophical raging against the dying of the light." —Newsweek

    Delving into an immense range of topics, from philosophy and literature to social criticism to mathematics and science, with essays that date from 1930s to the 1990s, Martin Gardner has astounded readers with his insight and erudition. The Night Is Large is the crowning achievement of his extraordinary career.

    Whether you were the king's court astrologer or a farmer marking the best time for planting, timekeeping and numbers really mattered. Mistake a numerical pattern of petals and you could be poisoned. Lose the rhythm of a sacred dance or the meter of a ritually told story and the intricately woven threads that hold life together were spoiled. Ignore the celestial clock of equinoxes and solstices, and you'd risk being caught short of food for the winter. Shesso's friendly tone and clear grasp of the information make the math "go down easy" in this marvelous book.BONUS: This book has over 100 illustrations! Click on the Google Preview link to get a glimpse.Excerpt from Math for Mystics: “It’s our collective malaise: Post-Traumatic Math Disorder.“Yet despite how we personally feel about mathematics, our distant ancestors willingly used numbers as pathways into the great patterns of Nature, avenues to understanding the Universe and their own place in it. Many ancient cultures had specific gods and goddesses they credited with inventing mathematical skills. With the aid of divine inspiration and assistance, humans nourished this numerical invention, continually pushing their skills and seeking greater clarity of expression. “Our starting point may seem like a Zero. But for now, before looking at numbers and math, let’s simply see it as a circle. No matter what our spiritual practice, we each live within the circle of creation, each within the circle—the cohesiveness—of our own form...” From John Michael Greer, Grand Archdruid, Ancient Order of Druids in America and author of The Druidry Handbook:“As thoughtful as it is readable, Renna Shesso’s Math for Mystics is the book I wish I had when I first started trying to make sense of the mathematics that underlie so much of modern magic and traditional occult lore. Not the least of its virtues is the way it makes magical number theory accessible even to those who think they don’t like or can’t handle math. It provides a first-rate introduction to a fairly neglected branch of magical lore.”

    Psychology is the only branch of learning in which I am particularly versed. To the psychologist the religious propensities of man must be at least as interesting as any other of the facts pertaining to his mental constitution. It would seem, therefore, as a psychologist, the natural thing for me would be to invite you to a descriptive survey of those religious propensities." When William James went to the University of Edinburgh in 1901 to deliver a series of lectures on "natural religion," he defined religion as "the feelings, acts, and experiences of individual men in their solitude, so far as they apprehend themselves to stand in relation to whatever they may consider the divine." Considering religion, then, not as it is defined by--or takes place in--the churches, but as it is felt in everyday life, he undertook a project that, upon completion, stands not only as one of the most important texts on psychology ever written, not only as a vitally serious contemplation of spirituality, but for many critics one of the best works of nonfiction written in the 20th century. Reading The Varieties of Religious Experience, it is easy to see why. Applying his analytic clarity to religious accounts from a variety of sources, James elaborates a pluralistic framework in which "the divine can mean no single quality, it must mean a group of qualities, by being champions of which in alternation, different men may all find worthy missions." It's an intellectual call for serious religious tolerance--indeed, respect--the vitality of which has not diminished through the subsequent decades.

    It provides a wide survey of Greek science, metaphysics, and moral and political philosophy, from their roots in myth to the philosophers and Sophists of the fifth century. A comprehensive selection of fragments and testimonia, translated by the author, is presented in the context of a thorough and accessible discussion. An introductory chapter deals with the sources of Presocratic and Sophistic texts and the special problems of interpretation they present.In its second edition, this work has been updated and expanded to reflect important new discoveries and the most recent scholarship. Changes and additions have been made throughout, the most significant of which are found in the chapters on the Pythagoreans, Parmenides, Zeno, Anaxagoras, and Empedocles, and the new chapter on Philolaus. The translations of some passages have been revised, as have some interpretations and discussions. A new Appendix provides translations of three Hippocratic writings and the Derveni papyrus.

    He considered the doctrines of faith an invitation to question, to think, and to learn; and he devoted his life to confronting and understanding the most elusive aspects of Christianity. His writings on matters such as free will, the nature of truth, and the existence of God make Anselm one of the greatest theologians and philosophers in history, and this translation provides readers with their first opportunity to read his most important works within a single volume.