The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

    These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

    From the early Greek influences to the Middle Ages and the Renaissance to the end of the 19th century, trace the fascinating foundation of mathematics as it developed through the ages. Aristotle, Galileo, Kepler, Newton: you know the names. Now here's what they really did, and the effect their discoveries had on our culture, all explained in a way the layperson can understand. Begin with the basis of arithmetic (Plato and the introduction of geometry), and discover why the use of Arabic numerals was critical to the development of both commerce and science. The development of calculus made space travel a reality, while the abacus prefigured the computer. The greats examined in depth include Leonardo da Vinci, a brilliant mathematician as well as artist; Pascal, who laid out the theory of probabilities; and Fermat, whose intriguing theory has only recently been solved.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Each self-contained chapter consists of three sections. The first describes the statistic, including how it is used and what information it provides. The second section reviews how it works, how to calculate the formula, the strengths and weaknesses of the technique, and the conditions needed for its use. The final section provides examples that use and interpret the statistic. A glossary of terms and symbols is also included.New features in the second edition include:an interactive CD with PowerPoint presentations and problems for each chapter including an overview of the problem's solution; new chapters on basic research concepts including sampling, definitions of different types of variables, and basic research designs and one on nonparametric statistics; more graphs and more precise descriptions of each statistic; and a discussion of confidence intervals.This brief paperback is an ideal supplement for statistics, research methods, courses that use statistics, or as a reference tool to refresh one's memory about key concepts. The actual research examples are from psychology, education, and other social and behavioral sciences.Materials formerly available with this book on CD-ROM are now available for download from our website www.psypress.com. Go to the book's page and look for the 'Download' link in the right-hand column.

    This discovery prompted a complete reevaluation of previous evidence for human origins.In the years since this dramatic discovery Johanson has continued to scour East Africa's Great rift Valley for the earliest evidence of human origins. In 1975 this team unearthed the "First Family", an unparalleled fossil assemblage of 13 individuals dating back to 3.2 million years ago; and in 1986 at the Rift's most famous location, Olduvai Gorge, this same team discovered a 1.8 million-year-old partial adult skeleton that necessitated a reassessment of the earliest members of our own genus Homo.Johanson's fieldwork continues unabated and recently more fossil members of Lucy's family have been found, including the 1992 discovery of the oldest, most complete skull of her species, with future research now planned for 1996 in the virtually unexplored regions of the most northern extension of the Rift Valley in Eritrea.From Lucy to Language is a summing up of this remarkable career and a stunning documentary of human life through time on Earth. It is a combination of the vital experience of field work and the intellectual rigor of primary research. It is the fusion of two great writing talents: Johanson and Blake Edgar, an accomplished science writer, editor of the California Academy of Sciences' Pacific Discovery, and co-author of Johanson's last book, Ancestors.From Lucy to Language is one of the greatest stories ever told, bracketing the timeline between bipedalism and human language. Part I addresses the central issues facing anyone seeking to decipher the mystery of human origins. In this section the authors provide answers to the basics -- "What are our closest living relatives?" -- tackle the controversial -- "What is race?" -- and contemplate the imponderables -- "Why did consciousness evolve?"From Lucy to Language is an encounter with the evidence. Early human fossils are hunted, discovered, identified, excavated, collected, preserved, labeled, cleaned, reconstructed, drawn, fondled, photographed, cast, compared, measured, revered, pondered, published, and argued over endlessly. Fossils like Lucy have become a talisman of sorts, promising to reveal the deepest secrets of our existence. In Part II the authors profile over fifty of the most significant early human fossils ever found. Each specimen is displayed in color and at actual size, most of them in multiple views. With them the authors present the cultural accoutrements associated with the fossils: stone tools which evidence increasing sophistication over time, the earliest stone, clay, and ivory art objects, and the culminating achievement of the dawn of human consciousness -- the magnificent rock and cave paintings of Europe, Africa, Australia, and the Americas.In the end From Lucy to Language is a reminder and a challenge. Like no species before us, we now seem poised to control vast parts of the planet and its life. We possess the power to influence, if not govern, evolution. For that reason, we must not forget our link to the natural world and our debt to natural selection. We need to "think deep", to add a dose of geologic time and evolutionary history to our perspective of who we are, where we came from, and where we are headed. This is the most poignant lesson this book has to offer.

    Murray's best-selling book "the most colorful and fun text to read in medical microbiology." Now it's back in an updated New Edition-and it's as succinct, user-friendly, and authoritative as ever. Readers will continue to enjoy its lucid discussions of how microbes cause disease in humans. Expert coverage of basic principles, the immune response, laboratory diagnosis, bacteriology, virology, mycology, and parasitology ensures they understand all the facts vital to the practice of medicine today. More than 550 brilliant full-color images make complex information easy to understand and illustrate the appearance of disease.The smart way to study!Elsevier titles with STUDENT CONSULT will help you master difficult concepts and study more efficiently in print and online! Perform rapid searches. Integrate bonus content from other disciplines. Download text to your handheld device. And a lot more. Each STUDENT CONSULT title comes with full text online, a unique image library, case studies, USMLE style questions, and online note-taking to enhance your learning experience.

    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.

    But in a world full of poisons, there was also an urgent practical need to name and recognize different plants, because most medicines were made from plant extracts.Anna Pavord takes us on a thrilling adventure into botanical history, traveling from Athens in the third century BC, through Constantinople, Venice, the medical school at Salerno to the universities of Pisa and Padua. The journey, traced here for the first time, involves the culture of Islam, the first expeditions to the Indies and the first settlers in the New World.In Athens, Aristotle's pupil Theophrastus was the first man ever to write a book about plants. How can we name, sort, and order them? He asked. The debate continues still, two thousand years later. Sumptuously illustrated in full colour, The Naming of Names gives a compelling insight into a world full of intrigue and intensely competitive egos.

    But what accounts for the incredible longevity of dinosaurs? A renowned scientist now provides a startling explanation that is rewriting the history of the Age of Dinosaurs. Dinosaurs were pretty amazing creatures--real-life monsters that have the power to fascinate us. And their fiery Hollywood ending only serves to make the story that much more dramatic. But fossil evidence demonstrates that dinosaurs survived several mass extinctions, and were seemingly unaffected by catastrophes that decimated most other life on Earth. What could explain their uncanny ability to endure through the ages? Biologist and earth scientist Peter Ward now accounts for the remarkable indestructibility of dinosaurs by connecting their unusual respiration system with their ability to adapt to Earth's changing environment--a system that was ultimately bequeathed to their descendants, birds. By tracing the evolutionary path back through time and carefully connecting the dots from birds to dinosaurs, Ward describes the unique form of breathing shared by these two distant relatives and demonstrates how this simple but remarkable characteristic provides the elusive explanation to a question that has thus far stumped scientists. Nothing short of revolutionary in its bold presentation of an astonishing theory, Out of Thin Air is a story of science at the edge of discovery. Ward is an outstanding guide to the process of scientific detection. Audacious and innovative in his thinking, meticulous and thoroughly detailed in his research, only a scientist of his caliber is capable of telling this surprising story.

    This book tells the version according to modern science. It is a unique account, starting at the Big Bang and traveling right up to the emergence of humans as conscious intelligent beings, 13.8 billion years later. Chapter by chapter, it sets out the current state of scientific knowledge: the origins of space and time; energy, mass, and light; galaxies, stars, and our sun; the habitable earth, and complex life itself. Drawing together the physical and biological sciences, Baggott recounts what we currently know of our history, highlighting the questions science has yet to answer.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

     Three and a half billion years ago, Mars resembled earth. It was warm and wet and could have supported primitive organisms. If life once existed on Mars, might it have originated there and traveled to earth inside meteorites blasted into space by cosmic impacts? Davies builds on recent scientific discoveries and theories to address larger questions of existence: What, exactly, is life? Is it the inevitable by-product of physical laws, as many scientists maintain, or an almost miraculous accident? Are we alone in the universe, or will life emerge on all earthlike planets? And if there is life elsewhere in the universe, is it preordained to evolve toward greater complexity and intelligence? Through his search for answers to these questions, Davies explores the ultimate mystery of mankind's existence -- who we are and what our place might be in the unfolding drama of the cosmos.

    The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.