It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable. Professor of Computer Science at the UCLA, Judea Pearl is the winner of the 2008 Benjamin Franklin Award in Computers and Cognitive Science.

    Not just a collection of anecdotes but a fair, reasoned appraisal of eccentric theory, it is unique in recognizing the scientific, philosophic, and sociological-psychological implications of the wave of pseudoscientific theories which periodically besets the world.To this second revised edition of a work formerly titled In the Name of Science, Martin Gardner has added new, up-to-date material to an already impressive account of hundreds of systematized vagaries. Here you will find discussions of hollow-earth fanatics like Symmes; Velikovsky and wandering planets; Hörbiger, Bellamy, and the theory of multiple moons; Charles Fort and the Fortean Society; dowsing and the other strange methods for finding water, ores, and oil. Also covered are such topics as naturopathy, iridiagnosis, zone therapy, food fads; Wilhelm Reich and orgone sex energy; L. Ron Hubbard and Dianetics; A. Korzybski and General Semantics. A new examination of Bridey Murphy is included in this edition, along with a new section on bibliographic reference material.

    It far surpasses any previous explanation of Relativity for laypersons.

    A fun and fascinating look at great scientific paradoxes.   Throughout history, scientists have come up with theories and ideas that just don't seem to make sense.  These we call paradoxes.  The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.  For example, how can a cat be both dead and alive at the same time?  Why will Achilles never beat a tortoise in a race, no matter how fast he runs?  And how can a person be ten years older than his twin?   With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle.  Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic.  In doing so, he brings to life a select group of the most exciting concepts in human knowledge.  Paradox is mind-expanding fun.

    Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory. This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems. The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, Euler's formula will still be beautiful and stunning and untarnished by time.

    40 illustrations throughout.

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    But now, with the aid of high-speed computers, scientists have been able to penetrate a reality that is changing the way we perceive the universe. Their findings -- the basis for chaos theory -- represent one of the most exciting scientific pursuits of our time.No better introduction to this find could be found than John Briggs and F. David Peat's Turbulent Mirror. Together, they explore the many faces of chaos and reveal how its law direct most of the processes of everyday life and how it appears that everything in the universe is interconnected -- discovering an "emerging science of wholeness."Turbulent Mirror introduces us to the scientists involved in study this endlessly strange field; to the theories that are turning our perception of the world on its head; and to the discoveries in mathematics, biology, and physics that are heralding a revolution more profound than the one responsible for producing the atomic bomb. With practical applications ranging from the control of traffic flow and the development of artifical intelligence to the treatment of heart attacks and schizophrenia, chaos promises to be an increasingly rewarding area of inquiry -- of interest to everyone.

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension. So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.

    Explaining why the whole is sometimes smarter than the sum of its parts, Johnson presents surprising examples of feedback, self-organization, and adaptive learning. How does a lively neighborhood evolve out of a disconnected group of shopkeepers, bartenders, and real estate developers? How does a media event take on a life of its own? How will new software programs create an intelligent World Wide Web? In the coming years, the power of self-organization -- coupled with the connective technology of the Internet -- will usher in a revolution every bit as significant as the introduction of electricity. Provocative and engaging, Emergence puts you on the front lines of this exciting upheaval in science and thought.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.