This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.

    Monk's life of Wittgenstein is such a one."--"The Christian Science Monitor."

    An authoritative introduction to "fuzzy logic" brings readers up to speed on the "smart" products and computers that will change all of our lives in the future.

    Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the humanist idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

    Inspired by and expanding on a series of lectures presented by Leonard Peikoff, David Harriman presents a fascinating answer to the problem of induction-the epistemological question of how we can know the truth of inductive generalizations.Ayn Rand presented her revolutionary theory of concepts in her book Introduction to Objectivist Epistemology. As Dr. Peikoff subsequently explored the concept of induction, he sought out David Harriman, a physicist who had taught philosophy, for his expert knowledge of the scientific discovery process.Here, Harriman presents the result of a collaboration between scientist and philosopher. Beginning with a detailed discussion of the role of mathematics and experimentation in validating generalizations in physics-looking closely at the reasoning of scientists such as Galileo, Kepler, Newton, Lavoisier, and Maxwell-Harriman skillfully argues that the inductive method used in philosophy is in principle indistinguishable from the method used in physics.

    Suitable for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory, this book aims to give students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences.

    Notions like denumerability, modal scope distinction, Bayesian conditionalization, and logical completeness are usually only elucidated deep within difficultspecialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists.The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outliningthe difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Godel's theorem.Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read withpleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.

    These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

    It is universally recognized as the standard English version of Aristotle. This revised edition contains the substance of the original translation, slightly emended in light of recent scholarship; three of the original versions have been replaced by new translations; and a new and enlarged selection of Fragments has been added. The aim of the translation remains the same: to make the surviving works of Aristotle readily accessible to English speaking readers.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    How can today's computers perform such a bewildering variety of tasks if computing is just glorified arithmetic? The answer, as Martin Davis lucidly illustrates, lies in the fact that computers are essentially engines of logic. Their hardware and software embody concepts developed over centuries by logicians such as Leibniz, Boole, and Godel, culminating in the amazing insights of Alan Turing. The Universal Computer traces the development of these concepts by exploring with captivating detail the lives and work of the geniuses who first formulated them. Readers will come away with a revelatory understanding of how and why computers work and how the algorithms within them came to be.

    The author suggests that, like the black holes of outer space, from which nothing, not even light, can escape, our contemporary cultural landscape contains numerous intellectual black-holes—belief systems constructed in such a way that unwary passers-by can similarly find themselves drawn in. While such self-sealing bubbles of belief will most easily trap the gullible or poorly educated, even the most intelligent and educated of us are potentially vulnerable. Some of the world’s greatest thinkers have fallen in, never to escape. This witty, insightful critique will help immunize readers against the wiles of cultists, religious and political zealots, conspiracy theorists, promoters of flaky alternative medicines, and various other nutcases by clearly setting out the tricks of the trade by which such insidious belief systems are created and maintained.

    It should prove a real boon to the student of Peirce." — The Modern SchoolmanCharles S. Peirce was a thinker of great originality and power. Although unpublished in his lifetime, he was recognized as an equal by such men as William James and John Dewey and, since his death in 1914, has come to the forefront of American philosophy. This volume, prepared by the Johnsonian Professor of Philosophy at Columbia University, formerly chairman of Columbia's philosophy department, is a carefully balanced exposition of Peirce's complete philosophical system as set forth in his own writings.The 28 chapters, in which appropriate sections of Peirce's work are interwoven into a brilliant selection that reveals his essential ideas, cover epistemology, phenomenology, cosmology, and scientific method, with especially interesting material on logic as the theory of signs, pure chance vs, pure law in the universe, symbolic logic, common sense, pragmatism (of which he was the founder), and ethics.Justus Buchler is author of Charles Peirce's Empiricism (1939), Philosophy: An Introduction (with J. H. Randall, Jr., 1942), and more recently, a series of books which form an ongoing philosophic structure: Toward a General Theory of Human Judgement (1951), Nature and Judgment (1855), and The Concept of Method (1961). It has been said of these volumes, "A fresh and vital system of ideas has been introduced into the world of contemporary philosophy." (Journal of Philosophy)."It is a very signal advantage to have this collection of Peirce's most important work within the covers of a single substantial volume. We should all be very grateful to Mr. Buchler." — John Laird, Philosophy

    In 1967, they said the USSR would have one of the fastest-growing economies in the year 2000; in 2000, the USSR did not exist. In 1911, it was pronounced that there would be no more wars in Europe; we all know how that turned out. Face it, experts are about as accurate as dart-throwing monkeys. And yet every day we ask them to predict the future — everything from the weather to the likelihood of a catastrophic terrorist attack. Future Babble is the first book to examine this phenomenon, showing why our brains yearn for certainty about the future, why we are attracted to those who predict it confidently, and why it’s so easy for us to ignore the trail of outrageously wrong forecasts.In this fast-paced, example-packed, sometimes darkly hilarious book, journalist Dan Gardner shows how seminal research by UC Berkeley professor Philip Tetlock proved that pundits who are more famous are less accurate — and the average expert is no more accurate than a flipped coin. Gardner also draws on current research in cognitive psychology, political science, and behavioral economics to discover something quite reassuring: The future is always uncertain, but the end is not always near.

    Unlike party puzzles or brain teasers, many paradoxes are serious in that they raise serious philosophical problems, and are associated with crises of thought and revolutionary advances. To grapple with them is not merely to engage in an intellectual game, but to come to grips with issues of real import. The second, revised edition of this intriguing book expands and updates the text to take account of new work on the subject. It provides a valuable and accessible introduction to a range of paradoxes and their possible solutions, with questions designed to engage the reader with the arguments and full bibliographical references to both classic and current literature on the topic.