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.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    Kerrane is a professor of English at the University of Delaware.

    The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Here is the brilliant manager stripped naked—the person underneath all the clowning, mugging, and double-talking. Robert Creamer shows us Casey at twenty-two, famous from his very first day in the big leagues. We see Casey’s playing career fall apart as he is traded, shunted to last-place teams, hampered by injuries, considered finished—until he bats a glorious home run in the 1923 World Series. Here are Casey’s managing successes and failures—dismissed by the Yankees, he returns to the limelight with his new and inept New York Mets, the team he single-handedly lifts into the nation’s consciousness.“I’m a man that’s been up and down,” Casey said in a serious moment. Certainly his knack for bouncing back made him a legend in our national pastime. Here are the stories and gags, the Stengelian style, the full dimensions of the man.

    What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

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

    It is intended to provide the essential primary texts for students of logic, metaphysics and philosophy of language.It contains, in particular, Frege's four essays 'Function and Concept', 'On Sinn and Bedeutung', 'On Concept and Object' and 'Thought', and new translations of key parts of the Begriffschrift, Grundlagen and Grundgesetze. Additional selections have also been made from his Collected Papers, Posthumous Writings and Correspondence. The editor's introduction provides an overview of the development and significance of Frege's philosophy, highlighting some of the main issues of interpretation. Footnotes, appendices and other editorial material have been supplied to facilitate understanding of the works of one of the central figures in modern philosophy.

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set- theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

    It addresses the technical side of The Beatles' sessions and was written with the assistance of many of the group's former engineers and technicians [1]. The book looks at every piece of recording equipment used at Abbey Road Studios during the Beatles' sessions, including all microphones, outboard gear, mixing consoles, speakers, and tape machines. Each piece is examined in great detail, and the book is illustrated with hundreds of full color photographs, charts, drawings and illustrations. How the equipment was implemented during the group's sessions is also covered. The effects used on the Beatles' records are addressed in great detail, with full explanations of concepts such as ADT and flanging. The Production section of the book looks at the group's recording processes chronologically, starting with their "artist test" in 1962 and progressing through to their final session in 1970. The book contains several rare and unseen photos of the Beatles in the studio. The studio personnel and the studio itself is examined.The authors spent over a decade researching the subject matter and offer up their findings in exhaustive detail. The 540-page hardcover book has been highly praised not only for its massive scope, but also for its presentation. The "Deluxe" version, released in September of 2006, was housed in a replica EMI multi-track tape-box, complete with faux time-worn edges. Rather than a listing of the tape's contents, the back of the box featured the book's contents, hand-written by former Beatles tape-op and engineer, Ken Scott. The book was also accompanied by several "bonus items", including reproductions of never-seen photos of the Beatles. The first printing of 3,000 books sold out in November of 2006, and a second printing was released in February of 2007. The book is currently in its fourth printing.The book has been critically praised by recognized Beatles authority Mark Lewisohn (who also contributed the book's Foreword), The New York Times[2][3], Mojo (magazine) (which gave it 5 stars), Beatles engineers Norman Smith, Ken Scott, and Alan Parsons, Yoko Ono, and many other individuals directly involved with the Beatles' work. The release of the book was celebrated in November 2006 with a party in Studio Two at Abbey Road [4]. In attendance were most of the Beatles' former engineers and technicians.

    Alternate cover edition for ISBN 0671425676Incisive, personal reporting that covers the five most recent baseball seasons and such events as Reggie Jackson's three World Series home runs, the triumph of the Phillies, and the bitter ordeal of the 1981 players' strike.