Mathematics and Logic

Author: Mark Kac
Publisher: Courier Corporation
ISBN: 9780486670850
Release Date: 1968
Genre: Philosophy

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Mathematical Logic

Author: Stephen Cole Kleene
Publisher: Courier Corporation
ISBN: 9780486317076
Release Date: 2013-04-22
Genre: Mathematics

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Calculus A Liberal Art

Author: W.M. Priestley
Publisher: Springer Science & Business Media
ISBN: 9781461216582
Release Date: 2012-12-06
Genre: Mathematics

Presenting mathematics as forming a natural bridge between the humanities and the sciences, this book makes calculus accessible to those in the liberal arts. Much of the necessary geometry and algebra are exposed through historical development, and a section on the development of calculus offers insights into the place of mathematics in the history of thought.

Why Cats Land on Their Feet

Author: Mark Levi
Publisher: Princeton University Press
ISBN: 9781400841721
Release Date: 2012-05-27
Genre: Mathematics

Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics. Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats. Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.


Author: Willard Van Orman Quine
Publisher: Harvard University Press
ISBN: 0674010485
Release Date: 2004
Genre: Philosophy

Through the first half of the twentieth century, analytic philosophy was dominated by Russell, Wittgenstein, and Carnap. Influenced by Russell and especially by Carnap, another towering figure, Willard Van Orman Quine (1908âe"2000) emerged as the most important proponent of analytic philosophy during the second half of the century. Yet with twenty-three books and countless articles to his creditâe"including, most famously, Word and Object and "Two Dogmas of Empiricism"âe"Quine remained a philosopher's philosopher, largely unknown to the general public. Quintessence for the first time collects Quine's classic essays (such as "Two Dogmas" and "On What There Is") in one volumeâe"and thus offers readers a much-needed introduction to his general philosophy. Divided into six parts, the thirty-five selections take up analyticity and reductionism; the indeterminacy of translation of theoretical sentences and the inscrutability of reference; ontology; naturalized epistemology; philosophy of mind; and extensionalism. Representative of Quine at his best, these readings are fundamental not only to an appreciation of the philosopher and his work, but also to an understanding of the philosophical tradition that he so materially advanced.

Descartes Dream

Author: Philip J. Davis
Publisher: Courier Corporation
ISBN: 9780486442525
Release Date: 2005
Genre: Mathematics

These provocative essays take a modern look at the 17th-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the applications' effectiveness; and how applied mathematics transform perceptions of reality. 1987 edition.

Adventures of a Mathematician

Author: S. M. Ulam
Publisher: Univ of California Press
ISBN: 0520910559
Release Date: 1991-06-23
Genre: Mathematics

The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Fran oise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.

Classic Problems of Probability

Author: Prakash Gorroochurn
Publisher: John Wiley & Sons
ISBN: 9781118314333
Release Date: 2012-04-30
Genre: Mathematics

Winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence. "A great book, one that I will certainly add to my personal library." —Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include: Buffon's Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invariance Various paradoxes raised by Joseph Bertrand Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem The Bayesian paradigm and various philosophies of probability Coverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox Classic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.

Zermelo s Axiom of Choice

Author: Gregory H. Moore
Publisher: Courier Corporation
ISBN: 9780486488417
Release Date: 2012-09-20
Genre: Mathematics

"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--

Logic for Computer Science

Author: Jean H. Gallier
Publisher: Courier Dover Publications
ISBN: 9780486780825
Release Date: 2015-06-18
Genre: Computers

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Concepts of Modern Mathematics

Author: Ian Stewart
Publisher: Courier Corporation
ISBN: 9780486134956
Release Date: 2012-05-23
Genre: Mathematics

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

Problem Solving Through Recreational Mathematics

Author: Bonnie Averbach
Publisher: Courier Corporation
ISBN: 9780486131740
Release Date: 2012-03-15
Genre: Mathematics

Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. Free solutions manual available for download at the Dover website.

Mathematical Logic for Computer Science

Author: Mordechai Ben-Ari
Publisher: Springer Science & Business Media
ISBN: 9781447141297
Release Date: 2012-06-16
Genre: Mathematics

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.