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Logic


The Art and Craft of Problem Solving

The Art and Craft of Problem Solving Lowest new price: $76.35
Lowest used price: $57.86
Author: Paul Zeitz

The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

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Languages and Machines: An Introduction to the Theory of Computer Science (3rd Edition)

Languages and Machines: An Introduction to the Theory of Computer Science (3rd Edition) Lowest new price: $158.62
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Author: Thomas A. Sudkamp

The third edition of Languages and Machines: An Introduction to the Theory of Computer Science provides readers with a mathematically sound presentation of the theory of computer science.  The theoretical concepts and associated mathematics are made accessible by a "learn as you go" approach that develops an intuitive understanding of the concepts through numerous examples and illustrations. 

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Axiomatic Set Theory (Graduate Texts in Mathematics)

Axiomatic Set Theory (Graduate Texts in Mathematics) Lowest new price: $75.64
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Author: Gaisi Takeuti
Brand: Brand: Springer

This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda­ mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.

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  • Used Book in Good Condition


Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) Lowest new price: $41.82
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Author: David A. Cox
Brand: Springer

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry―the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz―this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D).

The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of Maple™, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used.

From the reviews of previous editions:

 “…The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. …The book is well-written. …The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.”

 ―Peter Schenzel, zbMATH, 2007

 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.”

 ―The American Mathematical Monthly

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  • Springer

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Computational Complexity: A Modern Approach

Computational Complexity: A Modern Approach Lowest new price: $50.53
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Author: Sanjeev Arora
Brand: Brand: Cambridge University Press

This beginning graduate textbook describes both recent achievements and classical results of computational complexity theory. Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

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  • Used Book in Good Condition

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Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers

Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers Lowest new price: $36.66
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Author: Leslie Lamport

This work shows how to write unambiguous specifications of complex computer systems. The first part provides a concise and lucid introduction to specification, explaining how to describe, with mathematical precision, the behavioural properties of a system - what that system is allowed to do. The emphasis here is on safety properties. The second part covers more advanced topics, including liveness and fairness, real time properties, and composition. The books final two parts provide a complete reference manual for the TLA+ language and tools, as well as a mini-manual.

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The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse (Synthese Library)

The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse (Synthese Library) Lowest new price: $97.30
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Author: Johan van Benthem
Brand: Johan Van Benthem

That philosophical themes could be studied in an exact manner by logical meanS was a delightful discovery to make. Until then, the only outlet for a philosophical interest known to me was the production of poetry or essays. These means of expression remain inconclusive, however, with a tendency towards profuseness. The logical discipline provides so me intellectual backbone, without excluding the literary modes. A master's thesis by Erik Krabbe introduced me to the subject of tense logic. The doctoral dissertation of Paul N eedham awaked me (as so many others) from my dogmatic slumbers concerning the latter's mono­ poly on the logical study of Time. Finally, a set of lecture notes by Frank Veltman showed me how classical model theory is just as relevant to that study as more exotic intensional techniques. Of the authors whose work inspired me most, I would mention Arthur Prior, for his irresistible blend of logic and philosophy, Krister Segerberg, for his technical opening up of a systematic theory, and Hans Kamp, for his mastery of all these things at once. Many colleagues have made helpful comments on the two previous versions of this text. I would like to thank especially my students Ed Brinksma, Jan van Eyck and Wilfried Meyer-Viol for their logical and cultural criticism. The drawings were contributed by the versatile Bauke Mulder. Finally, Professor H intikka's kind appreciation provided the stimulus to write this book.

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  • The Logic of Time A Model Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse Synthese Library


A Field Guide to Lies: Critical Thinking in the Information Age

A Field Guide to Lies: Critical Thinking in the Information Age Lowest new price: $9.97
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Author: Daniel J. Levitin
Brand: Dutton Books

From The New York Times bestselling author of The Organized Mind and This is Your Brain on Music, a primer to the critical thinking that is more necessary now than ever.

We are bombarded with more information each day than our brains can process—especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them.

It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, distortions, and outright lies from reliable information? Levitin groups his field guide into two categories—statistical infomation and faulty arguments—ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning—not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some lying weasels in their tracks!

 

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  • Dutton Books

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The Logic Book

The Logic Book Lowest new price: $129.36
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List price: $787.00
Author: Merrie Bergmann

This leading text for symbolic or formal logic courses presents all techniques and concepts with clear, comprehensive explanations, and includes a wealth of carefully constructed examples. Its flexible organization (with all chapters complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose.

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The Lady or the Tiger?: and Other Logic Puzzles (Dover Recreational Math)

The Lady or the Tiger?: and Other Logic Puzzles (Dover Recreational Math) Lowest new price: $9.17
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List price: $14.95
Author: Raymond M. Smullyan
Brand: Dover Publications

"Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner
"Smullyan is not your run-of-the-mill puzzlemeister; he polishes up old chestnuts, spins variations on a theme, and peoples his logical world with a delightful cast of characters." — Science 82
"I believe Ray Smullyan to be the Lewis Carroll of our times. His little books of logic puzzles will be remembered long after most of us are forgotten." — Peter Denning, Chairman of the Computer Science Department, Naval Postgraduate School
"You may experience small frissons of delight as you follow Smullyan into the dizzying heights of Gödel's proof and the very nature of proof, truth, and logic in mathematics." — Kirkus Reviews
Discover scintillating new perspectives on the principles of mathematical logic with this puzzle treasury. Inspired by the classic tale of a prisoner's choice between two doors, these whimsically themed challenges allow readers to base their decisions on logic rather than luck. Nineteen chapters advance from relatively simple puzzles and meta-puzzles to highly complex paradoxes involving probability, time, and change. The author, a well-known philosopher and magician as well as a celebrated mathematician and logician, was acclaimed by The New York Times as "a master at translating difficult ideas into stories and puzzles that require no formal background, only patience and a passion to learn."

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