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Godel, Escher, Bach: An Eternal Golden Braid
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by
Douglas R Hofstadter
First published in 1979, this is a genuine interdisciplinary work of nonfiction, with dozens of historical references and subtexts. Critics and reviewers have summed up its meaning in varying ways, yet consistently with praise. A mixture of art, philosophy, music, math, technology, and cognitive science, the book's title only reflects one aspect ...
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Introduction to the Theory of Computation
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by
Michael Sipser
Designed for researchers in advanced numerical methods or parallel computing, this definitive reference focuses on solving large and sparse linear systems of equations using computers. readers are provided with appropriate conceptual background information and hands-on applications throughout the book.
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Discrete Mathematics
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Richard Johnsonbaugh
This best-selling book provides an accessible introduction to discrete mathematics through an algorithmic approach that focuses on problem- solving techniques. This edition has the techniques of proofs woven into the text as a running theme and each chapter has the problem-solving corner. The text provides complete coverage of: Logic and Proofs; ...
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Introduction to Automata Theory, Languages, and Computation
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John E Hopcroft
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The Art of Reasoning
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by
David Kelley
* Inviting prose * Lucid style * Familiar language * Practical applications * Real-world examples
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Introduction to Computer Theory
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by
Daniel I A Cohen
This text strikes a good balance between rigor and an intuitive approach to computer theory. Covers all the topics needed by computer scientists with a sometimes humorous approach that reviewers found "refreshing". It is easy to read and the coverage of mathematics is fairly simple so readers do not have to worry about proving theorems.
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Gödel's proof
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by
Ernest Nagel, James R Newman
Originally written in 1958, this text clearly explains the tenets and importance of Godel's classic proof, and its influence on mathematics and philosophy.
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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
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by
Daniel Solow
This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated with step-by-step examples.
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Everything and More: A Compact History of Infinity
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by
David Foster Wallace
The versatile David Foster Wallace tackles the concept of infinity, exploring its essential nature: is it simply an abstraction, or an actual mathematical entity? Wallace looks at Georg Cantor's 19th-century comments on the issue and includes his own thoughts on a question that has perplexed mathematicians for centuries.
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Understanding Symbolic Logic
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by
Virginia Klenk
This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small “ bites” that enable learners to master the material step-by-step, rather than being overwhelmed by masses of ...
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Logic for Dummies
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by
Mark Zegarelli
Logic concepts are more mainstream than you may realize. There's logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as "CSI" and "Numbers" incorporate a variety of logistical studies. "Logic For Dummies" explains a ...
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Philosophy of mathematics : selected readings
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by
Paul Benacerraf (Compiled by), Hilary Putnam
Seminal articles in the philosophy of mathematics by Russell, Quine, Godel and other major thinkers.
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Introduction to Languages and the Theory of Computation
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by
John C Martin
Introduction to Languages and the Theory of Computation is an introduction to the theory of computation that emphasizes formal languages, automata and abstract models of computation, and computability; it also includes an introduction to computational complexity and NP-completeness. Through the study of these topics, students encounter profound ...
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How to Prove It: A Structured Approach
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by
Daniel J Velleman
This new edition of Dan Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
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Symbolic logic
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by
Irving M. Copi
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To Infinity and Beyond: A Cultural History of the Infinite
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by
Eli Maor
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, ...
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Axiomatic Set Theory
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by
Patrick Suppes
By means of the Zermelo-Fraenkel system, Suppes provides best treatment of axiomatic set theory on upper undergraduate and graduate levels. Topics include relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, more
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Sorting
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by
Henry Pluckrose
Children can become mathematical problem solvers, learning to communicate and reason mathematically, by using the Math Counts series. The full-color photographs and simple text encourage talk about topics that are essentially mathematical.
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Logic: Techniques of Formal Reasoning
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by
Donald Kalish, Richard Montague, Gary Mar
Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the ...
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Discrete Mathematical Structures
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by
Bernard Kolman, Robert C Busby, Sharon Cutler Ross
Key Message: Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field, and will be especially helpful for readers interested in computer science. This book ...
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Incompleteness: The Proof and Paradox of Kurt Godel
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by
Rebecca Goldstein, Ph.D.
Considered the 20th century's greatest mathematician, Kurt Godel is the subject of this lucid and accessible study, which explains the significance of his theorems and the remarkable vision behind them, while bringing this eccentric, tortured genius and his world to life.
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Naive Set Theory
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by
Paul R. Halmos
From the Reviews: .,."He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know. ...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should ...
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Infinity and the Mind: The Science and Philosophy of the Infinite
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by
Rudy Von B Rucker
In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the ...
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With Good Reason: An Introduction to Informal Fallacies
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by
S Morris Engel
Appropriate for both logic and critical thinking courses, this concise, easy-to-read introduction to informal logic offers both comprehensive coverage of informal fallacies and an abundance of engaging examples of both well-conceived and faulty arguments. A long-time favorite of both students and instructors, the text continues in its sixth ...
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Foundations of Higher Mathematics
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by
Peter Fletcher
This text introduces students to basic techniques of writing proofs and acquaints them with some fundamental ideas. The authors assume that students using this text have already taken courses in which they developed the skill of using results and arguments that others have conceived. This text picks up where the others left off -- it develops the ...
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