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Books
Logic
Gödel, Escher, Bach: An Eternal Golden Braid
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Author: Douglas R. Hofstadter
Brand: Douglas R Hofstadter

Winner of the Pulitzer Prize A metaphorical fugue on minds and machines in the spirit of Lewis Carroll
Douglas Hofstadter's book is concerned directly with the nature of "maps" or links between formal systems. 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.
Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think. Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers. The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. Richard Dragan Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and nonEuclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; selfreference and selfrepresentation; Turing test for machine intelligence.
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 Godel Escher Bach An Eternal Golden Braid
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Thinking Mathematically (6th Edition)
Lowest new price: $125.93
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Author: Robert F. Blitzer
Brand: Robert F Blitzer

NOTE: This book is a standalone book and doesn't include an access code.
In Thinking Mathematically, Sixth Edition, Bob Blitzer’s distinctive and relatable voice motivates students from diverse backgrounds and majors, engaging them in the math through compelling, realworld applications. Understanding that most students in a liberal arts math course are not math majors, and are unlikely to take another math class, Blitzer has provided tools in every chapter to help them master the material with confidence, while also showing them the beauty and fun of math. The variety of topics and flexibility of sequence make this text appropriate for a one or twoterm course in liberal arts mathematics or general education mathematics. ALERT: Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. Packages Access codes for Pearson's MyLab & Mastering products may not be included when purchasing or renting from companies other than Pearson; check with the seller before completing your purchase. Used or rental books If you rent or purchase a used book with an access code, the access code may have been redeemed previously and you may have to purchase a new access code. Access codes Access codes that are purchased from sellers other than Pearson carry a higher risk of being either the wrong ISBN or a previously redeemed code. Check with the seller prior to purchase.
Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. If you would like to purchase both the physical text and MyMathLab, search for
0321923235 / 9780321923233 Thinking Mathematically plus NEW MyMathLab with Pearson eText  Access Card Package Package consists of: 0321431308 / 9780321431301 MyMathLab  Gluein Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321867327 / 9780321867322 Thinking Mathematically MyMathLab is not a selfpaced technology and should only be purchased when required by an instructor.
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An Illustrated Book of Bad Arguments
Lowest new price: $9.38
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List price: $14.95
Author: Ali Almossawi
Brand: Almossawi Ali

“A flawless compendium of flaws.” —Alice Roberts, PhD, anatomist, writer, and presenter of The Incredible Human Journey The antidote to fuzzy thinking, with furry animals! Have you read (or stumbled into) one too many irrational online debates? Ali Almossawi certainly had, so he wrote An Illustrated Book of Bad Arguments! This handy guide is here to bring the internet age a muchneeded dose of oldschool logic (really oldschool, a la Aristotle). Here are cogent explanations of the straw man fallacy, the slippery slope argument, the ad hominem attack, and other common attempts at reasoning that actually fall short—plus a beautifully drawn menagerie of animals who (adorably) commit every logical faux pas. Rabbit thinks a strange light in the sky must be a UFO because no one can prove otherwise (the appeal to ignorance). And Lion doesn’t believe that gas emissions harm the planet because, if that were true, he wouldn’t like the result (the argument from consequences). Once you learn to recognize these abuses of reason, they start to crop up everywhere from congressional debate to YouTube comments—which makes this geekchic book a must for anyone in the habit of holding opinions.
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 An Illustrated Book of Bad Arguments
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How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
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Author: G. Polya
Brand: Polya G

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out―from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft―indeed, brilliant―instructions on stripping away irrelevancies and going straight to the heart of the problem.
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 How to Solve It A New Aspect of Mathematical Method Princeton Science Library
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Reverse Mathematics: Proofs from the Inside Out
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Author: John Stillwell

This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis―finding the “right axioms” to prove fundamental theorems―and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenthcentury project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentiethcentury arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the “right axiom” to prove it. By using a minimum of mathematical logic in a wellmotivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
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Book of Proof
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Author: Richard Hammack
Brand: Richard Heath Hammack

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and nonconditional proof, disproof, induction, relations, functions and infinite cardinality.
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My Best Mathematical and Logic Puzzles (Dover Recreational Math)
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Author: Martin Gardner
Brand: Dover Publications

Over a period of 25 years as author of the Mathematical Games column for Scientific American, Martin Gardner devoted a column every six months or so to short math problems or puzzles. He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections, incorporating reader feedback on alternate solutions or interesting generalizations. The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mindbenders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.
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 My Best Mathematical and Logic Puzzles
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How to Prove It: A Structured Approach, 2nd Edition
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Author: Daniel J. Velleman
Brand: imusti

Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a stepbystep breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0521441161 Previous Edition Pb (1994) 0521446635
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 Cambridge University Press
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Language, Proof and Logic, 2nd Edition
Lowest new price: $73.69
Lowest used price: $6.55
List price: $80.00
Author: David BarkerPlummer
Brand: imusti

Language Proof and Logic is available as a physical book with the software included on CD and as a downloadable package of software plus the book in PDF format. The allelectronic version is available from Openproof at ggweb.stanford.edu.
The textbook/software package covers firstorder language in a method appropriate for first and second courses in logic. An online grading services instantly grades solutions to hundred of computer exercises. It is designed to be used by philosophy instructors teaching a logic course to undergraduates in philosophy, computer science, mathematics, and linguistics.
Introductory material is presented in a systematic and accessible fashion. Advanced chapters include proofs of soundness and completeness for propositional and predicate logic, as well as an accessible sketch of Godel's first incompleteness theorem. The book is appropriate for a wide range of courses, from first logic courses for undergraduates (philosophy, mathematics, and computer science) to a first graduate logic course.
The software package includes four programs:
Tarski's World 5.0, a new version of the popular program that teaches the basic firstorder language and its semantics;
Fitch, a natural deduction proof environment for giving and checking firstorder proofs;
Boole, a program that facilitates the construction and checking of truth tables and related notions (tautology, tautological consequence, etc.);
Submit, a program that allows students to submit exercises done with the above programs to the Grade Grinder, the automatic grading service.
Grade reports are returned to the student and, if requested, to the student's instructor, eliminating the need for tedious checking of homework. All programs are available for Windows, Macintosh and Linux systems. Instructors do not need to use the programs themselves in order to be able to take advantage of their pedagogical value. More about the software can be found at lpl.stanford.edu.
The price of a new text/software package includes one Registration ID, which must be used each time work is submitted to the grading service. Once activated, the Registration ID is not transferable.
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 Language Proof and Logic With Software
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Descartes' Error: Emotion, Reason, and the Human Brain
Lowest new price: $9.99
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Author: Anthony Damasio
Brand: Damasio, Antonio R.

Since Descartes famously proclaimed, "I think, therefore I am," science has often overlooked emotions as the source of a person’s true being. Even modern neuroscience has tended, until recently, to concentrate on the cognitive aspects of brain function, disregarding emotions. This attitude began to change with the publication of Descartes’ Error in 1995. Antonio Damasio—"one of the world’s leading neurologists" (The New York Times)—challenged traditional ideas about the connection between emotions and rationality. In this wondrously engaging book, Damasio takes the reader on a journey of scientific discovery through a series of case studies, demonstrating what many of us have long suspected: emotions are not a luxury, they are essential to rational thinking and to normal social behavior.
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