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

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 and 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.
Features:
 Music
 Art
 Mathematics
 Meditation on Human Thought and Creativity
 Artificial Intelligence
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Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers
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Author: Joseph Mazur

While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
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My Best Mathematical and Logic Puzzles (Dover Recreational Math)
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Author: Martin Gardner
Brand: Dover Publications

The noted expert and longtime author of Scientific American's Mathematical Games column selects 70 of his favorite "short" puzzles. Enthusiasts can challenge their skills with such mindbogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, Bronx vs. Brooklyn, and dozens more involving logic and basic math. Complete solutions included.
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How to Prove It: A Structured Approach
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Author: Daniel J. Velleman

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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How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
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Author: G. Polya

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" outfrom building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deftindeed, brilliantinstructions on stripping away irrelevancies and going straight to the heart of the problem.
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A Beginner's Guide to Mathematical Logic
Lowest new price: $15.45
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Author: Raymond M. Smullyan

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and firstorder logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.
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Descartes' Error: Emotion, Reason, and the Human Brain
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Author: Antonio Damasio

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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Math Bytes: Google Bombs, ChocolateCovered Pi, and Other Cool Bits in Computing
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Author: Tim Chartier

This book provides a fun, handson approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity lookalike? What is Homer Simpson's method for disproving Fermat's Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or resultsuch as Google's PageRank and the traveling salesman problemand the applications grow more challenging as you progress through the chapters. But don't worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Birdand much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pacea bit and a byte at a time.
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The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine
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Author: Charles Petzold

Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of presentday computer programming. The book expands Turing’s original 36page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficulttoread document accessible to present day programmers, computer science majors, math geeks, and others. Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.
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The Art and Craft of Problem Solving
Lowest new price: $58.99
Lowest used price: $47.41
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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