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Logic


Gödel, Escher, Bach: An Eternal Golden Braid

Gödel, Escher, Bach: An Eternal Golden Braid Lowest new price: $16.96
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Author: Douglas R. Hofstadter
Brand: Basic Books AZ

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 non-Euclidean 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; self-reference and self-representation; Turing test for machine intelligence.

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  • Basic Books AZ

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My Best Mathematical and Logic Puzzles (Dover Recreational Math)

My Best Mathematical and Logic Puzzles (Dover Recreational Math) Lowest new price: $4.10
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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 mind-benders 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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  • Dover Publications

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An Illustrated Book of Bad Arguments

An Illustrated Book of Bad Arguments Lowest new price: $11.13
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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 much-needed dose of old-school logic (really old-school, 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 geek-chic 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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The Art of Logic in an Illogical World

The Art of Logic in an Illogical World Lowest new price: $18.04
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Author: Eugenia Cheng

How both logical and emotional reasoning can help us live better in our post-truth world

In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic--for example, emotion--is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.


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

How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) Lowest new price: $6.00
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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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The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine

The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine Lowest new price: $6.98
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Author: Charles Petzold
Brand: imusti

Programming Legend Charles Petzold unlocks the secrets of theextraordinary and prescient 1936 paper by Alan M. Turing

Mathematician Alan Turing invented an imaginary computer knownas the Turing Machine; in an age before computers, he explored theconcept of what it meant to be computable, creating thefield of computability theory in the process, a foundation ofpresent-day computer programming.

The book expands Turing’s original 36-page paper withadditional background chapters and extensive annotations; theauthor elaborates on and clarifies many of Turing’sstatements, making the original difficult-to-read documentaccessible to present day programmers, computer science majors,math geeks, and others.

Interwoven into the narrative are the highlights ofTuring’s own life: his years at Cambridge and Princeton, hissecret work in cryptanalysis during World War II, his involvementin seminal computer projects, his speculations about artificialintelligence, his arrest and prosecution for the crime of "grossindecency," and his early death by apparent suicide at the age of41.

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  • John Wiley & Sons

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Book of Proof

Book of Proof Lowest new price: $12.40
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Author: Richard 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 non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

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Can You Solve My Problems?: Ingenious, Perplexing, and Totally Satisfying Math and Logic Puzzles

Can You Solve My Problems?: Ingenious, Perplexing, and Totally Satisfying Math and Logic Puzzles Lowest new price: $6.00
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Author: Alex Bellos
Brand: EXPERIMENT

Puzzle lovers, rejoice!

Bestselling math writer Alex Bellos has a challenge for you: 125 of the world’s best brainteasers from the last two millennia.

Armed with logic alone, you’ll detect counterfeit coins, navigate river crossings, and untangle family trees. Then—with just a dash of high school math—you’ll tie a rope around the Earth, match wits with a cryptic wizard, and use four 4s to create every number from 1 to 50. (It can be done!)

The ultimate casebook for daring puzzlers, Can You Solve My Problems? also tells the story of the puzzle—from ancient China to Victorian England to modern-day Japan. Grab your pencil and get puzzling!

Features:

  • EXPERIMENT

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Mastering Logical Fallacies: The Definitive Guide to Flawless Rhetoric and Bulletproof Logic

Mastering Logical Fallacies: The Definitive Guide to Flawless Rhetoric and Bulletproof Logic Lowest new price: $9.60
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Author: Michael Withey

“If I have learned anything in ten years of formal debating, it is that arguments are no different: without a good understanding of the rules and tactics, you are likely to do poorly and be beaten.”―HENRY ZHANG, President of the Yale Debate Association

Your argument is valid and you know it; yet once again you find yourself leaving a debate feeling defeated and embarrassed. The matter is only made worse when you realize that your defeat came at the hands of someone’s abuse of logic―and that with the right skills you could have won the argument.

The ability to recognize logical fallacies when they occur is an essential life skill. Mastering Logical Fallacies is the clearest, boldest, and most systematic guide to dominating the rules and tactics of successful arguments. This book offers methodical breakdowns of the logical fallacies behind exceedingly common, yet detrimental, argumentative mistakes, and explores them through real life examples of logic-gone-wrong.

Designed for those who are ready to gain the upper hand over their opponents, this master class teaches the necessary skills to identify your opponents’ misuse of logic and construct effective, arguments that win. With the empowering strategies offered in Mastering Logical Fallacies you’ll be able to reveal the slight-of-hand flaws in your challengers’ rhetoric, and seize control of the argument with bulletproof logic.

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How to Prove It: A Structured Approach, 2nd Edition

How to Prove It: A Structured Approach, 2nd Edition Lowest new price: $26.24
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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 step-by-step 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) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

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  • Cambridge University Press

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