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|Gödel, Escher, Bach: An Eternal Golden Braid
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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.
|The Fallacy Detective: Thirty-Eight Lessons on How to Recognize Bad Reasoning
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Author: Nathaniel Bluedorn
What is a fallacy? A fallacy is an error in logic a place where someone has made a mistake in his thinking. This is a handy book for learning to spot common errors in reasoning.- For ages twelve through adult.- Fun to use -- learn skills you can use right away.- Peanuts, Dilbert, and Calvin and Hobbes cartoons.- Includes The Fallacy Detective Game.- Exercises with answer key.
|Thinking Mathematically (6th Edition)
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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, real-world 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 two-term course in liberal arts mathematics or general education mathematics.
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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
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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.
- How to Solve It A New Aspect of Mathematical Method Princeton Science Library
|An Illustrated Book of Bad Arguments
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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.
- An Illustrated Book of Bad Arguments
|Language, Proof and Logic, 2nd Edition
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Author: David Barker-Plummer
Previous printings of Language, Proof and Logic contained a CD-ROM.For the current version of this pack-files accompanying the textbook can be downloaded by using the Registration/Book ID# printed on the reverse side of the card. The textbook/software package covers first-order language in a method appropriate for first and second courses in logic. An on-line 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 first-order language and its semantics; Fitch, a natural deduction proof environment for giving and checking first-order 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.
- Social Theory in the Twentieth Century and Beyond
- Prolegomena to Any Future Metaphysics: and the Letter to Marcus Herz, February 1772 (Hackett Classics)
- Modern Philosophy: An Anthology of Primary Sources, 2nd Edition
- Tell Me True: Memoir, History, and Writing A Life
- Aristotle: Introductory Readings (Hackett Classics)
- Calculus: Early Transcendentals
- The Immune System, 4th Edition
- Philosophy in the Middle Ages: The Christian, Islamic, and Jewish Traditions
- Plato: Five Dialogues: Euthyphro, Apology, Crito, Meno, Phaedo (Hackett Classics)
- Ethics: with The Treatise on the Emendation of the Intellect and Selected Letters (Hackett Classics)
|How to Prove It: A Structured Approach, 2nd Edition
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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 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
- Cambridge University Press
|Crossing the River with Dogs: Problem Solving for College Students
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Author: Ken Johnson
Crossing the River with Dogs: Problem Solving for College Students has been adapted from the popular high school text to provide an accessible and coherent college-level course in mathematical problem solving for adults. Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students. This text is appropriate for a problem solving, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.
|Descartes' Error: Emotion, Reason, and the Human Brain
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Author: Antonio 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.
- The Feeling of What Happens: Body and Emotion in the Making of Consciousness
- Looking for Spinoza: Joy, Sorrow, and the Feeling Brain
- Self Comes to Mind: Constructing the Conscious Brain
- The Strange Order of Things: Life, Feeling, and the Making of Cultures
- The Emotional Brain: The Mysterious Underpinnings of Emotional Life
- Synaptic Self: How Our Brains Become Who We Are
- Fundamental Neuroscience for Basic and Clinical Applications
- Neuroanatomy in Clinical Context: An Atlas of Structures, Sections, Systems, and Syndromes (Neuroanatomy: An Atlas of Strutures, Sections, and Systems ()
- The Creation: An Appeal to Save Life on Earth
- The Strange Order of Things: Life, Feeling, and the Making of Cultures
|The Art of Logic in an Illogical World
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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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