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Logic


Gödel, Escher, Bach: An Eternal Golden Braid

Gödel, Escher, Bach: An Eternal Golden Braid Lowest new price: $14.66
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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 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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Thinking Mathematically (6th Edition)

Thinking Mathematically (6th Edition) Lowest new price: $135.00
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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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 MyMathLab is not a self-paced technology and should only be purchased when required by an instructor.

 

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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: $28.67
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Author: Daniel J. Velleman
Brand: Brand: Cambridge University Press

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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Book of Proof

Book of Proof Lowest new price: $15.64
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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 non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

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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: $16.93
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Author: Charles Petzold
Brand: Petzold Charles

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 present-day computer programming.

The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read 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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Descartes' Error: Emotion, Reason, and the Human Brain

Descartes' Error: Emotion, Reason, and the Human Brain Lowest new price: $7.98
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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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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: $7.32
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Author: Michael Withey
Brand: Withey Michael

“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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It's Hard To Be a Russian Spy: The Great Collection Of Riddles & Brain Teasers From The Final Examination of Soviet and Russian Spies (Brain Teaser Puzzles for Adults)

It's Hard To Be a Russian Spy: The Great Collection Of Riddles & Brain Teasers From The Final Examination of Soviet and Russian Spies (Brain Teaser Puzzles for Adults) Lowest new price: $9.99
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Author: Igor Suvorov

There’s training to be an Olympic Athlete. Then there is training to a Russian Spy. Both extremely difficult and a much esteemed percentage of people around the world get to be picked for it. But there is no shadow of doubt which of these requires a person to be literally Jack of all trades - smart, cunning, highly intelligent, resilient and the perfect mix of brains and brawns.

There is an aura of mysticism surrounding Spies and very few people have told the tale of where it all began- in the training room. Put together by means that better remain cloaked, or perhaps a story for another time, author Igor Suvorov brings you a choice collection of fifty riddles and brain teasers that these Soviet and Russian spies had to clear in order to be deemed fit to be released to the field. Anyone can solve a riddle, but these are the riddles that only as few as 4% of untrained people will be able to solve!

As if that is not good enough, the person taking the exam has to clear 94% of all the presented questions. This is the holy grail of all spy brain teasers, a book that you can keep your brain sharp with, a tool with which you can spend endless hours poring over. Have you go what it takes? Time to find out! It's not just hard to be a Russian Spy; it’s VERY hard and only the sharpest mind will be one.

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On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages (SpringerBriefs in Computer Science)

On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages (SpringerBriefs in Computer Science) Lowest new price: $35.95
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Author: Brian Henderson-Sellers
Brand: Brand: Springer

Computing as a discipline is maturing rapidly. However, with maturity often comes a plethora of subdisciplines, which, as time progresses, can become isolationist. The subdisciplines of modelling, metamodelling, ontologies and modelling languages within software engineering e.g. have, to some degree, evolved separately and without any underpinning formalisms.

Introducing set theory as a consistent underlying formalism, Brian Henderson-Sellers shows how a coherent framework can be developed that clearly links these four, previously separate, areas of software engineering. In particular, he shows how the incorporation of a foundational ontology can be beneficial in resolving a number of controversial issues in conceptual modelling, especially with regard to the perceived differences between linguistic metamodelling and ontological metamodelling. An explicit consideration of domain-specific modelling languages is also included in his mathematical analysis of models, metamodels, ontologies and modelling languages.

This encompassing and detailed presentation of the state-of-the-art in modelling approaches mainly aims at researchers in academia and industry. They will find the principled discussion of the various subdisciplines extremely useful, and they may exploit the unifying approach as a starting point for future research.

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Reverse Mathematics: Proofs from the Inside Out

Reverse Mathematics: Proofs from the Inside Out Lowest new price: $24.95
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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 nineteenth-century 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 twentieth-century 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 well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

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