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› Find signed collectible books: 'Alfred Tarski: Life and Logic'
Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His mathematical work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in philosophy, linguistics and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon-vivant and a womanizer, who played the 'great man' to the hilt. Born in Warsaw in 1901 to Jewish parents, he changed his name and converted to Catholicism, but was never able to obtain a professorship in his home country. A fortuitous trip to the United States at the outbreak of war saved his life and turned his career around, even while it separated him from his family for years. By the war's end he was established as a professor of mathematics at the University of California, Berkeley. There Tarski built an empire in logic and methodology that attracted students and distinguished researchers from all over the world. From the cafes of Warsaw and Vienna to the mountains and deserts of California, this first full length biography places Tarski in the social, intellectual and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man, interlaced with an account of his major scientific achievements. [via]
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› Find signed collectible books: 'Axiomatic Set Theory'
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› Find signed collectible books: 'Basic Set Theory'

› Find signed collectible books: 'Combinatorics of Finite Sets'
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› Find signed collectible books: 'Concise Introduction to Logic'
Tens of thousands of students have learned to be more discerning at constructing and evaluating arguments with the help of Patrick J. Hurley. Hurley's lucid, friendly, yet thorough presentation has made A CONCISE INTRODUCTION TO LOGIC the most widely used logic text in North America. In addition, the book's accompanying technological resources, such as CengageNOW and Learning Logic, include interactive exercises as well as video and audio clips to reinforce what you read in the book and hear in class. In short, you'll have all the assistance you need to become a more logical thinker and communicator. [via]
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› Find signed collectible books: 'Contributions to the Founding of the Theory of Transfinite Numbers'
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› Find signed collectible books: 'The Core Model Iterability Problem'
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› Find signed collectible books: 'Elements of Set Theory'
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› Find signed collectible books: 'Everything And More: A Compact History Of Infinity'
Before discussing the merits of David Foster Wallace's Everything and More: A Compact History of Infinity, it is essential to define what the book is not. This volume in the "Great Discoveries" series is not a history of the personalities and social conditions that led to the "discovery" of infinity. Nor is it a narrative fixated on the cultish fear of--and obsession with--the infinite that has seemingly driven mathematicians insane over the centuries. Rather, Everything and More is a surprisingly rigorous march through the 2000 plus years of mathematical research that began with Aristotle; continued through Galileo, Isaac Newton, G.W. Leibniz, Karl Weierstrass, and J.W.R. Dedekind; and culminated in Georg Cantor and his Set Theory. The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. To propel his narrative, Wallace even develops a style that mirrors the mathematical language he probes. One difficulty in his focus on concepts and not a strict human chronology, though, is that his structure is dependent on frequent digressions (especially early on). Patience is required. Wallace demands that his reader walk through the equations, study the graphs and charts, and relearn college-level concepts to follow along on the exploration. Indeed, after one wrenching dip into Zenos paradoxes, Wallace spouts at his imagined complaining audience: "Deal." But the book should be deemed a success. If one grants him the attention he requires, Wallace has made the trip richly rewarding. --Patrick OKelley [via]
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› Find signed collectible books: 'Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem'
Born in 1601, Pierre de Fermat lived a quiet life as a civil servant in Toulouse, France. In his spare time, however, Fermat dabbled in mathematics, and somehow managed to become one of the great mathematical theorists of his century. Around 1637 he scribbled a marginal note in one of his books. In it, he stated that he had solved a celebrated number theory problem: "I have discovered a truly marvelous proof of this, which, however, the margin is not large enough to contain."
If only the margin had been wider! For more than 300 years, mathematicians labored to crack the secret of Fermat's Last Theorem, without any success. Finally, in 1995, a Princeton-based mathematician named Andrew Wiles solved the riddle. Amir Aczel's account of this brainteaser and its solution is an irresistible read. And for mathematical dolts--like myself, for instance--it includes a concise, profusely illustrated history of mathematical theory from the Bronze Age to our own fin-de-siecle. [via]
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› Find signed collectible books: 'A First Course in Abstract Algebra'
Considered a classic by many, A First Course in Abstract Algebra is an in-depth, introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The sixth edition of this text continues the tradition of teaching in a classical manner while integrating field theory and a revised Chapter Zero. New exercises were written, and previous exercises were revised and modified. [via]
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› Find signed collectible books: 'The Foundations of Mathematics'
"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books [via]
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› Find signed collectible books: 'Fuzzy Logic: The Revolutionary Computer Technology That Is Changing Our World'
"Fuzzy logic" is a way to program computers so that they can mimic the imprecise way that humans make decisions. This important book traces the dramatic story of Lofti Zadeh, the Iranian-American professor who developed this concept, and his struggle to sell it to the American academic and business communities. [via]
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› Find signed collectible books: 'Fuzzy Logic/the Discovery of a Revolutionary Computer Technology and How It Is Changing Our World'
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› Find signed collectible books: 'Georg Cantor: His Mathematics and Philosophy of the Infinite'
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› Find signed collectible books: 'Godel, Escher, Bach: An Eternal Golden Braid'
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. [via]
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› Find signed collectible books: 'The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings'
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› Find signed collectible books: 'Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra'
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› Find signed collectible books: 'Infinity And The Mind: The Science And Philosophy Of The Infinite'
A study of infinity in all its forms and its implications for the human mind. Within the realm of "Mindscape", part of a universe, the book shows that mathematics, science, and logic merge with the fantastic, and so much is revealed about the powers of the mind and its limitations. [via]
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› Find signed collectible books: 'An Introduction to Matrices, Sets and Groups for Science Students'
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› Find signed collectible books: 'The Joy of Sets: Fundamentals of Contemporary Set Theory'
This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science. [via]
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› Find signed collectible books: 'Lectures in Logic and Set Theory: Mathematical Logic'
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› Find signed collectible books: 'Lectures in Logic and Set Theory: Set Theory'
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› Find signed collectible books: 'Logic, Sets And Recursion'
Logic, Sets, and Recursion, Second Edition provides a comprehensive introduction to logic, the basic ideas of set theory, and mathematical induction at the undergraduate level. This text paves the way for students preparing to enter more advanced math courses, furnishing them with the experience to construct rigorous proofs with ease. It is intended to fill the gap between advanced mathematical logic texts and discrete mathematics texts that do not treat logic with the depth required in modern computer science. The Second Edition has incorporated a wealth of exercise sets to aid in students' retention and understanding of material presented in the text. [via]
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› Find signed collectible books: 'Math Structures for Computer Science'
The algorithms in this text have been rewritten in a language-neutral pseudocode making the book useful to computer science students. Each chapter begins with a "motivating problem" which occurs later as an exercise. Tables and bullet notes have been added througout, with examples. [via]
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› Find signed collectible books: 'Math-Terpieces: The Art of Problem-Solving'
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› Find signed collectible books: 'The Mathematical Experience'
We tend to think of mathematics as uniquely rigorous, and of mathematicians as supremely smart. In his introduction to The Mathematical Experience, Gian-Carlo Rota notes that instead, "a mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof ... is more often than not a way of making sure that our minds are not playing tricks." Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical aesthetics to non-Cantorian set theory. They make a convincing case for the idea that mathematics is not about eternal reality, but comprises "true facts about imaginary objects" and belongs among the human sciences. [via]
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› Find signed collectible books: 'Mathematical Ideas'

› Find signed collectible books: 'Mathematical Logic'
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› Find signed collectible books: 'Mathematical Methods in Linguistics'
Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language. [via]
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› Find signed collectible books: 'Mathematical Structures for Computer Science'
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› Find signed collectible books: 'Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics'
Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of Mathematical Structures for Computer Science covers all the topics in the CC2001 suggested curriculum for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes: Importance of logical thinking Power of mathematical notation Usefulness of abstractions [via]
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› Find signed collectible books: 'Matrices and Linear Algebra'
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› Find signed collectible books: 'More, Fewer, Less'
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› Find signed collectible books: 'The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity'
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› Find signed collectible books: 'Naive Set Theory'
From the Reviews: "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." - "Philosophy and Phenomenological Research". [via]
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› Find signed collectible books: 'Non-Newtonian Calculus'
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› Find signed collectible books: 'Parts of Classes'
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› Find signed collectible books: 'The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise'
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› Find signed collectible books: 'Schaum's Outline of Theory and Problems of Set Theory and Related Topics'
Confusing Textbooks? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
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Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
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› Find signed collectible books: 'Selected Works of Giuseppe Peano'
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› Find signed collectible books: 'Set Theory'
Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference. TOCI. Basic Set Theory.- Axioms of Set Theory.- Ordinal Numbers.- Cardinal Numbers.- Real Numbers.- The Axiom of Choice and Cardinal Arithmetic.- The Axiom of Regularity.- Filters, Ultrafilters and Boolean Algebras.- Stationary Sets.- Combinatorial Set Theory.- Measurable Cardinals.- Borel and Analytic Sets.- Models of Set Theory.- II. Advanced Set Theory.- Constructible Sets.- Forcing.- Applications of Forcing.- Iterated Forcing and Martin's Axiom.- Large Cardinals.- Large Cardinals and L.- Iterated Ultrapowers and LÄUÜ.- Very Large Cardinals.- Large Cardinals and Forcing.- Saturated Ideals.- The Nonstationary Ideal.- The Singular Cardinal Problem.- Descriptive Set Theory.- The Real Line.- III. Selected Topics.- Combinatorial Principles in L.- More Applications of Forcing.- More Combinatorial Set Theory.- Complete Boolean Algebras.- Proper Forcing.- More Descriptive Set Theory.- Determinacy.- Supercompact Cardinals and the Real Line.- Inner Models for Large Cadinals.- Forcing and Large Cardinals.- Martin's Maximum.- More on Stationary Sets.- Bibliography.- Notation.- Index.- Name Index. [via]
› Find signed collectible books: 'Set Theory and Its Logic'
This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before.
Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
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› Find signed collectible books: 'Set Theory and Its Philosophy: A Critical Introduction'
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› Find signed collectible books: 'Set Theory and Logic'
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› Find signed collectible books: 'Set Theory for the Working Mathematician'
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› Find signed collectible books: 'Set Theory, Logic and Their Limitations'
In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory. [via]
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› Find signed collectible books: 'Sets for Mathematics'
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› Find signed collectible books: 'Sets: Sorting into Groups'
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› Find signed collectible books: 'Sets, Logic and Categories'
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› Find signed collectible books: 'Sheaves in Geometry and Logic: A First Introduction to Topos Theory'
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› Find signed collectible books: 'Technical Methods in Philosophy'
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› Find signed collectible books: 'Theory of Sets'
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› Find signed collectible books: 'A Transition To Advanced Mathematics'
TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses. [via]
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› Find signed collectible books: 'Understanding the Infinite'
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› Find signed collectible books: 'Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena'
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› Find signed collectible books: 'Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being'
If Barbie thinks math class is tough, what could she possibly think about math as a class of metaphorical thought? Cognitive scientists George Lakoff and Rafael Nuñez explore that theme in great depth in Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. This book is not for the faint of heart or those with an aversion to heavy abstraction--Lakoff and Nuñez pull no punches in their analysis of mathematical thinking. Their basic premise, that all of mathematics is derived from the metaphors we use to maneuver in the world around us, is easy enough to grasp, but following the reasoning requires a willingness to approach complex mathematical and linguistic concepts--a combination that is sure to alienate a fair number of readers.
Those willing to brave its rigors will find Where Mathematics Comes From rewarding and profoundly thought-provoking. The heart of the book wrestles with the important concept of infinity and tries to explain how our limited experience in a seemingly finite world can lead to such a crazy idea. The authors know their math and their cognitive theory. While those who want their abstractions to reflect the real world rather than merely the insides of their skulls will have trouble reading while rolling their eyes, most readers will take to the new conception of mathematical thinking as a satisfying, if challenging, solution. --Rob Lightner [via]
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› Find signed collectible books: 'Gdel, Escher, Bach'
¿Puede un sistema comprenderse a sí mismo ? Si esta pregunta se refiere a la mente humana, entonces nos encontramos ante una cuestión clave del pensamiento científico. Y de la filosofía. Y del arte. Investigar este misterio es una aventura que recorre la matemática, la física, la biología, la psicología y, muy especialmente, el lenguaje. Douglas R. Hofstadter, joven y ya célebre científico, nos abre la puerta del enigma con la belleza y la alegría creadora de su estilo. Sorprendentes paralelismos ocultos entre los grabados de Escher y la música de Bach nos remiten a las paradojas clásicas de los antiguos griegos y a un teorema de la lógica matemática moderna que ha estremecido el pensamiento del siglo XX : el de Kurt Gödel. Todo lenguaje, todo sistema formal, todo programa de ordenador, todo proceso de pensamiento, llegan, tarde o temprano, a la situación límite de la autorreferencia : de querer expresarse sobre sí mismos. Surge entonces la emoción del infinito, como dos espejos enfrentados y obligados a reflejarse mutua e indefinidamente. Gödel, Escher, Bach: un Eterno y Grácil Bucle, es una obra de arte escrita por un sabio. Versa sobre los misterios del pensamiento e incluye, ella misma, sus propios misterios. / Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern 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.mathematics to the study of the human mind and the development of artificial intelligence. [via]
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