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Gödel's Proof

Gödel's Proof Lowest new price: $9.97
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Author: Ernest Nagel
Brand: Nagel, Ernest/ Newman, James R./ Hofstadter, Douglas R./ Hofstadter, Douglas R. (EDT)

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

Marking the 50th anniversary of the original publication of Gödel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible.

This reissuance of Nagel and Newman's classic has been vastly improved by the deft editing of Douglas Hofstadter, a protégé of Nagel's and himself a popularizer of Gödel's work. In the second edition, Hofstadter reworks significant sections of the book, clarifying and correcting here, adding necessary detail there. In the few instances in which his writing diverges from the spirit of the original, it is to emphasize the interplay between formal mathematical deduction and meta-mathematical reasoning--a subject explored in greater depth in Hofstadter's other delightful writings. --Clark Williams-Derry

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Introduction to Mathematical Philosophy

Introduction to Mathematical Philosophy Lowest new price: $5.85
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Author: Bertrand Russell

2017 Reprint of 1919 Edition.  Full facsimile of the original edition, not reproduced with Optical Recognition software.  Introduction to Mathematical Philosophy has been a seminal work for more than nine decades. It gives the general background necessary for any serious discussion on the foundational crisis of mathematics in the beginning of the twentieth century.  Requiring neither prior knowledge of mathematics nor aptitude for mathematical symbolism, the book serves as essential reading for anyone interested in the intersection of mathematics and logic and in the development of analytic philosophy in the twentieth century. Russell offers to his readers a penetrating discussion on certain issues of mathematical logic that embodies the dawn of modern analytic philosophy.

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Logic For Dummies

Logic For Dummies Lowest new price: $5.83
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Author: Mark Zegarelli
Brand: Mark Zegarelli

Logic concepts are more mainstream than you may realize. There’s logic every place you look and in almost everything you do, from deciding which shirt to buy to asking your boss for a raise, and even to watching television, where themes of such shows as CSI and Numbers incorporate a variety of logistical studies. Logic For Dummies explains a vast array of logical concepts and processes in easy-to-understand language that make everything clear to you, whether you’re a college student of a student of life. You’ll find out about:

  • Formal Logic
  • Syllogisms
  • Constructing proofs and refutations
  • Propositional and predicate logic
  • Modal and fuzzy logic
  • Symbolic logic
  • Deductive and inductive reasoning

Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.


  • Logic For Dummies

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How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics Lowest new price: $5.64
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Author: Eugenia Cheng
Brand: Basic Books AZ

"Whimsical...rigorous and insightful." -- New York Times Book Review

What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge "mathematics of mathematics," that is about figuring out how math works.

Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.


  • Basic Books AZ

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Everything and More: A Compact History of Infinity

Everything and More: A Compact History of Infinity Lowest new price: $10.94
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Author: David Foster Wallace
Brand: W W Norton Company

"A gripping guide to the modern taming of the infinite."―The New York Times. With a new introduction by Neal Stephenson.

Is infinity a valid mathematical property or a meaningless abstraction? David Foster Wallace brings his intellectual ambition and characteristic bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that there was more than one kind of infinity. Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics.

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 Zeno’s 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 O’Kelley


  • W W Norton Company

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Category Theory in Context (Aurora: Dover Modern Math Originals)

Category Theory in Context (Aurora: Dover Modern Math Originals) Lowest new price: $17.31
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Author: Emily Riehl
Brand: Riehl Emily

Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.

Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. While the reader will be rewarded for familiarity with these background mathematical contexts, essential prerequisites are limited to basic set theory and logic.


  • Category Theory in Context

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An Introduction to Symbolic Logic, 3rd Edition

An Introduction to Symbolic Logic, 3rd Edition Lowest new price: $13.42
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Author: Susanne K. Langer
Brand: Susanne K Langer

This is probably the clearest book ever written on symbolic logic for the philosopher, the general scientist, and the layman. For years it has received the appreciation of those who have been rebuffed by other introductory works because of insufficient mathematical training. No special knowledge of mathematics is required here; even if you have forgotten most of your high school algebra, you can learn to use mathematical logic by following the directions in this book.
Now revised and corrected, the book allows you to start with the simplest symbols and conventions and end up with a remarkable grasp of the Boole-Schroeder and Russell-Whitehead systems. It covers the study of forms, essentials of logical structure, generalization, classes, and the principal relations among them, universe of classes, the deductive system of classes, the algebra of logic, abstraction and interpretation, calculus of propositions, the assumptions of Whitehead and Russell's Principia Mathematica, and logistics. Appendices cover symbolic logic and the logic of the syllogism, the construction and use of truth-tables, and proofs of two theorems.
"One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.


  • An Introduction to Symbolic Logic 3rd Edition

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The Art and Craft of Problem Solving

The Art and Craft of Problem Solving Lowest new price: $76.35
Lowest used price: $58.64
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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Logic: Propositional Logic (Quick Study: Academic)

Logic: Propositional Logic (Quick Study: Academic) Lowest new price: $2.97
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Author: Inc. BarCharts
Brand: Brand: BarCharts

This 4-page study guide contains fundamental logic definitions and analysis which is specifically designed to aid science students.


  • Used Book in Good Condition

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Length (Math Counts)

Length (Math Counts) Lowest new price: $4.01
Lowest used price: $1.75
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Author: Henry Arthur Pluckrose
Brand: Childrens Pr

Photographs and text introduce the concept of length and how to measure it.


  • Length

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