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Reverse Mathematics: Proofs from the Inside Out

Reverse Mathematics: Proofs from the Inside Out Lowest new price: $14.80
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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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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: $9.43
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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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Crossing the River with Dogs: Problem Solving for College Students

Crossing the River with Dogs: Problem Solving for College Students Lowest new price: $83.15
Lowest used price: $62.69
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.


  • please read

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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: $6.28
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Author: Alex Bellos

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!



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What Is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles (Dover Recreational Math)

What Is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles (Dover Recreational Math) Lowest new price: $8.19
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Author: Raymond M. Smullyan
Brand: Dover Publications

"The most original, most profound, and most humorous collection of recreational logic and math problems ever written." — Martin Gardner, Scientific American
"The value of the book lies in the wealth of ingenious puzzles. They afford amusement, vigorous exercise, and instruction." — Willard Van Orman Quine, The New York Times Book Review
If you're intrigued by puzzles and paradoxes, these 200 mind-bending logic puzzles, riddles, and diversions will thrill you with challenges to your powers of reason and common sense. Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel's undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.


  • Used Book in Good Condition

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Language, Proof and Logic, 2nd Edition

Language, Proof and Logic, 2nd Edition Lowest new price: $52.52
Lowest used price: $4.41
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Author: David Barker-Plummer
Brand: imusti

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 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.


  • CSLI Publications

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Logic: A Very Short Introduction (Very Short Introductions)

Logic: A Very Short Introduction (Very Short Introductions) Lowest new price: $2.09
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Author: Graham Priest

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.

In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms, and proofs in mathematics.

ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

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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: $17.39
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Author: Emily Riehl

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.

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Gödel's Proof

Gödel's Proof Lowest new price: $9.52
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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.

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Philosophy and Model Theory

Philosophy and Model Theory Lowest new price: $25.87
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Author: Tim Button

Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics.
But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers.
The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures.
Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.

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