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Mathematics
Foundations and Logic


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Godel, Escher, Bach: An Eternal Golden Braid
Godel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter
Publisher Comments
This groundbreaking Pulitzer Prize-winning book sets the standard for interdisciplinary writing, exploring the patterns and symbols in the thinking of mathematician Kurt Godel, artist M.C. Escher, and composer Johann Sebastian Bach.... (read more)

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Logicomix: An Epic Search for Truth
Logicomix: An Epic Search for Truth
by Apostolos Doxiadis and Christos Papadimitriou
Staff Pick
Bertrand Russell hasn't been this entertaining since Bruce Duffy's 1987 novel The World As I Found It. Logicomix is an astoundingly entertaining graphic novel about the most unlikely of subjects: Bertrand Russell's struggle to find the logical foundation... (read more)

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I Am a Strange Loop
I Am a Strange Loop
by Douglas R. Hofstadter
Publisher Comments
Douglas R. Hofstadter's long-awaited return to the themes of Gödel, Escher, Bach — an original and controversial view of the nature of consciousness and identity. What do we mean when we say "I"? Can thought arise out of matter? Can a self,... (read more)

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Computability and Randomness
Computability and Randomness
by Andre Nies
Publisher Comments
The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of... (read more)

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Key Terms in Logic (Key Terms)
Key Terms in Logic (Key Terms)
by Jon Williamson
Publisher Comments
The Key Terms in Philosophy series offers clear, concise and accessible introductions to the central topics in philosophy. Each book offers a comprehensive overview of the key terms, concepts, thinkers and major works in the history of a key area of... (read more)

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Mathematics and Plausible Reasoning, Volume 2:  Patterns of Plausible Inference
Mathematics and Plausible Reasoning, Volume 2: Patterns of Plausible Inference
by G. Polya
Publisher Comments
Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive... (read more)

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Simplicity Theory (Oxford Logic Guides)
Simplicity Theory (Oxford Logic Guides)
by Byunghan Kim
Publisher Comments
Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics. Simplicity theory, a subject of model theory, studies a class of mathematical... (read more)

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Cime Summer Schools #48: Aspects of Mathematical Logic: Lectures Given at the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Varenna (Como), Italy, September 9-17
Cime Summer Schools #48: Aspects of Mathematical Logic: Lectures Given at the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Varenna (Como), Italy, September 9-17
by E Casari
Publisher Comments
H. Hermes: Basic notions and applications of the theory of decidability.- D. Kurepa: On several continuum hypotheses.- A. Mostowski: Models of set theory.- A. Robinson: Problems and methods of model theory.- S. Sochor, B. Balcar: The general theory of... (read more)

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Computer & the Information Revolution
Computer & the Information Revolution
by Georges Ifrah
Synopsis
The final volume in Georges Ifrah's history of numbers, this work explores the computer and the information revolution. It introduces the reader to the departure made from the decimal Base 10 to the spread of the binary Base 2, and examines the origins... (read more)

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Euclid in the Rainforest: Discovering Universal Truth in Logic and Math
Euclid in the Rainforest: Discovering Universal Truth in Logic and Math
by Joseph Mazur
Publisher Comments
How do we know that something is true? How do we know that things really are what they seem? Many people think math and science are the ultimate authorities on reality. Math defines abstract, universal truths; scientific truths are established by... (read more)

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On Godel (Wadsworth Philosophers Series)
On Godel (Wadsworth Philosophers Series)
by Jaakko Hintikka
Publisher Comments
This brief text assists students in understanding Godel's philosophy and thinking so that they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the "Wadsworth Philosophers Series... (read more)

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Frege's Theorem
Frege's Theorem
by Richard G Heck
Publisher Comments
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic... (read more)

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Philosophical Papers #01: Philosophical Papers: Volume 1, Mathematics, Matter and Method
Philosophical Papers #01: Philosophical Papers: Volume 1, Mathematics, Matter and Method
by Hilary Putnam
Publisher Comments
This book deals with the philosophy of mathematics and of science and the nature of philosophical and scientific enquiry, and with the philosophy of language and mind.... (read more)

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First-Order Logic
First-Order Logic
by Raymond M Smullyan
Publisher Comments
Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view... (read more)

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Conjecture and Proof
Conjecture and Proof
by Miklos Laczkovich
Publisher Comments
The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on 'Conjecture and Proof'.... (read more)

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Principia Mathematica - Volume One
Principia Mathematica - Volume One
by Alfred North Whitehead
Synopsis
An Unabridged, Digitally Enlarged Printing Of Volume I of III: Part I - MATHEMATICAL LOGIC - The Theory Of Deduction - Theory Of Apparent Variables - Classes And Relations - Logic And Relations - Products And Sums Of Classes - Part II - PROLEGOMENA TO... (read more)

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Trends in Logic #37: Le Niewski's Systems of Logic and Foundations of Mathematics
Trends in Logic #37: Le Niewski's Systems of Logic and Foundations of Mathematics
by Rafal Urbaniak
Publisher Comments
This meticulous critical assessment of the ground-breaking work of philosopher... (read more)

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Collected Works
Collected Works
by Kurt Godel
Publisher Comments
Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for... (read more)

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After Godel: Platonism and Rationalism in Mathematics and Logic
After Godel: Platonism and Rationalism in Mathematics and Logic
by Richard Tieszen
Publisher Comments
Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Godel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Godel's three philosophical heroes... (read more)

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The Mind's I: Fantasies and Reflections on Self and Soul
The Mind's I: Fantasies and Reflections on Self and Soul
by Douglas Hofstadter and Daniel Dennett
Publisher Comments
With contributions from Jorge Luis Borges, Richard Dawkins, John Searle, and Robert Nozick, The Mind's I explores the meaning of self and consciousness through the perspectives of literature, artificial intelligence, psychology, and other disciplines. In... (read more)

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