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An excellent introduction to mathematical logic, this book provides readers with a sound knowledge of the most important approaches to the subject, stressing the use of logical methods in attacking nontrivial problems.
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Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the ...

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"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incom...

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Das ist nicht Mathematik, das ist Theologie! This is not mathematics; this is theology. [Remark about David Hilbert's first proof of his finite basis theorem.]

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This textbook/software package covers first-order language in a method appropriate for first and second courses in logic. The unique on-line grading services instantly grades solutions to hundred of computer exercises. It is specially devised to be used by philosophy instructors in a way that is useful to undergraduates of philosophy, computer science, mathematics, and linguistics.
The book is a completely rewritten and much improved version of The Language of First-order Logic. Introduc...

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Language, Proof and Logic by Jon Barwise, John Etchemendy
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Language, Proof and Logic
LANGUAGE, PROOF AND LOGIC JON BARWISE & JOHN ETCHEMENDY In collaboration with Gerard Allwein Dave Barker-Plummer Albert Liu 7 7 SEVEN BRIDGES PRESS NEW YORK • LONDON

Logic and proof: online resources and websites
Logic and proof. Introduction to Logic A set of online tutorials for the study of elementary logic covering propositional and predicate calculus.

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Propositional Logic | Internet Encyclopedia of Philosophy
Propositional Logic. Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying ...

Classical Logic (Stanford Encyclopedia of Philosophy)
Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language has ...

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Overview of Randall Holmes's Home Page There is a section of personal data (with random links), (or you can see my curriculum vita curriculum vita (with publication ...

An Elementary Introduction to Logic and Set Theory ...
IV. Methods of Proof. Formal Proof. Informal Proof. Conditional Proof. Indirect Proof. Proof by Counter Example. Mathematical Induction. Formal Proof. A Formal Proof ...

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In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used.

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Free Ebook In the Light of Logic (Logic and Computation in Philosophy)

In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they...

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Temporal Logic (Stanford Encyclopedia of Philosophy)
The term Temporal Logic has been broadly used to cover all approaches to representation and reasoning about time and temporal information within a logical ...

Provability Logic (Stanford Encyclopedia of Philosophy)
Bibliography General references on provability logic. Artemov, S.N. and L.D. Beklemishev, 2004, “Provability Logic,” in Handbook of Philosophical Logic ...

Logic at Harvard
Logic at Harvard. There is a long tradition in logic at Harvard, one that continues to this day. This page contains information concerning the logic resources at ...

In Memoriam - Aldo Antonelli — Philosophy Department
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Modal Logic | Internet Encyclopedia of Philosophy
Modal Logic (draft: do not quote) Modal notions go beyond the merely true or false by embedding what we say or think in a larger conceptual space referring to what ...

Modal logic - Wikipedia, the free encyclopedia
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.

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Abstracts Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference. Joseph Y. Halpern (editor) This is the proceedings of the first TARK ...

Boolean algebra - Wikipedia, the free encyclopedia
History. Boole's algebra predated the modern developments in abstract algebra and mathematical logic; it is however seen as connected to the origins of both fields. [4]

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Free PDF Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly c...

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Prime Number -- from Wolfram MathWorld
iff is a prime number. Many prime factorization algorithms have been devised for determining the prime factors of a given integer, a process known as factorization or ...

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The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808 ...

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Millennium Prize Problems. Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved, as of August 2015: [6]

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Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to ...

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Properties of the zeta function In spite of the important relation between ζ(s) and the sequence of prime numbers, Riemann was not especially interested in number ...

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Georg Friedrich Bernhard Riemann (* 17. September 1826 in Breselenz bei Dannenberg (Elbe); † 20. Juli 1866 in Selasca bei Verbania am Lago Maggiore) war ein ...

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Literatuur. en) John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (John Henry Press, 2003) ISBN 0-309-08549-7

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This book is a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even "work" at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author...

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Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers (MSRI Mathematical Circles Library) (9780821868737): Alexander Zvonkin: Books

The MSRI Mathematical Circles Library Series
MSRI Mathematical Circles Library. Mathematical circles originated in Eastern Europe in the 1930s, spreading to Western Europe, Asia, and, eventually, to North America.

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For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture.
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Ludwig Wittgenstein: Later Philosophy of Mathematics. Mathematics was a central and constant preoccupation for Ludwig Wittgenstein (1889–1951). He started in ...

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Ludwig Wittgenstein's Philosophy of Mathematics is undoubtedly the most unknown and under-appreciated part of his philosophical opus. Indeed, more than ...

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According to a family tree prepared in Jerusalem after World War II, Wittgenstein's paternal great-grandfather was Moses Meier, a Jewish land agent who lived with his ...

Alan Turing - Bibliography
Other primary works. Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939, ed. Cora Diamond, Harvester Press (1976). This contains a complete ...

Analytic Philosophy | Internet Encyclopedia of Philosophy
Analytic Philosophy. The school of analytic philosophy has dominated academic philosophy in various regions, most notably Great Britain and the United States, since ...

Principia Mathematica - Wikipedia, the free encyclopedia
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912 ...

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Western Philosophy. Top About course Housekeeping Schedule Gallery Themes Stories Online Readings. Wildman's Weird Wild Web. Home Links Jokes Other Courses ...

Bertrand Russell (Stanford Encyclopedia of Philosophy)
Bibliography Primary Literature. Major Books and Articles by Russell; Major Anthologies of Russell’s Writings; The Collected Papers of Bertrand Russell

Alan Turing - Wikipedia, the free encyclopedia
Born: Alan Mathison Turing 23 June 1912 Maida Vale, London, England: Died: 7 June 1954 (aged 41) Wilmslow, Cheshire, England: Residence: Wilmslow, Cheshire, England

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Download PDF The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

This is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.
Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, howe...

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Most popular Russian puzzle book ever published. Marvelously varied puzzles ranging from simple "catch" riddles to difficult problems. Lavishly illustrated with clear ...

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More Mathematical Puzzles of Sam Loyd - Dover Publications
Martin Gardner: A Remembrance . The worldwide mathematical community was saddened by the death of Martin Gardner on May 22, 2010. Martin was 95 years old when he died ...

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This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are consid...

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Category Theory (Stanford Encyclopedia of Philosophy)
Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science, and is also applied to mathematical ...

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Mathematical sociology is the use of mathematics to construct social theories. Mathematical sociology aims to take sociological theory, which is strong in intuitive ...

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(graph above: absolute value of the gamma function in the complex plane, source: Wikimedia Commons) Here is an unordered list of online mathematics books, textbooks ...

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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity , [2] structure, [3] space, [2] and change.

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Welcome to the Ada Programming tutorial at Wikibooks. This is the first Ada tutorial covering the Ada 2005 and 2012 standards. If you are a beginner you will learn ...

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More Precisely provides a rigorous and engaging introduction to the mathematics necessary to do philosophy. It is impossible to fully understand much of the most important work in contemporary philosophy without a basic grasp of set theory, functions, probability, modality and infinity. Until now, this knowledge was difficult to acquire. Professors had to provide custom handouts to their classes, while students struggled through math texts searching for insight. More Precisely fills this key gap...

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Unschooling Math - Sandra Dodd on Life and Learning
LINKS: Karen James on Ethan's math interest. An unschooler goes to sixth grade, and how he did in math. Math Phobia Is this page inducing anxiety? "I don't want to ...

Care Ethics | Internet Encyclopedia of Philosophy
Care Ethics. The moral theory known as “ the ethics of care” implies that there is moral significance in the fundamental elements of relationships and ...

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Suicide (Stanford Encyclopedia of Philosophy)
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This site is intended as a resource for university students in the mathematical sciences. Books are recommended on the basis of readability and other pedagogical value.

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John Locke (Internet Encyclopedia of Philosophy)
John Locke (1632—1704) John Locke was among the most famous philosophers and political theorists of the 17 th century. He is often regarded as the founder of a ...

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Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines.

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Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today.
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The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic. The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is...

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The basic lambda calculus may be used to model booleans, arithmetic, data structures and recursion, as illustrated in the following sub-sections.

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Further reading. Hendrik Pieter Barendregt, 1984. The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, Volume 103 ...

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