 Games and Puzzles  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Almost 40 games or puzzles, with extensive discussions and solutions. Examples include the Monty Hall Dilemma, Lewis Carroll's problem; the game of Nim, the 3 glass puzzle, Northcott's game, the Tower of Hanoi, and many more. Most require a browser capable
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 Games Mathematicians Play  Gregory McColm; Dept. of Mathematics, Univ. of South Florida
Mathematical games from a logical point of view: strategies for games and using games in descriptive complexity. Contents include Bisimulation; Foundations; Game Theoretic Semantics; and Guarded Quantifiers. With an outline of the problem of what it means
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 Gateways to Advanced Mathematical Thinking (GAMT)  Michelle Manes; Education Development Center, Inc. (EDC)
The goal of this project is to research the ways in which high school and college mathematics students come to acquire flexible understandings of essential concepts needed for analytic and algebraic thinking. Integral to this research effort is the development
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 Gateway to Logic  Christian Gottschall; Dept. of Philosophy, Vienna
A collection of Webbased logic programs offering a number of logical functions. Client side processing (requires Java): sparse trees, alpha graphs (Peirce), Begriffsschrift notation (Frege), Polish notation, truth tables, normal forms, miscellaneous
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 Gödel and the Nature of Mathematical Truth  Edge interview with Rebecca Goldstein
Interview with Rebecca Goldstein, the philosopher and novelist, on her most recent book, Incompleteness: The Proof and Paradox of Kurt Gödel.
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 Gödel's Theorem and Information  Gregory J. Chaitin
Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor arguing that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast
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 Gödel's Theorem  Microsoft Encarta Online
Gödel's Theorem, also known as the Incompleteness Theorem, two theorems proposed by Austrianborn American logician Kurt Gödel. These theorems state that some parts of mathematics are based on ideas that cannot be proven within the system of
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 Göedel's Theorems  Math Academy Online/Platonic Realms
An article covering the completeness theorem, the incompleteness theorems, and Göedel's settheoretic independence result.
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 General Mathematics, NZ (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea.
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 Getting Across the River  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions such as "A man has a goat, a wolf and a cabbage. He must cross a river in a boat that will only carry one item at a time...."
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 The Grey Labyrinth  Kevin Lin
A collection of mindbenders in math and logic. When a solution to one puzzle is posted, another solutionless puzzle is added. With an archive of past puzzles, links to other puzzlerelated sites, and a bibliography of works that inspired this site.
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 Grothendieck Circle  Leila Schneps et al.
Alexandre Grothendieck's published articles, unpublished research, letters, and translations: The Cohomology Theory of Abstract Algebraic Varieties, Standard Conjectures on Algebraic Cycles, Hodge's General Conjecture Is False for Trivial Reasons, Groupes
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 Guessing the Prime Number Theorem and Treacherous Logic (Math Chat)  Frank Morgan, MAA Online
The Prime Number theorem says that the probability P(x) that a large integer x is prime is about 1/log x. At about age 16 Gauss apparently conjectured this estimate after studying tables of primes. Greg Martin suggested to me a heuristic way to approach
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 Habits of mind: an organizing principle for mathematics curriculum (Connected Geometry)  Cuoco, Goldenberg, Mark; Education Development Center, Inc. (EDC)
A curriculum the goal of which is not to train large numbers of high school students to be university mathematicians, but rather to allow high school students to become comfortable with illposed and fuzzy problems, to see the benefit of systematizing
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 The handling of geometry definitions in school textbooks  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Some historical background and a discussion of the value of students constructing their own understanding of mathematical proofs; misconceptions that arise from readymade definitions; and the advantage of a constructivist approach, which allows pupils
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 The Helsinki Logic Group  University of Helsinki, Finland
The Helsinki Logic Group is a team of logicians that has gathered in the Department of Mathematics of the University of Helsinki during the past ten years. The main topics of research are: Finite Model Theory  generalized quantifiers, games and descriptive
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 Hidden Variable Studios  Hidden Variable Studios, LLC
Makers of Tic Tactics, Threes, and other mathematical strategy apps for Android, iOS, Kindle Fire, and Nook HD.
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 High School Problem of the Week  Department of Mathematics, Southwest Missouri State University (SMSU)
Word problems in number theory, logic, algebra, analytic geometry, and other topics. Read the solution to the most recent problem, and archives of previous problems and their answers.
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 Hilbert II  Michael Meyling
A predicate calculusbased proof checker, which can check proofs drawn from many different Internet sites.
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 Ho Math and Chess Learning Centre, Vancouver, BC, and affiliates  Frank Ho
Site features downloadable math and mathematical chess materials, information on the centers and the classes they offer locally, and franchising details for the centers.
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 Homepage of Torsten Sillke  Torsten Sillke
A collection of puzzles statements, with references, on a variety of topics: operations research, such as crossing the bridge; logic, including liars and truth tellers, mastermind, and age problems; lateral thinking, also known as "situation puzzles";
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 Honeycomb Hotel: A Unit in Logic  Barbara De Roes
A lesson plan for grades 512+, for teaching deductive logic, using puzzles not dependent upon language. "Honeycomb Hotel is a game of logic and deduction.
You must determine which symbols are on which doors of the Honeycomb Hotel, and the exact path
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 Hooda Math  Michael and Teresa Edlavitch
Interactive games, math movies submitted by students, tutorials, and links for students and teachers.
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 How to Solve the Rubik's Cube v1.4  Mark Jeays
A complete solution to solving the cube from any position, credited to David Singmaster, who wrote the 1980 book Notes on Rubik's Magic Cube, except for Step 2, discovered independently by Mark Jeays.
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 How To Write Proofs  Larry W. Cusick
The mechanics of proofs and proof strategies, with examples and exercises: direct proof, proof by contradiction, proof by contrapositive, if, and only if (iff), proof by mathematical induction, unwinding definitions (getting started), constructive versus
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 Hypothèses / Géometrix  J. Gressier
Logiciel capable de corriger en direct un élève sur n'importe quel problème de construction géométrique. Il peut aussi le corriger sur la plupart des problèmes de démonstration en géométrie
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 Ideas, Concepts, and Definitions (MegaMath)  Nancy Casey; Los Alamos National Laboratory
A glossary and reference page to help students learn more about mathematics and find out what some of the special words mean. Topics: Doing What Mathematicians Do; Truth and Proof; Mathematical Objects and Their Properties; Modeling and Abstraction; Algorithms;
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 Imagiware
A commercial site that including several games. A Java triangle puzzle; Web Puzzler lets you unscramble an image; MasterWeb is like the board game MasterMind; "Nowwwhere" is a Webaccessible virtual world; and there is a version of Mancala, too.
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 Implications Rules  Alan Selby
Implication Rules: two puzzles that show the difference between one and twoway implication rules. Mastering the difference is a simple, first step, in rule and patternbased thought, needed to precisely read rules, definitions and statements in all
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 Institute for Logic (Institut für Formale Logik)  University of Vienna, Vienna, Austria
Research in the group is concentrated on axiomatic set theory, in particular: Inner models and large cardinals; Constructible models of set theory / core models; Consistency strengths; Coding; Forcing; and Descriptive set theory. Abstract Server; People
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 Institute for Logic, Language and Computation (ILLC)  University of Amsterdam, The Netherlands
An institute founded to further the scientific study of the structure, modification, and transmission of information. Currently, the groups participating in ILLC are based at the Faculty of Mathematics, Computer Science, Physics, and Astronomy, the Faculty
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 Institute for Mathematical Logic and Foundations of Mathematics  Department of Mathematics, University of Freiburg
Research (preprints and theses, reports), teaching (lectures in German, course materials), people, news, and information services. In English, German, and French.
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 Institute for Mathematics and Computer Science (IMACS)
A research and teaching institute based in South Florida. Through its distance
learning division (eIMACS), IMACS offers interactive mathematics courses designed for talented secondary school students. The first in this series is Logic for Mathematics,
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 The Interactive Mathematics Classroom  Rex Boggs
A digital library of thirdparty technology resources for teaching mathematics, from kindergarten to calculus. Register to comment on interactive whiteboard files, Powerpoints, TINspire documents, Excel spreadsheets, and other digital resources. RSS
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 Interactive Mathematics Miscellany and Puzzles  Alexander Bogomolny
"The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based  the more beautiful is the result." This awardwinning site offers
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 International Mathematical Olympiad (IMO) / Olympiade internationale de mathématiques (OIM)
The World Championship Mathematics Competition for High School, which takes place each year in a different country. Its membership (by invitation only) has gradually expanded to over seventy countries from all five continents. Latest competition results;
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 Introducing Mathematics
This website looks at some areas of mathematics that are not familiar to most people, such as Ramsey theory and set theory, but introduces them in an uncomplicated manner.
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 Introduction to Logic and Recursion Theory  Edward Boyden
Notes from a class taught by Prof. Sacks at M.I.T. in the spring of 1998, organized and reinterpreted. Propositional Calculus; FirstOrder Logic; Towards Completeness and Consistency; Recursion Theory – compare this to Sipser’s Computation, Part II; Clarity
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 Inventing Science: From Thales to Euclid  Gregory Crane, Tufts University
Classics 189: Greek Science. Euclid's synthesis remains the most successful single book on math every written, but advances were made in many other fields such as geography, astronomy and the natural sciences. Aristotle, in particular, laid the foundations
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 Inventor's Paradox  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A page that looks into different ways a specific statement may be related to a more general one. Pairs of statements in which: one is a clear generalization of another, whereas in fact the two are equivalent; one is a clear generalization of another and
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 Investigations in Mathematics  Eric S. Rowland
Openended problems for high school and college students to "approach creatively and in their own way": Pascal's simplices ("What is the generalization of Pascal's triangle?"), Pythagorean triples, regular polygons ("What is the area of a regular polygon
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 Invitation to MasterMind  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
Mastermind is a game played by a codemaker and a codebreaker. The codemaker selects a code, a sequence of four colors (digits, pegs or other symbols) chosen from a set of six colors (repetitions allowed). The codebreaker will then try to guess the code.
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 Isabelle  Paulson, Nipkow
A generic theorem proving environment developed at Cambridge University and TU Munich. Isabelle/HOL is currently the best developed object logic, including an extensive library of (concrete) mathematics, and various packages for advanced definitional
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 IsarMathLib
IsarMathLib is a library of proofs that have been checked with Isabelle
proof assistant, based on the Isabelle's ZF logic. The emphasis is put on
readibility. The proofs are written using Isar syntax and can be read and
followed by any person familliar
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 Islands & Divisions of Knowledge (Pattern Based Reason)  Alan Selby
Not seeing the difference between one and twoway implications is a common source of confusion in reading, writing and mathematics. Oneway implication rules can sometimes be put together to get further implication rules. One and twoway implications
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 Is Mathematical Teaching a Function of Time?  Andrej and Elena Cherkaev, eds.
A page of math humor, including definitions, anecdotes, math education jokes, theorems, puns, limerics, and links.
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 Is that a fact?  Keith Devlin (Devlin's Angle)
I'll bet that, like me, you have known for years that, as far as the brain is concerned, it's all down hill from the moment we get our driver's license. Every day, another ten thousand cells die. Or is it a hundred thousand? A million? No matter, it's
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 Ivan José online  Ivan José Varzinczak
Research on logicbased knowledge representation and reasoning in Artificial Intelligence. Research areas: logicbased knowledge representation and reasoning; description logics, ontology engineering and semantic web; nonmonotonic reasoning, belief revision
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 Jacopo Notarstefano
Interactive visualizations and puzzles: "Turing's sunflower," which connects leaf arrangements and Fibonacci numbers; "HavelHakimi," which presents nodes and their degrees to construct into a graph; "Fourcoloring a Dodecahedron"; and a logic puzzle
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 James Propp
James Propp studies tilings, games, and other aspects of combinatorics, probability, and dynamical systems. Many of his articles are available for download in PostScript and gzipped PostScript formats. Code for C programs related to tilings and cellular
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