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 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 ...more>> 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 ...more>> 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 ...more>> Gateway to Logic - Christian Gottschall; Dept. of Philosophy, Vienna A collection of Web-based 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 ...more>> 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. ...more>> Gödel's Theorem and Information - Gregory J. Chaitin Gödel's theorem may be demonstrated using arguments having an information-theoretic 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 ...more>> Gödel's Theorem - Microsoft Encarta Online Gödel's Theorem, also known as the Incompleteness Theorem, two theorems proposed by Austrian-born American logician Kurt Gödel. These theorems state that some parts of mathematics are based on ideas that cannot be proven within the system of ...more>> Göedel's Theorems - Math Academy Online/Platonic Realms An article covering the completeness theorem, the incompleteness theorems, and Göedel's set-theoretic independence result. ...more>> General Mathematics, N-Z (Funk & Wagnalls Multimedia Encyclopedia) - Lycos Zone: Mathematics Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea. ...more>> 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...." ...more>> The Grey Labyrinth - Kevin Lin A collection of mind-benders in math and logic. When a solution to one puzzle is posted, another solution-less puzzle is added. With an archive of past puzzles, links to other puzzle-related sites, and a bibliography of works that inspired this site. ...more>> 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 ...more>> 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 ...more>> 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 ill-posed and fuzzy problems, to see the benefit of systematizing ...more>> The handling of geometry definitions in school textbooks - Michael de Villiers; Mathematics Education, Univ. of Durban-Westville, South Africa Some historical background and a discussion of the value of students constructing their own understanding of mathematical proofs; misconceptions that arise from ready-made definitions; and the advantage of a constructivist approach, which allows pupils ...more>> 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 ...more>> 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. ...more>> 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. ...more>> Hilbert II - Michael Meyling A predicate calculus-based proof checker, which can check proofs drawn from many different Internet sites. ...more>> 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. ...more>> 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"; ...more>> Honeycomb Hotel: A Unit in Logic - Barbara De Roes A lesson plan for grades 5-12+, 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 ...more>> Hooda Math - Michael and Teresa Edlavitch Interactive games, math movies submitted by students, tutorials, and links for students and teachers. ...more>> 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. ...more>> 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 ...more>> 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 ...more>> 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; ...more>> 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 Web-accessible virtual world; and there is a version of Mancala, too. ...more>> Implications Rules - Alan Selby Implication Rules: two puzzles that show the difference between one- and two-way implication rules. Mastering the difference is a simple, first step, in rule and pattern-based thought, needed to precisely read rules, definitions and statements in all ...more>> Index Using Mathematics Subject Classification (MSC) - Dave Rusin; The Mathematical Atlas The index pages at this site are organized according to the Mathematics Subject Classification (MSC) scheme. (This is the scheme developed by the American Mathematical Society and Zentralblatt für Mathematik.) General headings include Foundations; ...more>> 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 ...more>> 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 ...more>> 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. ...more>> 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, ...more>> The Interactive Mathematics Classroom - Rex Boggs A digital library of third-party technology resources for teaching mathematics, from kindergarten to calculus. Register to comment on interactive whiteboard files, Powerpoints, TI-Nspire documents, Excel spreadsheets, and other digital resources. RSS ...more>> 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 award-winning site offers ...more>> 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; ...more>> 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. ...more>> 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; First-Order Logic; Towards Completeness and Consistency; Recursion Theory – compare this to Sipser’s Computation, Part II; Clarity ...more>> 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 ...more>> 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 ...more>> Investigations in Mathematics - Eric S. Rowland Open-ended 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 ...more>> 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. ...more>> 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 ...more>> 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 ...more>> Islands & Divisions of Knowledge (Pattern Based Reason) - Alan Selby Not seeing the difference between one and two-way implications is a common source of confusion in reading, writing and mathematics. One-way implication rules can sometimes be put together to get further implication rules. One and two-way implications ...more>> 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. ...more>> 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 ...more>> Ivan José online - Ivan José Varzinczak Research on logic-based knowledge representation and reasoning in Artificial Intelligence. Research areas: logic-based knowledge representation and reasoning; description logics, ontology engineering and semantic web; nonmonotonic reasoning, belief revision ...more>> Jacopo Notarstefano Interactive visualizations and puzzles: "Turing's sunflower," which connects leaf arrangements and Fibonacci numbers; "Havel-Hakimi," which presents nodes and their degrees to construct into a graph; "Four-coloring a Dodecahedron"; and a logic puzzle ...more>>
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