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Proof, Mathematical (Encarta Encyclopedia 2000) - Microsoft Encarta Online An argument that is used to show the truth of a mathematical assertion. In modern mathematics, a proof begins with one or more statements called premises and demonstrates, using the rules of logic, that if the premises are true then a particular conclusion ...more>> Proofs in Mathematics - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny A discussion of the value of proofs in the classroom, followed by a collection of proofs classified as either simple or charming. Simple proofs: Number of vowels in a Lewis Carroll game; Pigeonhole Principle; Number of X's and O's; Coloring points in ...more>> Proofs - James Garner An essay on different approaches using mathematical proofs: inductive reasoning, reasoning by analogy, deductive reasoning, direct method, contrapositive approach, etc. ...more>> Proofs Without Words - Cut the Knot!, Alexander Bogomolny Martin Gardner wrote, "There is no more effective aid in understanding certain algebraic identities than a good diagram. One should, of course, know how to manipulate algebraic symbols to obtain proofs, but in many cases a dull proof can be supplemented ...more>> Proof Techniques (Analysis Webnotes) - John Lindsay Orr; Dept. of Mathematics & Statistics, Univ. of Nebraska-Lincoln Techniques of writing proofs for: Showing two sets are equal; Showing a set is closed; How to show a sequence converges; and How to use a convergent sequence (to prove other things). ...more>> Proof: The Sum of Prime Twins is Divisible by 12 - Mathematics Dept., College of Marin Prime twins are prime numbers that are two numbers apart. For example 41 and 43 are prime twins. Can you PROVE that the sum of prime twins is divisible by 12? (This proof doesn't work for the prime twins 3 and 5.) ...more>> The ProvenMath Project - Michal Ryszard Wojcik and Michal Stanislaw Wojcik Proofs of the Fundamental Theorem of Algebra, the theorem about integration by change of variables for real-valued functions of n-variables, a derivation of Zorn's Lemma, and others. The site renders axioms and derives proofs using only ASCII characters. ...more>> Puzzlers - Bryan Clair, University of Chicago A collection of Clair's favorite puzzles (no discussion or answers are provided): The Nine Dots; Weighing Coins; The Dollar Hotel, Planning an Orchard; The Math Department; Tea and Cream; Bugs on a Square; River Crossing; More Crawling Bugs; The Unexpected ...more>> Puzzles - Martin Watson Blogs, comments, musings, design sketches, and photographs of mechanical puzzles by an avid collector and craftsman. Puzzle news, the author's own burrs (Watson's wormhole, digigrams, Dutch cubist), in-depth explorations of manipulative puzzles (Puzzles ...more>> The Puzzle TOAD - Tom Bohman, Oleg Pikhurko, Alan Frieze, and Danny Sleator, School of Computer Science, Carnegie Mellon University Send the authors your solutions to their challenging graph theory, number theory, geometry, discrete mathematics, logic, and other puzzles. Re-visit periodically to see the latest question, and download PDFs of solutions of past problems. ...more>> Puzzlies.net - Michał Barciś Play sudoku and griddler logic puzzles online. Log in to save game play and compete in the rankings. ...more>> The Puzzling World of Barry R. Clarke - Barry R. Clarke Brain teasers from Clarke's column in The Daily Telegraph (UK) and from his various puzzle books: liar problems, logic teasers, number conundrums, matchstick puzzles, lateral mind-benders, and more. With links to other puzzles sites and an article on ...more>> Query Interface to the Contents of the Mathematics Archives - University of Tennessee, Knoxville (UTK) Search software, abstracts and reviews; teaching materials, etc. by keyword. ...more>> Quiz Hub - Schmidel & Wojcik: Educational Web Weavers A collection of online interactive learning quizzes that help K-12 students enhance their core knowledge of English, languages, math, science, and social studies. Subscription required. ...more>> Raise Smart Kids - Inna Shapiro Download Powerpoint presentations of math problems, with answers: logic, basic arithmetic operations, natural numbers, pigeonhole principle, fractions, pouring, cutting, weighing, divisibility, and more. For Croatian translations of some of Shapiro's ...more>> Recent Papers in Category Theory - Prof. George F. Nassopoulos Recent papers in Category theory and its applications to functional analysis, global analysis, and abstract differential geometry. ...more>> The rec.puzzles Archive The index of the rec.puzzles archive. Puzzles are categorized by subject area and include solutions compiled from various sources and supposed to be definitive. Subjects include: analysis, arithmetic, combinatorics, competition, decision, geometry, group, ...more>> The rec.puzzles Archive - Massachusetts Institute of Technology (M.I.T.) A list of puzzles, categorized by subject area, from the newsgroup rec.puzzles. Puzzles include solutions compiled from various sources, supposed to be definitive. Subjects include analysis, arithmetic, combinatorics, competition, decision, geometry, ...more>> rec.puzzles FAQs by Newsgroup - Dept. of Computer Science, Universiteit Utrecht Information on the following topics: crosswords, analysis, arithmetic, combinatorics, competition, cryptology, decision, geometry, group, induction, Instructions, language, logic, physics, Pickover (Cliff), probability, real-life, references, series, ...more>> Reference Notes - Department of Mathematics, Cal. State U. San Bernardino (CSUSB) Notes on set theory, symbolic logic, methods of proof, basic proofs, functions, relations, binary operations, and groups. Also, Math Tools for practicing modular arithmetic and truth tables, or for solving Diophantine equations. Search the Notes, or scan ...more>> Reflections on Deep Blue - Keith Devlin (Devlin's Angle) We generally assume that the ability to play a good game of chess requires intelligence when it comes to people. Why not for chess-playing machines as well? Well, here is one argument that shows that things are not so simple. One aspect of human intelligence, ...more>> Resource Material - Spencer, Chan; Univ. of Toronto Mathematics Network A collection of resource material for use in classes or extracurricular activities in high schools: answers, explanations, and expositions of some common but deep math questions. In the process of answering three basic questions, this area delves into ...more>> Revathi Narasimhan - Department of Mathematics, Kean University College Math, College Algebra, and Calculus course resources and links include Narasimhan's own Interactive Calculus tutorial, which requires the LiveMath plug-in. See also Using Excel in Finite Math and Applied Calculus, freely downloadable Excel workbooks ...more>> Robbins Algebras are Boolean - William McCune, Automated Deduction Group, Argonne National Laboratory The Robbins problem - are all Robbins algebras Boolean? - has been solved: Every Robbins algebra is Boolean. This theorem was proved automatically by EQP, a theorem proving program developed at Argonne National Laboratory. Information on the solution; ...more>> The Roman Press, Inc. - Steven Roman Home page of a California mathematics professor, including research articles, books and textbooks, and software. ...more>> Rubik's Cube Information - Michael Reid All about Rubik's Cube - even a mailing list. Site contents include: the Nederlandse Kubus Club; Rubik's cube pages on the Web; Cube books; Sources of cube-like puzzles; the author's notes, including an optimal cube solver; other Cube solutions on the ...more>> Rubik's Cube Java Applet - Michael Schubart To twist the cube, press the mouse button over a cubelet face that belongs to the slice you want to move. Keeping the button pressed, drag the mouse in the desired direction; then release the button. Moving the whole cube is done in the same way - just ...more>> Rubix Corner - Duane Cash The site includes information regarding the Duane Cash Cube Collection now featured at Hessport's Rubikshop in their "collectibles" section. New puzzles include the Rubik's Triamese, Fusion, Fusion+, SpeedFusion, 5x3, and 4x3 Cubes, which give those interested ...more>> Science, Math, and Technology Tutorial (SMATT) - ThinkQuest 1996 Topics: Math History (biography of Descartes); Logic (how to construct logical arguments and put them into proofs); Math Tutorial (Basic Algebra with problems and solutions); Environmental Science (ozone in the atmosphere); Astronomy (implications of ...more>> Sciences exactes / Mathématiques - Encyclopédie Hachette Multimédia En Ligne Recherche Mathématiques par thème: Mathématiciens et logiciens; Mathématiques générales; Logique; Algèbre; Topologie; Analyse; Géométrie; Cinématique; Statistiques; Probabilités; ...more>> SCORE Mathematics Lessons - Jim Shaver, Schools of California Lessons by teachers that reflect California's Mathematics Framework and the NCTM Standards, organized by their main strands with links to descriptions of the strands: Functions, Algebra, Geometry, Statistics and Probability, Discrete Mathematics, Measurement, ...more>> Search Ask Dr. Math Archives - The Math Forum Search by keyword K-12 math questions answered by volunteer 'math doctors' in the U.S. and abroad. ...more>> Search for Math on the Internet - The Math Forum Keyword search of all searchable archives, Newsgroup archives, Dr. Math archives, Problems of the Week, Internet Math Library, or any combination thereof. ...more>> Self-Reference and Apparent Self-Reference - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny Various paradoxes, real and imagined, including verbal, logical, and mathematical examples, and links to: Blinking page with errors; Apparent paradox; Set of all subsets; An Impossible Page; Russell's paradox; and An Impossible Machine. ...more>> Shady Puzzles - LambdaMu Pte Ltd A logic and elimination (disjunctive syllogism) puzzle: the column and row headers identify the number and spacing of shaded squares within a grid--place shaded squares where they belong according to those guides. The site includes a history of the puzzles, ...more>> Simple Math Problems - Ki Woo Song Selected math problems from a variety of sources. Solutions may either be requested via e-mail or looked up from the source (references to articles are provided.) Topics include algebraic expressions; probability; physics, geometry, proofs, and brain ...more>> Sites with Problems Administered by Others - Math Forum Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, color-coded for the level(s) of the problems ...more>> Sketchpad Activities for Young Learners: Grades 3-5 - Nathalie Sinclair This collection of activities for grades 3-5 offers examples of the ways in which Sketchpad can be used across the range of mathematical subject areas in the elementary curriculum. ...more>> Smarandache Notions - J. Castillo A journal for papers related to the work of Florentin Smarandache, who in the 1960s proposed some new geometries: Non-Geometry, Counter-Projective Geometry, Anti-Geometry, and Paradoxist geometry, which would generalize and unite Euclid, Lobachevsky/Bolyai/Gauss, ...more>> SMART: Science and Mathematics Advancement and Resources for Teachers - Los Angeles Educational Partnership A program designed to help teachers in Los Angeles County (California, USA) develop their professional teaching skills and content knowledge. Links for Teachers, Students, Businesses and Institutions, Parents, and Community Members. Includes the SMART ...more>> SmartZoid SmartZoid provides online math evaluation and tutoring with a comprehensive free assessment for grades K-9. ...more>> SMILE Program Mathematics Index - Science and Mathematics Initiatives for Learning Enhancement Over 200 single-concept lesson plans in the following categories: Geometry and Measurement, Patterns and Logic, Probability and Statistics, Recreational and Creative Math, Practical and Applied Math, Arithmetic, Graphs and Visuals, Algebra and Trigonometry, ...more>> Social and Historical Aspects of Mathematics - Thompson, Wilkinson; Univ. of Wolverhampton (UK) Math history: the development of counting systems and notations (includes Egyptian, Sumerian, Babylonian, and Hindu-Arabic numerals); of notation and concepts in algebra; Changing systems of geometry from Euclid to Klein's programme (includes New Geometries, ...more>> Software for Texas Instrument Calculators - Nevil Hopley A collection of teaching programs for Texas Instruments calculators. Developed and tested in classrooms since 1998, the programs make the TI83, TI83+ & TI83+ Silver Edition more than just a calculator. Order by program, age group (ages 12-18), or topic ...more>> Software (Mathematics Archives) - University of Tennessee, Knoxville (UTK) An extensive collection of links to software, with abstracts and reviews, organized in four different ways: by platform (Macintosh, MSDOS) and then by subject; interactive texts (using a commercial package such as Mathematica, Maple or Mathkit to interact ...more>> South African Puzzle Club - sapuzzleclub.co.za "Refining the Art of Puzzling," this club serves as an online center for "like-minded people together with a passion for puzzles.... [to] grow the hobby of metagrobology in South Africa." With web forums, articles, galleries of mechanical puzzles, and ...more>> Stephen's Guide to Logical Fallacies - Stephen Downes Lists all known logical fallacies, with definitions, examples, and the steps needed to prove that the fallacy is committed. Site also includes links to logic references and resources. ...more>> STEPS Online Tutoring - TCYonline.com TCYonline.com provides one-on-one live online math tutoring and homework help for grade K-12 students. The service offers test prep for the SAT, ACT, GRE and GMAT and State Level exams 24x7, round the year. TCY also provides math education consulting ...more>> Strategy and Conflict: An Introductory Sketch of Game Theory - Roger A. McCain Game theory is an interdisciplinary approach to studying human behavior that touches on computer science, social sciences, and behavioral sciences. Designed as a supplement to existing texts as a means of making the basic ideas a bit more accessible, ...more>> Strawberry Macaw's Puzzle Page Although simple, this collection of four logic puzzles provides a challenge for students of any age. The interactive puzzles are: The Fox, the Duck, and the Bag of Corn; The Three Gallon and Five Gallon Cans; The Twenty-Three Matches Game; and The Game ...more>>

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