 SelfReference and Apparent SelfReference  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.
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 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 gridplace shaded squares where they belong according to those guides. The site includes a history of the puzzles,
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 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, colorcoded for the level(s) of the problems
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 Sketchpad Activities for Young Learners: Grades 35  Nathalie Sinclair
This collection of activities for grades 35 offers examples of the ways in which Sketchpad can be used across the range of mathematical subject areas in the elementary curriculum.
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 Smarandache Notions  J. Castillo
A journal for papers related to the work of Florentin Smarandache, who in the 1960s proposed some new geometries: NonGeometry, CounterProjective Geometry, AntiGeometry, and Paradoxist geometry, which would generalize and unite Euclid, Lobachevsky/Bolyai/Gauss,
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 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
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 SmartZoid
SmartZoid provides online math evaluation and tutoring with a comprehensive free assessment for grades K9.
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 SMILE Program Mathematics Index  Science and Mathematics Initiatives for Learning Enhancement
Over 200 singleconcept 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,
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 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 HinduArabic numerals); of notation and concepts in algebra; Changing systems of geometry from Euclid to Klein's programme (includes New Geometries,
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 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 1218), or topic
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 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
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 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.
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 STEPS Online Tutoring  TCYonline.com
TCYonline.com provides oneonone live online math tutoring and homework help for grade K12 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
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 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,
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 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 TwentyThree Matches Game; and The Game
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 Structures Directory  Vaughan Pratt
An email directory of logicians, algebraists, and programming linguists working primarily on structural problems in mathematics and computer science.
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 Subtle Logic, Winning Game  Ivars Peterson (MathTrek)
Seemingly simple games can serve as thoughtprovoking exercises in mathematical logic. They can provide deep insights into subtle issues that confront logicians who are interested in the foundations of mathematics. Socalled Ehrenfeucht games have proved
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 SuccessMaker mathematics courses  Pearson Education, Inc.
A learning environment combining a management system, assessment, and curriculum resources to provide administrators, teachers, and students with tools to improve academic performance. Also available from http://www.pearsonschool.com/index.cfm?locator=PSZk99.
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 Sudoku
Flashbased game: enter a 9x9 grid so that every column, every row and each of the nine 3x3 segement contains the numbers 1 to 9. The game provides hints when you are stuck and has different levels.
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 Sudoku  Pappocom, aka Wayne Gould
Finish filling in the 9x9 grid so that every row, every column, and each of the nine 3x3 boxes contains the digits 1 through 9. Different from a magic square, this puzzle requires no arithmetic, only reasoning and logic to deduce which digit to put where.
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 Sudoku  PedagoNet
Sudoku online. New puzzles generated regularly; archive of past puzzles.
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 Sudoku Shuffle  ridiculopathy.com
Play a Flash version of Sudoku online or print out one of these logic puzzles. Choose a level of difficulty and whether to play with number tiles or letter tiles.
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 A Su Doku solver
Solvers for sudoku puzzles, with documentation, source code, and binaries. Frequently asked questions about this numeric puzzle include "Su Doku" or "Sudoku"? How does the solver work? How do I compose a Su Doku problem? How few cells could appear on
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 Syllogism 1.0  Ben Sharvy
Software to download. Enter a syllogism of any length. The program will tell you whether it is a valid syllogism, and if not, why not. It will also analyse the links between terms in the syllogism. BASIC code, and a version compiled for the Mac.
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 The Syllogistic Machine  Johan Mårtensson
A JavaScript machine for checking the properties of Aristotelian syllogisms, with links to Mårtensson's OnLine Logic Book.
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 Teaching Logic and Reasoning in an Illogical World  DIMACS Symposium
A July 1996 symposium: Participants, schedule, list of papers, and the papers themselves in html, ascii, or postscript. Sample papers: S. Maurer: Teaching reasoning, broadly and narrowly; C. Nelan: Student's attitude toward the relationship between language
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 Technologies: Past and Future  Cut the Knot!, Alexander Bogomolny, with Don Greenwell
A discussion of the similarities in browsing through books and surfing the Internet, the serendipitous discoveries that can be made, fallacious geometric and other puzzles, and an interesting integer matrix, with recommendations of books to read and sites
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 Terry McConnell's Home Page  Terry McConnell, Mathematics Department, Syracuse University
Download PDFs of tests given in McConnell's introductory calculus, Math 295. "Stuff" ranges from a remark on average velocity and an expository paper showing the details of how to derive the second order correction to the period of a plane pendulum using
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 Theorem of the Day  Robin Whitty, London South Bank University
Every day, Whitty posts a PDF of a different theorem, lemma, law, formula, or identity  each "as selfcontained as possible." With pictorial interpretation; proof; glossary briefly explaining some parts of the mathematical language; references to related
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 Theoretical Computer Science  Elsevier Science
The journal is mathematical and abstract in spirit, but derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and to provide more efficient methodologies. All papers introducing or studying
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 The Theory Group  University of St. Andrews, U.K.
The Theory Group investigates aspects of theoretical computer science including: specification; automated theorem proving techniques and applications (especially in computer algebra); computational logic, including logic programming and proof theory;
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 Things Impossible  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Essays on impossible things, including trisecting an angle, doubling a cube, squaring a circle, moving pegs five places in one direction (via checkerjumps), finding the center of a given circle with the straightedge alone, representing the square root
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 Think & Derive  Chris Long
Monthly mathematical columns from May 1994 through April 1996 written for Central New Jersey Mensa's Forvm. Problems and puzzles, many with solutions.
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 Think Maths  Matt Parker
This group of mathematics speakers visits schools to perform maths talks and workshops in the UK. Sessions present math in ways that "grab the attention of students and remind them that maths is something to be enjoyed." Free downloads include domino
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 This is MegaMathematics! (MegaMath)  Nancy Casey; Los Alamos National Laboratory
The frontier of mathematics is an exciting place, where mathematicians experiment and play with creative and imaginative ideas, many of them accessible to young children; others (infinity is a good example) whose profound mathematical importance is not
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 Three Skills For Algebra  Alan Selby
This book describes three skills key to the algebraic way of writing and thinking, offering a first image of mathematics beyond arithmetic. It also describes the first elements of logic or rulebased reason, needed in all disciplines for writing or a
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 Tim's Interactive Puzzle Solution Center  Alex Sakharov
A growing collection of interactive online logic puzzles including Cannibals and Missionaries, Eight Queens, Gunport, and math puzzles of various difficulty levels.
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 Topics in High School Mathematics  Martin Cohen
Lesson ideas on geometric series, mathematical induction, Pythagorean triples, combinatorics, continuity, modular arithmetic, rotations and revolutions, and more.
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 To teach definitions in geometry or teach to define?  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
This paper argues from a theoretical standpoint that students should be actively
engaged in the defining of geometric concepts like the quadrilaterals, and
presents some data relating to a teaching experiment aimed at developing
students' ability to
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 The Tower of Hanoi  Andrew Cumming
Interactive version of the famous logic puzzle, in html and VRML versions, with a separate page about solving it.
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 Tower of Hanoi on the Web  Miroslav Kolar
The legend: A group of Eastern monks are the keepers of three towers on which sit 64 golden rings. Originally all 64 rings were stacked on one tower with each ring smaller than the one beneath. The monks are to move the rings from this first tower to
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 Traffic Jam Activity  Suzanne Alejandre
A classroom activity (also called Hop, Skip, Jump) aligned to the NCTM and California Standards, to be explored through large movement experience, manipulatives, and an interactive Java applet. Students then revisit the activity, look for patterns, and
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 Tribute to Invariance  Cut the Knot!, Alexander Bogomolny
As a competitive activity, the Squares and Circles game is not very challenging in itself. That is to say, the outcome of the game does not depend on how the game proceeds. The challenge is to come up with this realization and establish its veracity.
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 Trisecting the Angle  Steven Dutch; University of Wisconsin  Green Bay
Why is trisecting an angle with a straightedge and compass impossible? Discussion includes several other proofs of impossibility (the largest prime number, the square root of 2, repeating patterns in the plane) and some alternate methods of trisection
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 The Truth Tree's Math and Logic Board  Bob Scott, Ron Savori
A collection of math and logic problems, from Pascal's Pizza Parlor and Leaning Ladders to The Old Lady and the Eggs and The Rickety Table Disaster. Register to solve these and other problems and compete with other visitors to The Truth Tree.
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 Two Equals One?  Jim Loy
A proof that 2=1, what's not "legal" about it, and a discussion of infinity.
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 UC Berkeley Mathematics Department
Department info; a collection of the Berkeley [Ph.D.] preliminary exams; undergraduate study hints and survival guide; Notherian Ring (women in mathematics at Berkeley  includes WWW sites of interest to women mathematicians or grad students); Center
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 The Ultimate Puzzle Site  van Gassel, Heijmans, van Veldhoven
A site in English and Dutch by three Dutch students. Contents include: Various Basic Puzzles and Riddles (no mathematics); Harder Puzzles and Riddles (no mathematics); Mathematical and Logicdeductional Puzzles with solutions; BrainTeasers; and Complex
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 Uncertain Reasoning Group  Mathematical Logic  Dept. of Mathematics, Manchester Univ., U.K.
Homepage for a research group that investigates uncertain knowledge, how to represent it, and how to reason with it intelligently. People, research topics, seminars, Web resources.
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 Uncle Bob's Puzzles  Robert & Claire Mead, Haverhill, NH, USA
Math and logic problems (no solutions); if you have questions, want a hint, or want to submit a solution you're invited to email the author. Asterisks indicate greater difficulty: Blind Cowboy; A Game of Catch; The Next Three; Grandpa's Birthday; Square
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