 Tomás Oliveira e Silva
From an assistant professor in the Electronics and Telecommunications Department of the University of Aveiro, Portugal. On the Collatz problem: maximum number tested (N): 91·2^50 = 102456891522678784.
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 Tony Phillips  Dept. of Mathematics, SUNYStony Brook
Ongoing Web math projects: Honors Calculus; Visualizing Women in Mathematics, the Physical Sciences and Technology; Calculus Reform; Geometry of the Binary Tetrahedral Group in SU(2); Mazes; Tides; Integrating Research and Education (RAIRE); Math Photo
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 Tools for Decision Analysis: Analysis of Risky Decisions  Hossein Arsham
Decision making under risk is presented in the context of decision analysis using different decision criteria for public and private decisions based on decision criteria, type, and quality of available information, together with risk assessment. Also
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 Tools for Exploring Mathematics (TEMATH)  Mathematics Dept., UMass Dartmouth
A software package useful for learning and teaching algebra, precalculus, calculus, linear algebra, and applied mathematics, with a graphical interface that makes it easy to use for the computer novice. Information about TEMATH, a tour of the programs,
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 Too Much to be a Coincidence? (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: In the September ACBL Bridge Bulletin, Noreen Wurdemann of the Bahamas reports that the two bridge hands below were dealt out at her club. She says that she is "100% certain there was no hankypanky." What is the probability of
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 Top 100 Mathematics Software  Adam Testad, Kuala Lumpur, Malaysia
A top 100 list of mathematics software: shareware, freeware, payware, some hardware, and some Web sites. A selection from over 24,000 products with references to download sites, suppliers page, and PC literature references.
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 Topical Index of Internet Resources (The Chaos Hypertextbook)  Glenn Elert
An extensive list of links to sites related to Elert's Chaos Hypertextbook. Major categories include: Chaos (Dynamical Systems); Dimension; FAQs; Feigenbaum Constants (Bifurcation Diagrams); Fractals; Image Compression; Iterated Function Systems (IFS);
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 Topics in Arithmetic and Elementary Mathematics  E. Lee Lady; University of Hawaii
Materials used in a university course for prospective elementary school teachers, to teach them how to be interested in mathematics. Materials are in PDF and DVI, and include: representing numbers in other bases, divisibility tests, periodic decimal expansions,
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 Topics in Calculus  Alan Cooper, Dept. of Mathematics & Statistics, Langara College
Calculus resources for college students: a topicbytopic guide to Webbased materials. Topics include: Precalculus review; limits and continuity; derivatives; approximation; antiderivatives; integration; infinite series; parametric equations; polar coordinates;
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 Topics in Calculus  E. Lee Lady; University of Hawaii
Files in PDF, DVI, and Postscript formats, to help students learn to use calculus in applications and to have confidence in setting up formulas using derivatives and integrals. Contents include: a conceptual approach to applications of integration, maxmin
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 Topics in Geometry  Don Shimamoto, Swarthmore College
Six sketches related to hyperbolic geometry. One illustrates that hyperbolic reflection in the Poincare disk corresponds to Euclidean inversion. Two sketches illustrate transformations that may or may not be hyperbolic rotation and translation. One sketch
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 Topics in Integral and Differential Calculus  Teresinha Kawasaki
Interactive, illustrated introductions to polynomial functions, trigonometric functions, exponential and logarithmic functions, the derivative, differentiation formulas and the chain rule, differentiating trigonometric functions, maxmin problems, integration,
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 Topics in Mathematical Recreations
Arithmetic and geometric puzzles; polyhedra; fractals and chaos; board and positional puzzles; pi and its calculations, and tiling patterns, which can be thought of as making an infinite polyhedron. Includes a bibliography ranging from Abbott's Flatland
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 Topics in Mathematics  Felynx Cougati Project; University of Alberta
An extensive site in the following topics: Foundational Ideas (Space and Dimension; Sets and Functions); Differential Calculus (Single Variable; Several Variables); Linear Algebra (Vector Spaces; Matrices; Linear Maps; Determinants); Topology (Topological
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 Topics in Precalculus  Alan Cooper, Dept. of Mathematics & Statistics, Langara College
Precalculus resources for college students: a topicbytopic guide to Webbased materials. Topics include: The Real Numbers; Cartesian Coordinates; Relations and Functions; Linear Functions; Quadratic Functions; Polynomials; Rational Functions; Radicals
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 Topics in Probability  Wlodzimierz Bryc
Books in DVI, PS and HTML formats: Normal Distribution: characterizations with applications; Applied Probability & Stochastic Processes; Large Deviations: Performance analysis.
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 Topological Knot Theory Information & Research  Claremont High School, Claremont, CA
Files and data related to the knot theory work developed by students at Claremont High School. A TeX file contains source code for the Paper "Tabulating Alternating Knots Through 14 Crossings," by B.Arnold, C.Candy, K.Erdener, J.Fan, J.Hoste, R.J.Muir,
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 Topological Space: Definition and Basic Theorems  Michal Wojcik
This page contains the definitions of the following concepts: topological space, open set, closed set, interior, closure. Contains the most basic theorems about these concepts together with an easytoread proof which is slightly informal in some places.
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 The Topological Zoo  The Geometry Center
For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each
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 Topology Atlas  Shakhmatov and Watson; York University, Toronto, Ontario, Canada
A multipurpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely
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 Topology Enters Mathematics  MacTutor Math History Archives
Linked essay describing the development of topology as a mathematical discipline from Euler through the early 20th century, including 17 references (books/articles).
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 Topology (Graphics Archive, Special Topics)  The Geometry Center
Properties of objects that don't change when they are stretched or twisted (Klein bottle, Moebius band).
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 Toposes, Triples and Theories  Michael Barr and Charles Wells
A revised and corrected version of the original (1983) Grundlehren der math is available free for downloading. Formats: DVI, PDF, PostScript.
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 Tostaky.Biz  Jerome Verstrynge
JavaScript utilities formatted for the smaller screens of tablets and smartphones: timer, stopwatch, world clocks, and other timekeeping tools; and unit converters for area, force, length, torque, weight, and more.
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 Touch3D
A commercial Macintosh program for 3Dmodeling, concept design, industrial design, quick prototyping, mockups, packaging, scale models, physical renderings, production preparation, and unfolding/unwrapping. Touch3D is a complete 3D modeling/unfolding
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 Tournament of Towns  Math Net, University of Toronto
A worldwide problem solving competition in mathematics. The contest attracts students of all mathematical interests and abilities with its inclusive rules and creative problems  some as challenging as those of the International Mathematical Olympiad.
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 Toward a Fairer Expansion Draft  Ivars Peterson (MathLand)
When new teams are brought into an established league, the team owners usually take turns picking players from a pool of available talent. The conventional method for such drafts, however, often produces unfair results. For example, if one of two owners
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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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 TPSE Math
Pursuing mathematically rich and relevant education for all undergraduate students — whatever their chosen field of study — at U.S. community colleges, 4year colleges, and research universities. The website for Transforming PostSecondary
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 Tractrix Java Applet Class  PHD Computer Consultants Ltd
Download Tractrix.zip, a Java applet that makes the kind of pretty swirling patterns which Dutch mathematician Huygens originally named in 1692. Specify applet width and height, background and foreground color, coordinate pairs that will identify corners,
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 Traffic Jam  Math Forum
Equal numbers of people face each other with one open slot between them. Everybody faces the open slot. If there are 6 people there will be 7 slots, 6 of
which must always have people in them. People must attempt to exchange places without turning around.
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 Transmath  A CBL Mathematics Tutor  Joanna Brown
Transmath is a computerbased (Windows platform) mathematics tutor designed to strengthen and consolidate the basic mathematical knowledge of students commencing numerate degrees. Module exercises, featuring animations, come with constructive interactive
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 Transversal of a Latin Square  Jay's Corner
A transversal in a Latin Square is a collection of positions, one from each row and one from each column, so that the colors that are in these positions are all different. This page shows an example of a transversal in a 4x4 Latin square
See also Transversals
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 The Traveling Salesman Problem (TSP)  Vasek Chvátal
The problem: given a finite number of cities and the cost of travel between each pair of them, find the cheapest way of visiting them all and returning to your starting point. This site includes a link to TSPLIB, Gerhard Reinelt's library of some hundred
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 The Travelling Monkey  Ivars Peterson (MathLand)
One of the classic problems of planning ahead concerns a traveling salesman who must visit customers in a number of cities scattered across the country and then return home. The problem is to find the shortest possible route visiting each city only once.
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 Travelling Salesman's Problem  Gunno Törnberg
Algorithms to solve the travelling salesman's problem (a travelling salesman is to visit a number of cities; how to plan the trip so every city is visited once and just once and the whole trip is as short as possible?) Links to Java applets; the shell
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 The Travelling Salesman's Problem  Manu Konchady
A trucking or delivery company is focused on optimum delivery cost. This can be achieved by using a system which determines the best highway route for each load. An optimum highway route can be displayed on a map. A route with 16 nodes is used to test
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 TreeAge Software, Inc.
Producer of decision analysis software. Product information, interactive demos and trial download, FAQ and technical support, ordering, and registration.
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 TREEFROG selfassessment system  Strickland, AlJumeili
An MSDOS and Windows program for checking math skills, based on mathematical rules. A student is presented with an expression (say integral of x cos x d x, or x2+3x+2 = 0) and told to convert it to another equivalent form (function of x + constant, x
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk
Triangle generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Instructions for
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 Triangle: A TwoDimensional Quality Mesh Generator and Delaunay Triangulator  Jonathan Richard Shewchuk, Carnegie Mellon University
A triangle that generates exact Delaunay triangulations, constrained Delaunay triangulations, and quality conforming Delaunay triangulations. The latter can be generated with no small angles, and are thus suitable for finite element analysis. Created
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 Triangle Centers  Clark Kimberling; Dept. of Mathematics, Univ. of Evansville, Evansville, IN
A listing, with description and illustration, of 20thcentury triangle centers (including: Schiffler Point, Exeter Point, Parry Point, congruent isoscelizers point, Yff Center of Congruence, isoperimetric point and equal detour point, AjimaMalfatti Points,
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 Triangle in Square Puzzles  Erich's Puzzle Palace; Erich Friedman
Eight puzzles involving cutting squares into triangles under certain constraints. Answers provided.
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 Triangle Puzzle  Evelyn Sander, Geometry Forum Archives, The Geometry Center
Pick an arbitrary point in the interior of an equilateral triangle. Now go halfway towards one of the three vertices (you get to pick which vertex). Now you are at a new point in the triangle. Again go halfway towards any vertex. Continue this process.
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 Triangles and Simplices (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on triangles and their higherdimensional generalizations (simplices), with a particular interest in partitioning regions into triangles, tetrahedra, or higher dimensional simplices, for various applications
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 Triangles in Elliptic Geometry  Thomas Banchoff, The Geometry Center
An examination of some properties of triangles in elliptic geometry, which for this purpose are equivalent to geometry on a hemisphere. The aim is to construct a quadrilateral with two right angles having area equal to that of a given spherical triangle.
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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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 Triceron Archive: Integral Calculus  Triceron.com
An enviroment for exchanging data, among others, theoretical and practical educational resources on integral calculus. Triceron carries a categorised directory of hyperlinks to www/ftp sites, usenet newsgroups, irc channels, freenet sites, usenet servers
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 Tricki  Gowers, Timothy; Sisask, Olof; and Frolkin, Alex
A wiki "repository of mathematical knowhow" that encompasses techniques ranging from the very general to those that concern particular subareas of mathematics. Browse problemsolving ideas by technique: for finding algorithms and algorithmic proofs,
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 Tricky Crossings  Ivars Peterson (MathLand)
Have you heard the one about an itinerant entertainer traveling with a wolf, a goat, and a basket of cabbages? The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the wolf
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