 Topology  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to general topology, the study of sets on which one has a notion of "closeness"  enough to decide which
functions defined on it are continuous. Thus it is a kind of generalized geometry (we are still
...more>>
 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).
...more>>
 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
...more>>
 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
...more>>
 Tracking  Education Week on the Web
Should schools  as the engine of democracy  provide relatively similar curricula for all students? Or should they instead sort students by skill levels and prepare them for their different roles as adults? A discussion of the pros and cons of tracking,
...more>>
 Traditional Schooling: Articles and Research  Carolyn K., Hoagies' Gifted Education Page
Articles and reports on traditional schooling issues: Academic Acceleration; Advocacy; Bullies; Curriculum Adjustments; Early (or late) Kindergarten; Educational Theories; Grouping; Individualized Education Profiles (IEPs); Mentors; Success Stories; Testing
...more>>
 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.
...more>>
 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,
...more>>
 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.
...more>>
 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
...more>>
 Tricky Dice  Ivars Peterson (MathTrek)
The game involves four specially numbered dice. You let your opponent pick any one of the four dice. You choose one of the remaining three dice. Each player tosses his or her die, and the higher number wins the throw. Amazingly, in a game involving 10
...more>>
 Tricky Tables (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The shape of a billiard table has a lot to do with the types of shots you can make in a game of billiards. Which of the odd tables pictured do you think would be your best bet for hitting another ball? Suppose you have a circular table, or a rectangular
...more>>
 The Trigonometric Functions  MacTutor Math History Archives
Linked essay sketching trigonometry from its beginnings out of the early correspondence between astronomy and mathematics through the 18th century, with 17 references (books/articles).
...more>>
 A Trillion Dollars  Jim Loy
Illustrating large numbers: 100, 1,000, and 10,000 vertical lines; imagining a trillion.
...more>>
 Triogram Models  Hansen, Kooperberg, Sardy
An electronic version of a paper that introduces the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. Java applets are included and a PostScript version of the entire paper
...more>>
 Trisecting an Angle  MacTutor Math History Archives
Linked essay tracing the history of the classical Greek problem of trisecting an
arbitrary angle using for the construction only ruler and compass (which is
impossible)  but, failing that, finding some other method.
...more>>
 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
...more>>
 Trisection Of An Angle  Jim Loy
A discussion of what can and can't be constructed using compasses (for drawing circles and arcs, and duplicating lengths) and straightedge (without marks on it, for drawing straight line segments).
...more>>
 Triumph of the Nerds: A History of the Computer  Robert X. Cringely; PBS Online
A companion Web site for the Public Broadcasting System television special hosted by Robert Cringely, "Triumph of the Nerds: The Rise of Accidental Empires." Learn how youthful amateurs, hippies, and selfproclaimed "nerds" accidentally changed the world.
...more>>
 Troublesome Weather Trends  Ivars Peterson (MathTrek)
In the February Bulletin of the American Meteorological Society, Statistician Kevin J. Coakley of the National Institute of Standards and Technology in
Boulder, Colo. argues that ... daily temperatures don’t vary randomly. They generally tend to rise
...more>>
 Trouble with WildCard Poker  Ivars Peterson (MathLand)
Poker originated in the Louisiana territory around the year 1800. Ever since, this addictive card game has occupied the time and teased the minds of generations of gamblers. It has also attracted the attention of mathematicians and statisticians. The
...more>>
 Truel in the Sun  Ivars Peterson (MathTrek)
Brilliant sunshine bakes a huddled row of ramshackle, weatherbeaten buildings lining a dusty thoroughfare. Two gunfighters slam out of a decrepit saloon and stalk toward their posts at either end of the street. Facing each other, they prepare to draw
...more>>
 TSM4: 'Using the Internet for Mathematics'  Oundle School, Peterborough, UK
A oneday conference for teachers held 11 May 1998 at Oundle School, Peterborough, UK. Technology for Secondary and College Mathematics (TSM) is a teacher training initiative based at Oundle School. Online Workshops: "How to download text and images off
...more>>
 TSPBIB (Traveling Salesman Problem)  Pablo Moscato
A comprehensive listing of papers, source code, preprints, technical reports, etc., available on the Internet about the Traveling Salesman Problem (TSP) and some associated problems such as Fractal TSP Instances and VRP Instances, with links to software
...more>>
 Turbulence, Chaos and Disordered Systems
A research group at the Eindhoven University of Technology in the Netherlands investigating turbulence, selforganization, chaos, and complexity in fluids. Descriptions of projects and full text of related thesis projects.
...more>>
 Turn of the Screw  Ivars Peterson (MathTrek)
Mathematician Chris Rorres of Drexel University in Philadelphia has taken a close look at Vitruvius's specifications for constructing an Archimedes screw... Recent years have seen a revival of interest in the Archimedes screw, particularly for its proven,
...more>>
 Turtle Tracks  Ivars Peterson (MathTrek)
One way to describe a geometric figure is in terms of the path generated by a moving point. Using the computer language LOGO, children can produce a list of commands to govern the motion of a "turtle" and trace out a geometric track on the computer screen.
...more>>
 Tversky's Legacy Revisited  Keith Devlin (Devlin's Angle)
"Amos Tversky died earlier this year. To mathematicians, the Stanfordbased psychologist is best known for the research he did with his colleague Daniel Kahneman in the early 1970s, into the way people judge probabilities and estimate likely outcomes
...more>>
 The "TwoDimensional Factorial" and a New Solution for the Probability of Completing Sets in Random Sampling  Jeffrey D. Lindsay
In finding a new solution to a classic probability problem, The Collector's Problem, concerning the collection of items in a set, a new and useful recursive function has been found, the "twodimensional factorial." A Web adaptation of J.D. Lindsay, "A
...more>>
 Two Equals One?  Jim Loy
A proof that 2=1, what's not "legal" about it, and a discussion of infinity.
...more>>
 Two Points of View  Tom O'Brien
"Children are not stones or recording devices. They are, first of all, sensemakers." In summarizing his work with practicing teachers on the four basic operations, the author responds to H. H. Wu's article, "What's Sophisticated about Elementary Mathematics?"
...more>>
 Tying Down a Random Walk  Ivars Peterson (MathTrek)
For many men, the ordeal of fashioning a neat tie knot is fading into the distant past. It seems ironic that two physicists have now put necktie knots back on center stage. Thomas M. A. Fink and Yong Mao of the Cavendish Laboratory in Cambridge, England,
...more>>
 UC Berkeley Wavelet Group  Univ. of California at Berkeley
People, papers and publications.
...more>>
 ULTRALAB  Anglia Polytechnic University, U.K.
A research centre that writes software for learners of all ages and researches all aspects of the use of technology in learning. Reports, papers, and articles; 'old' software and hardware computing archive.
...more>>
 Unbreakable Ciphers  Jim Loy
Proving that if the method of encryption is complicated enough, almost any encrypted message can be unbreakable.
...more>>
 Undergraduate Research Project in Random Tilings  Propp, Wilson
This project investigates different regions of random tilings of nxn squares with 1x2 dominoes: square, hexagon, fortress, dungeon, and Aztec diamond (the set of lattice squares completely inside a square tilted 45 degrees, discovering that the dominoes
...more>>
 Understanding (Learning and Mathematics)  Greeno, Riley; Math Forum
In their 1987 article, "Processes and Development of Understanding," James G. Greeno of Stanford University and Mary S. Riley of San Diego State University examine why younger children seem to lack the ability of older children to solve mathematical word
...more>>
 Understanding Mathematics: A study guide  Peter Alfeld, University of Utah
A resource and source of encouragement, with questions and Alfeld's comments (Are you frustrated working through heaps of meaningless problems that are all alike? Does the thought "I can look it up if I have to" occur to you frequently? Do you feel that
...more>>
 Understanding 'Rate' Word Problems  Rick Garlikov
A conceptual explanation of doing various kinds of math "rate" problems (e.g., "distance/speed/time" problems, problems involving combining work done by different agents working at different rates of speed, quantity/proportion problems, etc.).
...more>>
 Unfair Dice  Ivars Peterson (MathTrek)
Dice represent an intriguing example of the interplay between randomness, chance, and physical law. The simplest mathematical model of a standard die is based on the assumption that the die is a perfect cube. A cube has six faces, and each face has an
...more>>
 The United States and the Metric System  Office of Information Services, National Institute of Standards and Technology (NIST)
A capsule history, with questions and answers, a metric chocolate chip cookie recipe, and some sample size relations (kilogram of butter to pound, etc.).
...more>>
 Unlucky in Cards (Math Chat)  Frank Morgan, MAA Online
In his Contract Bridge syndicated column Phillip Alder says that the odds against getting a "Yarborough  a hand with no card higher than a nine" are 1827 to 1, and that the odds against two players getting a Yarborough on the same deal are about 182
...more>>
 Unsilence Students' Voices  Suzanne Alejandre
Article discussing how to provide an opportunity for all students to contribute to math classroom discussions. Originally published in the September, 2012, issue of the CMC ComMuniCator, journal of the California Mathematics Council, this article intersperses
...more>>
 U.S. Department of Education
Extensive and varied education information in categories including: educational initiatives (President's and Secretary's priorities), funding opportunities, student financial assistance, research and statistics, news and events, programs and services,
...more>>
 Using Technology to Enhance Engaged Learning for AtRisk Students (NCREL)  Barbara Means; Pathways to School Improvement
A "critical issue": An increasing number of educators are calling for high standards and challenging learning activities for atrisk students. New technologies can provide meaningful learning experiences for all children, especially those at risk of educational
...more>>
 Using Technology to Support Education Reform  Means, Blando, Olson, Middleton, Morocco, Remz, & Zorfass
1993 publication of the Office of Educational Research and Improvement, U. S. Department of Education. Includes sections on educational technologies, support for student learning activities, support for teacher functions, effects on student achievement,
...more>>
 Using Technology to Transform Mathematics Teacher Education: An Example from Graphing Instruction  Lisa Denise Murphy
An examination of how an example of a use of technology in mathematics education  microcomputerbased laboratory (MBL) work used to teach students about line graphs  fits Pea's framework (the effects of transformation are less predictable than those
...more>>
 US Third in Math Olympiad (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: a small creature needs to find its way from a random point on an milewide strip of land to the sea on either side, by going distance r in a random direction and then (if it has not yet found the water), turning once t degrees
...more>>
 Vagn Lundsgaard Hansen
A personal home page with links to: a mathematical story "I am the greatest," solving and proving/explaining the isoperimetric problem for quadrilaterals; Mathematics and the Public  some experiences with the popularization of mathematics; and Mathematics
...more>>
 The Valuation Theory Home Page  FranzViktor Kuhlmann
A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research. The home page offers: information about conferences and special events; names and email addresses of mathematicians working
...more>>
 
