 The Twelve Days of Christmas and Pascal's Triangle  Judy Brown, DIMACS and The Math Forum
A lesson in which, using Pascal's triangle, students find the number of items given each day in the song, "The 12 Days of Christmas."
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 The Twelve Days of Christmas  Judy Brown, DIMACS and The Math Forum
A lesson in which students find the number of items given each day in the song, "The 12 Days of Christmas." This project is designed to be used as a warmup activity during the 12 days preceding Christmas.
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 Twenty Tosses (TEAMS)  Jeannie Toshima; TEAMS Distance Learning, Los Angeles County Office of Education
Toss a coin twenty times, and share class results. Students predicted how many heads or tails they might get if they toss a coin 20 times; tossed coins 20 times and recorded their results; compared their predictions with the actual results; teachers collected
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 Twistors  What Are They?  Fedja Hadrovic
Notes briefly introducing the basic definitions of twistor theory, which might provide an "elegant formalism for both general relativity and quantum theory. Roger Penrose was first led to the concept of twistors in his investigation of the structure of
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 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
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 The TwoHeaded Quarter by Joseph Ganem  Chartley Publishing, LLC
A companion site to The TwoHeaded Quarter, written by a physicist scrutinizing daytoday financial decisions, such as "How far should you drive to buy cheaper gas?" and "Is money saved when you buy on sale?" and "How far should you drive to save money?"
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 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?"
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 Twos Complement  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about two's complement, a way to encode negative numbers into ordinary binary so that addition still works.
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 Two Trains  Math Forum, a Classic Problem from the Ask Dr. Math FAQ
Two trains leave different cities heading toward each other at different speeds. When and where do they meet?
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 TwoYear College Professors' Place  Math Forum
Links to some of the best Internet resources for twoyear or community college professors: professional organizations, publications, and careerrelated links.
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 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,
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 Types of Functions  Eger, Champaneria, Garmendia; Interactive Mathematics Online (IMO)
Definitions, plots, and examples of composite functions; even and odd functions; inverse functions; linear, quadratic, and cubic functions; monotonic functions; periodic functions. Also, Java "formulae enabled" pages.
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 Typing Math  Math Forum, Ask Dr. Math FAQ
How should I type exponents? What about square roots? Why not use tabs? May I send attachments?
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 UBC Calculus Online: Supplement to Math 100  Dept. of Mathematics, University of British Columbia, Vancouver, BC, Canada
An online supplement to mathematics courses being taught within the University of British Columbia Department of Mathematics. Course notes (functions, the Function Zoo, What is the derivative?, Tools for Calculating Derivatives; Applications of the Derivative;
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 UBC Calculus Online: Supplement to Math 101  Dept. of Mathematics, University of British Columbia, Vancouver, BC, Canada
An online supplement to mathematics courses being taught within the University of British Columbia Department of Mathematics. Course notes (Definite Integrals and the Fundamental Theorem of Calculus; Applications of the Definite Integral; Techniques for
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 UberSmart Math Facts  David Kocur
UberSmart Math Facts is a flash card program intended to help kids memorize the basic addition, subtraction, multiplication, and division facts. Site also has printable worksheets for noncomputer practice. Try it free for 30 days or purchase a license.
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 UBUYACAR  Maricopa Center for Learning and Instruction
An online problembased learning manual for students that poses the question: "You are interested in purchasing a new vehicle. What should your annual salary be to afford the car you want?" Students move through a problemsolving process. A Tutor's Manual
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 UCALC  Daniel Corbier
Windows shareware tools to compute compound interest, convert from miles to kilometers, solve a quadratic equation, plot a 3D surface, or simply add up bills. Features include: Expression Evaluator (evaluates expressions such as "5+4*1013"); Unit Converter;
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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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 UC Berkeley Wavelet Group  Univ. of California at Berkeley
People, papers and publications.
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 UCLA Statistics Homepage
Departmental info; paid or free consulting, tutoring; statistics preprints; theses and dissertations; UCLA statistics calculators; Journal of Statistical Software; UCLA electronic textbook; case studies and data sets; Center for Teaching Statistics; UCLAStat
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 UCLA Statistics Series: Preprints  Dept. of Statistics, University of California at Los Angeles (UCLA)
Papers on statistics that have been or will be submitted for publication.
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 UC Museum of Paleontology  University of California at Berkeley
Online exhibits, education and outreach programs, catalogs and collections, and links to other science and museum sites. Paleontology incorporates many different kinds of data from different fields. Search for type specimen data from the museum's Catalogs
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 UCSB Department of Mathematics Center for Mathematical Inquiry  Regents of the University of California
Developing "inquirybased learning approaches in the teaching of mathematics and a research base that examines teaching and learning through inquirybased practices." See past workshops, course materials for University of California Santa Barbara (UCSB)
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 UK Mirror Service  Joint Information Systems Committee, Higher Education Funding Councils, UK
Formerly HENSA, this national software archive service benefits the higher education and research community in the UK, funded by the Joint Information Systems Committee of the Higher Education Funding Councils. It maintains copies of electronic archives
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 The UK National Lottery  MerseyWorld
Using real data allows due emphasis to be given to the context and so may encourage crosscurricular links. The UK lottery site has links to many pages with varied statistical information about winning ticket numbers and prizes (see Lottery Links).
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 UltimaCalc: the Ultimate Algebraic Graphing Calculator  Anand Shraddhan
An algebraic graphing calculator for Windows that plots functions, creates charts, and calculates and displays various forms of regression. Also calculates standard deviation and related statistics, solves triangles, and finds roots of polynomials.
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 Ultimate Calculators  Graham Lancaster
Free online loan calculators, mortgage calculators (comparison calculator, basement suite calculator), investment property calculators, tax calculators, investing calculators (retirement income calculator, 401k calculator), capital budget calculators
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 The Ultimate Online Review Book  ThinkQuest 1997
Previous New York State Regents Exams available to help you study for standardized tests. Tests and answer keys from the early 1990s are organized into Sequential Math 1, Sequential Math 2, Sequential Math 3.
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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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 Ultra Fractal  Frederik Slijkerman
A Windows shareware program that creates images of fractals, allowing you to write your own fractal formulas, coloring algorithms, and geometric transformations in a simple formula language. A layering feature lets you combine different fractals and coloring
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 Ultra Fractal Gallery  Frederik Slijkerman
A gallery of fractal images created using Ultra Fractal, a Windows shareware program.
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 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.
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 Ululab
Makers of Slice Fractions, a wordless puzzle through ice and lava to clear a path for a woolly mammoth. Also available in French.
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 UMass Lowell WebMathematica Scripts  Kenneth M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell
Download Mathematica scripts. Abstract Algebra: generate Cayley tables of EAAM groups, Zn, and the ring Zn; connect the dots to visualize finite cyclic groups; polynomial extensions; and a game on finding a morphism between two groups. Modeling: exponential
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 UMI's Online Dissertation Services  Bell & Howell Information and Learning Company
UMI publishes and archives dissertations and theses; sells copies on demand; and maintains the definitive bibliographic record for over 1.4 million doctoral dissertations and master's theses. Information on preparing a dissertation for publication; finding
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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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 Uncle Dan's Algebra Videos  Dan Suttin, Homespun for Homeschoolers
A set of 12 videos plus a CD containing 180page workbook and linebyline solution key. Samples and ordering information available on the site. Uncle Dan offers to email the 180page algebra workbook file as a free gift to anyone who emails him and
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 Uncle Kenny's Mathematics Pronunciation Guide  Kent Kromarek
Billed as a "megametamathematical guide for proper American English
pronunciation of terms and names, for the diacritally challenged," this guide
includes many mathematicians and mathematical terms encountered in high school
and the first two years
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 Uncorking Work Problems (SMILE)  David Drymiller, Marie Sklodowska Curie Metro High School
A lesson designed to teach students to solve problems about work using the formula work = rate x time; to solve equations containing rational expressions; and to strengthen basic skills learned in algebra. From the Practical and Applied Math section of
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 Uncovering Mathematics with Manipulatives and Calculators  Texas Instruments, Inc.
A text that provides K6 activities emphasizing problem solving, reasoning, communications, and connections, clustered into four content strands: number sense; patterns, relations, and functions; measurement and geometry; and probability and statistics.
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 UNdata  United Nations Statistics Division
Search across the UN's statistical databases: education, human development, population, trade, gender, and more. Preview, download, and filter results by sources such as the State of the World's Children (SOWC) and Millennium Development Goals (MDG).
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 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
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 Undergraduates' Page (Mathematics Archives)  University of Tennessee, Knoxville (UTK)
Suggestions and links designed to give undergraduate students information specifically for them. Societies, Undergraduate Projects and Research; Summer Programs, etc.; Competitions; Careers in Mathematics; Undergraduate Publications; Other WWW Sites.
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 Understanding Algebra  James Brennan, Boise State University
In addition to "stuff to play with" on the web (a Graphing Applet (for exploring slope and intercepts of straight lines), a Prime Factorization Machine, a Prime Number List, a Quadratic Equation Solver, and a Quadratic Function Plotter), this book's full
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 Understanding Calculus  Faraz Hussain
An online book that introduces calculus through concepts and engineering applications. Read the illustrated chapters free online, or download the entire work as a PDF for a fee.
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 Understanding Fractions (SMILE)  Florida Bradley, Hartigan School
A lesson designed to teach students to recognize and understand equal fractions in relation to a whole unit. From the Arithmetic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning Enhancement.
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 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
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 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
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