 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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 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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 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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 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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 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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 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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 Una experiencia didáctica con CabriGeomètre: el seguimiento de trayectorias para manipuladores planos irredundantes  María José GonzálezLópez, Universidad de Cantabria,España
Una actividad geométrica consistente en realizar la simulación del movimiento de robots manipuladores planos con dos grados de libertad rotacionales y/o prismáticos, utilizando el entorno computacional CabriGéomètre.
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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 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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 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 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 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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 Understanding Mathematics: From Counting to Calculus  Keith Kressin, K Squared Publishing, Inc.
A comprehensive book for anyone who desires clear and concise math explanations, written for a nontechnical audience to cover the math fundamentals normally taught from first grade through college (for more information, see the Table of Contents).
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 Une Balade dans le Monde des Polyèdres  Maurice Starck
Les polyèdres convexes, non convexes, et intéressants: les polyèdres uniformes, les stellations de l'icosaèdre, des tétraèdres remarquables, le découpage d'un tétraèdre par un plan, les deltaèdres
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 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
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 Unfolding Orbifolds  Heidi Burgiel; The Geometry Center
A study of how a pattern can be reconstructed from an orbifold, using both handson exploration and the computer program TesselMania!. These activities are a good introduction to the movie Shape of Space. From Math 5337, Technology in the Geometry Classroom,
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 Unicursal curves and knot diagrams (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
A unicursal curve in the plane is a curve that you get when you put down your pencil, and draw until you get back to the starting point. As you draw, your pencil mark can intersect itself, but you're not supposed to have any triple intersections. You
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 Unification of System of Linear Equations, Matrix Inversion, and Linear Programming  Prof. Hossein Arsham; University of Baltimore
Remarks on unification of systems of equations, matrix inversion, and linear programming, that is, the links between these topics. Includes references and further reading.
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 The Uniform Polyhedra  Roman Maeder
A shortened version of the notebook Polyhedra.ma from Illustrated Mathematics [Gloor/Amrhein/Maeder95]. Uniform polyhedra have regular faces and congruent vertices. Allowing for nonconvex faces and vertex figures, there are 75 such polyhedra, as well
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 Unifpack (Web version 2.0)  Carlos O'Ryan Lira
A set of programs and C libraries for studying Riemann Surfaces with symmetry. Unifpack accepts a presentation of a finite group and calculates the Cayley graph of the group for that presentation. If the presentation is "admissible," Unifpack can calculate
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 Union of Bulgarian Mathematicians (UBM)
A voluntary, creative, nonpolitical organisation whose purpose is to bring together people who are interested in Mathematics and Computer science or are involved in activities related to those fields. Contact info, meetings.
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 UnitConversion.org
Perform online unit conversions for volume, distance, temperature, time, speed, and more for a total of 2,100 kinds of units in 78 different categories.
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 Unit Converter
The converter works for units of area, energy, pressure, volume,
temperature, mass, length, numbers, velocity etc. You put in a number and
select a base unit and select a unit to convert to. The conversion result
will immediately appear in the output
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 UnitJuggler: Online Unit Conversions  Pierre Di Marco
UnitJuggler offers free unit conversions, for distance and length, area, volume, weight and mass, temperature, time, and more.
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 The Units of Measure C++ Library  Keith Nicewarner
The purpose of this library is to try to make it more difficult to make
coding mistakes that incorrectly mix units of measure. This is done with a
set of C++ classes that provide typesafe manipulation of units of measure
for various properties.
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 Units of Measurement for Ada  Dmitry A. Kazakov
Public domain software for dealing with physical measurement units. The library provides physically correct unit arithmetic and tools for input and output of units, which including support of various irregular units. As an illustrative example a platformindependent
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 The Universal Currency Converter  Xenon Laboratories Incorporated
An interactive currency table. Versions are available in English, Spanish, and Swedish. The Universal Currency Converter™ allows you to perform interactive foreign exchange rate conversion on the Internet. Type the amount of source currency in the input
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 Universal Math Solver  Stanislav Kublanovsky
Software that solves problems of arithmetic, algebra, trigonometry, calculus, and other mathematics. Graphs, tables, and automated verbal and written commentaries — also available in French, Russian, Dutch, German, Italian, Spanish, and Hebrew —
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 Universal Math Solver (UMS)  Severny Ochag International
UMS allows students to solve problems simply by entering them from any source, and provides a complete solution and presentation of the whole calculation process, accompanied by an audio commentary. See a screen shot or download a demo. Available in French,
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 The Universe of Discourse  Mark Dominus
Blog by the perl programmer who authored the book HigherOrder Perl and columns for The Perl Journal. Posts, which date back to November, 2005, have included "Fibonaccilike sequences," "More Liber Abaci," "The 3n+1 domain," "Biblical infallibility and
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 University Departments  Canadian Mathematical Society (CAMEL)
An alphabetical list of Canadian university departments. Also links to
All U.S. Mathematics Departments online and
More Mathematics Departments in Universities around the World.
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