 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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 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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 Understanding Projective Geometry (Question Corner and Discussion Area)  University of Toronto Mathematics Network
An indepth explanation of projective geometry in response to a high school student's question.
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 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.).
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 Understanding Temperatures  NASA Lewis Learning Technologies Project
These were the low temperatures recorded for January 15 in these cities: Minneapolis:  6 degrees; Cleveland: 5 degrees; Fargo: 11 degrees; Chicago: 2 degrees; Milwaukee: 3 degrees; Detroit: 1 degree. Which city had the low temperature closest to 0
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 Undusting Napier's Bones  Alexandros Diploudis; HeriotWatt University, UK
Biographical information about the Scottish mathematician John Napier, generally considered the inventor of logarithms, with a Java simulation of Napier's bones, a method for performing arithmetic operations by the manipulation of rods (called "bones"
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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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 UniformMotion Problems: Just Playing With Cars (SMILE)  David Drymiller, Morgan Park High School
A lesson that uses batteryoperated cars to teach students to solve uniform motion word problems using rate X time = distance; and gives them practice in measuring in the metric and English systems. From the Practical and Applied Math section of a collection
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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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 Unique Online Math Flash Cards  Lambert Smith, MathRUS.com
Customizable formatting characterizes these flash cards for addition, subtraction, some multiplication and some division. Free 30day trial; afterwards, a subscription is paywhatyoucan. The author writes: "This website for online math flash cards differs
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 Unit Conversion and Day of the Week  Stephen Phillips
Convert between units of distance, area, volume, mass, speed, temperature, pressure, energy, power, or force online, or find the day of the week for a given date. There is also a list of conversion factors for various units, including units of radiation,
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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 Conversions, Unit Cancellation  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about unit conversions and cancellations, from "Convert: 3.25 cm to millimeters...." to "If you can run 100 meters in 10 seconds, how long, in days, hours, and minutes, does it take you to run 12,800,000 meters?"
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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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 Unit Converter
Key in units to convert. Available tabs include area, volume, time, density, length, temperature, moment of inertia, forces, distributed load, bending moment, and section modulus.
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 Uniteasy: Scientific Unit Conversion and Dictionary
The site contains a variety of unit converters, including for space and time (angle, area, length, time, velocity, volume, solid angle, and astronomical distance), electricity, acoustics, chemical, mechanics, magnetism, IT, heat/energy, light, and radiation.
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 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.).
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 United States Historical Census Data Browser  Paul Bergen
A database on the people and the economy of the US for each state and county from 1790 to 1970. Data include historical census figures and general population characteristics such as "number of free white females," "number of free colored males," and "number
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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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 UnitMath Example: Geometric Solids  Paul M. Price
Examples of how to use UnitMath with geometric solids: box (rectangular parallelepiped), cone (right circular), cylindrical solids (can  right circular cylinder; horizontal cylinder, partly filled), oblate spheroid, prolate spheroid, spherical solids
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 UnitMath  Paul M. Price
A calculation utility program for Mac or Windows, designed to answer questions written as equations made up of numbers, units (a unit is a quantity in terms of which the magnitudes of other quantities of the same type can be stated), precision, and operators.
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 Unit Measurement Conversion  NASA Lewis Learning Technologies Project
Which statement is NOT correct? 96 cups = 6 gallons; 9 days = 216 hours; 84 ounces = 7 pounds; 2 miles = 10,560 feet. A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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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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 Units of Measurement  NASA Lewis Learning Technologies Project
Which object is matched with its appropriate unit of measurement? Milligrams for the weight of a textbook; Kilometers for the length of a sailboat; Grams for the weight of a needle; Kiloliters for the capacity of a reservoir. A detailed answer is provided.
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 UnitWiz
An online calculator converts units of length, area, density, energy, force, mass, power, pressure, speed, temperature, or volume.
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 Univalg  eGroups, Inc.
Mailing list for use by the Universal Algebra community: subscribe here, or browse archive by month. (Universal Algebra is a technical branch of mathematics related to algebra and model theory.)
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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 Framework for Science and Engineering  Part 5: Category theory  Petr Ivankov
Software for use in Category Theory. The web site describes its function and operation.
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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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 Université de Montréal  Département d'informatique et de recherche opérationnelle
In French, with some pages available in English as well: Fondé en 1966, le DIRO fut le second département d’informatique créé au Canada. La recherche de pointe de son corps professoral, l’ampleur de son activité académique et son rayonnement international
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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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 The University of Chicago School Mathematics Program (UCSMP)
A K12 curriculum begun in 1983, with educational materials designed to bring the real world into the classroom, emphasizing reading, problemsolving, everyday applications, and the use of calculators, computers, and other technologies. Unnecessary repetition
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 The University of Minnesota Calculus Initiative  The Geometry Center
Interactive technologybased modules for the engineering calculus sequence which emphasize geometric concepts of calculus while examining applications of mathematics to the physical and life sciences. Available are: the Rainbow Lab, Numerical Integration
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 University of South Carolina High School Math Contests  David Sumner
Problems from the University of South Carolina (USC) High School Math Contests, since 1994. Walk step by step through illustrated solutions to each problem using the "next step" button. The delivery of questions is designed for competitive timing. Also,
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 UniVirtual Slide Rule Emulator  Andrew Davie
A realtime, fully configurable, slide rule emulator in Java. Zoom, reconfigure onthefly, and work multiple slides and multiple cursors, each of which supports multiple gauge marks and hairlines.
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 Unizor  Zor Shekhtman
Whiteboard lectures for teenagers on algebra, trigonometry, vectors, matrices, combinatorics, probability, and statistics. Sign in for structured study, assignment functions, and more.
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 Unlocking Ways to Make Your Math Simple  Rajinder Goswami
An ebook meant to enhance calulating skills. It focuses on comprehension, speed, and accuracy. Two Flash examples provided; download the whole book for a fee.
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 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
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 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
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 Unsolved Problems in Function Theory  Alexandre Eremenko
Files available in PDF format: Some constants studied by Littlewood; Meromorphic functions satisfying certain differential equations (E. Hille); Does every universe contain a place where you can stay at rest? (Lee Rubel); Holomorphic curves with few inflection
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 Unsolved Problems in Number Theory, Logic, and Cryptography  Tim Roberts
This site "concentrates only on problems which are easily understandable to the amateur.... explainable on a single screen (perhaps 200 words), using simple terminology." Read brief descriptions of open problems such as the Chromatic Number, the Collatz
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 Unstructured Grids (UG)  Institut für Computeranwendungen, UniversitU7auml;t Stuttgart
A flexible software tool for the numerical solution of partial differential equations on unstructured meshes in two and three space dimensions using multigrid methods. Its basic design is flexible enough to support many different discretization schemes.
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