- 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 '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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- 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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- 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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- 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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- 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,
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- Using Technology to Enhance Engaged Learning for At-Risk 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 at-risk students. New technologies can provide meaningful learning experiences for all children, especially those at risk of educational
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- 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,
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- 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 - microcomputer-based laboratory (MBL) work used to teach students about line graphs - fits Pea's framework (the effects of transformation are less predictable than those
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- 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 mile-wide 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
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- 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
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- The Valuation Theory Home Page - Franz-Viktor 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
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- Valuing as the Key to Unsilencing - Suzanne Alejandre
"At the heart of the Common Core State Standards (CCSS) Initiative is the valued learner, a learner with an active voice in his/her own learning. Under No Child Left Behind (NCLB) practices and assessment many students' voices have fallen silent.... Valuing
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- Various Calendars - Jim Loy
An elementary introduction to the different calendars used throughout Western history (Julian, Gregorian), Ancient Egypt, and by the Mayans.
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- VedicMaths.Org - Clive Middleton, Kenneth Williams, and Mark Gaskell
Learn about the ancient system of mathematics of the Vedas through interactive tutorials, research and teaching articles, recommended books and websites, a list of sutras translated from the original Sanskrit, a calendar of events, newsletter, and references
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- The Vertex Coloring Algorithm - Ashay Dharwadker
A polynomial-time algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem.
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- The Vertex Cover Algorithm - Ashay Dharwadker
A polynomial-time algorithm for finding minimal vertex covers in a graph.
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- The Vibonacci Numbers (Computing Science) - Brian Hayes, American Scientist
A new mathematical constant, from a branch of the Fibonacci number family in which, instead of always adding two terms to produce the next term, you either add or subtract, depending on the flip of a coin at each stage in the calculation. Hayes writes,
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- Victor Shoup's Home Page
Download research papers on cryptographic protocols and on algorithms for solving problems in the area of number theory and algebra. The Courant Institute researcher freely offers a standard for public-key encryption, a simple LaTeX class for preparing
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- Viewing Four-dimensional Objects in Three Dimensions - Barbara Hausmann; The Geometry Center
"Given that humans only visualize three dimensions, how is it possible to visualize four dimensional, or higher, objects? This question is the underlying idea of a short novel written over a hundred years ago by Edwin A. Abbot called Flatland. Flatland
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- Views from Flatland (MatheMUSEments!) - Ivars Peterson (Math Muse for Kids)
What do you think the world would look like if you and everything in it were squished flatter than a pancake? Like shadows, you and your friends would freely flit about the surface. But if you couldn't rise above or below the surface, objects with any
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- A Viral Dilemma - Ivars Peterson (MathTrek)
An article that discusses how, in effect, a virus is caught up in a version of the prisoners' dilemma, a widely studied game in which acting for individual advantage clashes with acting for the collective benefit. Game theorists devised the prisoners'
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- Virtual Math Museum - Richard Palais
A virtual "mathematical museum" being developed and improved by an international group of mathematicians called the 3DXM Consortium (the same group responsible for the development of the 3D-XplorMath mathematical visualization program). Topics include
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- Virtual Trips to Black Holes and Neutron Stars - Robert Nemiroff
A published paper understandable to undergraduates: "Visual Distortions Near a Black Hole and Neutron Star," Nemiroff, R. J. 1993, American Journal of Physics, 61, 619. Gravitational Principles and Mathematics; General Description of Visual Distortion
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- Visiting Artlandia - Ivars Peterson (MathTrek)
Have you ever admired any of the bold, colorful designs splashed across a variety of fabrics used for scarves, neckties, shirts, and other apparel? There's a chance that you may come across the work of a physicist. Igor Bakshee got into fabric design
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- A visit to James Clerk Maxwell's House - MacTutor Math History Archives
Linked essay outlining the life and work of Edinburgh-born mathematician James Clerk Maxwell, with an outline of his childhood, pictures of his home, some mathematical poetry, and references (books/articles).
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- Visualization of Complex Dynamical Systems - Visualization and Animation Group, Institute of Computer Graphics, Vienna University of Technology
Software or technical reports to download (in gzipped PostScript format) related to the graphical representation of complex dynamical systems.
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- Visual Mathematics (VisMath): Art and Science Electronic Journal of ISIS-Symmetry - Nagy, Jablan
The electronic journal of ISIS-Symmetry (International Society for Interdisciplinary Studies of Symmetry), published by the Mathematical Institute, Belgrade, Yugoslavia. Papers, conferences, the Nexus Network Journal of Architecture and Mathematics On-line,
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- Visual Modelling Group - University of Brighton
This research group focuses on giving formal semantics to existing notations, developing new visual notations, and reasoning with them. The Visual Modelling Group has developed a constraint diagram notation that visually expresses mathematical constraints
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- Vladimir Trifonov's Research Page - Vladimir Trifonov
The site includes papers "Natural geometry of nonzero quaternions" (International Journal of Theoretical Physics 46 (2) (2007) 251-257) and “GR-friendly description of quantum systems” (IJTP, DOI 10.1007/s10773-007-9474-3).
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- Vladimir Voevodsky
Lectures, publications, a library of Coq files, and more by the mathematician developing univalent foundations, which start with a view of mathematics where sets parametrize collections of objects without "internal structure" while more general homotopy
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- Volumes Of Cones & Pyramids - Jim Loy
A short essay on deriving the volume of cones and pyramids.
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- Vygotsky - Cristina Guerra
A brief description of Vygotsky's theories about thought, language, and intellectual development.
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- Vygotsky's Distinction Between Lower and Higher Mental Functions and Recent Studies on Infant Cognitive Development - Eugene Subbotsky; Psychology Department, University of Lancaster, UK
One of the major theoretical advances of Vygotsky's approach to cognitive development was his thesis that human mental functions are social in origin. In making this claim, Vygotsky was confronted with the difficulty of reconciling it with the fact that
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- Vygotsky - Trish Nicholl
This paper includes sections entitled Higher and lower mental functions; Intramental vs intermental abilities; The zone of proximal development (ZPD); Psychological tools; and Semiotic potential and the decontextualisation of mediational means. With references.
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- Wallace-Bolyai-Gerwien Theorem - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
According to the Wallace-Bolyai-Gerwien theorem, all simple polygons of equal area are equidecomposable by dissection. The site offers a proof of the theorem and several dynamic illustrations of equidecomposition in special cases.
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- Wanted: A New Mix - Keith Devlin (Devlin's Angle)
An essay on the insularity of mathematicians. "...mathematics as a whole should be prepared to embrace as a useful and bona fide part of the enterprise, collaborative investigations involving mathematicians together with experts in other disciplines."
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- Waterloo Fractal Compression Project - Edward R. Vrscay
A research project dedicated to the study of fractal analysis and Iterated
Function Systems/Fractal Transforms from theoretical and practical perspectives, focussing on image and signal compression. Both mathematical and non-mathematical introductions
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- Wavelet Digest: wavelet.org - Wim Sweldens
A free monthly newsletter with all kinds of information concerning wavelets; announcement of conferences, preprints, software, questions, etc. The latest issue and searchable copies of back issues (beginning in 1992) are available; links to other wavelet
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- The Wavelet Tutorial - Robi Polikar
The engineer's ultimate guide to wavelet analysis: a tutorial that explains basics of signal processing with a focus on the technique of wavelet transformations (WT). Basic concepts of importance in understanding wavelet theory; Short Term Fourier Transform
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- WebCalC - The WebMath Group
An on-line calculus course with easy to read text, fully worked examples, problem solutions, quizzes, and online linking. To view WebCalC, you need the software Scientific Notebook (a free viewer version is available). The site includes links to publications
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- Weighing the Evidence - Keith Devlin (Devlin's Angle)
Hundreds of thousands of years of evolution have equipped us with many useful mental abilities - our instinct to avoid many dangerous situations and our use of language are two obvious examples. However, evolution has not equipped us to handle statistical
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- Weird Dice (MatheMUSEments!) - Ivars Peterson (Math Muse for Kids)
In the dice game Piggy, you and your opponent take turns rolling a pair of ordinary dice. Your score is the sum of the face values of the dice, so if you roll a three and a four, you get seven points. The first player to reach 100 points wins. Suppose
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- Welcome to PERTH: PEerless on EaRTH - Dave Watson
Dave Watson's main interest is computational geometry, and he specializes in spatial interpolation. Books/software on Contouring (a survey of published bivariate contouring and interpolation methods), Tessellations, Spherical Tessellations, Isolines,
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- The Western Reserve Reading Project - The Ohio State University
With over four hundred pairs of twins participating in annual data collection sessions over the past ten years, the Western Reserve Reading Project (WRRP) explores how the environment affects children's ability to learn "by evaluating how genes and environmental
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- We Use Math - BYU Mathematics Department
From actuary to urban planner, read short descriptions of the scores of careers that use math -- or log in to submit your own career entry. Each occupation's write-up includes its salary range, educational background, the specific math courses it requires,
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- What Can Mathematics Do For The Businessperson? - Keith Devlin (Devlin's Angle)
In business, the ability to dig beneath the surface of a problem to see what
the real underlying issues are, and the capacity for clear and logical thought, can be extremely valuable. And learning mathematics provides an excellent way to develop that
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- What Does It Take to Be an Expert Problem Solver? - Annie and John Selden; Mathematical Association of America
Organized into five sections: Expert-Novice Studies Have Often Concentrated
on Textbook Problems; Solving Nonroutine Problems; Are Mathematicians Expert Problem Solvers? How Might One Teach Problem Solving? and The Importance of Affect. From the MAA's
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- What do we know about mathematics curricula? - Alan Schoenfeld, Journal of Mathematical Behavior
In the absence of either large-scale empirical proof of success or the existence of compelling and documentable standards, there is reason to be cautious. The traditionalists are nervous for good reason. It should be noted, however, that the resistance
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