- 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.
...more>>
- The Vertex Cover Algorithm - Ashay Dharwadker
A polynomial-time algorithm for finding minimal vertex covers in a graph.
...more>>
- 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,
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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'
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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).
...more>>
- 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.
...more>>
- 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,
...more>>
- 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
...more>>
- 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).
...more>>
- Volumes Of Cones & Pyramids - Jim Loy
A short essay on deriving the volume of cones and pyramids.
...more>>
- Vygotsky - Cristina Guerra
A brief description of Vygotsky's theories about thought, language, and intellectual development.
...more>>
- 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
...more>>
- 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.
...more>>
- 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.
...more>>
- 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."
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- 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,
...more>>
- 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,
...more>>
- 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
...more>>
- 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
...more>>
- 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
...more>>
- What, How, and the Web - Cut the Knot!, Alexander Bogomolny
More on place value. "There is an obvious confusion there between two questions, what to teach and how to teach it. Does the failure of the New Math to present a specific topic necessarily imply that teaching this topic has no merit? The New Math has
...more>>
- What is the best way to lace your shoes? - Burkard Polster, Nature
"The two most popular ways to lace shoes have historically been to use 'criss-cross' or 'straight' lacing -- but are these the most efficient? Here we demonstrate mathematically that the shortest lacing is neither of these, but instead is a rarely used
...more>>
- What Is the Collaborative Classroom? (NCREL) - M.B. Tinzmann, B.F. Jones, T.F. Fennimore, J. Bakker, C. Fine, and J. Pierce
New learning and thinking curricula require collaboration. An article that addresses shared knowledge and authority among teachers and students; teachers as mediators; heterogeneous groupings of students; teacher and student roles; interactions; challenges
...more>>
- What Is Your Answer to That Question? - Cut the Knot!, Alexander Bogomolny, with Don Greenwell
The question - Why study mathematics? - appears in a multitude of guises and a plethora of variants... Mathematics is often compared to art. Like literature, mathematics has metaphor, ambiguity, paradox, and mystery. It has history. Mathematics has contributed
...more>>
- What's Going On During Mathematics Awareness Month - Keith Devlin (Devlin's Angle)
"This year's theme is mathematics and biology. Two important examples of how mathematics is used in biology are: in developing computer models of the human heart, which are helping us to understand how the heart works and, more importantly, how it goes
...more>>
- What Should I Look For in a Math Classroom? - Mathematical Sciences Education Board (MSEB)
A set of practical guidelines, with explanations of their relevance. From the Mathematical Sciences Education Board of the National Research Council.
...more>>
- What's Noteworthy on Learners, Learning & Schooling - Mid-continent Regional Educational Laboratory (McREL)
"The major challenges for educational reform today are putting the pieces together to create sustainable systemic change and scaling up systemic reform to encompass all schools, all programmatic areas, all levels of schooling and diverse social contexts."
...more>>
- What's Sophisticated about Elementary Mathematics? - Hung-Hsi Wu
"The characteristics of coherence, precision, and reasoning are not just niceties; they are a prerequisite to making school mathematics learnable." In this American Educator article originally published Fall, 2009, the author goes on to unpack whole number
...more>>
- What Will Be the Effect of a Standards-based Education on College Students? - Judith Roitman
This article, by Judith Roitman of the University of Kansas, appeared in the April 1995 FOCUS, the newsletter of the MAA. Among other things, Roitman discusses the need for dialog between K-12 teachers and their college counterparts, and difficulties
...more>>
- What Works Clearinghouse
Reviews of the effectiveness of educational intervention programs, products, practices, and policies. Among other curricula, the WWC has reviewed studies of the Middle School Math Curricula interventions Cognitive Tutor, Compass Learning, Connected Mathematics
...more>>
- When Is Easter? - Jim Loy
"Easter is my favorite holiday, because of the bizarre way in which its date is determined. When is Easter? Here is how you can answer that question..." (Easter is the next Sunday, after the Paschal Moon date.)
...more>>
- When mathematics has to be theater - Keith Devlin (Devlin's Angle)
A mathematician's entry into the world of commercial multimedia - the creation of an interactive calculus textbook on CD-ROM.
...more>>
- When mathematics is plain sailing - Keith Devlin (Devlin's Angle)
In the ocean waters off New Zealand, an intense mathematical olympiad has just begun: The America's Cup - a yacht race, the premier international event in
ocean sailing. Competition is fierce. The technical challenges are enormous. And the costs are
...more>>
- Where to Start? - Cut the Knot!, Alexander Bogomolny
A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations. An interactive column
...more>>
- Where Will the New Millennium Begin? (Math Chat) - Frank Morgan; Christian Science Monitor
Assuming the third millennium arrives on January 1, 2001, where on Earth should the celebration begin?
...more>>
- Which Countries Are Most Like Stars? (Math Chat) - Frank Morgan, MAA Online
Which countries in the world have a point such that the shortest line from
every other point in the country stays inside the country? (ignore mountains and valleys). Mathematicians call such countries starlike. Are there any countries such that the shortest
...more>>
- Which One Is Older? (Math Chat) - Frank Morgan, MAA Online
Creative solutions to the challenge: how can two people determine which is older without revealing their ages? Math videos available from the Mathematical Sciences Research Institute via the MAA. "Mathematics in Arcadia," "Fermat's Last Theorem," as seen
...more>>
- Whips and Dinosaur Tails - Ivars Peterson (MathTrek)
The loud crack of a deftly flicked bullwhip is a small sonic boom, generated when the whip’s thin, highly flexible tip exceeds the speed of sound. Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate
...more>>
| |
|
The Math Forum is a research and educational enterprise of the Drexel University School of Education.