Multimedia Tools for Communicating Mathematics: Compression, Simplification, and Multiresolusion

This book presents multimedia tools currently being used to communicate mathematics. It includes nineteen of the twenty nine presentations at an international workshop that gathered fifty seven participants. The workshop was organized at the Centro de Matematica e Aplicações Fundamentais at the University of Lisbon, in November 2000, with the collaboration of the Sonderforschungsbereich 288 at the University of Technology in Berlin, and of the Center for Experimental and Constructive Mathematics at Simon Fraser University in Burnaby, Canada. It took place under the auspices of the Sociedade Portuguesa de Matemática and the European Mathematical Society, being sponsored by a special grant from the Fundação para a Ciência e a Tecnologia of Portugal.

The MTCM2000 had the purpose of providing an overview of the multimedia tools and algorithms used to enhance interactive presentations and experiments; it also presented the limitations of these tools and the underlying mathematical problems. In what follows we will briefly refer to each of the articles included in the book.

1. "Computer Animated Mathematics Videotapes", by Tom M. Apostol

   This presentation discusses Project MATHEMATICS! launched in 1987 by the author and James Blinn. By the year 2000, this project had produced ten videotapes, each less than 30 minutes in length, used as support materials in high schools and community colleges. The article describes the visualization techniques employed in the last five videotapes of the series: Sines and Cosines, Parts I, II, and III; The Tunnel of Samos, and Early History of Mathematics.

2. "A Virtual Reconstruction of a Virtual Exhibit", by Thomas F. Banchoff and Davide P. Cervone

   A physical exhibit originally staged by the Providence Art Club in 1996 inspired a virtual art gallery "Surfaces Beyond the Third Dimension", as a site on the world-wide web. A virtual visit of this art gallery by a Portuguese mathematician was the starting point of a collaboration between the authors and a team of mathematicians and computer professionals in Portugal. The result of this cooperation was the traveling exhibit "Para Além da Terceira Dimensão", which visited nearly every university in Portugal. The article describes the process and some of the difficulties of this project.

3. "An Intuitive Approach to Elementary Mathematics on the Web", by Bruce Bauslaugh, Richard Cannings, Claude Laflamme, and W. Keith Nicholson

   This article presents the linear algebra package ILAW: Interactive Linear Algebra on the Web. It provides an overview of the project and discusses the interface and its implementation, math & text display, mathematical exploration tools, labs & quizzes, lessons & notes, and the computing aspects of the package.

4. "OpenMath Technology for Interactive Mathematical Documents", by Olga Caprotti, Arjeh M. Cohen, Hans Cuypers, and Hans Sterk

   This paper presents a new version of an interactive course on first and second year university algebra, Algebra Interactive. It emphasizes the ways of communicating mathematics between computers, between software applications and over the Internet using MATHML and OpenMath, as well as new technologies such as XML and XSL.

5. "The StageTools Package for Creating Geometry for the Web", by Davide P. Cervone

   The StageTools package for Geomview has some very useful features for generating three-dimensional graphics, features that a missing from other commercial software packages. The presentation describes the two modules of the StageTools package: the CenterStage module and the StageManager module, with their advantages and disadvantages.

6. "Communicating and Learning Mathematics with Hypervideo", by Teresa Chambel and Nuno Guimarães

   This paper presents, with case studies, the use of hypervideo in communicating and learning of mathematics, in view of the challenges and concerns regarding the enrolment of students in mathematics programs and the teaching of mathematics in colleges.

7. "Collaboration in a Multimedia Laboratory", by Eliane Cousquer

   This is a very interesting paper, based on the author's experience in setting up and directing a multimedia laboratory in a teacher training college in the North of France. An academic science network of self-learning centers was set-up in 1987, and, in 2000, eleven universities were part of this network. Based on her early work in this network, the author set up the Laboratoire Multimedia Informatique et Apprentissage in a training college in the North of France in 1999. This helped the development of collaboration and distributed cognition in the North of France, the use of technologies in teacher training, and the set up of teams for the research of the use of technologies in mathematics.

8. "jDvi-A Way to Put Interactive TeX on the Web", by Tim Hoffman

   This is a very technical paper, explaining in some detail the use of jDvi, a tool written by the author of the Sfb288 at Technische Universitat Berlin, and used to extend TEX and LaTEX documents with multi-media features such as color, hyper links, and JAVA applets.

9. "Visual Calculus- Development and Tools", by Lawrence S. Husch

   This paper refers to the Visual Calculus Project, a collection of modules for the use of those who want to use software packages to demonstrate concepts from calculus in class. It has an extensive list of references (sites on the world-wide web.)

10. "EG-Models-A New Journal for Digital Geometry Models", by Michael Joswig and Konrad Polthier

    This article introduces a new electronic journal for the publication of digital geometry models. This very good journal is entitled Electronic Geometry Models, and can be found at http://www.eg-models.de/.

11. "The Future of Mathematical Software", by Ulrich H. Kortenkamp

    The author of this article has been, for a long time, both a user and an author of mathematical software. This paper gives his views of the development of mathematical software in the past, as well as the prospects and the requirements for the future developments. The paper analyzes the evolution of the mathematical software in the last 30 years and has very many links to useful web sites.

12. "A Dynamic Setup for Elementary Geometry", by Ulrich H. Kortenkamp and Jurgen Richter-Gebert

    This is a very interesting mathematical paper, where some mathematical proofs are really enhanced by software that allows static elementary geometry to be transformed in dynamic mathematical geometry: the elements of a construction are allowed to move around. The discussion progresses then towards more difficult mathematical concepts, and can be followed further at the web site http://www.cinderella.de/.

13. "Dynamic Geometry on WWW", by Gilles Kuntz

    In this paper, the limitations of some pedagogical web sites for dynamic geometry are discussed, and the project "Cabri-Java", with its advantages, is introduced. Also, there are a few useful web links, most importantly http://www-cabri.imag.fr/cabrijava/.

14. "Minimalistic Tools for Mathematical Multimedia", by Erich Neuwirth

    This paper presents ways to use standard software tools, found on most PCs, in illustrating mathematical concepts and mathematical applications. It refers to some of the author's projects, available o his web site http://sunsite.univie.ac.at/.

15. "Publication of Interactive Visualizations with JavaView", by Konrad Polthier, Samy Khadem, Eike Preuss, and Ulrich Reitebuch

    This paper presents JavaView, a 3D software package for doing geometry and numerical experiments online. One of its important features is its possibility to easily integrate with other software such as Mathematica and Maple. In the references there are mentions of several web sites.

16. "The Solver Learning Environment for Solving Mathematical Word Problems: Pupils' Discussions", by Heli Ruokamo

    Many young students consider word problems to be quite difficult. Therefore teachers always have tried to find ways to help their pupils with these types of problems, and the Solver Learning Environment was produced for this purpose; it was used in a teaching experiment in 1995 in Finland, using fifteen years old students. This paper presents the students' discussions vis-à-vis this experiment.

17. "Interactive Knot Theory with KnotPlot", by Robert G. Scharein and Kellogg S. Booth

    This paper describes KnotPlot, a topological drawing tool, and its applications in computational knot theory. KnotPlot is an experimental software, and its constant development can be followed at http://www.pims.math.ca/knotplot/.

18. "Developing Gato and CATBox with Python: Teaching Graph Algorithms through Visualization and Experimentation", by Alexander Schliep and Winfried Hochstattler

    This paper describes the authors' efforts in developing CATBox, the Combinatorial Algorithm Tool-Box: an interactive course combining a textbook with the visualization software Gato, the Graph Animation Tool-Box. In the references, there is a comprehensive list of related web links.

19. "Rescalable Real-Time Interactive Computer Animations", by John M. Sullivan

    This presentation refers to the multiple ways animation can be used as a tool for communicating three-dimensional geometry, with a special mention of the Optiverse. More details can be found at http://new.math.uiuc.edu/optiverse/.

Mihaela Poplicher is an assistant professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.