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Math on the Internet / Mathématiques sur l'internet
(June Lester, Organizer)

JONATHAN BORWEIN, CECM, Simon Fraser University
CEIC: International Mathematical Union Initiatives

I will describe - and hopefully show - some of the ambitious initiatives underway within the International Mathematical Union's (IMU) new standing Committee on Electronic Information and Communication (CEIC).

These efforts centre on Math-Net which will include a global preprint harvesting system and a unified system of ``secondary home pages'' capable of dealing unobtrusively with metadata. There will shortly be a CEIC web site at (See also some of the streaming video presentations at ``Mathematical Communication'' on the Camel front page.)

CLAUDE LAFLAMME, Deparment of Mathematics and Statistics, University of Calgary Calgary, Alberta  T2N 1N4
Interactive Mathematics on the Web using Java and TEX

We will demonstrate the power of Java combined with TEX to create computational tools, explorations in elementary mathematics and randomly generated quizzes with interactive interfaces, all based on standard mathematical notation. The Java based quizzes are automatically marked, and include extensive feedback to both instructors and students. We conclude with a demonstration of ILAW: Interactive Linear Algebra on the Web. ILAW is an internet tutorial that combines HTML, RealAudio, TEX, Java, and other e-commerce tools, to provide students with online narrated lessons, course notes, exploratory and computational tools,quizzes, secure marking sheets and retrievable completed quizzes.

BILL CASSELMAN, Department of Mathematics, University of British Columbia, Vancouver, British Columbia
Archimedes animated

Following some recent suggestions of Tom Hales, the mathematician who has proved Kepler's conjecture, I am going to present a Java-enabled argument explaining the two-dimensional analogue (that the hexagonal lattice gives rise to the densest circle packing), originally proven by Thue.

STAN DEVITT, Radical Flow Inc.
Mathematical semantics, OpenMath and the Web

The effective integration of mathematical notation into the Web has been, to say the least, challenging. Even if the issues of fonts, resizing, base-line alignment, etc., are addressed, pictures of formulae or of printed pages are simply not enough to support the intelligent and automatic re-use of data. OpenMath is designed to allow us to record the mathematical sense of an expression in a manner that can be re-used by a wide variety of software including search engines.

The automatic re-use of mathematical data by mathematical software requires much more than the use of TEX or LATEX. Such traditional markup is little better than pictures when it comes to automatically capturing and identifying the mathematical sense of an expression. A mechanism is needed that allows an author to explicitly associate a particular use of a notation with a specific definition. OpenMath provides necessary concepts and structure to support this. This conceptual structure is one of the key underpinnings of the content side of W3C's MathML.

This talk introduces the key concepts of OpenMath, shows how it relates to MathML, and then investigates some of the consequences of having such an infrastructure in place.

ANGEL DIAZ, IBM, T. J. Watson Research Center, Hawthorne, New York  10532, USA
XML Based Interactive Scientific Publishing With The Mathematical Markup Language

The widespread adoption of the World Wide Web has resulted in a powerful medium for the dissemination of information, as well as a popular platform for application deployment. However, the transition from paper to web-based interactive scientific articles, books, journals and courseware has brought new challenges to users of the World Wide Web. Students, scientists, and engineers are now faced with the task of rendering the 2-D presentational structure of mathematics, as well as harnessing a wealth of scientific and technical software across international boundaries and markets.

This report will provide an overview of a new generation of markup language standards and software applications aimed at facilitating the transition from static documents to live scientific and technical offerings! Indeed, we will take a hands-on approach to describe how the World Wide Web Consortium (W3C) Mathematical Markup Language (MathML) 2.0 specification and general purpose Extensible Markup Language (XML) processes can be used to create truly reusable scientific content. Much like TeX and LaTeX, MathML provides a so called "lingua franca" for mathematical rendering. However, MathML also includes conventions for encoding mathematical semantics that can form a basis for machine to machine communication.

Much like the world wide adoption of HTML, MathML has grown in popularity due to it's implementation across a wide range of products. Members of the W3C Math Working Group include representatives from American Mathematical Society, Design Science, IBM, Microsoft, Waterloo Maple, and Wolfram Research to name a few [ Group]. As a result, authors can today create a web presence where students can dynamically manipulate and perform scientific computations using a wide range of software applications across a variety of computer platforms!

LARRY HUSCH, Department of Mathematics, University of Tennessee, Knoxville, Tennessee  37996, USA
Visual calculus-a report

The Visual Calculus Project is a collection of web-based modules which can be used in the teaching and/or learning of single variable calculus ( Some of the innovative features of the materials will be demonstrated. The modules have been used as supplementary materials to the course for the past two and a half years. There will be a discussion of how the modules have been used and the students' reactions to the modules. Future plans, including plans to offer this as a web- based course, will also be discussed.

NICHOLAS JACKIW, KCP Technologies, Emeryville, California  94608, USA
JavaSketchpad: web-based dynamic geometry

As interactive geometry technologies mature, existing software packages are undertaking new Web-based components, and new packages are emerging in entirely on-line formats. This talk will introduce JavaSketchpad, a Web-based viewer for interactive mathematical visualizations created using The Geometer's Sketchpad. In addition to providing an illustration medium for general on-line mathematics and mathematics education publishing, JavaSketchpad is heavily used in distance learning contexts, and as a constituent component of the ESCOT project's attempt to create a toolkit for the construction of didactic mathematics environments served over the Internet. This talk will address such application contexts, as well as report more generally on ongoing efforts to foster the Internet as a location in which mathematics is performed, rather than one in which it is merely described.

LOKI JÖRGENSON, Canadian Mathematical Society, Department of Mathematics and Statistics, Burnaby, British Columbia  V5A 1S6
Three years later: are the CMS' digital journals a success?

Out of the blocks early in the Web game, the CMS has chased its own elusive and sometimes maddening technological tail. Making it on the World Wide Web has proven challenging-the players, the rules and even the purpose of the game have changed regularly. The question to be asked is: Has the CMS succeeded in its efforts at digital publishing? Has it kept up with the pace of progress? And where does it go from here?

ULRICH KORTENKAMP, Freie Universität Berlin
Interactive geometry

Geometry has lately regained importance in mathematics, supported by the introduction of computers. Their capabilities to visualize and communicate give new means to talk, discuss and think geometry. As a win-win-partnership, geometry software can also be enhanced both algorithmically and ergonomically by using results that stem from the golden years of geometry almost 100 years ago.

The Internet has given this connection a new boost: Apart from only visualizing data, geometry on the Internet offers true interactivity, and the programming language Java is the key to deliver this to any place in the world. Also, the desire to offer interactive exercises and automatic animations as in Cinderella ( forces us back to the foundations of dynamic geometry and gives new insights on the connection of Euclidean, non-Euclidean and projective geometry, continuity, and Riemann manifolds.

KONRAD POLTHIER, Technical University Berlin, FB 3 Mathematik, 10623  Berlin Germany
Mathematical visualization and online experiments with JavaView

The future of mathematical communication is strongly related with the internet. On a number of examples, we give an overview how mathematical 3d-visualization imbedded in online publications will provide new insight into complex phenomena, influence the international cooperation of researchers, and allow to create online hyperbooks combining interactive experiments and mathematical texts.

Using the software JavaView we discuss practical aspects of online publications and give technical details on the ease of implementations. We present sample interactive documents with visualization examples, report on the work on a multimedially enhanced reference dissertation in mathematics, and show different numerical online experiments from mathematical research. Further information:

PAUL R. WELLIN, Wolfram Research
Mathematica and Mathematics on the Web

The talk will focus on recently released and developing web technologies from Wolfram Research. Included will be demonstrations of MathML authoring, the use of style sheets in Mathematica and LaTeX, and the new J/Link tookit integrating Mathematica and Java.

ERIC WOOLGAR, Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta
A proposal for a mathematics digital library

There has in the past been expressed the desire to see a web archive based in Canada and storing electronic material for University/College and K-12 courses. There is now a proposal to build such an archive, by adapting to mathematics software presently under development in the Biological Sciences Dept of the University of Alberta. I will discuss this software and the proposed model for a peer-reviewed archive of mathematics material that the software would support. It's my intention to provoke discussion concerning the need for such an archive and the policies under which it would operate, and to ascertain whether there is sufficient interest in the mathematical community in Canada to proceed to implement this server.


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