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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
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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 www.ceic.math.ca. (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
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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
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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
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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
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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 [http://www.w3.org/Math/#Working 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
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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 (http://archives.math.utk.edu/visual.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
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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?
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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
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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 (http://www.cinderella.de) 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
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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:
http://www-sfb288.math.tu-berlin.de/vgp/
- PAUL R. WELLIN, Wolfram Research
Mathematica and Mathematics on the Web
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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
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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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