This book on multimedia tools for communicating
mathematics arose from presentations at an international workshop
organized at the Centro de Matemática 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 Centre for Experimental and Constructive Mathematics at Simon
Fraser University in Burnaby, Canada. The MTCM2000 meeting aimed at the
scientific methods and algorithms at work inside multimedia tools, and
it provided an overview of the range of present multimedia projects, of
their limitations and the underlying mathematical problems. The workshop
gathered fifty seven participants, twenty nine presentations and a round
table. It took place under the auspices of the Sociedade Portuguesa de
Matematica and the European Mathematical Society, and was sponsored by a
special grant from the Fundação para a Ciência e a Tecnologia of Portugal.
This book presents some of the tools and algorithms
currently being used to create new ways of making enhanced interactive
presentations and experiments. It is, we hope, an invaluable and
up-to-date reference book on multimedia tools presently available for
mathematics and related subjects.
The current sources for mathematical knowledge are
still largely classical journals and books, even if they are now often
available from an electronic archive such as the Los Alamos Server.
Nevertheless, a number of new online sources have appeared and hint at
what is on the horizon: for example, Neil Sloane's server of
integer sequences, Finch's
Constants at MathSoft, or the newly established EG-Models server in Berlin with its
peer-refereed geometry models. Many people are making or have made large
collections of varied mathematical resources of potential interest for a
broad mathematical community. The internet has appeared in full battle
dress and allows individuals to make such material widely accessible on
common platforms.
Currently, many tools and projects focus on the
enhancement of digital publications aiming to provide interactive
research, experiments and teaching tools online. As of yet they provide
limited functionality. We believe that the diversity of multimedia
tools for the doing of mathematics will grow substantially in the near future
and will profoundly effect the way mathematicians do mathematics.
This was also a general outcome of the lively and participated round
table held at MTCM2000. Co-ordinated by J.F. Rodrigues, the discussion
concentrated on four main topics, each one addressed by an invited
participant: business models for multimedia tools (R. Fitzgerald and
J. Borwein), new online services to provide mathematical knowledge (T. Banchoff),
new mathematical algorithms and data structures for online mathematics (K. Polthier),
and multimedia tools of the future (J. Richter-Gebert).
Besides new tools, new mathematical algorithms and data
structures are needed for doing mathematics online. Although in the near
future bandwidth will increase dramatically and will open unforeseen
possibilities for creative people, the net will still limit the size of
experiments, much as today's 3d experiments in numerical mathematics are
limited by available computer memory. For instance, as a consequence
reduction of the amount of unnecessary data transferred during
experiments will continue to be a central research issue.
We hope that the methods and tools discussed in this
book and the accompanying CD will provide fruitful and stimulating
ground for the further development of multimedia tools for mathematical
education, communication and research.
Jonathan Borwein
Maria Haydée Morales
Konrad Polthier
José
Francisco Rodrigues