This book on multimedia tools for communicating mathematics arose from presentations at an international workshop organized at the Centro de Matemätica e Aplicaääes 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 Fundassäo para a Ciäncia 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 Haydäe Morales

Konrad Polthier

Josä
Francisco Rodrigues