Interactive mathematics on the Internet

     

Introduction

We describe in this paper our project WIMS (WWW Interactive Mathematics Server), a project aimed at a systematic approach of providing internet-accessi ble mathematical computations.

Internet-accessed mathematical computations present several advantages over locally installed mathematical softwares. With interfaces based on the html protocol, many common computation needs can be carried out by the user without prior learning of the syntax of a particular software. And software installation and maintenance costs are considerably reduced.

User-friendly access to mathematical computations also means the design of computer-generated mathematical exercises with sophisticated analyses of answers. When it is an Internet server which generates the exercises and processes the answers, analyses of students' progress can be easily achieved, with data and results well-protected against cheating, a feature otherwise hard to realize by locally installed softwares.

In order to obtain a high degree of mathematical sophistication, the basic design concept of the Wims project is server-side interactivity via http protocol, with a modular structure at two levels, which make the system easily enhanceable.

On the one hand, each application (exercise or tool) under the system can be independently created, modified or removed, allowing the system to host a large number of such applications. On the other hand, the system calls various mathematical softwares (numerical or symbolic computation, visualization, proof assistant) as background engines, with an independent interface designed for each such software. This provides an easy means for Wims applications to make use of the power of these softwares in a very versatile way.

As a result, we are able to create applications with unique features for web-based mathematics (interactive theorem proving, animated visualization for user-supplied expressions, exercises with multiple good answers or multi-step answers, etc). And in a few domains such as first year linear algebra where enough application s have been developed, the system is ready for serving mainstream educational use.

Design choices as well as capabilities, shortcomings and unsolved problems of the system are discussed in the paper. Most technical details are omitted in order to keep the paper within a reasonable length and readability. Interested readers can refer to Wimsdoc or the source code for these details.

A few other topics are also omitted, such as facilities for user contributions.