Algebra Interactive grew out of algebra lectures given at the Eindhoven University of Technology, The Netherlands, over the past few years. It was developed as IDA: Interactive Document on Algebra. (We still refer to Algebra Interactive as IDA rather than AI.) Its aim is to bring elementary algebra to life through modern means, and provide students with a sophisticated learning environment with emphasis on computational and algorithmic aspects. New technology enriches the material in that

• many examples allow for experimenting,
• dynamic illustrations occur throughout the text,
• buttons enable focusing on specific aspects (proofs, examples, excercises, illustrations),
• on-line multiple choice tests are offered,
• on-line calculators pertaining to the subjects covered are available,
• various ways of cross referencing are supported.

Detailed information on the features of Algebra Interactive is given separately.

New technology

On the technological side, the text is written in HTML with its usual features, but the dynamics comes about through applets, javascripts and so-called gapplets that enable interfacing with the computer algebra package GAP (included on the CD-rom). The term gapplet is a contraction of course of GAP and applet. Gapplets usually show input-output fields, where the reader is invited to experiment with a specific kind of computation, thus illustrating our algorithm oriented approach. Applets provide visual illustrations of various notions related to, e.g., prime numbers, symmetry and permutations. In addition to their use in the gapplets, javascripts are used for handling the presentation of the text, e.g., for hiding/showing text.

Topics

Algebra Interactive covers topics ranging from arithmetic with integers and with polynomials (including modular arithmetic) to permutations in the first five chapters, and then unifies the many common aspects of these arithmetic structures in the remaining chapters on groups and rings.

To our students

Algebra Interactive offers a new challenge compared to traditional text books and we recommend that you grasp the material by experimenting with the examples, working through the exercises, testing yourself, etc. However, working with the interactive notes will not replace the full benefits of pad and pencil, it rather adds to them. So keep pad and pencil at hand while you work your way through.

OpenMath

Algebra Interactive is not the end of the story. It is part of the OpenMath project that ultimately aims at providing a flexible working environment for mathematicians and scientists using mathematics. Flexibility refers to such aspects as activating mathematical expressions in an electronic document, manipulating them by mathematical back engines (of which the reader need not be aware) and putting results back into the document.