Coordinating mathematical content and presentation markup in interactive mathematical documents

This paper presents a method for representing mathematical content and presentation markup in interactive mathematical documents that treats each view of the information on a separate and equal footing. By providing extensible, overridable, default mappings from content to presentation in a way that supports efficient mappings back from the presentation to the underlying content, a user interface for an interactive textbook has been implemented where the user interacts with high-quality presentation markup that supports user operations defined in terms of the mathematical content. In addition, the user interface can be insulated from content-specific information, while still being enabled to transfer that information to other programs for computation. This method has been employed to embed interactive mathematical content into the IBM techexplorer [11] Interactive Textbook for Linear Algebra. The issues involved in the implementation of the interactive textbook also shed some light on the problems faced by the MathML working group [6] in representing both presentation and content for mathematics for interactive web documents.