Expository Mathematics in the Digital Age
The Basic Document and HTML
The Basic Structure
As noted in the Introduction, an expository, web-based mathematics document will typically have a number of elements that go beyond what is possible with ordinary print. The author should strive to make full use of the web as a medium for the communication of mathematics. Those "elements that go beyond print" include
Of course, very few expository articles will have all of these elements. But almost every expository article could benefit from some of these elements.
HTML, the Hypertext Markup Language, plays a special role as the lingua franca of the web. HTML provides the following essential services:
HTML is text-based and open source, so articles are easy to edit and rearrange. Portions can be extracted and reused.
An expository article should consist of basic exposition in HTML together with other elements (graphics, worksheets, mathlets, video) that enhance the mathematical exposition. These are the elements that go "beyond print"; HTML is the expository glue that holds them together. The hyperlinkng capabilities of HTML also allows the author to create documents with non-traditional structures, so that an article can have multiple paths. For example, an article might have an elementary path for students and a more advanced path for teachers. An article might have complicated or technical proofs in pop-up windows. For more information, see Mathematics with Structure and Style.
If possible, the basic expository part of a web-based article should not be encoded in Word, PDF, or other formats. These formats may be "standards" in the sense that they are widely used, but they are proprietary standards, controlled by specific corporations (Microsoft and Adobe for the examples just used), not open standards. The underlying files are not text-based, so editing, rearranging, extraction, and reuse are difficult or impossible. Worst of all, much of the inherent interactivity of the web is lost with these formats.