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Expository Mathematics in the Digital Age - Introduction

Kyle Siegrist

Many of the words that have been used for decades to describe expository publications in mathematics no longer make sense in the digital age:

  • Authors are no longer just those whose works are printed in books and paper journals by commercial or institutional publishers. Increasingly, ordinary teachers and students create, re-use, and post expository mathematics on school web sites.
  • One posted, these works are published in the sense that they are immediately accessible to persons throughout the world. In principle, any school web site has the same reach as JOMA or the MAA. Professional journals and societies are no longer the gatekeepers of scholarship.
  • Web-based expository documents are no longer papers consisting of text (and the occasional figure) printed on paper. Increasingly, these documents combine expository text, rich graphics, audio and video clips, interactive mathlets, worksheets, source files, and other elements--elaborately hyperlinked to each other and to myriad other resources on the web.
  • Writers must do much more than just write. They must also program (often in several languages), compile, link, and design.
  • Readers do much more than just read. They also listen, watch, compute, and interact. In fact, the users of web documents are not just persons. At an intermediate level, web documents must be processed by hardware and software agents of all sorts: standard computers, hand-held devices, printers, search engines, mathematical software, and devices to help disabled persons.

Writing expository, web-based mathematics is difficult. As already noted, an author not only needs to have a deep understanding of the underlying mathematical topic and good general writing skills, but also programming skills, technical expertise, design skills, and an appreciation for the new possibilities that web technologies afford.

In the pages that follow, we will discuss "best practices" for expository mathematics in the digital age. Our hope is that this discussion will be helpful, not only for potential JOMA authors, but for ordinary teachers and students as well. Again, whether we publish in journals or not, many of us are authors and users of web-based materials.

For general web document, some basic "best practices" are now widely accepted by experts, although still largely unknown by average authors. Naturally, these general practices apply to mathematical exposition as well. By and large, they are based on two core principles: access and reuse.

Accessibility refers to the extent to which a web document can be processed by a variety of devices (hardware and software), depending on the user and the purpose, and with particular attention to persons with disabilities. To elaborate on our previous list, such devices include

  • ordinary computers with different platforms (hardware, operating systems, browsers).
  • hand-held devices such as PDAs, small tablet PCs, iPods
  • printers
  • readers for visually impaired persons
  • audio-to-text devices for hearing impaired persons.
  • search engines
  • computer algebra systems that could process the mathematics in the document

Reuseability refers to the ease of breaking a web document into separate parts that have value on their own, and can be reused by the author and by others. For mathematical articles, such components might include

  • fragments of expository text
  • mathematical expressions
  • mathlets
  • graphics
  • audio and video clips
  • worksheets in Mathematica, Maple and similar programs
  • source files for programming languages

For mathematical exposition, "best practices" are still evolving. JOMA hopes to encourage the discussion and to play a significant role in the formulation of these practices.

Kyle Siegrist, "Expository Mathematics in the Digital Age - Introduction," Convergence (May 2006)