More Than Just a Grade: The HOM SIGMAA Student Contest Fosters Writing Excellence at UMKC - Appendix 1 (Writing Mathematics)

Richard Delaware (University of Missouri – Kansas City)

This appendix includes course requirements and advice on writing mathematics that I share with students in my course.

Basic Technical Paper Requirements in my Course

  • Your paper must be typed.
  • 12 point size font, Times New Roman preferred
  • Double spaced for main text
  • Single spaced for document or separate line quotations
  • One inch margins
  • Page numbers
  • Word count at top right of first page
  • 4,000–5,000 words usually, not including title page and works cited pages
  • Later: A title page with working title, your name, the course, the date, draft number
  • Later: Works cited page, numbered sequentially, listed alphabetically by first author, following MAA rules
  • Your comments within a document text must be in [square brackets].
  • Adding line breaks to the document text to break it into coherent parts is OK.
  • Practice use of MS Equation editor, or other mathematical symbolic software
  • Practice how to draw and include sketches or images; hand drawn figures are OK during draft stages


Advice from Writing Experts

From Strunk and White, The Elements of Style, 1972 edition:

  • II-10:   Use the active voice.
  • II-11:   Put statements in positive form.
  • II-12:   Use definite, specific, concrete language: “deal in particulars and report the details that matter.”
  • II-13:   Omit needless words.
  • II-15:   Express co-ordinate ideas in similar form. [Extremely important in mathematics.]
  • II-16:   Keep related words together. [Also, keep related pictures together with related words.]
  • V-5:     Revise and rewrite.
  • V-6:     Do not overwrite.
  • V-7:     Do not overstate.
  • V-16:   Be clear.

The references below, such as [6, p. 10], are to the list of publications about writing mathematics that follow these bullet points:

  • From [6, p. 10]: “All the best writers whom I know read their work aloud to themselves. Reading your words aloud forces you to make sense of what you have written, and to deliver it as a coherent whole. If you have never tried this technique, then your first experience with it will be a revelation.”
  • From [6, p. 92]: “Envision your reader sitting on a park bench reading your expository [paper], or putting his feet up and drinking a cup of coffee while reading. Do not imagine your reader with a pencil gripped in his fist, slaving away over each detail of your paper.”
  • From [2, p. 8]: “Keep the reader informed of what you are doing and of how things stand. I have always enjoyed reading Sierpinski: first he tells you what he is going to do, then he does it, then he tells you he did it. … If you use a key term or symbol after a long spell without it, recall its definition or refer to where it was introduced. Your readers will be grateful.”
  • From [2, p. 20]: “Write simple unaffected prose. Writing is harder than speaking because your tone of voice isn’t available to help make your point clear. Keep sentences crisp—think of what you want to say and say it. Mathematics is hard enough to read without convoluted writing that makes it harder.”
  • From [5, p. 94]: “All writing benefits from revision. Your first attempt can always be made clearer, more concise, more forceful. Effective revision is a skill that is acquired through practice. … Put a draft aside for a few days, so that you can examine it with a fresh mind. Then analyze the draft in different ways. Read it aloud and listen to the rhythm. Read it at high speed. Does the text flow? Are the sentences of varying length? Read at the page level, focusing on the shape and the density of ink on the page. … Is there a good balance between equations and text? Does the paper look inviting? Do the key ideas stand out?”
  • From [7, p. 90]: “There is a place for rigor in every kind of learning. All of us need to sharpen our thinking, and when we are challenged we should have to become more precise about what it is we are saying, how we are saying it, whether we are marshalling good arguments, and the like.”
  • From [8, p. 11]: “Experienced writers know that they have to get something down on paper (or up on the screen) as fast as they can, just to have a draft that they can revise into a better one. … When you revise your early confusion into something clearer you better understand your own ideas. And when you understand your ideas better, you express them more clearly, and when you express them more clearly, you understand them even better … and so it goes.”
  • From [9, p. 31]: “Care lavished on expression is not some optional embellishment bestowed upon your work; it is the means through which your work begins to exist. Your research turns up raw materials—very raw. Writing and rewriting make them into finished, usable products. Until brought out in full view by the best possible arrangement of words, your results remain incomplete, doubtful, hidden from every mind but your own. And your own, as your first draft shows, is none too clear.”
  • From [9, p. 228]: “Rewriting is nothing but able tinkering. … Only an apprenticeship under a vigilant critic will gradually teach a would-be writer how to find and correct all the blunders and obscurities that bespangle every first draft.”
  • From [9, p. 230]: “You discover what you really think by hacking away at your first spontaneous utterance.”


References on Writing Mathematics

  1. How to Write Mathematics, Norman Steenrod, Paul Halmos, Menahem Schiffer, Jean Dieudonne, American Mathematical Society, 1973, 1981, 64 pages
  2. Writing Mathematics Well: A Manual for Authors, Leonard Gillman, Mathematical Association of America, 1987, 49 pages
  3. Mathematical Writing, Donald Knuth, Tracy Larrabee, Paul Roberts, MAA Notes, Number 14, Mathematical Association of America, 1989, 115 pages
  4. Using Writing to Teach Mathematics, Edited by Andrew Sterrett, MAA Notes, Number 16, Mathematical Association of America, 1990, 139 pages
  5. Handbook of Writing for the Mathematical Sciences, Nicholas Higham, Society for Industrial and Applied Mathematics, 1993, 241 pages
  6. A Primer of Mathematical Writing, Steven Krantz, American Mathematical Society, 1997, 223 pages
  7. Writing in the Teaching and Learning of Mathematics, John Meier, Thomas Rishel, MAA Notes, Number 48, Mathematical Association of America, 1998, 100 pages
  8. Style: Ten Lessons in Clarity and Grace, 6th Edition, Joseph M. Williams, Addison Wesley Longman, 2000, 309 pages
  9. The Modern Researcher, 3rd Edition, Jacques Barzun, Henry F. Graff, Harcourt Brace Jovanovich, 1977, 378 pages