Choosing appropriate notation is an important aspect of mathematical communication.
- be simple
- be memorable
- conform to conventions
Information about using notation in mathematics is presented in the following resources:
- Leonard Gillman’s “The Use of Symbols: A Case Study,” Writing Mathematics Well: A Manual for Authors, The MAA, 1987, pp 37-44.
A case study of how to simplify the notation in a symbol-laden article.
- Atish Bagchi and Charles Wells’ “On the Communication of Mathematical Reasoning,” PRIMUS vol. 8, pages 15-27 (1998).
This article addresses conventions and pitfalls related to various aspects of notation and wording.
- Eric Schechter’s “Common Errors in College Math”
This online compendium of common student errors includes many examples relating to notation and to expressing mathematics symbolically.
- Stephen Maurer’s Undergraduate Guide to Writing Mathematics discusses notation in many places, including the sections “Expressions and Statements” (9.7), “Symbols and Fonts” (9.17), “Words or Symbols?” (9.21), and in the appendix of Symbol Tables.
- Undergraduates often have difficulty translating between notation and “natural language.” To help students with this difficulty, see this lesson plan about translating between notation and words from M.I.T.’s communication-intensive offering of Real Analysis.
- Michael Downes’ Short Math Guide for LaTeX explains how to use LaTeX to set notation, and includes occasional commentary about when certain notation should be used.
- “Mathematics as a Language” from the website Cut the Knot
This blog points out the power of mathematical notation by comparing the original statements of some theorems to their statements using modern notation.
- “Mathematical Notation: Past and Future” by Stephen Wolfram, 2000. Transcript of a keynote address presented at MathML and Math on the Web: MathML International Conference 2000
Please feel free to contribute additional resources for this page (e.g., a glossary of symbols providing common meanings of various symbols in different areas of mathematics).