Mathematical Communication is a developing collection of resources for engaging students in writing and speaking about mathematics, whether for the purpose of learning mathematics or of learning to communicate as mathematicians.

Wording and punctuation

To learn the wording and punctuation conventions of mathematics, students benefit from individualized feedback on their writing and presentations.

Resources for Undergraduates

  • Stephen Maurer’s Undergraduate Guide to Writing Mathematics contains a glossary of mathematical terms as well as sections on when to use displays, saying what you mean, style, words vs. symbols, etc.
  • Some students may find math dictionaries to be helpful.
    • E. J. Borowski and J. M. Borwein’s Collins dictionary of mathematics is also available as the online database The MathResource Dictionary. Searching is free; browse for a fee.
    • J. A. Glenn and G. H. Littler, A dictionary of mathematics, 1984.
    • W. Karush, The crescent dictionary of mathematics, 1962.
      This dictionary includes terms from arithmetic through undergraduate-level topics such as game theory and linear programming.
    • G. James and R. C. James, Mathematics Dictionary, 2nd ed., D. Van Norstrand Co., 1959
  • This excerpt from Reuben Hersh’s “Math Lingo vs. Plain English: Double Entendre” on the website Cut the Knot gives many examples of differences in meaning between mathematical English and “plain English.” The entire article is published in The American Mathematical Monthly, vol 104, No 1, January 1997, pp 48-51.
  • Haynes Miller has some helpful observations about wording and style.  See Sections B and C of his Notes on Writing Mathematics.
  • Ivars Peterson makes important observations about wording for communication with non-mathematicians.
  • Stephen Maurer addresses common student confusion about equations, expressions, and functions by demystifying the difference with examples and counterexamples of correct uses of these terms.
  • Kevin Lee’s “Guide to Writing Mathematics” includes guidance and examples for how to use punctuation when combining equations and text.
  • Steven Kleiman’s “Writing a Math Phase Two Paper” includes some punctuation examples in Section 4.
  • 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.

Resources for K-12 educators and students

See further resources on the page of writing resources.

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