[Math] English words in written mathematics

educationproof-writingreference-requestsoft-question

I recently marked over $100$ assignments for a multivariable calculus course. One question which a lot of people did poorly was proving a given set was open. Aside from issues relating to rigour and logic (or lack thereof), I noticed an issue that I wasn't as aware of before this experience. A lot of students used English words incorrectly (from a mathematical point of view) when writing sentences within their proof.

Some of the words/phrases I am referring to are:

  • As
  • Assume
  • Let
  • Suppose
  • Hence
  • Therefore
  • Such that
  • There exists

Is anyone aware of a reference which explains how to use these words and phrases (and others that frequently occur) in a mathematical context?

Best Answer

Charles Wells, The Handbook of Mathematical Discourse; it’s available as a PDF here. His site abstractmath.org may also be useful.

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