This worksheet is about how changing the order of quantifiers changes the meaning of a mathematical statement. It was created by Todd Kemp and modified by Kyle Ormsby for M.I.T.’s communication-intensive offering of Real Analysis.
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This simple form guides students to critique each other’s presentations as well as to jot notes for themselves about strategies to use and pitfalls to avoid when they give their own presentations. Because this form is simple it’s easy for students to use, but some guidance and encouragement may be needed from the instructor for students to go beyond the basic “It was good.”
Read more →This case study describes an e-mail flame war. Discussion questions guide students to identify why each participant acted as they did and at which stages the flame war could have been diffused. Attribution for the case study goes to Les Perelman, and attribution for the discussion questions goes to Susan Ruff.
Read more →This worksheet, compiled by Susan Ruff, is used after a mini-lecture on information order and connectivity. The worksheet enables students to check and solidify their understanding of how to order information within sentences to strengthen connectivity between sentences. From M.I.T.’s communication-intensive offering of Real Analysis.
Read more →Two samples of the same writing, labeled # and %, are used to start a discussion about audience preferences and to illustrate how to order information to create connectivity. Students then test their understanding by revising the third sample. This file is set up so that if it is printed 2-sided, the samples # and % appear on separate pieces of paper for ease of comparison. Written by Joel Lewis.
Read more →This proof of the Cauchy-Schwarz Inequality is used to start a discussion about proof elegance. The class compares this proof with the proof of the Cauchy-Schwarz inequality given in Proofs from the Book by Aigner and Ziegler. The class discusses which proof one would discover first and how it’s a good idea, after having proved something, to think about rewriting it. This writing sample was developed by Mohammed Abouzaid and Peter Speh.
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