This brief fabricated sample of student writing was used in class to model peer critique (two instructors act as students, one of whom is critiquing the writing of the other). The sample addresses the question of whether there are “gaps” in the rational numbers. Written by Joel Lewis with modifications by Peter Speh and Mohammed Abouzaid.

Read more →# Posts Tagged *Real analysis*

This 6-page report on the initial version of MIT’s communication-intensive offering of Real Analysis discusses the relationship between the analysis lectures and the communication recitations, the percentage of the grade assigned to each, necessary staffing, the recitation activities and assignments, the teaching of LaTeX, and the support from Writing Across the Curriculum. A semester table summarizing recitation activities and assignments is included as are recommendations for future offerings of the course.

Read more →Two proofs of the fact that 1+2+ … + n = n(n+1)/2. One proof uses induction; the other organizes the terms of twice the sum so each of n pairs sums to n+1. These proofs are used to start a class discussion about elegance.

Read more →A beamer presentation titled “More with LaTeX: Tools for slides, graphics, bibliographies, and all that” Also addresses various pros and cons of giving slide presentations in mathematics.

Read more →This (fabricated) draft student paper is designed to start a class discussion about when conceptual explanations are needed in mathematical writing. The paper is about an algorithm for finding square roots. The first proof shows that the algorithm is correct, but the point of the second proof is never clearly stated (it shows that the algorithm is efficient). Written by Joel Lewis for M.I.T.’s communication-intensive offering of Real Analysis, based on Rudin’s Exercise 16 in Chapter 3.

Read more →This intentionally mediocre presentation of the proof that convergent implies Cauchy is used to begin a class discussion of when the motivation for a proof should be given before the proof and when it should be given after the proof. Written by Joel Lewis.

Read more →These sample peer critiques of writing are used to generate discussion about effective critique, to prepare students for critiquing each other’s mathematics papers. From MIT’s communication-intensive offering of Real Analysis.

Read more →This assignment from the second week of Real Analysis (Fall 2009) prods students to think rigorously. It includes questions requiring students to translate notation and to learn to LaTeX a table. Developed by the 18.100C team, especially Joel Lewis and Craig Desjardins.

Read more →This assignment is from M.I.T.’s communication-intensive offering of Real Analysis. After students receive peer critique on their proofs, they are assigned to revise the proofs. This assignment gives some brief revision guidance.

Read more →These three samples of proofs by contradiction are used to illustrate when contradiction should (and shouldn’t) be used as a proof strategy. Students identify which proofs shouldn’t use contradiction and suggest revisions of those proofs. Developed by Todd Kemp and Joel B. Lewis.

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