In the MIT Department of Mathematics’ Undergraduate Seminar in Theoretical Computer Science, which is taken primarily by juniors and seniors, students write a term paper on a topic of their choice. To do so, they must find and read sources, including mathematics research articles. Attached are a suggested reading strategy (student resource) and an in-class activity designed to introduce students to the reading strategy and to familiarize them with some of the common features of mathematics papers that facilitate the finding of information within the paper. Course lead: Zachary Remscrim Communication lecturer: Susan Ruff

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The questions on this form guide students to provide effective critique of their peers’ presentations. The form includes the topics “Voice and body,” “Interaction with the audience,” “Structure,” and “Content.” Each topic contains some more specific sample questions to clarify the point and scope of the topic (e.g., “I could tell where the speaker was headed at all times.”)

Read more →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 →This one-page reading assignment presents questions for students to consider as they read a draft of one of their instructor’s published papers. This assignment precedes a workshop on how to write a paper, in which the students discuss the draft and a revised version of the paper as well as writing process. From Pedro Reis’ Undergraduate Seminar in Physical Applied Mathematics at MIT.

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 →This student information sheet is given to students to fill out on the first day of class to indicate their writing backgrounds and their interests relevant to the class. From Pedro Reis’ Undergraduate Seminar in Physical Mathematics at M.I.T.

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 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.

Read more →This lesson plan and handout are for an 80-minute workshop to prepare students to write their term papers. During the workshop, an instructor provides guidance for choosing an appropriate focus for the paper (counterexample: “Everything I know about the Island of Corsica”); students talk with classmates to focus their topics; and the class discusses rhetorical differences among papers, presentations, and psets; the writing in two versions of the same paragraph; the structure of a paper; LaTeX; and acknowledging sources. From Mia Minnes’ Undergraduate Seminar in Logic.

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