To help students learn to write proofs, Russell E. Goodman of Central College has developed Proof-Scrambling Activities. Students must correctly order the scrambled sentences of a proof. These activities help students identify when a proof is logically correct, to recognize how authors use words like “therefore,” “next,” etc., to indicate the direction of the logic, and to gain experience reading and comprehending proofs. Enclosed are two activities, a quiz, and notes for educators.

Read more →# Posts Tagged *Structure*

The article “Maximum Overhang” by Mike Paterson, Yuval Peres, Mikkel Thorup, Peter Winkler, and Uri Zwick won the 2011 David P. Robbins Prize, an MAA Writing Award. This pdf of the article is annotated to point out to students how to write a mathematics paper. The annotations address the structure and content of an introduction, how to integrate equations, text, and figures, how to guide the audience through the content, how to cite, etc. The article addresses the question of how far a stack of blocks can extend from the edge of a table. It was published in the American

Read more →These slides are for a workshop on how to write a math paper. They provide successive examples of good and better writing. In the class, students are asked to read each sample and assess how well it achieves the stated goals for the paper.

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 →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.

Read more →These 8-page notes address the parts of a paper; mathematical style for attribution, citation, and internal references; the distinction between belief and proof; and a miscellany of 15 common errors. These errors range from grammatical issues such as articles and comma splices to errors of precision, notational consistency, and sequencing of information. Examples are included.

Read more →These drafts of an article by Mark McLean illustrate how a proof can be improved by pulling out a lemma. Although the article is on an analysis topic beyond the understanding of Real Analysis students, Mohammed Abouzaid has drawn attention to the structure of the article by highlighting relevant guiding text, so the improvement caused by pulling out a lemma is clear.

Read more →This assignment guides students to choose a term paper topic that will enable them to “add value” beyond what is provided in their sources (e.g., explaining the material clearly to an audience of students, synthesizing the presentations in multiple sources, etc.). The assignment, which is from M.I.T.’s Principles of Applied Mathematics, includes a list of suggested topics in discrete applied mathematics.

Read more →Guidance from Steven Kleiman for how to write a math paper, written for a now defunct writing requirement but with much good general guidance. Because the guidance is written in the form of a journal article, the text file can act as a template for students to use to create their own papers. This zip file includes supporting style files (from M.I.T.’s Undergraduate Journal of Mathematics, no longer in publication). Before use, the extensions for math2e and thmp2e must be changed from .txt to .sty

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