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 *Wording*

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 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 →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

Read more →One of the things that irritates me most when I’m reading, whether it’s a novel, a newspaper article, or a mathematics paper, is the misplaced “only.” If you write “Here we only calculate the position of two vertices” you probably mean “Here we calculate the position of only two vertices.” The word “only” is there to emphasize something, and it should be as close as possible to what you want to emphasize to be effective and to convey the desired meaning. As described in Mathematical Writing (MAA, 1989), newspaper copy editor Rosalie Stemer gives the following sequence of examples to

Read more →Terms such as “clearly,” “obviously,” and “it can easily be shown that” do not belong in the mathematical literature. Authors who use them (and editors who allow them) do a great disservice to their readers. Jokes about the mathematical abuse of these terms have been around for a long time, including the following translations of “clearly” and its kin: Clearly: I don’t want to write down all the “in-between” steps. Trivial: If I have to show you how to do this, you’re in the wrong class. Obviously: I hope you weren’t sleeping when we discussed this earlier, because I refuse

Read more →The language of mathematics can throw up barriers to broad dissemination of information about mathematics. Mathematical statements are supposed to be precise, devoid of the ambiguities of ordinary speech. The language is unusually dense and relies heavily on a specialized vocabulary. The meaning and position of every word and symbol make a difference. Mathematician William Thurston once expressed the difference between reading mathematics and reading other subject matter in this way: “Mathematicians attach meaning to the exact phrasing of a sentence, much more than is conventional. The meanings of words are more precisely delimited. When I read articles or listen to speeches

Read more →To learn the wording and punctuation conventions of mathematics, students benefit from individualized feedback on their writing and presentations. Resources for Undergraduates Stephen Maurer’s Undergraduate Guide to Writing Mathematics contains a glossary of mathematical terms as well as sections on when to use displays, saying what you mean, style, words vs. symbols, etc. Some students may find math dictionaries to be helpful. E. J. Borowski and J. M. Borwein’s Collins dictionary of mathematics is also available as the online database The MathResource Dictionary. Searching is free; browse for a fee. J. A. Glenn and G. H. Littler, A dictionary of

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