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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This one-page handout about acknowledging sources in mathematics papers addresses how to avoid using wording from sources and how to cite information or wording. Examples are included (with citation).
Read more →When you go to the trouble of writing an article for publication, it’s worth spending some time thinking about and composing an appropriate title. The title is your first chance to engage prospective readers—to get their attention immediately. A poorly chosen title can mean a significantly smaller audience than your work might deserve. In Writing Mathematics Well: A Manual for Authors (MAA, 1987), Leonard Gillman advised: “Keep your title short and include key words to make it informative.” Striking the right balance between brevity and informativeness (while still attracting attention), however, can be harder than it sounds. Consider, for example,
Read more →As a mathematician, Paul R. Halmos (1916-2006) made fundamental contributions to probability theory, statistics, functional analysis, mathematical logic, and other areas of mathematics. He was also widely recognized as a masterly mathematical expositor. And he served as editor (1981-1985) of the American Mathematical Monthly. Halmos described his approach to writing in an essay published in the book How to Write Mathematics (American Mathematical Society, 1973). One paragraph presents the essence of the process: “The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do
Read more →Many of the following resources were found by undergraduate researcher Noor Doukmak: How to give an effective math talk Giving Good Talks by Satyan L. Devadoss From the Early Career Section of Notices of the American Mathematical Society, Nov 2019 10 Ancient Rules for Giving a Conference/Seminar/Research Talk in Mathematics, by A. Kercheval From the Early Career Section of Notices of the American Mathematical Society, Nov 2019 How to Talk Mathematics by Paul Halmos Touches on the issues of simplicity, details, proofs, problems, organization, preparation, brevity, techniques, flexibility, and short talks. Talks are not the same as papers by Terry
Read more →[The following notes are from Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry at MIT. Many of the files below can be downloaded in one zip folder.] Here are some files to help you write mathematics in a way that is more professional in style and format. The following files are the two source files and two compiled versions of the guide, “Writing a Math Phase Two Paper:” piiUJM2.tex || figure.ps || piiUJM2.dvi || piiUJM2.pdf This guide gives a lot of tips on writing a short math paper, and also serves as a model of one.
Read more →The sheer volume of advice available “out there” on writing mathematics can be quite intimidating. Here’s a (nonexhaustive) list of interesting pieces. Many of these were found by undergraduate researcher Artur Araujo. Writing mathematics well (audience is mathematicians) Terry Tao’s blog contains several posts dedicated to this topic: On Writing links to many of Terry’s posts on various aspects of writing mathematics well. Be considerate of your audience. From the Early Career Section of Notices of the American Mathematical Society “Journaling” by Robert Lazarsfeld, Jan 2019 “Writing for Mathematical Reviews” by Kelly Jabbusch, Feb 2019 “Writing, and Reading, Referee Reports” by Arend Bayer,
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