# A Brief Introduction to Mathematical Writing

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2 Krantz [1997], Higham [1998], and Knuth et al. [1989]. You might also consult Turner [b] for a brief introduction to proofs. If you plan to do much mathematical writing, I suggest learning to use L A TEX, which is the standard tool to typeset papers in mathematics, physics, economics, and other disciplines. In this case, you might find Turner [a] for some basic L A TEX typesetting commands. 2 Mathematical Formulae Mathematical writing contains one element that is not found in other writing: formulae. You must keep several things in mind when you incorporate mathematical formulae into your writing. 2.1 Combining Words and Formulae You must incorporate your formulae and equations into your sentences using all the standard rules of English. Symbols may correspond to different parts of speech. They may form a complete sentence: = 2. 3xy < 2. 5x R. 9 s t. In this example, the symbols =, <,, and act as verbs. On the other hand, an expression such as 5x 2 y 10y contains no verb and thus is not a complete sentence. Read these expressions aloud to hear the difference. You must contain formulae and equations in complete sentences with proper punctuation. In particular, every sentence must end with a period. Consult your style manual for the rules regarding other punctuation marks. Pay particular attention to the colon :. Students often misuse it. It should only follow an independent clause that can stand on its own as a sentence. Consider this example: We can use the distance formula d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 to determine the distance between any two points (x 1, y 1 ) and (x 2, y 2 ) in R 2. For our example, (x 1, y 1 ) = ( 1, 16) and (x 2, y 2 ) = (3, 1), so plugging these values into the distance formula tell us the distance between the two points: d = (3 ( 1)) 2 + (1 16) 2 = ( 15) 2 =

7 Many writers use the first person such as I and we to avoid the passive voice. Be careful, though. Overusing the first person can turn off readers, too. Remember to allow other objects to be active: results can mean something, data can show something, etc. References Diana Hacker. A Pocket Style Manual. Bedford/St. Martin s, Boston, MA, 4th edition, Diana Hacker. Rules for Writers. Bedford/St. Martin s, Boston, MA, 5th edition, Nicholas J. Higham. Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2nd edition, Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts. Mathematical Writing. Mathematical Society of America, Washington, DC, Steven G. Krantz. A Primer of Mathematical Writing. American Mathematical Society, Providence, RI, White Strunk, Jr. and E. B. White. The Elements of Style. Allyn & Bacon, Needham Heights, MA, 4th edition, William J. Turner. Basic L A TEX typesetting. a. William J. Turner. A brief introduction to proofs. b. 7

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