Mathematical Writing - Vivaldi Franco 2014
Preparation and Structure
Some Writing Tips
There are things one must keep in mind when preparing any document.
· Begin by writing your document in draft form, or at least write down a list of key points. Few people are able to produce good writing at the first attempt.
· Consider the background of your readers; are they familiar with the meaning of the words you use? It’s easy to write a mathematics text that’s too difficult; it’s almost impossible to write one that’s too easy.
· Form each sentence in your head before writing it down. Then read carefully what you have written. Read it aloud: how does it sound? Have you written what you intended to write? Is it clear? Don’t hesitate to rewrite.
· Split the text into paragraphs. Each paragraph should be about one ’idea’, and it should be clear how you are moving from one idea to the next. Be prepared to re-arrange paragraphs. The first idea you thought of may not have been the best one; the sequence of arguments you have chosen may not be optimal.
· When you finish writing, consider the opening and closing sentences of your document. The former should motivate the readers to keep reading, the latter should mark a resting place, like the final bars in a piece of music.
· Word processing has changed the way we write, and often a document is the end-product of several successive approximations. After prolonged editing, one stops seeing things. If you have time, leave your document to rest for a day or two, and then read it again.
Exercise 1.2
Improve the writing, following the guidelines given in this chapter.
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Footnotes
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Abbreviation for the Latin exempli gratia, meaning ’for the sake of example’.
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Abbreviation for the Latin et cetera, meaning ’and the rest’.
3
If necessary, consult a thesaurus.
© Springer-Verlag London 2014