If you are comparing two numerical methods then

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source or obtained by Monte Carlo simulation. If you are comparing two numerical methods then instead of using run times provided by others you could do your own testing on your own machine. 6.4 When found, make a note of Whenever you use a reference for the first time, record it in some fixed place (a file card in a file box, a notebook or a file in your computer). Otherwise, you may find that, when you write up, you cannot remember where you found the result you need. Since the time scale for the essay is so short and the number of references that you are likely to use is small the advice just given may not be necessary now but if you go on to write a PhD it is vital. In the 1930’s many math- ematicians carried notebooks in which they jotted down problems, ideas, references and so on as they occurred to them. I suspect that this custom died out because it is easy to carry a large notebook in a suit pocket and hard to carry one in the back pocket of a pair of jeans, (‘Is that a Nachschrift in 26
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your pocket or are you just pleased to see me?’) Perhaps the custom should be revived with filofaxes. 7 Further advice 7.1 Books on writing There are several good books about writing. You should start with The Elements of Style by Strunk and White [12]. It is American and aimed at general journalism but has the virtue of being very short indeed. If you want something longer and British then The Complete Plain Words by Sir Ernest Gowers 11 [2] is worth reading. 7.2 And what they say Here is some of the advice given by such authorities. 1) Omit needless words. 2) Keep your sentences short. 3) Keep your paragraphs short. 4) Use active rather than passive forms of verbs. (Replace ‘It has been shown by Brown that the method works when n < 6.’ by ‘Brown showed that the method works when n < 6.’) The imperative is also useful, particularly in proofs. (‘Take n = 6.’) 5) Prefer the familiar word to the far-fetched. 6) Prefer the concrete word to the abstract. 7) Prefer the single word to the circumlocution. The final piece of advice is mine. 8) Use ‘we’ when you are doing something with the reader. ‘We see that F is closed.’ ‘We now check that G is Abelian.’ Use ‘I’ when expressing an opinion or (in later life) talking about something you have done. ‘I think method A is more transparent.’ ‘In an earlier paper [13] I showed that all primes (with at most one exception) are odd.’ 7.3 A digression It is clear that mathematics papers meant for an international audience should use simple English with as little decoration as possible. What is more interesting is that, for the last 200 years, this has been the preferred 11 Great-grandfather of our own Professor W. T. Gowers. 27
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style when the English write for the English. Good written English is mod- elled on good spoken English. Good English style should be invisible as a pane of glass leaving the reader free to concentrate on content.
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