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Essay - How to Write a Part III Essay T W Krner o Trinity...

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How to Write a Part III Essay T. W. K¨orner Trinity Hall These unofficial notes replace an earlier set by Marj Batchelor which were becoming illegible through repeated photocopying. Many of the key pieces of advice are taken almost word for word from her notes though the elegant picture of a small crustacean has, I am afraid, vanished. I should be glad to have suggestions for additions, correc- tions and improvements (by e-mail to [email protected] or oth- erwise) both from essay writers and essay markers. These notes were last revised in 2009. Contents 1 Introduction 3 1.1 What is the essay? . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Essay length . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Shakespeare it is not . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Nor is it research . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Technical points 6 2.1 How to count words . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Meetings with your assessor . . . . . . . . . . . . . . . . . . . 6 2.3 How to contact your assessor . . . . . . . . . . . . . . . . . . . 6 2.4 Unfair means . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Making a timetable . . . . . . . . . . . . . . . . . . . . . . . . 7 3 How to read a paper 8 3.1 Why are mathematics papers hard to read? . . . . . . . . . . 8 3.2 How do we read a proof? . . . . . . . . . . . . . . . . . . . . . 9 3.3 Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Some papers are just long proofs . . . . . . . . . . . . . . . . 9 3.5 But all papers have context . . . . . . . . . . . . . . . . . . . 10 3.6 A possible moral . . . . . . . . . . . . . . . . . . . . . . . . . 10 1
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4 How to write your essay 11 4.1 Your purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 Your topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 The crustacean style . . . . . . . . . . . . . . . . . . . . . . . 11 4.4 Your outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.5 Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.6 The introduction . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.7 The conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.8 A note on omissions . . . . . . . . . . . . . . . . . . . . . . . 16 4.9 Layout is important . . . . . . . . . . . . . . . . . . . . . . . . 16 4.10 But layout is no substitute for clear explanation . . . . . . . . 17 4.11 Stylistic points . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Starting, keeping going and stopping 19 5.1 Word processing . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 The first draft . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.3 The daily task . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.4 What to do when you are stuck . . . . . . . . . . . . . . . . . 21 5.5 Transferring the first draft to your word processor . . . . . . . 21 5.6 Standard advice on word processing . . . . . . . . . . . . . . . 22 5.7 Revision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.8 Revise, rewrite or reject . . . . . . . . . . . . . . . . . . . . . 22 5.9 Know yourself . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.10 Abandoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.11 Stopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6 Sources 24 6.1 Form of acknowledgement . . . . . . . . . . . . . . . . . . . . 25 6.2 Secondary references . . . . . . . . . . . . . . . . . . . . . . . 25 6.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.4 When found, make a note of . . . . . . . . . . . . . . . . . . . 26 7 Further advice 27 7.1 Books on writing . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.2 And what they say . . . . . . . . . . . . . . . . . . . . . . . . 27 7.3 A digression . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.4 Mathematical writing . . . . . . . . . . . . . . . . . . . . . . . 28 7.5 Valediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2
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1 Introduction It is as foolish to write an essay on essay writing as it is to lecture on lecturing or give a course on teaching. We do not learn to write mathematics by following a set of rules. We learn by imitating other mathematicians or avoiding their mistakes 1 . Eventually, with practice, we acquire our own voice. On the other hand, there are a few tricks of the trade which will convert a ghastly expositor into a bad one, a bad expositor in to a moderate one and a moderate one into a good one. I shall try to give some of them. You may disagree with some or all of what I say. That does not matter. What matters is that you should think about the problems of mathematical writing. 1.1 What is the essay? Every Part III student has the option of replacing a three hour examination paper by an essay. In the ‘standard essay’ you are asked to read two or three mathematics papers and then write a connected account of their contents.
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