How to write a Part III Essay: From Outline to Essay
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1 Fundamentals How to write a Part III Essay: From to Essay Julia Goedecke Graduate Education Officer, DPMMS 3 February 2016, Wednesday Part III talks Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
2 Fundamentals 1 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion 2 3 Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
3 Overview Fundamentals Main Points Transfer of Understanding. Own your essay. Crustacean style: Structure visible. Be ruthless in editing. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
4 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion 1 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion 2 3 Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
5 Purpose of Essay Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion AIM Transfer of Understanding If this aim is met, then secondary aims follow. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
6 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion Not Shakespeare No elegant prose required. Clear mathematics required. Clear explanations required. Not Research Research is hard. (PhD: 3 years to get one good original idea) Writing maths is hard. Reading maths is hard. Use essay to get practice in reading and writing mathematics. (Some exceptions, e.g. project-, data- or experiment-based essays: Essay setter will tell you.) Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
7 Something New Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion Don t just copy what you ve read. Your own judgement of what to include, what to leave out. Your own overview/structure of the material. Your own (selection of) examples. Your own connections between results, examples, techniques... Your own way of explaining proofs/techniques/experimental results/physical insight. Sometimes: your own proof of a known result/ interpretation of experiment/heuristic argument... Rarely: your own extension of a result/experiment... Make it your own! Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
8 Fundamentals Principle of technical writing Essay: What is it? Crustacean style Introduction and Conclusion Aim is: To explain. Make it easy for reader to grasp the essentials. Sign-post important definitions/results/techniques... Achieve this through crustacean style of writing. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
9 Fundamentals Crustaceans vs Vertebrates Essay: What is it? Crustacean style Introduction and Conclusion Vertebrates - Skeleton within Appropriate for Novels. Key pieces of information buried mid-paragraph. Construction/plan of plot not visible from outside. Crustaceans - Skeleton outside Use for (front page reporting and) Mathematics. Organisation and structure visible at a glance. First paragraph shows content of section, etc. Important pieces of information highlighted, not burried. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
10 Fundamentals Introduction and Conclusion Essay: What is it? Crustacean style Introduction and Conclusion These are important! Introduction Advertisement and map. Big picture. Conclusion To round off. Final insight? Tantalising open questions? Further directions? Short overview/placing in larger context? Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
11 Fundamentals 1 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion 2 3 Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
12 Fundamentals Recall How to give a talk. Prepare a Part III Seminar talk on essay. One focus for talk. Slightly more for essay: two or three connected foci. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
13 : Judgements Fundamentals What material to include? What order to present things? What details to include?... Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
14 Fundamentals What material to include? Some main core expected by essay setter: talk to them. Choose content to make a coherent whole. Background (e.g. from lectures) can usually be assumed. Don t write a book or PhD thesis! Better to explain less material very well than lots of material superficially. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
15 Fundamentals What order to present things? Difference between educational order and logical order. Example Point of essay is Theorem A and Corollary B, which depend on Lemmas 1,2,3 (tedious, not illuminating). Organisation: 1 Introduction 2 Statement of Lemmas 1,2,3 3 Statement and Proof of Theorem A 4 Statement and Proof of Corollary B 5 Proofs of Lemmas 1,2, Conclusion Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
16 Fundamentals What details to include? Pure Maths Transfer of understanding! Important proofs need to be there. General case needed or only special case? Giving main ideas/steps of a proof often shows more understanding than writing out full proof. For hard/long proof could explain on example/simple case. Full proofs for everything or not: expectations differ. Check with Essay Setter! Further developments etc. can be summarised. Topic as tree : can assume roots and prune branches, but can t remove section of trunk. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
17 Fundamentals What details to include? Transfer of understanding! Applied Maths One view-point: Include details of model/experiment/calculation that are essential for interpretation/understanding of scientific conclusions. Don t include technical details if not essential for understanding. Different Essay Setters might have different views, check! Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
18 Fundamentals What details to include? Theoretical Physics One view-point: Give evidence that you ve done the calculations yourself. Make clear you are a mathematician who understands what s going on rather than a (very intelligent) lawyer who has reviewed and paraphrased some maths papers. Different Essay Setters might have different views, check! Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
19 Fundamentals Typesetting vs handwriting For first draft, use pen(cil) and paper! Why? Concentrate on mathematics, not layout. Concentrate on global shape of essay, not local. Word processing encourages prolixity, repetition and slack construction. Don t spend time on typesetting equations, diagrams,... Write first draft quickly. Don t refer to papers/books at this stage. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
20 Revision process Fundamentals Separate writing and editing/revision process! Print out double spaced. Put on editor hat and be ruthless. Repeat several times. Penultimate draft: give to essay setter. Write Acknowledgements after this. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
21 Revise or Rewrite Fundamentals REVISION mostly is: changing punctuation, changing word here and there, inserting extra step in an argument,... Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
22 Revise or Rewrite Fundamentals REVISION mostly is: changing punctuation, changing word here and there, inserting extra step in an argument,... More serious changes needed: REWRITE passage. Will flow better than hacked about original. Piecemeal revision likely to produce inconsistencies. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
23 Revise or Rewrite Fundamentals REVISION mostly is: changing punctuation, changing word here and there, inserting extra step in an argument,... More serious changes needed: REWRITE passage. Will flow better than hacked about original. Piecemeal revision likely to produce inconsistencies. Alternative to revision and rewriting: OMISSION. If it doesn t fit even after rewriting: leave out. Hard to do, but sometimes necessary. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
24 Fundamentals 1 Fundamentals Essay: What is it? Crustacean style Introduction and Conclusion 2 3 Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
25 Essay setter Fundamentals? When should I talk to/contact my essay setter? (When you decided to do the essay.) When you have an outline. When you have penultimate draft. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
26 Essay content Fundamentals? How can I compress the contents of three books/papers into 8000 words? Don t try! (That is part of the challenge.) Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
27 Collaboration Fundamentals? May I talk to research students while I m learning the material? Yes, BUT: acknowledge students by name.? May I talk to other Part III students while I m learning the material? Yes, BUT: acknowledge students by name.? May I compare notes/get help while writing the essay? No. (Stop collaborating at First Draft.) Faculty plagiarism guidelines Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
28 Writing resources Fundamentals? Are there any other resources about writing? Marj Batchelor Get Writing Tom Körner How to write a Part III Essay Strunk and White, The Elements of Style. (Moore Library, PE1408.S ) Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
29 Summary Fundamentals Main Points Transfer of Understanding. Own your essay. Crustacean style: Structure visible. Be ruthless in editing. Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
30 Fundamentals Go and write good essays! Julia Goedecke (DPMMS) From to Essay 03/02/ / 28
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