¶¶Òõ¶ÌÊÓƵ

Before you start your Honours or Project year, you should speak to members of staff about possible thesis topics. Find out who works in the areas that you are interested in and who you find it easy to talk mathematics with. If at all possible, settle on a topic and supervisor before the start of the first semester of your Honours or Project year.

Most students see their supervisor about once a week, although this is usually open to negotiation between the student and the supervisor. Even if you haven't done much between visits it is a good idea to have a regular chat so that your supervisor can keep track of how you are going. You can expect your supervisor to:

• Help you select - and modify - your topic.
• Direct you to useful references on your topic.
• Help explain difficult points.
• Provide feedback on the direction of your research.
• Read and comment on drafts of your thesis.
• Help prepare you for your talk.
• Give general course advice.

Your thesis or project report is an overview of what you have been studying in your Honours or Project year. Write it as if you were trying to explain the area of mathematics or statistics that you have been looking at to a fellow student.

• Include an introduction that explains what the project is all about, and what its contents are. (It is sometimes better to leave writing this part to the end!) For many reports, a conclusion or summary is appropriate.
• Your thesis should be a coherent, self-contained piece of work.
• Your writing should conform to the highest standards of English. Aim at clarity, precision and correct grammar. Start sentences with capital letters and end them with full-stops. Don't start sentences with a symbol.
• Take great care with bibliographic referencing. Wherever some material has an external source, this should be clear to the reader. Don't just write in the introduction: 'This report contains material from [1],[2] and [3]' - give the references for the material wherever it is used. Don't gratuitously pad your reference list with references that are not referred to in the text. Check current journals for acceptable referencing styles.
• Be careful not to plagiarise. What constitutes plagiarism is perhaps a little different in mathematics and statistics compared to some other subjects since there is a limit to how different you may be able to make a proof (at least in its basic structure). We do, however, expect the report to be written in your own words. A basic rule is: if you put a fact or an idea in your report which is not your own, the reader should be able to tell where you got this fact or idea.
• The University has  which all students should familiarise themselves with.

Generally, mathematics reports and theses are almost always typed in LaTeX. If you are going to type it yourself, you should allow a certain amount of time to become familiar with this software. Indeed, starting to learn LaTeX well before you actually want to write is a very good idea.

You should not underestimate the time it takes to produce a polished document. You will almost certainly need several drafts. It is very difficult to concentrate on getting the mathematics, spelling, grammar, layout, etc., all correct at once. Try getting another student to proofread what you have written - from their different viewpoint they may pick up on lots of things that you can't see.

P R Halmos (1970) in How to write mathematics, Enseignement Math. ((2) 16, 123-152) has the following advice:
"The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do so, and to do it clearly:

• you must have something to say (i.e., some ideas), and you must have someone to say it to (i.e., an audience)
• you must organize what you want to say, and you must arrange it in the order you want it said in
• you must write it, rewrite it, and re-rewrite it several times
• and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation.

That's all there is to it."

His other advice includes:

1. Say something: "To have something to say is by far the most important ingredient of good exposition---so much so that if the idea is important enough, the work has a chance to be immortal even if it is confusingly misorganized and awkwardly expressed..... To get by one the first principle alone is, however, only rarely possible and never desirable."
2. Audience: "The second principle of good writing is to write for someone. When you decide to write something, ask yourself who it is that you want to reach." Your broad audience will be fellow Masters and Honours students, who may not be experts in your thesis topic. "The author must anticipate and avoid the reader's difficulties. As he(/she) writes, he(/she) must keep trying to imagine what in the words being written may tend to mislead the reader, and what will set him(/her) right."
3. Organise: "The main contribution that an expository writer can make is to organize and arrange the material so as to minimize the resistance and maximize the insight of the reader and keep him(/her) on the track with no unintended distractions". 
4. Think about the alphabet: "Once you have some kind of plan of organization, an outline, which may not be a fine one but is the best you can do, you are almost ready to start writing. The only other thing I would recommend that you do first is to invest an hour or two of thought in the alphabet; you'll find it saves many headaches later. The letters that are used to denote the concepts you'll discuss are worthy of thought and careful design. A good, consistent notation can be a tremendous help".
5. Write in spirals: "The best way to start writing, perhaps the only way, is to write on the spiral plan. According to the spiral plan the chapters get written in the order 1,2,1,2,3,1,2,3,4 etc. You think you know how to write Chapter 1, but after you've done it and gone on to Chapter 2, you'll realize that you could have done a better job on Chapter 2 if you had done Chapter 1 differently. There is no help for it but to go back, do Chapter 1 differently, do a better job on Chapter 2, and then dive into Chapter 3... Chapter 3 will show up the weaknesses of Chapters 1 and 2".
6. Write good English: "Good English style implies correct grammar, correct choice of words, correct punctuation, and, perhaps above all, common sense."

More information on how to write mathematics:

• Lee, K. A guide to writing mathematics
• Lee, K. Some notes on writing mathematics 
• Jackson, M. Some notes on writing in mathematics

• Honours thesis

• Postgraduate Coursework Project

• Third Year Project Courses