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General Projects Advice

• 1. Your project report should aim to inform and empower the reader about its subject
  (do not think of it as you showing off to your teacher).
  In particular do not forget to say at the beginning what the reader can expect to get out of reading the report.
  It might be helpful to have a specific idea of the kind of reader you are aiming at (see below for a suggestion), and of why it is that _you_ are in a position to empower them with your report. (Indeed, explain both of these things at the start of the report!)
• 2. Your project report should be your job application "calling card".
  This is a very useful perspective on report writing, giving a good example of the kind of `reader' to have in mind in item 1. above. Think about it! No prospective employer thinks of you in the way your teacher thinks of you. They do not employ you in order to assess you! They employ you to get the job done - to empower them to get the job done - by any means necessary. There is no point in showing off as such. Just show the reader that you can empower _them_.
• 3. Plagiarism? No! Why!?
  Well, the answer is implied by 1. above. There is no point in plagiarism. It does not empower the reader. _Tell_ the reader your sources. This empowers them.
  So instead of hiding your sources, have Plenty of References!
• 4. Unless it clearly empowers the reader (which is very rare), then... NO HISTORY! (if your project is in History of Maths then this is different - but then it won't be a project set or assessed by me!)
  The simplest thing is - if you found that you wrote some History in your draft project, then just DELETE it. This is a maths project not a history project.
  There are _no_ marks available for History stuff in a normal Maths project. But you can lose marks by burying the good stuff in irrelevant stuff!
• 5. Do not use terms you have not defined.
  Do not define something using terms you have not yet defined!
  For example do not say "Definition: The Linking number of a link is ..."
  if you have not already defined what a _link_ is!
  You can pass the job of defining "link" (or indeed any other term you use) on to a good reference where it is defined - that is fine.
  But do this _before_ you use the term yourself.
• 6. Have an informative Title (one or two lines), an Abstract (one or two paragraphs), and an Introduction (one or two pages).
  These should (as quickly as possible) tell the reader if this document is `for them'.
  Then have some Sections on Method and Results. Then a Conclusion.
• 7. Compare and constrast.
  This is a Science project, so show that your work has been rigorously tested by comparing and contrasting approaches.
  For example, if you use references or sources at somepoint, maybe you can say something useful about the set of possible references you could have used at this point, and why you chose the subset you chose.
  ...Perhaps you chose the _original_ source (a good choice), or perhaps you chose one which you feel is particularly clear on the point in question!?
• 8. Write as a Mathematician. Whoever your audience is, _this_ is what you bring to the party!
  Write proper mathematics at every possible opportunity. Mathematics is the language of truth and clarity (these are hard things to achieve! but it is worth trying).
• 9. Give references something like this:
  "The definition of a knot is given in [Birman68] (Definition 3.7). See also [Crowell-Fox66] (Definition 1.11). Although the wording is slightly different in [Crowell-Fox66], it will be clear that these two definitions are equivalent."
  Here [Birman68] and [Crowell-Fox66] refer to specific references in your reference list at the end of the report.
• 10. Evidence all claims.
  ...Again, this is Mathematics. You can't just go around making claims without proving them.
  This means _all_ claims. If you claim, say, that a subject is "popular" or "useful", you must prove it!! (Or else delete your claim.)
• more to follow ...