Aims: The 3rd year essay offers the opportunity of producing an original and personal account of a mathematical topic of your own choice going beyond the scope of existing lecture modules. It will test your ability to understand new mathematical ideas without detailed guidance, to use the library in a resourceful and scholarly way, and to produce a personal account of a piece of maths. The essay should be 15-25 pages in length, and comparable in content to ten lectures from a 3rd year maths module. As a rough guide, you should expect to spend at least 100 hours on this option. You are supposed to find a member of staff willing to give you, and advise on, a choice of the topic (to learn about scientific interests of members of staff in the domain of mathematics you are interested in is already a part of your task) who will be also responsible for the marking and suggesting the second marker.

Deadlines:

• Project registration: You need to find your supervisor within the first weeks of Term 1 and register for your essay (name of the supervisor and tentative title of the essay) by noon on Monday of week 3 (October 14th).
• Progress Report: worth 5% of the overall mark. Due Tuesday January 14th 2025 at noon (Tuesday of week 2 in term 2).
• Essay submission: The essay must be submitted to Moodle by 12:00 noon on Tuesday April 1st 2025.
• Presentation: the oral presentation should be completed in week 3 or 4 of Term 3.

Essay: The essay makes up 80% of the mark for this module. It will be marked on various aspects such as presentation, referencing, content, understanding and originality. The markers will be given more guidance, but they do have the flexibility to give more weight to some aspects than others depending on whether the essay is, for example, an exposition of a known result or an investigation of an original problem. Cases of plagiarism will be dealt with severely, so please make sure that you reference material that has been taken from elsewhere correctly (see, for example, the documents listed in the resources for the second year essay).

Oral Presentation: 15% of the module mark comes from an oral presentation. This presentation should consist of a talk of approximately 20-30 minutes length followed by questions. The whole process should take less than one hour. You should arrange the time and venue for the talk with the supervisor of the essay, and it is usual for both the supervisor and second marker to attend.

The purpose of the presentation is to demonstrate your understanding of the material contained within the essay and to clarify anything that the examiners feel requires further explanation; the marking will reflect this. With this in mind, in preparation you should concentrate on organising the content in a coherent manner (and choosing which aspects of the essay to concentrate on and which to leave out). You should not spend a lot of time producing a glossy presentation - all that is required is a simple but clear presentation and a willingness to answer questions on the content of your essay. If you wish you may use the blackboard, or a short handout, or uncomplicated slides.

The oral is not supposed to be a performance, and students who are nervous or find public speaking difficult will not be at a disadvantage. Marks will be given for clarity and organisation of the presentation, and for answering questions about and demonstrating understanding of the material in the essay.

Tip: You should also bear in mind that 20 to 30 minutes is not actually a very long time (as you may appreciate from your second year essay presentation), and should certainly try to make sure that you have a dry run through beforehand, perhaps in front of housemates.