Instructions for Independent Projects
As you know, at the end of the semester you will be completing an independent project in which you will discover, learn and communicate a piece of mathematics that complements and builds upon what we have learned in class. There will be two components to this project: (1) a formal, written report which is approximately five typewritten pages, and (2) a 1520 minute oral presentation.
Schedule

I would like to “meet” with each of you at least three times about your project. The first "meeting" consists of your emailing me with the name(s) of your partners. The second “meeting” required of you consists of your emailing me with the nature of your topic along with a list of some of the references that you have found. The third meeting will be more technical. I would like each of you to schedule a meeting with me (or just attend one of my office hours) in order to discuss some of the technical details of your project.

Presentation

For your oral presentation, you are free to use the blackboard or, if you prefer, PowerPoint. (Please let me know in advance which you plan on using so that I can be sure that we have whatever IT equipment is needed.) Your presentation should be no more than 20 minutes long. It will likely be impossible to give all of the technical details about your project in this little time. So think very carefully about what details are important and what details are more technical and can safely be omitted. The oral presentations will take place in class on May 3 and May 5.
Some advice concerning the presentation: If you are planning to use the blackboard, give some thought to how you want to display information (what to leave on the board and what to erase) and how much you plan on writing. Remember to write large enough that everyone can read easily from a distance. Rather than trying to include all of the nittygritty technical details of your topic, try to think about two or three large, overarching ideas you would like to convey. And bear in mind that your audience will likely never have thought about your topic before. So it will take time for them to absorb what you have said. Additionally, it is not necessary to give every detail in your presentation. In fact, you are unlikely to have enough time to do so. Instead, you should try to give the audience themain idea, perhaps giving a “proof by example” in order to convey the main idea and avoid distracting technical details. Last, but not least, remember that you have only 20 minutes. So it is incredibly important that you rehearse! A good rule of thumb is to prepare your talk, and then prepare it again with half of the material deleted. Then prepare it a third time with half of the material deleted. This will help you discover the core of what you need to say and will result in a much clearer presentation that is less likely to overwhelm your audience. 
Written Report 
Your report should be written very carefully and formally, in the usual LemmaTheorem style. If at all possible it should be typed. (Microsoft Word has a built in equation editor that you can use. Alternatively, you are more than welcome to typeset your paper using some flavor of LaTeX. If you have any questions about using LaTeX please let me know.) You must include correct citations to the literature (articles, textbooks, etc). The final version of your written report is due at the time of the final exam: Thursday May 11, 79pm.
Some advice concerning the written report: your paper will give you the opportunity to include the technical details that you might not be able to cover in the oral presentation. Still though, you should focus on a few important ideas rather than lots and lots of technicalities. Please try to write with good style, using correct English grammar and mathematical notation. You should also include a formal bibliography at the end of the report that includes any books, papers or internet sites you have used. References to items in the bibliography should be made in the following manner: Recall that by Lagrange’s Theorem, the order of a subgroup divides the order of the group [1, Theorem 11.1]. Therefore... Bibliography: [1] M.A. Armstrong, Groups and Symmetry, SpringerVerlag (1988) Some excellent advice on how to write a good mathematical paper can be found at: http://www.math.uiuc.edu/~berndt/writingmath.pdf 
Timetable 
April 3  Name of partner(s) communicated (email is fine).
April 17  Topic for project communicated, along with references (again, email is fine). April 24  By this date you should have already met with me to discuss some of the technical details of your project. May 35  In Class Presentations. May 11  Written report due. 
Grading 
Your grade on this project will be out of 30 points.
Miscellaneous: Emailing me the name of your partners (2 points) Emailing me with project topic (2 points) Meeting with me in person to discuss technical details (2 points) Presentation: Mathematical correctness (5 points) Clarity (3 points) Quality of presentation (5 points) Written Report: Mathematical correctness (5 points) Quality of writing / organization (5 points) Use of sources (3 points) 
Suggested Topics 
A list of potential project topics is available here.
