Guidelines for Presentations

The ultimate goal in each of your presentations is to give the kind of presentation you would be happy to listen to and that you would be proud of. The key to a great presentation is preparation.

Here are some simple guidelines:

• Be well-prepared
• Explain why anyone (even a student of mathematics) would be interested in your topic/theorem. You might want to illustrate this with a good example. Give some of the background that leads up to the specific topic you are going to discuss. State any important prerequisites/theorems that would be useful to know to help make your presentation more complete. If you are going to present a proof of a difficult theorem, you may want to state it first, explain what it says, show why it's useful, and then proceed to the proof. If the proof seems a little obtuse, it's always nice to hear what's really going on intuitively behind all the rigor. Come talk to me if you are having trouble organizing your thoughts; I may be able to help out.
• Make sure you give adequate references in your talk. For Presentation One find at least one other textbook or reference for your topic. This will help you prepare and will also give you a possibly different perspective. For Presentation Two, your list of references should be more extensive. For example, any background/historical results should be given appropriate attribution. Something like: "In 1968 Johnson proved the following result about differentiable functions on funky spaces; the main result I will present is the 2004 result of Smith which extended these results to quasi-funky spaces." If you proved a theorem, don't be shy - make sure you tell us!
• Expect questions from your colleagues. Think ahead of time about what someone who is not as well versed in your topic might ask. If you are going to say that something is trivial or simple, be prepared to justify that with a quick response if someone calls you on it. If someone asks a question and you are not sure what the answer is, it's OK to say you don't know. Someone else may be able to answer the question. If no one has an answer then take it as an opportunity for a further investigation.
• To keep your colleagues involved in your talk, ask them questions to get an idea of how they are understanding what's going on.
• Think about how you will lay the talk out on the chalkboard. You can't write down everything you say, but what you do choose to write down should be important. If you state a theorem, and are going to refer to it often (or prove it) try to keep it on the board for as long as possible. That will give your colleagues an opportunity to digest it.
• If you are a little nervous, that is normal. Remember that 2 hours is a long time. You don't have to talk fast and rush your presentation. Take your time; you are in control!
• Since you are probably not used to lecturing for an hour or longer, bring a favorite beverage to ease the strain on your vocal cords.
• Have fun!