Facilitator: Dr. E. Sander (S&T I, Rm 251, 993-1490, esander@gmu.edu)

Seminar time: Tuesdays 3:30-4:20, S&T I, Room 242.

Description: This course is a 1-credit seminar course, required for math Ph.D. students. It is designed to prepare you for the presentation aspect of a career in mathematics. This is beneficial in the long term, since even in mathematics, good research is not appreciated unless it is well presented. The short term benefit is that it helps you to get comfortable presenting graduate level mathematics prior to the oral exam. The seminar consists of mathematical presentations by students. Each student is required to give a presentation, in addition to attending the presentations of others.

Attendance: Attendance at the presentations of others is required. There will be an attendance sheet.

Participation: I want to strongly encourage you all to ask questions. While you are watching the talk, try to think of a question to ask that you are interested in hearing the answer to. Answering and asking questions are both very important skills. (The speaker can't practice answering questions if you don't ask them.) This is certainly not something that I can force you to do, but the atmosphere will be far better if there is a two way interaction going on. Please ask questions and make the atmosphere more interactive! Also note that it is a courtesy to the speaker that there needs to be at least one question after a talk. That means that the chair will need to think of a question in case nobody else asks. But the rest of you should not let that happen!

Chairing a session Each person will chair one talk. That involves introducing the speaker, closing the talk with asking for questions, making sure that there is at least one question, and leading a second applause after questions.

Research seminar requirement: As part of learning about mathematical presentations, you are required to attend five additional research seminars in math or a related field. The Math Colloquium is an excellent choice, as are the specialized math department seminars. By the last day of classes, submit to me a list of the titles and dates of five seminars that you attended.

Presentation: During the semester, each student will give a mathematical presentation. The expectation for the presentation is comensurate with the students' point in the program. Thus more advanced students will be presenting their own research, whereas students who are not as far along will be presenting research papers or material from advanced graduate texts. In either case, the material should be at an appropriate level to be understood and appreciated by the audience. That is, it should be it should be graduate material which is new to the other students (not seen within any of the beginning graduate courses), but not presented at a level too advanced for the audience.

In order to prepare for this presentation, you are required to choose a faculty mentor, who will work very closely with you to help you prepare the presentation. You and your mentor will agree on a topic. You will meet with your mentor to discuss a talk outline. Your mentor will receive a copy of your talk in advance and make comments which need to be incorporated in time for the presentation. Your mentor will also attend the talk. A good mathematical talk, especially when you are first starting, takes time to prepare. Do not underestimate the need to start in advance. Here is a timeline showing what is required for the preparation of the presentation:

• Well in advance (at least three weeks): Choose your mentor. The mentor may help you choose the material for your presentation. Even if you choose the material yourself, the mentor must approve the material (at least two weeks in advance).
• At least one week in advance: You must meet with the mentor and give an outline of what you plan to cover.
• At least one week in advance: Email me an abstract for your talk.
• At least two days in advance: You are required to show your mentor a copy of your presentation materials. Remember that the goal is to improve your presentation skills. Thus you need to give your mentor time for comments which can be incorporated.
• At least one day in advance: You will receive comments from the mentor.
• You will be graded on timing. To make sure you have the timing right, before your talk, practice it to yourself or a friend.

Changes from the fall semester: This semester, the new emphasis is on timing. Each talk needs to be 50 minutes long. If you are often nervous and talk too fast, then you should slow down. In case that doesn't work, make sure you have enough extra material! Divide the talk as follows:

• The first 10 minutes are introductory. They should put your problem into perspective, explaining the problem, its applications and implications within and outside of the field, and why it is of interest. Everyone in the room should be able to fully understand everything you say without any trouble. To make sure you're not overestimating us, ask yourself: Would my (non-mathematician) brother or sister understand? (If you're an only child, how about your college roomate or your grandparents?)

• The next 30 minutes should still be accessible, but this is more detailed and potentially a little more sophisticated mathematically. If you have lost more than half the audience, you are not at the right level.

• The last 10 minutes are at a high level. This is where you get to say something to the people in your field. Your mentor should still be able to follow what you say, but the rest of us may not. Say it in such a way that we can be impressed that you know so much.

• A conclusion is important. I suggest that you give some ideas of future research, open questions, and any applications.

• Sample presentation in Beamer.
• Sample presentation in Prosper.

Grading: Your grade is based on the presentation, attendance, participation, chairing a session, and completion of the the research seminar requirement.

Course Web Page: http://math.gmu.edu/~sander/courses/m795f07/

Previous semester:
Fall, 2007 Graduate Seminar Main Page
Fall, 2007 Graduate Seminar Schedule of talks