Senior Exercise Description

The purpose of the senior exercise is to engage each senior in the exploration and communication of mathematical ideas beyond material covered in courses taken, or to be taken, by that student.

Requirements

1. Find an advisor
2. Choose a topic. Your topic and your advisor are not independent, so it is conceivable that after you choose a topic you may have to switch advisors.
3. Write a proposal, which must be approved by the department. It should describe the topic you would like to study and the sources you will use.
4. Give an oral presentation on your topic.
   At your talk, you must distribute a 1-2 page handout to be used by the audience for reference. It should include key definitions, theorems, examples, and sources, and have your name and title/topic at the top.
   You may consult your notes and the sources listed on your handout for your presentation.
5. Take a written exam
   You have one week from the time you receive the exam to complete it.
   The only person with whom you may discuss the exam is your advisor. Only questions of clarification are appropriate, questions of substance are not.

Sept. 2: you must have chosen an advisor.
Sept. 11: a rough draft of your proposal must have been submitted to your advisor.
Sept. 18: a final draft of your proposal, including sources, must have been submitted to your advisor for approval by the department.
Sept. 30: if your initial topic was not approved, a new proposal must have been submitted.
Nov. 6: all presentations have been completed by this day.
Nov. 13: all written exams have begun.

The senior exercise results will be available immediately following Thanksgiving break.

Evaluation

The department evaluates your senior exercise (with the results distinction/pass/fail) by looking at the following factors:

• Meeting deadlines
  Failure to meet a deadline may result in failure of the senior exercise.
• The oral presentation
  • Your presentation should be clear and well-organized.
  • You will be evaluated on your ability to select, from among a range of ideas, those that are most central to your subject and to present them in such a way as to give the Abig picture@ rather than all of the details.
  • You will be expected to avoid significant errors (a quality presentation would have only errors equivalent to typos).
  • You will be expected to field questions of clarification. (However, the public presentation is not an oral exam under a different name.)
• The written exam
  • You will be graded on precision and rigor, completeness, and clarity of expression.
  • Avoid errors.

In the event of a failure a student will be given a comprehensive exam around the time of spring break.

Expectations

Choice of Topic

Your topic should be of suitable difficulty--not too easy and not too hard. Your advisor can help in judging this. The department will also look at these questions when approving the topics.

Preparing the material

This is your senior exercise, not your advisor's. You will be expected to work largely independently. However, you will probably meet with your advisor on a regular basis, so that she or he may monitor your progress and help with the rough spots.

You will be expected to work out the details that are not explicitly set out in your references, so as to put together a complete picture of your topic.

You will be expected to coordinate and systematize material from lyour various sources into a coherent whole. Since different sources will likely use different notation, you will have to standardize this also.

If there are connections between your topic and your previous course work, you will be expected to find and explore them.

Preparing and giving your presentation

A substantial portion of your presentation should be accessible to the junior math majors.

For reference, you will be expected to provide the department with a copy of either the notes (or outline) for you talk or your transparencies or both.

It is expected that you will need to omit significant portions of the mathematical details from your talk in the interests of time. Remember, the purpose of the talk is to give the "big picture."

The written exam

One of the main purposes of the written exam is to see you carefully write out mathematics. Be sure to be prepared to fill in the mathematical details of the topics you studied in your senior exercise.

Tips

Choice of Topic

Your senior exercise will be easier and more rewarding if you choose a topic that really interests you. If there is some mathematical question that has intrigued you, speak to your advisor about its suitability as a senior exercise topic.

When you are looking for a topic, browse through the journals in Finkbeiner Reading Room (ASC 13). The Mathematical Monthly, the College Mathematics Journal and the Mathematics magazine are especially likely choices.

Of course, a couple of hours browsing in the mathematics stacks in the library is also a must.

Make sure that your sources contain enough of the mathematical meat to avoid unpleasant surprises as you research the topic. (That is, you do not want to find out that an innocent sentence like "it can be shown that..." would qualify as a master's thesis.)

Preparing and giving your presentation

Remember that you will be giving two talks at once. One will be a talk about your ideas; the other should be a talk about mathematical details. Discuss this with your advisor.

Do not include anything in your presentation which you do not thoroughly understand.

Have your talk and your handouts prepared far enough in advance of the talk so that you can consult with your advisor on their appearances.

Be sure to practice your talk in front of a live audience. You may want to ask your advisor and/or some of the other seniors to listen to you and make suggestions for improvement.

If you plan to use overhead slides (this is not required), you should be aware of three very important rules of thumb:

1. The writing should be large (letters about half an inch high work well).
2. There should not be too much on each transparency.
3. A dozen or so transparencies are plenty for a 50 minute talk.

Photocopying of overhead slides and handouts is done at the expense of the mathematics department. Get your advisor to help with this.

When people get nervous they have a tendency to talk too fast. Be sure to slow down even if you feel that you are already going slowly.

If you are asked a question to which you do not know the answer, feel free to say so. Do not try to snow the audience.

Preparing for the written exam

Between your oral presentation and the time you pick up your exam, you may consult with your advisor. Keep in mind the following guidlines. Your advisor may answer any questions that you pose. He or she may not give you any indication of what questions will be on the exam.

If you felt weak on any particular portion of your oral presentation, work on it and talk to your advisor about it.