The Mathematics Major

The Senior Comprehensive Requirement

Tim McGue '07 discusses the Multivariate Second Derivative Test.

During the senior year each student majoring in mathematics will select a topic related to an upper-level mathematics course he or she is taking (or took in the junior year) as the subject for the Senior Comprehensive Requirement. This topic should delve into material beyond the scope of the course. The student will develop this topic with the guidance of the course instructor to produce a paper. The student will then give a talk, based on that paper, to the department faculty, other math majors, and any additional interested parties.

The following deadlines must be met to insure that the project is completed in time for the May graduation date. Those seniors anticipating December graduation must contact their academic advisor the previous spring to set up an appropriate time table.

• By October 15, the student will have:
1. chosen the course that he/she wishes to be the focus of their project;
2. arranged for the instructor of that course to act as a mentor;
3. initiated discussions with the mentor on choices for the topic.
• By November 30, the student will have submitted to his/her mentor for distribution to the mathematics faculty:
1. a one- or two-paragraph description of what he/she intends to address in the paper;
2. a preliminary bibliography of the sources the student intends to use. (This preliminary list may change over the course of the project.)
• By March 15, the student will submit their completed paper to their mentor. The mentor will distribute copies of the paper to the mathematics faculty.
• By the end of the second to the last full week of classes, the student will give their talk to the mathematics faculty, the mathematics majors, and other interested parties.

Failure to adhere to these deadlines could jeopardize the student’s timely graduation.

The paper will typically be about ten double-spaced pages in length, not including the title page and the bibliography. The Mathematics Department faculty, including all tenured and tenure-track faculty, will read the paper and evaluate it on the basis of four components:

1. mathematical correctness;
2. thoroughness and appropriateness of material included;
3. clarity of presentation;
4. mechanical issues such as spelling, punctuation, grammar, neatness of diagrams.

Each faculty reader will grade the paper on a modified pass/fail basis, and notify the mentor whether the paper has received a pass, a conditional pass, or a fail. Comments to guide the student in preparing their talk, and revising their paper, should that be necessary, will be included with the grade. A pass means that the faculty reader considers the paper to be acceptable and recommends that the student move on to preparing their talk, taking into account any comments or suggestions made by the faculty reader. A conditional pass means that the faculty reader would like to see some minor changes made in the paper (and incorporated into the talk), but recommends that the student proceed to prepare their talk. A fail means that the faculty reader does not consider the paper to be acceptable in its present form. Reasons will be provided by the faculty reader for the failure. The paper will be accepted if no more than one faculty reader has failed the paper. If the paper is not accepted initially, the student will resubmit the paper after making corrections to address the concerns raised by readers.

After the paper is accepted, the student will develop the talk from the paper. The talk will be approximately 30 minutes long, followed by a question-and-answer period. The talk will be graded by the readers who graded the paper. Grading will be based on the same four components as the paper, except that the mechanical issues will now also include diction, pronunciation, volume, and organization of board work (and/or other media). The talk will be graded either pass or fail, and will be accepted if no more than one of the faculty readers present fails the talk. Any talk that is not accepted initially will be given again with adjustments made to resolve problems noted by the faculty.

A student must have both the paper and the talk accepted to complete the Senior Comprehensive Requirement. Note: An honors project in mathematics with a grade of C or better will fulfill the Senior Comprehensive Requirement.

Last revised October 2007.