- Group Comps
- Individual Comps
- 2012-2013 project descriptions
- 2013-2014 project descriptions
- Past Comps
Math Comps is designed to assist students in completing the transition from classroom learning of our discipline to independent learning. There are two varieties of mathematics comps: individual comps and group comps. The department will make every effort to accommodate students’ preferences between these two options. Both options include a requirement that majors accumulate a total of eight talk-credits during the junior and senior years by attending the comps talks of their colleagues.
Majors are expected to do comps during the senior year. Students finishing the sophomore year may petition the department to be allowed to do comps during the junior year, but such petitions are granted only in very unusual circumstances. In particular, a desire to ease the workload of completing a double major is not a sufficient reason to grant such a petition. In the (rare) case that a junior is granted an early comps, senior math majors will be given first priority in the choice of comps project.
The essence of group comps is a prolonged, shared experience of doing mathematics. The faculty takes a very broad view of what, exactly, this means. We intend to offer opportunities for students: to engage in original research; to apply mathematics in significant, real-world settings, typically with an industrial, governmental, or non-profit partner; to study original historical documents; and to engage in pedagogical research. Specific projects will vary from year to year with topics limited only by the imaginations of our faculty and students. Group comps typically run for at least two terms. The default expectation is that each project culminates in both a public presentation of the results and a paper submitted to the faculty.
Students typically work in groups of two to four supervised by a single faculty member. Students should expect regular group meetings with the advisor (once or twice weekly is typical), as well as other regular meetings with the group without the advisor, in addition to time spent working alone. Comps should be a top academic priority; faculty expect to see an intense commitment to the project from every student in the group. Distinction may be earned in group comps for work exhibiting exceptional levels of creativity, synthesis, and/or depth of understanding.
Timetable: Each spring, faculty members present potential group projects to mathematics majors then in their junior year, and junior majors rank the projects they prefer. Faculty then assign students to projects, taking student preferences into account as much as possible.
Once underway, a typical two-term project will follow the timetable below; three-term projects require the obvious adjustments.
- Term 1: Research, regular meetings, end-of-term evaluation.
- Term 2: Research, regular meetings (weeks 1-4)
- Talk and paper preparation (weeks 5-8)
- Public talk (week 8 or 9)
- Paper due (week 10)
Evaluation: At the end of term one, to ensure adequate progress is being made by all, each student will complete a project evaluation including feedback on the work of all group members. At this point students not making adequate progress may be removed from a project and assigned, instead, a three-credit individual comps project.
At the end of term two a pair of faculty members (including the advisor) will read the paper and conduct an individual interview of each comps student. They will present a recommendation of pass, fail, or distinction to the department. (Note: Grades, including distinction, are assigned to each student, not each project.)
Junior and senior math-majors earn one talk-credit for attendance at an hour-long group comps project presentation.
This comps experience is designed for students who prefer an individual library research project to a group project of faculty-supervised research. It is intended to be an exercise in independent learning of mathematics. It is available in both a three-credit and a six-credit version. Students choosing this option will specify the area of mathematics in which they wish to work. Faculty will provide the student with a packet of reading material to be mastered. That packet may contain, for example, a book chapter or one or more articles from The American Mathematical Monthly or The American Statistician.
Six credits: Students will give a thirty-minute public lecture and write an expository paper (typically fifteen to twenty pages long) on the content of his or her packet. A committee of two or three faculty members will conduct an oral examination of the student after the public lecture to assess the depth of understanding. The material to be mastered should be expected to be deeper and more extensive than that in the three-credit version. Students should be prepared to do background reading to obtain complete understanding of the assigned material. The student will recruit two other volunteer math majors to observe and critique a practice lecture in advance of the public lecture. The work of mastering the material, preparing the talk and writing the paper will be divided over two consecutive terms with three credits earned in each term. Distinction may be earned in six-credit individual comps for work exhibiting exceptional levels of creativity, synthesis, and/or depth of understanding.
Three credits: Students who elect this version will give a thirty-minute public lecture on the content of the packet. (Students should be prepared to do background reading to obtain complete understanding of the assigned material.) The student must recruit at least two other math majors to observe and critique a practice talk in advance of the public lecture. After the public lecture, a group of two or three faculty members will conduct a private oral examination to verify the depth of the student’s mastery of the material. The work for the three-credit comps experience will be confined to one term and is not eligible for distinction.
Junior and senior math-majors earn one-half of a talk-credit for attendance at a thirty-minute individual public comps talk.