Expectations: The essence of math comps is a prolonged 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significant, real-world settings, typically with an industrial, governmental, or non-profit partner; to study original historical documents; to engage in pedagogical research; and other projects limited only by the imaginations of our faculty and students. In general the experience should be, at least, two terms long. 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 small groups of two to four supervised by a single faculty member. Students should expect two weekly group meetings with the advisor, and at least that many weekly 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.

Timetable: Each spring, faculty members present potential projects to mathematics majors currently in their junior year, and junior majors rank the projects they most prefer. Faculty then assign students to projects, taking student preferences into account as much as possible. Students finishing their sophomore year may petition the department to be allowed to complete comps during their junior year, but such petitions are generally only granted in unusual circumstances. Although the department will make an effort to honor the comps preferences of students who have been been given permission to complete comps during their junior year, students who are taking comps during their senior year will receive preference when they are assigned to comps projects.

Once underway, a typical two-term project will follow the timetable below; three-term projects require the obvious adjustments.

Term 1: Research, regular meetings.

Term 2: Research, regular meetings (weeks 1-4)

Talk and paper preparation (weeks 5-8)

Public talk (week 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, an individual comps project consisting of a public talk on a library research topic of the faculty's choosing and a three-hour written examination.

At the end of term two a pair of faculty members (including the advisor) will conduct an individual interview of each comps student. The same two faculty members will read the student's group paper. These two will present a recommendation of pass, fail, or distinction to the department. (Note: Grades are assigned to each student, not each project.)

Finally, each student is required to attend at least eight comps (or colloquium) talks during the junior and senior years.