- Ph.D Programs
- Master's Programs
- Quantitative Finance and Risk Management
Thesis Proposal, Committee, & Preliminary Examination
By the beginning of the third year of study in the AIM Ph.D. program, students should be seriously focusing on a partner discipline by entering into a working relationship with
- a co-advisor from the Department of Mathematics, and
- a co-advisor from another department representing the partner discipline.
During the third year of study, students will work with their two co-advisors to prepare a thesis proposal. When the proposal is written and a committee is assembled, each student will then take a Preliminary examination (based on the proposal and related coursework) administered by the committee. Upon successful completion of the Preliminary examination and a sufficient fraction of the required coursework for the AIM Ph.D., the Director will recommend that the student advance to candidacy.
The AIM Thesis Proposal
Preparing for interdisciplinary research requires the mastery of background information from two distinct fields of study, as well as careful planning. The AIM Thesis Proposal is a document that crystallizes the process of preparing for an extended research project. Unlike the Mathematics Ph.D. degree, the AIM Ph.D. degree emphasizes the Thesis Proposal because writing high-quality research proposals is an important skill to develop for work in many research careers.
The Thesis Proposal should be prepared by the student in collaboration with both co-advisors. The proposal should contain
- a careful review of the relevant literature,
- a well thought-out plan for the dissertation research, and
- any Prelim results already obtained.
The AIM Thesis Proposal should also explain how the dissertation work is expected to make an original contribution, using novel mathematical ideas, to the partner discipline field. The length of the written document is not specified, but rather is determined by the two co-advisors accounting for the required contents. An average AIM Thesis Proposal is approximately 20 pages in length.
Assembling a Dissertation Committee
As the AIM Thesis Proposal nears completion, the student should assemble a dissertation committee, consisting of individuals who will follow the dissertation work to its completion, and in particular who will administer the Preliminary examination and defense of the dissertation. The dissertation committee is made up of at least four people, including:
- the mathematics co-advisor,
- the partner discipline co-advisor,
- a second faculty member from the Department of Mathematics, and
- one more faculty member representing any department (including mathematics).
Once the committee members have expressed their agreement to serve on the dissertation committee, the student should provide each with a copy of the AIM Thesis Proposal.
The Preliminary Examination
When the committee has had sufficient time to review the AIM Thesis Proposal, the student should next work with the committee and Department of Mathematics staff to schedule a time and location for the 2-hour Preliminary examination. The Preliminary examination takes the form of a presentation by the student to the dissertation committee based on the AIM Thesis Proposal. The student should plan for a 50-minute presentation, although it may take longer if the committee members wish to ask questions during the talk. After the presentation is finished, the committee may ask other questions, possibly related to other relevant coursework or preparation that is not covered in the proposal document or presentation. Generally speaking, students should expect questions broadly related to the partner discipline and associated mathematics. The result of the examination will be decided by the committee in attendance at the conclusion.
Advancing to Candidacy
Candidacy refers to the final stage of the Ph.D., in which the student is focused on original research as planned in the AIM Thesis Proposal and the careful writing of the doctoral dissertation. Once the student has
- taken the AIM Student Seminar course (Math 501) for the first three semesters,
- passed two AIM QR Examinations within the first 13 months of graduate study,
- written an AIM Thesis Proposal and passed the Preliminary examination, and
- completed most of the required coursework,
then he or she will be eligible to advance to candidacy. The Rackham Graduate School mandates that a student in the candidacy stage of the Ph.D. degree can only register for one three-credit course in each semester (excluding filler courses like MATH 995), so the requirement of completing most of the coursework is crucial to allow graduation by the end of the fifth year of study. The Rackham Graduate School also requires that all Ph.D. students achieve candidacy by the beginning of the fall semester of the fourth year of study, or be placed on academic probation.