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Stage 3

This stage begins with admission to Candidacy and finishes with a successful Thesis Defense. This is the most difficult part of the Program. No student should expect to complete it in less than twenty-four months.

Post Candidacy Course Requirement

After entering Candidacy a student is required to take one graduate mathematics course for credit during each of the next two semesters in residence.

Thesis Advisor

A student should normally be involved in thesis research by the time he or she achieves Candidacy, and the Advisor becomes the student's Thesis Advisor.

Thesis Research

Students normally do thesis research in the major area of the Preliminary Examination.

Most students find that doing research is very different from attending courses and participating in seminars. In research, one is alone for the first time, trying to develop mathematical ideas from unfamiliar material without the security of knowing that the answers have been worked out in advance. Luck, talent, inspiration and perseverance certainly contribute to success. Moreover, the last quality in sufficient quantity can help overcome deficiencies in the first three. Involvement with one's work is, without a doubt, an essential requirement.

The time required to complete this phase of the Program should not be underestimated.


When the Thesis Advisor is satisfied that a student has done sufficient research for the Ph.D., the student prepares a draft of the dissertation. The Doctoral Committee then appoints two Readers (one being the Thesis Advisor and the second being another member of the Dissertation Committee) to submit independent evaluations and decides on the basis of these reports whether or not to approve the work.

The student's Thesis Advisor usually serves as one Reader. The student must give the Readers sufficient time to read the draft so that they can react and pass on valuable suggestions. In any case, the draft must be in the hands of the Readers at least eight weeks before their evaluation is required.

After the draft has been approved by the Doctoral Committee, the student prepares a final manuscript in accordance with the many detailed regulations described in the Graduate School's “Dissertation Handbook”, available in the Rackham Building. The student should obtain a copy of this handbook early in the term in which the thesis is expected to be completed, because many of Rackham’s deadlines, for example that for a format check, are strictly enforced. The thesis should not be printed in final form prior to the approval of the Doctoral Committee.

Dissertation Committee

The Dissertation Committee consists of five members, four of whom should be from Mathematics and one of whom must be from outside the Department. It is usually chaired by the Thesis Advisor and includes both Readers of the student's thesis. One of the members from the Mathematics Department must be from outside the student's area. The student is expected to ask faculty members to be on the Committee after consultation with the Thesis Advisor and approval by the Doctoral Committee concerning its composition. The Chair of the Doctoral Committee can sometimes help in suggesting members for the Committee from outside the Department. The student would be well advised to choose the Committee early so they may be consulted as the research progresses.

Thesis Defense

When the thesis is in final form, the student is examined orally on its contents and related topics by the Dissertation Committee. Copies of the Thesis should be in their hands at least two weeks before the Thesis Defense. The Graduate School should be notified by the Graduate Studies Office of the time and place for the examination at least one week before it is to take place. It is advisable to make these arrangements as far in advance as possible as a matter of courtesy and to avoid dates when members of the Committee may be out of town; this is especially so if the exam is to occur during the summer months. There are several other important deadlines which must be met before a Dissertation Defense can be scheduled---see the "Dissertation Handbook''.