The PhD in Mathematics
requires a dissertation written under the direction of a major professor (PhD advisor). Eligibility to submit a dissertation requires that the student first formally advance to candidacy for the PhD degree. We describe here the requirements for advancement to PhD candidacy.
The Major Professor and Supervisory Committee
Students are responsible for finding a professor who agrees to direct their dissertation work. This should be done as soon as possible, so that the major professor may assist in choosing qualifying exams and courses appropriate to the intended research area. Major professors are faculty from the math department, although it is possible to have a co-director from another department (see the Director for more details).
On request, and when mutually agreeable to the student, professor, and department chair, the department chair will officially appoint the major professor and then, in a timely manner, the remainder of the supervisory committee. In any case, students must have a major professor and supervisory committee before taking the PhD Candidacy Exam.
The PhD degree requires the following:
Completion of the Master's degree requirements
Passing the two semester course sequence MAA 5616-5617 Measure & Integration I & II
Passing two qualifiers
Passing the PhD candidacy exam
Passing the dissertation defense
PhD students must pass two qualifier exams.
Each exam is based on two-semester courses. The options are:
Measure and Integration I and II
Foundations of Computational Mathematics I and II
PDE I and II
Complex Analysis I and II A qualifier exam can also be based on any two half-qualifiers from the following three options:
PDE I; Stochastic Differential Equations; Numerical PDE I Note: For one of these exams, a student's supervisory committee may seek approval to substitute another written exam based on material at a similar level and scope; contact the Director for further information.
PhD Candidacy Exam
After passing the qualifier exams and satisfying the requirements of the master's degree, the student must pass the PhD candidacy exam, comprised of two parts:
The student will prepare a carefully written expository paper on an advanced topic selected with the guidance of the major professor. Students are advised to use dissertation format for the paper. The paper will be distributed to the supervisory committee for comment at least two weeks in advance of the Exam date.
- On the announced day, the student will deliver a short public lecture on the material covered by the PhD Candidacy Exam paper. Then, in closed session, the supervisory committee will examine the candidate on the topic of the PhD Candidacy Exam paper. Questions from the committee may concern general knowledge of the chosen topic and need not be limited to the material specifically covered by the PhD Candidacy Exam paper. The student must demonstrate scholarly competence and knowledge sufficient to begin work on dissertation research. The supervisory committee decides whether the student has passed the exam.