Each student must take a preliminary examination by the end of the first year (offered twice a year). The examination includes the calculus sequence, linear algebra and probability/statistics, and may be retaken only once. A passing grade on the preliminary examination is 80 percent, and students who score 60-80 percent will continue with the master’s program.
Before acceptance to the first proposal defense, students must take the series of qualifying comprehensive examinations (three written, two-hour examinations and one oral examination) on three topics chosen with the approval of their major advisor, and based on the student’s coursework. Written examinations must be taken within one week, followed by the oral examination within two weeks after passing the written examinations. Passing grades for each of the qualifying examinations is 75 percent and a failed examination should be retaken within three weeks. Any examination may be retaken only once. Students who fail the written qualifying examination series may earn a master’s degree on passing a final program examination. Further examination and committee requirements include:
- Examinations taken after completion of coursework.
- At least 60 days before the examination series, the examination committee must be formed, the corresponding document signed by all committee members and the department head, and filed with the graduate school.
- The examination series must be taken within a three-week period.
- The oral examination should include advanced topics in the area(s) of the proposed research at the discretion of student’s advisor.
The doctoral dissertation includes:
- Two proposals
- Dissertation coursework (a minimum of 24 credit hours)
The first proposal will be based on forthcoming research. A proposal defense must be preceded by at least three credit hours of research (six hours are recommended). A student can take as many hours as needed for the completion of the proposal defense. However, only a maximum of nine credit hours will be counted toward the dissertation. A minimum of 15 credit hours of dissertation must be taken after the proposal defense.
At least 60 days before the proposal defense, the dissertation committee must be formed unless it is identical to the examination committee. In the former case, a corresponding document signed by all dissertation committee members must be filed with the graduate school. On successful oral defense of the proposal, the student is allowed to continue their research.
Before the dissertation defense, the student defends the second proposal, which must include a virtual submission of a written grant proposal to a funding agency (such as NSF) and approved by the dissertation committee, followed by an oral presentation and discussion. The topic of the research must be related to the dissertation.
The dissertation is expected to represent original research that expands the boundary of knowledge in modern mathematics. Before the defense, the student is expected to present at a conference and have at least one paper published or accepted for publication in an established academic journal with ranking.
The dissertation must be written and orally defended. A written thesis of the dissertation must be sent to each committee member at least 30 days before the scheduled defense.