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Ph.D. Program Requirements
This page provides a summary of the major milestones for doctoral students in the mathematics program. For complete details, all students should refer to the official Math Graduate Handbook.
Expected Timeline
Year 1
Focus on foundational coursework and take the Placement Exam before the first semester. Begin preparing for Qualifying Exams.
Year 2
Complete both Qualifying Exams by the beginning of the spring semester. Select a dissertation advisor.
Year 3
Complete all coursework. Pass the Oral Exam by the end of the year.
Years 4 & 5
Submit the Prospectus and focus on dissertation research, culminating in the final defense.
Program Milestones
1. Coursework
Ph.D. students are required to complete 48 credit hours (16 courses) of approved graduate work. Most 7000-level courses count towards this requirement. Students work closely with the Director of Graduate Studies to select a course sequence that provides both breadth and depth.
2. Placement Exam
Every first-year Ph.D. student must take a 4-hour placement exam on undergraduate Linear Algebra and Vector Calculus before their first semester. This exam is a diagnostic tool to ensure readiness for the doctoral curriculum.
3. Qualifying Exams
Students must pass two comprehensive 4-hour written qualifying exams by the start of the spring semester of their second year. Each exam may be attempted a maximum of two times. Exams are offered in August and January in the following subjects:
- Algebra
- Analysis
- Applied Mathematics
- Differential Geometry*
- Partial Differential Equations*
- Probability and Statistics
- Scientific Computation
- Topology
*Offered every other year.
4. Oral Exam
After passing qualifying exams and choosing an advisor, students must pass an oral exam covering advanced material relevant to their dissertation research. This exam must be passed by the end of the third year.
5. Prospectus
Students must write a 4-8 page prospectus outlining their dissertation problem and investigation plan, and present it orally to their committee.
6. Dissertation & Defense
The final step is the completion and successful oral defense of a dissertation containing original research that makes a genuine contribution to the field.
