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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
Before the semester starts, take the Placement Exam and consider using the one or two "freebie" attempts offered for the Qualifying Exams. Afterward, focus on the foundational coursework needed to prepare for any remaining requirements.
Year 2
Complete both Qualifying Exams by the beginning of the spring semester. Select a dissertation advisor. Complete all required coursework.
Year 3
Pass the Oral Exam by the beginning of the spring semester. Begin research and submit the Prospectus.
Years 4 & 5
Focus on dissertation research, culminating in the final defense.
Program Milestones
1. Placement Exam
Every incoming 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. Students are also offered one or two "freebie" attempts at the Qualifying Exams during this pre-semester period, providing a no-penalty opportunity to satisfy some requirements early.
2. Coursework
Ph.D. students are required to complete 33 credit hours (11 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.
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 beginning of spring semester 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 (and primary) step is the completion and successful oral defense of a dissertation containing original research that makes a genuine contribution to the field.
