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Doctor of Philosophy (Ph.D.) Program Description

Our Mission

The mathematical sciences Ph.D. program will prepare and train experts and leaders in the mathematical sciences. Our Ph.D. graduates will be experts in their research field, be familiar and competent in a broad array of mathematical sciences techniques, and will be effective communicators and teachers of basic mathematical sciences who can mentor and lead future mathematical scientists.

Program Structure

Our program is structured to both broaden and deepen our students' knowledge in the mathematical sciences and ultimately to transition these students from accomplished and highly competent students to talented and insightful researchers.


Entering students are expected to have basic courses in linear algebra, differential equations, a computer language, and statistics, and foundational courses in advanced calculus (or real analysis), modern abstract algebra and probability.

Preliminary Exams

The first priority of a beginning Ph.D. student is to pass the preliminary exams. Graduate students are required to receive 2 Passes without accumulating 3 Fails within 3 years of entering the graduate program. MS students are allowed to take prelims and all passes and fails will count towards their progress. Any prelims taken by a graduate student become part of their permanent prelim record.

Breadth Requirement

Ph.D. students are required to complete two breadth courses in each of the following areas: algebra and discrete math, analysis, computational math, operations research and stochastics, statistics. Transfer courses and coursed completed as a Masters student en route to the Ph.D. may be counted toward this requirement.

Ph.D. Coursework

The coursework of a Ph.D. student must include at least 27 hours of non-research, non-professional development graduate courses at the 8000 level or above. Courses taken in order to fulfill another degree may not be counted. The Ph.D. coursework should also include at least 18 hours of Math 9910 (dissertation research).

Comprehensive Oral Examination

Within one year of completing the preliminary examinations, a Ph.D. student must complete a comprehensive oral examination given by his or her dissertation committee. This oral examination is designed to demonstrate the student's readiness to begin his or her Ph.D. research.

Research and Dissemination of Results

The final and most difficult requirement of the Ph.D. degree is the Ph.D. dissertation. Ph.D. students are required to write a Ph.D. dissertation detailing their original and significant contributions to the body of research in their area of concentration and defend it.