The Ph.D. program is open to students who have a broad mathematical background and who have demonstrated ability and evidence of special aptitude for research in mathematics in their prior work. Students with B.S. or B.A. degrees can apply directly to the Ph.D. program.

To graduate with a Ph.D. the student has to satisfy all of the following requirements:

• Course Credits: Although no specified number of course credits is required for the Ph.D., usually at least 24 credits of course work beyond the Master's level is necessary.
• Ph.D. Preliminary Exams: pass four prelims. These exams are officially referred to as "the written part of the qualifying exam".
• Pass an oral exam. This exam is the "oral part of the qualifying exam", and is meant to further the student's education, scholarship and professional development. It should cover material in the broad area in which the student intends to write a dissertation, but should not focus on the actual thesis research. The student is expected to present the material he/she has studied, and to answer questions about that material. The exam is prepared by the student's advisory committee, and is normally taken at the end of the third year or beginning of the fourth year.
• Satisfy the Language Requirement.
• Write a dissertation under the direction of a member of the Ph.D. Mathematics Graduate Faculty.