# PhD in Mathematics

The doctorate in mathematics is offered with concentrations in either mathematics or statistics. The broad requirements for these programs are as follows:

- Each student must pass a preliminary examination at the Master’s level by the end of the first year and a qualifying examination within two years of entering the program. Mathematics students must pass two topics chosen from algebra, topology and analysis. For statistics students, the two topics must be measure-theoretic probability and probability and statistics.
- A minimum of 90 hours of graduate credit must be completed; 60 hours if the student holds a master’s degree upon entry. MATH 6930 and MATH 6940 do not count in these hours. Mathematics students must complete two-semester sequences at the 6000 level in algebra, topology, real analysis and complex analysis and one other 6000 level sequence. Statistics students must complete probability and statistics, measure-theoretic probability, statistical methods, data analysis and multivariate statistics.
- The student must pass an oral examination in the general area of the intended thesis research within one year of passing the qualifying examination.
- All doctoral students are expected to participate in the MATH 6940 on undergraduate teaching methods and to spend two consecutive semesters in supervised teaching. Enrollment in the Proseminar is mandatory every semester if credit hour limitations allow it.

The student must write a Ph.D. doctoral dissertation under the direction of a faculty member. Before completing the dissertation, the student must report on it in an open seminar. An outside examiner must approve the completed dissertation, and the student must defend it before a faculty committee appointed for that purpose.