## Ph.D. Program

The main goal of the Ph.D. program is to train mathematicians and statisticians who intend to make research in these areas their life work. Since 1967 when the University of Toledo joined the Ohio university system, the Department of Mathematics and Statistics has offered a strong doctoral program and its graduates now occupy academic positions in colleges and universities around the world.

##### Requirements

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

- A student must pass a qualifying examination within two years of entering the program.
Mathematics students (pre and applied) must pass two topics chosen from algebra, topology,
differential equations and real analysis. For statistics students, the two topics
must be measure-theoretic probability-theory of statistics and real analysis.
**A minimum of 90 hours of graduate credit must be completed**; 60 hours if the student holds a master’s degree upon entry. Colloquium (6930) and Proseminar (6940) are excluded. Mathematics students (pure and applied) must complete two semester sequences at the 6000 level in algebra, topology, real analysis and complex analysis. Statistics students must complete measure-theoretic probability, theory of statistics and other 6000-level courses selected in consultation with the Statistics graduate advisor.- 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 spend two consecutive semesters in supervised
teaching. Enrollment in the Proseminar is mandatory every semester if credit hour
limitations allow it. The University of Toledo 2017-2018 Graduate Catalog– College
of Natural Sciences and Mathematics.
- 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.

More in-depth information can be found in the Graduate Guide.

**Dissertation**

The defining stage of the Ph.D. program is the writing and defense of a dissertation, demonstrating the student's ability to independently attack and solve in an original manner a significant mathematical or statistical problem. No firm timetable can be given for completion of this stage but generally, it can be expected to take two to three years. Possible areas for thesis research in the department include group theory, non-commutative algebra and representation theory, operator theory, harmonic analysis, several complex variables, partial differential equations, dynamical systems, differential geometry, mathematical physics, mathematical biology, geometric topology, control theory and statistics.