PhD in Pure Mathematics
The Ph.D. degree with emphasis in pure mathematics is intended to prepare a student for a career in university and industrial research and college instruction. Recipients of the Ph.D degree in pure mathematics are expected to have significant breadth across the core areas of mathematics as well as skills to undertake independent and original research in a particular area.
Departmental Requirements for Ph.D. in Pure Mathematics
Credit requirements
A total of 75 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-18 credit hours for the Ph.D. dissertation.
Core requirements
All candidates for the Ph.D. in pure mathematics are required to take five, three-credit-hour core course; and to complete each of these core courses with a grade of B or better. The five core courses for the Ph.D. in Pure Mathematics are
1. Advanced Linear Algebra (MATH 5023)
2. Real Analysis I (MATH 5143)
3. Complex Analysis I (MATH 5283)
4. Algebra I (MATH 5613)
5. Topology I (MATH 5313)
Additional courses
In addition to the core course requirements, every plan of study must contain 18-21 hours of graduate courses in the mathematical sciences (mathematics, statistics, or computer science).
Preliminary Research Project
When the student is nearing the completion of core courses, they should commence work on their preliminary research project (PRP) proposed by a faculty advisor. The PRP is a two-semester project involving some light, but original research (6 hours of MATH 6090 taken over two semesters). In the first semester, the student begins the project by taking a reading course under the direction of their advisor. Once sufficient background knowledge has been attained, in the second semester, the student works on their research and completes the project. The PRP concludes with a written document (in the style of an academic journal article) and an oral presentation.
Qualifying exam
The student must pass an oral qualifying exam over the area of specialization for the Ph.D. dissertation. This exam covers material on a reading list presented to the student by the advisory committee. Its purpose is to test the student's readiness to begin dissertation work. To prepare for the qualifying exam, students may register for 3 hours of MATH 6010.
Dissertation proposal
An outline of the proposed dissertation research must be presented to the student's advisory committee for approval (either as a written document, oral presentation, or both). To prepare the dissertation proposal, students may register for 3 hours of MATH 6000.
Dissertation
A dissertation must be written according to Graduate College guidelines. The dissertation consists of an original research contribution in pure or applied mathematics. It must be prepared according to the style required of doctoral dissertations and defended.
Graduate College requirements
All requirements listed in the university catalog must be satisfied.