**Departmental Requirements for Ph.D. in Mathematics:****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.

**Credit requirements:** A total of 90 hours above the B.S. degree or 60 hours above the M.S. is required, including 15-24 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 at least 12 hours of graduate courses in the mathematical sciences (mathematics, statistics, or computer science).

**Preliminary Research Project**: Once the student has chosen his/her doctoral advisor, he/she should commence work on his/her preliminary research project proposed by the advisor. The student begins the project by taking a reading course (MATH 6010) under the direction of his/her advisor in order. Once sufficient background knowledge has been attained and actual research has begun, the student enrolls in Doctoral Research Project (MATH 6090) until the completion of the project. The preliminary research project 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.

**Dissertation proposal**: An outline of the proposed dissertation research must be presented to the student's advisory committee for approval.

**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.