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## Ph.D. in Applied Mathematics

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

The Ph.D. degree with emphasis in applied mathematics is intended to prepare a student for a variety of careers in industry, in government research laboratories, and in university research and teaching. Application of mathematics is an important skill to be cultivated by students based on an ability to discern occurrences of mathematical structures in the human environment.

**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 applied mathematics are required to complete 24 credit hours of core courses. These must include three of the following four options plus six credit hours from the approved electives given below. A minimum GPA of 3.0 must be maintained in core courses.

- Real Analysis I and II (MATH 5143 and 5153)
- Complex Analysis I and II (MATH 5283 and 5293)
- Numerical Analysis for Differential Equations (MATH 5543) and Finite Element Methods (MATH 5563)
- Partial Differential Equations (MATH 5233) and Ordinary Differential Equations (MATH 5243)

**Electives:** Any of the courses in the above four options, MATH 5133, MATH 5213, MATH 5303, MATH 5580, MATH 5593, MATH 5613, MATH 5623.

**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).

**Comprehensive exams:** A Ph.D. student in applied mathematics must select three of the four areas from the core requirements listed above and for each must pass a comprehensive exam covering material in that area. The mathematics comprehensive exams are administered in January, May/June, and August. See the separate document covering timetables and requirements. Students who have passed two comprehensive exams may, with the approval of the student's advisor, substitute a minor thesis (as described below) for one of the comprehensive exams.

**Minor thesis**: The minor thesis must be a creative, written work of research or exposition on a topic of mathematical content. Further requirements are given in a separate document.

**Language requirement**: The student's advisory committee must be satisfied that the student has a strong working ability with a computer language or symbolic computation.

**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 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.