The doctoral program prepares students for a career in research and teaching at the university level or in basic research in a nonacademic setting.

**Requirements for Degree.**

- Credit hours (54): minimum 36 coursework hours in mathematics courses numbered 600 or above (Math 521, 522, 540, 541, 571, 572 may be substituted) with a grade of B or better in each, plus 18 dissertation hours (Math 799R). More than nine credit hours of Math 695R being counted towards the coursework hours requires approval of the graduate coordinator. Graduate level courses in other departments can be counted toward the courswork hours with the approval of the graduate coordinator.
- Required courses: complete six credit hours in one of the three areas: Applied Mathematics, Analysis, and Algebra, and complete six credit hours in one of the remaining two areas.
- Examinations. See below for changes. (Current policy on Defense of Dissertation remains unchanged.)
- Dissertation. A Ph.D. student must register for and complete a minimum of 18 hours of dissertation credit Math 799R. No more than 18 hours may count toward the 54 hours required, and all 18 hours may not be taken in one term or semester. Registration for dissertation credit and work on the dissertation must be concurrent. A Ph.D. student may not register for Math 799R until that student has completed the Examiniation requirement and completed 27 credit hours of the required 36 credit hours of coursework.
*Defense of Dissertation:* A final oral defense of the dissertation is conducted by a faculty committee consisting of the student’s research adviser, two other readers of the dissertation (one of whom may be an outside examiner) and two other members of the faculty.

The Examination requirement ensures that Ph.D. students have acquired a sufficient level of mathematical mastery to undertake high-level research. The Examination requirement can be met by way of coursework or by way of written examination, as explained below, in two of three broadly defined areas of Applied Mathematics, Analysis, and Algebra, by the end of year two. Failure of a Ph.D. student to meet the Examination requirement by the end of year two will result in the discontinuation of funding at the end of year two.

Continuing Ph.D. students have the option to meet the Examination requirement under the current or new system.

__Coursework__. To meet the Examination requirement by way of coursework, a Ph.D. student will need to earn an A- or better in four courses, or their equivalents at another institution, with two of the four courses in one of the three areas and two courses in one of the remaining two areas. Courses in the area of Applied Mathematics include but are not limited to Math 510, Math 511, Math 521, Math 522, Math 611, and Math 636. Courses in the area of Analysis included but are not limited to Math 532, Math 540, Math 541, Math 565, Math 641, and Math 655. Courses in the area of Algebra include but are not limited to Math 561, Math 571, Math 572, Math 586, Math 656, and Math 676. A graduate course or its equivalent at another institution can only be used to count towards one of the three areas. For example, Math 636 (Probability 1) is both Applied Mathematics and Analysis, but it can only be counted for one of these two areas. The Graduate Committee will maintain a list of associations of graduate courses with the three areas.

__Written examinations__. To meet the Examination requirement by way of written examination, a Ph.D. student will need to pass written examinations in two of the three areas. The written examinations will be based on published syllabi associated to the basic courses listed below. If a Ph.D. student as earned an A-or better in two courses associated to one of the three areas, but not in two courses in another area, the Ph.D. student need only pass one written examination in an area not met by coursework. Written examinations will be offered in August/September, January, and May.

- Applied Mathematics: Math 521 and Math 522
- Analysis: Math 540 and Math 541
- Algebra: Math 571 and Math 572

The Graduate Committee may change the basic courses associated to any of the three areas, but there will always be two basic courses associated to each of the three areas. No written examinations are available for other courses.