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The Ph.D. degree allows you to individualize your program of study, so in addition to courses in mathematics, you might include courses in computer science, engineering, and other applied areas.

Program requirements: Two tracks are offered: Pure Mathematics and Applied Mathematics. A total of 72 credits is required. Of these, 18 credits of dissertation work (MTH 699) are required. Within the first year of the Ph.D. program, the student, in conjunction with the Graduate Committee, will select a research advisor (major professor) from the graduate faculty of the Department of Mathematics and Applied Mathematical Sciences, including persons holding limited joint appointments. At this time, the student鈥檚 doctoral committee is selected and the program of study is carefully prepared by the student with their major professor. The program of study must be approved by the student鈥檚 doctoral committee, the department chairperson or graduate program director, and the dean of the Graduate School. Soon after that, in a similar manner, the dissertation proposal must be prepared and approved. The candidate shall successfully defend their dissertation in an oral defense. This is an oral exam, usually two hours long, administered by the candidates dissertation defense committee composed of the doctoral committee and two additional members approved by the Graduate School. This oral exam is in addition to the oral part of the comprehensive exam (see below).

For the pure mathematics track, required courses are MTH 515, 525, 535, 536, and 562. For candidates without a master鈥檚 degree in mathematics, 1) subject to the approval of the department chairperson and graduate program director, at most 12 credits can be taken outside of the mathematics program (MTH or AMS); 2) the qualifying exam must be passed in MTH 435, 436, and 513; those holding course credit in these courses may waive this requirement. For candidates with a master鈥檚 degree in mathematics, 1) prerequisites MTH 435, 436, and 513 must be taken; 2) up to 30 credits from a master鈥檚 degree in mathematics may be applied towards the Ph.D.; and 3) all but at most 6 credits of their remaining credits must be for mathematics courses (MTH or AMS) at the 500-level or higher.

For the applied mathematics track, at least 30 of the 54 non-dissertation credits must be in mathematics (MTH or AMS). Areas of concentration are determined by and selected from among the research interests of the graduate faculty of the program, which includes members of other departments who are formally designated as graduate faculty in mathematics. Up to 24 credits for courses in the student鈥檚 selected area of concentration may be applied to this degree. For candidates without a master鈥檚 degree in mathematics, the qualifying exam must be passed in MTH 435, 436, and 513. For candidates with a master鈥檚 degree in mathematics or a closely related area, 1) up to 30 credits from the M.S. in mathematics or an area closely related to mathematics may be applied towards the Ph.D.; and 2) all of their remaining credits must be for courses at the 500-level or higher; permission of the department chairperson and graduate program director is required if more than 12 of the remaining credits need to be taken outside of the mathematics program (MTH or AMS).

Ph.D. Comprehensive Examination. Shortly before the completion of formal course work, each doctoral candidate shall take the Ph.D. comprehensive examinations. These consist of a 10-hour written part to be taken over eight days and, on successful completion of the written part, an oral part (normally within four weeks).

• Pure Math
• Applied Math