Mathematics, Ph.D.

Admission

Admission to the program requires a positive evaluation from both the mathematics graduate program advisor as well as at least one additional mathematics faculty member that might potentially serve as the supervising advisor. If the applicant has expressed a desire to pursue interdisciplinary work, then, in addition to the above requirement, a positive evaluation is also required from the partner discipline graduate program advisor and a potential partner discipline co-advisor.

To be admissible to the Ph.D. program in Mathematics, applicants must submit a satisfactory official GRE score and satisfy all Graduate School requirements for admission and must show exceptional promise to do independent research in mathematics and its applications. Strong letters of recommendation are essential to any positive admission decision.

Admission to the program will be open not just to candidates with an undergraduate degree in mathematics, but also to candidates with a degree in a relevant application area where mathematics is an essential ingredient, who have an acceptable knowledge of mathematics and are determined to expand this knowledge with a view to applying it in a partner discipline.

Requirements

For students without a Master’s degree, course work for the Ph.D. in Mathematics consists of 72 credit hours to be made up of a minimum of 48 credit hours of elective courses, independent study, and directed doctoral reading, and a minimum of 18 credit hours of a Mathematics Doctoral Dissertation. For students already holding a Master’s degree, a variable number of hours may be applied toward the Ph.D. degree, as determined by the Departmental Graduate Committee and approved by the Graduate School.

Students enrolled in the program with a partner discipline must take a minimum of 12 and up to a maximum of 24 credit hours in courses with a high mathematical content from outside the Department of Mathematics, for example (depending on the chosen partner discipline) in Computer Science, Chemical/Mechanical/Petroleum Engineering, Physics/Biology, Bioinformatics/Biostatistics, Psychology, Operations Research/Finance/Economics. Students whose dissertation research is primarily within mathematics (i.e. not essentially interdisciplinary) may take up to 15 credit hours in courses from outside the Department of Mathematics. Such courses must be approved by the advisor.

No more than 15 hours of 6000-level courses, approved by the advisor, can be used for the degree.

Up to 12 credit hours of graduate level work beyond the M.S. degree from a recognized research institution taken prior to enrollment in the doctoral program may be transferred with approval by the Advisory Committee, and the Graduate School.

Advisory Committee

Students in the Ph.D. program will be advised initially by the Graduate Advisor for Mathematics. The student must select a research area and a supervising research advisor (and, if appropriate, co-advisors) by the end of the second semester after enrollment in the program. The supervising advisor must be a member of the mathematics graduate faculty. The student, after consultation with the supervising advisor and co-advisors, will recommend the other members of the Advisory Committee to the Dean of the Graduate School by the end of the third semester of enrollment. The Advisory Committee must have at least four graduate faculty members, consisting of at least two members from the Department of Mathematics and one member from outside the department. One member of the Advisory Committee may be a qualified expert from outside the university. At least half of the committee must be full time mathematics graduate faculty members at the University of Tulsa. The Advisory Committee approves the dissertation and administers the final oral examination.

Qualifying Examinations

Following successful completion of the course requirements and the selection of a supervising advisor and/or co-advisor, and not later than 30 months after entering the program, a student must show competency for admission to Ph.D. candidacy by passing a set of three written qualifying examinations. Two of these examinations will be in mathematics, to be selected, as appropriate, from among the departmental areas of expertise that include analysis, numerical analysis, geometry/topology, statistics, and biomathematics. For students who choose to complete the program exclusively in mathematics, the third one will be on specialized material related to the dissertation topic, as decided by the research advisor or the Advisory Committee. For students involved with a partner discipline, the third examination will be in that discipline. Students entering the program with a master’s degree will take these examinations within 20 months. In the event of failure, the failed sections may be retaken once. The written examination will consist of questions submitted by the departmental graduate faculty and will be evaluated by them.

Dissertation Proposal

After passing the qualifying examination, subject to approval by the Dean of the Graduate School, Ph.D. students submit and defend a research proposal on their intended dissertation topic before the end of the semester following the qualifying examination. The proposal is presented orally before the Advisory Committee in a forum open to any students or faculty who wish to attend.

Dissertation

Each Ph.D. candidate must write a dissertation on the results of their research, thus demonstrating the student’s ability to conduct independent and original investigation in the selected area of specialization. Since this is a mathematics degree, the Ph.D. dissertation must contain an appropriate amount of original mathematical content. Candidates are expected to make adequate progress toward their degree each semester that they are enrolled in the program. The dissertation must follow the general procedures and format approved by the Graduate School and must be presented to the full Advisory Committee for review and examination.

Final Oral Examination

Each Ph.D. candidate will present a seminar on their research to the university community, followed by a final oral examination before the Advisory Committee. The examination will include a defense of the dissertation and questioning in areas related to the research. Upon acceptance of the dissertation and successful completion of the oral examination, the Advisory Committee will recommend the candidate to the Dean of the Graduate School for the award of the degree of Ph.D. in Mathematics.