Mathematics with Computation, Ph.D.

Program Requirements

• 42 credit hours
• Students must satisfy coursework, examinations, and dissertation requirements.
• Students must complete 18 hours of graduate core coursework, at least 9 of which at the 800-level, and a minimum of 18 hours of dissertation work to reflect the research emphasis of the program. The remaining 6 hours must be at the 800-level or dissertation.
• As part of the graduate course work, students must complete 3 two-course sequences from the list of core courses.
• Students must complete a computational project as part of the dissertation work.
• The typical period for completing the program is three years for full-time students and five years for part-time students. Exceptions will be made according to the Graduate School Academic Policies and Procedures.

Entrance Qualifying Examinations

Entrance Qualifying Examinations (EQE) are comparable in content and level to written qualifying examinations of traditional doctoral programs.

Each student must take an EQE in advanced linear algebra, an EQE in analysis, and one EQE in either abstract algebra or mathematical statistics.

Students interested in applying to the doctoral program will be given the opportunity to take MS-level courses to prepare for the EQEs.

EQEs will be offered twice a year: during the summer and at the end of the fall semester. Students should complete the EQEs the summer before entering the program and no later than the end of their first fall semester. A student who does not pass one or more exams will be given a second chance at the next offering. A maximum of two attempts is allowed; failure to pass any of the examinations on the second attempt will result in dismissal from the program. 

Though it is typically expected that students will take core courses or MS-level courses to prepare for (some of) the EQEs, if suitably prepared, they may take any course except for MATH 999 Doctoral Dissertation Research (1-9) .

Core Courses (18 Credits)

Students must complete three of the following two-course sequences with no more than one from the sequences in Differential Equations and in Dynamical Systems.

One or more core course requirements may be waived if their content overlaps with prior graduate coursework. Petitions for such waiver should be presented to the Graduate Program Director. Students receiving a core course waiver must take additional graduate courses to fulfill the 42 credit hours required.

Comprehensive Examinations

• Students must complete two written Comprehensive Examinations (CEs), each covering material from one of the core sequences.
• Comprehensive Examinations are offered twice a year: once in summer and again in winter.
• Full-time students should complete both CEs during the summer following their first year in the program or no later than the end of the fall of their second year.
• Part-time students should complete both CEs by the summer following their second year in the program.
• A student who does not pass a CE will be given a second chance at the next offering.
• Failure to successfully complete either of the CEs within two attempts will result in dismissal from the program. 

Doctoral Proposal Oral Examination

There will be a Dissertation Proposal Oral examination (DPO) administered by the dissertation advisory committee (comprised of appropriate graduate faculty) to determine if the dissertation topic is appropriate, and if the student is adequately prepared for work on the dissertation. 

• Full-time students are expected to take the DPO before the end of the first year in the program.
• Part-time students are expected to take the DPO before the end of their second year in the program.
• The student must submit a dissertation proposal including a description of the problem to be investigated, an outline of the methodology to be used, and a bibliography at least two weeks before the DPO
• After the DPO, the dissertation advisory committee will approve the proposal, approve the proposal with minor revisions, or reject the proposal. 
• The DPO may be repeated only once. 
• Failure to successfully complete the DPO will result in dismissal from the program.

Note: The rationale for the timelines is based on the research-intensive focus of the program: students are expected to have identified a research area and possible advisors upon entering the program.

Dissertation and Doctoral Defense Examination

Students must write a dissertation under the direction of the dissertation committee chair (doctoral advisor) to complete the program. The dissertation defense  will be an oral examination conducted by the dissertation advisory committee. It is expected that the dissertation will contribute to advancing the relevant field of study and be publishable in a reputable journal.

Computational Project Component

All students in the program must complete a computational project that will become an integral part of the dissertation.Computational projects will lead to one or more of the following: creation of new computational methods or tools to advance mathematical understanding (including algorithms, symbolic software packages, and visualization); computer-assisted proofs and experimental mathematics (i.e. formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses); development of large numerical or statistical codes yielding new mathematical data.

Transfer Credit Policy

Students may transfer up to nine credit hours of coursework from an accredited institution. Requests for transfer credits will be evaluated by the Graduate Steering Committee.