The doctoral program is designed to provide the highest level of academic study and research in applied mathematics. The goal is to produce qualified professionals for teaching and research positions in the academic world, as well as equivalent positions in industry and government. The demand for these professionals continues to exceed the current production and is expected to remain so for the foreseeable future.
The degree of Doctor of Philosophy is conferred in recognition of both breath of competence in applied mathematics and technical research abilities, as evidenced by production of an acceptable dissertation. The required work consists of advanced studies in preparation for specialized research, and in the completion of original research resulting in a significant contribution to the body of knowledge in the area.
Many courses of the graduate program have sections that are taught in the evening (after 5:30 p.m.). This is done to help parttime students cope with time limitations caused by their other occupation. On the other hand, when planning advancement towards the Ph.D. degree, one should not neglect the fact that independent research for dissertation work requires large amounts of time to be invested by the candidate. A thoughtful planning of obligations outside of graduate study, especially for the period of preparation of the dissertation, should therefore be performed in advance. Special dissertation fellowships can help to compensate for financial responsibilities.
Doctoral Program
The requirements for the Ph.D. degree include the following:
1. Course work
A minimum of 60 hours of courses numbered 4000 or above.
Mathematics Option, at least 33 hours must be in courses numbered 5000 or above.
Computer Science Option, at least 45 hours must be in courses numbered 5000 or above.
At most 9 hours of a student's enrollment in Mathematics 7990 (Dissertation Research) may be counted. Students are expected to maintain a 3.0 average on a 4.0 scale. All courses numbered below 5000 must be completed with a grade of at least B. Courses outside the Department of Mathematics and Computer Science will require approval of the graduate director.
When students who have earned a Master's degree are admitted to the doctoral program, appropriate credits of course work may be applied toward meeting the requirements for the doctoral degree, subject to Graduate School regulations and the approval of the graduate director. The same applies to those with some appropriate graduate credits but without a completed Master's degree.
2. Ph.D. Candidacy
Advancement to Ph.D. Candidacy is a fourstep process consisting of:
 Completing 18 hours of 5000 level courses other than Mathematics 7990  Ph.D. Dissertation Research
 Passing the qualifying examination.
 Selecting a Dissertation Committee, preparing a dissertation proposal, and defense of the proposal.
Qualifying Examination
Basic Requirement  Pass one written examination covering fundamental topics. This examination would normally take place within the first 12 credit hours of study after admission to the Ph.D. program.
Mathematics Option: Topics from real analysis, complex analysis and linear algebra (Mathematics 4100, 4160, 4450).
Computer Science Option: Topics from the theory of programming languages, operating systems, analysis of algorithms, and computer systems (CS 4250, 4760, 5130, 5700).
After fulfilling the basic requirement above, the student must meet one of the following:

Pass a written examination in an area of the student's interests. This area will be approved by the graduate committee and will be based on a set of two or more graduate courses taken by the student. This examination would normally take place within the first 24 credit hours of study after admission to the Ph.D. program.

Write a survey paper in a specialized area under the direction of a member of the graduate faculty. The student should propose to take this option when he/she has already finished at least 2 graduate level courses and has the approval of the graduate committee. The paper should be submitted within four semesters, at which time an oral examination given by a committee of at least three members of the graduate faculty must be passed.

In both parts above, the graduate committee will determine of the topics are consistent with the option that the student is pursuing.
3. Dissertation Committee and Dissertation Proposal
After completing the comprehensive examinations, each student chooses a dissertation advisor and prepares a Dissertation Proposal. Usually students choose an advisor from contacts made through their course work. For a list of faculty research interests, see our Research Faculty page. The dissertation committee will be formed, and the student will meet with this committee for an oral defense of his dissertation proposal. The dissertation proposal is a substantial document describing the problem to be worked on and the methods to be used, as well as demonstrating the student's proficiency in written communication. Upon approval by the dissertation committee, the dissertation proposal is filed with the Graduate School of the University. Acceptance of the dissertation proposal must occur before the end of the sixth semester of study or before completing four credit hours of dissertation research (Mathematics 7990), whichever comes later.
4. Dissertation and Dissertation Defense
Each Ph.D. candidate must write a dissertation, which is an original contribution to the field on a topic approved by the candidate's dissertation committee and the department. It must meet the standards and requirements set by the Graduate School. The preparation of a dissertation usually takes several years. The dissertation advisor and members of the dissertation committee advise the candidate on research during this period. The candidate must remain in continuous enrollment until the degree is conferred. Students may enroll in Mathematics 7990 (Dissertation Research) for a maximum of nine hours.
The candidate submits the completed dissertation to the dissertation committee for provisional approval. Submission to the dissertation committee should take place at least 10 weeks before Commencement. One copy, certified as complete and provisionally acceptable by all members of the dissertation committee, is further submitted to the Graduate School. The candidate's Dissertation Defense is a final oral examination open to all Graduate Faculty. Candidates submit a defense announcement, including an abstract of the dissertation, at least three weeks before the examination. The final draft of the dissertation must be certified by the chairperson of the dissertation committee using the appropriate form "Final Approval of the Doctoral Dissertation". Microfilming by UMI is required.
All doctoral degree work must be completed within 8 years after the first course of the doctoral program of study. More than 30 credit hours must be completed in residence at the University of MissouriSt. Louis. This determines the maximum number of hours that are transferable from another graduate program. At some point in their course work, doctoral students must successfully complete a minimum of 15 hours over three consecutive terms, which may include summer.
For further information about our Graduate Degrees in Mathematics and Computer Science, financial aid, and the regulations of the Graduate School, see our page on advanced degrees.