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
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
part-time 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.
The requirements for the Ph.D. degree include the following:
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
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.
Advancement to Ph.D. Candidacy is a four-step 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.
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,
- 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
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
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
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.
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 Missouri-St. 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