Ph.D. in Mathematical and Computational Sciences | UMSL

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Ph.D. in Mathematical and Computational Sciences

The doctoral program is designed to provide the highest level of academic study and research in mathematical and computational sciences. 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 mathematical and computational sciences 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.

CS Program Coordinator: Sanjiv Bhatia

Math Program Coordinator: Qingtang Jiang


Doctoral Program

The program has three options:

  • Mathematics Option
  • Computer Science Option
  • Statistics Option

The requirements for the Ph.D. degree include the following:

1. Course work
2. Ph.D. candidacy
3. Dissertation Committee and Dissertation Proposal
4. Doctoral dissertation

The requirements are described in detail below.

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.

Statistics Option, at least 33 hours must be in courses numbered 5000 or above.

At most 9 hours of a student's enrollment in 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 four-step process consisting of:

    1. Completing 18 hours of 5000 level courses other than Ph.D. Dissertation Research as appropriate for the selected option.
    2. Passing the comprehensive examination.
    3. Selecting a PH.D. Committee, preparing a dissertation proposal, and defense of the proposal. 
Qualifying Examination    

A student must fulfill the following requirements.

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.  If failed twice, the student will be dismissed from the program. 

Mathematics Option:

Topics from real analysis, complex analysis and linear algebra:

  • MATH 4100     Real Analysis I                                   3
  • MATH 4160     Complex Analysis I                           3
  • MATH 4450     Linear Algebra                                   3

Total Hours                                                                      9

Computer Science Option:

Topics from the theory of programming languages, operating systems, analysis of algorithms, and computer systems: 

  • CMP SCI 4250     Programming Languages                3
  • CMP SCI 4760     Operating Systems                           3
  • CMP SCI 5130     Advanced Data Structures and Algorithms   3
  • CMP SCI 5700     Computer Systems                           3

    Total Hours                                                                 12

Statistics Option: Topics from real analysis, linear algebra, mathematical statistics:

  • MATH 4100       Real Analysis I                                    3
  • MATH 4450       Linear Algebra                                    3
  • MATH 4200       Mathematical Statistics I                  3
  • MATH 4210       Mathematical Statistics II                 3

    Total Hours                                                                 12

Additional Requirements

After fulfilling the basic requirement above, the student must meet one of the following:

      1. 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.

      2. 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. The dissertation committee will be formed, and the student will meet with this committee for an oral defense of his/her 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. 

4.  Doctoral Dissertation

Each Ph.D. candidate must write a dissertation that is an original contribution to the field on a topic approved by the candidate's Ph.D. committee and the department, and which meets  the standards and requirements set by the Graduate School including the public defense of the dissertation. Student working on a dissertation may enroll in Ph.D. Dissertation Research, as appropriate for the selectedoption. A maximum of 9 hours Dissertation Research can be used toward the required hours of work in courses numbered 5000 or above.