The following areas are available:
Master of Science in Computer Science
Graduate Studies
The Department of Mathematics and Computer Science offers an M.A. degree in mathematics, Ph.D. degree in applied mathematics, and an M.S. degree in computer science.
Admission
Applicants must meet the general admission requirements of the Graduate School, described elsewhere in this Bulletin. Additional admission requirements for specific programs are listed below.
Mathematics Programs
Applicants must have at least a bachelor's degree in mathematics or in a field with significant mathematical content. Examples of such fields include computer science, economics, engineering and physics. An applicants record should demonstrate superior achievement in undergraduate mathematics.
Individuals may apply for direct admission to either the M.A. or Ph.D. program. Candidates for the M.A. degree may choose to concentrate in either pure or applied mathematics. A student in the M.A. program may petition the department for transfer to the Ph.D. program upon successful completion of 15 credit hours and fulfillment of additional requirements as listed below.
Students intending to enter the Ph.D. program must have a working ability in modern programming technologies. A student with a deficiency in this area may be required to take courses at the undergraduate level in computer science.
Applicants for the Ph.D. program must, in addition, submit three letters of reference and scores from the Graduate Record Examination (GRE) general aptitude test and the subject test in mathematics. Applicants who did not major in mathematics may substitute the subject test in another field.
Computer Science Program
Applicants for the M.S. Degree in Computer Science must have at least a bachelor's degree, preferably in computer science or in a related area. Students with bachelor's degrees outside computer science must demonstrate significant proficiency in computer science, either by taking the GRE subject area examination or by explicitly showing competence in the following areas. (Any area requirement can be satisfied through suitable experience or completed coursework, if approved by the Graduate Director.)
- Programming experience equivalent to at least two semesters, including knowledge of a modern structured language and a modern object-oriented language.
- Elementary data structures.
- Assembly language programming, computer architecture, or computer organization.
- Design and analysis of algorithms
- Basic knowledge of the Unix operating system and program development environment.
Students must also have completed mathematics courses equivalent to the following:
- Two semesters of calculus.
- Elementary linear algebra.
- Discrete mathematical structures.
- Elementary probability or statistics
A student missing some of the above requirements may be admitted on restricted status if there is strong supportive evidence in other areas. Special regulations of the Graduate School applying to students while they are on restricted status are described elsewhere in this Bulletin.
Preliminary Advisement
Incoming students are assigned advisers with whom they should consult before each registration period to determine an appropriate course of study. If necessary, students may be required to complete undergraduate course work without receiving graduate credit.
Master of Arts in Mathematics
Candidates for the M.A. degree must complete 33 hours of course work. All courses numbered below 400 must be completed with grades of at least B. The courses taken must include those listed below in either group A) or group B), together with additional courses discussed in C). Students who have already completed courses equivalent to those in A) or B) may substitute other courses numbered above 300. All substitutions of courses for those listed in A) or B) require the prior approval of the graduate director.
A) Pure mathematics core:
310(4100), Advanced Calculus
316(4160), Functions of a Complex Variable
340(4400), Introduction to Abstract Algebra I
345(4450), Linear Algebra
380(4800), Introduction to Topology
B) Applied mathematics core:
310(4100), Advanced Calculus
316(4160), Functions of a Complex Variable
320(4200), Mathematical Statistics
323(4330), Numerical Analysis I
345(4450), Linear Algebra
C) M.A. candidates must also complete 18 hours of course work numbered 400 or above, chosen with the prior approval of the graduate director. Courses may be chosen to develop expertise in either pure or applied mathematics.
Thesis Option Part of C) may consist of an M.A. thesis written under the direction of a faculty member in the Department of Mathematics and Computer Science. A thesis is not, however, required for this degree. A student who wishes to write a thesis should enroll in 6 hours of Math 490(6900), M.A. Thesis. Students writing an M.A. thesis must defend their thesis in an oral exam administered by a committee of three department members which includes the thesis director.
M.A. degree students may have several of the courses in B) as part of their undergraduate record. Those who anticipate enrolling in the Ph.D. program are advised to use the opportunity to replace courses in B) they have had at the undergraduate level with courses such as
311(4110), Advanced Calculus II
380(4800), Introduction to Topology and if possible
331(4310), Analysis of Variance and Design of Experiments
340(4400), Introduction to Abstract Algebra I
364(4640), Introduction to Differential Geometry
 |
The requirements for the Ph.D. degree include the following:
1. Course work
2. Ph.D. candidacy
3. Doctoral dissertation
The requirements are described in detail below.
1. Course Work
A minimum of 60 hours of courses numbered 300 or above is required, including dissertation work. At least 33 hours must be in courses numbered 400 or above. All courses numbered below 400 must be completed with a grade of at least B. In addition to course work, all Ph.D. students are required to attend and participate in applied mathematics seminars.
Distribution Requirement
Among the courses presented for the degree there must be six courses from the following list such that at least three areas are represented and at least two courses are chosen from each of two of these areas:
I. Analysis and Applied Mathematics
402(5020), Classical Applied Mathematics
403(5700), Topics in Applied Mathematics
410(5100), Theory of Functions of a Real Variable
416(5160), Functions of a Complex Variable
418(5710), Topics in Analysis
430(5300), Partial Differential Equations
470(6700), Functional Analysis
II. Numerical Analysis
423(5720), Topics in Numerical Analysis
427(5270), Numerical Linear Algebra
III. Optimization and Operations Research
435(5350), Operations Research - Deterministic Models
436(5360), Operations Research - Stochastic Models
437(5370), Quality Management
460(5040), Calculus of Variations
IV. Computational Mathematics
404(5600), Topics in Computation
405(5050), Computational Curves and Surfaces
406(5060), Computational Harmonic Analysis
407(6070), Time-Frequency Analysis
408(6080), Advances in Wavelet Analysis
V. Probability and Statistics
420(6200), Probability Theory
428(6600), Topics in Probability Theory
432(5320), Applied Statistics
2. Advancement to Ph.D. Candidacy
Advancement to Ph.D. candidacy is a four-step process consisting of:
A) Completing distribution requirement.
B) Passing the comprehensive examinations.
C) Selecting a Ph.D. committee and preparing a dissertation proposal.
D) Defending the dissertation proposal.
Comprehensive Examinations
Comprehensive examinations are offered in the following areas:
Applied Mathematics
Real Analysis
Complex Analysis
Numerical Analysis
Optimization
Operations Research
Computational Mathematics
Probability
Statistics
The examinations are given on a rotating basis through the academic year; more detailed information on the individual examinations can be found in the Department of Mathematics and Computer Science Graduate Student Handbook. Each student must pass four comprehensive examinations. Upon permission by the Graduate Director and the Graduate School, a student may take one examination in a field which is not fully represented by any one of the above areas. This exam is created by a panel of three professors in consultation with the Graduate Director. The panel may include one professor from another department if special expertise outside mathematics and computer science is needed. This examination may be administered as an oral exam.
Students must apply to take each examination at least 45 days before the examination is offered. A student may attempt a comprehensive examination over a particular area no more than twice; the second attempt must be within 13 months of the first attempt.
Selection of a Ph.D. Committee and Preparation of a Dissertation Proposal .
The student is required to identify a dissertation adviser and an area of specialization for the dissertation. The area of specialization can be in a discipline complementary to mathematics. Usually, students select an adviser from contacts made through course work or in the seminar series. The adviser and student will then form a Ph. D. committee which may include faculty from other departments at UM-St. Louis. The committee advises the student on course work and research.
Each student must prepare a dissertation proposal. This is a substantial document describing the problem to be worked on and the methods to be used. It should also demonstrate the student's proficiency in written communication. The proposal is to be submitted to the Ph.D. committee for approval.
Dissertation Proposal Defense. If the Ph.D. committee finds the student's dissertation proposal acceptable, a defense is scheduled. This is a public event in which the student demonstrates mastery of the necessary skills to begin research.
3. 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 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. Students working on a dissertation may enroll in Math 499(7990), Ph.D. Dissertation Research; a maximum of 9 hours in Math 499(7990) can be used toward the required hours of work in courses numbered 400 or above.
|
Candidates for the M.S. degree in Computer Science must complete 30 hours of course work, subject to the Graduate School regulations. All courses numbered below 400 must be completed with grades of at least B. Outside computer science, upto 6 hours of related course work is allowed upon permission of the Graduate Director.
Students must receive credit in all areas of the following core requirements. Waiving or substituting for a specific requirement can be done on the basis of prior course work or experience (at the discretion of the Graduate Director), but it will not reduce the total hours required for the degree.
- Operating Systems (CS 376(4760) or CS 476(5760)
- Programming Languages (CS 325(4250)
- Computer Systems (CS 470(5700)
- Software Development (one of CS 450(5500), CS 452(5520), CS 454(5540), or CS 456(5560)
- Advanced Data Structures and Algorithms (CS 413(5130)
Financial Assistance
Any student who intends to apply for financial assistance, in the form of a teaching assistantship or a research assistantship, is required to have three letters of recommendation submitted with the application to the graduate program in Mathematics or Computer Science. The application must include scores on the GRE general aptitude test. Applicants are also encouraged to submit scores in the GRE subject area test in Mathematics or Computer Science. Applications for financial assistance should be submitted before February 15 prior to the academic year in which the student expects to begin graduate study. Notifications of awards are generally made March 15, and students awarded financial assistance are expected to return letters of acceptance by April 15.
|