Department of Mathematics and Computer Science Home Page
Faculty
A Prabhakar Rao., Professor*, Chairperson
Ph.D., University of California, Berkeley
Charles Chui, Curators’ Professor*
Ph.D., University of Wisconsin
Richard Friedlander, Professor*, Associate Chairperson
Ph.D., University of California, Los Angeles
Qingtang, Jiang, Professor*
Ph.D., Peking University
Sanjiv K. Bhatia, Associate Professor*
Ph.D., University of NebraskaLincoln
Haiyan Cai, Associate Professor*
Ph.D., University of Maryland
Uday K. Chakraborty, Associate Professor*
Ph.D., Jadavpur University
Ronald Dotzel, Associate Professor*
Ph.D., Rutgers University
Wenjie He, Associate Professor*
Ph.D., University of Georgia
Cezary Janikow, Associate Professor*
Ph.D., University of North Carolina at Chapel Hill
Kyungho Oh, Associate Professor*
Ph.D., Purdue University
Shiying Zhao, Associate Professor*
Ph.D., University of South Carolina
Adrian Clingher, Assistant Professor
Ph.D., Columbia University
Hyung Woo Kang, Assistant Professor*
Ph.D. KAIST
Martin Pelikan, Assistant Professor*
Ph.D., University of Illinois at UrbanaChampaign
Galina N. Piatnikskaia, Affiliate Associate Professor
Ph.D., Moscow PhysicalTechnical Institute
Donald E. Gayou, Affiliate Assistant Professor
Ph.D., Iowa State University
John Antognoli, Senior Lecturer
M.A., University of MissouriSt. Louis
Monica L. Brown, Lecturer
M.S., Southern Illinois University, Edwardsville
Preetam S. Desai, Lecturer
M.S., University of MissouriSt. Louis
Qiang Sun Dotzel, Lecturer
M.A., University of MissouriSt. Louis
Dorothy Gotway, Lecturer
M.A., University of KansasLawrence
Nazire Koc, Lecturer
M.S., Southern Illinois University, Carbondale
Shahla Peterman, Senior Lecturer
M.S., University of WisconsinMadison
Emily Ross, Senior Lecturer
M.A., Saint Louis University
Raymond Balbes, Professor Emeritus*
Ph.D., University of California, Los Angeles
William Connett, Professor Emeritus*
Ph.D., University of Chicago
Deborah Tepper Haimo, Professor Emerita*
Ph.D., Harvard University
Wayne L. McDaniel, Professor Emeritus*
Ph.D., Saint Louis University
Stephen Selesnick, Professor Emeritus*
Ph.D., University of London
Jerrold Siegel, Professor Emeritus*
Ph.D., Cornell University
Grant V. Welland, Professor Emeritus*
Ph.D., Purdue University
Frederick Wilke, Associate Professor Emeritus*
Ph.D., University of MissouriColumbia
*members of Graduate Faculty
General Information
Degrees and Areas of Concentration
The Department of Mathematics and Computer Science offers work leading to the B.A. in mathematics, the B.S. in mathematics, the B.S. in computer science, and, in cooperation with the College of Education, the B.S.Ed. in secondary education with an emphasis in mathematics. The department also offers minors in computer science, mathematics, and statistics.
At the graduate level, the department offers a Master of Arts (M.A.) degree in mathematics, a Master of Science (M.S.) degree in computer science and a Ph.D. in applied mathematics.
The program leading to the B.A. in mathematics provides a broad grounding in different areas of mathematics, giving students the depth necessary to pursue various aims such as graduate studies or other career choices.
The B.S. in mathematics provides a substantial background in mathematics, statistics and computer science to produce graduates who can work as mathematicians. Both the B.A. and the B.S. in mathematics allow optional courses that enable the student to focus on areas of interest like pure or applied mathematics.
The B.S.Ed. in secondary education with an emphasis in mathematics introduces students to those branches of mathematics most relevant to the teaching of secondary school mathematics.
The B.S. in computer science prepares students for employment in modern computing technology and careers in computer science.
Students pursuing the M.A. degree in mathematics may choose an emphasis in either pure or applied mathematics. The pure mathematics emphasis is well suited for students preparing to teach at the high school, junior college, or four year liberal arts college level. Those who concentrate on applied courses in the M.A. program build a foundation for the application of mathematics in industry and the continuation of their education in the Ph.D. program in applied mathematics.
The M.S. degree in computer science emphasizes practical aspects of the field.
The Ph.D. in applied mathematics prepares students for a leadership role involving research and development in both industrial and academic settings.
Students may enroll in any of these graduate programs on a parttime basis.
Career Outlook
A degree in mathematics or computer science prepares wellmotivated students for interesting careers.
Our graduates find positions in industry, government, and education. The demand for individuals well trained in statistics, computer science, and applied mathematics is greater than the available supply. In addition, a number of graduates in mathematics have elected careers in business, law and other related fields where they find logical and analytical skills valuable.
Graduates in computer science and mathematics from UMSt. Louis are located throughout the country, and they also have a strong local presence. They have careers in banking, health care, engineering and manufacturing, law, finance, public service, management, and actuarial management. Many are working in areas such as systems management, information systems and data management, scientific computing, and scientific positions in the armed services. Others have careers in education, especially at secondary and higher levels.
Department Scholarships
The Department of Mathematics and Computer Science offers four scholarships for students who are majoring in mathematics or computer science.
The Mathematical Sciences Alumni Scholarship is a monetary award for outstanding undergraduates at the junior or senior level.
The Edward Z. Andalafte Memorial Scholarship is a monetary award for outstanding undergraduate students at the sophomore level or higher. Applicants for each of these two scholarships must have a grade point average of 3.5 or higher in at least 24 hours of graded course work at the University of MissouriSt. Louis, and show superior achievement in courses in the mathematical sciences.
The Raymond and Thelma Balbes Scholarship in Mathematics is a monetary award for students at the sophomore level or higher who are pursuing a degree in mathematics, have an overall GPA of at least 3.0 and a GPA of at least 3.2 in mathematics and who have completed three semesters of calculus.
The Joseph M. and Mary A. Vogl Scholarship in Mathematics is a need based monetary award for mathematics majors. Application forms for these scholarships may be obtained from the Department of Mathematics and Computer Science.
The deadline for application for all of these scholarships is March 15, and the scholarships must be used for educational fees or for books at UMSt. Louis starting in the fall semester following the application
Undergraduate Studies
General Education Requirements
All majors must satisfy the university and appropriate school or college general education requirements. All mathematics courses may be used to meet the university’s general education breadth of study requirement in natural sciences and mathematics.
Satisfactory/Unsatisfactory Restrictions
Majors in mathematics and computer science may not take mathematical sciences or related area courses on a satisfactory/unsatisfactory basis. Students considering graduate study should consult with their advisers about taking work on a satisfactory/unsatisfactory basis.
Degree Requirements
All mathematical sciences courses presented to meet the degree requirements must be completed with a grade of C or better. At least four courses numbered 3000 or above must be taken in residence. Students must have a 2.0 grade point average in the mathematical sciences courses completed.
Students enrolling in introductory mathematics courses should check the prerequisites to determine if a satisfactory score on the Mathematics Placement Test is necessary. The dates on which this test is administered are given in the Schedule of Classes. Placement into introductory courses assumes a mastery of two years of high school algebra.
A minimum grade of C is required to meet the prerequisite requirement for any course except with permission of the department.
Note: Courses that are prerequisites for higherlevel courses may not be taken for credit or quality points if the higherlevel course has been satisfactorily completed.
Many students are qualified, as a result of having studied calculus in high school, to begin their major with Math 1900, Analytic Geometry and Calculus II, or Math 2000, Analytic Geometry and Calculus III. These students are urged to consult with the department before planning their programs. Credit for Math 1800, Analytic Geometry and Calculus I, will be granted to those students who complete Math 1900 with a grade of C or better.
Similarly, students who are ready to begin their computer science studies with CS 2250, Programming and Data Structures, will be granted credit for CS 1250, Introduction to Computing, once they complete CS 2250 with a grade of C or better.
Degree Requirements in Mathematics
All mathematics majors in all undergraduate programs must complete the mathematics core requirements.
Core Requirements
1) The following courses are required:
1250, Introduction to Computing
1320, Applied Statistics I
1800, Analytic Geometry and Calculus I
1900, Analytic Geometry and Calculus II
2000, Analytic Geometry and Calculus III
2020, Introduction to Differential Equations
2450, Elementary Linear Algebra
3000, Discrete Structures
4100, Advanced Calculus I
2) The related area requirements as described below must be satisfied.
Students seeking a double degree, either within this department or with another department, do not have to fulfill the related area requirements.
Bachelor of Arts in Mathematics.
In addition to the core requirements and the College of Arts and Sciences' foreign language requirement, three mathematics courses at the 4000 level or higher must be completed. Of these, one must be 4400, Introduction to Abstract Algebra
B.S.Ed. in Secondary Education with emphasis in mathematics.
In addition to the core requirements and the required education courses, three mathematics/statistics courses at the 4000 level or higher must be completed. Of these, one must be
4400, Introduction to Abstract Algebra, and one must be chosen from:
4660, Foundations of Geometry or 4670, Introduction to NonEuclidean Geometry
Bachelor of Science in Mathematics
In addition to the core requirements, the B.S. in Mathematics degree requires:
1) Completing all of the following:
4160, Functions of a Complex Variable
4400, Introduction to Abstract Algebra
4450, Linear Algebra
2) Completing an additional three courses numbered above 4000 in mathematics, statistics or computer science, at least one of which must be in mathematics/statistics.
Degree Requirements in Computer Science
Candidates for the Bachelor of Science in Computer Science degree must complete the following work:
1) Computer Science
1250, Introduction to Computing
2250, Programming and Data Structures
2260, ObjectOriented Programming with C++
2700, Computer Systems: Architecture and Organization
2710, Computer Systems: Programming
2750, Advanced Programming with Unix
3000, Discrete Structures
3130, Design and Analysis of Algorithms
4250, Programming Languages
4280, Program Translation Techniques
4760, Operating Systems
2) Mathematics and Statistics
1320, Applied Statistics I
1800, Analytic Geometry and Calculus I
1900, Analytic Geometry and Calculus II
2000, Analytic Geometry and Calculus III
2450, Elementary Linear Algebra
3) Philosophy
4458, Ethics and the Computer
4) Five more elective courses, numbered above 3000 if in computer science, and above 2010 if in mathematics or statistics. At least three of these elective courses must be in computer science, and at least one must be in mathematics or statistics.
5) Satisfy the related area requirements as described below.
Related Area Requirements
Candidates for the B.A. in Mathematics must satisfy the requirements in one of the groups below with a grade of C or better. Candidates for the B.S.Ed. in Mathematics, B.S. in Mathematics and B.S. in Computer Science must satisfy the requirements in two of the groups below with a grade of C or better.
Candidates for the B.S. in Computer Science may not choose group 1. Candidates for the B.A. in Mathematics, B.S.Ed. in Mathematics, or B.S. in Mathematics may not choose group 2 or 3. If candidates for any of these three latter degrees choose group 4, then they cannot apply either of the two courses listed in that group towards the additional 4000 level mathematics courses (beyond the core requirements) that must be completed for each of these degrees.
Students seeking a double degree, either within this department or with another department, do not have to fulfill the related area requirements.
Related Area Courses
1) Computer Science:
Two courses from the following list:
2250, Programming and Data Structures
2700, Computer Systems: Architecture and Organization
3130, Design and Analysis of Algorithms
4140, Theory of Computation
4410, Computer Graphics
4440, Digital Image Processing
2) Mathematics (Analysis):
Two courses from the following list:
2020, Introduction to Differential Equations
4030, Applied Mathematics I
4100, Advanced Calculus
4160, Functions of a Complex Variable
4230, Numerical Analysis I
3) Mathematics (Algebra):
Two courses from the following list:
4350,Theory of Numbers
4400, Introduction to Abstract Algebra
4450, Linear Algebra
4550, Combinatorics
4) Statistics:
4200, Mathematical Statistics I
4210, Mathematical Statistics II
5) Biology:
2102, General Ecology
2103, General Ecology Laboratory
6) Biology:
2012, Genetics
4182, Population Biology
7) Chemistry:
1111, Introductory Chemistry I
1121, Introductory to Chemistry II
8) Chemistry:
3312, Physical Chemistry I
and another 3000level, or above, chemistry course.
9) Economics:
4100, Introduction to Econometrics,
and one of either:
4110, Applied Econometrics or 4130, Econometric and Time Series Forecasting
10) Philosophy :
3360, Formal Logic
3380, Philosophy of Science
4460, Advanced Formal Logic
11) Physics:
2111, Physics: Mechanics and Heat
2112, Physics: Electricity, Magnetism, and Optics
12) Physics:
3221, Mechanics
and another 3000 level, or above, physics course
13) Business Administration:
3320, Introduction to Operations Management
and one of the following courses:
4312, Business Forecasting
4324, Production and Operations Management Service Systems
4326, Quality Assurance in Business
4330, Production and Operations Management  Logistics
4350, Operations Research
14) Engineering:
2310, Statics
2320, Dynamics
Minor Requirements
The department offers minors in computer science, mathematics, and statistics. All courses presented for any of these minors must be completed with a grade of C or better.
Minor in Computer Science
The requirements for the minor are:
1250, Introduction to Computing
2250, Programming and Data Structures
2700, Computer Systems: Architecture and Organization
and two additional courses computer science courses numbered above 2700.
A minimum of two computer science courses numbered above 2700 must be taken in residence in the Department of Mathematics and Computer Science at UMSt. Louis.
Minor in Mathematics
The requirements for the minor are:
1800, Analytic Geometry and Calculus I
1900, Analytic Geometry and Calculus II
2000, Analytic Geometry and Calculus III
and two additional threehour mathematics courses numbered above 2400. A minimum of two mathematics courses numbered 2000 or above must be taken in residence in the Department of Mathematics and Computer Science at UMSt. Louis.
Minor in Statistics
The requirements for the minor are:
1320, Applied Statistics I
4200, Mathematical Statistics I
and two additional courses in statistics numbered above 4200. A minimum of two statistics courses numbered above 2000 must be taken in residence in the Department of Mathematics and Computer Science at UMSt. Louis.
Graduate Studies
The Department of Mathematics and Computer Science offers an M.A. degree in mathematics, a 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 applicant’s 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 recommendation and scores from the Graduate Record Examination (GRE) general aptitude test.
Computer Science Program
Applicants to the Graduate Program in Computer Science must meet the general graduate admission requirements of the Graduate School, described in the U.M.St. Louis Bulletin. Students seeking admission to the program must formally apply for admission to the Graduate School either online or by traditional means. Additional requirements are listed below.
Applicants must have at least a bachelor’s degree, preferably in computer science or in a related area. Applicants with bachelor’s degrees outside of computer science must demonstrate significant proficiency in computer science, either by taking the GRE subject area examinations or by explicitly showing competence in the following areas:
 C programming (CS 1250 and CS 2250).
 An object oriented programming language (C++ or Java) (CS 2260).
 A course in data structures (CS 2250).
 A course in assembly language programming, computer architecture, or computer organization (CS 2700).
 A course in design and analysis of algorithms (CS 3130).
 Programming with Unix, including shell scripts and tools (CS 2750).
Students must also have satisfactorily completed mathematics courses equivalent to the following UMSt. Louis courses:
 Two semesters of calculus (Math 1800 and 1900).
 A course in elementary linear algebra (Math 2450).
 A course in discrete mathematics (Math 3000).
 An elementary course in probability or statistics (Math 1320).
A student missing some of the above requirements may be admitted on restricted status if there is strong supportive evidence in other areas. The student will have to take the missing courses, or demonstrate proficiency to the satisfaction of the Graduate Director. Special regulations of the Graduate School that apply to students 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.
Degree Requirements
Master of Arts in Mathematics
Candidates for the M.A. degree must complete 30 hours of course work. All courses numbered below 5000 must be completed with grades of at least B. The courses taken must include those listed below in group A together with additional courses discussed in B.
Students who have already completed courses equivalent to those in A) may substitute other courses numbered above 4000. All substitutions of courses for those listed in A) require the prior approval of the graduate director.
A) Mathematics core:
4100, Advanced Calculus
4160, Functions of a Complex Variable
4450, Linear Algebra
B) M.A. candidates must also complete 15 hours of course work numbered 5000 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 B) 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 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.
Doctor of Philosophy in Applied Mathematics
The program has two options:
1) Mathematics Option
2) Computer Science Option
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 4000 or above.
In the Mathematics Option, at least 33 hours must be in courses numbered 5000 or above.
In the 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 Math 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 applied 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 threestep process consisting of:
A)
Completing 18 hours of 5000 level courses other than Math 7990, Ph.D. Dissertation Research.
B) Passing the comprehensive examination.
C)
Selecting a Ph.D. committee and 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.
Mathematics Option: Topics from advanced calculus,
Complex variables and linear algebra (Math 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).
Additional Requirement
After fulfilling the basic requirement above, the student must meet one of the following:
a. 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.
b. 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 a) and b), the graduate committee will determine if the topics are consistent with the option that the student is pursuing.
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.
Doctoral Dissertation
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 7990, Ph.D. Dissertation Research. A maximum of 9 hours in Math 7990 can be used toward the required hours of work in courses numbered 5000 or above.
Master of Science in Computer Science
Candidates for the M.S. degree in Computer Science must complete 30 hours of course work, subject to the Graduate School regulations. Of these, at least 18 hours must be numbered 5000 or above, with at least one course numbered 6000 or above, chosen with the prior approval of the Graduate Director. All courses numbered below 5000 must be completed with grades of at least B. Outside computer science, up to 6 hours of related course work is allowed upon permission of the Graduate Director.
Students must satisfy all of the following core requirements:
 Operating Systems, CS 4760
 Programming Languages, CS 4250
 Computer Systems, CS 5700
 Software Engineering, CS 5500
 Advanced Data Structures and Algorithms, CS 5130
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.
Additionally, students must attend at least five different seminars or colloquium presentations in the department.
Thesis Option
Students may choose to write an M.S. thesis 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 CS 6900, Thesis. Students writing an M.S. thesis must defend their thesis in an oral exam administered by a committee of three department members which includes the thesis director.
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.
Career Outlook
Graduates from the Department of Mathematics and Computer Science have little difficulty in finding positions in industry, government, and education. The demand for individuals welltrained in statistics, computer science, and applied mathematics is greater than the available supply. In addition, a number of graduates in mathematics have elected careers in business and other related fields where they have found their logical and analytical skills to be wellrewarded.
