Faculty

A Prabhakar Rao., Professor*, Chairperson
Ph.D., University of California, Berkeley
Charles Chui, Distinguished Professor*
Ph.D., University of Wisconsin
Raymond Balbes, Professor Emeritus*
Ph.D., University of California, Los Angeles
William Connett, Professor Emeritus*
Ph.D., University of Chicago
Richard Friedlander, Professor*, Associate Chairperson
Ph.D., University of California, Los Angeles
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*
Ph.D., Cornell University
Grant V. Welland, Professor Emeritus*
Ph.D., Purdue University
Sanjiv K. Bhatia, Associate Professor*
Ph.D., University of Nebraska-Lincoln
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
Cezary Janikow, Associate Professor*
Ph.D., University of North Carolina at Chapel Hill
Qingtang Jiang, Associate Professor
Ph.D., Peking University
Kyungho Oh, Associate Professor*
Ph.D., Purdue University
Frederick Wilke, Associate Professor Emeritus*
Ph.D., University of Missouri-Columbia
Shiying Zhao, Associate Professor*
Ph.D., University of South Carolina
Galina N. Piatnitskaia., Affiliate Associate Professor
Ph.D., Moscow Physical-Technical Institute
Wenjie He, Assistant Professor*
Ph.D., University of Georgia
Hyung Woo Kang, Assistant Professor
Ph.D. KAIST
Martin Pelikan, Assistant Professor
Ph.D., University of Illinois at Urbana-Champaign
Donald E. Gayou, Affiliate Assistant Professor
Ph.D., Iowa State University
John Antognoli, Senior Lecturer; Coordinator of Evening Program
M.A., University of Missouri-St. Louis
Monica L. Brown, Lecturer
M.S., Southern Illinois University, Edwardsville
Aarti Dahiya, Lecturer
M.S., University of Missouri-St. Louis
Preetam S. Desai, Lecturer
M.S., University of Missouri-St. Louis
Qiang Sun Dotzel, Lecturer
M.A., University of Missouri-St. Louis
Dorothy Gotway, Lecturer
M.A., University of Kansas-Lawrence
Marlene Gustafson, Senior Lecturer Emerita
M.A., Western Reserve University
Leslie Johnson, Lecturer
M.S., Southeast Missouri State University
Nazire Koc, Lecturer
M.S., Southern Illinois University, Carbondale
Mary Kay McKenzie, Senior Lecturer Emerita
M.S., Saint Louis University
Shahla Peterman, Senior Lecturer
M.S., University of Wisconsin-Madison
Gillian Raw, Senior Lecturer Emerita
M.A., Washington University
Emily Ross, Senior Lecturer
M.A., Saint Louis University
Paul Schneider, Senior Lecturer
M.A., Saint Louis University
Cynthia Siegel, Senior Lecturer Emerita
M.A., University of Chicago

*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 part-time basis.

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 UM-St. 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 two 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 students at the sophomore level or higher, including graduate students. Applicants for each of these 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 Missouri-St. Louis, and showsuperior achievement in courses in the mathematical sciences. Application forms may be obtained from the Department of Mathematics and Computer Science. The deadline for application for both scholarships is March 15, and the scholarships must be used for educational fees or for books at UM-St. 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 higher-level courses may not be taken for credit or quality points if the higher-level 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 Mathematics 1800, Analytic Geometry and Calculus I, will be granted to those students who complete Mathematics 1900 with a grade of C- or better.

Similarly, students who are ready to begin their computer science studies with Computer Science 2250, Programming and Data Structures, will be granted credit for Computer Science 1250, Introduction to Computing, once they complete Computer Science 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 Non-Euclidean Geometry

ii) 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, Object-Oriented 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 4000 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.

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 3000-level, 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:
4330, Production and Operations Management - Logistics
4324, Production and Operations Management - Service Systems
4312, Business Forecasting
4326, Quality Assurance in Business
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 coursescomputer 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 UM-St. 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 three-hour 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 UM-St. 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 UM-St. 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 of the Graduate Record Examination (GRE) general aptitude test.

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.

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 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. At least 33 hours must be in courses numbered 5000 or above. All courses numbered below 5000 must be completed with a grade of at least B. Up to 9 hours can be in Math 7990, Ph.D. Dissertation Research. Courses outside the Department of Mathematics and Computer Science will require approval of the graduate director.

2. Advancement to Ph.D. Candidacy
Advancement to Ph.D. candidacy is a four-step process consisting of:

A) Completing 18 hours of 5000 level courses
other than Math 7990, Ph.D. Dissertation
Research.
B) Passing the comprehensive examinations.
C) Selecting a Ph.D. committee and preparing a
dissertation proposal.
D) Defending the dissertation proposal.

Qualifying Examination
A student must fulfill the following requirements.

Basic Requirement
Pass one written examination covering the fundamental topics from advanced calculus, complex variables and linear algebra-Math 4100, Math 4160, and Math 4450. This examination would normally take place within the first 12 credit hours of study after admission to the Ph.D. program.

Additional Requirement
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.

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 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. 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 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 4760 or CS 5760
Programming Languages, CS 4250
Computer Systems CS 5700
Software Development, one of CS 5500, CS 5520, CS 5540, or CS 5560
Advanced Data Structures and Algorithms, CS 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.

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 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 and other related fields where they have found their logical and analytical skills to be well-rewarded.