**Department of Mathematics and Computer Science Home Page **

**Faculty **

**A Prabhakar Rao.,** Professor, Interim Chairperson

Ph.D., University of California, Berkeley

**Charles Chui, **Curators’ Professor

Ph.D., University of Wisconsin

**Uday K. Chakraborty,** Professor

Ph.D., Jadavpur University

**Qingtang Jiang, **Professor

Ph.D., Peking University

**Sanjiv K. Bhatia,** Associate Professor

Ph.D., University of Nebraska-Lincoln

**Haiyan Cai,** Associate Professor

Ph.D., University of Maryland

**Adrian Clingher,** Associate Professor

Ph.D., Columbia 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

**Hyung Woo Kang,** Associate Professor

Ph.D. Korea Advanced Institute of Science and Technology (KAIST)

**Shiying Zhao,** Associate Professor

Ph.D., University of South Carolina

**Shahla Peterman,** Teaching Professor

M.S., University of Wisconsin-Madison

**Galina N. Piatnitskaia,** Teaching Professor

Ph.D., Moscow Physical-Technical Institute

**Michael Schulte,** Associate Teaching Professor

M.S., Florida Institute of Technology

**Qiang Sun Dotzel,** Assistant Teaching Professor

M.A., University of Missouri-St. Louis

**Nazire Koc, **Assistant Teaching Professor

M.S., Southern Illinois University, Carbondale

**Emily Ross, **Assistant Teaching Professor

M.A., Saint Louis University

**Jennifer Shrensker,** Assistant Teaching Professor

M.A., Washington University

**Albert Stanger, **Academic Coordinator and Assistant Teaching Professor

M.A., University of Missouri-St. Louis

**Joyce Langguth,** Teaching Associate

B.S. Ed., Southeast Missouri State University

**Raymond Balbes, **Professor Emeritus

Ph.D., University of California, Los Angeles

**William Connett,** Professor Emeritus

Ph.D., University of Chicago

**Richard Friedlander,** Founders Professor

Ph.D., University of California, Los Angeles

**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 Missouri-Columbia

**John Antognoli,** Teaching Professor Emeritus

M.A., University of Missouri-St. Louis

## General Information

**Degrees and Areas of Concentration
**The Department of Mathematics and Computer Science offers work leading to the Bachelor of Arts (B.A.) in mathematics, the Bachelor of Science (B.S.) in mathematics, the B.S. in computer science, and, in cooperation with the College of Education, the Bachelor of Secondary Education (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 Doctor of Philosophy (Ph.D.) in applied mathematics – with options in mathematics and computer science.

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. Students pursuing the B.A. or the B.S. in mathematics will graduate with analytic and writing skills in mathematics and will have knowledge of content in core areas of the subject. They will have been exposed to applications of mathematics and they will possess critical thinking and quantitative skills.

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 curriculum provides a firm foundation for both more traditional computer science as well as for the technical aspects of the emerging information technology areas This is accomplished through fundamental courses in mathematics and statistics, a rigorous list of core computer science courses, as well as by emphasizing written and oral communication skills, problem solving, and exposure to modern technology. In addition, the program offers a variety of interest specific electives such as graphics, image processing, AI, database systems, networking, security, object-oriented and web-based technology. Given the ever-widening impact of digital technology on daily life, it appears that Computer Science graduates will enjoy significant employment opportunities.

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. Our graduates will have abilities in the basic areas of algebra and analysis, and a breadth of knowledge in core subjects at the graduate level. They will study at least one area of mathematics or statistics in depth and will understand some of the contemporary research in applied mathematics and statistics. They will develop the ability to prepare and deliver oral and written presentations and the ability to pursue mathematical knowledge independently.

The M.S. degree in computer science emphasizes practical aspects of the field. Our graduates will develop expertise in at least one modern programming language. They will possess a breadth of knowledge of core areas in computer science, and will develop depth of knowledge in one area of the subject. They will be prepared to independently learn and adapt new technology and they will develop the ability to read current research in some areas. They will have the capability to prepare and deliver oral and written presentations on topics in computer science.

The Ph.D. in applied mathematics has options in mathematics and computer science. The mathematics option prepares students for a leadership role involving research and development in both industrial and academic settings. Students choosing this option will develop abilities in the basic areas of algebra and analysis and will possess breadth of knowledge in core subjects at the graduate level. They will study at least one area of mathematics or statistics in depth and will understand contemporary research in applied mathematics and statistics. They will develop the ability to prepare and deliver oral and written presentations, and they will possess the ability to pursue and produce mathematical knowledge independently.

Students choosing the computer science option will develop a breadth of abilities in the core areas of computer science at the graduate level. They will gain a depth of ability in contemporary research in their chosen subfield of computer science, and will be able to pursue independent research in their area of specialization.

Students may enroll in any of these graduate programs on a part-time basis.

## Career Outlook

A degree in mathematics or computer science prepares well-motivated 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 UMSL 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 many scholarships available to department majors.

**The Alumni Scholarship** is a monetary award for outstanding undergraduate students open to all junior and senior department majors.

**The Edward Z. Andalafte Memorial Scholarship **is a monetary award for outstanding undergraduate department majors 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 Missouri-St. Louis, and show superior achievement in courses taken in the department.

**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.

**Computer Science Scholarship** is a monetary award for outstanding computer science majors with preference given to freshman and sophomore students. Applicants must have a grade point average of 3.5 or higher in courses taken in the department.

**The Boeing Company Scholars Program in Computer Science** is a monetary award for full-time (at least 12 hours) upper-level undergraduate students in computer science. Recipients must have a minimum GPA of 3.2 and must maintain a GPA of 3.0. Preference will be given to traditionally underrepresented populations.

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 UMSL 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 on the department’s website. 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 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 CMP SCI 2250, Programming and Data Structures, will be granted credit for CMP SCI 1250, Introduction to Computing, once they complete CMP SCI 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:

**CMP SCI 1250,**Introduction to Computing

**MATH 1320,**Applied Statistics I

**MATH 1800,**Analytic Geometry and Calculus I

**MATH 1900,**Analytic Geometry and Calculus II

**MATH 2000,**Analytic Geometry and Calculus III

**MATH 2020,**Introduction to Differential Equations

**MATH 2450,**Elementary Linear Algebra

**MATH 3000,**Discrete Structures

**MATH 4100,**Real Analysis 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

**MATH 4400,**Introduction to Abstract Algebra, and one must be chosen from:

**MATH 4660,**Foundations of Geometry

**or**

**MATH 4670,**Introduction to Non-Euclidean 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:

**MATH 4160, ** Complex Analysis I

**MATH 4400, **Introduction to Abstract Algebra

**MATH 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.

**Related Area Requirements for majors in Mathematics**

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 and B.S. in Mathematics must satisfy the requirements in two of the groups below with a grade of C-or better.

If candidates choose group 2, 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:

**CMP SCI 2250,** Programming and Data Structures

**CMP SCI 2700,** Computer Architecture and Organization

**CMP SCI 3130,** Design and Analysis of Algorithms

**CMP SCI 4140,** Theory of Computation

**CMP SCI 4410,** Computer Graphics

**CMP SCI 4440,** Digital Image Processing

**2) Statistics:
MATH 4200,** Mathematical Statistics I

**MATH 4210,**Mathematical Statistics II

**3) Biology:
BIOL 2102,** General Ecology

**BIOL 2103,**General Ecology Laboratory

**4) Biology:
BIOL 2012,** Genetics

**BIOL 4182,**Population Biology

**5) Chemistry:
CHEM 1111,** Introductory Chemistry I

**CHEM 1121,**Introductory Chemistry II

**6) Chemistry:
CHEM 3312,** Physical Chemistry I and another 3000-level, or above, chemistry course

**7) Economics:
ECON 1001,** Principles of Microeconomics

**ECON 1002,**Principles of Macroeconomics

**ECON 4100,**Introduction to Econometrics

**8) Philosophy:
PHIL 3360,** Formal Logic

**PHIL 3380,**Philosophy of Science

**PHIL 4460,**Advanced Formal Logic

**9) Physics:
PHYSICS 2111,** Physics: Mechanics and Heat

**PHYSICS 2112,**Physics: Electricity, Magnetism, and Optics

**10) Physics:
PHYSICS 3221,** Mechanics and another 3000 level, or above, physics course

**11) Business Administration:
LOG OM 3320**, Introduction to Operations Management and one of the following courses:

**LOG OM 4321,**Production and Operations Management

**LOG OM 4326,**Quality Assurance in Business

**LOG OM 4330,**Business-Logistics Systems

**LOG OM 4350,**Management Science Methods

**12) Engineering:
ENGR 2310,** Statics

**ENGR 2320,**Dynamics

## Degree Requirements in Computer Science

Candidates for the **B. S. Computer ****Science ** degree must complete the following work:

**1) Computer Science Core**

**CMP SCI 1250,** Introduction to Computing

**CMP SCI 2250,** Programming and Data Structures

**CMP SCI 2261, **Object-Oriented Programming

**CMP SCI 2700,** Computer Architecture and Organization

**CMP SCI 2750,** System Programming and Tools

**CMP SCI 3010,** Web Programming

**CMP SCI 3130,** Design and Analysis of Algorithms

**CMP SCI 4250,** Programming Languages

**CMP SCI 4280,** Program Translation

**CMP SCI 4500,** Software Engineering

**CMP SCI 4760,** Operating Systems

**2) Computer Science Electives**

Five more elective computer science courses, numbered above 3000.

**3) Mathematics and Statistics **

**MATH 1320, ** Applied Statistics I

**MATH 1800,** Analytic Geometry and Calculus I

**MATH 1900,** Analytic Geometry and Calculus II

**MATH 2450,** Elementary Linear Algebra

**MATH 3000,** Discrete Structures

**4) Additional Skills
ENGL 3130,** Technical Writing

There are no related area requirements for majors in Computer Science

**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:

**CMP SCI 1250,**Introduction to Computing

**CMP SCI 2250,**Programming and Data Structures

and three additional computer science courses numbered 2000 or above.

A minimum of two computer science courses numbered above 2000 must be taken in residence in the Department of Mathematics and Computer Science at UMSL.

**Minor in Mathematics
**The requirements for the minor are:

**MATH 1800,**Analytic Geometry and Calculus I

**MATH 1900,**Analytic Geometry and Calculus II

**MATH 2000,**Analytic Geometry and Calculus III

**and two additional three-hour mathematics courses**numbered above 2400, excluding 2510. A minimum of two mathematics courses numbered 2000 or above must be taken in residence in the Department of Mathematics and Computer Science at UMSL.

**Minor in Statistics
**The requirements for the minor are:

**MATH 1320,**Applied Statistics I

**MATH 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 UMSL.

**Certificate in Actuarial Studies** (pending CBHE approval)

Actuaries use the tools of economics, finance, and mathematics to evaluate and price risk. They are employed by insurance
companies, pension funds, consulting firms, and a variety of other financial institutions. The actuarial profession has
consistently been ranked as one of the most desirable professions in which to be employed. To become an actuary one must
satisfy certain educational requirements, pass exams offered by the Society of Actuaries, and complete professional courses.

The Certificate in Actuarial Studies is designed to provide the education needed for entry level employment in the actuarial profession. Those who complete the certificate will satisfy the Validation by Educational Experience requirement of the Society of Actuaries and be prepared to take the first two actuarial examinations (P and M).

Completion of the certificate requires the following courses. Please note that many of these courses have prerequisites so anyone pursuing the certificate should work carefully with an academic advisor.

Required Courses:

**MATH 4200**, Mathematical Statistics I

**MATH 4210**, Mathematical Statistics II

**MATH 4010**, Financial Mathematics I

**MATH 4020**, Financial Mathematics II

**FINANCE 3500**, Financial Management

**FINANCE 3521**, Financial Engineering: Applying Derivatives

## Graduate Studies

The Department of Mathematics and Computer Science offers an M.A. degree in mathematics, a Ph.D. degree in applied mathematics (with options in mathematics and computer science), 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. Students in the M.A. program who want to transfer to the Ph.D. program upon successful completion of 15 credit hours must fill out a new application through Graduate Admissions.

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 Programs
**

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 (proving related academic or professional experience, or taking a test) in the following areas. Courses in parenthesis are UMSL courses that can be used to fulfill the requirement.

- Programming skills in C or C++ and Java (CMP SCI 1250 or 2250, and 2261)
- Proficiency with Object-Oriented concepts and terminology (CMP SCI 2261)
- Proficiency with dynamic data structures (CMP SCI 2250)
- Proficiency with computer organization, architecture, or assembly level programming (CMP SCI 2700)
- Proficiency with design and time/space analysis of algorithms (CMP SCI 3130)
- Familiarity with Unix/Linux/OSX and with command-line scripting with tools (CMP SCI 2750)

Students must also have satisfactorily completed mathematics courses equivalent to the following UMSL 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 otherwise demonstrate proficiency. Special regulations of the Graduate School that apply to students on restricted status are described in the UMSL 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.

Students interested in the Ph.D. program in applied mathematics with the computer science option must follow the requirements for that program and that option.

## 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:
**

**MATH 4100,**Real Analysis I

**MATH 4160,**Complex Analysis I

**MATH 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 three-step 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 real analysis, complex analysis, 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 (CMP SCI 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 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. 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, CMP SCI 4760
- Programming Languages, CMP SCI 4250
- Computer Systems, CMP SCI 5700
- Software Engineering, CMP SCI 5500
- Advanced Data Structures and Algorithms, CMP SCI 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.