Mathematics and Computer Science

Campus Address: 311 Express Scripts Hall
Web Site: http://www.umsl.edu/mathcs
Main Number: 314-516-5743
Fax Number: 314-516-5400

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, as well as a Certificate in Actuarial Studies.

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.

Undergraduate Programs Overview

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.

The Certificate in Actuarial Studies is designed to provide the education needed for entry level employment in the actuarial profession.

Dual Programs

The Department offers dual degree programs in mathematics and computer science for students with strong academic records.  The B.A./B.S. and M.A. dual degree program in mathematics and B.S./M.S. dual degree program in computer science are designed to provide an opportunity for strong undergraduate majors  to start earning graduate work credit before actually completing their undergraduate degree and to shorten, or accelerate, the time required as graduate students to earn their degrees.

Graduate Programs Overview

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.

The 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 in 311 Express Scripts Hall (ESH)..

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 1250Introduction To Computing3
    MATH 1320Applied Statistics I3
    MATH 1800Analytic Geometry And Calculus I5
    MATH 1900Analytic Geometry And Calculus II5
    MATH 2000Analytic Geometry And Calculus III5
    MATH 2020Introduction To Differential Equations3
    MATH 2450Elementary Linear Algebra3
    MATH 3000Discrete Structures3
    MATH 4100Real Analysis I3
    Total Hours33
  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 MATH 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, 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 4160Complex Analysis I3
    MATH 4400Introduction To Abstract Algebra I3
    MATH 4450Linear Algebra3
    Total Hours9
  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
Select two of the following:6
Programming And Data Structures
Computer Organization and Architecture
Design And Analysis Of Algorithms
Theory Of Computation
Computer Graphics
Introduction to Digital Image Processing
2) Statistics
MATH 4200Mathematical Statistics I3
MATH 4210Mathematical Statistics II3
3) Biology
BIOL 2102General Ecology3
BIOL 2103General Ecology Laboratory2
4) Biology
BIOL 2012Genetics3
BIOL 4182Population Biology3
5) Chemistry
CHEM 1111Introductory Chemistry I5
CHEM 1121Introductory Chemistry II5
6) Chemistry
CHEM 3312Physical Chemistry I3
And another 3000-level, or above, chemistry course.3
7) Economics
ECON 1001Principles Of Microeconomics3
ECON 1002Principles Of Macroeconomics3
ECON 4100Introduction To Econometrics4
8) Philosophy
PHIL 3360Formal Logic3
PHIL 3380Philosophy Of Science3
PHIL 4460Advanced Formal Logic3
9) Physics
PHYSICS 2111Physics: Mechanics And Heat5
PHYSICS 2112Physics: Electricity, Magnetism, And Optics5
10) Physics
PHYSICS 3221Mechanics3
And another 3000 level, or above, physics course.3
11) Business Administration
LOG OM 3320Introduction To Operations Management3
and one of the following courses:
LOG OM 4321Production and Operations Management3
LOG OM 4326Quality Assurance In Business3
LOG OM 4330Business Logistics Systems3
LOG OM 4350Management Science Methods3
12) Engineering
ENGR 2310Statics3
ENGR 2320Dynamics3

Degree Requirements in Computer Science

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

1) Computer Science Core
CMP SCI 1250Introduction To Computing3
CMP SCI 2250Programming And Data Structures3
CMP SCI 2261Object-Oriented Programing3
CMP SCI 2700Computer Organization and Architecture3
CMP SCI 2750System Programming and Tools3
CMP SCI 3010Web Programming3
CMP SCI 3130Design And Analysis Of Algorithms3
CMP SCI 4250Programming Languages3
CMP SCI 4280Program Translation3
CMP SCI 4500Introduction to Software Engineering3
CMP SCI 4760Operating Systems3
2) Computer Science Electives
Select five more elective computer science courses, numbered above 3000.15
3) Mathematics and Statistics
MATH 1320Applied Statistics I3
MATH 1800Analytic Geometry And Calculus I5
MATH 1900Analytic Geometry And Calculus II5
MATH 2450Elementary Linear Algebra3
MATH 3000Discrete Structures3
4) Additional Skills
ENGL 3130Technical Writing3
Total Hours70

There are no related area requirements for majors in Computer Science

BS and MS Dual Degree in Computer Science

The Integrated BS/MS ("2+3") dual degree program involves dual credit for qualified undergraduate Computer Science students.  It allows the students to concurrently earn credit for some graduate courses while working on their undergraduate degree, reducing the total hours needed for the subsequent MS degree by up to 12 credit hours.

Entry Requirements

Undergraduate majors can apply for provisional admission to this program if:

  1. They have completed at least 60 credit hours of coursework.
  2. Their overall GPA is 3.0 or higher.
  3. Non-CS majors must at the same time become CS majors.

Upon acceptance to the program in the provisional status, the student continues to work toward his/her undergraduate degree in computer science.

After completion of a minimum of 90 hours and no more than 30 hours away from the undergraduate degree, a provisionally admitted student applies for formal admission to the graduate program.  At this point, the student must meet the entry requirements for admission to the M.S. degree in Computer Science.

Degree Requirements

After acceptance into the program, the student continues to complete his/her undergraduate degree.  The student is reclassified as a graduate student from the next semester and must pay graduate fees. The student will be assigned a graduate adviser to help optimize the transition to the graduate program.  The student continues taking the undergraduate courses but is also allowed to take courses reserved for graduate students.  The student completes all the courses to fulfill the requirements to complete his/her M.S. degree in Computer Science – but must also complete the undergraduate requirements.  Up to 12 credit hours can be counted towards both the undergraduate and graduate degrees, substantially reducing the  hours needed to complete the graduate program by itself.

A student may file for and receive the undergraduate degree at any time when all the requirements are completed, before or in the same semester in which the Master's degree is completed. A student must still complete all the requirements to get a B.S. degree, regardless of whether the student files for the degree or not.  A student may choose to finish the studies just with a B.S.

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 1250Introduction To Computing3
CMP SCI 2250Programming And Data Structures3
Select three additional computer science courses numbered 2000 or above. 9
Total Hours15

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 1800Analytic Geometry And Calculus I5
MATH 1900Analytic Geometry And Calculus II5
MATH 2000Analytic Geometry And Calculus III5
Select two additional three-hour mathematics couses numbered above 2400 16

 

 

1

excluding MATH 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 1320Applied Statistics I3
MATH 4200Mathematical Statistics I3
Select two additional courses in statistics numbered above 4200. 6
Total Hours12

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 

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

FINANCE 3500Financial Management3
FINANCE 3521Financial Engineering: Applying Derivatives3
MATH 4200Mathematical Statistics I3
MATH 4210Mathematical Statistics II3
MATH 4010Financial Mathematics I3
MATH 4020Financial Mathematics II3
Total Hours18

Residency Requirement: Of the above required six courses at least five must be taken at the University of Missouri-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 (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 by 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 CMP SCI 2250, and CMP SCI 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 MATH 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 4100Real Analysis I3
MATH 4160Complex Analysis I3
MATH 4450Linear Algebra3
Total Hours9

 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. 

BA/BS and MA Dual Degree Program in Mathematics

This is an integrated BA/BS and MA ("2+3") dual degree program in Mathematics: it is designed to provide an opportunity for mathematics majors at the University of Missouri-St Louis (UMSL) with a strong academic record to start earning graduate work credit before actually completing their undergraduate degree and to shorten, or accelerate, the time required as graduate students to earn their master’s degree. A student in this program can apply up to 12 credit hours of 4000-and-above level courses towards both programs.

Entry Requirements

  • Undergraduate math majors can apply for provisional admission for this program if:
  1. They have completed at least 60 credit hours of coursework and
  2. Their GPA is 3.0 or higher.

Students submit their applications to the department. Once a student is admitted in this provisional status, the student continues to work toward his/her undergraduate degree until the student completes 90-102 undergraduate credit hours. Meanwhile the student will be advised to complete the required courses for graduate admission.

  • A provisionally admitted student is reviewed for formal admission after completing 90 undergraduate credit hours. Minimal requirements for admission include:
  1. GPA of 3.0 or higher at the time of the review
  2. MATH 1320, MATH 2020, MATH 2450, MATH 3000 - all completed with a grade of B- or higher.

A student’s application meeting the minimal requirements does not mean the student is automatically admitted in this program. The math graduate committee will review the application and make a decision. In case the application is approved, the student needs to complete a formal application for admission into the graduate program and is recommended for admission by the graduate committee.

Degree Program

  1. The current separate requirements for BA/BS and MA in math remain unchanged.
  2. Once the student is admitted in this program, the student is allowed to take graduate courses (paid with graduate fees).
  3. The student in this program can apply up to 12 credit hours of 4000-and-above level courses towards both the bachelor and master’s degrees. The student may get the BA/BS and MA degrees at the same time.
  4. In case a student cannot complete the master’s degree for some reason, up to 12 credit hours of graduate level courses can be applied towards the BA/BS degree.
  5. Students will pay graduate fees for all courses after being admitted and starting the program.

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:
    1. Completing 18 hours of 5000 level courses other than MATH 7990, Ph.D. Dissertation Research.
    2. Passing the comprehensive examination.
    3. 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 4100Real Analysis I3
MATH 4160Complex Analysis I3
MATH 4450Linear Algebra3
Total Hours9

Computer Science Option

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

CMP SCI 4250Programming Languages3
CMP SCI 4760Operating Systems3
CMP SCI 5130Advanced Data Structures And Algorithms3
CMP SCI 5700Computer Systems3
Total Hours12

Additional Requirement

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

  1. Pass a written examination in an area of the student’s interests. This area will be approved by the graduate committee and will be based on a set of two or more graduate courses taken by the student. This examination would normally take place within the first 24 credit hours of study after admission to the Ph.D. program.
  2.  Write a survey paper in a specialized area under the direction of a member of the graduate faculty. The student should propose to take this option when he/she has already finished at least 2 graduate level courses and has the approval of the graduate committee. The paper should be submitted within four semesters, at which time an oral examination given by a committee of at least three members of the graduate faculty must be passed.

 In both parts 1) and 2), 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:

CMP SCI 4760Operating Systems3
CMP SCI 4250Programming Languages3
CMP SCI 5700Computer Systems3
CMP SCI 5500Software Engineering3
CMP SCI 5130Advanced Data Structures And Algorithms3
Total Hours15

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 CMP SCI 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.

BS and MS Dual Degree in Computer Science

The Integrated BS/MS ("2+3") dual degree program involves dual credit for qualified undergraduate Computer Science students.  It allows the students to concurrently earn credit for some graduate courses while working on their undergraduate degree, reducing the total hours needed for the subsequent MS degree by up to 12 credit hours.

Entry Requirements

Undergraduate majors can apply for provisional admission to this program if:

  1. They have completed at least 60 credit hours of coursework.
  2. Their overall GPA is 3.0 or higher.
  3. Non-CS majors must at the same time become CS majors.

Upon acceptance to the program in the provisional status, the student continues to work toward his/her undergraduate degree in computer science.

After completion of a minimum of 90 hours and no more than 30 hours away from the undergraduate degree, a provisionally admitted student applies for formal admission to the graduate program.  At this point, the student must meet the entry requirements for admission to the M.S. degree in Computer Science.

Degree Requirements

After acceptance into the program, the student continues to complete his/her undergraduate degree.  The student is reclassified as a graduate student from the next semester and must pay graduate fees. The student will be assigned a graduate adviser to help optimize the transition to the graduate program.  The student continues taking the undergraduate courses but is also allowed to take courses reserved for graduate students.  The student completes all the courses to fulfill the requirements to complete his/her M.S. degree in Computer Science – but must also complete the undergraduate requirements.  Up to 12 credit hours can be counted towards both the undergraduate and graduate degrees, substantially reducing the  hours needed to complete the graduate program by itself.

A student may file for and receive the undergraduate degree at any time when all the requirements are completed, before or in the same semester in which the Master's degree is completed. A student must still complete all the requirements to get a B.S. degree, regardless of whether the student files for the degree or not.  A student may choose to finish the studies just with a B.S.

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.

Sample Four Year Plans 

Mathematics BA  Mathematics BS  Computer Science BS

Mathematics BA

First Year
FallHoursSpringHours
INTDSC 100311CMP SCI 12503
ENGL 11003MATH 18005
MATH 10303General Education 9
MATH 10352 
General Education6 
 15 17
Second Year
FallHoursSpringHours
MATH 13203MATH 20005
MATH 19005Foreign Language 10015
General Education 9General Education6
 17 16
Third Year
FallHoursSpringHours
MATH 30003MATH 20203
ENGL 31003MATH 24503
Foreign Language 10025MATH 4000+ level course3
Elective or minor3Foreign Language 21013
 14 12
Fourth Year
FallHoursSpringHours
MATH 41003MATH 44003
MATH 4000+ level course3Related area course3
Related area course3Elective or minor9
Elective or minor6 
 15 15
Total Hours: 121
1

INTDSC 1003 is required only for first-time freshmen and transfer students with less than 24 college credits.

Please Note: This plan is an example of what a four year plan could look like for a typical student. Placement exam scores in math as well as the completion of coursework may change the plan. It should not be used in the place of regular academic advising appointments. All students are encouraged to meet with their advisor each semester. All requirements are subject to change.

Mathematics BS

First Year
FallHoursSpringHours
INTDSC 10031MATH 18005
ENGL 11003CMP SCI 12503
MATH 10303General Education 9
MATH 10352 
General Education 6 
 15 17
Second Year
FallHoursSpringHours
MATH 13203MATH 20005
MATH 19005General Education 9
General Education9 
 17 14
Third Year
FallHoursSpringHours
MATH 30003MATH 20203
ENGL 31003MATH 24503
General Education6CMP SCI/ MATH/ STAT 4000+ level course3
 Related area course3
 General Education3
 12 15
Fourth Year
FallHoursSpringHours
MATH 41003MATH 44003
CMP SCI/ MATH/ STAT 4000+ level course3MATH 41603
MATH/STAT 4000+ level course3MATH 44503
Related Area courses6Related Area courses6
 15 15
Total Hours: 120
1

INTDSC 1003 is required only for first-time freshmen and transfer students with less than 24 college credits. 

Please Note: This plan is an example of what a four year plan could look like for a typical student. Placement exam scores in math as well as the completion of coursework may change the plan. It should not be used in the place of regular academic advising appointments. All students are encouraged to meet with their advisor each semester. All requirements are subject to change.

Computer Science BS

First Year
FallHoursSpringHours
INTDSC 100311CMP SCI 12503
ENGL 11003MATH 18005
MATH 10303General Education9
MATH 10352 
General Education6 
 15 17
Second Year
FallHoursSpringHours
CMP SCI 22503CMP SCI 22613
MATH 13203CMP SCI 27003
MATH 19005CMP SCI 27503
General Education 6General Educaton 6-8
 17 15-17
Third Year
FallHoursSpringHours
CMP SCI 30103CMP SCI 42503
MATH 24503CMP SCI 31303
MATH 30003CMP SCI 3000+ level elective6
ENGL 31303General Education3
General Education  
 12 15
Fourth Year
FallHoursSpringHours
CMP SCI 42803CMP SCI 45003
CMP SCI 3000+ level elective6CMP SCI 47603
General Education6CMP SCI 3000+ level elective3
 Elective or minor6
 15 15
Total Hours: 121-123
1

INTDSC 1003 is required only for first-time freshmen and transfer students with less than 24 college credits.

 Please Note: This plan is an example of what a four year plan could look like for a typical student. Placement exam scores in math as well as the completion of coursework may change the plan. It should not be used in the place of regular academic advising appointments. All students are encouraged to meet with their advisor each semester . All requirements are subject to change.

Computer Science Courses

CMP SCI 1010 Introduction To Computers And The Internet: 3 semester hours

Prerequisites: None. Covers basic concepts and components of a PC: survey of popular applications including e-mail, word processors, spreadsheets, overview of the Internet, popular browsers, World Wide Web, search engines, multimedia, web pages, security, and privacy. Credit not granted for both CMP SCI 1010 and INFSYS 1800.

CMP SCI 1011 Introduction to the Internet and World Wide Web: 3 semester hours

Intended for any student wishing to utilize the Internet and World Wide Web more effectively. Topics include networking basics, the Internet and World Wide Web, browsers, search engines, Web Services, utilities, tools, online privacy and security. Students will learn to develop a personal web page using skills acquired in the course.

CMP SCI 1012 Learning to Program Using Virtual Worlds: 3 semester hours

Introduces modern programming principles without requiring the knowledge of a traditional programming language. Instead, this course utilizes a novel graphical approach that enables the student to create, populate, and manipulate virtual 3-dimensional worlds which resemble video games. The development of these worlds allows students to gain direct experience and skills in using computers to solve problems. Students will create worlds of varying complexity.

CMP SCI 1250 Introduction To Computing: 3 semester hours

Prerequisites: MATH 1030 with B-or better, or MATH 1100, or MATH 1800. Provides an introduction to the concepts of computation, problem solving, and computer systems. Covers fundamental programming constructs, basic data types, and modularization using a modern high level language. Problem solving skills are developed through a progression of programming projects.

CMP SCI 2250 Programming And Data Structures: 3 semester hours

Prerequisite: CMP SCI 1250. Continuation of CMP SCI 1250. Discusses properties and implementation of abstract data types such as lists, trees, stacks and queues. Introduces procedural and class abstraction, basic program architecture, use of interfaces, modular programming, and file processing.

CMP SCI 2261 Object-Oriented Programing: 3 semester hours

Prerequisite: CMP SCI 2250. Introduces object-oriented concepts, terminology, and notation (UML) using Java. Covers encapsulation, classes, objects, inheritance, and the use of class libraries. Additional topics may include graphical user interfaces, applets, and related tools and technologies.

CMP SCI 2700 Computer Organization and Architecture: 3 semester hours

Prerequisite: CMP SCI 2250. Introduces details of computer systems from architectural and organizational points of view. Covers data representation, basic digital logic circuits, memory types and hierarchies, I/O and storage devices, CPU architectures such as RISC, CISC, parallel, and multi-core.

CMP SCI 2750 System Programming and Tools: 3 semester hours

Prerequisites: CMP SCI 2250. Covers systems programming, scripting, libraries, utilities, and development tools. Additional programming topics include piping, binary files, exception handling, command-line arguments and symbolic debugging. This course also explores tools available in the Unix/Linux environments.

CMP SCI 3010 Web Programming: 3 semester hours

Prerequisite: CMP SCI 2250 Provides a survey of current Web technologies including markup languages (such as HTML/XHTML, CSS, XML), client side languages (such as JavaScript), server side languages (such as PERL, PHP), and Web protocols. This course requires client-server computing projects.

CMP SCI 3130 Design And Analysis Of Algorithms: 3 semester hours

Prerequisites: CMP SCI 2250, MATH 1320, MATH 2450, and MATH 3000. Addresses the design and analysis of fundamental algorithms in computer science. Studies basic sorting algorithms, priority queues, order statistics, search trees, and hash tables. Analysis techniques may involve time and space complexity analysis of both iterative and recursive algorithms, analysis of algorithm correctness, and amortized complexity analysis. Additional topics may include data compression, string manipulation, greedy algorithms, dynamic programming, and graph traversal.

CMP SCI 3710 Assembly Language Programming: 3 semester hours

Prerequisite: CMP SCI 2700. Explores machine architecture concepts and principles through a study of assembly language programming. Topics covered include integer and floating point arithmetic, procedures, conditional processing, strings, macros, and interfaces to high level languages. Programming projects using a commercially available assembly language will be required.

CMP SCI 4010 Advanced Web Development with Java: 3 semester hours

Prerequisites: CMP SCI 2261 and CMP SCI 3010, or consent of instructor. Covers more advanced Java topics, along with related concepts and technologies for Web development. Topics may include database connectivity, multi threading, security, networking, MVC pattern, testing and source control for Java applications, and server-side topics such as servlets and web servers.

CMP SCI 4030 Introduction to Intelligent Web: 3 semester hours

Prerequisites: CMP SCI 2261, CMP SCI 2750, CMP SCI 3010, and CMP SCI 3130. Covers the application of artificial intelligence and other modern techniques to help construct, navigate, and experience the Web. Topics may include retrieval models, classification, mining, association, topology, and indexing algorithms such as PageRank and HITS. Credit cannot be earned for both CMP SCI 4030 and CMP SCI 5030.

CMP SCI 4140 Theory Of Computation: 3 semester hours

Prerequisite: CMP SCI 3130. Provides an introduction to the theory of computation. Describes basic computational models, such as finite state machines, pushdown automata, Turing machines and grammars. Covers the concept of nondeterministic computation and the relationships between different computational models. Discusses decidability, reducibility, and classification of problems into complexity classes based on their time and space complexity, such as P, NP, and PSPACE.

CMP SCI 4250 Programming Languages: 3 semester hours

Prerequisite: CMP SCI 2261 and CMP SCI 3010 or Graduate Standing. Studies the principles, approaches, and trade-offs in modern programming languages, including a comparative study of syntax, semantics, and pragmatics. Examines major programming paradigms: object-oriented, imperative, functional and logic.

CMP SCI 4280 Program Translation: 3 semester hours

Prerequisites: CMP SCI 2700, CMP SCI 2750, CMP SCI 3130 and CMP SCI 4250. Focuses on methods, techniques, and mechanisms used to create the abstraction from high level programming to machine level execution. This course also requires an individual, semester long project.

CMP SCI 4300 Introduction To Artificial Intelligence: 3 semester hours

Prerequisites: CMP SCI 2261, CMP SCI 2750 and CMP SCI 3130. Provides an introduction to artificial intelligence. The list of topics may include search, planning, knowledge-based reasoning, probabilistic inference, machine learning, natural language processing, and practical applications.

CMP SCI 4340 Introduction to Machine Learning: 3 semester hours

Prerequisites: CMP SCI 2261, CMP SCI 2750 and CMP SCI 3130. Provides an introduction to machine learning in the context of applications such as data mining, natural language processing, and adaptive computer systems. The course reviews several supervised, unsupervised, and reinforcement machine learning techniques such as naive Bayes networks, clustering, and decision trees. Selected concepts in computational learning theory may also be covered. Credit cannot be granted for both CMP SCI 4340 and CMP SCI 5340.

CMP SCI 4410 Computer Graphics: 3 semester hours

Prerequisites: CMP SCI 2750 and CMP SCI 3130. Covers the theoretical foundation and algorithms for computer graphics. Students learn the basics of graphics programming for modeling, rendering, and animation of 2D and 3D objects. Vector and raster graphics, and different display devices are also discussed. A brief discussion of special graphics hardware, such as GPU, may be presented.

CMP SCI 4420 Introduction to Digital Image Processing: 3 semester hours

Prerequisites: CMP SCI 2750 and CMP SCI 3130. Focuses on image analysis and visual perception. Students learn data structures and algorithms for image processing, region and texture analysis, image filtering, edge detection, contour following, and image enhancement in both spatial and frequency domain. Other topics may include color processing, coding for storage, retrieval, transmission, and image restoration. Credit cannot be granted for both CMP SCI 4420 and CMP SCI 5420.

CMP SCI 4500 Introduction to the Software Profession: 3 semester hours

Prerequisite: CMP SCI 2261, CMP SCI 2700, CMP SCI 2750, CMP SCI 3010, and CMP SCI 3130. Focuses on software development and on the skills required for success in the software profession. Topics related to software development may include software process, models and views, software architectures, documentation, and testing strategies. Topics related to the profession may include ethics, licensing, copyright, trademarks, and professional conduct. Individual and group projects, research, and presentations may be required in this capstone course.

CMP SCI 4520 Introduction to Object-Oriented Analysis And Design: 3 semester hours

Prerequisite: CMP SCI 2261, CMP SCI 3010, CMP SCI 3130. Covers object-oriented development, illustrated with a visual modeling language and following an agile process. Discusses elements of analysis, requirements, design, implementation, and deployment such as use cases, static and dynamic diagrams, patterns, and frameworks. This course includes a semester long project starting with requirements and culminating with deployment. Credit not granted for both CMP SCI 4520 and CMP SCI 5520.

CMP SCI 4610 Database Management Systems: 3 semester hours

Prerequisites: CMP SCI 2750 and MATH 3000. Focuses on database theory and applications, with emphasis on the relational model. Topics include database design, modeling, file systems, indexing, integrity constraints, relational algebra, normalization, transaction processing, and concurrency control. Students are exposed to emerging DBMS technologies and applications. Several programming projects will be required, using a popular SQL server.

CMP SCI 4730 Computer Networks And Communications: 3 semester hours

Prerequisites: CMP SCI 2750 and MATH 1320. Covers communication systems in the context of the ISO and TCP/IP standards for systems interconnection. Covers various types of networks including wide area networks, local area networks, and fiber optic networks.

CMP SCI 4760 Operating Systems: 3 semester hours

Prerequisites: CMP SCI 2700, CMP SCI 2750, and CMP SCI 3130. Covers the structure of a generic operating system, considering in detail the algorithms for interprocess communication, process scheduling, resource management, memory management, file systems, and device management. Presents examples from contemporary operating systems. This course also requires practical projects implemented within a modern operating system or simulator environment.

CMP SCI 4780 Computer and Network Security: 3 semester hours

Prerequisite: CMP SCI 2750. Covers major issues relevant to providing security in a networked environment. The course includes algorithms and protocols for secure communications between computers.

CMP SCI 4880 Individual Studies: 1-3 semester hours

Prerequisites: Consent of the instructor. This course allows a student to pursue individual studies under the supervision of a faculty member. It may include development of a software project. The course may be repeated for credit.

CMP SCI 4890 Topics In Computer Science: 3 semester hours

Prerequisites: Consent of the Instructor. Covers a special topic in computer science to be determined by recent developments in the field and the interests of the instructor. Course may be repeated for credit.

CMP SCI 5010 Enterprise Web Development: 3 semester hours

Prerequisite: CMP SCI 4010 or consent of instructor. Covers design and implementation issues for enterprise web development, and some popular advanced technologies. Topics include MVC and persistence frameworks, such as Spring and Hibernate. Other topics may include Java Web services, EJB, messaging standards such as JMS, and Java EE design patterns. Students will develop enterprise-level web application projects using the.

CMP SCI 5030 Intelligent Web: 3 semester hours

Prerequisite: Consent of the instructor. Covers the application of artificial intelligence and other modern techniques to help construct, navigate, and experience the Web. Topics may include retrieval models, classification, mining, association, topology, and indexing algorithms such as PageRank and HITS. Topics are the same as CMP SCI 4030 but material is covered at a greater depth and additional projects are required. Credit cannot be earned for both CMP SCI 4030 and CMP SCI 5030.

CMP SCI 5130 Advanced Data Structures And Algorithms: 3 semester hours

Prerequisite: An elementary course in analysis of algorithms or consent of the instructor. This course covers analysis of time and space complexity of iterative and recursive algorithms along with performance bounds, design of data structures for efficent performance, sorting algorithms, probabilistic algorithms, divide and conquer strategies, various algorithms on graphs, and np completeness.

CMP SCI 5320 Introduction To Evolutionary Computation: 3 semester hours

Prerequisites: CMP SCI 4300 or consent of instructor. This course introduces the concepts of nature-inspired problem solving population dynamics, Darwinian selection, and inheritance. It discusses problems applicable to evolutionary algorithms, overviews the existing models and instances, and analyzes specific instances such as genetic algorithms and genetic programming.

CMP SCI 5340 Machine Learning: 3 semester hours

Prerequisites: Consent of instructor. Provides an introduction to machine learning in the context of applications such as data mining, natural language processing and adaptive computer systems. Reviews several supervised, unsupervised, and reinforcement machine learning techniques such as naive Bayes networks, clustering and decision trees. Selected concepts in computational learning theory may also be covered. Topics are the same as CMP SCI 4340 but material is covered at a greater depth and additional projects are required. Credit cannot be granted for both CMP SCI 4340 and CMP SCI 5340.

CMP SCI 5420 Digital Image Processing: 3 semester hours

Prerequisites: Consent of instructor. Covers topics in image analysis and visual perception. Students learn data structures and algorithms for image processing, region and texture analysis, image filtering, edge detection, contour following, and image enhancement in both spatial and frequency domain. Other topics may include color processing, coding for storage, retrieval, transmission, and image restoration. Topics are the same as CMP SCI 4420 but material is covered at a greater depth and additional projects are required. Credit cannot be granted for both CMP SCI 4420 and CMP SCI 5420.

CMP SCI 5500 Software Engineering: 3 semester hours

Prerequisite: Consent of instructor. Introduces software engineering as a discipline, discusses stages of the software life cycle, compares development models such as waterfall, prototyping and incremental/iterative, covers requirements analysis, effort and cost estimation, compares structured and object-oriented analysis and design methods. Discusses verification/validation, quality assurance, software reliability, testing methods, maintenance, documentation, project management and team structure, metrics, and available tools.

CMP SCI 5520 Object Oriented Analysis And Design: 3 semester hours

Prerequisite: Consent of the instructor. Covers object-oriented development, illustrated with visual modeling language and following an agile process. Discusses elements of analysis, requirements, design, implementation, and deployment such as use cases, static and dynamic diagrams, patterns and frameworks. A semester long project, starting with requirements and culminating with deployment, is required. Topics are the same as CMP SCI 4520 but material is covered at a greater depth and additional projects are required. Credit not granted for both CMP SCI 4520 and CMP SCI 5520.

CMP SCI 5700 Computer Systems: 3 semester hours

Prerequisite: Background in computer organization or architecture or consent of the instructor. This course focuses on parallel computing architectures, including RISC, pipelining, vector processing, SIMD, MIMD, and array processing. It introduces different memory and I/O subsystems, hardware description languages, and it demonstrates performance enhancement using different architectures studied.

CMP SCI 5740 High Performance Computing: 3 semester hours

Prerequisite: Consent of the instructor. Introduces algorithms for multiprocessor and multi-core architectures. Students learn the models of modern parallel computation and techniques to take advantage of parallel architectures for distributed and shared memory multi-processor architectures.

CMP SCI 5880 Computer Science Independent Project: 1-3 semester hours

Prerequisites: Graduate standing and consent of instructor This course offers the student an opportunity to work on an advisor-supervised project, individually or in a group. A student may repeat the course for up to 6 credit hours total, but at most 6 hours can be accumulated for CMP SCI 5880 and CMP SCI 6900.

CMP SCI 5890 Topics In Computer Science: 1-3 semester hours

Prerequisites: Graduate standing and consent of the instructor This course offers various topics not offered on a regular basis. It may be taken more than once for credit with the consent of the department.

CMP SCI 5900 Graduate Internship in Computer Science: 3 semester hours

Prerequisites: Consent of AdvisorThe internship provides for a student to attain field experience in an organization related to Computer Science. A student is employed off-campus for an assignment of at least 320 hours working on a project as directed by his/her supervisor in the host organization. The project should be approved by the student's academic advisor, or a designated faculty member, who will monitor the student's progress. The student is responsible for having the project supervisor at the company establish contact with the academic advisor to establish schedule and goals, and a procedure to evaluate the goals. The student will submit a written report to the advisor at the end of internship. The course cannot be repeated for credit. Students completing this course will be allowed only up to three hours of Independent Study (CMP SCI 5880).

CMP SCI 6320 Advances In Evolutionary Computation: 3 semester hours

Prerequisite: CMP SCI 5320 or consent of instructor. This course focuses on some advanced topics in Genetic and Evolutionary Computation, both theoretical and practical. Topics may include competent genetic algorithms, learning classifier systems, and Markov models. A substantial part of the course will be based on recent literature. Projects may involve literature research, developing specific applications or implementing a specific model.

CMP SCI 6340 Genetic Programming: 3 semester hours

Prerequisite: CMP SCI 5320 or consent of instructor. This course provides an in-depth exploration of Genetic programming, including advanced concepts such as scalability, evolution of modularity and regularity, and constrained evolution with CGP, STGP, or CFG-based GP. It may be reading, research, or application oriented.

CMP SCI 6410 Topics In Computer Graphics: 3 semester hours

Prerequisites: CMP SCI 4410 or consent of instructor This course covers various aspects of advanced graphics techniques, such as geometric modeling, rendering, shading, texturing, and computer animation. The course proides an indepth study of recent advanced topics in computer graphics.

CMP SCI 6420 Topics In Image Processing And Multimedia: 3 semester hours

Prerequisites: CMP SCI 5400, CMP SCI 5420 or consent of instructor. This course covers new developments in digital image processing, computer vision, and multimedia. Topics to be covered may include image databases, object tracking, and large-scale data visualization.

CMP SCI 6740 High Performance Computing: 3 semester hours

Prerequisites: CMP SCI 5740, or Graduate standing and consent of instructor. Looks at the current state of the art in parallel and distributed computing, with emphasis on programming in such environments. Introduction to the state of the art in code optimization and grid computing environments.

CMP SCI 6900 Thesis: 1-6 semester hours

Prerequisites: Completion of at least 12 graduate credits and approval of research topic by thesis advisor. This course is designed for those students intending to present a thesis as part of their M.S. program. At most 6 hours can be accumulated for CMP SCI 5880 and CMP SCI 6900.

Mathematics Courses

MATH 0005 Intermediate Algebra: 3 semester hours

Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Preparatory material for college level mathematics courses. Covers systems of linear equations and inequalities, polynomials, rational expressions, exponents, quadratic equations, graphing linear and quadratic functions. This course carries no credit towards any baccalaureate degree.

MATH 1020 Contemporary Mathematics: 3 semester hours

Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Presents methods of problem solving, centering on problems and questions which arise naturally in everyday life. May include aspects of algebra and geometry, the mathematics of finance, probability and statistics, exponential growth, and other topics chosen from traditional and contemporary mathematics which do not employ the calculus. May be taken to meet the mathematical proficiency requirement, but may not be used as a prerequisite for other mathematics courses. Designed for students who do not plan to take calculus. Credit will not be granted for MATH 1020 if credit has been granted for MATH 1310, MATH 1800, MATH 1100, MATH 1102, or MATH 1105. Concurrent enrollment in MATH 1020 and any of these courses is not permitted.

MATH 1021 Choice and Chance: 3 semester hours

Same as PHIL 1021. Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. This course provides an introduction to inductive logic and the theory of probability in an organized and systematic way, so as to give students tools for more effective decision-making. We will introduce the probability calculus, basic concepts of utility theory, decision theory and different approaches to understanding probability. This course is designed to be accessible to students of all levels. Satisfies mathematics proficiency.

MATH 1025 Geometry in the Real World: 3 semester hours

Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Presents topics in geometry designed to enrich the student's understanding of mathematics. Geometry as it applies to the physical world and such fields as art, music, nature, motion, architecture and city planning will be examined. This course is designed to be accessible to students of all levels. Satisfies mathematics proficiency.

MATH 1030 College Algebra: 3 semester hours

Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Topics in algebra and probability, polynomial functions, the binomial theorem, logarithms, exponentials, and solutions to systems of equations.

MATH 1035 Trigonometry: 2 semester hours

Prerequisite: MATH 1030 or MATH 1040, or concurrent registration in either of these two courses, or a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. A study of the trigonometric and inverse trigonometric functions with emphasis on trigonometric identities and equations.

MATH 1040 College Algebra for Science and Engineering: 4 semester hours

Prerequisites: A satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Topics in this course include factoring, simplifying rational functions, functions and their graphs, solving linear and nonlinear equations, polynomial functions, inverse functions, the binomial theorem, logarithms, exponentials, solutions to systems of equations using matrices, solutions to nonlinear systems of equations, and sequences.

MATH 1100 Basic Calculus: 3 semester hours

Prerequisite: MATH 1030 or MATH 1040 or a satisfactory score on the UMSL ALEKS Placement Examination, obtained at most one year prior to enrollment in this course. Introduction to plane analytic geometry and basic differential and integral calculus with applications to various areas. No credit for Mathematics majors. Credit not granted for both MATH 1800 and MATH 1100.

MATH 1102 Finite Mathematics: 3 semester hours

Prerequisites: MATH 1030 or MATH 1040 or a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. Introductory logic and set theory, partitions and counting problems, elementary probability theory, stochastic processes, Markov chains, vectors and matrices, linear programming, and game theory.

MATH 1105 Basic Probability And Statistics: 3 semester hours

Prerequisites: MATH 1030 or MATH 1040 or a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. An introduction to probability and statistics. Topics include the concept of probability and its properties, descriptive statistics, discrete and continuous random variables, expected value, distribution functions, the central limit theorem, random sampling and sampling distributions. Credit not granted for more than one of MATH 1310, MATH 1320, and MATH 1105.

MATH 1150 Structure Of Mathematical Systems I: 3 semester hours

Prerequisites: 45 hours of college credit and a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course OR successful completion of MATH 1030 no more than 2 years prior to enrollment in this course. A study of sets, relations, functions, whole numbers; the integers and their properties, and the rational and real number systems.

MATH 1310 Elementary Statistical Methods: 3 semester hours

Prerequisite: MATH 1030 or MATH 1040 or a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. An introduction to the basic tools and elementary methods of statistics, such as testing of hypotheses, analysis of variance, method of least squares, and time series. A student may not receive credit for more than one of MATH 1310, MATH 1320, and MATH 1105.

MATH 1320 Applied Statistics I: 3 semester hours

Prerequisites: MATH 1800 or MATH 1100. This is the first course of a one-year sequence in introductory probability and statistics. It provides a comprehensive introduction to those models and methods which are most likely to be encountered by students in their careers in applied mathematics and the sciences. Topics include descriptive statistics, basics of probability theory, random variables and their distributions, sampling distributions, confidence intervals, and hypothesis testing for population means and population proportions. A student may not receive credit for more than one of MATH 1310, MATH 1320 and MATH 1105.

MATH 1800 Analytic Geometry And Calculus I: 5 semester hours

Prerequisites: MATH 1030 and MATH 1035, or MATH 1040 and MATH 1035, or a satisfactory score on the UMSL ALEKS Math Placement Examination, obtained at most one year prior to enrollment in this course. This course provides an introduction to differential and integral calculus. Topics include limits, derivatives, related rates, Newton's method, the Mean-Value Theorem, Max-Min problems, the integral, the Fundamental Theorem of Integral Calculus, areas, volumes, and average values.

MATH 1900 Analytic Geometry And Calculus II: 5 semester hours

Prerequisite: MATH 1800. Topics include conic sections, rotation of axes, polar coordinates, exponential and logarithmic functions, inverse (trigonometric) functions, integration techniques, applications of the integral (including mass, moments, arc length, and hydrostatic pressure), parametric equations, infinite series, power and Taylor series.

MATH 2000 Analytic Geometry And Calculus III: 5 semester hours

Prerequisite: MATH 1900 Topics include vectors, cylindrical and spherical coordinates, vector-valued functions, arc length and curvature, functions of several variables, partial and directional derivatives, gradients, extrema, Lagrange multipliers, multiple integrals, change of variables, surface area, vector fields, Stokes' Theorem.

MATH 2020 Introduction To Differential Equations: 3 semester hours

Prerequisite: MATH 2000. Topics will be chosen from: linear differential equations, equations with constant coefficients, laplace transforms, power series solutions, systems of ordinary differential equations.

MATH 2450 Elementary Linear Algebra: 3 semester hours

Prerequisite: MATH 1100 or MATH 1900. An introduction to linear algebra. Topics will include complex numbers, geometric vectors in two and three dimensions and their linear transformations, the algebra of matrices, determinants, solutions of systems of equations, eigenvalues and eingenvectors.

MATH 2510 Structure Of Mathematical Systems II: 3 semester hours

Prerequisite: MATH 1150. An introduction to probability and statistics. An intuitive study of elementary geometry. Introduction to the deductive theory of geometry and to coordinate geometry.

MATH 3000 Discrete Structures: 3 semester hours

Prerequisites: MATH 1900 or MATH 1100, and CMP SCI 1250 or equivalent. Treats fundamental ideas in discrete structures and serves as a foundation for subsequent courses in both Mathematics and Computer Science. Provides an introduction to techniques of mathematical reasoning with examples derived from computer science. Topics include logic, set algebra, equivalence relations and partitions, functions, mathematical induction, elementary number theory, cardinality, recurrence relations, basic combinatorial methods, trees and graphs. Credit not granted for more than one of CMP SCI 3000, and MATH 3000.

MATH 3100 Problem Solving In Mathematics: 1 semester hour

Prerequisite: MATH 2000 Course will train students to solve and write solutions to challenging mathematical problems, like those found in competitive exams like the Putnam Exam.

MATH 3520 Structure Of Mathematical Systems III: 3 semester hours

Prerequisite: MATH 2510 Together with MATH 1150 and MATH 2510, this course teaches the mathematics necessary for middle school mathematics certification. Topics from MATH 1150 and MATH 2510 are continued. Other topics include geometric constructions, similarity, coordinate geometry, normal distribution, combinatorics, and trigonometry.

MATH 4010 Financial Mathematics I: 3 semester hours

Prerequisites: MATH 1900 or MATH 1100, and MATH 1320 or LOG OM 3300 (or equivalents). An introduction to the theory of interest, annuities (certain), annuities with differing pay periods, amortization schedules and sinking funds.

MATH 4020 Financial Mathematics II: 3 semester hours

Prerequisites: MATH 4010. Premium-discount formula for bonds, bond amortization, term structure of interest rates and pricing theory for options.

MATH 4030 Applied Mathematics I: 3 semester hours

Prerequisite: MATH 2020 and MATH 2450. Topics chosen from Fourier series, special functions, partial differential equations, and boundary value problems.

MATH 4060 Applied Differential Equations: 3 semester hours

Prerequisites: MATH 2020 and MATH 2450 The study of ordinary differential equations and partial differential equations is continued with applications in such areas as physics, engineering and biology.

MATH 4100 Real Analysis I: 3 semester hours

Prerequisites: MATH 2000 and MATH 3000. Introduction to real analysis in one variable. Topics include the real number system, limits, continuity, differentiability, and sequences and series of functions.

MATH 4160 Complex Analysis I: 3 semester hours

Prerequisites: MATH 2020 or both MATH 3000 and MATH 2000. Complex numbers and their geometrical representation, point sets, analytic functions of a complex variable, complex integration, Taylor and Laurent series, residue theorem, conformal mapping.

MATH 4200 Mathematical Statistics I: 3 semester hours

Prerequisites: MATH 1320 and MATH 2000. Introduction to the theory of probability and statistics using concepts and methods of calculus.

MATH 4210 Mathematical Statistics II: 3 semester hours

Prerequisites: MATH 4200. Continuation of MATH 4200. Sampling distributions, extimation theory, properties of estimators, hypothesis testing, NeymanPearson Theorem, likelihood ratio tests, introduction of analysis of variance and linear models. Basics of some nonparametric procedures.

MATH 4230 Numerical Analysis I: 3 semester hours

Prerequisites: MATH 2020, MATH 2450, and the ability to program in an upper-level language Solutions of equations, interpolation and approximation numerical differentiation and integration, and numerical solutions of initial value problems in ordinary differential equations. Selected algorithms will be programmed for solution on computers.

MATH 4260 Introduction To Stochastic Processes: 3 semester hours

Prerequisites: MATH 4200 Basic theory and applications of stochastic processes. Markov chains, recurrent and transient states, stationary distributions, ergodic theorem, renewal processes, discrete martigales and stationary processes.

MATH 4350 Theory Of Numbers: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000, or consent of instructor Properties of integers, multiplicative functions, congruences, primitive roots, and quadratic residues.

MATH 4390 Topics In Probability And Statisitcs: 3 semester hours

Prerequisites: Consent of Instructor. A seminar on special topics in probability and statistics to be determined by the interests of the instructor. May be repeated for credit provided different topics are studied.

MATH 4400 Introduction To Abstract Algebra I: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000, or consent of the department Introduction to groups, rings, and fields, with emphasis on groups and rings.

MATH 4450 Linear Algebra: 3 semester hours

Prerequisites: MATH 3000, MATH 2000 and MATH 2450. Topics selected from vector spaces, bases, linear transformations, matrices, canonical forms, eigenvalues, hermitian and unitary matrices, inner product spaces, and quadratic forms.

MATH 4500 Special Readings: 1-10 semester hours

Prerequisites: MATH 3000, MATH 2000 and consent of instructor.

MATH 4550 Combinatorics: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000. Advanced counting methods are introduced, including the use of generating functions for the solution of recurrences and difference equations. Additional topics may include: graphs and trees, combinatorial designs, combinatorial games, error-correcting codes, and finite-state machines.

MATH 4660 Foundations Of Geometry: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000, or consent of the department A development of portions of Euclidean geometry from a selected set of axioms, including a discussion of consistency, independence, categoricity, and completeness of the axioms.

MATH 4670 Introduction To Non-Euclidean Geometry: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000, or consent of the department A summary of the history of the non-Euclidean geometries and a study of hyperbolic plane geometry.

MATH 4800 Introduction To Topology: 3 semester hours

Prerequisites: MATH 3000 and MATH 2000, or consent of the department A study of topological spaces, including the concepts of limit, continuity, connectedness, compactness, etc. Special emphasis placed on, and examples taken from, the space of real numbers.

MATH 4890 Topics In Mathematics: 3 semester hours

Prerequisite: Consent of Instructor.

MATH 5060 Computational Harmonic Analysis: 3 semester hours

Prerequisites: MATH 4030, MATH 4100 and MATH 4450 The course covers the basics of Fourier analysis and wavelet analysis. Topics include Fourier transforms and series, discrete Fourier transform, discrete cosine transform and their fast computational schemes, fast wavelet transform, and the lifting scheme. Additional topics include industrial standards for image compression and several aspects of signal processing.

MATH 5100 Real Analysis II: 3 semester hours

Prerequisites: MATH 4100 Introduction to measure and integration. Topics include the Riemann-Stieltjes integral, Lebesgue measure, measurable functions, the Lebesgue integral, Radon-Nikodym and Fubini theorems and the basics of Lp-spaces.

MATH 5110 Differentiable Manifolds: 3 semester hours

Prerequisites: MATH 4100, MATH 4450, and MATH 4800. An introduction to smooth manifolds and maps. Topics will include the Implicit Function Theorem, Sard's Theorem, transversality, intersection and degree theory, differential forms and integration on manifolds.

MATH 5140 Set Theory And Metric Spaces: 3 semester hours

Prerequisites: MATH 4100 or consent of instructor. Naive set theory, cardinal arithmetic, ordinal numbers, the axiom of choice and equivalents, metric spaces, convergence, continuity, compactness, contraction principals and applications. Construction of completions and examples like real numbers and p-adic numbers. Other topics could include the Stone-Weierstrass theorem and metrizability theorems.

MATH 5160 Complex Analysis II: 3 semester hours

Prerequisites: MATH 4160 and either MATH 4100 or MATH 4800. A second course in complex analysis, emphasizing the theory of analytic functions, and including various topics like the Riemann mapping theorem, normal families, analytic continuation, representations of analytic functions, and elliptic functions.

MATH 5320 Applied Statistics: 3 semester hours

Prerequisites: MATH 4210 or consent of instructor The course studies classical and recently developed statistical procedures selected from areas including analysis of variance, multivariate analysis, nonparametric or semi-parametric methods and generalized linear models. Emphasis is on application of procedures, including the rationale underlying choice of procedures.

MATH 5500 Directed Readings: 1-6 semester hours

Prerequisite: Consent of instructor. Independent readings at an advanced level.

MATH 5550 Topics In Advanced Math For The Teacher: 3 semester hours

Prerequisite: Consent of Instructor. This course will look at various topics in Algebra, Analysis, and Geometry that will deepen a teacher's understanding of the Mathematics of the precollegiate curriculum. It can be taken more than once for credit.

MATH 5600 Topics In Computation: 3 semester hours

Prerequisite: consent of instructor. The course will cover various advanced topics in computation, and can be taken more than once for credit. Examples of such topics are: computer graphics, computer architecture, theories of language, analysis of operating systems, numerical geometry and computer aided design, etc.

MATH 5700 Topics In Applied Mathematics: 3 semester hours

Prerequisite: consent of instructor. The course will cover various advanced topics on applied mathematics, and can be taken more than once for credit. Examples of such topics are: fast transforms, digital filters, etc.

MATH 5710 Topics In Analysis: 3 semester hours

Prerequisites: MATH 5100 or consent of instructor. Topics selected from the areas of Fourier analysis, harmonic analysis, functional analysis, special functions, generalized functions, and partial differential equations. May be taken more than once for credit with consent of department.

MATH 5820 Topics In Algebra: 3 semester hours

Prerequisite: Consent of instructor. Topics selected from the theory of groups, rings, fields, algebras and other algebraic systems. May be taken more than once for credit with consent of department.

MATH 6900 Masters Thesis: 1-6 semester hours

Prerequisite: Consent of instructor. Thesis work under the supervision of a faculty member. The course is designed for those students intending to present a thesis as part of their M.A. program. Students who do not write a thesis cannot apply MATH 6900 to a degree.

MATH 7990 Ph.D. Dissertation Research: 1-9 semester hours

Prerequisites: Completion of Comprehensive. May be taken for no more than nine hours.

Haiyan Cai
Associate Professor and Chair
Ph.D., University of Maryland

Uday K. Chakraborty
Professor
Ph.D., Jadavpur University

Qingtang Jiang
Professor
Ph.D., Peking University

Prabhakar A. Rao
Professor
Ph.D., University of California, Berkeley

Sanjiv K. Bhatia
Associate Professor
Ph.D., University of Nebraska-Lincoln

Adrian Clingher
Associate Professor
Ph.D., Columbia University

Ronald Dotzel
Associate Professor
Ph.D., Rutgers University

Ravindra Girivaru
Associate Professor
Ph.D., University of Madras

Wenjie He
Associate Professor
Ph.D., University of Georgia

Cezary Janikow
Associate Professor
Ph.D., University of North Carolina at Chapel Hill

Henry Kang
Associate Professor
Ph.D., Korea Advanced Institute of Science and Technology (KAIST)

Nevena Maric
Assistant Professor
Ph.D., University of Sao Paulo

Jianli Pan
Assistant Professor
Ph.D., Washington University

Yuefeng Wu
Assistant Professor
Ph.D., North Carolina State University

Shahla Peterman
Teaching Professor
M.S., University of Wisconsin-Madison

Galina N. Piatnitskaia
Teaching Professor
Ph.D., Moscow Physical-Technical Institute

Qiang Sun Dotzel
Associate Teaching Professor
M.A., University of Missouri-St. Louis

Emily Ross
Associate Teaching Professor
M.A., Saint Louis University

Michael Schulte
Associate Teaching Professor
M.S., Florida Institute of Technology

Nazire Koc
Assistant Teaching Professor
M.S., Southern Illinois University, Carbondale

Jennifer Shrensker
Assistant Teaching Professor
M.A., Washington University

Albert Stanger
Assistant Teaching Professor and Math Academic Center Supervisor
M.A., University of Missouri-St. Louis

Charles Chui
Founders Professor
Ph.D., University of Wisconsin

Richard Friedlander
Founders Professor
Ph.D., University of California, Los Angeles

Raymond Balbes
Professor Emeritus
Ph.D., University of California, Los Angeles

William Connett
Professor Emeritus
Ph.D., University of Chicago

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

Frederick Wilke
Associate Professor Emeritus
Ph.D., University of Missouri-Columbia

John Antognoli
Teaching Professor Emeritus
M.A., University of Missouri-St. Louis