The University of Texas at Arlington Graduate Catalog 2004-2006 Vol LXXXVII - July 2004

department web page: www.uta.edu/math/

department contact: math@uta.edu

graduate web page:

graduate contact:

Danny Dyer

469 Pickard Hall

817.272.3246

Mathematics

M.S., M.A.

Mathematical Sciences

Ph.D.

(See Interdepartmental and Intercampus Programs.)

Thesis and Thesis Substitute

Tie Luo

429 Pickard Hall, 817.272.3597

Dragan, Dyer, Han, Ladde, Liao, C. Liu, Luo, Nestell

Cordero, Hawkins, Heath, Korzeniowski, Kribs-Zaleta, D. Liu, Shipman, Su, Vancliff

Epperson, Jorgensen, Kojouharov, Shan

Corduneanu, Greenspan, Moore

The objectives of the Mathematics Department's program at the master's level are (1) to develop the student's ability to do independent research and prepare for more advanced study in mathematics, and (2) to give advanced training to professional mathematicians, mathematics teachers, and those employed in engineering, scientific, and business areas.

Graduate work will be offered in algebra, complex and real variables, differential equations, functional analysis, geometry, mathematical education, numerical analysis, operations research, probability, statistics and topology.

For unconditional admission, a student must meet the following requirements:

- A B.A. or B.S. degree in mathematics or closely related field.
- An overall GPA in the final 60 hours of coursework of a 3.0 or better, as calculated by the Graduate School, on a 4.0 scale.
- Minimum of 350 on the verbal and 650 on the quantitative portions of the Graduate Record Examination (GRE).
- For applicants whose native language is not English, a minimum score of 550 on the Test of English as a Foreign Language (or an equivalent score on a computer-based test) or a score of 40 on the Test of Spoken English.
- Three favorable letters of recommendation from people familiar with the applicant's academic work.

Applicants who do not satisfy requirements 2 or 3 above may be considered for unconditional admission if further review of their undergraduate transcript, recommendation letters, correspondence or direct interactions with mathematics faculty, and statement of professional or research interests indicates that they are qualified to enter the Master's Program without deficiency.

If an applicant does not meet a majority of standards for unconditional admission outlined above, they may be considered for probationary admission after careful examination of their application materials. Probationary admission requires that the applicant receive a B or better in the first 12 hours of graduate coursework at UTA.

Students who are unconditionally admitted will be eligible for available scholarship and/or fellowship support. Award of scholarships or fellowships will be based on consideration of the same criteria utilized in admission decisions. To be eligible, candidates must be new students coming to UTA in the fall semester, must have a GPA of 3.0 in the last 60 undergraduate credit hours plus any graduate credit hours as calculated by the Graduate School, and must be enrolled in a minimum of 6 hours of coursework in both long semesters to retain the fellowship.

Applicants may be denied admission if they have less than satisfactory performance on a majority of the admission criteria described above.

A deferred decision may be granted when a file is incomplete or when a denied decision is not appropriate. An applicant unable to supply all required documentation prior to the admission deadline, but who otherwise appears to meet admission requirements, may be granted provisional admission.

For unconditional admission a student must meet items 1-3 or 3-5.

- A B.S. or B.A. degree with at least 18 hours of mathematics coursework with a GPA of at least 3.0, as calculated by the Graduate School on a 4.0 scale.
- Minimum of 400 on the verbal and 600 on the quantitative portions of the Graduate Record Examination (GRE).
- Three favorable letters of recommendation from people familiar with the applicant's academic work and/or professional work.
- A B.S. or B.A. degree.
- Certified to teach mathematics at the Secondary Level (Secondary Mathematics Certification).

Applicants who do not satisfy requirements 1 or 2 above may be considered for unconditional admission if further review of their undergraduate transcript, recommendation letters, correspondence or direct interactions with mathematics faculty, and statement of professional or research interests indicates that they are qualified to enter the Master's Program without deficiency.

If an applicant does not meet a majority of standards for unconditional admission outlined above, they may be considered for probationary admission after careful examination of their application materials. Probationary admission requires that the applicant receive a B or better in the first 12 hours of graduate coursework at UTA.

Applicants may be denied admission if they have less than satisfactory performance on a majority of the admission criteria described above.

A deferred decision may be granted when a file is incomplete or when a denied decision is not appropriate. An applicant unable to supply all required documentation prior to the admission deadline, but who otherwise appears to meet admission requirements, may be granted provisional admission.

For unconditional admission a student must meet the following requirements:

- A master's degree or at least 30 hours of graduate coursework in mathematics or closely related fields.
- A minimum GPA of 3.0, as calculated by the Graduate School, on a 4.0 scale in graduate coursework.
- Minimum of 350 on the verbal and 700 on the quantitative portions of the Graduate Record Examination (GRE).
- For applicants whose native language is not English, a minimum score of 550 on the Test of English as a Foreign Language (or an equivalent score on a computer-based test) or a score of 40 on the Test of Spoken English.
- Three favorable letters of recommendation from people familiar with the applicant's academic work and/or professional work.

Applicants who do not satisfy requirements 2 or 3 above may be considered for unconditional admission if further review of their undergraduate transcript, recommendation letters, correspondence or direct interactions with mathematics faculty, and statement of professional or research interests indicates that they are qualified to enter the Doctoral Program without deficiency.

If an applicant does not meet a majority of standards for unconditional admission outlined above, they may be considered for probationary admission after careful examination of their application materials. Probationary admission requires that the applicant receive a B or better in the first 12 hours of graduate coursework at UTA.

Students who are unconditionally admitted will be eligible for available scholarship and/or fellowship support. Award of scholarships or fellowships will be based on consideration of the same criteria utilized in admission decisions. To be eligible, candidates must be new students coming to UTA in the fall semester, must have a GPA of 3.0 in the last 60 undergraduate credit hours plus any graduate credit hours as calculated by the Graduate School, and must be enrolled in a minimum of 6 hours of coursework in both long semesters to retain the fellowship.

Applicants may be denied admission if they have less than satisfactory performance on a majority of the admission criteria described above.

A deferred decision may be granted when a file is incomplete or when a denied decision is not appropriate. An applicant unable to supply all required documentation prior to the admission deadline, but who otherwise appears to meet admission requirements, may be granted provisional admission.

The Department of Mathematics offers master's degree programs in mathematics with additional emphasis in applied mathematics, computer science, mathematics education, pure mathematics, and statistics. All students are to use either the thesis or thesis-substitute plan.

All master's students must complete one of the following:

- General Mathematics core requirements:

MATH 5300: Computer Programming and Applications

MATH 5307: Mathematical Analysis I

MATH 5308: Mathematical Analysis II

MATH 5333: Linear Algebra and Matrices

One of the following tracks:

Applied Mathematics: MATH 5350, 5351, and either 5320 or 5321

Computer Science: MATH (5348 and 5349) or (5338 and 5339), and either 5371 or 5373, and six approved hours in computer science engineering

Mathematical Education: Nine hours from MATH 5336, 5337, 5340-5348, 5352

Pure Mathematics: MATH 5317, and two from MATH 5304, 5331, 5334 - General Statistics core requirements:

MATH 5300: Computer Programming and Applications

MATH 5307: Mathematical Analysis I

MATH 5333: Linear Algebra and Matrices- One of the following three courses:

MATH 5356: Applied Multivariate Statistical Analysis

MATH 5357: Sample Surveys

MATH 5392: Regression Analysis

MATH 5305: Statistical Methods

MATH 5312: Mathematical Statistics I

MATH 5313: Mathematical Statistics II

In addition:

- Those students enrolled in the thesis substitute plan must take MATH 5395, and all except those in the computer science track must take at least nine other hours of electives.[1]
- Those students enrolled in the thesis plan must take at least six hours of MATH 5398-5698, and all except those in the computer science track must take at least three other hours of electives.[1]

- One of the following three courses:

[1] Electives may not be chosen from MATH 5336, 5337, 5340-5348, 5352.

Students in every degree plan must pass a final exam.

The master of arts program in the Department of Mathematics is designed for teachers who are interested in strengthening their understanding of mathematics and enriching their mathematics teaching. The program prepares teachers in subjects such as geometry, algebra, precalculus, analysis/calculus, probability, statistics, discrete mathematics, number theory, and the use of mathematics-specific technologies. The program embraces a philosophy of teaching and learning mathematics that is consistent with the landmark Standards documents produced by the National Council of Teachers of Mathematics.

The requirements for the master of arts degree are 30 hours of graduate courses from the Department of Mathematics and a 3 hour project.

All students must complete the following:

- Required Courses (6) and Project:

MATH 5340: Concepts and Techniques in Discrete Mathematics

MATH 5341: Concepts and Techniques in Geometry

MATH 5342: Concepts and Techniques in Algebra

MATH 5343: Concepts and Techniques in Probability and Statistics

MATH 5344: Mathematics-Specific Technologies

MATH 5345: Concepts and Techniques in Analysis

MATH 5395: Project - Individual, Director-Approved Research - Elective Courses (4):

MATH 5300: Computer Programming and Applications

MATH 5305: Statistical Methods

MATH 5307: Mathematical Analysis I

MATH 5308: Mathematical Analysis II

MATH 5333: Linear Algebra and Matrices

MATH 5336: Concepts and Techniques in Number Theory

MATH 5337: Concepts and Techniques in Calculus

MATH 5346: Concepts and Techniques in Problem Solving

MATH 5347: Concepts and Techniques in Modeling and Applications

MATH 5352: Concepts and Techniques in Precalculus

MATH 5380: Seminar - Study of Current Mathematics Topics

MATH 5392: Selected Topics in Mathematics

A unique and dynamic program leading to the Doctor of Philosophy degree in the mathematical sciences will aim at both real and demonstrated competency on the part of the student over material from various branches of mathematical sciences. The Doctor of Philosophy degree in Mathematical Sciences provides a program of study that may be tailored to meet the needs of those interested in applied or academic careers. This unique program allows students to pursue topics ranging from traditional mathematics studies to applied and theoretical problems in biology, chemistry, computer science, engineering, geology, information systems, physics and psychology. The nature of the dissertation will range from research in mathematics to the discovery and testing of mathematical models for analyzing given problems in sciences and in locating and developing mathematical and computational techniques for deducing the properties of these models as to solve these problems effectively and efficiently. Such dissertations will be concerned with research problems from such areas as pure mathematics, applied mathematics, probability, statistics, computer science, biology, biometry, chemistry, engineering, geology, information systems, physics, management sciences, and operational sciences.

The Department of Mathematics offers doctoral degree programs in Mathematics (algebra, applied mathematics, game theory, geometry, numerical analysis) and in Statistics.

All doctoral students must complete one of the following:

- General MATHEMATICS core requirements:

MATH 5308: Mathematical Analysis II

MATH 5317: Real Analysis

MATH 5320: Ordinary Differential Equations

MATH 5322: Complex Variables

MATH 5327: Functional Analysis I

MATH 5331: Abstract Algebra I

One of the following four courses:

MATH 5319: Probability Theory

MATH 5321: Partial Differential Equations

MATH 5334: Differential Geometry

MATH 5338: Numerical Analysis I

In addition to the mathematics core requirements students are also required to take three area related courses. - General STATISTICS core requirements:

MATH 5305: Statistical Methods

MATH 5307: Mathematical Analysis I

MATH 5308: Mathematical Analysis II

MATH 5312: Mathematical Statistics I

MATH 5313: Mathematical Statistics II

MATH 5317: Real Analysis

MATH 5319: Probability Theory

MATH 5322: Complex Variables

MATH 5327: Functional Analysis I

MATH 5333: Linear Algebra

In addition to the statistics core requirements, students are also required to take two statistics courses from MATH 5311, 5314, 5353, 5354, 5356, 5357, 5358, 5359, 6353, 6356, 6357.

Students in every degree plan must pass a comprehensive exam.

[2] Effective for students entering the graduate program starting Fall 2001. Returning students may choose the old core requirements.

For additional information on the mathematical sciences program, see the program entry in the Interdepartmental and Intercampus Programs section of this catalog.

The grade of R (research in progress) is a permanent grade; completing course requirements in a later semester cannot change it. To receive credit for an R-graded course, the student must continue to enroll in the course until a passing grade is received.

An incomplete grade (the grade of X) cannot be given in a course that is graded R, nor can the grade of R be given in a course that is graded X. To receive credit for a course in which the student earned an X, the student must complete the course requirements. Enrolling again in the course in which an X was earned cannot change a grade of X. At the discretion of the instructor, a final grade can be assigned through a change of grade form.

Three-hour thesis courses and three- and six-hour dissertation courses are graded R/F/W only (except social work thesis courses). The grade of P (required for degree completion for students enrolled in thesis or dissertation programs) can be earned only in six- or nine-hour thesis courses and nine-hour dissertation courses. In the course listings below, R-graded courses are designated either "Graded P/F/R" or "Graded R." Occasionally, the valid grades for a course change. Students should consult the appropriate Graduate Advisor or instructor for valid grade information for particular courses. (See also the sections titled "R" Grade, Credit for Research, Internship, Thesis or Dissertation Courses and Incomplete Grade in this catalog.)