## Mathematics

### College of Science

### Chair Jianzhong Su

Email math@uta.edu

Phone 817.272.3261

Fax 817.272.5802

#### Degrees / Certificates

**Master’s Degrees**

Mathematics (General Mathematics), M.S.

Mathematics (General Statistics), M.S.

Mathematics Teaching, M.A.

Mathematics, M.A.

**Doctoral Degrees**

Mathematical Sciences, Mathematics, Ph.D.

Mathematics (General Mathematics), B.S. to Ph.D.

Mathematics (General Mathematics), Ph.D.

Mathematics (General Statistics), B.S. to Ph.D.

Mathematics (General Statistics), Ph.D.

**Certificates**

Applied Statistics Certificate

#### Graduate Faculty

**Professor**

**Associate Professor**

**Assistant Professor**

#### Graduate Advisors

*Mathematics, M.A.*

*Applied Statistics Certificate*

*Mathematical Sciences, Mathematics, Ph.D.*

*Mathematics (General Mathematics), B.S. to Ph.D.*

*Mathematics (General Mathematics), M.S.*

*Mathematics (General Mathematics), Ph.D.*

*Mathematics (General Statistics), B.S. to Ph.D.*

*Mathematics (General Statistics), M.S.*

*Mathematics (General Statistics), Ph.D.*

#### Department Information

#### Courses

## Department Information

- Master of Science Program
- Master of Arts Program
- Certificate of Applied Statistics Program
- Doctoral Program
- Doctoral Program (B.S.-Ph.D. track)

Master of Science Degree Requirements

Master of Arts Degree Requirements

Certificate of Applied Statistics Requirements

Ph.D. Degree Requirements for the B.S.-Ph.D. track

### Objective

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, mathematics education, numerical analysis, operations research, probability, statistics and topology.

### Admissions Requirements

#### Master of Science Program

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) if taken prior to August 2011. Minimum of 143 on the verbal and 151 on the quantitative portions of the GRE it faken after August 2011.
- For applicants whose native language is not English, a minimum score of 550 on the Test of English as a Foreign Language (or a minimum score of 213 on a computer-based test, or a minimum score of 79 on an internet-based test) or a minimum 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 UT Arlington.

Students who are unconditionally admitted or admitted on probation 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 UT Arlington 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.

#### Master of Arts Program

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

- A B.S. or B.A. degree with at least 24 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) if taken prior to August 2011. Minimum of 146 on the verbal and 148 on the quantitative portions of the GRE if taken after August 2011.
- 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 with a GPA of at least 3.0, as calculated by the Graduate School on a 4.0 scale.
- 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 UT Arlington.

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.

#### Certificate of Applied Statistics Program

The admission standard is the same as that of Master of Science Program.

#### Doctoral Program

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) if taken prior to August 2011. Minimum of 143 on the verbal and 155 on the quantitative portions of the GRE if taken after August 2011.
- For applicants whose native language is not English, a minimum score of 550 on the Test of English as a Foreign Language (or a minimum score of 213 on a computer-based test, or a minimum score of 79 on an internet-based test) or a minimum 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 UT Arlington.

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.

#### Doctoral Program (B.S.-Ph.D. track)

For unconditional admission a student must meet the following requirements:

- A bachelor's degree in mathematics or in a closely related field.
- A minimum GPA of 3.00 on the 4.00 scale in undergraduate course work, as calculated by the UT Arlington Graduate School.
- A minimum of 350 on the verbal part and 700 on the quantitative part of the Graduate Record Examination (GRE) if taken prior to August 2011. Minimum of 143 on the verbal and 155 on the quantitative portions of the GRE if taken after August 2011.
- For an applicant whose native language is not English, a minimum score of 550 on the Test of English as a Foreign Language (or a minimum score of 213 on a computer-based test, or a minimum score of 79 on an internet-based test) or a minimum score of 40 on the Test of Spoken English.
- At least three letters of recommendation from people familiar with the applicant's academic work and/or professional work.

Applicants who do not satisfy requirement 2 or/and 3 above may be considered for an unconditional admission if a further review of their undergraduate transcript(s), recommendation letters, correspondence or direct interactions with mathematics faculty, and statement of professional or research interests indicates that they are qualified to enter the B.S.-Ph.D. track program without deficiency.

If an applicant does not meet a majority of standards for an unconditional admission outlined above, he/she may be considered for a probationary admission after a careful examination of his/her application materials. A probationary admission requires that the applicant receive grades of B or better in the first 12 hours of graduate course work at UT Arlington.

An applicant may be denied admission if he/she has less than satisfactory performance on a majority of the admission criteria described above.

A deferred decision may be granted when the applicant's file is incomplete or when a denial on his/her admission is not appropriate. An applicant who is unable to supply all required documentation prior to the admission deadline but who otherwise appears to have met admission requirements may be granted provisional admission.

Students who are unconditionally admitted or admitted on probation 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 UT Arlington 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.

### Master of Science Degree Requirements

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 students in Master of Science program 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 5338 and 5339, and either 5371 or 5373, and six approved hours in computer science engineering

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

Pure Mathematics: MATH 5331 (replaces MATH 5300), either 5317 or 5322, either 5332 or 5334, and either 5304 or 5326

Core requirements can also be fulfilled by completing core requirements in the BS-Ph.D. track in the Doctoral program.

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

Core requirements can also be fulfilled by completing core requirements in the BS-Ph.D. track in the Doctoral program.

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]}

- 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] Electives may not be chosen from MATH 5336, 5337, 5340-5348, 5352, 5370, 5375-5379.

Students in every degree plan must pass a final exam.

### Master of Arts Degree Requirements

The master of arts program in the Department of Mathematics is designed for those who are interested in strengthening their understanding of mathematics and enriching their mathematics teaching. The program focuses on enhancing mathematics teaching through preparation in topics grounded in secondary school mathematics from an advanced standpoint. 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 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 5346: Concepts and Technique in Problem Solving

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 5340: Concepts and Techniques in Discrete Mathematics

MATH 5347: Concepts and Techniques in Modeling and Applications

MATH 5348: Advanced Algebra in Secondary School Mathematics

MATH 5352: Concepts and Techniques in Precalculus

MATH 5380: Seminar - Study of Current Mathematics Topics

MATH 5392: Selected Topics in Mathematics

### Certificate of Applied Statistics Requirements

The Certificate in Applied Statistics offers individuals with an undergraduate degree an opportunity to receive graduate instruction in applied statistics as a means of maintaining and enhancing their professional development. The certificate program will provide coursework in statistics to an individual whose undergraduate major was outside the area of statistics. Since the requirements for the certificate are substantially less than those for the Master’s Degree in Mathematics with a concentration in Statistics, the certificate can be earned in a much shorter time span.

The Certificate in Applied Statistics requires that the students take and successfully complete the following courses.

1: Required Courses (2):

STATS 5312: Mathematical Statistics I

STATS 5313: Mathematical Statistics II

2: Electives (3 courses chosen from the following list of courses)

STATS 5305: Statistical Methods

STATS 5314: Experimental Design

STATS 5353: Applied Linear Model

STATS 5356: Applied Multivariate Statistical Analysis

STATS 5357: Sample Surveys

STATS 5358: Regression Analysis

MATH 5392: Selected Topics in Statistical Quality Control

MATH 5392: Selected Topics in Statistical Methods in Clinical Research

Upon completion of the 15 hours of graduate courses from lists 1 and 2 with a minimum GPA of 3.0, the student is awarded the Certificate in Applied Statistics. The expected time to completion is 1 to 2 years. The time limit for completion of the certificate program is 6 years.

### Ph.D. Degree Requirements

A dynamic program leading to the Doctor of Philosophy degree in the mathematics will aim at both real and demonstrated competency on the part of the student over material from various branches of mathematics. The Doctor of Philosophy degree in Mathematics provides a program of study that may be tailored to meet the needs of those interested in applied or academic careers. This program allows students to pursue topics ranging from traditional mathematics studies to applied mathematical problems in engineering and sciences. The nature of the dissertation will range from research in mathematics to the discovery and testing of mathematical models for analyzing given problems in engineering and 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 pure mathematics, applied mathematics, mathematics education and statistics.

The Department of Mathematics offers doctoral degree programs in Mathematics (algebra, applied mathematics, geometry, mathematics education, numerical analysis and 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 5339: Numerical Analysis II

- General STATISTICS core requirements:
- MATH 5308: Mathematical Analysis II
- MATH 5312: Mathematical Statistics I
- MATH 5313: Mathematical Statistics II
- MATH 5314: Experimental Design
- MATH 5317: Real Analysis
- MATH 5319: Probability Theory
- MATH 5322: Complex Variables or MATH 5327: Functional Analysis I
- MATH 5356: Applied Multivariate Statistical Analysis

Students in every degree plan must pass the preliminary and comprehensive examinations.

### Ph.D. Degree Requirements for the B.S.-Ph.D. track

The student must complete either the mathematics or statistics core requirements.

- General MATHEMATICS core requirements:
- MATH 5307: Mathematical Analysis I
- 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
- MATH 5333: Linear Algebra
- One of the following four courses:
- MATH 5319: Probability Theory
- MATH 5321: Partial Differential Equations
- MATH 5334: Differential Geometry
- MATH 5339: Numerical Analysis II

- General STATISTICS core requirements:
- MATH 5307: Mathematical Analysis I
- MATH 5308: Mathematical Analysis II
- MATH 5312: Mathematical Statistics I
- MATH 5313: Mathematical Statistics II
- MATH 5314: Experimental Design
- MATH 5317: Real Analysis
- MATH 5319: Probability Theory
- MATH 5322: Complex Variables or MATH 5327: Functional Analysis I
- MATH 5333: Linear Algebra
- MATH 5356: Applied Multivariate Statistical Analysis

The requirements for the preliminary and comprehensive examinations are the same as the other tracks in the Ph.D. program.

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

No course information is available at this time...