Mathematics - Graduate Programs

Objective

The objectives of the UT Arlington Mathematics Department’s graduate program are:

  • Develop the students’ ability to do independent research and prepare them for more advanced studies in mathematics.
  • Provide advanced training and preparation for professional careers as  mathematicians, mathematics teachers, and those employed in engineering, scientific and business fields.

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

Admissions Requirements

Master of Science Program

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

  1. A B.A. or B.S. degree in mathematics or closely related field.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

  1. 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.
  2. 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.
  3. Three favorable letters of recommendation from people familiar with the applicant's academic work and/or professional work.
  4. 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.
  5. 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.

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:

  1. General Mathematics core requirements1:

    MATH 5307MATHEMATICAL ANALYSIS I3
    MATH 5333LINEAR ALGEBRA AND MATRICES3
    Select one of the following tracks:
    Applied Mathematics:15
    MATH 5300INTRODUCTION TO SCIENTIFIC COMPUTING3
    MATH 5308MATHEMATICAL ANALYSIS II3
    Select three of the following:9
    APPLIED MATHEMATICS I
    APPLIED MATHEMATICS II
    ORDINARY DIFFERENTIAL EQUATIONS
    APPLIED PARTIAL DIFFERENTIAL EQUATIONS
    Computer Science:15
    MATH 5300INTRODUCTION TO SCIENTIFIC COMPUTING3
    MATH 5308MATHEMATICAL ANALYSIS II3
    MATH 5338NUMERICAL ANALYSIS I3
    MATH 5339NUMERICAL ANALYSIS II3
    MATH 5371APPLIED NUMERICAL LINEAR ALGEBRA3
    or MATH 5373 NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
    Mathematics Education:15
    MATH 5300INTRODUCTION TO SCIENTIFIC COMPUTING3
    MATH 5308MATHEMATICAL ANALYSIS II3
    Select three of the following:9
    CONCEPTS AND TECHNIQUES IN NUMBER THEORY
    CONCEPTS AND TECHNIQUES IN CALCULUS
    CONCEPTS AND TECHNIQUES IN DISCRETE MATHEMATICS
    CONCEPTS AND TECHNIQUES IN GEOMETRY
    CONCEPTS AND TECHNIQUES IN ALGEBRA
    CONCEPTS AND TECHNIQUES IN PROBABILITY AND STATISTICS
    MATHEMATICS-SPECIFIC TECHNOLOGIES
    CONCEPTS AND TECHNIQUES IN ANALYSIS
    CONCEPTS AND TECHNIQUES IN PROBLEM SOLVING
    CONCEPTS AND TECHNIQUES IN MATHEMATICAL MODELING WITH APPLICATIONS
    ADVANCED ALGEBRA IN SECONDARY SCHOOL MATHEMATICS
    CONCEPTS AND TECHNIQUES IN PRECALCULUS
    Pure Mathematics: 15
    MATH 5322COMPLEX VARIABLES I3
    MATH 5331ABSTRACT ALGEBRA I (replaces MATH 5300)3
    Select 3 from the following:9
    GENERAL TOPOLOGY
    ALGEBRAIC TOPOLOGY
    HOMOLOGICAL ALGEBRA
    ALGEBRAIC GEOMETRY
    ABSTRACT ALGEBRA II
    DIFFERENTIAL GEOMETRY
    Or select 3 from the following:9
    GENERAL TOPOLOGY
    MATHEMATICAL ANALYSIS II
    APPLIED PARTIAL DIFFERENTIAL EQUATIONS
    REAL ANALYSIS
    FUNCTIONAL ANALYSIS I
    DIFFERENTIAL GEOMETRY
  2. General Statistics core requirements1:

    MATH 5300INTRODUCTION TO SCIENTIFIC COMPUTING3
    MATH 5307MATHEMATICAL ANALYSIS I3
    MATH 5333LINEAR ALGEBRA AND MATRICES3
    MATH 5305STATISTICAL METHODS3
    MATH 5312MATHEMATICAL STATISTICS I3
    MATH 5313MATHEMATICAL STATISTICS II3
    Select one of the following:3
    APPLIED MULTIVARIATE STATISTICAL ANALYSIS
    SAMPLE SURVEYS
    REGRESSION ANALYSIS
    Total Hours21
    • In addition:

      1. Those students enrolled in the thesis substitute plan must take MATH 5395 SPECIAL PROJECT, and must take at least nine other hours of electives2.

      2. Those students enrolled in the thesis plan must take at least six hours of MATH 5398 THESIS / MATH 5698 THESIS, and must take at least three other hours of electives2.

        1

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

        2

        Electives may not be chosen from MATH 5336 CONCEPTS AND TECHNIQUES IN NUMBER THEORY, MATH 5337 CONCEPTS AND TECHNIQUES IN CALCULUS, 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 5346 CONCEPTS AND TECHNIQUES IN PROBLEM SOLVING, MATH 5347 CONCEPTS AND TECHNIQUES IN MATHEMATICAL MODELING WITH APPLICATIONS, MATH 5348 ADVANCED ALGEBRA IN SECONDARY SCHOOL MATHEMATICS, MATH 5352 CONCEPTS AND TECHNIQUES IN PRECALCULUS, MATH 5370 PROBLEM SOLVING IN K-8 MATHEMATICS, MATH 5375 CONSTRUCTING WHOLE NUMBER ANDOPERATIONS IN K-8 MATHEMATICS, MATH 5376 CONSTRUCTING RATIONAL NUMBERAND OPERATIONS IN K-8 MATH, MATH 5377 ALGEBRAIC THINKING IN K-8 MATHEMATICS, MATH 5378 GEOMETRY CONCEPTS IN K-8 MATHEMATICS, MATH 5379 MEASUREMENT CONCEPTS IN K-8 MATHEMATICS. However, students in the Mathematics Education track may choose three hours from Math 5336, 5337, 5340-5348,5352, 5370, 5375-5379. Students in the Computer Science track may choose three approved hours of electives in science and/or engineering. Elective courses for pure-mathematics track must be chosen from MATH 5300, MATH 5304, MATH 5308, MATH 5317, MATH 5321, MATH 5326,MATH 5327, MATH 5329, MATH 5330, MATH 5332, MATH 5334, MATH 5380, or MATH 5392 courses offered in the pure-mathematics track.

Students in every degree plan must pass a final Master's 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 and Project
MATH 5341CONCEPTS AND TECHNIQUES IN GEOMETRY3
MATH 5342CONCEPTS AND TECHNIQUES IN ALGEBRA3
MATH 5343CONCEPTS AND TECHNIQUES IN PROBABILITY AND STATISTICS3
MATH 5344MATHEMATICS-SPECIFIC TECHNOLOGIES3
MATH 5345CONCEPTS AND TECHNIQUES IN ANALYSIS3
MATH 5346CONCEPTS AND TECHNIQUES IN PROBLEM SOLVING3
MATH 5395SPECIAL PROJECT (Individual, Director-Approved Research)3
Elective Courses
Students must successfully complete 12 additional hours of electives. Electives may not be chosen from MATH 5375-MATH 5379.12
Total Hours33

Admission Requirements

For unconditional admission a student must meet the following requirements:

  1. A master's degree or at least 30 hours of graduate coursework in mathematics or closely related fields.
  2. A minimum GPA of 3.0, as calculated by the Graduate School, on a 4.0 scale in graduate coursework.
  3. 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.
  4. 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.
  5. 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:

  1. A bachelor's degree in mathematics or in a closely related field.
  2. A minimum GPA of 3.00 on the 4.00 scale in undergraduate course work, as calculated by the UT Arlington Graduate School.
  3. 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.
  4. 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.
  5. 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.

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:

  1. General MATHEMATICS core requirements:

    MATH 5308MATHEMATICAL ANALYSIS II3
    MATH 5317REAL ANALYSIS3
    MATH 5320ORDINARY DIFFERENTIAL EQUATIONS3
    MATH 5322COMPLEX VARIABLES I3
    MATH 5327FUNCTIONAL ANALYSIS I3
    MATH 5331ABSTRACT ALGEBRA I3
    Select one of the following:
    PROBABILITY THEORY
    APPLIED PARTIAL DIFFERENTIAL EQUATIONS
    DIFFERENTIAL GEOMETRY
    NUMERICAL ANALYSIS II
    In addition to the mathematics core requirements, the student is required to take three area-related courses.
    Total Hours18
  2. General STATISTICS core requirements:

    MATH 5308MATHEMATICAL ANALYSIS II3
    MATH 5312MATHEMATICAL STATISTICS I3
    MATH 5313MATHEMATICAL STATISTICS II3
    MATH 5314EXPERIMENTAL DESIGN3
    MATH 5317REAL ANALYSIS3
    MATH 5319PROBABILITY THEORY3
    MATH 5322COMPLEX VARIABLES I3
    or MATH 5327 FUNCTIONAL ANALYSIS I
    MATH 5356APPLIED MULTIVARIATE STATISTICAL ANALYSIS3
    In addition to the statistics core requirements, the student is also required to take two statistics courses from the following:6
    APPLIED PROBABILITY AND STOCHASTIC PROCESSES
    FUNDAMENTALS OF STOCHASTIC ANALYSIS
    APPLIED LINEAR MODELS
    CATEGORICAL DATA ANALYSIS
    SAMPLE SURVEYS
    REGRESSION ANALYSIS
    SURVIVAL ANALYSIS
    GENERALIZED LINEAR MODELS
    TIME SERIES ANALYSIS
    NONPARAMETRIC STATISTICS
    Total Hours30

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.

  1. General MATHEMATICS core requirements:

    MATH 5307MATHEMATICAL ANALYSIS I3
    MATH 5308MATHEMATICAL ANALYSIS II3
    MATH 5317REAL ANALYSIS3
    MATH 5320ORDINARY DIFFERENTIAL EQUATIONS3
    MATH 5322COMPLEX VARIABLES I3
    MATH 5327FUNCTIONAL ANALYSIS I3
    MATH 5331ABSTRACT ALGEBRA I3
    MATH 5333LINEAR ALGEBRA AND MATRICES3
    Select one of the following:3
    PROBABILITY THEORY
    APPLIED PARTIAL DIFFERENTIAL EQUATIONS
    DIFFERENTIAL GEOMETRY
    NUMERICAL ANALYSIS II
    In addition to the mathematics core requirements, the student is required to take three area-related courses.
    Total Hours27
  2. General STATISTICS core requirements:

    MATH 5307MATHEMATICAL ANALYSIS I3
    MATH 5308MATHEMATICAL ANALYSIS II3
    MATH 5312MATHEMATICAL STATISTICS I3
    MATH 5313MATHEMATICAL STATISTICS II3
    MATH 5314EXPERIMENTAL DESIGN3
    MATH 5317REAL ANALYSIS3
    MATH 5319PROBABILITY THEORY3
    MATH 5322COMPLEX VARIABLES I3
    MATH 5333LINEAR ALGEBRA AND MATRICES3
    MATH 5356APPLIED MULTIVARIATE STATISTICAL ANALYSIS3
    In addition to the statistics core requirements, the student is also required to take two statistics courses from the following:6
    APPLIED PROBABILITY AND STOCHASTIC PROCESSES
    FUNDAMENTALS OF STOCHASTIC ANALYSIS
    APPLIED LINEAR MODELS
    CATEGORICAL DATA ANALYSIS
    SAMPLE SURVEYS
    REGRESSION ANALYSIS
    SURVIVAL ANALYSIS
    GENERALIZED LINEAR MODELS
    TIME SERIES ANALYSIS
    NONPARAMETRIC STATISTICS
    Total Hours36

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.

Certificate of Applied Statistics Program

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

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.

Required Courses
STATS 5312MATHEMATICAL STATISTICS I3
STATS 5313MATHEMATICAL STATISTICS II3
Electives
Select three of the following:9
STATISTICAL METHODS
EXPERIMENTAL DESIGN
APPLIED LINEAR MODELS
APPLIED MULTIVARIATE STATISTICAL ANALYSIS
SAMPLE SURVEYS
REGRESSION ANALYSIS
SELECTED TOPICS IN MATHEMATICS (Statistical Quality Control)
SELECTED TOPICS IN MATHEMATICS (Statistical Methods in Clinical Research)
Total Hours15

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.