**Department of Mathematics**

http://www.utdallas.edu/nsm/math/

**Faculty**

**Professors**: Larry P. Ammann,
Michael Baron, Sam Efromovich, M. Ali Hooshyar, Wieslaw Krawcewicz, Patrick L. Odell (Emeritus), Istvan Ozsvath, Viswanath
Ramakrishna, Ivor Robinson (Emeritus), Robert Serfling,
Janos Turi, John W. Van Ness (Emeritus)

**Associate Professors**: Zalman I. Balanov, Pankaj Choudhary, Mieczyslaw Dabkowski

**Assistant Professors**: Yan Cao, Tobias Hagge, Quiongxia (Joanne) Song

**Adjunct Professors**: Jose Carlos Gomez Larranage,
Adolfo Sanchez Valenzuela

**Affiliated Faculty**: Herve Abdi
(BBS), Raimund J. Ober
(EE), Alain Bensoussan (SOM), Thomas Butts and Titu Andreescu (SME), John Wiorkowski (SOM)

**Objectives**

The
Mathematics Department at The University of Texas at Dallas offers graduate
study in five areas:

Applied Mathematics, Engineering Mathematics, Mathematics,
Statistics, and an interdisciplinary degree in Bioinformatics and Computational
Biology.
The degree programs offer students the opportunity to prepare for careers in
these disciplines themselves or in any of the many other fields for which these
disciplines are such indispensable tools. As other sciences develop, problems
which require the use of these tools are numerous and pressing.

In
addition to a wide range of courses in mathematics and statistics, the Mathematics
Department offers a unique selection of courses that consider mathematical and
computational aspects of engineering, biology and
other scientific problems.

The
Master of Science degree programs are designed for persons seeking
specializations in Applied Mathematics, Engineering Mathematics, Mathematics, Statistics,
or Bioinformatics and Computational Biology.

The
Master of Science degree is available also for those who plan to teach Mathematics
or Statistics above the remedial level at a community college or at a college
or university. The Master of Science degree is recommended as a minimum, since
an earned doctorate is sometimes required.

For
information concerning the Master of Arts in Teaching in Mathematics Education,
designed for persons who are teaching in grades 6-12, see the Science and
Mathematics Education section.

The
Doctor of Philosophy degree programs cover two basic areas of concentration: Statistics,
and

Applied Mathematics. They are designed for those who plan
to pursue academic, government, financial, actuarial, or industrial careers.

**Facilities**

The
faculty, staff and students have access to a large network of workstations and
servers on campus.

**Admission Requirements**

The
University´s general admission requirements are discussed here.

Specific
additional admission requirements for students in degree programs in the
Department of Mathematics
follow. Students lacking undergraduate prerequisites for graduate courses in
their area must complete these prerequisites or receive approval from the
graduate adviser and the course instructor before registering.

One
of the components of a student´s academic history which is evaluated when the
student is seeking admission to the graduate program is his/her performance on
certain standardized tests. Since these tests are designed to indicate only the
student´s potential for graduate study, they are used in conjunction with other
measures of student proficiency (such as GPA, etc.) in determining the
admission status of a potential graduate student. Accordingly, there is no
rigid minimum cut–off score for admission to the program. Most applicants
admitted to either the MS or PhD programs have GRE scores

of at least 400
verbal, 700 quantitative, and 1200 combined. However,

exceptions are made
in some cases when other credentials are especially strong.

Higher standards prevail for applicants
seeking Teaching Assistantships.

**Degree Requirements **

The
University´s general degree requirements are discussed here.

Students
seeking a Master of Science in Mathematics must complete a total of 12
three–credit hour courses. In some cases, credit for 3 hours is approved for
good mathematics background. The student may choose a thesis plan or a non-thesis
plan. In the thesis plan, the thesis replaces two elective courses with
completion of an approved thesis (six thesis hours). The thesis is directed by
a Supervising Professor and must be approved by the Head of the Mathematics
Department.

Each
student must earn a 3.0 minimum GPA in the courses listed for the student´s
program.

**Applied Mathematics Concentration**

MATH
5301-5302 Elementary Analysis I and II (or equivalent)

MATH 6303 Theory of Complex Functions

MATH 6313 Numerical Analysis

MATH 6315 Ordinary Differential Equations

MATH 6318 Numerical Analysis of Differential Equations

MATH 6319-6320 Principles and Techniques in Applied Mathematics I and II

MATH 6308 Inverse Problems and their Applications

MATH 6321 Optimization

Plus two guided electives.

**Engineering Mathematics Concentration**

MATH
5301-5302 Elementary Analysis I and II (or equivalent)

MATH 6303 Theory of Complex Functions

MATH 6313 Numerical Analysis

MATH 6315 Ordinary Differential Equations

MATH 6318 Numerical Analysis of Differential Equations

MATH 6319-6320 Principles and Techniques in Applied Mathematics I and II

MATH 6331 Systems, Signals and Control

MATH 6305 Mathematics of Signal Processing

plus two guided electives.

**Traditional Mathematics Major**

MATH
5301-5302 Elementary Analysis I and II (or equivalent)

MATH 6303 Theory of Complex Functions

MATH 6313 Numerical Analysis

MATH 6315 Ordinary Differential Equations

MATH 6318 Numerical Analysis of Differential Equations

MATH 6301 Real Analysis

MATH 6302 Real and Functional Analysis

MATH 6306 Topology and Geometry

MATH 6311 Abstract Algebra I

plus two guided electives.

**Statistics Concentration**

STAT 6331 Statistical Inference I

STAT 6337-38 Statistical Methods I, II

STAT 6339 Linear Statistical Models

STAT 6341 Numerical Linear Algebra and Statistical Computing

One course from each of any two of the following sets of courses:

{STAT 6329, STAT 6343, STAT 7334} Stochastic Processes or Experimental Design
or Nonparametric and Robust Statistical Methods

{STAT 6348, STAT 7331} Multivariate Analysis

{STAT 6347, STAT 7338} Time Series Analysis

Students must choose remaining courses as electives approved by the Graduate
Advisor for Statistics. Up to two of the following prerequisite 5000-level
courses may be counted as electives: MATH 5301, 5302, Elementary Analysis I, II
and STAT 5351, 5352 Probability and Statistics I, II.

**Other Requirements**

Electives
must be approved by the graduate adviser. Typically, electives are 6000- and
7000-level Mathematics or Statistics courses. Courses from other disciplines
may also be used upon approval.

Substitutions
for required courses may be made if approved by the graduate adviser.
Instructors may substitute stated prerequisites for students with equivalent
experience.

**Master of Science in
Bioinformatics and Computational Biology**

Master
of Science in Bioinformatics and Computational Biology (BCBM) is offered
jointly by the Departments of Mathematics and Molecular and Cell Biology. This
program combines coursework from the disciplines of biology, computer science,
and Mathematics. The BCBM program seeks to answer the demand for a new breed of
scientist that has fundamental understanding in the fields of biology,
mathematics, statistics, and computer science. With this interdisciplinary
training, these scientists will be well prepared to meet the demand and
challenges that have arisen and will continue to develop in the biotechnology
arena.

Faculty
from the Mathematics Department (MMS) and the Molecular and Cell Biology Department
(MCB) participate in the Bioinformatics and Computational Biology program, with
the Mathematics Department serving as the administrative unit. Both departments
participate in advising students.

For
the Master´s degree in Bioinformatics and Computational Biology, beginning
students are expected to have completed multivariate calculus, linear algebra,
two semesters of general Chemistry, two semester of organic Chemistry, two
semesters of general physics, programming in C/C++, and two semesters of
biology.

Requirements
for completing a degree in BCBM are:

**Core courses: **

BIO
5410 Biochemistry

BIO 5420 Molecular Biology

BIO 5381 Genomics

STAT 5351 Probability and Statistics I

STAT 5352 Probability and Statistics II

MATH 6341 Bioinformatics

Additional core courses for the Computational Biology track:

MATH 6313 Numerical Analysis

MATH 6343 Computational Biology

MATH 6345 Mathematical Methods in Medicine & Biology

**Additional core courses for the Bioinformatics
track:**

CS
5333 Discrete Structures

CS 5343 Algorithms Analysis and Data Structures

CS 6360 Database Design

**Elective**: A minimum of 7 semester credit hours of elective, approved by
the student´s adviser. Typically, electives are 6000- and 7000- level courses
in mathematics, statistics, biology or computer
science.

Courses from other disciplines may also be used upon approval.

**Doctor of Philosophy**

The
University´s general degree requirements are discussed here.

Each
Doctor of Philosophy degree program is tailored to the student. The student
must arrange a course program with the guidance and approval of the graduate
adviser. Adjustments can be made as the student´s interests develop and a
specific dissertation topic is chosen. A minimum of 90 semester hours beyond
the bachelor´s degree is required.

**Applied Mathematics
Concentration**

MATH
6301 Real Analysis

MATH 6302 Real and Functional Analysis

MATH 6303 Theory of Complex Functions I

MATH 6306 Topology and Geometry

MATH 6311 Abstract Algebra I

MATH 6313 Numerical Analysis

MATH 6315 Ordinary Differential Equations

MATH 6316 Differential Equations

MATH 6318 Numerical Analysis of Differential Equations

MATH 6319-6320 Principles and Techniques in Applied Mathematics I and II

MATH 7313 Partial Differential and Integral Equations I

MATH 7319 Functional Analysis

**Statistics Concentration**

MATH
6301 Real Analysis

STAT 6331- 6332 Statistical Inference I, II

STAT 6337- 6338 Statistical Methods I, II

STAT 6339 Linear Statistical Models

STAT 6344 Probability Theory I

STAT 7330 Decision Theory

STAT 7331 Multivariate Analysis

STAT 7334 Nonparametric Statistics

STAT 7338 Time Series Modeling and Filtering

STAT 7345 Stochastic Processes

**Electives and Dissertation**

An additional 18-24 credit hours for Applied Math and
18-24 credit hours for Statistics designed for the student´s area of
specialization are taken as electives in a degree plan designed by the student
and the Graduate Advisor. This plan is subject to approval by the Department
Head. After completion of the first 3 or 4 academic semesters of the course
program, the student must pass a Ph.D. Qualifying Examination in order to
continue on to the research and dissertation phase of the Ph.D. program.

Finally, a dissertation is required and must be approved by the graduate
program. Areas of specialization include, for example:

•**Applied
Mathematics**: applied analysis, biomathematics, differential equations,
relativity, scattering theory, systems theory, signal processing.

•**Statistics**:
statistical inference, applied statistics, biostatistics, statistical
computing, probability, stochastic processes, time
series analysis, multivariate analysis, nonparametric and robust statistics,
asymptotic theory.

Other
specializations are possible, including interdisciplinary topics. There must be
available a dissertation research adviser or group of dissertation advisers
willing to supervise and guide the student. A dissertation Supervising
Committee should be formed in accordance with the UT Dallas policy memorandum
(87-III.25-48). The dissertation may be in Applied Mathematics or inStatistics exclusively, or it may include considerable
work in an area of application.

**Research**

Within
the Mathematics program opportunities exist for work and/or research in Applied
Mathematics, Engineering Mathematics, Mathematics, and Statistics. The
opportunity to take course work in several of the other university programs
also allows the student to prepare for interdisciplinary work.

Special
topics within the Applied Mathematics research area include functional
analysis, operator theory, differential and integral equations, optimization,
numerical analysis, system theory and control with application in material and
molecular sciences, inverse problems with applications in geosciences and
medical sciences, relativistic cosmology, differential geometry, applications
of topology to biology, and mathematical and computational biology with
applications in cardiovascular physiology, neurobiology and cell biology.

Special
topics within the Statistics research area include: probability theory, applied
probability, stochastic processes, mathematical statistics, statistical
inference, asymptotic theory, time series analysis, Bayesian analysis, robust
multivariate statistical methods, robust linear models, robust and
nonparametric methods, nonparametic curve estimation,
sequential analysis, statistical computing, remote sensing, change-point
problems, and spatial statistics

For
a complete list of faculty and their areas of research, visit the website www.utdallas.edu/nsm/math/faculty .

Last Updated: September 28, 2011