**Department of Mathematical Sciences**

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

**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), John Wiorkowski

Associate Professors: Pankaj Choudhary,
Mieczyslaw Dabkowski

**Assistant Professors**: Yan Cao, Tobias Hagge

**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)

**Senior Lecturers**: Frank R. Allum, Malgorzata Dabkowska, Nermine El
Sissi, Anatoly Eydelzon, Bentley Garrett, Yuly Koshevnik, David L. Lewis,
Charles R. McGhee, , Joanna R. Robinson, William Scott, Paul Stanford

The
Mathematical Sciences Department at The University of Texas at Dallas offers
graduate study in five majors: 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 Mathematical
Sciences 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,
bioinformatics and computational biology.

The Master
of Science degree is available also for those who plan to teach mathematical
sciences 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, financial or industrial careers.

The faculty,
staff and students have access to a large network of Sun workstations and
servers on campus. In addition, the Department has a classroom equipped
with a cluster of 20 high–end Linux PCs that are used for instruction and
special research purposes.

The
University’s general admission requirements are discussed here.

Specific
additional admission requirements for students in Mathematical Sciences 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. However, a student
with at least a Graduate Record Examination (GRE) combined score of 1050 with
at least 550 on the math portion would have a reasonable probability of
admission as a Master’s student, assuming that the student’s other credentials
were in order. Similarly, a student with a GRE score of 1200 (with at least 650
in the quantitative portion) would have a reasonable probability of admission
as a Ph.D. student, assuming that all other credentials were in order. Higher
standards prevail for students seeking Teaching Assistantships.

The
University’s general degree requirements are discussed here.

Students
seeking a Master of Science in Mathematical Sciences 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
Mathematical Sciences Department.

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

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.

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.

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.

Students seeking a Master of Science in Mathematical Sciences with a major in
Statistics must complete the following core courses:

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 from among the following electives:

MATH 6301, MATH 6302, MATH 6313, MATH 6331 or any 6300- or 7300-level
statistics courses. Also, a maximum of 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.

Electives
must be approved by the graduate adviser. Typically, electives are 6000- and
7000-level mathematical sciences 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 (BCBM) is offered jointly
by the Departments of Mathematical Sciences and Molecular and Cell Biology.
This program combines coursework from the disciplines of biology, computer
science, and mathematical Sciences. 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
both Mathematical Sciences (MMS) and Molecular and Cell Biology (MCB)
participate in the Bioinformatics and Computational Biology program, with the
Mathematical Sciences 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:

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

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 mathematical sciences, biology or computer science.

Courses from other disciplines may also be used upon approval.

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.

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

MATH 6301 Real Analysis

MATH 6302 Real and Functional 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

MATH 6303 Theory of Complex Functions I, or MATH 6313 Numerical Analysis, or

MATH 6315 Ordinary Differential Equations I, or MATH 7319 Functional Analysis

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 adviser. 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:

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

• **Statistics**: statistical inference, applied statistics, statistical
computing, probability, stochastic processes, linear models, time series,
statistical classification, 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 Mathematical Sciences exclusively or
it may involve considerable work in an area of application.

Within the
Mathematical Sciences programs 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 research areas 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,
mathematical and computational biology with applications in cardiovascular
physiology, neurobiology and cell biology; probability theory, applied
probability, stochastic processes, mathematical statistics, statistical
inference, asymptotic theory, statistical time series, Bayesian analysis,
robust multivariate statistical methods, robust linear models, robust and
nonparametric methods, sequential analysis, statistical computing, signal
processing, remote sensing, change-point problems, forecasting and applications
in their respective areas such as energy finance, semiconductor manufacturing,
psychology, actuarial sciences, physical and medical sciences.

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

Last Updated: March 1, 2011