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

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

**Associate Professor**: Michael Baron

**Assistant Professors**: Pankaj Choudhary, Mieczyslaw Dabkowski

Adjunct Professors: Jose Carlos Gomez Larranage, Adolfo
Sanchez Valenzuela

**Affiliated Faculty**: Thomas Butts and Titu Andreescu (Science and Mathematics
Education)

**Senior Lecturers**: Frank R. Allum, William Donnell, Bentley Garrett, Yuly
Koshevnik, Grigory Kramer, David L. Lewis, Joanna R. Robinson, William Scott,
Paul Stanford, H. Edward Stone

The Mathematical Sciences Department at The University of Texas at

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 with at least four members
from the Mathematical Sciences faculty. 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.