Graduate Mathematics Program
Rick Kreminski, Head
Binnion Hall 305
(903)886-5157
The
graduate program aims to give thorough training to the student in one or more
areas of mathematics, to stimulate independent thinking, and to provide an
apprenticeship in development of creative research. Such training prepares the
student for employment in a high school, a junior college, a four-year college,
continued study of mathematics at the doctoral level, or in one of the many
non-academic areas in which mathematicians work. Students have access to powerful software packages. Many
courses include computer applications.
The course offerings are
generally in Commerce, Texas. In
addition, some classes are transmitted via distance-education mechanisms to
remote sites. We also provide math
courses for those seeking a Master’s degree in a degree program offered by the
College of Education and Human Services.
Many of these math courses are offered at our Mesquite campus.
Programs
of Graduate Work
Graduate
work in mathematics leading to the master’s degree is offered with an emphasis
in algebra, analysis, or probability-statistics, in addition to many special
topics offerings. Emphases for secondary and middle school teachers are
specially planned to meet their individual and particular objectives.
A student
may select courses leading to a minor in applied mathematics.
Admission
Requirements
Students
entering the M.S. or M.A. program for a career in higher education,
professional work, or further advanced study in mathematics must meet the background
requirements which include the calculus sequence, discrete mathematics, and at
least two upper level undergraduate mathematics courses from the areas of
algebra, analysis, topology, statistics, and probability.
Secondary
mathematics teachers and other students entering the master’s degree program
with goals other than as a professional mathematician or advanced study in
mathematics should have an undergraduate minor in mathematics, that is,
Calculus I, II, and III, and three advanced math courses.
Acceptance
will be based on admission to the Graduate School, scores on the Graduate
Record Examination (GRE), undergraduate grade point average, and mathematics
background (as outlined above).
Master of
Science or Master of Arts Degree in Mathematics
Option I
(10 courses, Thesis)
The
courses to be selected from the following as prescribed:
1. At
least four courses including one sequence from: 501-502; 511-512; 538-539;
543-544
2. At
most four courses from: 517, 531, 537, 561, 564, 565, 580, 597
3. 518—Thesis,
(6 hrs.)
Option II
(12 courses, Non-Thesis)
The
courses to be selected from the following as prescribed:
1. A core
of at least eight courses in mathematics, including 595, with a minimum of four
courses, including at least one sequence from: 501-502; 511-512; 538-539;
543-544
2. The
remaining four graduate electives may be selected in math from those courses
not used in the core, or from courses outside of mathematics with the approval
of the mathematics department.
3. Math
529 may not be used.
Minor in
Applied Mathematics
Satisfactory
completion of four to six of the following courses will meet requirements for a
minor in mathematics: Math 501, 502, 511, 512, 515, 517, 531, 537, 538, 539,
543, 544, 561, 597; Phys 517.
Note: The
Department reserves the right to suspend from the program any student, who in
the judgment of a duly constituted departmental committee, does not meet the
professional expectations of the field.
Graduate
Courses
Mathematics
(Math)
500. Discrete
Mathematics. Four semester hours.
Study of
formal logic; sets; functions and relations; principle of mathematical
induction; recurrence relations; and introductions to elementary number theory;
counting (basic combinatorics); asymptotic complexity of algorithms; graph
theory; and NPcompleteness. This course is useful to those taking graduate
classes in computer science. It may be taken for graduate credit towards a
masters in mathematics only by consent of the department. Prerequisite: Consent
of the instructor.
501-502. Mathematical
Statistics. Six semester hours.
Probability,
distributions, moments, point estimation, maximum likelihood estimators,
interval estimators, test of hypothesis. Prerequisite: Math 225.
511-512.
Advanced Calculus. Six semester hours.
Properties
of real numbers, continuity, differentiation, integration, sequences and series
of functions, differentiation and integration of functions of several
variables. Prerequisite: Math 436 or 440.
515. Dynamical Systems. Three semester hours.
Iteration
of functions; graphical analysis; the linear, quadratic and logistic families;
fixed points; symbolic dynamics; topological conjugacy; complex iteration;
Julia and Mandelbrot sets. Computer algebra systems will be used. Recommended
background: Math 192 and Math 331.
517. Calculus
of Finite Differences. Three semester hours.
Finite
differences, integration, summation of series, Bernoulli and Euler Polynomials,
interpolation, numerical integration, Beta and Gamma functions, difference
equations. Prerequisite: Math 225.
518. Thesis. Six
semester hours.
This
course is required of all graduate students who have an Option I degree plan.
Graded on a (S) satisfactory or (U) unsatisfactory basis. Prerequisite: Consent
of instructor.
529. Workshop
in School Mathematics. Three semester hours.
This
course may be taken twice for credit. A variety of topics, taken from various
areas of mathematics, of particular interest to elementary and secondary school
teachers will be covered. Consult with instructor for topics.
531. Introduction
to Theory of Matrices. Three semester hours.
Vector
spaces, linear equations, matrices, linear transformations, equivalence
relations, metric concepts. Prerequisite: Math 334 or 335.
536. Cryptography. Three
semester hours. (Same as CSci 568)
The
course begins with some classical cryptanalysis (Vigenere ciphers, etc). The
remainder of the course deals primarily with number-theoretic and/or algebraic
public and private key cryptosystems and authentication, including RSA, DES,
AES and other block ciphers. Some cryptographic protocols are described as
well. Prerequisites: Graduate standing in mathematics or consent of the
instructor.
537. Theory
of Numbers. Three semester hours.
Factorization
and divisibility, diophantive equations, congruences, quadratic reciprocity,
arithmetic functions, asymptotic density, Riemann’s zeta function, prime number
theory, Fermat’s Last Theorem. Prerequisite: Consent of instructor.
538-539. Functions
of a Complex Variable. Six semester hours.
Geometry
of complex numbers, mapping, analytic functions, Cauchy-Riemann conditions,
Complex integration. Taylor and Laurent series, residues. Prerequisite: Math
511.
543-544. Abstract
Algebra. Three semester hours.
Groups,
isomorphism theorems, permutation groups, Sylow Theorems, rings, ideals,
fields, Galois Theory. Prerequisite: Math 334.
571. Higher Order Approximations for Teachers.
Three semester hours.
This
course, specifically for teachers, explores algebra-based techniques for
powerful, highly accurate numerical approximations. Graphing calculators and
some computer software will be used. Approximations for areas and volumes of
regions, solutions to equations and systems of equations, sums of infinite
series, values of logarithmic and trigonometric functions, and other topics are
covered.
572. Modern Applications of Mathematics for
Teachers. Three semester hours.
This
course, specifically designed for teachers, covers a range of applications of
mathematics, specific topics may vary but have included classical (private key)
encryption, data compression ideas, coding theory ideas (Hamming 7,4 code),
private and public key cryptography, data compression including wavelets,
difference equations (population models, disease models) and stochastic
difference equations (stock), GPS systems, computed tomography (E.g. CAT
scans), polynomial interpolation/Bezier curves, coding theory, and topics from
student presentations.
573. Calculus of Real and Complex Functions for
Teachers. Three semester hours.
This
course is designed for teachers, and explores similarities and differences
between functions whose domain and range consist of sets of real numbers, and
sets of complex numbers. Complex numbers are reviewed, with nontraditional
applications to plane geometry. Alternate approaches to the meaning of the
derivative are given so as to provide links between the notions of f’ (X) and
f’ (z) (x real, z complex), and ways of understanding derivatives of inverse
functions and composite functions. The geometry of functions of a complex
number are explored. Cauchy-Riemann equations are derived and utilized. Power
series in both the real and complex context are compared.
595. Research
Literature and Techniques. Three semester hours.
This
course provides a review of the research literature pertinent to the field of
mathematics. The student is required to demonstrate competence in research
techniques through a literature investigation and formal reporting of a
problem. Graded on a (S) satisfactory or (U) unsatisfactory basis.
Prerequisite: Consent of instructor.
597. Special
Topics. One to four semester hours.
Organized
class. May be repeated when topics vary.
Courses in
Applied Mathematics with Computer Applicability – these courses earn graduate
mathematics credit
561. Statistical
Computing and Design of Experiments. Three semester hours.
A computer
oriented statistical methods course which involves concepts and techniques
appropriate to design experimental research and the application of the
following methods and techniques on the digital computer: methods of estimating
parameters and testing hypotheses about them, analysis of variance, multiple
regression methods, orthogonal comparisons, experimental designs with
applications. Prerequisite: Math 401 or 501.
Curriculum
for Secondary Teachers (MTE) – these courses generally do not earn graduate
mathematics credit
520. Foundations
of Complex Analysis. Three semester hours.
The
properties of complex numbers are studied, and some emphasis is given to
analytic functions and infinite series. Teachers of analysis or trigonometry
will benefit from this course. Recommended background: Math 225.
530. Foundations
of Mathematics. Three semester hours.
The
fundamental properties of sets, logic, relations, and functions will be
studied. This course will be helpful to secondary teachers by giving them a
better understanding of the terms and ideas used in modern mathematics.
550. Foundations
of Abstract Algebra. Three semester hours.
The
fundamental properties of algebraic structures such as properties of the real
numbers, mapping, groups, rings, and fields. The emphasis will be on how these
concepts can be related to the teaching of high school algebra. Recommended
background: Math 331 or 530.
560. Foundations
of Euclidean Geometry. Three semester hours.
Various
geometries, including Euclidean geometry, will be studied. Background for a
better understanding of Euclidean geometry will be emphasized. Recommended
background: High school geometry or Math 301.
580. Topics
from the History of Mathematics. Three semester hours.
A
chronological presentation of historical elementary mathematics. The course presents
historically important problems and procedures. Prerequisite: Graduate standing
with equivalent of undergraduate minor in mathematics. This course does qualify for Master’s
programs in mathematics.
597.
Special Topics. One to four semester hours.
Organized
class. May be repeated when topics vary.
Graduate Mathematics Faculty
Stuart Anderson, Ph.D.
Professor and Head of Mathematics
B.A., M.S., University of North Texas; Ph.D., University of Oklahoma. Associate Member.
Farhad T. Aslan, Ph.D.
Professor of Mathematics
B.S., Midwestern University; M.S., University of North Texas; Ph.D., Texas Christian University. Senior Member.
Hasan Coskun,
Ph.D.
Assistant
Professor of Mathematics
B.S., Middle East
Technical University; M.S., Stevens Institute of Technology; Ph.D., Texas
A&M University, Associate Member
Richard Kreminski, Ph.D.
Professor and Head of Mathematics
S.B., Massachusetts Institute of Technology; M.A., Ph.D., University of Maryland. Associate Member.
Nicholay Sirakov, Ph.D.
Assistant Professor of Math and Computer Science
B.S., M.S., Sofia University; Ph.D., Bulgarian Academy of Sciences, Associate Member