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 may use the modern computing facilities located in the University Computer Center.
There are terminals and PC's in the mathematics department which are all available to all
students.

Programs of Graduate Work

    Graduate work in mathematics leading to the master's degree is offered with an emphasis in
algebra, analysis, geometry, topology, or probability-statistics. 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.

Special Departmental 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.

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, 517, 531, 537, 538, 539, 543, 544, 561, 565,

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, would not meet the professional
expectations of the field.

Graduate Courses
Mathematics (Math)

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.

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.

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.

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

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

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.