DEPARTMENT OF MATHEMATICS AND STATISTICS
MATHEMATICS PROGRAM
MATHEMATICS COURSE DESCRIPTIONS
MTH 560 Special Topics. Topics and courses are selected to suit individual needs of students. Methods of independent study and research are stressed. The course may be repeated for additional credit. Prerequisite: Consent of program coordinator. Credit 3.
MTH 561 Theory and Applications of Probability. Topics include probability axioms and properties, conditional probability, random variables, probability distributions, moment generating functions, laws of large numbers, and the Central Limit Theorem. Also listed as STA 561. Prerequisite: STA 472 (or equivalent) or consent of the instructor. Credit 3.
MTH 570 Fourier Analysis and Applications. This course is a study of applied harmonic analysis. Topics include Fourier analysis, wavelet analysis, and applications of these topics. Prerequisite: MTH 466 or MTH 588 or the consent of the instructor. Credit 3.
MTH 580 Research Project in Mathematics Education. In this course, the student will develop a project based on one of the core areas (Algebra, Geometry, Analysis, or Probability and Statistics) appropriate for use in teaching. This course is a capstone for candidates pursuing the degree of MA of Mathematics. Prerequisites: MTH 586, MTH 587, MTH 588, MTH 589. Credit 3.
MTH 581 Algebra: Structure and Applications. This course includes the study of algebraic structures (such as groups, rings, integral domains, and fields) and their properties, and activities and concepts related to the algebra of real numbers that are applicable to middle school teachers. The course is designed for in-service middle school mathematics teachers. Credit 3.
MTH 583 Seminar in Geometry and Measurement for Elementary Teachers. This course will include a study of congruency, similarity, transformations, coordinate geometry, and measurement. It is specifically designed for elementary school teachers with a mathematics specialization who wish to obtain the master’s degree in elementary education with a minor in mathematics. Prerequisites: Elementary school mathematics certification and MTH 383 or equivalent. Credit 3.
MTH 584 Seminar in Mathematical Systems for Elementary Teachers. This course will include a study of the development of the natural number system, the development of the integers, the development of the rational number system, and the development of the real number system. It is specifically designed for elementary school teachers with a mathematics specialization who wish to obtain the master’s degree in elementary education with a minor in mathematics. Prerequisites: Elementary school mathematics certification and MTH 384 or equivalent. Credit 3.
MTH 585 Mathematics seminar for Junior High School Teachers. This course includes topics from arithmetic, algebra, geometry, number theory and other mathematical areas at a level appropriate for junior high school teachers. Prerequisite: Consent of instructor. Credit 3.
MTH 586 Seminar in Algebra For Teachers. This course consists of a survey of several abstract algebraic systems including groups, rings, integral domains, and fields. Prerequisite: Certification in secondary school mathematics and MTH 377 or equivalent. Credit 3.
MTH 587 Seminar in Geometry For Teachers. This course is a study of topics in geometry including constructions and transformations. Prerequisite: Certification in secondary school mathematics and MTH 363 or equivalent. Credit 3.
MTH 588 Seminar in Analysis For Teachers. This course includes topics from set theory, number systems, functions, real sequences, limits, continuity, differentiation and integration. Prerequisite: Certification in secondary school mathematics and MTH 143 or equivalent. Credit 3.
MTH 589 Seminar in Probability and Statistics For Teachers. This course includes topics from probability theory, distribution functions, descriptive statistics, and inferential statistics. Prerequisite: Certification in secondary school mathematics and MTH 379 or equivalent. Credit 3.
MTH 595 Digital Image Processing. The emphasis of this course is on the analysis of digital image processing algorithms used for solving problems in areas such as image enhancement and restoration, image registration, pattern recognition, and image segmentation. Prerequisite: MTH 377 and programming experience. Credit: 3 hours
MTH 596 Optimization. The emphasis of this course is on modern algorithms and computational methods needed for solving optimization problems. Applications to current industrial problems will be given, and the theory of operations research will be developed. Prerequisite: MTH 377 and MTH 244, or consent of instructor. Credit: 3 hours
MTH 597 Discrete Mathematics. Discrete structures are emphasized in this course, which includes a study of combinatorics, graph theory, and number theory. The applications of these structures in computers and communications will be highlighted. Prerequisites: MTH 477 or MTH 586 or equivalent. Credit: 3 hours
MTH 632 Introduction To Topology. This course is a rigorous introduction to point set topology. Topics include continuity, connectedness, compactness, metrization theorems, separation theorems, and the Tychonoff theorem. Prerequisites: MTH 364 or equivalent. Credit: 3 hours
*MTH 633 Foundations of Analysis I. This course is the first half of the analysis sequence. The analysis sequence includes topics from advanced multivariate calculus, normed linear spaces, measure theory, including Lebesgue and Borel measures, measurable functions, Lebesgue integration, and spaces of integrable functions. Prerequisites: MTH 461 and MTH 466, equivalent, or consent of instructor. Credit 3.
*MTH 634 Foundations of Analysis II. This course is the second half of the analysis sequence. The analysis sequence includes topics from advanced multivariate calculus, normed linear spaces, measure theory, including Lebesgue and Borel measures, measurable functions, Lebesgue integration, and spaces of integrable functions. Prerequisites: MTH 633 or consent of instructor. Credit 3.
*MTH 635 Algebra I. This course is in the first half of the algebra sequence. The algebra sequence will include Group and Ring theory. Special topics include groups, group actions, the Sylow Theorems, rings, modules, fields, field extensions, and an introduction to Galois Theory. Prerequisites: MTH 477 or equivalent. Credit 3.
*MTH 636 Algebra II. This course is the second half of the algebra sequence. The algebra sequence will include Group and Ring theory. Specific topics include groups, group actions, the Sylow Theorems, rings, modules, fields, field extensions, and an introduction to Galois Theory. Prerequisites: MTH 631 (Algebra I) or equivalent. Credit 3.
MTH 668 Numerical Linear Algebra. This course is a study of vector spaces and matrices. Topics include solving linear systems, least square methods, eigenvalue and eigenvector theory, and applications of these topics. Prerequisite: MTH 377 or consent of instructor. Credit 3.
MTH 673 Applied Analysis. This course studies properties of normed spaces and functions defined on normed spaces. Special emphasis is placed on Euclidean n-space. Topics include limits, continuity, differentiation, and integration. Prerequisite: MTH 466 or MTH 588 or consent of the instructor. Credit 3.
MTH 677 Abstract Algebra. Algebraic structure is emphasized in this course, which includes a study of groups, rings, fields, and their applications in coding theory and cryptography. Prerequisite: MTH 477 or MTH 586 or consent of instructor. Credit 3.
MTH 679 Functions of a Complex Variable. Included in this course are studies of the complex number system, analytic functions, integration theory and the calculus of residues. Additional topics of special interest to the class may be included. Prerequisite: MTH 244 or consent of instructor. Credit 3.
MTH 694 Scientific Computation. Topics include solutions of equations, approximation and interpolation, numerical differentiation and integration, the fast Fourier transform, and numerical simulation. Also listed as CS 694. Prerequisites: MTH 244 and some programming experience, or consent of instructor. Credit 3.
MTH 698, 699 Research and Thesis. Credit 3.
* Subject to action by the Board of Regents, The Texas State University System and/or the Texas Higher Education Coordinating Board