DEPARTMENT OF MATHEMATICS

Computer Science
Statistics

[Course Descriptions]

Mathematics Program

Graduate degree plans in Mathematics can be designed to prepare students for careers in industry, business, or education, or for further study in mathematics. Both the Master of Arts and Master of Science degrees in Mathematics are available. Students pursuing the Master of Education degree, Plan I or Plan II, may specialize in Mathematics as a teaching field.

Included in each degree program is a core of courses selected to provide the background necessary for further study in an area of specialization. Before nine semester hours of graduate Mathematics have been completed, each student meets with the appropriate graduate advisor to review his/her academic progress and career plans, and to receive counseling concerning the direction of the remaining course work. Based on this meeting, a Graduate Study Plan is filed on the student's behalf with the department and college offices.

Admission Requirements

Students seeking admission to the graduate program in Mathematics must meet the basic requirements of Graduate Studies specified in the ADMISSION section of this catalogue. In addition the following are required:

1. A combined (V + Q + A) GRE score of at least 1500
2. At least two letters of recommendation that address qualifications for graduate study
3. For international students whose native language is not English, a TOEFL score of at least 600

A permanent faculty advisory committee is assigned to each student after admission to candidacy. Committee appointments are made by the graduate advisor in consultation with the department chair. Committee appointments may be changed if a revision of the Graduate Study Plan indicates that such a modification is needed. In programs that include the writing of a thesis, the advisory committee also serves as the thesis committee.

An oral examination is administered by the advisory committee for each Master of Arts and Master of Science degree candidate. [NOTE: The oral examination must be scheduled with the Graduate Advisor at least three weeks in advance. Request forms are available in the department office.] Comprehensive examinations for the Master of Education, Plan I or Plan II are administered by the Department of Curriculum and Instruction, but they include questions prepared and evaluated by members of the Mathematics faculty.

Requirements specified in the degree programs that follow are subject to minor modification by the department. Also, to ensure a balanced program, all electives must be approved by the department chair or an authorized representative of the graduate Mathematics faculty.

Master of Arts, Plans I and II.

These programs are designed for persons who will specialize in Mathematics teaching at the pre-university or two-year college level.

COMMON REQUIREMENTS:

1. Core courses: MTH 586, 587, 588, and 589.
2. An oral examination over core courses.
3. 9 semester hours elective work in approved courses offered for graduate credit in Mathematics.
4. A 3-semester-hour directed reading and research course in Mathematics. This course must include a written report on the research.

ADDITIONAL REQUIREMENTS:

1. Plan I must include a 12 semester hour minor in a discipline that could serve as a second teaching field.
2. Plan II must include 12 additional semester hours of approved graduate coursework, either all in Mathematics or Statistics or 6 hours in each of two fields from the following list: Mathematics, Computer Science, Statistics, and Secondary Education.

Master of Science, Plans I and II.

COMMON REQUIREMENTS:

1. Core courses: MTH 561, 568, 573, and 594.
2. One of the following:
   1. A thesis of 6 semester hours and 6 additional hours of approved courses offered for graduate credit in Mathematics.
   2. 9 semester hours of approved courses offered for graduate credit in Mathematics and a 3-semester-hour directed reading and research course. This course must include an oral presentation of the research results to the department, and a written report on the research.
3. An oral examination over core courses (and the thesis, where applicable).

ADDITIONAL REQUIREMENTS:

1. Plan I must include a 12-semester-hour minor in an approved field.
2. Plan II must include 12 semester hours of additional study in approved courses offered for graduate credit in Mathematics.

Master of Education, Plan I. This program is designed to provide additional study in a teaching field for the professional elementary school teacher and is initiated by the College of Education and Applied Science. Students with elementary school certification with a 24-semester hour undergraduate specialization in Mathematics may elect 12-18 graduate semester hours in Mathematics on this 36-semester hour program. Mathematics 583, 584, and 585 or approved substitutes are required.

Master of Education, Plan II. This program is designed to provide additional study in a teaching field for the professional secondary school teacher and is initiated by the College of Education and Applied Science. Students may elect from 12-24 semester hours in Mathematics on this 36-semester-hour program. Course requirements are adjusted to meet individual student needs. A core of three courses chosen from Mathematics 586, 587, 588, and 589 is required, and Mathematics electives must be approved by the department chair or his/her designated representative. The Mathematics component of the (written) comprehensive examination is based upon the content of the required Mathematics core.

GRADUATE COURSES

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 568 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 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 573 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 577 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 579 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 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 594 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 594. Prerequisites: MTH 244 and some programming experience, or consent of instructor. 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 698, 699 RESEARCH AND THESIS. Credit 3.

*Subject to action by the Board of Regents, The Texas State University System, and the Texas Higher Education Coordinating Board.