PURPOSE:
The primary purpose of this program is to prepare students to teach mathematics at the secondary school and junior college levels.
GENERAL REQUIREMENTS:
All pertinent regulations set forth in the Graduate Studies Bulletin and the Bulletin of the College of Natural Sciences and Mathematics must be observed. The student must consult the departmental Director of Graduate Studies prior to beginning his/her graduate program so that proper records may be established within the department. It is the student's responsibility to be informed about current degree requirements. It is the joint responsibility of the student and the student's advisor to maintain communications and to track the student's progress toward meeting those requirements.
FORMAT:
This is primarily a distance education program; courses are offered online and it is possible to complete the entire program in that format. It is also be possible to take approved on-campus courses as alternatives to online courses.
PREREQUISITES FOR ADMISSION:
To be admitted to the program, a student must have completed a bachelor's degree with a 3.0 GPA over the last 60 hours of all course work and should have a good background in mathematics. A student need not have majored in mathematics to be admitted. However, it is expected that the student has completed a standard 3-semester calculus sequence and has had at least 9 semester hours of mathematics at the junior or senior level, preferably in courses such as abstract algebra, linear algebra, advanced calculus, differential equations, or geometry. The Graduate Record Examination (GRE) is required for admission
PROGRAM DESCRIPTION:
The program requires 33 semester hours of course work with at least 24 semester hours at the 5000 level or above, and including:
• A minimum of 21 semester hours in mathematics with at least 15 semester hours at the 5000 level or above.
• A 3-semester hour Master’s tutorial.
• A maximum of 9 semester hours of approved elective course work.
ONLINE COURSES:
MATH 5330: ABSTRACT ALGEBRA. Prerequisites: three semesters of calculus or consent of instructor. The theory of groups is used to discuss the most important concepts and constructions in abstract algebra.
MATH 5331: LINEAR ALGEBRA WITH APPLICATIONS. Prerequisites: three semesters of calculus or consent of instructor. Systems of linear equations, matrices, vector spaces, linear independence and linear dependence, determinants, eigenvalues; applications of the linear algebra concepts will be illustrated by a variety of projects.
MATH 5332: DIFFERENTIAL EQUATIONS. Prerequisites: MATH 5331 or consent of instructor. Linear and nonlinear systems of ordinary differential equations; existence, uniqueness and stability of solutions; initial value problems; higher dimensional systems; Laplace transforms. Theory and applications illustrated by computer assignments and by projects.
MATH 5333: ANALYSIS. Prerequisites: three semesters of calculus or consent of instructor. A survey of the concepts of limit, continuity, differentiation and integration for functions of one variable and functions of several variables; selected applications are used to motivate and to illustrate the concepts.
MATH 5336: DISCRETE MATHEMATICS. Prerequisites: three semesters of calculus or consent of instructor. Discrete Mathematics and Its Applications, Kenneth H. Rosen, fifth edition. McGraw Hill, Chapters 1, 3, 7, plus the Zermelo Fraenkel Axioms and equivalence of sets.
MATH 5350: INTRODUCTION TO DIFFERENTIAL GEOMETRY. Prerequisites: three semesters of calculus or consent of instructor. Multi-variable calculus, linear algebra, and ordinary differential equations are used to study the geometry of curves and surfaces in 3-space. Topics include: Curves in the plane and in 3-space, curvature, Frenet frame, surfaces in 3-space, the first and second fundamental form, curvature of surfaces, Gauss's theorem egregium, minimal surfaces.
MATH 5382: PROBABILITY. Prerequisites: three semesters of calculus and one semester of linear algebra, or consent of instructor. Sample spaces, events and axioms of probability; basic discrete and continuous distributions and their relationships; Markov chains, Poisson processes and renewal processes; applications.
MATH 5383: NUMBER THEORY. Prerequisite: Three semesters of calculus or consent of instructor. Divisibility and factorization, linear Diophantine equations, congruences and applications, solving linear congruences, primes of special forms, the Chinese remainder theorem, multiplicative orders, the Euler function, primitive roots, quadratic congruences, representation problems and continued fractions.
MATH 5385: STATISTICS. Prerequisites: three semesters of calculus, or consent of instructor. Data collection and types of data, descriptive statistics, probability, estimation, model assessment, regression, analysis of categorical data, analysis of variance. Computing assignments using a prescribed software package (e.g., EXCEL, Minitab) will be given.
MATH 5386: REGRESSION AND LINEAR MODELS. Prerequisites: three semesters
of calculus, one semester of linear algebra, and MATH 5385, or consent of instructor. Simple and multiple linear regression, linear models, inferences from the normal error model, regression diagnostics and robust regression, computing assignments with Matlab, R, Minitab, or SAS.
MATH 5397: FUNDAMENTALS OF OPTIONS PRICING. Prerequisites: three semesters of calculus and an advanced undergraduate course in Probability, or consent of instructor. Option contracts, asset price dynamics, binomial pricing model, Ito’s calculus, Black-Scholes pricing model, hedging and arbitrage.
MATH 5397: SURVEY OF UNDERGRADUATE MATHEMATICS: Prerequisites: three semesters of calculus or consent of instructor. A review of undergraduate courses in linear algebra, differential equations, analysis, probability, and abstract algebra.
Courses under development:
MATH 53xx: DISCRETE MATHEMATICS II
MATH 53xx: GEOMETRY
MATH 53xx: GRAPH THEORY
MATH 53xx: MATHEMATICAL MODELING
MATH 53xx: TECHNOLOGY IN MATHEMATICS CLASSES
COMPLETION OF THE PROGRAM:
The Department of Mathematics typically offers four or five of these courses each semester during the academic year, and at least two courses during the summer sessions. It is possible to complete the program in two years by taking two courses each semester for two academic years and one course in the corresponding summer sessions.
For additional information on the MAM program, please contact Dr. Garret Etgen:
e-mail: etgen@math.uh.edu
Phone: 713-743-3510
Address: Department of Mathematics
University of Houston
Houston, TX 77204-3008
