Web site at: http://www.math.utep.edu/
4.- Mathematics (MATH) Courses (Graduate only)
5195 Graduate Seminar (1-0)
Conferences and discussions of various topics in mathematics and statistics by faculty, graduate students, and outside
speakers. Required of all graduate students during each semester of full-time enrollment. May not be counted more than once
toward the degree requirement.
5311 Applied Mathematics (3-0)
Mathematics 5311 is designed to introduce the student to those areas of mathematics which are useful in engineering and
science. Topics are chosen from Differential Equations, Fourier Series, Calculus of Variations, and Theory of Algorithms. The
course may be repeated once as content changes. Prerequisite: Instructor approval.
5321 Principles of Analysis (3-0)
Investigation of convergence, continuity, differentiability, compactness and connectedness, the Riemann-Stieljes integral, and
sequences of functions. Prerequisite: MATH
3341.
5325 Principles of Algebra (3-0)
Groups, including subgroups, quotient spaces and homomorphisms, Ring Theory, including ideals and quotients, homomorphisms
and polynomial rings. An introduction to modules and fields, including field extensions. Prerequisites: MATH
3325 and department
approval.
5329 Numerical Analysis (3-0)
Introduction to approximation theory, interpolation, numerical differentiation and integration, solutions of linear and non-linear
equations, numerical solution of differential equations, optimization. Emphasis is on error analysis and stability. Several practical
examples and computer programs will be covered. Prerequisites: The analysis equivalent of MATH
3341 and a working knowledge of
a high-level programming language.
5330 Computational Methods of Linear Algebra (3-0)
Numerical methods involved in the computation of solutions of linear systems of equations, eigenvalues, linear least squares
solutions; linear programming; error analysis. Prerequisites: MATH
3323 and a working knowledge of a high-level programming
language.
5331 Real Variables (3-0)
Lebesgue integration, integration with respect to measure, absolute continuity, Fundamental Theorem of Calculus for the
Lebesgue integral. Prerequisite: MATH
5321.
5341 General Topology (3-0)
Topics include: Separation, compactness, connectedness, paracompactness, metric spaces, and metrization of topological
spaces. Prerequisite: MATH
5321.
5343 Numerical Solutions to Partial Differential Equations (3-0)
Introduction to finite difference and finite element methods for the solution of elliptic, parabolic, and hyperbolic partial
differential equations. Prerequisites: (1) MATH
2326 or MATH
3326; MATH
3323; and MATH 4
4329, each with a "C" or better or their
equivalents and (2) knowledge of a high level programming language.
5351 Complex Variables (3-0)
Complex integration and the calculus of residues. Analytical continuation and expansions of the analytic function. Entire,
meromorphic, and periodic functions. Prerequisite: MATH
5321 or its equivalent as approved by the instructor.
5360 Introduction to Research in Mathematics Education (3-0)
An introduction to current research literature in mathematics education focusing on the relations between theories of cognition
and learning and philosophies of mathematics. Topics may include constructivism, Vygotskian theory, genetic epistemology, and
technological cognition. The course may be repeated once for credit as content changes. Prerequisites: MATH
3300 with a grade
of "C" or better and department approval.
5365 Technology in the Mathematics Classroom (3-0)
An introduction to technology used in mathematics education such as graphing calculators, computer algebra systems, course
specific software and the use of the Internet, and an exploration of its appropriate and effective use in the mathematics classroom.
Prerequisite: Department approval.
5370 Seminar (3-0)
Various topics not included in regular courses will be discussed. May be repeated once for credit as the topics vary.
Prerequisite: Instructor approval.
5380 Mathematical Statistics I (3-0)
The probabilistic foundations of mathematical statistics. Probability spaces, random variables, univariate and multivariate
probability distributions, conditional distributions, expectation, generating functions, multivariate transformations, modes of
convergence, and limit theorems. Prerequisite: STAT
3330 or its equivalent as approved by instructor.
5381 Mathematical Statistics II (3-0)
A continuation of Mathematical Statistics I. Parametric statistical models, sufficiency, exponential families, methods of
estimation, comparison of estimators, confidence intervals, hypothesis testing, optimal tests, likelihood ratio tests, large sample
theory. Prerequisite: MATH
5380.
5385 Statistics in Research (3-0)
An introduction to statistical modeling of a univariate response conditional on a test of explanatory variables. Classical
formulation of multiple linear regression and analysis of variance. Some discussion of experimental design from power
considerations. Selected topics from generalized linear models, nonparametric regression, and quasi-likelihood estimation. Emphasis
is on model building, fitting, validation, and subsequent inferences. Analysis of real data using major statistical software packages.
Prerequisite: MATH
3323, STAT
4380, or instructor approval.
5386 Stochastic Processes (3-0)
Random walks, discrete time Markov chains, and Poisson Process. Further topics such as continuous time Markov chains,
branching processes, renewal theory, and estimation in branching processes. Prerequisites: (1) MATH
4341 and (2) STAT
3330 or
MATH
5380.
5388 Multivariate Data Analysis (3-0)
Statistical analysis of a multivariate response. Multivariate multiple linear regression, principal components, factor analysis,
canonical correlation, and discriminate analysis. Applications with the use of statistical packages will be considered. Prerequisite:
MATH 5385 or equivalent.
5390 Nonparametric Statistics (3-0)
Distribution-free statistical methods; nonparametric one and two sample tests and analysis of variance; goodness-of-fit tests;
nonparametric measures of association; and robust procedures. Prerequisite: MATH
5380 or equivalent.
5391 Time Series Analysis (3-0)
Time domain and frequency domain aspects of discrete time stationary processes, correlation functions, power spectra,
filtering, linear systems, and ARMA models for nonstationary series. An introduction to the analysis of multiple time series. Some
use of statistical software will be included. Prerequisite: MATH
5380 or equivalent.
5392 Statistical Computing (3-0)
A study of stochastic simulation and select numerical methods used in statistical computation. Prerequisites: A high-level
programming language, linear algebra, and STAT
4380 or equivalent.
5396 Graduate Research (0-0-3)
A written report on an appropriate subject in mathematics or statistics is required. May not be counted towards the 24 hours
of course work in the thesis option, but may be substituted for three hours of thesis credit. May not be repeated for credit.
Prerequisite: Instructor approval.
5398 Thesis (0-0-3)
Initial work on the thesis.
5399 Thesis (0-0-3)
Continuous enrollment required while work on thesis continues. Prerequisite: MATH
5398 or department approval.
![[top of page]](../img/up.gif)
