**Course Descriptions**

**Mathematics
and Applied Mathematics Courses**

**MATH 5301 Elementary Analysis I** (3 semester hours) Real numbers,
differentiation, integration, metric spaces, basic point set topology, power
series, analytic functions, Cauchy’s theorem. Prerequisite: Multivariable
calculus (MATH 2421) and theoretical concept of calculus (MATH 3310) or
equivalent. (3-0) Y

**MATH 5302 Elementary Analysis II** (3 semester hours) Continuation of MATH
5301. Prerequisite: MATH 5301. (3-0) Y

**MATH 5304 Applied Mathematical Analysis for Non-Majors** (3 semester
hours) Techniques of mathematical analysis applicable to the social, behavioral
and management sciences. Differential and integral
calculus of one and many variables. No credit allowed to mathematical
sciences majors. Prerequisite: College Algebra (3-1) S

**MATH 5305 Higher Geometry for Teachers** (3 semester hours) Topics in
modern Euclidean geometry including distinguished points of a triangle, circles
including the nine-point circle, cross ratio, transformations; introduction to
projective geometry. No credit allowed to mathematical sciences majors except
those in M.A.T. program. Prerequisite: Junior level mathematics course. (3-0) T

**MATH 5306 Non-Euclidean Geometry for Teachers** (3 semester hours) The relations among elliptic, Euclidean and hyperbolic
geometries, Euclidean models of elliptic and hyperbolic geometries. No credit
allowed to mathematical sciences majors except those in M.A.T. program.
Prerequisite: Junior-level mathematics course. (3-0) T

**MATH 5313 Modern Algebra for Teachers** (3 semester hours) Study of modern
algebra involving groups, rings, fields and Galois theory.
No credit allowed to mathematical sciences majors except those in M.A.T.
program. Prerequisite: Junior-level mathematics course. (3-0) R

**MATH 5390 Topics in Mathematics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum). (3-0) R

**MATH 6301 Real Analysis** (3 semester hours) Measure theory and
integration. Hilbert and Banach spaces.
Prerequisites: Undergraduate analysis course (e.g., MATH 4301-2 or MATH 5301-2)
undergraduate course in linear algebra (MATH 2418) or equivalent. (3-0) Y

**MATH 6302 Real and Functional Analysis** (3 semester hours) Continuation
of MATH 6301, Hilbert and Banach space techniques. Prerequisite: MATH 6301.
(3-0) Y

**MATH 6303 Theory of Complex Functions I** (3 semester hours) Complex
integration, Cauchy’s theorem, calculus of residues, power series, entire
functions, Riemann mapping theorems. Riemann surfaces,
conformal mapping with applications. Prerequisite: Undergraduate
analysis (e.g., MATH 4301-2). (3-0) Y

**MATH 6304 Theory of Complex Functions II** (3 semester hours) Continuation
of MATH 6303. Prerequisite: MATH 6303. (3-0) T

**MATH 6305 Mathematics of Signal Processing** (3 semester hours) The course is devoted to a mathematical foundation of some
of the key topics in signal processing: discrete and continuous signal
transforms, analysis and design of filters [e.g. lattice filters], least square
methods and algorithms. Prerequisites: Undergraduate analysis (MATH 4301-2 or
MATH 5301-2); undergraduate course in linear algebra (MATH 2418); undergraduate
course in complex variables (MATH 3379) or equivalent. (3-0)
T

**MATH 6306 Topology and Geometry** (3 semester hours) Topics in topology,
differential geometry and their applications to areas such as biological
sciences and engineering. Prerequisite: Undergraduate analysis (MATH
4301-2 or MATH 5301-2). (3-0) T

**MATH 6307 Wavelets and Their Applications** (3 semester hours) An
introduction to windowed Fourier and continuous wavelet transforms, generalized
frames, discrete wavelet frames, multiresolution analysis, Daubechies’
orthogonal wavelet bases, and their applications in partial differential
equations and signal processing. Prerequisite: Undergraduate linear algebra
(MATH 2418) and differential equations (MATH 2420) or equivalent (3-0). T

**MATH 6308 Inverse Problems and Applications** (3 semester hours) Exact and
approximate methods of nondestructive inference, such as tomography and inverse
scattering theory in one and several dimensions, with applications in physical
and biomedical sciences and engineering. Prerequisite: Undergraduate linear
algebra (MATH 2418) and differential equations (MATH 2420) or equivalent. (3-0) T

**MATH 6311 Abstract Algebra I** (3 semester hours) Basic properties of
groups, rings, fields, and modules. Topics selected from group
representations, Galois theory, local rings, algebraic
number theory, classical ideal theory, basic homological algebra, and
elementary algebraic geometry. Prerequisite: Undergraduate algebra course (MATH
3311) or equivalent. (3-0) T

**MATH 6313 Numerical Analysis** (3 semester hours) A study of numerical
methods including the numerical solution of non-linear equations, linear
systems of equations, interpolation, iterative methods and approximation by
polynomials. Prerequisites: Knowledge of a high level programming
language, Linear algebra (MATH 2418) and multivariable calculus (MATH 2451).
(3-0) T

**MATH 6315 Ordinary Differential Equations** (3 semester hours) The study of ordinary differential equations with emphasis
on existence, uniqueness, linear systems, boundary value problems, and
stability. Prerequisites: Undergraduate course in linear algebra (MATH 2418) or
equivalent; undergraduate analysis (MATH 4301/4302 or Math 5301-53022);
undergraduate course in ordinary differential equations (MATH 2420). (3-0) Y

**MATH 6316 Differential Equations** (3 semester hours) Continuation of MATH
6315 and an introduction to partial differential equations.
Prerequisite: MATH 6315. (3-0) T

**MATH 6318 Numerical Analysis of Differential Equations** (3 semester
hours) Practical and theoretical aspects of numerical methods for both ordinary
and partial differential equations are discussed. Topics selected from: initial
value problems for ordinary differential equations, two-point boundary value
problems, projection methods, finite difference, finite
element and boundary element approximations for partial differential equations.
Prerequisites: MATH 6313 or equivalent. (3-0) T

**MATH 6319 Principles and Techniques in Applied Mathematics I** (3 semester
hours) Mathematical methods usually used in applied sciences and engineering.
Topics chosen from basic linear space theory; Hilbert spaces; fixed point
theorems and applications to differential and integral equations; spectral
theorem; distributions; Sobolev spaces; the Fourier transforms; complex
function theory, calculus of residues; exact, approximate and asymptotic
solutions to Laplace, heat and wave equations, Eikonal and WKB methods, and
special functions. Prerequisite: Undergraduate linear algebra (MATH 2418), and
differential equations (MATH 2420) or equivalent. (3-0) T

**MATH 6320 Principles and Techniques in Applied Mathematics II** (3
semester hours) Continuation of Math 6319. Prerequisite: MATH 6319. (3-0) T

**MATH 6321 Optimization** (3 semester hours) Introduction to theoretical
and practical concepts of optimization in finite and infinite dimensional
setting, least-squares estimation, optimization of functionals, local and
global theory of constrained optimization, iterative methods. Prerequisites:
Undergraduate ordinary differential equations (MATH 2420) and linear algebra
(MATH 2418). (3-0) T

**MATH 6331 Linear Systems and Signals** (3 semester hours) Basic principles
of systems and control theory: state space representations, stability,
observableness, controllability, realization theory, transfer functions,
feedback. Prerequisites: Undergraduate course in linear algebra (MATH 2418) and
undergraduate analysis course (MATH 4301/4302) or MATH 5301-5302. (3-0) T

**MATH 6332 Advanced Control** (3 semester hours) Theoretical and practical
aspects of modern control methodologies in state space and frequency domain, in
particular LQG and H-infinity control: coprime factorizations, internal
stability, Kalman filter, optimal regulator, robust control, sensitivity
minimization, loop shaping, model reduction. Prerequisite: MATH 6331. (3-0) T

**MATH 6336 Nonlinear Control Systems** (3 semester hours) Differential
geometric tools, input-output maps, feedback linearization, nonlinear observers,
input-output linearization, output tracking, and regulation.
Prerequisites: MATH 6315 and MATH 6331. (3-0) T

**MATH 6339 Control of Distributed Parameter Systems** (3 semester hours)
Theoretical and technical issues for control of distributed parameter systems
in the context of linear infinite dimensional dynamical systems: Evolution
equations and control on Euclidean space, elements of functional analysis,
semigroups of linear operators, abstract evolution equations, control of linear
infinite dimensional dynamical systems, approximation techniques.
Prerequisites: Undergraduate course in partial differential equations (MATH
4362) and analysis (MATH 4301). (3-0) T

**MATH 6341 Bioinformatics** (3 semester hours)
Fundamental mathematical and algorithmic theory behind current bioinformatics
techniques are covered and implemented. They include hidden Markov
models, dynamic programming, genetic algorithms, simulated annealing, neural
networks, cluster analysis, and information theory. Prerequisites: Knowledge of
Unix and a high level programming language. (3-0) T

**MATH 6343 Computational Biology** (3 semester hours) Mathematical and
computational methods and techniques to analyze and understand problems in
molecular biology are covered. Topics include sequence homology and
alignment, genetic mapping, protein folding, and DNA computing. Prerequisite:
MATH 2418 or equivalent. (3-0) T

**MATH 6345 Mathematical Methods in Medicine and Biology** (3 semester
hours) Introduction to the use of mathematical techniques in solving biologically
important problems. Some examples of topics that might be covered are
biochemical reactions, ion channels, cellular signaling mechanisms, kidney
function, nerve impulse propagation. Prerequisites:
MATH 2417, MATH 2419, MATH 2420 recommended. (3-0) T

**MATH 6364 Stochastic Calculus in Finance** (3 semester hours) Brownian
Motion, Ito Calculus, Feynman-Kac formula and an outline of Stochastic Control,
Black Scholes Analysis, Transaction Costs, Optimal Portfolio Investment.
Prerequisites: STAT 4351 or equivalent, and MATH 2451 or equivalent. (3-0) T

**MATH 6390 Topics in Mathematics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum). (3-0) R

**MATH 6V81 Special Topics in Mathematics** (1-9 semester hours) Topics vary
from semester to semester. May be repeated for credit as
topics vary. ([1-9]-0) S

**MATH 7313 Partial Differential and Integral Equations I** (3 semester
hours) Topics include theory of partial differential and integral equations. Classical and modern solution techniques to linear and nonlinear
partial differential equations and boundary value problems. Introduction to the theory of Sobolev spaces. Prerequisite:
MATH 6316 recommended. (3-0) T

**MATH 7314 Partial Differential and Integral Equations II** (3 semester
hours) Continuation of MATH 7313. General theory of partial
differential and integral equations, with emphasis on existence, uniqueness and
qualitative properties of solutions. Prerequisite: MATH 7313. (3-0) T

**MATH 7316 Wave Propagation with Applications** (3 semester hours) Study of
the wave equation in one, two and three dimensions, the Helmholtz equation,
associated Green’s functions, asymptotic techniques for solving the propagation
problems with applications in physical and biomedical sciences and engineering.
Prerequisites: MATH 6303, MATH 6318. (3-0) T

**MATH 7319 Functional Analysis** (3 semester hours) Elements of operator
theory, spectral theory, topics in Banach and operator algebras.
Prerequisites: MATH 6301-2. MATH 6303 recommended. (3-0) T

**MATH 7390 Topics in Mathematics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum). (3-0) R

**MATH 8V02 Individual Instruction in Mathematics** (1-6 semester hours)
Topics may vary. May be repeated for credit. ([1-6]-0)
S

**MATH 8V04 Topics in Mathematics** (1-6 semester hours) May be repeated for
credit. ([1-6]-0) R

**MATH 8V07 Research** (1-9 semester hours) Open to students with advanced
standing subject to approval of the Graduate Adviser. May be
repeated for credit. ([1-9]-0) S

**MATH 8V98 Thesis** (3-9 semester hours) May be repeated for credit.
([3-9]-0) S

**MATH 8V99 Dissertation** (1-9 semester hours) May be repeated for credit.
([1-9]-0) S

**Statistics
Courses**

**STAT 5191 Statistical Computing Packages** (1 semester
hour) Introduction to use of major statistical packages such as SAS, BMD, and
Minitab. Based primarily on self-study materials.
No credit allowed to mathematical sciences majors. Prerequisite: One semester
of statistics. (1-0) S

**STAT 5351 Probability and Statistics I** (3 semester hours) A mathematical
treatment of probability theory. Random variables, distributions,
conditioning, expectations, special distributions and the central limit
theorem. The theory is illustrated by numerous examples. This is a basic course
in probability and uses calculus extensively. Prerequisite: Multivariable
calculus (MATH 2451). (3-0) T

**STAT 5352 Probability and Statistics II** (3 semester hours) Theory and
methods of statistical inference. Sampling,
estimation, confidence intervals, hypothesis testing, analysis of variance, and
regression with applications. Prerequisite: STAT 5351. (3-0) T

**STAT 5390 Topics in Statistics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum).(3-0) R

**STAT 6326 Sampling Theory** (3 semester hours) Introduction to survey
sampling theory and methods. Topics include simple random, stratified,
systematic, cluster, unequal probability, multistage,
spatial sampling designs. Estimation of means, proportions,
variances, ratios, and other parameters for a finite population, optimal
allocation, detectability, multiplicity. Prerequisite: STAT 5351. (3-0)
T

**STAT 6329 Applied Probability and Stochastic Processes** (3 semester
hours) Basic random processes used in stochastic modeling, including Poisson,
Gaussian, and Markov processes with an introduction to renewal processes and queuing
theory. Measure theory not required. Prerequisite: STAT 5351. (3-0) T

**STAT 6331 Statistical Inference I** (3 semester hours) Introduction to
fundamental concepts and methods of statistical modeling and decision making.
Basic distribution theory. Decision
theory. Exponential families of models. Sufficiency. Estimation and hypothesis
testing. Likelihood methods and optimality, Large sample approximations . Prerequisites: STAT 5352 or equivalent and
MATH 5302 or equivalent. (3-0) Y

**STAT 6332 Statistical Inference II** (3 semester hours) Elementary and advanced
asymptotic methods, treating sample quantiles,
U-statistics, differentiable statistical functions and influence curves, the
MLE, L-statistics, M-statistics, and the bootstrap. Advanced aspects of statistical inference,
likelihood-based inference, robust statistics. General forms of Neyman-Pearson lemma. Metrics
on spaces of probability distributions. Prerequisites: STAT 6331 Pre-/Co-Requisite:
STAT 6344. (3-0)T

**STAT 6337 Advanced Statistical Methods I** (3 semester hours) Statistical
methods most often used in the analysis of data. Study of
statistical models, including multiple regression, nonlinear regression,
stepwise regression, regression diagnostics, balanced and unbalanced analysis
of variance, analysis of covariance, and log-linear analysis of multiway
contingency tables. Prerequisites: MATH 2418 and STAT 5352 or STAT 6331.
(3-0) T

**STAT 6338 Advanced Statistical Methods II** (3 semester hours) This course continues STAT 6337. Topics include oneway and multiway analysis of variance, fixed, random,
and mixed effects models, nested designs, repeated measures designs, fractional
designs, Latin squares, diagnostics, and implementation of statistical methods
in SAS.. Prerequisite: STAT
6337. (3-0) T

**STAT 6339 Linear Statistical Models** (3 semester hours) Vectors of random
variables, multivariate normal distribution, quadratic forms. Theoretical treatment of general linear models, including the
Gauss-Markov theorem, estimation, hypotheses testing, and polynomial
regression. Introduction to the analysis of variance
and analysis of covariance. Prerequisites: STAT 6331 and MATH 2418 or
equivalent. (3-0) T

**STAT 6341 Numerical Linear Algebra and Statistical Computing** (3 semester
hours) A study of computational methods used in
statistics. Topics to be covered include the simulation of stochastic
processes, numerical linear algebra, QR decomposition and least squares
regression, SV decomposition and multivariate data, statistical programming
languages, and graphical methods. Prerequisite: STAT 5352 or STAT 6337. (3-0) T

**STAT 6343 Experimental Design** (3 semester hours) This
course focuses on the planning, development, implementation and analysis of
data collected under controlled experimental conditions. Repeated measures
designs, Graeco-Latin square designs, randomized block designs, balanced
incomplete block designs, partially balanced incomplete block designs,
fractional replication and confounding. The course requires substantial use of
computer facilities. Prerequisite: STAT 6338 or equivalent knowledge of fixed
and random effects crossed ANOVA designs. (3-0) T

**STAT 6344 Probability Theory I** (3 semester hours) A measure theoretic
coverage of probability theory. Measure, integration, Fubini’s theorem, random
variables, distribution functions, characteristic functions, independence, laws
of large numbers, central limit theorem, three-series theorem, Glivenko-Cantelli
theorem, conditional probability and expectation, introduction to martingales.
Prerequisite: MATH 6301. (3-0) T

**STAT 6347 Applied Time Series Analysis** (3 semester hours) Methods and
theory for the analysis of data collected over time. The course covers
techniques commonly used in both the frequency domain (harmonic analysis) and
the time domain (autoregressive, moving average models). Prerequisite: STAT
6337 or equivalent. (3-0) T

**STAT 6348 Applied Multivariate Analysis** (3 semester hours) The most frequently used techniques of multivariate
analysis. Topics include T/T2, MANOVA, principal components, discriminant
analysis and factor analysis. Prerequisite: STAT 5352 or STAT 6331. (3-0) T

**STAT 6365 Statistical Quality and Process Control** (3 semester hours)
Statistical methodology of monitoring, testing, and improving the quality of
goods and services is developed at the intermediate level. Topics include
control charts for variables and attributes, assessment of process stability
and capability, construction and interpretation of CUSUM, moving average charts
and V-masks, optimal sampling techniques, and evaluation of
operating-characteristic curves and average time to detection. Prerequisite: STAT
5351or equivalent. (3-0) T

**STAT 6390 Topics in Statistics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum). Topics selected from but not limited
to choices such as spatial statistics, nonparametric curve estimation,
functional data analysis, statistical learning and data mining, actuarial
science, sampling theory, statistical quality and process control, sequential
analysis, survival analysis, longitudinal data analysis, categorical data
analysis, and clinical trials, for example. (3-0) R

**STAT 6V99 Statistical Consulting** (1-3 semester
hours) Practical experience in collaboration with individuals who are working
on problems which are amenable to statistical analysis. Problem
formulation, statistical abstraction of the problem, and analysis of the data.
Course may be repeated but a maximum of three hours may be counted toward the
requirements for the master’s degree. Prerequisite: Consent of instructor.
([1-3]-0) T

**STAT 7330 Decision Theory and Bayesian Inference** (3 semester hours)
Statistical decision theory and Bayesian inference are developed at an
intermediate mathematical level. Prerequisites: MATH 5302 or equivalent, and STAT
6331. (3-0) T

**STAT 7331 Multivariate Analysis** (3 semester hours) Vector space
foundations and geometric considerations. The multivariate normal
distribution: properties, estimation, and hypothesis testing. Multivariate t-test. Classification
problems. The Wishart distribution. General linear hypothesis and MANOVA. Principal components,
canonical correlations, factor analysis. Multivariate
nonparametric and robust methods. Prerequisite: STAT 6331 or equivalent.
(3-0) T

**STAT 7334 Nonparametric and Robust Statistical Methods** (3 semester
hours) Topics chosen from Order statistics, ranks, L-statistics, M-statistics,
R-statistics. One- and multi-sample location and scale
problems. Nonparametric ANOVA. Pitman asymptotic relative efficiency. Minimax
asymptotic variance and minimum bias criteria for robust estimation. Robust confidence limits. Optimal influence curves.
Nonparametric/robust density and regression curve estimation. Nonparametric and robust methods for multivariate data.
Prerequisite: STAT 6331 or equivalent. (3-0) T

**STAT 7338 Time Series Modeling and Filtering** (3 semester hours) Theory
of correlated observations observed sequentially in time. Stationary
processes, power spectra, stationary model fitting, correlation analysis and
regression. Prerequisite: STAT 6331 or equivalent. (3-0) T

**STAT 7345 Advanced Probability and Stochastic Processes** (3 semester
hours) Taught as a continuation of STAT 6344. Martingales, Kolmogorov’s
existence theorem, random walk, Markov chains, the Poisson process, the general
birth and death process, other Markov processes, renewal processes, Brownian
motion and diffusion, stationary processes, and the empirical process.
Prerequisite: STAT 6344. (3-0) T

**STAT 7390 Topics in Statistics** (3 semester hours) May be repeated for
credit as topics vary (9 hours maximum) Topics selected from but not limited to
choices such as spatial statistics, nonparametric curve estimation, functional
data analysis, statistical learning and data mining, actuarial science,
sampling theory, statistical quality and process control, sequential analysis,
survival analysis, longitudinal data analysis, categorical data analysis, and
clinical trials, for example. (3-0) R

**STAT 8V02 Individual Instruction in Statistics** (1-6 semester hours) May
be repeated for credit. ([1-6]-0) S

**STAT 8V03 Advanced Topics in Statistics** (1-6 semester hours) May be
repeated for credit. ([1-6]-0) R

**STAT 8V07 Research in Statistics** (1-9 semester hours) Open to students
with advanced standing, subject to approval of the graduate adviser. May be repeated for credit. ([1-9]-0) S

**STAT 8V98 Thesis** (3-9 semester hours) May be repeated for credit.
([3-9]-0) S

**STAT 8V99 Dissertation** (1-9 semester hours) May be repeated for credit.
([1-9]-0) S

Last Updated: March 1, 2011