**Mathematical Sciences 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 2451) 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: MATH 1314 (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. Prerequisite:
Undergraduate algebra course (MATH 3311) or equivalent. (3-0) Y

**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) Y

**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 4301-2 or Math 5301/5302);
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 advanced linear algebra;
Hilbert spaces; positivity; quaternions; integral equations; Fourier analysis;
distributions; convexity; asymptotic methods; 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 computation 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, and 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 6301/6302. 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 Advisor. 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 incluence 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 one way 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) Measure theoretic coverage of probability
theory. Axioms of probability,
Integration. Distributions and
moments. Probability Inequalities. Convergence of probability measures. Laws of large numbers. Central limit theorem. Three-series theorem. Zero-one laws. Glivenko-Cantelli theorem. Law of iterated logarithm. 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) Currently used techniques of multivariate
analysis. Topics include Hotelling's T
test, the multivariate linear model, principal components analysis, factor
analysis, cluster analysis, classification problems, graphics and visualization
tools. Emphasis on computations with R
or other software. Additional topics may
be covered based on current research of the instructor. 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 5351 or 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 statics, 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 date. 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, Autocovariance function. ARMA models.
Optimal forecasting in time domain and in frequency domain. Spectral representation. Estimation and model selection. Nonstationary time series models.
Prerequisite: STAT 6331. (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 7348 Multivariate Analysis** (3 semester hours) Vector space foundations and geometric
considerations. Multivariate normal
distribution. Hotelling's T test. Wishart distribution. Multivariate linear hypotheses. Dimension Reduction. Principal components. Factor analysis. Classification and clustering problems. Additional topics may be covered based on
current research of the instructor.
Emphasis on theoretical underpinnings of methods. Prerequisite: STAT 6331 or equivalent. (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: November 16, 2012