**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 4301-2 or Math 5301-2); 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 or MATH 5301-2. (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

**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 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.
Exponential families of models, sufficiency, estimation, hypothesis testing,
likelihood methods, optimality, analysis of variance, linear models, decision
theory. Prerequisites: Undergraduate analysis MATH 4301-2, STAT 5351 or
equivalent and MATH 5302 or equivalent. STAT 5352 strongly recommended. (3-0) Y

**STAT 6332 Statistical Inference II** (3 semester hours) Topics chosen from
elementary and advanced asymptotic methods, including sample quantiles,
U-statistics, differentiable statistical functions, the MLE, L-statistics,
M-statistics, the bootstrap, advanced aspects of statistical inference,
likelihood-based inference, robust statistics, linear models and the analysis
of discrete data.. Prerequisites: STAT 6331 and STAT 6344 should be taken
either before or concurrently. (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, balanced and
unbalanced analysis of variance, analysis of covariance and log-linear analysis
of multiway contingency tables. Prerequisites: MATH 2451 and STAT 5352 or STAT
6331. (3-0) T

**STAT 6338 Advanced Statistical Methods II** (3 semester hours)
Continuation of STAT 6337. 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, 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 substantive 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 STAT 6339 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 5311, or 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). (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 4301 and MATH 4302 or MATH
5302 and either STAT 6331 or STAT 6338. (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 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 estimation.
Nonparametric inference for counting processes. 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 models fitting, correlation analysis and regression.
Prerequisite: STAT 6331 or equivalent. (3-0) T

**STAT 7345 Advanced Probability and Stochastic Processes** (3 semester
hours) Possible topics include 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,
and stationary processes. 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). (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