Graduate Courses

Mathematics & Statistics

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Course Descriptions:

MAA6417: Complex Analysis
Prerequisite:  MAA 4211. Holomorphic functions, Cauchy's theorem. power series, conformal mapping, harmonic functions, residues.
3
MAD6405: Numerical Analysis
Prerequisites: MAC 2313, MAS 3105 and a scientific computing language. Nonlinear equations, interpolation, numerical integration, direct and indirect solutions of linear equations, eigenvalue problems and error analysis for the above numerical methods.
3
MAE6871: Mathematical Connections
Prerequisites: Graduate standing in mathematics education. In this course we study connections among various branches of mathematics. These include geometry and number theory, geometry and complex numbers, surfaces and algebra, geometry and algebra (including impossible constructions), and interesting numbers such as PI, EPISILON, IOTA, EPSILON.
3
MAE6879: Mathematical Applications Around Us
Prerequisites: Graduate standing in mathematics education. Topics will be chosen from graph theory, coding, voting and apportionment, scaling, geometric and numerical patterns in nature, probability, or other areas of application. Projects will be assigned for individual research relating mathematics to art, music, biology, game theory, or other areas of application.
3
MAP6336: Ordinary Differential Equations
Prerequisites: MAP 2302, MAA 4211 and MAS 3105. Existence and uniqueness theorems, properties of solutions of ordinary differential equations, linear and non-linear systems, stability.
3
MAP6345: Partial Differential Equations
Prerequisites: MAP 2302, MAS 3105 and MAA 4211. First order equations; classification of second order linear equations; wave, heat, and Laplace equations; separation of variables and Fourier Series.
3
MAP6385: Scientific Computing
Emphasis will be on the practical aspects of implementing numerical schemes and the use of well established software packages. Some consideration will be given to stability and accuracy questions. Topics may include: numerical solutions of nonlinear equations, interpolation, simulation and optimization.
3
MAP6489: Mathematical Biology
Prerequisite:  MAP 2302, MAS 3105, and MAA 4211
Description: This course covers basics of mathematical models which are used to study population dynamics, diseases, and cells. Techniques covered include ordinary differential equations, and discrete and continuous dynamical systems. Analytical and numerical tools suitable for analysis and visualization of the solutions of these problems are presented.
3
MAP6605: Topics in Financial Mathematics
Prerequisite:  MAA 4211 and 4212, STA 4321, or permission of the department. Topics will include an introduction to options and derivatives, pricing via arbitrage, binomial and multi-period models, Brownian motion, Ito integral, Black-Scholes stochastic differential equation, and application to option pricing, hedging, valuing by utility, and exotic options.
3
MAS6145: Advanced Linear Algebra
Prerequisite:  MAS 3105. Vector spaces, linear transformations, eigenvalues and eigenvectors, similarity transformations, positive definite matrices, canonical forms and other topics in linear algebra.
3
MAS6218: Topics in Number Theory
Prerequisites: MHF 3203 and MAS 3203 or MAD 3107 or permission of the instructor This course will consist of topics from analytic, algebraic, computational, or elementary number theory. Possible topics include, but are not limited to: congruences, reciprocity laws, quadratic forms, prime number theorem, Diophantine equations, Gaussian sums, quadratic residues, number fields, class number, units, and partitions.
3
MAS6311: Abstract Algebra
Prerequisite:  MAS 4301 or permission of instructor. Algebraic structures, sub structures, quotient structures, modules, algebras and field extensions.
3
MAS6933: Topics in Algebra
Prerequisites: MAS 4301 or permission of instructor. Selected topics from ring theory, group theory, algebraic geometry, algebraic number theory, category theory, homological algebra.
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MAS6938: Topics in Applied Algebra
Prerequisites: MAS 4301 and permission of the department. This course will consist of topics such as combinatorics, graph theory, coding theory, automata theory or design theory.
3
MAT5932: Special Topics in Mathematical Sciences
Prerequisite:  Permission of the department. This is an introductory graduate level courses in mathematics, designed to support graduate programs in other departments in the University. The course may be repeated for a total of 9 credits under different topics.
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MAT6908: Directed Individual Study
Prerequisite:  Permission of the department. May be repeated for 9 credits under different topics.
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MAT6933: Special Topics in Mathematics
Prerequisite:  Permission of the department. May be repeated for 9 credits under different topics.
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MAT6971: Thesis
Prerequisite:  Permission of the department. May be repeated for 6 credits.
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STA5126: Statistical Methods for the Social Sciences
This course covers the statistical methods most often used in social science research. Topics include regression and correlation analysis, analysis of variance, categorical data and nonparametric statistics. This course cannot be used to satisfy degree requirements by statistics and mathematics majors.
3
STA5931: Special Topics in Statistical Sciences
Prerequisite:  Permission of the department. This is an introductory graduate level course in statistics, designed to support graduate programs in other departments in the University. This course may be repeated for 9 credits under different topics.
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STA6106: Computer-Intensive Methods in Statistics
Prerequisite:  STA 4321. This course will cover a variety of statistical methods which are dependent on the availability of massive computational power. The course will include but is not limited to topics such as simulation techniques, randomization tests, Monte Carlo techniques, bootstrap methods, and numerical optimization methods. The course will involve extensive computer programming on the part of the students.
3
STA6166: Statistical Methods I
Prerequisite:  MAS 3105 and STA 4321. This is the first in a two-term sequence in statistical methods. This course is a blend of the theory and applications of regression analysis and of the design and analysis of data. It focuses on linear regression with one predictor variable, inferences involving regression coefficients and correlation analysis, diagnostics and remedial measures, multiple linear regressions and its diagnostics, and an introduction to the analysis of variance. Emphasis is placed on the application of these techniques to data and interpretation of the results. The course uses the statistical analysis software (SAS) for data analysis.
3
STA6167: Statistical Methods II
Prerequisite:  STA 6166. This is the second in a two-term sequence in statistical methods. In this course, the focus is exploration of multiple regression (including model building, diagnostics, and remedial measures), multifactor studies using analysis of variance and covariance, and other topics in the analysis of categorical or multivariate data. The course uses the statistical analysis software (SAS) for data analysis.
3
STA6205: Design of Experiments
Prerequisite:  STA 6166 or both STA 3163 and STA 4321 This course covers principles of design, single factor and multifactor design, randomized blocks, randomized incomplete blocks, Latin squares, factorial designs, split plot and related designs. It also covers random and mixed effects model for Analysis of Variance designs. The course uses the statistical analysis software SAS for data analysis.
3
STA6226: Sampling
Prerequisite:  STA 6166 or both STA 3163 and STA 4321. This course focuses on survey designs and covers simple probability samples, ratio and regression estimation, stratified sampling, and cluster sampling with equal and unequal probabilities. Some complex survey designs may also be included. The course uses the statistical analysis software SAS for data analysis.
3
STA6326: Mathematical Statistics I
Prerequisite:  MAA 4211 and STA 4321. This is the first in a two-term sequence in mathematical statistics. It covers topics such as probability, random variables, expected values, sampling distributions, Central Limit Theorem, estimation, properties of estimators, and order statistics.
3
STA6327: Mathematical Statistics II
Prerequisite:  STA 6326 This is the second in a two-term sequence in mathematical statistics. It covers introductions to the theories of point estimation, interval estimation, and hypothesis testing. Topics on sufficiency, completeness, likelihood, and their applications to the exponential family are also covered.
3
STA6446: Probability
Prerequisites: MAS 3105, MAA 4211 and STA 4321 This is a course in advanced topics in probability. It covers probability distributions, conditional probability and conditional expectations. Some of the fundamental stochastic processes (Markov chains, the Poisson process, Renewal Theory, Brownian motion) will be covered.
3
STA6505: Categorical Data Analysis
Prerequisite:  STA 6166. This course is an introduction to the methods used to analyze categorical responses and contingency tables. Topics include models for binary response variables, logistic regression, logit models for categorical data, loglinear models and the estimation of model parameters.
3
STA6666: Statistical Quality Control
Prerequisite:  Permission of the department. This course covers the statistical properties, as well as the design, implementation, and operation, of various statistical process control (SPC) schemes including those based on Shewhart, cumulative sum, and moving average control charts. Methods appropriate for conducting a capability study will also be covered. The role of SPC in process improvement will be examined, as well as statistical models useful in quality control. Additional selected topics such as acceptance sampling will be presented as time permits. The statistical analysis software SAS will be used extensively.
3
STA6707: Multivariate Methods
Prerequisite:  MAS 3105, STA 6166. This course introduces a range of multivariate methods used for analyzing complex data sets with large numbers of variables. The following topics will be covered: multivariate analysis of variance, correlation, discriminant analysis, and factor analysis.
3
STA6908: Directed Individual Study
Prerequisite:  Permission of the department. May be repeated for 9 credits under different topics.
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STA6938: Seminar in Statistics
Various topics in statistics. May be repeated for 9 credits under different topics.
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STA6940: Statistical Consulting
Prerequisites: Permission of instructor. The course is designed to give students hands-on experience with statistical consulting. The course covers problem formulation, statistical techniques, data analysis, and interpretation of the results of consulting problems. The course may be repeated for a total of 9 credits.
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STA6971: Thesis
Prerequisites: Permission of the department. May be repeated for 6 credits under different topics.
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