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Course Rotation for Graduate Courses

Course Descriptions

• MATH 515 Advanced Linear Algebra – Advanced topics in linear algebra. This course may cover topics useful in such applications as matrix factorizations, finite element methods, multivariable statistics, stochastic models and parallel programming for scientific computations.
• MATH 535 Complex Variables I – Algebra of complex numbers, classifications of functions, differentiation, integration, mapping, transformations and infinite series.
• MATH 571 Numerical Analysis I – Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, and numerical methods for solving linear systems.
• MATH 575 Operations Research I – Philosophy and techniques of operations research, including game theory; linear programming, simplex method and duality; transportation and assignment problems; introduction to dynamic programming; and queuing theory. Applications to business and industrial problems.
• MATH 625 Advanced Calculus – Topics will include set theory; point set topology in Rn and in metric spaces; limits and continuity; infinite series; sequences of functions.
• MATH 630 Differential Equations in Computing – This course explores the theory and application of differential equations within computational frameworks. Students will study ordinary and partial differential equations (ODEs and PDEs) and learn how these models are implemented and solved using modern computational tools. Emphasis is placed on numerical methods, algorithm design, and software applications for solving real-world problems in science, engineering and data-driven modeling. Prerequsite: MATH 515
• MATH 675 Operations Research II – A continuation of Operations Research I. Topics include the theory of the simplex method, duality theory and sensitivity analysis, game theory, transportation and assignment problems, network optimization models and integer programming. Prerequisites: MATH 575.
• MATH 716 Theory of Algebraic Structures I – Abelian Groups, homomorphisms, permutation groups, Sylow theorems, group representations and characters.
• MATH 741 Measure and Probability – Fundamentals of measure theory and measure-theoretic probability, and their applications in advanced probabilistic and statistical modeling.
• MATH 751 Applied Functional Analysis – Selected topics from functional analysis and its applications to differential equations and numerical methods, concept and theory of functional analysis, and variational formulation of boundary value problem. Existence and uniqueness of solutions, variational methods of approximation and finite element methods.
• MATH 770 Numerical Linear Algebra – Analysis of numerical methods for solving systems of linear equations. Methods for solving underdetermined and overdetermined systems. Methods for numerically calculating eigenvalues and eigenvectors of symmetric and nonsymmetric matrices. Prerequisite: Knowledge of programming language and of matrix algebra.
• MATH 771 Numerical Analysis II – Continuation of MATH 571 including approximation theory, matrix iterative methods and boundary value problems for ordinary and partial differential equations. Prerequisite: MATH 571.
• MATH 773 Numerical Optimization – This course will survey widely used methods for continuous optimization, focusing on both theoretical foundations and implementations using software. Topics include linear programming, line search and trust region methods for unconstrained optimization and a selection of approaches for constrained optimization.
• STAT 510 SAS Programming I – The Base SAS programming language for data reading and manipulation, data display, summarization and graphing. Introduction to statistical procedures, high resolution graphics, the Output Delivery System and some menu-driven interfaces.
• STAT 514 Basic R Programming – An introduction to the R programming language. Topics will include the R programming language and environment, preparation and summarization of data, presentation of data, and programming basics.
• STAT 515 R Programming – The R programming language and environment, preparation and summarization of data, programming basics, data presentation and visualization, app creation and advanced programming techniques.
• STAT 535 Applied Bioinformatics – This practical course is designed for students with biological background to learn how to analyze and interpret genomics data. Topics include finding online genomics resources, BLAST searches, manipulating/editing and aligning DNA sequences, analyzing and interpreting DNA microarray data, and other current techniques of bioinformatics analysis. Prerequisites: STAT 281 or STAT 381.
• STAT 541 Statistical Methods II – Analysis of variance, various types of regression and other statistical techniques and distributions. Sections offered in the areas of biological science and social science. Credit not given for both STAT 541 and STAT 582.
• STAT 542 Exploratory and Cloud-Based Data Analysis – Introduction to the complete exploratory data analysis process, including both local and cloud-based data collection, preparation and analysis, interpretation of analysis, and communication of interpretation. Data sets used will be related to the majors, disciplines, or professions of class participants.
• STAT 545 Nonparametric Statistics – Covers many standard nonparametric methods of analysis. Methods will be compared with one another and with parametric methods where applicable. Attention will be given to: (1) analogies with regression and ANOVA; (2) emphasis on construction of tests tailored to specific problems; and (3) logistic analysis.
• STAT 551 Predictive Analytics I – Introduction to Predictive Analytics. This course will examine the fundamental methodologies of predictive modeling used in financial and predictive modeling such as credit scoring. Topics covered will include logistic regression, tree algorithms, customer segmentation, cluster analysis, model evaluation and credit scoring. Prerequisite: STAT 482 or STAT 786 (or equivalent).
• STAT 553 Applied Bayesian Statistics – Introduction to the philosophy and practice of Bayesian statistics. Statistical methods from simple regression models through generalized linear multilevel models are studied from a Bayesian perspective. Emphasis is placed on building understanding through computational approaches using examples and simulation exercises. Prerequisite: STAT 514 or STAT 515.
• STAT 560 Time Series Analysis – Statistical methods for analyzing data collected sequentially in time where successive observations are dependent. Includes smoothing techniques, decomposition, trends and seasonal variation, forecasting methods, models for time series: stationarity, autocorrelation, linear filters, ARMA processes, nonstationary processes, model building, forecast errors and confidence intervals. Prerequisites: STAT 541 or STAT 581 or STAT 686.
• STAT 600 Statistical Programming – Fundamentals of statistical programming languages including descriptive and visual analytics in R and SAS, and programming fundamentals in R and SAS including logic, loops, macros and functions.
• STAT 601 Modern Applied Statistics I – Topics include statistical graphics, modern statistical computing languages, nonparametric and semiparametric statistical methods, longitudinal and repeated measures, meta-analysis and large-scale inference. Prerequisite: STAT 541. Corequsite: STAT 600.
• STAT 602 Modern Applied Statistics II – Topics include data mining techniques for multivariate data, including principal component analysis, multidimensional scaling and cluster analysis; supervised learning methods and pattern recognition; and an overview of statistical prediction analysis relevant to business intelligence and analytics. Prerequisite: STAT 601
• STAT 651 Predictive Analytics II – This course will examine advanced methodologies used in financial and predictive modeling. Topics covered include segmented scorecards, population stability, ensemble models, neural networks, MARS regression and support vector machines. Prerequisites: STAT 551.
• STAT 661 Design of Experiments I – Analysis of variance, block designs, fixed and random effects, split plots and other experimental designs. Includes use of SAS Processing GLM, Mixed, etc. Prerequisites: STAT 541.
• STAT 684 Statistical Inference I – A theoretical study of the foundations of statistics, including probability, random variables, expectations, moment generating functions, sample theory and limiting distributions. Prerequisites: STAT 381.
• STAT 685 Statistical Inference II – A theoretical study of the foundations of statistics, including most powerful tests, maximum likelihood tests, complete and sufficient statistics, etc. Prerequisite: STAT 684.
• STAT 686 Regression Analysis I – Methodology of regression analysis, including matrix formulation, inferences on parameters, multiple regression, outlier detection, diagnostics and multicollinearity. Prerequisites: MATH 515 and STAT 684.
• STAT 687 Regression Analysis II – Advanced regression methodology, including nonlinear regression, logistic regression, Poisson regression and correlation analysis. Prerequisites: STAT 686.
• STAT 715 Multivariate Statistics – Multiple, partial and canonical correlation test of hypothesis on means; multivariate analysis of variance; principal components; factor analysis; and discriminant analysis. Prerequisites: MATH 515 and STAT 685.
• STAT 716 Asymptotic Statistics – This course will cover modern statistical approximation theorems relating to the current statistical and machine learning literature in Mathematical Statistics. Specific topics to be covered are: Review of Stochastic Convergence (Almost-Sure representations, Convergence of Moments, Lindeberg-Feller Central Limit Theorem, etc.), Delta Method, Moment Estimators, and M- and Z- Estimators. An additional selection of 2-4 topics will also be covered that are related to the research focus of the Ph.D. students in the class. Prerequisites: STAT 715, STAT 684, and MATH 741.
• STAT 721 Statistical Computing and Simulation – Computationally intensive statistical methods that would not be feasible without modern computational resources and statistical simulation techniques, including random variable generation methods, Monte Carlo simulation and importance sampling, kernel smoothing and smoothing splines, bootstrap, jackknife and cross validation, regulation and variable selection in regression, EM algorithm, concepts of Bayesian inference, Markov chain, Monte Carlo methods such as Gibbs sampling, and the Metropolis-Hasting algorithm. Prerequisites: STAT 686 and STAT 715.
• STAT 731 Survival Analysis – Introduction to survival data, censoring and truncation, survival function and hazard function, non-parametric methods for estimating survival curves, comparing two or more survival curves, semi-parametric proportional hazards regressions, model diagnostics, accelerated failure time and other parametric models. Prerequisites: STAT 541 or STAT 381.
• STAT 732 Statistical Genomics – Topics will include genomic data, data visualization, regression modeling and applications in genomics, dimension reduction, variable selection, genome-wide association mapping, experimental design, dose-response modeling, and simultaneous inferences in genomic data analyses. Prerequisites: STAT 541.
• STAT 736 Bioinformatics – This course is an introduction to bioinformatics for students in mathematics and physical sciences. This course will include a brief introduction to cellular and molecular biology and will cover topics such as sequence alignment, phylogenetic trees and gene recognition. Existing computational tools for nucleotide and protein sequence analysis, protein functional analysis and gene expression studies will be discussed and used.
• STAT 742 Spatial Statistics – Geostatistical data analysis with variogram, covariogram and correlogram modeling. Spatial prediction and Kriging, spatial models for lattices and spatial patterns. Prerequisite: STAT 541 or STAT 56 or STAT 684 or STAT 686.
• STAT 752 Advanced Data Science – This course will cover current research in the mathematical and statistical sciences. The focus of the class is to introduce Ph.D. students to the ongoing research programs of the faculty and advanced methodologies outside of the traditional core classes related to the rapidly evolving disciple of data science. This class can be taken multiple times for credit. Prerequisite: STAT 687 and STAT 715 or Permission of instructor.
• STAT 762 Advanced Experimental Design - Linear Model interpretation in vector spaces and projections, use of generalized inverses, identifiability and estimability of contrasts, normal equations, Gauss-Markov Theorem, MVUE, distribution theory for quadratic forms, complex designs such as crossover, splitplot and repeated measures, asymptotics for general linear models, familiarity with nonparametric regression models. Prerequisite: STAT 685 and STAT 687.