## Course Rotation for Graduate Courses

Fall Semester Courses | Spring Semester Courses | |
---|---|---|

MATH 515 Advanced Linear Algebra MATH 571 Numerical Analysis I MATH 575 Operations Research I MATH 625 Advanced Calculus I MATH 751 Applied Functional Analysis MATH 773 Numerical Optimization (even years) | MATH 675 Operations Research II MATH 716 Algebraic Structures I MATH 741 Measure & Probability MATH 770 Numerical Linear (even years) MATH 771 Numerical Analysis II (odd years) | |

STAT 541 Statistical Methods II STAT 553 Applied Bayesian Statistics STAT 560 Time Series Analysis | STAT 510 SAS Programming I STAT 514 Introduction to R (1 credit) STAT 515 R Programming (3 credits) STAT 535 Applied Bioinformatics STAT 541 Statistical Methods II STAT 545 Nonparametric Statistics STAT 551 Predictive Analytics I | |

STAT 601 Modern Applied Statistics I STAT 651 Predictive Analytics II STAT 684 Statistical Inference I STAT 687 Regression Analysis II | STAT 602 Modern Applied Statistics II STAT 661 Design of Experiments STAT 685 Statistical Inference II STAT 686 Regression Analysis I | |

STAT 715 Multivariate Statistics STAT 716 Asymptotic Statistics (odd years) STAT 736 Bioinformatics STAT 742 Spatial Statistics (even years) STAT 752 Advanced Data Science (even years) STAT 762 Advanced Experimental Design | STAT 721 Stat. Computation and Simulation STAT 731 Survival Analysis (even years) |

**Summer Courses **

STAT 514 Introduction to R (1 credit, online)

STAT 541 Statistical Methods II (online)

STAT 600 Statistical Programming (online)

Courses offered occasionally: STAT 752 Advanced Data Science, MATH 535 Complex Variables, MATH 511 Number Theory, MATH 792 Dynamical Systems, others upon demand...

## Course Descriptions

**MATH 535 Complex Variables I**- Algebra of complex numbers, classifications of functions, differentiation, integration, mapping, transformations, infinite series.**MATH 571 Numerical Analysis I**- Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, numerical methods for solving linear systems. Pre-requisite: MATH 225.**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. Prerequisite: MATH-315, or (MATH-281 and MATH-125), or instructor consent.**MATH 616 Algebraic Structures I**- Abelian Groups, homomorphisms, permutation groups, Sylow theorems, group representations and characters. Pre-requisite: MATH 413.**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 475/575**MATH 725 Advanced Calculus I**- Topics will include set theory; point set topology in Rn and in metric spaces; limits and continuity; infinite series; sequences of functions. Pre-requisite: MATH 425.**MATH 733 Dynamical Systems**- Topics related to understanding the long-term behavior of dynamical systems, including attracting sets, orbit structure, orbit densities, ergodic theory, chaos, and fractals.**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, variational formulation of boundary value problem. Existence and uniqueness of solutions, variational methods of approximation, finite element methods**MATH 770 Numerical Linear Algebra**Analysis of numerical methods for solving systems of linear equations. Methods for solving under-determined and over-determined systems. Methods for numerically calculating eigenvalues and eigenvectors of symmetric and non-symmetric matrices.**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. Pre-requisite: 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.**MATH 774 Advanced Scientific Computation**- Advanced topics in scientific computation. This course may cover topics such as matrix factorizations, finite element methods, multivariable optimizations, stochastic differential equations, and parallel programming for scientific computations. Pre-requisite: MATH 571.**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 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. Pre-requisites: 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. Pre-requisites: STAT 281, MATH 381, or STAT 381, STAT 210 or STAT 410. Credit not given for both STAT 541 and STAT 582.**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. Pre-requisites: STAT 281, MATH 381 or STAT 381.**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. Pre-requisite: STAT 482 or STAT 786 (or equivalent).**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. Pre-requisite: STAT 582.**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 700, STAT 541 or equivalent.**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 701**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. Pre-requisites: STAT 551 or STAT 786.**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. Pre-requisites: STAT 541 or STAT 582.**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. Pre-requisites: 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.**STAT 686 Regression Analysis I**- Methodology of regression analysis, including matrix formulation, inferences on parameters, multiple regression, outlier detection, diagnostics, and multicollinearity. Pre-requisites: STAT 381.**STAT 687 Regression Analysis II**- Advanced regression methodology, including nonlinear regression, logistic regression, poisson regression, and correlation analysis. Prerequisites: STAT 786.**STAT 715 Multivariate Statistics**- Multiple, partial, canonical correlation test of hypothesis on means; multivariate analysis of variance;principal components; factor analysis; and discriminant analysis. Pre-requisites: STAT 441 or STAT 541, STAT 482.**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 PhD students in the class. Prerequisites: STAT 715, STAT 784, MATH 741.**STAT 721 Statistical Computing & 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. Pre-requisites: STAT 786.**STAT 731 Biostatistics**- Statistical methods commonly used in the biological and health sciences, including study designs such as parallel, crossover, adaptive designs, randomization procedure, sample size determination, data collection process and analysis methods including survival data analysis. Pre-requisites: STAT 541 or STAT 582.**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, spatial patterns. Pre-requisite: STAT 541 or STAT 786.**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 PhD 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: permission of instructor.