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Nov 25, 2024
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2013-2014 Graduate Catalog [Archived Catalog]
Mathematics and Statistics (MATH, STAT, CSS) Course Offerings
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Mathematics and Statistics
CSS 890 - Seminar in Computational Science and Statistics Credits: 1
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CSS 891 - Independent Study Credits: (1-3)
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CSS 892 - Topics Credits: (1-3)
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CSS 898 - Thesis/Dissertation Credits: (1-36)
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MATH 511 - Theory of Numbers Credits: 3
A study of the theory of prime numbers, distribution of primes, congruencies, quadratic reciprocity, numerical functions, diophantine equations, simple continued fractions, and algebraic numbers. Pre-requisites: MATH 224, Calculus II or its equivalent.
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MATH 540 - Mathematics of Finance Credits: 3
An introduction to the fundamental concepts of financial mathematics. Topics include simple and compound interest, annuities, amortization, sinking funds, bonds, stocks, rates of return, term structure of interest rates, cash-flow duration and immunization. Prerequisites: Pre-requisite: STAT 381.
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MATH 541 - Applied Probability Theory Credits: 3
Topics in probability including an introduction to the axiomatic development of probability, random variable and distributions with emphasis on the exponential, binomial and Poisson distributions. Applications to discrete stochastic processes such as Markov chains and queuing theory are covered in some detail. Prerequisites: Pre-requisite: STAT 381 or instructor consent.
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MATH 561 - Introduction to Topology Credits: 3
A first course in point-set topology, covering the elementary concepts of metric and general topological spaces; closure, interior, boundary, connectedness, compactness, and separation. Special attention is given to continuity of functions.
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MATH 571 - Numerical Analysis I Credits: 3
Analysis of rounding errors, numerical solutions of nonlinear equations, numerical differentiation, numerical integration, interpolation and approximation, numerical methods for solving linear systems. Prerequisites: Pre-requisite: MATH 225.
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MATH 574 - Scientific Computation II Credits: 3
A continuation of Scientific Computation I. Topics will include computational methods used for mathematical modeling, such as numerical methods for solving linear systems and methods for solving initial value problems. Numerical methods will be applied to mathematical models. Simulation and validation of models will be discussed. Prerequisites: Pre-requisite: MATH 321 and MATH 374
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MATH 575 - Operations Research Credits: 3
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. Pre-requisites: Introductory statistics and one year of calculus; STAT 575 and CSC 575, or instructor consent.
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MATH 590 - Seminar Credits: (1-2)
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MATH 591 - Independent Study Credits: (1-3)
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MATH 592 - Topics Course Credits: 1-3
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MATH 716 - Theory of Algebraic Structures I Credits: 3
Abelian Groups, homomorphisms, permutation groups, Sylow theorems, group representations and characters. Prerequisites: Pre-requisite: MATH 413.
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MATH 717 - Theory of Algebraic Structures II Credits: 3
Rings, Modules, Fields, Galois theory, solvable groups, commutative rings and modules. Prerequisites: Pre-requisite: MATH 716.
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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
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MATH 732 - Ordinary Differential Equations Credits: 3
Existence theorems for solutions of ordinary differential equations, theory of linear differential equations and systems of linear differential equations oscillation theory. Pre-requisites: Take 1 group: MATH 321, MATH 725 or MATH 321 and MATH 425.
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MATH 733 - Complex Variables I Credits: 3
Algebra of complex numbers, classifications of functions, differentiation, integration, mapping, transformations, infinite series. Pre-requisites: MATH 725.
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MATH 741 - Measure and Probability Credits: 3
Fundamentals of measure theory and measure-theoretic probability, and their applications in advanced probabilistic and statistical modeling.
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MATH 742 - Partial Differential Equation Credits: 3
Series, solutions, total differential equations, simultaneous equations, approximate solutions, partial differential equations of first and second orders, applications. Pre-requisites: MATH 321 and MATH 225.
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MATH 771 - Numerical Analysis II Credits: 3
Continuation of MATH 571 including approximation theory, matrix iterative methods and boundary value problems for ordinary and partial differential equations. Pre-requisites: MATH 571.
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MATH 774 - Advanced Scientific Computation Credits: 3
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 771.
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MATH 775 - Operations Research II Credits: 3
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
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MATH 788 - Research Paper Credits: (1-2)
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MATH 790 - Seminar Credits: 1
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MATH 791 - Independent Study Credits: (1-3)
Includes Directed Study, Problems, Readings, Directed Readings, Special Problems, and Special Projects. Students complete individualized plans of study which include significant one-on-one student-teacher involvement. The faculty member and students negotiate the details of the study plans. Enrollments are usually 10 or fewer students. Meetings depending upon the requirements of the topic.
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MATH 792 - Topics Credits: (1-3)
Course content is not wholly included in the regular curriculum. Guest artists or experts may serve as instructors. Enrollments are usually of 10 or fewer students with significant one-on-one student/teacher involvement. Includes current topics, advanced topics and special topics. A course devoted to a particular issue in a specified field.
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MATH 798 - Thesis Credits: (1-7)
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STAT 510 - Programming Using SAS Credits: 2
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. Notes: (information and presentation graphics).
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STAT 512 - Programming Using SAS II Credits: 2
A continuation of STAT 510, including SAS/STAT, SAS Macro, IML, and projects in data simulation. Prerequisites: Pre-requisites: STAT 410 or 510
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STAT 514 - R Programming Credits: 1
An introduction to the R programming language. Topics will include the R programming language and environment, preparation and summarization of data, presentation of data, programming basics, and additional selected advanced topics.
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STAT 535 - Applied Bioinformatics Credits: 2
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
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STAT 541 - Statistical Methods II Credits: 3
Analysis of variance, various types of regression, and other statistical techniques and distributions. Sections offered in the areas of Biological Science and Social Science. Prerequisites: STAT 281, MATH 381, or STAT 381, STAT 210 or STAT 410. Credit not given for both STAT 541 and STAT 581.
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STAT 545 - Nonparametric Statistics Credits: 3
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. Prerequisites: STAT 281, STAT 381.
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STAT 551 - Predictive Analytics I Credits: 3
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-requisites: STAT 582.
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STAT 560 - Time Series Analysis Credits: 3
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: Pre-requisite: STAT 582.
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STAT 582 - Probability and Statistics II Credits: 3
Introduction to statistical design, one-way completely randomized design, testing contrasts and multiple comparison procedures, simple and multiple linear regression, factorial designs, fractional factorial designs and mixed models. SAS software is used extensively. Prerequisites: MATH/STAT 381. Credit will not be given for both STAT 482 and STAT 441.
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STAT 590 - Seminar Credits: (1-2)
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STAT 591 - Independent Study Credits: (1-3)
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STAT 592 - Topics Credits: (1-3)
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STAT 715 - Multivariate Analysis I Credits: 3
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 or STAT 582.
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STAT 721 - Statistic Computing/Simulation Credits: 3
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 582 or STAT 786.
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STAT 731 - Biostatistics Credits: 3
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.
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STAT 736 - Bioinformatics Credits: 3
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.
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STAT 742 - Spatial Statistics Credits: 3
Geostatistical data analysis with variogram, covariogram and correlogram modeling. Spatial prediction and kriging, spatial models for lattices, spatial patterns. Prerequisites: Pre-requisite: STAT 687.
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STAT 751 - Predictive Analytics II Credits: 3
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.
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STAT 756 - Quantitative Genetics Credits: 3
Theory and application of quantitative genetic analysis to applied breeding problems; estimation and partitioning of genetic variances; genetic covariance and regression; heritability and selection response; index selection; linkage and quantitative trait loci (QTL) analysis. Pre-requisites: BIOL 371, STAT 541.
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STAT 760 - Quality Control Credits: 3
Application of statistical techniques to the control of quality and the development of economical inspection methods. Collection, analysis, and interpretation of operations data; control charts and sampling procedure. Prerequisites: STAT 281 or STAT 381 Cross-Listed: ME 760
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STAT 761 - Design of Experiments II Credits: 3
Continuation of STAT 661. One-way classification models with heterogeneous errors, two-way classification analysis in the unbalanced case, analysis in the unbalanced case, analysis of mixed models, repeated measures. Pre-requisites: STAT 541 or STAT 582.
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STAT 762 - Design of Surveys Credits: 3
Methods of construction and analyzing designs for experimental investigations; concepts of blocking, randomization, and replication; factorials; multiple comparisons; model checking; analysis of covariance. Pre-requisites: STAT 441 or STAT 541, STAT 482 or STAT 582.
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STAT 784 - Statistical Inference I Credits: 3
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
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STAT 785 - Statistical Inference II Credits: 3
A theoretical study of the foundations of statistics, including most powerful tests, maximum likelihood tests, complete and sufficient statistics, etc.
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STAT 786 - Regression Analysis I Credits: 3
Methodology of regression analysis, including matrix formulation, inferences on parameters, multiple regression, non-linear regression, outlier detection, diagnostics, and multicollinearity. Pre-requisites: STAT 441 or STAT 541, STAT 482 or STAT 582.
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STAT 787 - Regression Analysis II Credits: 3
Advanced regression methodology, including nonlinear regression, logistic regression, poisson regression, and correlation analysis. Prerequisites: STAT 687
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STAT 788 - Research Paper Credits: (1-2)
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STAT 790 - Seminar Credits: 1
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STAT 791 - Independent Study Credits: (1-3)
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STAT 792 - Topics Credits: (1-3)
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STAT 798 - Thesis Credits: (1-7)
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