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Course Criteria
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3.00 Credits
This is the second course in a two-semester course on Mathematical Statistics. Topics include decision theory, estimation, hypothesis testing, regression, correlation, and analysis of variance. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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3.00 Credits
This course provides an introduction to various approaches to statistical learning including empirical processes, classification and clustering, nonparametric density estimation and regression, model selection and adaptive procedures, bootstrapping and cross-validation. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 203 AND MATH 220 AND MATH 350
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3.00 Credits
Neural networks, nearest neighbor procedures, Vapnik Chervonenkis dimension, support vector machines, structural risk minimization induction, regularization methods and boosting and bagging in classification and regression NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 440
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3.00 Credits
This course is a study of numerical methods and analysis of their accuracy, robustness, and speed. Topics include numerical solution of ordinary differential equations, approximations of functions, solving simultaneous linear equations by direct and iterative methods, computing eigenvalues and eigenvectors, and solving systems of non-linear equations. Standard computer software will be used. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 203 AND MATH 323 AND MATH 246
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3.00 Credits
This course provides an introduction to the theory of linear models for analyzing data. Topics include analysis of variance and regression models, as well as Bayesian estimation, hypothesis testing, multiple comparison, and experimental design models. Additional topics such as balanced incomplete block designs, testing for lack of fit, testing for independence, and variance component estimation are also treated. The approach taken is based on projections, orthogonality, and other vector space concepts. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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3.00 Credits
This course provides an introduction to deterministic models in operations research. Topics include linear programming, network analysis, dynamic programming, and game theory. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 203 AND MATH 221 AND ( CSCI 220 OR MATH 245 )
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3.00 Credits
This course provides an introduction to probabilistic models in operations research. Topics include queueing theory, applications of Markov chains, simulation, integer programming and nonlinear programming. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
Prerequisite:
MATH 203 AND MATH 530 AND ( CSCI 220 OR MATH 245 )
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3.00 Credits
Posterior distributions using observed data are calculated and used for inferences about model parameters. Classical statistical methods are compared with the Bayesian methods and classical models such as linear regression, ANOVA, and generalized linear models are extended to include the Bayesian paradigm. Monte Carlo methods, Gibbs sampling and Metropolis-Hastings algorithms. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions..
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3.00 Credits
Stochastic Processes are sequences of random variables indexed in either discrete or continuous time unit. They can be used to model systems that involve random elements as they evolve over time. In this course we will study Poisson processes, Markov chains, renewal processes, martingales, random walks, and Brownian motion. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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3.00 Credits
Time series are sequences of data points measured typically at successive uniform time intervals. They are used in signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, and control engineering. Time series analysis is a collection of methods for analyzing time series data in order to extract meaningful characteristics of the data. In this course we will study stationary processes, forecasting techniques, ARMA models, spectral analysis, non-stationary and seasonal models, and multivariate time series. NOTE: Please refer to the appropriate academic catalog for additional course information concerning prerequisites, co-requisites and course restrictions.
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