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Course Criteria
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3.00 Credits
No Description Available
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3.00 Credits
No Description Available
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3.00 Credits
This course provides a proof-based introduction to Complex Analysis. Topics include the complex number system, analytic and harmonic functions, power series, integrations, residue theory, analytic continuation, conformal mapping, and applications. 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 the three main classes of partial differential equations (hyperbolic, parabolic, and elliptic) that arise in the description of wave motion, diffusion processes, and potential theory. Topics include the study of initial and boundary value problems, and solution methods such as fundamental solutions and separation of variables. Additional topics may include the method of characteristics, Sturm-Liouville theory, Green's functions, integral transformations, and nonlinear partial differential equations. 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 is a calculus based probability and statistics course. Topics will include probability functions and densities, mathematical expectations, sums of random variables, and sampling distributions. 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 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.
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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.
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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.
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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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