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Course Criteria
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3.00 Credits
Prerequisites: MATH 4030, MATH 4100, and MATH 4450. The course covers the basic of Fourier analysis and wavelet analysis. Topics include Fourier transforms and series, discrete Fourier transform, discrete cosine transform ad their fast computational schemes, fast wavelet transform, and the lifting scheme. Additional topics include industrial standards for image compression and several aspects of signal processing.
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3.00 Credits
Prerequisites: MATH 4100. Introduction to measure and integration . Topics include the Riemann-Stieltjes integral, Lebesgue measure, measurable functions, the Lebesgue integral, Radon-Nikodym and Fubini theorems and the basics of Lp-spaces.
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3.00 Credits
Prerequisites: MATH 4100, 4450, and 4800. An introduction to smooth manifolds and maps. Topics will include the Implicit Function Theorem, Sard's Theorem, transversality, intersection and degree theory, differential forms and integration on manifolds.
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3.00 Credits
Prerequisites: MATH 4100 or consent of instructor. Na?ve set theory, cardinal arithmetic, ordinal numbers, the axiom of choice and equivalents, metric spaces, convergence, continuity, compactness, contraction principles and applications.? Construction of completions and examples like the real numbers and p-adic numbers.? Other topics could include the Stone-Weierstrass theorem and metrizability theorems.
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3.00 Credits
Prerequisites: MATH 4160, and either MATH 4100 or 4800. A second course in complex analysis, emphasizing the theory of analytic functions, and including various topics like the Riemann mapping theorem, normal families, analytic continuation, representations of analytic functions, and elliptic functions.
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3.00 Credits
Prerequisite: MATH 4230 and MATH 4450 or consent of the instructor. The course includes solution of general and special linear systems. Techniques include methods such as splitting or Krylov subspaces. Additional topics are the eigenvalue problem and the method of least squares.
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3.00 Credits
Prerequisites: MATH 4100, 4160, 4450, and 4800. Classification of partial differential equations; Cauchy, Dirichlet, and Neumann problems; the fundamental solution; existence theorems of potential theory; eigenvalue problems; and Tricomi's problem.
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3.00 Credits
Prerequisites: MATH 4210 or consent of instructor. The course studies classical and recently developed statistical procedures selected from areas including analysis of variance, multivariate analysis, nonparametric or semiparametric methods and generalized linear models. Emphasis is on application of procedures, including the rationale underlying choice of procedures.
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3.00 Credits
Prerequisites: MATH 4450 or equivalent. A study of deterministic methods and models in operations research. This course provides an introduction to operations research and focuses on model building, solution and interpretation of results. Topics include formulation, solution, duality and sensitivity analysis in linear programming, integer programming, network flow models, nonlinear optimization, and dynamic programming.
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3.00 Credits
Prerequisites: MATH 4200 or equivalent. ?A study of stochastic methods and models in operations research. Provides an introduction to probabilistic models for decision making under uncertainty. Topics include stochastic processes, queuing theory and models, probabilistic inventory theory and models, Markovian decision problems, simulation and reliability.
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