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Course Criteria
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3.00 Credits
Existence theorems for linear and nonlinear equations, systems of first order linear equations, nonlinear equations and stability, applications. Prerequisite: C or better in MATH 337.
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3.00 Credits
Boundary value problems, Sturm-Liouville theory, singular boundary conditions, Fourier series, partial differential equations of mathematical physics, e.g., heat, wave, and Laplace's equation in one and several dimensions. Applications. Prerequisite: C or better in MATH 337.
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3.00 Credits
Fall, Summer. Axiomatic probability; conditional probability; random variables/vectors; distribution functions; expectations; moment-generating functions; special distributions; functions of random variables/vectors; random sampling and sampling distributions; central limit theorem; weak law of large numbers. Prerequisite or corequisite: MATH 233 or MATH 235.
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3.00 Credits
Spring. Statistical models; point estimation; interval estimation; testing statistical hypotheses; analysis of discrete data; nonparametric methods. Prerequisite: C or better in MATH 441.
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3.00 Credits
Spring of odd years. Probability models for applications, finite Markov chains, queueing systems, Poisson process, applications to genetics, diffusion, computer systems. Prerequisites: C or better in MATH 332 and MATH 441.
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3.00 Credits
Fall odd years. Introduction to modern techniques in data analysis, including stem-and-leafs, box plots, resistant lines, smoothing and median polish. Prerequisite: C or better in MATH 247, MATH 341, or MATH 441 or consent of instructor. Approved for Distance Ed.
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3.00 Credits
Fall. Study of numerical methods for interpolation and approximation, integration and differentiation, solution of non-linear equations and systems of linear and non-linear equations. Prerequisites: C or better in MATH 332 and programming experience. Not open to students with credit for CS 451.
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3.00 Credits
Study of numerical methods for the algebraic eigenvalue problem; solutions of ordinary differential equations; and topics from approximation theory, numerical solution of partial differential equations, optimization techniques and sparse matrix computations. Prerequisites: C or better in MATH 337 and MATH 451 or CS 451. Not open to students with credit for CS 452.
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3.00 Credits
Spring odd years. Complex numbers, complex valued functions, differentiation of complex valued function, analytic functions, power series, integration, contour integrals, residues and poles, conformal mapping, applications. Prerequisites: C or higher in MATH 233 or MATH 235, and C or higher in MATH 332, or consent of instructor.
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3.00 Credits
Fall. Completeness and order axioms; limits of sequences; limits of functions and continuity; open, closed and compact sets; uniform continuity; differentiation and the mean value theorem; the Riemann integral. Prerequisites: C or higher in MATH 233 or MATH 235, and C or higher in MATH 322 and MATH 332, or consent of instructor.
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