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Course Criteria
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4.00 Credits
An introduction to the theory of knots and links. Topics covered include Reidemeister moves, knot invariants, including 3-colorings, the linking number, the Alexander polynomial, the Kauffman bracket and Jones polynomial. As time permits, some applications in biology and/or chemistry will be discussed. Prerequisite: MATH 3121.
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4.00 Credits
Introduction to theory of functions of complex variables. Prerequisite: MATH 3300.
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4.00 Credits
Pointwise and uniform covergence, Taylor series, Riemann integration, sets of measure zero, Lebesgue's theorem on the Riemann integral, the metric space of continuous functions, and selected topics. Prerequisite: MATH 3300.
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4.00 Credits
Topological spaces, metric spaces, continuity, connectedness and compactness. Prerequisite: MATH 3300.
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4.00 Credits
Differential equations of physics: the wave equation, the heat equation, Laplace's equation; boundary-value problems. Elementary Sturm-Liouville theory, Fourier series, Fourier and Laplace transforms, Bessel functions, selected topics. Prerequisite: MATH 3331.
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4.00 Credits
Introduction to dynamical systems and applications. Variational calculus, Lagrangian dynamics, principle of critical action, Hamiltonian systems and symplectic mechanics, Hamilton-Jacobi equation, chaotic and nonlinear systems, fractals. Prerequisites: MATH 3100, 3300, 3331, or consent of instructor.
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4.00 Credits
Continuation of MATH 3750. Numerical solution of linear systems, matrix norms, approximation of functions, algebraic eigenvalues. Prerequisite: MATH/CS 3750.
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4.00 Credits
Sequel to MATH 3841. Topics to be drawn from linear and/or nonlinear programming. Linear programming topics may include integer programming, game theory, network programming; nonlinear programming topics include optimality conditions and solution procedures for unconstrained and constrained optimization problems. Prerequisite: MATH 3841. May be repeated once for credit with consent of the chair, for a maximum of 8 units.
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4.00 Credits
Topics selected from quasi-Newton methods for multi-variable unconstrained optimization; nonlinear least squares; quadratic programming; constrained optimization with nonlinear constraints; convex optimization. Prerequisites: MATH 3750 and 3841 or permission of instructor. May be repeated once for credit, with consent of the Mathematics Graduate Studies Committee, for a maximum of 8 units.
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4.00 Credits
(See CS 4845 for course description.)
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