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This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.
Introduction to quantum computing and quantum information theory, formalism of quantum mechanics, quantum gates, algorithms, measurements, coding, and information. Physical realizations and experiments. Crosslisted with PHYS 4782
Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems
A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.
The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem
Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces
Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.
Topics from complex function theory, including contour integration and conformal mapping
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series
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