http://hdl.handle.net/1721.1/33995 Mathematics (18) http://hdl.handle.net/1721.1/49826 18.950 Differential Geometry, Spring 2005 Wickramasekera, Neshan Geethike This course is an introduction to differential geometry. Metrics, Lie bracket, connections, geodesics, tensors, intrinsic and extrinsic curvature are studied on abstractly defined manifolds using coordinate charts. Curves and surfaces in three dimensions are studied as important special cases. Gauss-Bonnet theorem for surfaces and selected introductory topics in special and general relativity are also analyzed. From the course home page: Course Description This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied. Sun, 29 May 2005 22:58:59 GMT http://hdl.handle.net/1721.1/49827 18.440 Probability and Random Variables, Fall 2005 Dudley, R. M. (Richard M.) This course introduces students to probability and random variable. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem. Mon, 28 Nov 2005 22:58:59 GMT http://hdl.handle.net/1721.1/49508 18.175 Theory of Probability, Spring 2007 Panchenko, Dmitry A. Laws of large numbers and central limit theorems for sums of independent random variables, conditioning and martingales, Brownian motion and elements of diffusion theory. Tue, 29 May 2007 22:58:59 GMT http://hdl.handle.net/1721.1/49420 6.854J / 18.415J Advanced Algorithms, Fall 2001 Goemans, Michel A first-year graduate course in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Data structures. Network flows. Linear programming. Computational geometry. Approximation algorithms. Alternate years. From the course home page: Course Description This is a graduate course on the design and analysis of algorithms, covering several advanced topics not studied in typical introductory courses on algorithms. It is especially designed for doctoral students interested in theoretical computer science. Wed, 28 Nov 2001 22:58:59 GMT