For more detailed course information, click on a course title below.
Computational Mathematics (CM) 730 Introduction to Symbolic Computation (0.50) LEC
Course ID: 000626
An introduction to the use of computers for symbolic mathematical computation, involving traditional mathematical computations such as solving linear equations (exactly), analytic differentiation and integration of functions, and analytic solution of differential equations.
Computational Mathematics (CM) 740 Fundamentals of Optimization (0.50) LEC
Course ID: 012176
Linear optimization: Farkas' Lemma, duality, Simplex method, geometry of polyhedra. Combinatorial optimization: integrality of polyhedra, total unimodularity, flow problems, weighted bipartite matching. Continuous optimization: convex sets, Separation Theorem, convex functions, analytic characterizations of convexity, Karush-Kuhn-Tucker Theorem.
Computational Mathematics (CM) 750 Numerical Solution of Partial Differential Equations (0.50) LEC
Course ID: 000724
Discretization methods for partial differential equations, including finite difference, finite volume and finite element methods. Application to elliptic, hyperbolic and parabolic equations. Convergence and stability issues, properties of discrete equations, and treatment of non-linearities. Stiffness matrix assembly and use of sparse matric software. Students should have completed a course in numerical computation at the undergraduate level.
Computational Mathematics (CM) 761 Computational Inference (0.50) LEC
Course ID: 003090
Introduction to and application of computational methods in statistical inference. Monte Carlo evaluation of statistical procedures, exploration of the likelihood function through graphical and optimization techniques including EM. Bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods.
Computational Mathematics (CM) 762 Data Visualization (0.50) LEC,TUT
Course ID: 012612
Visualization of high dimensional data including interactive methods directed at exploration and assessment of structure and dependencies in data. Methods for finding groups in data including traditional and modern methods of cluster analysis. Dimension reduction methods including multi-dimensional scaling, nonlinear and other methods.
Computational Mathematics (CM) 763 Statistical Learning - Classification (0.50) LEC
Course ID: 003091
Given known group membership, methods which learn from data how to classify objects into the groups are treated. Review of likelihood and posterior based discrimination. Main topics include logistic regression, neural networks, tree-based methods and nearest neighbour methods. Model assessment, training and tuning.
Computational Mathematics (CM) 764 Statistical Learning - Function Estimation (0.50) LEC
Course ID: 003092
Methods for finding surfaces in high dimensions from incomplete or noisy functional information. Both data adaptive and methods based on fixed parametric structure will be treated. Model assessment, training and tuning.
Computational Mathematics (CM) 770 Numerical Analysis (0.50) LEC
Course ID: 012670
Introduction to basic algorithms and techniques for numerical computing. Error analysis, interpolation (including splines), numerical differentiation and integration, numerical linear algebra (including methods for linear systems, eigenvalue problems, and the singular value decomposition), root finding for nonlinear equations and systems, numerical ordinary differential equations, and approximation methods (including least squares, orthogonal polynomials, and Fourier transforms).