Course subject: Computational Mathematics (CM)

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.

Visualization methods applied to data. Both human perception and statistical properties inform the methods used to display and visually explore categorical, continuous, time-ordered, map, and high dimensional data. Order and layout effects on tables and graphics. Statistical concepts visually presented include variability, densities, quantiles, conditioning, and hypothesis testing. Interactive graphics include linking, brushing, motion, and the navigation of high dimensional spaces guided via projection indices. Glyphs (e.g. cartoon, statistical, or heatmap) and radial and parallel coordinates.

This course introduces modern applied regression methods for continuous response modelling, emphasizing both explainability and predictive power. Topics cover a wide selection of advanced methods useful to address the challenges arising from real-world and high-dimensional data; methods include robust regression, nonparametric regression such as smoothing splines, kernels, additive models, tree based methods, boosting and bagging, and penalized linear regression methods such as the ridge regression, lasso, and their variants. Students will gain an appreciation of the mathematical and statistical concepts underlying the methods and also computational experience in applying the methods to real data.