8 graduate courses in the Spring 2025 Graduate Calendar.
From the Spring 2025 Graduate Calendar. Also this year: Fall 2024, Winter 2025.
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.
Archived calendar entryRequirements, Spring 2025Course outlines
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.
Archived calendar entryRequirements, Spring 2025Course outlines
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.
Archived calendar entryRequirements, Spring 2025Course outlines
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. Topics include expectation-maximization, bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods.
Archived calendar entryRequirements, Spring 2025Course outlines
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.
Archived calendar entryRequirements, Spring 2025Course outlines
Classification is the problem of predicting a discrete outcome from a set of explanatory variables. Main topics include logistic regression, neural networks, tree-based methods, support vector machines and nearest neighbour methods. Other topics include model assessment, training and tuning.
Archived calendar entryRequirements, Spring 2025Course outlines
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.
Archived calendar entryRequirements, Spring 2025Course outlines
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).
Archived calendar entryRequirements, Spring 2025Course outlines