# Appendix A - Courses

## Mathematics

MATH*6011 Dynamical Systems I U [0.50]
Basic theorems on existence, uniqueness and differentiability; phase space, flows, dynamical systems; review of linear systems, Floquet theory; Hopf bifurcation; perturbation theory and structural stability; differential equations on manifolds. Applications drawn from the biological, physical, and social sciences.
MATH*6012 Dynamical Systems II U [0.50]
The quantitative theory of dynamical systems defined by differential equations and discrete maps, including: generic properties; bifurcation theory; the center manifold theorem; nonlinear oscillations, phase locking and period doubling; the Birkhoff-Smale homoclinic theorem; strange attractors and deterministic chaos.
MATH*6021 Optimization I U [0.50]
A study of the basic concepts in: linear programming, convex programming, non-convex programming, geometric programming and related numerical methods.
MATH*6022 Optimization II U [0.50]
A study of the basic concepts in: calculus of variations, optimal control theory, dynamic programming and related numerical methods.
MATH*6031 Functional Analysis U [0.50]
Review of metric, normed, and inner product spaces; Banach contraction principle; brief introduction to measure and integration; elementary Fourier analysis; adjoint and compact operators; nonlnear operators and the Frechet derivative; Baire category theorem; principle of uniform boundedness; open mapping theorem; principle ot uniform boundedness; closed graph theorem.
MATH*6041 Partial Differential Equations I U [0.50]
Classification of partial differential equations. The Hyperbolic type, the Cauchy problem, range of influence, well- and ill-posed problems, successive approximation, the Riemann function. The elliptic type: fundamental solutions, Dirichlet and Neumann problems. The parabolic type: boundary conditions, Green's functions and separation of variables. Introduction to certain non-linear equations and transformations methods.
MATH*6042 Partial Differential Equations II U [0.50]
A continuation of some of the topics of Partial Differential Equations I. Also, systems of partial differential equations, equations of mixed type and non-linear equations.
MATH*6051 Mathematical Modelling U [0.50]
Selected advanced topics in mathematical modelling, possibly in conjunction with the departmental Mathematics and Statistics Clinic.
MATH*6071 Biomathematics U [0.50]
The application of mathematics to model and analyze biological systems. Specific models to illustrate the different mathematical approaches employed when considering different levels of biological function.
MATH*6091 Topics in Analysis U [0.50]
Selected topics from topology, real analysis, complex analysis, and functional analysis.
MATH*6400 Numerical Analysis I U [0.50]
Topics selected from numerical problems in: matrix operations, interpolation, approximation theory, quadrature, ordinary differential equations, partial differential equations, integral equations, nonlinear algebraic and transcendental equations.
MATH*6410 Numerical Analysis II U [0.50]
One or more topics selected from those discussed in Numerical Analysis I, but in greater depth.
MATH*6990 Mathematics Seminar U [0.00]
Students will review mathematical literature and present a published paper.