Appendix A - Courses
Mathematics
| MATH*6010 Analysis U [0.50] |
|---|
| Half the course covers metric spaces, normed linear spaces, and inner product spaces, including Banach's and Schauder's fixed point theorems, Lp spaces, Hilbert spaces and the projection theorem. The remaining content may include topics like operator theory, inverse problems, measure theory and spectral analysis. |
| 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*6020 Scientific Computing U [0.50] |
|---|
| This course covers the fundamentals of algoithms and computer programming. This may include computer arithmetic, complexity, error analysis, linear and nonlinear equations, least squares, interpolation, numerical differentiation and integration, optimization, random number generators, Monte Carlo simulation; case studies will be undertaken using modern software. |
| 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; nonlinear 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] |
|---|
| The process of phenomena and systems model development, techniques of model analysis, model verification, and interpretation of results are presented. The examples of continuous or discrete, deterministic or probabilistic models may include differential equations, difference equations, cellular automata, agent based models, network models, stochastic processes. |
| 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*6181 Topics in Applied Mathematics I U [0.50] |
|---|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
| MATH*6182 Topics in Applied Mathematics II U [0.50] |
|---|
| This course provides graduate students, either individually or in groups, with the opportunity to pursue topics in applied mathematics under the guidance of graduate faculty. Course topics will normally be advertised by faculty in the semester prior to their offering. Courses may be offered in any of lecture, reading/seminar, or individual project formats. |
| 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. |