My research requires a strong background in analysis, differential equations, and linear algebra, plus the numerical aspects of these subjects. It is important to begin establishing a strong foundation in the first two years so that by the time you begin working on a thesis project, you can enroll in advanced (600+) graduate courses in order to begin acquiring the detailed knowledge needed for the project.
In the first two-three years:
Analysis: M517, M617, M618
Statistics and Probability: ST520, ST521, ST720
Linear Algebra: M560
Partial Differential Equations: M545, M546, M645
Numerical Methods for Partial Differential Equations: M550 or M652
In order to decide if we should work together on a thesis project, I will ask you to do a reading course in which we choose an advanced graduate textbook in an area of mutual interest and then you lecture me on the main ideas in the book once a week over a semester or two. This should be undertaken in the second or third year of studies.
Courses that you will take sometime before you leave:
Complex Analysis: M519
Ordinary Differential Equations I: M640
Dynamical Systems: M540
Variational Methods and Optimization: M620, M621
Other topics of interest include any of the topology courses, differentiable manifolds, linear and nonlinear programming