Limited-Edition Courses Upper Division & Graduate Courses

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Fall 2015

Math 213B: Introduction to Riemannian Geometry

Professor Simic; MW 10:30 am - 11:4 5am

Riemannian metric and Levi-Civita connection. Geodesics, completeness and Hopf-Rinow theorem. Curvature. First and second variations of arc-length. Spaces of constant curvature. Additional topics selected by the instructor such as theorems of Myers, Hadamard, Synge, and Gauss-Bonnet.

213b reimann

Prerequisite: Math 213A or instructor consent.

Math 238: Advanced Complex Variables

Professor Obaid; TR 10:30 am - 11:45 am

A course specializing in one or more of the advanced branches of the theory of complex functions.

Prerequisite: Math 138 or instructor consent.

Math 131B: Approximations and Function Spaces

Professor Hsu; MW 12:00 pm - 1:15 pm

This course looks at the question: what's the best way to approximate a given function by "good" functions, such as polynomials or sums of trigonometric functions?

The search for the precise meaning of "best" leads to the idea of a spaces of functions, and most prominently, the function spaces known as Hilbert spaces.  We will combine a study of the fundamentals of Hilbert spaces, harmonic analysis (e.g., Fourier series), and operator theory, with applications.

Prerequisite: Math 131A or instructor consent.