We will follow Trefethen and Bau's text pretty closely, chapter by chapter. Here's a slightly different conceptual organization of the course than provided by Trefethen and Bau's table of contents, with rough dates. By the end of the semester, you should have a pretty good grasp of each of the topics mentioned herein.
Fundamentals, Sept 1 – 22
Direct methods, Sept 24 – Oct 22
Iterative methods, Oct 27 – Nov 26
Optimization, (time permitting) Dec 1 – Dec 10