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, Aug 31 – Sept 23
Direct methods, Sept 28 – Oct 21
Iterative methods, Oct 26 – Nov 25
Optimization, (time permitting) Nov 30 – Dec 14