====== IAM 961 course outline ======

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 
    * linear algebra review: mat-vec mult, inverses, rank, span, etc.
    * orthogonality, norms, SVD
    * Trefethen lectures 1 -- 5
 

**Direct methods**, Sept 28 -- Oct 21
    * QR factorization: Gram-Schmidt and modified Gram-Schmidt algorithms, Householder algorithm, least squares
    * conditioning, stability, and accuracy
    * LU decomposition (a.k.a. Gaussian elimination), pivoting
    * Trefethen chapters 6-23

**Iterative methods**, Oct 26 -- Nov 25
    * eigenvalue algorithms: Rayleigh quotient, inverse iteration, QR algorithm, shifts
    * SVD algorithms
    * Krylov subspace methods: Arnoldi iteration, GMRES, and conjugate gradients
    * Trefethen chapters 24-40

**Optimization**, (time permitting) Nov 30 -- Dec 14
    * Newton's method, trust-region modifications