As a grad student at Purdue (2010-2016) I helped organize student seminars in the Math and CS departments. Once I had taken all the courses relevant to my expertise (linear algebra and graph theory), I felt a need for topics courses to bridge the gap between the standard curriculum and the more advanced research tools I saw in scholarly publications.
In Spring 2014 I founded the “PUNLAG” seminar (Purdue University Numerical Linear Algebra Group) for students who wanted to explore advanced topics.
(For abstracts, hover over title)
Standard Graph Algorithms as Generalized Matrix-Vector Products (Bryan Rainey, 3/10/16)Video
Finding a best rank-1 approximation in the 1-norm (Varun Vasudevan, 3/3/16)
An Introduction to Information Based Complexity Theory (Nicole Eikmeier, 2/18/16) Video
Totally Unimodular Matrices in Linear Programming (Nate Veldt, 1/14/16) Video
The Gauss-Southwell method: intro and applications (Kyle Kloster, 10/2015)
The Fiedler and PageRank vectors, Part 2 (Kyle Kloster, 10/2015)
The Fiedler and PageRank vectors, Part 1 (Kyle Kloster, 10/2015)
Circulant matrices, the FFT, and eigenvalues: Part 2 (Kyle Kloster, 4/6/15)
Intro to circulant matrices and the Fourier transform (Kyle Kloster, 3/30/15) Video
The matrix representation of fast multipole method (FMM) in 1D (Difeng Cai, 3/23/15) Video
Erasure coding for linear system solvers (Yao Zhu, 3/20/15) Video
Intro to Fast Multipole Method (Nicole Eikmeier, 3/9/15) Video
Matrix Calculus, and Functions of Matrices (Kyle Kloster, 3/2/15)
Sources: Functions of Matrices (Higham, 2008); Matrix Calculus and Zero-One Matrices (Turkington, 2002); These excellent slides from Pedar Olsen, Steven Rennie, and Vaibhava Goel; and to see just how much a headache notation can be, see the wikipedia page on this topic.
Fast Solvers for HSS Eigenvalue Problems (Jimmy Vogel, 2/23/15) Video 1, Video 2
Fast Solvers for HSS Linear Systems (Jimmy Vogel, 2/16/15) Video
An Introduction to Rank Structured Matrices (Jimmy Vogel, 2/9/15) Video
Introduction to Kronecker Products 2 (Kyle Kloster, 2/2/15) Video
Introduction to Kronecker Products 1 (Kyle Kloster, 1/26/15) Video
Krylov and QR and polynomials (Kyle Kloster, 1/15/15) Video
Back in 2014 when I founded the seminar I compiled the following list of courses most relevant to the themes of the seminar.
MA511 Applied Linear Algebra (~every semester, maybe FA?)
Note, 511 is probably more useful for people interested in numerical linear algebra from a practical standpoint. 554 is much more about pure math theory, whereas 511 supplies the theory for people interested in applying it.