Spring 2014 Course Notes
Math 57 - A Second Course in Linear Algebra: Working Group
This course will explore various topics that get short shrift in first linear algebra courses, or don't get reached at all. Sample topics are below. Will be run as a seminar if enrollment is small enough. While I will lecture on some topics at the start, eventually most of the material will be taught through student presentations. I know only some of this material and look forward to learning more with you.
Text: None, but multiple copies of several books will be on reserve and some material is freely available online.
Homework: Problems and projects; On some material I will distribute problem sets, which I hope we will discuss in class, in the style of M28S. Students will need to choose homework problems for material they lecture on.
Prerequisites: Math 28/28S, or some proof-oriented course in addition to Math 27 or equivalent.
- linear functionals, dual and double dual spaces
- complex vector spaces and matrices
- extensions of diagonalization (symmetric matrices, Jordan form)
- quadratic forms and positive forms
- additional factorizations: singular value and polar form
- matroids and other independence systems
- numerical linear algebra (efficient and accurate algorithms)
- linear algebra gems and applications introduced by you
Usually M29 is a W course, with an enrollment cap. However, this spring M29 will tentatively *not* be a W course, so that the enrollment need not be capped and the anticipated heavy enrollment can be accepted. (Heavy enrollment is anticipated because the course has been lotteried the last 2 times it was offered and we do not have staff to offer an extra section.) If the enrollment turns out to be 20 or less, the W will be reinstated. If the enrollment is higher, we hope to meet all the pent-up demand and return to the usual W status in the future.
Either way, I will cover the same topics this spring that I usually cover, with the same algorithmics flavor; but without a W there will be no papers and there will probably be a second midterm instead. Those students who must have another NSE W course should not expect to get it from M29 this spring.