Advanced Linear Algebra (Math 390, Spring 2021)

Course Information


Books

SCLA and FCLA by Beezer;
TB and SW are a close fit to our course's goals;
GVL, HJ and DW are encyclopedic reference works;
HLA is meant to be a comprehensive, encyclopedic resource.


Course Calendar

Course Introduction, Vector Spaces (Tuesday, January 19)
Vector Space Properties (Thursday, January 21)
Linear Transformations (Friday, January 22)
Representations (Monday, January 25)
Problem Session (Tuesday, January 26)
Eigenvalues I (Thursday, January 28)
Eigenvalues II (Friday, January 29)
Invariant Subspaces (Monday, February 1)
Problem Session (Tuesday, February 2)
Similarity and Diagonalization (Thursday, February 4)
Similarity and Diagonalization (Friday, February 5)
Characteristic Polynomial (Monday, February 8)
Problem Session (Tuesday, February 9)
Matrices (Thursday, February 11)
Direct Sums, Orthogonal Complements (Friday, February 12)
Review, Problems (Monday, February 15)
Exam 1 (Tuesday, February 16)
Jordan Canonical Form (Monday, February 22)
Jordan Canonical Form (Tuesday, February 23)
Jordan Canonical Form (Thursday, February 25)

Sage

Sage is open-source software for advanced mathematics. There are several ways to use it, here are two of the easiest.

Main website for Sage: Sage Website


Presentation Advice


Project Topics

These are simply suggestions. Some I know well, some I know little about. Some are excellent choices, some will be harder than others. And you are not limited to just these topics. Many of these have been done by UPS students before (see Math 420 Spring 2014), so you need to be sure your approach is substantially different.

Theory
Practice
Applications

This is: http://buzzard.ups.edu/courses/2021spring/390s2021.html
Maintained by: Rob Beezer
Last updated: January 20, 2021