Math 310 — The Classical Matrix Groups
Spring 2020

Instructor: Elizabeth Meckes
Office: Yost 208
Phone: 368-5015
Email: ese3 [at] cwru.edu
Office Hours: MWF, 2-3, or by appointment.

Textbook:
Matrix Groups for Undergraduates, 2e, by Kristopher Tapp

Course web page:
http://www.cwru.edu/artsci/math/esmeckes/math310/.

All course information is posted here.

About this course:
This course gives an introduction to the classical matrix groups: the orthogonal and special orthogonal groups, the unitary and special unitary groups, and the symplectic group. The classical groups are used as a vehicle to introduce and connect a wide variety of topics within mathematics, ranging from linear and abstract algebra to topology and geometry to representation theory. Topics include the topology of the groups, Lie algebra structure, Riemannian structure, the Lie bracket, and the adjoint representation.

Prerequisites:
MATH 307 is required. MATH 308 would be helpful but is not required; I will fill in group theory background as needed, depending on the audience.

Course plan:
Mondays and Wednesdays will be lectures. Fridays will be student presentations of problems. You should do as many of the problems from the book as you can as we go along (I'll let you know which ones we've covered enough for as we go), and on Fridays we will go through the problems with students volunteering to present their solutions. I will not assign specific problems to specific students, but you are expected to present on a regular basis.

Attendance:
Attendance at every class is required. If you ever need to miss class because of travel or other pre-arranged circumstances, let me know as soon as you know yourself. If you have to miss class due to illness or other emergency, let me know as soon as you are able.

Reading:
I won't be able to cover every detail from the book in class; you are expected to read the book as we go.

Scribing:

Each Friday, one student will be the designated scribe. It will be their job to take good notes on the solutions presented and to type up clean versions of all those solutions. The scribe will submit their typed solutions to me one week after the problem session at which they served as scribe. I will give notes and suggested revisions, and the final version will be submitted to me and to the rest of the class one week later.

Grading:
Your course grade will be computed as follows: