Math 115A

Summary

This course has two different roles in the UCLA curriculum

• This is the second course in linear algebra. It begins with abstract vector spaces, reviewing concepts from the first course in this more abstract setting. The course then covers additional topics, including product and quotient spaces, dual vector spaces, inner product spaces, adjoints, real and complex eigenvalues and eigenvectors, and self-adjoint and normal operators.

• This is the first proof writing course many students encounter and so it focuses on writing techniques and style. This includes explicit instruction on logic, and various proof techniques, including proof by contrapositive, proof using quantifiers, proof by induction, and proof by contradiction.

I taught this course in Winter 2021 and am scheduled to teach this course in Winter 2022.

I teach this course with a partially flipped format and with an emphasis on active learning and team learning.

Sample materials

Here is a copy of the syllabus

Here are some sample HW assignments- Note many of these problems are taken from Axler's Linear Algebra Done Right

Some class days are run in a flipped format. This means that students watch a pre-recorded video (sample) in place of the lecture (and we instead spend class time doing exercises together.

Here are some sample Groupwork assignments. Group work is done with your assigned team, and with the assistance of the instructor, the TA, and the LAs. We're always looking for more LAs for this course, so if you have taken this course and are interested in math education please consider applying.