Below are my lecture notes from the remote class, written in real-time over Zoom. View (at your own peril -- errors likely abound!) by clicking the dashed arrows. Some super-cool stuff is highlighted via yellow text.
References for these lecture notes include Axler's Linear Algebra Done Right, Katznelson's A Terse Introduction to Linear Algebra, math3ma, and various other versions of this course (Akshay Venkatesh, Sheel Ganatra).
Discussion: What is a proof? When is a proof? Why is a proof?
A definition of a vector space over the real numbers, with examples.