I will assume students are already familiar with (real and complex) vector spaces, inner products, linear transformations, matrices and matrix algebra, determinants, and eigenvalues and eigenvectors. (These ideas will be reviewed at the beginning of the course, but very quickly.)
You may have seen announcements for this course stating that there would be no official textbook. After seeing the new second edition, I decided that it would be an appropriate textbook, and I will follow it loosely in the course. However, some course topics do not appear in the textbook and some may be covered rather differently than in the book.
Throughout this class, you need to justify your answers even when the problem doesn't explicitly ask for explanation; this typically means writing in complete English sentences. When deciding how much detail to include, here's the standard to keep in mind: your solution to a problem should be complete and clear enough that one of your classmates, who has paid attention in class but hasn't thought about that specific problem yet, could read your solution and understand exactly how it works. If you only try to convince me that you understand the solution, then you almost certainly won't write enough.
Students may work together on homework. However, each student must figure out how to write up his or her own solution to be turned in. That means for example that you and a friend may figure out together how to prove a statement, but the written-out proofs you turn in should not be verbatim copies of each other.
Reading and homework problems will be posted on this page.