Basic course description
Math 207a is a topics course in the basic theory of Hopf algebras. Enrollees should have taken Math 200b or have equivalent experience with graduate level algebra including tensor products.
Syllabus
Lectures Lectures will be prerecorded--- see the information below. Most likely there will be two longer lectures rather than 3 each week. I recommend you set standard times each week to watch the lectures (for example our scheduled class time) to keep yourself on track, but you may choose to watch them whenever is convenient for you.
Accessing Lectures We are recording lectures using EVT, an lecture capture and notetaking system. To access recordings: see the instructions sent separately by e-mail. If you would like to audit the course, please e-mail the instructor to get access instructions.
Homework Homework problems will be posted at the right side of this page. You are not required to hand in written solutions, but I encourage you to work through as many as possible. Once weekly the class will convene on Zoom to discuss homework problems and I will ask several students (arranged beforehand) to present their solutions to some problems. I plan to have these homework discussions Fridays 4-5pm, our usual class time, as that should not conflict with your other classes.
Grading Your grade in the class will be based on your participation in the homework discussions. Every registered student should plan to present a solution at some point.
Office hours I will not schedule regular office hours, but I will happily meet any student on Zoom by appointment. I will set up a Piazza page and I encourage mathematical questions to be posted there so everyone can participate in the discussion. You will receive an invitation to the Piazza page if you are registered. If you are not registered but would like to be invited to join the Piazza page send me an e-mail.
References The lectures will not follow any particular book, though there are many books which contain this basic material. In addition to the lectures, I will try to post some course notes. As a good basic reference I recommend Susan Montgomery's book "Hopf Algebras and their actions on Rings", which is available in paperback or e-book from the AMS bookstore at a reasonable price. I am not aware of any free online access to Montgomery's book. Another basic reference is "Hopf Algebras" by David Radford. Normally our campus does not have an e-copy of Radford's book but it is available in a library of e-books that we have temporary access to this quarter through Proquest's e-book central. To access it, first get on the university network using a VPN, so you have access to library resources. Then go to https://ebookcentral.proquest.com/lib/ucsd/home.action and search for Radford's book.