I’ll be teaching a course on quantum mechanics this year here at Columbia, from a point of view aimed somewhat at mathematicians, emphasizing the role of Lie groups and their representations. For more details, the course webpage is here.

The course is being taught online using Zoom, with 37 students now enrolled. I’ve set things up in my office to try and teach using the blackboard there, and will be interacting with the students mostly via Zoom. As an experiment, I’ve also set up a Youtube channel. If all goes well you should be able to find a livestream of the class there while it’s happening, which is scheduled for 4:10-5:25 Tuesdays and Thursdays, starting tomorrow, September 8. I’ll also try and make sure the recorded livestreams get uploaded and saved at this playlist. Unfortunately I won’t be able to interact with people watching on Youtube, should have my hands full trying to get to know the students enrolled here in the course, with only this virtual connection.

Peter, making your course widely available is really good of you. Thanks.

Hello Peter. The link from your syllabus to John Preskill’s lecture notes on quantum computation (http://www.theory.caltech.edu/people/preskill/ph229) is giving me Caltech’s 404 page, both with and without the #lecture anchor.

I taught graduate statistical physics via Zoom back in the spring. It’s definitely a different experience than lecturing live, with a lot less feedback. With the students on mute, you of course don’t get the laughs at little jokes, and because everyone is visible in tiny boxes if at all, body language is much harder to read. It can feel like speaking into a void. But I still got reasonable questions in the video chats and by e-mail, the performance on problem sets and the midterm was in line with my expectations, and the final presentations that the students gave went well.

Good luck!

Interacting with students is quite challenging in this remote setting. I suggest having a shared Google Doc between you and your students where students can give their feedback and ask questions increasing interaction in students themselves and Zoom chat is not really that easy to navigate. Furthermore, A YouTube channel named 3blue1Brown, which just started doing some live streaming, published an article with some tips for remote lessons like live quizzing, etc that you may find useful to integrate in your system. (https://www.3blue1brown.com/blog/livestream-setup ). Thanks for making the lectures public.

That’s really cool, but can you also try to make your PSets/Assignments widely available?

You should check out Richard Borcherd’s Youtube channel. At the moment it has great content for undergrads. Definitely worth keeping an eye on (sorry if I posted this comment twice!)

Use a visualizer. The quality is much better than with a blackboard, unless you have a seriously good camera and audio equipment. They’re going for $100 on Amazon.

Jeff Berkowitz,

Thanks. Fixed.

E.K. Shaji,

The assignments will be pretty much the ones in the book, although I may be revising those and adding some more. They’re listed on the course page

https://www.math.columbia.edu/%7Ewoit/QM/fall2020.html

Peter, will you be placing solutions to problems on your web page for those watching on Youtube?

I,

No, I won’t be making solutions to the problems available. Having solutions to problems available makes people less likely to engage with the whole point of such things. What’s important is not solving a problem, it’s what you learn by struggling with understanding how to solve the problem.

Peter,

Doesn’t putting the solutions up a few weeks after each problem set have the same benefits? Plus the students get feedback on whether they’re right. Alternatively, you could stream lectures where you go over the problems afterwards.

Michael Ball,

Richard’s name is Borcherds, not Borcherd.

I,

I generally go over some of the problems that students have had trouble with in class, likely will also do that this year, so that would be on the videos. The “give solutions to the students after the problems are due” model only works if everyone is doing the problems with the same due date, and the solutions don’t become public. I hope lots of people are reading the book, and now watching the lectures, at very different times, and best for all of them if they struggle through the problems.

Something one doesn’t appreciate as a student typically is that it’s quite hard to come up with good problems at the right level. The problems in the book took a lot of effort to come up with, and they are not that great, could use a lot more work to improve them and come up with more. I hope to do some of that this year, but it’s a task I find difficult and not rewarding (even though it really is important for the students).

Robert A. Wilson

Noted

Thanks for making available. Zoom screen sharing could let you display PowerPoint or other visuals prepared in advance and might let the discussion flow more smoothly, avoiding delays while something gets written on the chalkboard. Also, not pushing for speed and thus avoiding false starts might result in a similar overall pace.

Bill93,

Thanks for the comments/suggestions, that’s helpful.

I should probably make much more explicit the relation of what I’m doing in class to the book. For most of the lectures, essentially I’ll be going over one chapter of the book, but what I’m not trying to do is give a polished lecture covering everything in that chapter. Instead the idea is to try and emphasize the main ideas, go over confusing points carefully, encourage students to stop me with questions and have lots of time for them.

I could in principle screen share the page of the book corresponding to what I’m talking about. What would really be ideal is if students try reading the chapter beforehand, mark it up with their questions, then during the lecture stop me if their question is not clarified by what I say when I get to that point (sorry to those of you on Youtube who can’t ask questions. If people email me questions before the lecture I may or may not be able to say something about them during the lecture).

Hi Peter,

I look forward to the rest of this series. One slight issue: when I try to save the first video to watch later, Youtube tells me that this is forbidden since “This action is turned off for content that is made for children.”

Do you happen to know how this might be overcome?

pmcs,

Thanks for pointing this out. That should be fixed now. I had selected a “for kids” option, thinking that meant “all right for kids” (why shouldn’t kids be learning about unitary Lie algebra representations?). Instead it meant “intended for kids”, which is different.

Students of this class might also enjoy A. Zee’s book titled “Group Theory in a Nutshell for Physicists.” It’s an excellent tour of the Lie groups and why we care about them; kind of a much more fleshed-out and beginner-friendly version of Georgi’s famous “Lie Algebras in Particle Physics.”

Another nice resource is Frederic P Schuller’s “Lectures on the Geometric Anatomy of Theoretical Physics” on YouTube, which is a sort of grand tour of the relevant mathematical structures starting with the definition of sets, topology, fields, groups, etc. He has a shorter “winter school” version that also includes some exercises.

Thanks for making your lectures and text available here – I’ve enjoyed the first several lectures and hope to continue!