I have a tip for following lectures (or any technical talk, really) that I've been meaning to write about for a while. As you follow along with the speaker, try to predict what they will say next. These can be either local or global predictions. Guess what they will write next, or what will be on the next slide. With some practice (and exposure to the subject area) you can usually get it right. Also try to keep track…
Essentially the lectures served as an inefficient way of delivering me a set of notes which I’d then reference during homework sessions. I could often predict what was coming next in the lecture but the really hard parts were the key parts in some technical lemmas that were necessary to complete the theorem. Learning how to figure out a key step like that had to come completely on my own (with no spoilers).
In a lot of ways, math lectures really started to turn into an experience similar to watching a Let’s Play of a favourite video game. Watching those can tell you exactly what you need to do to get past the part where you’re stuck but they don’t in general make you better at video games. For that you need to actually play them yourself.