So here is a bit of context: a while back (June-July), I studied a little bit of Abstract Algebra from an introductory book. Now, I would like to study more, in a complete fashion, using Herstein's book "Topics in Algebra". But I don't really know how to do it.
The first time around, I followed my usual self-study routine: write down definitions, theorems and some examples, and, in between, try to explain to myself the meaning of some things, as I would if I had to teach someone who has never seen it before. After that, I would do some exercises (mostly the harder ones) and move on to the next chapter. This routine worked really well for me whenever I used it, and I seem to remember a lot (not very surprising, since I am pretty much mimicking what I'd do on a formal class).
However, now will be my second time seeing many concepts and I feel like writing everything down again will be sort of... unnecessary? I have never done this before, studying something only to study the same thing again but deeper, so I have no idea how to adapt my study routine to this case...
I know it is a very personal subject, but do you guys have any tips? Have you ever been through this? Any help is greatly appreciated!
Thanks in advance!