Someone showed my a very very elegant proof of a simple fact: The number of even sized subsets of a set is the same as the number of odd sized subsets, proof: sum even binomial coefficients - sum of odd binomial coefficients $= (1-1)^n$.
I got very stuck on the second part of problem 0.6 in Reid. I solved the first part though. I thought I would power through this book and have no trouble doing anything but I guess not. Anyway I can't concentrate well on maths today because I'm stressed about my future.
Having RSI is extremely limiting and I don't know how I will generate income for myself. I am scared.
Next day,
The problem I got really stuck on (on chapter 0 of the book! mean..) was what are the k-automorphisms of $k(T)$. I managed to solve the problem about $k[T]$ using the degree. It turns out you can generalize that approach to solve the harder one: <https://drexel28.wordpress.com/2012/02/28/automorphisms-of-ktk/>
It was frustrated and it made me want to give up on the book but that's not a good attitude. There's no reason why you should be able to solve every single thing, I guess?
Next there was a good chapter about ideals including a nice isomorphism result I had come up with earlier when doing algebraic number theory. I did most of the problems for it too.
After that modules!
The modules stuff is really cool - the theory includes stuff like determinants and how that proves nakayama lemma as well as short-exact-sequences. I worked on this section and tried to prove the results before reading any proofs in the book - that really helped to understand it better.
Next up the problems from the modules section...
I'm glad I got past the bit I couldn't do in chapter 0 and continued the book - it's a nice feeling of progress.