[todd8]

I've had 4 semesters of abstract algebra because I was a math major. I found even the first two semesters difficult courses. Math had always come easy to me when I was young so I didn't really understand that at the university level mathematics would require some serious study; naturally, I would have gotten a lot more out of the early algebra classes if I had put more work into them.

I had much better intuition for analysis than for algebra. The results in algebra are just more surprising than those in analysis for me. My attempts at proofs in algebra were kind of like random-walks where I would eventually stumble upon the answer and then I would have to reconstruct the logical steps to get there without all of the unnecessary circumlocution.

Years later, as a much better student, I took a graduate course in group theory and really enjoyed it because I actually spent some time studying the subject.

I really love the way that abstract algebra deals with such simple, almost meager entities: sets with just a few basic operators. The theorems about these completely abstract, virtual and not actual things, reveal properties that are foundational for all math and somehow underly our reality.