As I was reading over Galois' wikipedia page, I noticed that he (Galois) read a book called "Réflexions sur la résolution algébrique des équations" at age 15, which I then read has to do with the Lagrange resolvent of polynomial equations, and from there I somehow got to the fundamental theorem of algebra blah blah blah you know how wikipedia is...
And to make a long story short, I realized that there seems to be a heck of a lot of very complex, interesting-looking algebra (especially on the proof side of things) that I didn't even get close to in Algebra 1 and 2 back before I even knew what a proof was. I'm just wondering whether it's worth it to go back and look over some of the "advanced algebra" the we glossed over in early high school.
I recently finished calc 1 and I'm currently learning some basic set theory/logic/proof-writing stuff (reading How to Prove it) because I started to get interested in proof construction.
I plan to read Spivak's this summer (I'll be a freshman in college next fall), but is it worth it to also go back to stuff the we only learned superficially in 9-11th grade or will I get into that in abstract algebra and whatnot in the years to come?
Sorry about how long this was… the background on my excursions on wikipedia was probably unnecessary.