/sci/ - Science & Math

Why did he choose to throw his life away?

>>10066896 >>10066754
math fags unironically die virgin

>>10030779

How are some people so smart? What goes on in their heads? Do they experience reality differently? How can a 19 year old have such a grasp of mathematics that some people strive for their entire lives and never reach?

Are any lads here still about to take finals this week? Got both my real analysis and abstract algebra finals on Tuesday and it's safe to say I'm boned.

I've been studying Galois theory, and things haven't really been clicking for me at all, I feel like I'm missing the "big picture" or something. Everything feels pretty unmotivated. Broadly, I don't really know why do we care about field extensions. Some of the more specific definitions are difficult for me to swallow, not technically, but really I don't feel like I know what exactly they're supposed to capture. For example, in ring theory, being a Euclidean domain means you can do division like in the integers, being a UFD means you have something analogous to prime factorization, being a PID means that ideals end up always having a simple form. I don't feel I have this sort of understanding for splitting fields, normal extensions, the automorphism group, etc.

If anyone has some thoughts on this, it would be appreciated. I'd also be open to book suggestions. I've been using Dummit and Foote, which seems ok but not great on this topic to me at least.