(September 27, 2018 at 7:13 pm)Kernel Sohcahtoa Wrote:(September 27, 2018 at 8:07 am)polymath257 Wrote: How far into the abstract algebra did you get? I always really enjoyed Galois theory. That there is a *proof* that 5th degree polynomials can't be solved via radicals is just *fun*. But you need to do quotient rings and some field theory first.
Thanks for your reply, Polymath. Galois Theory sounds exciting; however, I'm eager to take a break from abstract algebra and explore another topic.
That said, I've studied the following topics: groups; fundamental theorems of groups; cyclic groups; subgroups; direct products; functions; symmetric groups; equivalence relations and cosets (I really enjoyed this section); counting the elements of a finite group; normal subgroups and quotient groups (this section was neat); homomorphisms (these are cool); homomorphisms and normal subgroups (I enjoyed this section; it covers the isomorphism theorems, which are very neat IMO); Rings (I enjoyed this section). I'm currently studying subrings, ideals, and quotient rings. Once I'm finished with this section, I'm either going to pack it in and conclude my self-study or cover the section on ring homomorphisms and then call it quits.
You might try some basic algebraic topology: the fundamental group is readily accessible and leads to lots of interesting ideas.
