(September 28, 2018 at 5:34 pm)Kernel Sohcahtoa Wrote:(September 27, 2018 at 9:06 pm)polymath257 Wrote: You might try some basic algebraic topology: the fundamental group is readily accessible and leads to lots of interesting ideas.
Polymath, I want to thank you for mentioning Galois Theory and for mentioning the proof about quintics: it seems very interesting that for n is greater than or equal to 5, there is no general formula for finding the roots of nth degree polynomials in terms of radicals. Getting underneath ideas like these, understanding/enjoying them, and gaining an appreciation for them, are the reasons why I chose to self-study mathematics as a hobby.
I will complete the chapter on ring homomorphisms. Completing this section, along with the others that I've completed, will be equivalent to a course in Abstract Algebra I. Afterwards, I plan on studying the following topics: polynomials; polynomial rings and fields; Unique Factorization Domains; Extensions of Fields; Normal and Separable Extensions; Galois Theory; Solvability. Based on my understanding, this second stretch of material will be the equivalent of a course in Abstract Algebra II.
P.S. You've motivated me to continue my studies of abstract algebra. Thank you.
We can study along side each other, but I suspect only one of us is going to be bubbling over with glee and enthusiasm. :p
