Studying Mathematics Thread

[Kernel Sohcahtoa]

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.

Galois theory is actually why group theory got going. There is some wonderful structure here relating roots of polynomials, isomorphisms of fields into themselves, and the structure of groups.

In any case, the progression you give looks good.

if you have any questions, feel free to ask! BTW, what book(s) are you using?

I didn't realize that Galois theory got group theory going.  I really enjoyed group theory,  so now I have  more motivation to get underneath Galois theory.

I'm primarily using Abstract Algebra by Saracino.  For whatever reason, his method of instruction and his style of proof-writing work well for me; I'm grateful that he has written his book, as it has made abstract algebra pretty accessible to me.  On occasion, I'll open up A Book of Abstract Algebra by Pinter or A First Course in Abstract Algebra by Fraleigh if I find that a particular concept is a little vague in Saracino. Also, if I have any questions and I'm able to express them in a precise and coherent manner (IMO, this is an art-form in itself), then I'll post them here.  Thanks.