Studying Mathematics Thread

[polymath257]

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.

Looking at the Pinter book, I had forgotten to mention the questions about ruler and compass constructions, which are related in some interesting ways to Field and Galois theory.

So, the question of which regular polygons can be constructed by ruler and compass has been completely answered (well, except for some number theory issues). The fact that trisecting a general angle and doubling a cube cannot be done via ruler and compass also follows from this directly.

Just scanning the table of contents suggests Pinter's book will cover this.

Definitely feel free to ask questions either publicly or via PM. I'm always willing to help with math.