(September 29, 2018 at 10:50 am)Kernel Sohcahtoa Wrote:(September 29, 2018 at 9:16 am)polymath257 Wrote: 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.
What attributes do you like about one particular book over another? Do you favor a more narrative description where the author writes like they're speaking to you, or do you like step-by-step solutions with notes on the side telling you what's going on? Or is it another attribute entirely, like examples being more like just general equations to solve vs. examples having a practical, real-world application that you can relate to?
