I'm Korean high school student who wants to study how to prove that degree ≥5 polynomial equations are not solvable. I know some of Set Theory and will study abstract algebra with 'A First Course in Abstract Algebra - Fraleigh'.

But I have a little time because I have to study hard other subjects to entrance into a good university. So, I want to study some part of Fraleigh.

Please let me know what sections are necessary to study that theorem. Thanks in advance.

  • 5
    $\begingroup$ If you've never studied any algebra at all before then the answer is probably "all sections". $\endgroup$ – Erik Vesterlund Jul 8 '13 at 7:18
  • 1
    $\begingroup$ Adding to @ErikVesterlund's answer, your goal is Galois theory, which requires strong knowledge of both group and field theory. $\endgroup$ – icurays1 Jul 8 '13 at 7:24
  • $\begingroup$ Groups, Fields and Galois theory $\endgroup$ – user5402 Jul 8 '13 at 7:25

You can skip a great part of the book: at least sections 7, 11, 12, 16, 17, 21, 24, 25, 27, 28, 32, 36, 37, 38 to 47,52,54,55.
You can skip more but it would require personal contact and feed-back from you to tell you what exactly: maybe some advanced student or instructor could help.
Fraleigh is a wonderfully user-friendly book for beginners, but his fine treatment of the homology of simplicial complexes, free groups, non-commutative rings, Gröbner bases, ... is definitely not required for your purpose.

Full disclosure
I am answering this question because Fraleigh was the book I taught myself abstract algebra and field theory with, a long time ago.
Understanding Kronecker's construction for creating an extension field containing a root of an irreducible polynomial over a field was one of the most exhilarating experiences in my (mathematical) life and I owe them to Fraleigh's pedagogical talent.

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  • $\begingroup$ I'm glad it helped you, YongRyu. $\endgroup$ – Georges Elencwajg Jul 8 '13 at 12:24

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