I'm looking into studying Galois Theory and potentially doing some undergraduate research within the field. What are some texts one would recommend for the subject.
Thank you.
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2Lang's Algebra has an exposition of the theory as well as a host of useful problems – TomGrubb Aug 03 '17 at 00:41
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See https://math.stackexchange.com/a/152824/589 and https://math.stackexchange.com/a/53661/589. – lhf Aug 03 '17 at 01:21
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I know it is not a "big name", but Ian Stewart's Galois Theory served me well. I went into the class with some linear algebra and group theory, and came out with a good grasp of Galois Theory and some of its famous consequences.
A really nice feature is that he reaps some benefits of the theory before it is fully explained. Like after he explains the degree of a field extension, he then does some non-constructability proofs (one example: he shows that you can't trisect an angle of $\pi /3$ radians with a compass and straight-edge.) I'm not sure if this is standard, but it gives you a sense of satisfaction early on.
Also the introductory chapters are historically rich in a way I haven't seen before.
yberman
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And the multiple choice questions at the end of each chapter are also very helpful. Nice book, recommended! – Nicky Hekster Aug 03 '17 at 06:19
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It can be found here: http://math.illinoisstate.edu/schebol/teaching/407-14-files/Stewart-galois_theory.pdf – Nicky Hekster Aug 03 '17 at 08:08
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Emil Artin's Lectures on Galois Theory. The best there is. Only $82$ pages. Try it, you'll love it!
Robert Lewis
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2Though I disagree with this as an introductory text, after you go through the subject this is a great reference. Also the Dover edition is cheap as beans. It belongs on every mathematician's shelf. – yberman Aug 03 '17 at 03:39