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I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example). So far, I have worked with Tignol's "Galois Theory of Algebraic Equations". Any additional suggestions would be appreciated, whether it is a textbook or a website, but the language should be English. Solutions are welcome, but no necessity.

Thanks in advance!

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I really like the exercises in Lang's Algebra. There's a little bit of everything in there.

Milne's notes have exercises at the end of every chapter, a chapter of review exercises, and a two-hour exam; solutions (or at least hints) for all of these are given at the end. A lot of the action takes place over $\mathbf Q$, but I saw a fair number of questions about finite fields and they seemed good.

Keith Conrad's handouts don't have a lot of exercises, but when I had to review this stuff I found it helpful to look at the statements of his examples, try them for myself, and then read his methods. There are usually myriad ways to solve exercises in this area.

Teruyoshi Yoshida has fun example sheets, in addition to complete course notes.

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  • $\begingroup$ Thanks to you, too; I wanted to get Lang's book as a reference, but I'll take a look at the exercises as well. $\endgroup$ – Clifford B. Jul 25 '11 at 15:46
  • $\begingroup$ No problem! Lang's book is divisive, but it can teach you a lot, and the field theory chapters are probably its best; George Bergman's companion to the book could be useful as well. $\endgroup$ – Dylan Moreland Jul 25 '11 at 15:54
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Try these books:

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  • $\begingroup$ Thanks, I will check them out as soon as possible. $\endgroup$ – Clifford B. Jul 25 '11 at 14:00
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Many pages of exercises at J K Verma's website, here.

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Have you tried working out through

(I) Abstract Algebra by dummit Foote

(II)Field and Galois theory by Patrick Morandi

Both of these books are rich with exercise problem and he questions are very diverse. I would recommend you to go through this as it helped me tremendously

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