Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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!

share|cite|improve this question
up vote 9 down vote accepted

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.

share|cite|improve this answer
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. – Clifford B. Jul 25 '11 at 15:46
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. – Dylan Moreland Jul 25 '11 at 15:54

Try these books:

share|cite|improve this answer
Thanks, I will check them out as soon as possible. – Clifford B. Jul 25 '11 at 14:00

Many pages of exercises at J K Verma's website, here.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.