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I used a textbook called Classical Galois Theory With Examples by Lisl Gaal this past semester and thought that it was really helpful. It has a bunch of examples and proofs. More importantly, it leaves a lot to the reader, but has blanks for the reader to fill in as they go. Obviously I could pick up any textbook that is super brief, but I like being able to "complete" the textbook as I go.

So I was wondering if there were any other textbooks structured like Gaal's (in any area)?

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  • $\begingroup$ You might want to look for books that can (explicitly or implicitly) be used as a textbook for a graduate course, as these often come with exercises, sometimes also difficult ones or research questions. I'm right now reading "Combinatorics of Coxeter groups" and it has tons and tons of exercises, but regarding the topic you are looking for, you might find nice books in the series springer.com/series/136 . $\endgroup$ – Dirk May 16 '17 at 9:16
  • $\begingroup$ Yeah I have plenty of books that do that, I just liked the approach Gaal's took to it. Seems like it might be unique in the way it did so and problem books are the closest. $\endgroup$ – Jeff L. May 16 '17 at 19:14
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I am not familiar with Gaal's book, so I'm not sure how similar my recommendations are, but they seem rather similar to what you're looking for in terms of "filling in the blanks". I recommend looking for books with "problem-based approach" or "problem-oriented approach" in the title. I have looked through a couple of these, and they present some definitions, examples, and theorems, but most of the content is a series of exercises that guide the reader into solving interesting problems and proving some of the results stated in the text (and sometimes coming up with the statement of the result). Here are a few that I found:

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    $\begingroup$ This seems to be the closest to the type of book I'm looking for. Thank you. Btw the second link doesn't work. $\endgroup$ – Jeff L. May 16 '17 at 19:13

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