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I'm seeking a reference for a somewhat introductory-level abstract algebra text that focuses on solving problems, or has a motivated discussion of the major topics. I've found most texts I've skimmed though to have two issues for me:

  1. The text more or less assumes that the reader is an undergraduate with little or no exposure to writing proofs.
  2. The text just seems too hopelessly abstract for me. Mainly, they seem to consist of defining a bunch of objects and essentially pushing around symbols to prove theorems related to those definitions but seemingly unrelated to anything else.

I know that algebra originated, at least in part, as an attempt to solve algebraic equations...is there a text that will cover what I need to know, perhaps from that perspective? Or from a slightly more "applied" perspective?

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    $\begingroup$ had you seen what wikipedia tells about? $\endgroup$
    – janmarqz
    Nov 3 '16 at 1:25
  • $\begingroup$ I am confused by "Advanced abstract" in the title and "too hopelessly abstract" in the body. What do you want to do with abstract algebra? $\endgroup$
    – user233746
    Nov 3 '16 at 12:02
  • $\begingroup$ @Alex -- I realize that it sounds a bit contradictory! Basically, I am looking for an abstract algebra text that perhaps has a slightly more applied, or motivated, approach that also doesn't treat the reader as though the text is their first interaction with proof-driven mathematics. Does that make more sense? $\endgroup$
    – Patrick Rinker
    Nov 3 '16 at 14:43
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Dan Saracino's Abstract Algebra: A First Course has proved excellent for me. It is relatively easy to read, especially in the first chapters, and seems to motivate pretty much every theorem it proves. It is not focused on applications, but I think you will be able to relate to its perspective.

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  • $\begingroup$ I will take a look...thank you! $\endgroup$
    – Patrick Rinker
    Nov 3 '16 at 14:52
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Ian Stewart's Galois Theory. Has history, is motivated by solving equations, and requires relatively little background.

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