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:
- The text more or less assumes that the reader is an undergraduate with little or no exposure to writing proofs.
- 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?