>>13
Not
>>12 but I DO happen to be finishing my PhD in Maths (topology, specifically properties of certain metrics on Cantor sets) and all of his comments are pertinent and sound.
Algebra is maths. It's simple maths that should be a basic prerequisite for being considered human, but it's still maths. Just because something's actually applied and useful doesn't mean it's not math.
TL,DR: Fuck you.
OP: Abbott is a decent introductory book, good if you're just starting, but not in depth enough for serious study. Analysis is where the computationally useful but conceptually simple math begins to give way to the really interesting and beautiful stuff. Start there if you can.