[auvrw]

your strategy of working exercises is a good one. it can also apply to results in the text: attempt to prove the result independently before reading the proof supplied in the text. if you find this practice enjoyable, it might be a sign that you'd like to study pure math.

texts: carothers for reading like a novel, rudin for taking apart like a car engine...

... or, drop all your classes and learn to formulate everything in the terms of measure theory from the beginning. halmos's texts on any (mathematical) subject are almost always well balanced ...

... o! that reminds me. also, there's this thing called "functional analysis" that'll be worth looking into after basic topology is well-cemented.