For each sub-topic, most math books give you the tools first and then teach you problems they should be used on. Read the problems first, and think how you might solve them (don't expect to figure it out, but if you do, great!). Then, go back and learn the tools, trying mostly discern the "how" and the "why" as opposed to the "what". Math is all about "how" and the "why". As some motivation, whenever a new thing clicks, it is very satisfying! :) But it definitely is a tough process.
Good luck!
Could you pls expand on the diff between the "how" and the "what"?
I'm 10 years out of school and haven't really needed to flex my math muscles in years.
If you just want to get your foot in with pure math I'd recommend studying basic abstract algebra and analysis at the same time. For abstract algebra look into Hungerford (Intro, not his grad text), for analysis, maybe Rudin, or Kolmogorov and Smirnov.