I would like recommendations for a small, low-intensity course of study to improve my understanding of pure mathematics. I'm looking for something fairly easygoing, with low time-commitment, that can fit into my existing fairly heavy study schedule. My primary areas of interest are proofs, set theory and analysis, but I don't want to solve the whole problem right now. I want a small, marginal push in the right direction.

My existing maths background is around undergrad-level, but heavily slanted towards applied methods (calculus, linear algebra), statistics and algorithms. My knowledge of pure maths is pretty fractured, not terribly coherent, and mostly exists to serve the applied areas. I am unlikely to undertake any more formal study in pure mathematics, so if I want to consolidate this, I'll have to do it myself.

This came to my attention as I've recently started teaching myself Haskell. This is mostly an intellectual exercise, but at some point in the future I would like to work with provable systems. I can recognise the homology between some constructs in Haskell and mathematical objects, but others I don't notice until they're explicitly pointed out. I get the very strong impression that my grasp on functional programming would be a lot more powerful if I had a stronger grounding in pure maths.