I've been out of school for a while and working as a programmer. I want to start taking some masters courses for applied math (PDEs, numerical analysis, etc) and need to become familiar again with the advanced math I used to use in undergrad. I took two semesters of real analysis as an undergrad, but don't remember a lot of the rigor, or how to properly use concepts for proofs (MVT, partitions of an interval, etc). I remember the intuition behind the stuff that stumps a lot of undergrads, like epsilon-N/delta, but [your deity here] knows if I could still properly write proofs. So should I just go back through a book like Spivak to practice proofs, etc? Or is there a better/more advanced book I should be using that anyone can recommend? Same question with Algebra, even though it's tagged as Analysis. I had two semesters of algebra in which we did Group Theory (first semester), and then second semester was Ring and Field theory, finishing up with a bit of an intro to Galois theory. We worked through Charles Pinter's A Book of Abstract Algebra, skipping only the 2 "optional" chapters on number theory and geometry. I have a copy of Gallian, that I may go back through, but was wondering if something like Lang may be better.