Once upon a time, long ago and far away, I was a math major. My life ended up going in a very different direction, but doing math always made me so calm and happy, I decided I should take it up again in my retirement.

But unfortunately I'm very, very rusty. I've started working through Velleman's How to Prove It as a refresher, since proofs were always my strong suit & favorite part of math. Stuff involving actual numbers & calculation was my nemesis, but fortunately this book uses set theory as proof fodder and that's much more fun than yucky old numbers .

My goal is to re-work through Pinter's A Book of Abstract Algebra, which was the textbook we used in my favorite math class ever. But I'm finding that Pinter occasionally uses Algebra II/Precalculus stuff in problems and examples, and it's scary how little I remember about natural logs, polynomials, trigonometry, or anything so useful.

So I'm wondering if recommend a brisk & challenging refresher book for this stuff, something that'snottargeted for the math-phobic? Ideally something with actual proofs, which help me understand things much better than eye-glazing & repetitive hand-holding, but I'd happily take something that had review and challenging problems w/ enough solutions/examples to get by with.