I'll take this opportunity to once again plug Strang's excellent linear algebra series [1] with associated textbook [2]. Also right now I'm working through some

I'll take this opportunity to once again plug Strang's excellent linear algebra series [1] with associated textbook [2]. Also right now I'm working through some Cornell lecture notes [3] (that read a lot like a textbook) on manifolds and differential forms. It's meant for college sophomores and juniors who have taken linear algebra and vector calculus, though it provides a very good calculus supplement in the appendix. For me, it's perfect: the tone is informal enough to provide motivation to continue, but the definitions and proofs are fairly rigorous. It's about the only self-study math text that I think I might finish. Hope this helps, not sure if it's over/under your level. [1]: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... [2]: http://www.amazon.com/exec/obidos/ASIN/0980232716/ref=nosim/mitopencourse-20 http://www.amazon.com/exec/obidos/ASIN/0980232716/ref=nosim/... [3]: http://www.math.cornell.edu/~sjamaar/papers/manifold.pdf http://www.math.cornell.edu/~sjamaar/papers/manifold.pdf