Good text on algorithm complexity
It is my very personal opinion that the book of Jon Kleinberg and Éva Tardos is the best book for studying the design and analysis of efficient algorithms. It might be not as comprehensive as Cormen et al. but it is a great textbook. Let me point out, why I think this book might suit your interests best


you don't need heavy math machinery for the proofs
the book gives often a great intuition why something is working (or not), this is in my opinion very important for beginners and self learners
a very intuitive approach to NP-completeness
it has a great chapter how to deal with NP-complete problems in practice
it focuses on design patterns, which might help you to design your own clever algorithms


You should also notice, that there is a lot of free material in the WWW available. Great lecture notes are provided by Jeff Erickson. And you can even watch the whole MIT class on "Introductions to algorithms" taught by Charles Leiserson and Erik D. Demaine. Cool stuff!