The best text-book I can suggest for you is: "How to Think About Algorithms - Loop Invariants and Recursion" By Jeff Edmonds.

It takes you through all the relevant mathematics required to learn about basics of CS based topics you are looking for (algorithms, proofs and other practical applications).

It also acts as a good primer for learning basic Computer Algorithms. The USP of book is it's noob friendly and I think perfectly suited to your needs.

Check it out here: http://www.amazon.com/Think-About-Algorithms-Jeff-Edmonds/dp...

This looks like a draft version of the book:

http://www.amazon.com/Think-About-Algorithms-Jeff-Edmonds/dp...

Because of this, I wonder a bit what's the legal status of this .pdf, but maybe I'm overreacting...