For a good book on mathematics and programming, I recommend The Haskell Road to Logic, Maths and Programming by Kees Doets and Jan van Eijck. It uses the functional programming language Haskell, which "allows implementations to remain very close to the concepts that get implemented". The level seems to be about what you describe.
We do not assume that our readers have previous experience with either
programming or construction of formal proofs. We do assume previous
acquaintance with mathematical notation, at the level of secondary
Functional programming and Haskell are useful in themselves, but they also give you long term benefits in programming ability even in more traditional paradigms. If you plan to do program in procedural/object-oriented languages (e.g. java) you'll still need to do some short term work to learn them.
Another book in a similar vein is Discrete Mathematics Using a Computer by Cordelia Hall and John O'Donnell. It also aims to teach mathematics using Haskell, but I am less familiar with it.
For a book dedicated to Haskell itself at an introductory level, I recommend the excellent Programming in Haskell by Graham Hutton.
For a book just covering the mathematics for computer science I second Concrete Mathematics which was recommended in another post. I also recommend an excellent book I don't hear mentioned much, Mathematical Foundations of Computer Science by Fejer and Simovici, although it's probably a bit terse/difficult for the level of "mathematical maturity" you mention.