I would highly recommend Software Foundations. This book is quite good at introducing you to Coq one step at a time. There is a lot of theorem proving, yes, but that’s part of the deliciousness of dependent types. It’s a great feeling when the line between “programming” and “proving” starts to blur.
I’m lacking in the math and logic parts, though.
I think Software Foundations does a pretty good job of bringing you up to speed for the logic you need to know. Already being comfortable with the concept of implication helps, though.