I was a real math geek in high school, and was taught "new math" at the time, so I got a pretty good introduction to math at a theoretical level. Still, Mathematical Background by John Sowa is a good overview of math concepts. He doesn't cover the connection to computer science directly, but a lot of this stuff underlies software concepts we engineers encounter everyday.
You can get along without the math background, but it helps to have it under your belt. For example, did you know relational databases are called that because they are based on the mathematical concept of relations? See section 5.
In some places, he uses terms only in their mathematical sense, without touching on the more common computer science uses. For example, "idempotency" referring to operations, but not to functions: a function f is idempotent if f(f(x)) = f(x) for all x.