I'm writing a book just for you :)

It's called "Practical Math: A Tour of Mathematics in Production Software" (https://pmfpbook.org points to an announcement and mailing list)

The idea is to give a large swath of examples of math used to solve real problems, and collectively to give a good answer to your question. And to have the examples be appreciable by the average programmer, in the sense that they could reasonably expect to adapt the underlying ideas in their own work.