Hardly at all if he's going to basic. But I've also heard that they are starting to become more lax on the rules concerning trainees. Just be prepared to only be able to write him until he's in his last week or two.
Your degree honestly doesn't matter. I majored in History with 1 SEMESTER of math and I was branched Engineers. They'll teach you everything you need to know at your BOLC. Maybe once you're in the Army for a while you'll be able to do something specific to your degree, but not initially...just...