Something like group/ring theory needs to be abstract. In fact, many practical applications of those things are themselves in applied math and physics. Somethi

Something like group/ring theory needs to be abstract. In fact, many practical applications of those things are themselves in applied math and physics. Something like differential equations or the calculus of variations is fun for examples but then you’re just teaching a physics class ;) Indeed, even the most practical applied mathematician needs to have put in hours learning the abstract things.