Well... my initial thought was that it's mostly, like, you plug specific case information into a general equation called a "spell" and turn the crank, and that spits out parameters like how much mana you need, and mana flow rate; basically a spell is a recipe for creating specific effects that changes based on local conditions.
To put it into a military metaphor, the kinds of equations that artillery officers use to calculate range and account for wind and whatever.
So a device is all the on-board hardware+software that works underneath the hood of a tank compared to Napoleonic dudes with a howitzer and a gradated sight.
But then Yuuno's like "I'm a specialist at complicated magic and I don't use a device" and I'm wondering if you really need all that much math or if he's Gauss reborn. And maybe the reason he had such a hard time with Raising Heart is, it runs on Windows for it's OS and he's used to Unix.
I just, I find it really unlikely that math is THAT important when we compare the performance of Nanoha--who's schoolwork is more practicing the operations than actually doing real math--to the performance of Yuuno (doesn't need a device) to Mid-Childan soldiers like Teana and Subaru--who enlisted at 12, having finished their compulsory schooling and are probably done formally learning math. I mean they might still get necessary applied-skills stuff but, well, Nanoha didn't need any of that.
I guess my feeling is, maybe it's arrogant of me, but what with the engineering degree and all, I probably have more experience with formal math education than the production staff, and my feeling is, they don't realize solving math problems in your head while trying to lazor someone, while trying to avoid getting lazored, while flying around... they didn't realize how stupid hard that sounds.