About Video Game Design

This is called a design document. That's how games are normally designed. First there's a design document, and it's a document about... the design.

I guess you would need to know as much math as your game design involves...

Then the programmers do all the other work.

Look up "game design documents".

Don't go to Devry, from personal experiance with my father he went to Devry and got a degree in Information Technology (Networking, etc) and they didnt teach him nearly enough of what he needed to know, more business then anything and now hes having ar eally hard time finding a job in that field.

Also if you want to make games but arent good at math, maybe look into going to the Art Academy of California or the Art Insititte of California, both are great programs for model, and envirornment design for games and movies. Thats if you want to go the model/art route.

Just a note: game-designer isn't an entry-level position, and unless you've got some serious education and preferrably a good deal of experience, I believe there's little chance to get anywhere as a game designer-only.
You will need experience with games before you can call yourself a good designer. Creating levels for existing games, or modding them, might be a good way to get insight without having to write any code. Level-design can come pretty close to game-design... I've created levels for Half-Life for 6+ years and it definitely helped me getting a better insight. I think. ;)

Design docs are a way to tell the design to the rest of the team. They cover the important points that the team needs to know in order to create the game the designer has in mind. They're mostly there to prevent a 'splintered' vision, where everyone has a different idea of what game they're working on, and they're used as a reference.
There are various 'guidelines' for them, but personally I believe every situation calls for their own type of design doc. I'm working with 1-4 page docs that are mostly a listing of what menu's and game modes/items should be in the game, anything else we need to know we just ask. Works fine for small groups and similarly small games. For my own game, I'm writing a more extensive document and various other lists and notes, because it helps me organize my thoughts on the design and it's usefull to get feedback on the design from friends, plus it should be helpfull when I need artists and such...

In other words, I don't believe in a theoretical designer only. You've got to create games or levels or whatever and see in reality if they work, what people enjoy in them and what should be improved or removed. And that's very possible without being a programmer or a math-specialist.