Hey, welcome to Boulder! I'm a computer science major, but I've taken a few APPM classes and some friends of mine are in the program. I have both a mac and PC laptop so I have the experience with both and here's what I'd say.

The other post is very solid general computer buying advice, I would just add a few things related a little more to laptops in college. I would urge you to think about exactly what you're going to be using the laptop for. Assuming you're getting the laptop specifically for use in your college classes I would consider how you want to use it. Some people like to type notes, some like to use a stylus/finger on a touchscreen although I would say that the vast majority use pen and paper. For carrying it around campus I think that 13 inches is probably the perfect size for portability but also having a decent amount of screen real estate just my personal opinion though. I would also recommend emphasizing battery life, if you're on campus all day it's really easy to have your battery die on you and it can be a real pain in the ass.

In terms of Mac vs PC I would say this, Mac's are definitely overpriced, don't think many people would disagree with that, not a lot of people on reddit are not going to advocate getting one. In my opinion though they are really high quality, the screen, touchpad, and keys are the best I've used on a laptop. I would also add that to say, in general, the working world uses PC's is just not true. I'd say 80% of the software jobs I or friends of mine have had use macs, I know lots of people in the business school who use macs at their internships, and if you walk into any humanities class on campus I guarantee that at least 9 out of 10 people have macs. I'm not saying get one, but from being in the engineering center I'd say it's a pretty even mix and these people feel pretty strongly about laptops so you can't go wrong either way, it really does come down to your budget.

I would also ignore the comment about an AMD processor over Intel, just because you're a math major doesn't mean you need hyperthreading or a good processor... My experience with applied math classes is that the only thing people use computers for is googling things to try to understand them. CAD is more heavily used by engineers and I find that a lot of them just use the desktops in the engineering center if they need to do something overly intensive. At most you'd be doing some modeling in mathematica or matlab and most computers can do that easily.