I probably didn't make this clear, but I do agree with you. If you want to study mathematics you need to study lots of areas which is why they have general requirements like that for getting degrees in mathematics.

But if you are an undergraduate looking for a particular subject to get you in the "mathematics groove" I think (1) is a good recommendation for independent study alongside classes, (3) is really a way to lay a foundation for mathematical maturity; certainly a class on proofs and logic would be necessary before almost any of my recommendations.

Again: I didn't mean my list to be a list of "only study these things" so much as "if you want more math, these might be good places to look."