Can I take upper division courses without first taking my core classes?

Firstly, I'm a Mathematics student who will graduate in about 2.5 semesters. I need to take many more math courses and would like to start the focus on those and finish the majority of my core classes during summer semesters. I'm declaring my math major, but can I do that without first taking the required classes such as chem 1? It is not a requisite to any of my other math courses, so will the college allow me to do that while declaring a math major?