If I swap one of my math classes for another due to my schedule because I’m unavailable at that time will the work I did for the last class transfer over or will I have to start all over again in that class?
I think this is something that would have to be discussed with admissions at your school, or perhaps the math professor(s) in question. The policies for things like this are going to vary from school to school. Assuming that the two courses are otherwise equivalent aside from being different sections, it’s a possibility.