Asymmetrical Key Encryption

I was going to try to write a paper on Public Keys. I've done some research trying to figure out the specifics of how it works. I'm not looking for an abstraction of what happens, but specific details of the math behind it.

I'm under somewhat of a time crunch, so before I throw everything I have at this, I was wondering if someone could tell me if I could understand how it works given my mathematical background.

I am familiar with basic calculus and some basic statistics. Somehow I'm not sure if that is enough. Does anyone know if this is something I could figure out? Does anyone know if there is a laymans explanation of the details? Any help you got would be appreciated, thanks in advance.