Asking a professor to be my advisor (math) I'm applying to graduate school and there is a professor at my home university I am interested in working with.  As a bit of background, I have been doing undergraduate research with this professor for about a year now and he seems to like me (though maybe he's nice to everyone.  I can't be certain).  My research under him has been going well as hes told me I've been doing good work.  In fact, he uses exclamation marks sometimes, which I find to be odd.  Fast forwarding a bit, I've recently wrapped up the project.  Given my academic history with him, if he was interested in working with me, would he ask me to be his student (sorry if this comes off as having an inflated ego, I don't have one.) All in all, I'm not sure how to proceed in asking him.
Just ask. There is nothing to lose. Many of us would be hesitant to ask a student, realizing that there are advantages to moving on and coming in contact with different faculty and their ideas. He might even suggest that you move on, actually, and don't take that as a negative. 

If that happens, ask for his advice on your next steps. And try to keep in touch with him over the next years. An email every year might be welcome if you are progressing nicely. 

These things are best done in person if that is an option. 

But think about whether this prof (the easy option) or moving on is the best option for your future.