What to do during year off between grad and undergrad?

[alligatorman]

I will be graduating with a degree in Math in one year, and I plan on pursuing a PhD. I want graduate schools to consider my final two semesters when looking at my application, so I've decided to take a year off. (I'd apply for a spring semester, but most of the top schools don't allow this.)

My question is, what I can do during my year off? Of course, I can travel or get a job and make some money, but I would rather do something that helps with my graduate admission.

Are there any research programs or internships for college graduates, particularly mathematics students, that would help in my admission?

 

[Crosson]

I would suggest volunteering to be a research assistant for a professor at the school you just graduated from. Or else just start diving into research on your own.

 

[Vanadium 50]

I was in a similar situation, albeit with a degree in physics, not math. I worked in the "real world" for the year in-between, and I carefully chose a company that would pay for college classes as one of their benefits. I think I ended up with 4 courses that way.

I had no trouble getting into grad school - I explained what I did and why I did it in my application.