Grad School

Good day, /sci/. Judging by the people who frequent here, I think this is as good a place as any to ask.

How difficult is it to get into grad school? I want to study mathematics, preferably at Purdue. To that end, I'm double majoring (math and stats) and have decent grades (3.8). I'm also involved in extra-curricular activities.

What, if anything, am I missing? I'm currently a 3rd year student, so I have time to implement recommendations if you have any.

I don't think I get american terms for shit.

Grad school is post-graduate education right? So like getting an MA or PhD or some shit?

As far as I'm aware, being 3 years into an undergraduate maths degree, you basically need to spend the first 2 years of any graduate degree learning more maths before you can even understand the questions that you'd be trying to solve for a thesis, never mind original research.

Unless you are on good terms with a professors who wants some boring shit done for him, technical lemmas and the like, I doubt you'll be doing much research.