Well you have another year to apply so you should not worry. And yes, I figured that they would need upper division classes. A lot of them say that. It also makes sense since it is a bit easier to compare people if they have taken the standard upper division classes like analysis and algebra...
If you are interested in applied mathematics the SAMSI institute Raleigh, N.C. still has an open application for their week long program. It's a pretty good place and I've done two of their undergrad workshops. Here is their website...
I e-mailed them. I got an early offer from NC state which I ended up accepting after they e-mailed. When I e-mailed them they said they just did not have a position to offer me. They did not say anything about filling up all their positions yet. I would e-mail all the places you are interested...
Just got an acceptance letter for the NC State REU! Awesome! They want to know if I am going by March 9th, so hoping to hear from other schools. I can just e-mail them to know if I am in or not? NC State was not at the top of my list but I would definitely like going there.
I applied to 12 REU's. UNL, Chanel Islands, UCSB, Mt. Holyoke, NC State, OSU, Clarkson SUNY POTSDAM, Rose-Hulman, Penn State, Michigan State, Claremont College, and Northern Arizona University. Boy was it fun! Hoping to hear back from some soon.