Chances of getting into an REU as a math major with a 4.0 GPA

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i'm going into the second semester of my sophomore year. I'm a math major, looking to go to grad school for pure math.

i was just wondering my chances of getting into an reu this summer (anywhere/anytype)

including this upcoming semester i will have taken:
-multivariable calc
-*advanced multivariable calc
-advanced calculus (intro to analysis)
-intro to combinatorics
-diff eq
-intro to pde's
-logic/proofs
-topology
-linear algebra (mostly computational)
-*linear algebra (rigorous)
-*complex analysis
-*differential topology
(*'s are ones that i will am taking this semester)

i have a 4.0 in these math classes, but no research experience.
i could probably get pretty good recommendations.

i would absolutely love to get into an reu, not only as a resume booster, but to get some experience in what i want to pursue as a career. i just wanted to gauge my candidacy.
if it is favorable, any advice? i.e. how many to apply to, where to apply, what to look for

thanks in advance.
 
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I got into one last year as a freshman with fewer classes than that.
 


Your coursework looks strong, and sometimes REU's seek to find people who don't have research experience (as the purpose of these NSF programs is, to some extent, to help out students from other institutions when the research opportunities at their home institution are slight or non-existent).

What programs have you applied to?
 


i haven't applied to any yet. i was just getting ready to start looking at specific programs and filling out applications. (is this somewhat late?)

how many do you think i should apply to?
 


I'd apply to at least 3-4, possibly more. Look at deadlines... I think as long as you fax it by the deadline you'll be given full consideration.

I'm not directly in the maths... so perhaps others can offer you advice on particular programs. It would help them if you listed some of the maths research areas you might be interested in.. that will help them make suggestions.
 


my topology class was the class that i was most interested in. however, this is by no means something definite. in fact, i think it would be great to be exposed to something different.
 


i'm looking through all the different reu sites and there are so many of them.
any advice on how to narrow down my choices?

also, what should i focus on in my statements of purpose?