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Recommendations on analysis or probability programs

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I'm a senior in a 50-ish math department with my math GPA being 3.9 (one 1.5 in an elective and all others 4.0, including two graduate algebra and one graduate analysis. I'm taking graduate topology and probability currently). No REU experience. I'll take my math GRE this month, so anything there is unknown.

I'm looking for a PhD program that offers financial support for the first two years. I don't have a very specific interest yet but it would probably end up in  either analysis or probability.

So here are the questions:

1. How lacking of research experience will impact me both considering application and financial support?

2. I will also apply some statistics programs but I'm struggling on how to write my SOP for it. Since the majority of my courses are pure math courses and my interest is also focused there. Is there anyway to persuade them that I'll still be suitable for their program that is not theoretical oriented? 

3. Which level of programs should I be looking to based on my background? Since I cannot determine my research field now, I'd be likely to go for those schools with larger departments.

Thank you!


Edited by vadupleix
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