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Quick explanation of what I'm interested in: I am currently an undergrad applied math major with a minor in physics at a large state university known for its strength in engineering. I love studying math and its applications, specifically physical applications hence the minor. I recently began work on a senior project in MHD, and am doing some lightweight volunteer research for a physics professor at my school. I've been taking as many math and science courses at my school as I can manage, usually between 4 and 5 per semester, because I just love the work I do and the subjects I learn about.

Here's a list of some programs that my searching turned up, that I am interested in:

Columbia - Ph.D. Applied Mathematics

Columbia - Ph.D. Atmospheric and Planetary Science

Cornell - Ph.D. Applied Mathematics

Cornell - Ph.D. Theoretical and Applied Mechanics

Brown - Ph.D. Applied Mathematics

NYU - Ph.D. Mathematics

NYU - Ph.D. Atmosphere Ocean Science

UMD - Ph.D. Applied Mathematics

I am aware that these programs are competitive, and that my chances of being accepted aren't fantastic, so I'm trying to fit some other programs on this list that would be nice safety schools, or even just something I haven't thought of yet.

I have actually only recently started looking into degree programs for atmospheric science, but my interest comes from the compelling course offerings and immediate applications for research.

So, if you actually read this far (Thanks!) what schools or types of programs would you recommend I look into? They don't necessarily have to be for degrees in mathematics, but they have to be math-intensive, and have the potential for applications to physical sciences.

TL;DR: What are some good graduate degree programs for someone who is interested in applied math and physics?