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I am currently revising my statement of purpose for several applied math master program. I wounder if I should mention some specific area of interests or specific name of faculty? The problem with me is that my undergraduate is rather "theoretical" , that I haven't taken many applied math courses and the purpose of my master is to further explore my interests. But the lack of specific interest on SOP seems a little bit odd for me.

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Short answer: be honest and concrete.

It's not typically expected that you have very specific, highly focused interests for masters programs in mathematics. For a masters, you won't get too specialized anyway (at least assuming you're not doing a thesis). Read the application directions carefully to see if the schools are looking for anything in particular, but what I look for in SOPs is a sense of the applicant's goals, background, motivation, seriousness and maturity. (And maybe other things in special cases.)

You should try to explain your goals as clearly as you can, but be honest about it. So you don't need to say something specific like you want to do KAM theory for Hamiltonian PDEs, but if you can give specific examples of things that made you want to study applied math, that would be good. If you can list specific topics in applied math that you would like to learn about, also good. It's also not a bad idea to get an feeling for the strengths of the departments you're applying to and say why you're interested in them (e.g., strong in xxx, but you don't need to mention specific faculty, unless you're honestly really interested in workin with them).

See also here and here for other points of view.

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