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I'm not sure what gradate level MT means these days but knowing enough in order to understand SDEs and probability theory is a minimum requirement. For the rest, their pervasiveness is limited in the current context. (disclaimer: I had 3 MT courses as undergrad but it was quire a dry subject). Related to MT is Lebesgue integration and Functional Analysis which are the basis for a lot of applied stuff.

Of course, each school will have its own specific requirements.


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