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This puts me in a weird place because while I've learned the necessary math, none of it is on my transcript. (In fact, many professors in our psychology department literally forbid students to take graduate math courses).

Is anyone sufficiently familiar with sociophysics to know whether there are ways for people like me to prove I have sufficient math background to switch programs? If I want to work with a professor in a physics department solely on applications of statistical mechanics to questions in social sciences, do I need to prove that I understand topics in physics that are not directly relevant to such questions just to get into a department?

Thanks for any help.