I am a student AT (the name of the university), IN (the name of the department or faculty). As for the definite article, the issue depends entirely on the name of the university. Consider the following statement: I study at THE University of Massachusetts Boston, and my sister studies at Boston University. When the word 'Boston' comes before 'University', it sufficiently defines it. In the first example, however, when the name starts with the word 'University', we have a singular noun that requires a definite article. Therefore, I agree with both John and Dennis, as they have used different examples to illustrate their points.

I like Dennis's answer, and I myself would say it that way.

It is possible to say I am a student at the University of Wisconsin for example

I am a grad student AT *** University e.g I am a grad student at Bishops University