We say "I'm studying at university". There is no need to add an article.

You also need to add an article! "I'm studying at a university"

Azimux is correct for America. However, here in the UK, a university can award its own degrees and has a charter giving it various guarantees of independence. A college usually depends on a fully-fledged university validating its degrees, or may even be part of a university, as in Oxford or Cambridge colleges. Or a college may be little to do with degree-level education at all, such as a Further Education college. Description taken from http://wiki.answers.com/Q/What_is_the_difference_between_a_college_and_university