courting is old school. just invite her to study with you and find out her interests. if you two break down that shy barrier then you can commence the Boom Boom
if you wish to be with her you must treat her friends as your friends, after all they are the gate keepers to Boom Boom
FRIENDSHIPS are like a sand castle WITH THA SMALLEST THING, everything will FALL APART!!!!!! Also, just get her some alcohol.
It's possible that she cares a lot but doesn't believe that you are really interested. Just be there for her be a friend and show her the kind of man you are. Drop hints and ask if she would like to study together. It's important to get to know her outside of the classroom if you want to stand any chance of progressing to 'boom boom' (very eloquently put farmer )