The girl I like has a boyfriend?!?

So the story goes like this: This girl was in my art class. I sat nex to her for about 3 weeks and then got moved again due to disiplne. So in the three weeks, we had an awesome connection we agree on music, both play guitar, just all around made for eachother almost. Then when class ended we stopped talking D: Now I hear she has a boyfriend. Should I wait and see if they break up, try to talk to her even though she has a boyfriend, or just give up and move on completley? Thanks