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Just walk by her and make a comment or observation as you pass. Don't stop walking, assess the situation.
If she responds and there's something to latch onto. Rock back but don't face her entirely. And either talk to her more about the same topic, or transition to something else.
If she responds with something you can't latch onto easily. Either rock back and transition as above, or just smile and continue walking. You'll now have a reason to talk to her next time.
I actually like that idea. Since this is a classmate, you don't necessarily need to close on your first encounter. You can do a stepping stone approach and break the ice one day, then use that as a reason to start up a full conversation the next.
Also, you can just be straightfoward and honest and just introduce yourself to her and come across as a normal, friendly guy with no particular agenda. Walk right up to her and say "I noticed you were new here, I'm Jeff, what's your name?" Smile and be genuine. Tell her you just wanted to introduce yourself but you're really busy right now and you have to go but you'll see her around. There's not a lot of ways you can fail with an approach like that.
CHAT