I've known this girl for about six months (we had friends in common), but we really started to talk a little bit more this month but there is still not a deep knowing of each other. I am into her, but she is quite shy (even though she is really pretty) and tends to be tough and push guys away. Sometimes she pushes me away by being a little rude or showing disinterest in talking, and other times she is quite friendly and eager to talk. Some people say that she is probably into me (I have been told that she seemed upset when I wasn't in class and often she holds eye contact with me sometimes while smirking), but I really don't know, and I am afraid not. I want to ask her out as soon as there is a good chance (we both have been very busy lately)

I know that her birthday is next week, do you think it would appropriate and "alpha" to give her a present (something not too much a expensive) or I shouldn't?