<human>: Can you succinctly summarize the text in 1-3 sentences?

Ok, I'd [27F] like to ask a guy Tim [early 20'sM] from uni out. We have been sitting next to each other for the past 3 weeks and my intuition strongly tells me he likes me. We have only spoken once last week, but I would like to get to know him better. He smiled kind of shyly when I spoke to him last week, and he shared his iPad with me when I told our group I forgot the text for class.

Thing is, I have been told by so many friends that it is the guy's job to do the asking. My worry is he's too shy and won't ask so I will miss the opportunity, or doesn't want to (is waiting for me to). He is only in one of my classes so I see him once a week, which means if I don't ask I have to wait another week.

So my question is: should I ask him? Am I reading too much into this? I am a DEEP thinker and a stresshead so this mulls in my head all the time. Does it really make the girl look desperate if she asks? Also, any advice or tips?
<bot>: I am a huge stresshead and worried about asking a guy I like out. PLEASE help ease the worry in my mind. :(