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

I am 26 years, live in Europe and just started my PhD. I got out of a 2.5 year relationship roughly 1 month ago. My ex just didn't have the feelings anymore. The breakup was not messy at all. But nevertheless, we are on no contact, since I think this is the best to move on. I am doing fine and I think I am ready to date again.

This was just some background info. 

There is this girl in the same department in university, who I find cute. 

Last semester (back in december) I supervised an experiment for some students, and she was also part of it. Therefore I know her name and her email adress. But at that time I was in a relationship, so I did not ask her out or anything.

When we meet on the hallway, we both smile and greet each other. I want to ask her out on a date, and think about the best way to do it. When I see her, she is usually with her friends.

Now to my original question: Is it okay to write her an email and ask her out? I could also write her a message in Facebook (I am not friends with her there). I just don't know if this is too awkward and I should wait for an opportunity to approach her alone in the department at some time.
<bot>: Want to ask a girl in college out on a date. She is usually together with friends but I know her email adress. Is it okay to write an email to ask her out?