My second cold approach (sort of):

I was walking out of the University library when a random girl (HB5) held the door to the stairs open for me, I thought "Fuck it, let's do something with this" So here we go:

Me: Hi there, what's your name?

Her: Louise (smiling and taking her earphones out )(not her real name)

Me: What course are you doing Louise?

Her: Business Studies, how about you? (smiling)

Me: Economics

Her: I did Economics as part of my first year, I didn't enjoy it, it was way too complicated to me (on reflection this feels like a shit test)

Me: Imagine how I felt doing it at A-Level

Her: (Laughs). Do you have (Lecturer name)?

Me: Yeah, I have heard stories about him (smirking)

Her: He's a good lecturer, (plus something else which I can't remember)

Leaving the Library, I say bye, she says "Nice to meet you" while Smiling even more.

Any tips?

I took some advice about not being in my head too much and second guessing myself, it probably helped that I wasn't that attracted to her, but I'm still looking to improve.

Thanks