<human>: Can you condense the text into three sentences or less?

Background: Started grad school last month.  In my stat. mech. class (yay physics), there is this woman who is really good looking and probably smarter than I am.

Story: On Wednesday, I decided it was a good idea to talk to this girl.  Using all my skills (lol) and being super clever, I approached her after class and said, "Hi, I'm James, I don't think I caught your name."  We talked, I told her that a group of my friends were going to be doing homework together for that class and was wondering if she wanted to join us.

Later that day, she found my email on the school site and sent me her email so that I would have it. (Good sign?)  Well, we set up to have a homework session today and the only person other than myself to show up was her which I did my best to not make awkward.  The problem was that I was completely useless.  I have my skill sets and infinite series is not one of them at the moment.  Basically, I felt like dead weight while she explained it to me.

Now, because of what happened there is a chance that she doesn't see this as worth her time studying which if that is the case, is there anything I should do?  And if not, anything I can do to slowly work towards asking her out without it being weird.  One problem is that I don't even know if she is single.  My goal was to go a week or two doing homework with her and my friends and then ask her if she was interested in going to get coffee or tea with me.
<bot>: Woman in class I want to at least go on a date with, kinda messed it up.  She is better looking than I am and probably smarter but that won't stop me.  Any advice?