go over
...On Tuesdays we sat together, by his desk, or in the cafeteria, or on the steps of Pearlman Hall, going over the work (senior thesis).

we: I and my professor

What does 'go over' mean here? To examine something or to think about something?
Can you give me some other examples?

Question

go over
...On Tuesdays we sat together, by his desk, or in the cafeteria, or on the steps of Pearlman Hall, going over the work (senior thesis).

we: I and my professor

What does 'go over' mean here? To examine something or to think about something?
Can you give me some other examples?

Answer

Hi. "Go over" here basically means to review.

You would use this if you are "going over" something that you want to make changes to or improve upon (like a senior thesis), something you are receiving feedback on (a test or paper that is already completed), or you could use it to mean "study"

I need to go over (review/study) my notes again one more time before the test. 
I like to go over (review) my notes before giving a presentation. 
After the test, the teacher went over (reviewed) the answers with the class. (The teacher talked about each question and explained the answers.)

Hope that helps!

Answer

Very good answer.  The only thing  I would correct in your question (we: I and my professor) would be:  "My professor and I" if this was at the beginning of the sentence.  Know what I mean? :)