We’re going to visit UCLA the week before Thanksgiving with my son (potentially an applied math major). Unfortunately all guided tours are already full, so we’ll have to do a self-guided tour using the brochure on the website. It would probably have to be on a Sunday too. Any insider hints of what to pay attention to and how to get a better feeling of the campus atmosphere?
The guided tours are all outdoors. No one knows who is ‘officially’ part of the tour or not. You would probably be able to add yourselves onto the back of a tour. Just wait until everyone goes outside of the student center and gets into groups with the guides and join one.
Thank you @Mom2Engineers but there are no guided tours on Sunday, and on other days we’ve already signed up for other colleges.
Try and walk around the Hill (where all the dorms are). Most students don’t go on campus on Sunday.
We have a tour scheduled for Saturday. Is it correct that there’s no information session, just the tour? It would be the only college we’ve visited that has that structure.
We visited in summer 2016 and there was an information session before the tour. After the information, everyone went outside the building and self-selected a tour guide to take then around the campus.
Have your son talk to current students. Probably easier to do if he’s on his own and not with his parents behind him 
He could go to one of the cafeterias or a place like Kerckhoff Coffee House and ask current students if they have a few minutes to chat, introducing himself as a prospective student. Then he could ask about campus life, what they like and don’t, etc. Same with approaching groups of students sitting around outside.
There are also math-related clubs such as http://www.math.ucla.edu/~umsa/ they have links on the page on how to contact them, he could try and ask if someone could meet him for coffee so he could talk to a current student