Disclaimer: My D was in EECS honors program. My answers below are what I learned from her. They may not be correct for other majors/schools.
- is there any correlation between graduating with honors in math and taking honor classes?
I don’t think so. In fact, I don’t think there are “honor classes” at UCB.
- what percent of students graduating with BS in math, and graduating with honors?
Math departments must have the statistics somewhere…
- what role honor classes play in admission to PhD program?
The honors program (EECS of course) gives the students better access to advisors and to research opportunities. That helps in preparing the student for PhD program application. But in themselves, honor classes have no effect on grad school admissions.
My D graduated with honors and was admitted to a PhD program, but I don’t think that had anything to do with her being in EECS Honors Program.