Hello! I majored in Applied Math at UCSD during my undergrad. I chose to pursue a different field for my PhD training, but I was very involved with the math department both in academics and administrative things, so I just want to share this one point based on my experience.
You are definitely right about the great research at UCSD. It is almost the accepted fact among undergrad students that some professors are very much devoted to research to the degree that their teaching is mostly quite lame. Certainly it is natural for professors to focus on research, but this overall tendency is much more obvious in the math department than others. Among students the math department is famous for not caring too much about their undergrads, which means you will possibly enjoy the high availability of advisors.
I can certainly name a couple of professors who are genuinely passionate about teaching and I enjoyed their lectures very much. But the overall vibe is that the department does not really care that much about the undergrad teaching aspect. On the flip side, that could potentially be a plus for graduate students.
