Undergrad overwhelmed by a graduate math class I'm an undergraduate studying math and I'm taking a graduate math class for the first time this semester. I've taken the undergraduate prerequisites, but it's still very challenging, which I was expecting.

I'm starting to get overwhelmed by the content and the pace of the course. The professor is not only very famous in the field but also tends to brush off most things as 'basic' during lectures and doesn't seem to like to answer students' questions in detail. I find it intimidating to approach the professor or go to office hours because I feel like I don't even know the basics. I'm the only undergraduate in the class, but it seems like other graduate students are also finding the content quite intense.

I also don't have anyone to work with, and I find it very difficult to just randomly approach people in the class, not only because I'm introverted but mostly because I feel very embarrassed of my lack of understanding. I'm really interested in the subject and I want to give it my best. It's hard to tackle the problem set even after consulting multiple books, and I feel more discouraged and unsure of myself. I'd appreciate some advice from people with more experience.
Mathematician here: We've all been in a similar situation when transitioning from undergrad to grad classes. You write that you are "embarrassed" due to your lack of understanding; don't worry, others probably are having issues also. But if you do think you aren't getting basics, then it is more, not less important that you talk to your fellow students and the professor. 

However, the main thing you should realize is that this is a pretty regular experience. What matters is how you react to it; don't get demoralized but put the effort in. And don't hesitate to ask questions, even in class; your fellow students are likely confused about some of the same things you are.