I did a math minor at UCLA, and he taught the upper-division linear algebra class I took. He didn't like the book, so he decided to write his own lecture notes, which formed a book unto themselves. They're still available online at http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/. If you ever have the itch to learn linear algebra, read them, they're quite excellent.

It was pretty obvious at class and obvious hours he was crazy smart -- but I had no way of knowing he was Fields Medal smart. But unlike other crazy smart professors I've had, he's a very gifted teacher as well. I mostly learned by reading the books and considered the lectures as an ancillary learning aid, but his lectures were very illuminating. I'm glad he now has a blog to teach a wider audience at http://terrytao.wordpress.com/, but unfortunately most of it is beyond what I can understand. If you're a math die-hard, be sure to read that.