[herodotus]

I did my undergraduate degree at Wits University in Johannesburg. My Real Analysis course was SO boring. The lecturer basically wrote on the board:

Lemma: ......

Proof: ....

etc.

Theorem: Let epsilon < K, ....

Proof: ....

--QED--

which we all dutifully copied into our notebooks. Very uninspiring.

But when I got to the University of Waterloo for graduate studies, I had a real competitive advantage over my peers for the theory courses I took: I knew what a proof was, and how to do one.

[WoahNoun]

I think the problem a lot of people have (even math majors) is expecting the lecture to be the first introduction to the topic. It's like taking a literature class and going to lecture without doing the reading. Reading (or even just skimming) the next section/chapter of the book before the lecture allows you to focus and ask questions on the parts of the material you didn't understand during the lecture. I very rarely wrote down full proofs in my notes during the lecture. I focused on the lecture itself and wrote down the pieces that I wanted to remember.

[constantcrying]

>which we all dutifully copied into our notebooks. Very uninspiring.

I had 5 years of that, a very enjoyable time.