I had a look at some university undergraduate mathematics textbooks on subjects I would need to do some catching up. I notice that there are a huge number of exercises. Now the question comes up in my mind:
if I do all those exercises will I be all that better off?
Somehow I don't feel so. I often feel that if you drown in exercises you
1) can lose the feeling that there might be more advanced topics
2) cant' see the forest for the trees.
I'm not saying that I'm certain of these assumptions, but it's worth thinking about.
It's interesting to compare some self-contained advanced texts like Walter Rudin's Real and Complex analysis
with more elementary texts. Of course one might argue that you should read the text that corresponds to
your level of maturity. This answer is a bit pat.
Rudin's book is known for very short clever proofs of theorems in analysis. At the same time it could be argued that slick proofs might not help understanding the subject as much as stodgy proofs.
No comments:
Post a Comment