Most helpful positive review
4 of 4 people found the following review helpful
Gee, a math book that really teaches, how unusual
on April 22, 2003
I tried to learn complex analysis from Ahlfors, I wouldn't recommend you try it although it is a good book. The problem is there are certain subtleties in complex variables that are NOT obvious. There are few authors of math books that remember that we do not know these subtleties. I could go on a tirade about the general state of math literature for hours, but my only remark here is that in my view most authors seem to be trying to impress someone other than the students, maybe other professors ? Anyhow, this book is a definite departure from this nonsense. There are 12 chapters each with many exercises. The first couple of chapters have over forty and since I try to do them all, well ... If you read this book carefully and do the execises you WILL know this subject. You could teach it. You don't see Thm 184.108.40.206.8 followed by Proof. What you do see is a clear presentation of the ideas with PICTURES and EXPLANATIONS that you can understand, of course you really find out about that "understand" part when you get to the exercises. The biggest problem I had was getting out of the old way of thinking and into a more geometric way of thinking. Couldn't recommend it more highly. Another author who writes to teach is Victor Bryant. His book Yet Another Introduction to Analysis is great for a highschool senior or 1st year college. (He is with me on the state of math literature.) Also, Hans Schwerdtfeger's book Geometry of Complex Numbers goes well with Needham and is very cheap ! I'm surprised Needham didn't include it in the bibliography. It's a little gem and covers some of the same material.