Customer Reviews

Making Transcendence Transparent: An intuitive approach to classical transcendental number theory

5 star:		(0)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

This is a good introduction to the study of transcendental numbers, and it is pretty new (2004).
The authors provide motivation for complex proofs by working up from simpler proofs for special cases. For example, they prove various properties of the exponential function, and these culminate in proof of the full Lindemann theorem. Likewise a series of special cases leads up to proof of the Gelfond-Schneider theorem.
There is a nice description of Mahler's classification of transcendental numbers.
Chapter 7 concerns elliptic functions and does a good job of introducing the concepts surrounding elliptic curves.
One weakness in this book is that it does not have a good bibliography. It could better fill its niche in the market if the authors had made one. Moreover, there are many proofs I would like to see laid out better, and for this reason I have decided to give just 4 stars.