In addition to general mathematical maturity,
this book assumes you have the following background:
- Basics of finite group theory
- Commutative rings, ideals, quotient rings
- Some elementary number theory
- Basic Galois theory of fields
- Point set topology
- Basic of topological rings, groups, and measure theory
For example, if you have never worked with finite groups before, you
should read another book first. If you haven't seen much elementary
ring theory, there is still hope, but you will have to do some
additional reading and exercises. I will briefly review the basics of
the Galois theory of number fields.
Some of the homework problems involve using a computer, but I'll give
you examples which you can build on. I will not assume that you have
a programming background or know much about algorithms. If you don't
have PARI [ABC+] or [BCP97], and don't want to install
either one on your computer, you might want to try the following
online interface to PARI and :
http://modular.fas.harvard.edu/calc/
William Stein
2004-05-06
