- 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

Some of the homework problems involve using a computer, but there
are examples which you can build on. We will not assume that you have
a programming background or know much about algorithms. Most
of the book uses Sage `http://sagemath.org`, which is
free open source mathematical software. The following is an example
Sage session:

sage: 2 + 2 4 sage: k.<a> = NumberField(x^2 + 1); k Number Field in a with defining polynomial x^2 + 1

William Stein 2012-09-24