Math 330 - Fall 2006
Algebraic Number Theory

Lucy and Lily, an algebraic number theory game. (For the website to play the game, go here. A lower-dimensional version of the same idea is here.)

Frobenius' proof of the existence of Frobenius elements (an application of localization)

Dirichlet's unit theorem.

Some calculations of class groups using the Minkowski bound.

Orbits of SL₂ and class numbers.

Review of Galois theory.

Integer rings without a power basis.

A non-free integral extension.

Polynomials over a finite field.

Totally ramified primes and Eisenstein polynomials.

Discriminants and ramified primes.

Factoring prime ideals.

Primitive vectors and SL_n. (revised version posted on 10/9)

Unique ideal factorization in rings of integers. (revised version posted on 10/9)

Algebras over a field.

Separability for field extensions.

Prime ideal factorization in quadratic fields.

The Gaussian Integers.

Lecture notes on algebraic number theory by James Milne (1998), René Schoof (1994), Peter Stevenhagen (2004), and Tom Weston (1999). More online lecture notes on algebraic number theory are listed here.

The course is over.