Math 581e: Algebraic Number Theory (Fall 2012) -- Syllabus
Basics
Content
This is a graduate-level course on algebraic number theory (though
undergraduates are welcome!). This course will be mostly theoretical
(we will prove a lot of results), augmented by tutorials about how to
compute with the objects we encounter. We will give complete proofs of
the two main theorems of algebraic number theory: finiteness of class
groups and the unit theorem. You will also learn how to use Sage to
compute with all of the objects discussed in the course.
The course textbook is available online.
Main Course Topics
- Commutative algebra
- Dedekind domains
- Ideal class groups
- Unit groups
- Decomposition and inertia groups, ramification
- Algebraic number theory computation using Sage
Prerequisites
In addition to general mathematical maturity (you know what a proof
is, and you've written some), I will assume that you are familiar with
finite groups, linear algebra, commutative rings, ideals, elementary
number theory, Galois theory of fields, topology of R^{n}, and
the Sage mathematics software.
Your Grade
- Homework: There will be weekly homework assignments, worth
50% of your grade. Your lowest two homework grades will be dropped. No
late homework will be accepted. Homework will typically be due on
Fridays.
- Final Projects: There will be a final project, which is
worth 50% of your grade. It will be due December 7, 2012. Start thinking about your project now!
Browse projects from 2007,
2005,
2004.