Math 8803, Algebraic Number Theory
Fall 2006
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Instructor: Matt Baker
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Time and place: MWF 10:05 - 10:55, Skiles 246
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E-mail: mbaker@math.gatech.edu.
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Office: 263 Skiles
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Office Hours: Mondays 11-12 and Wednesdays 1-2
Course texts:
- "Algebraic Number Fields" (2nd edition) by Gerald J. Janusz (required)
- "A Brief Guide to Algebraic Number Theory" by H.P.F. Swinnerton-Dyer
(recommended)
Files available for downloading: (pdf format)
Prerequisites:
Course outline:
This course is intended to be an introduction to Algebraic Number Theory.
The major topics to be covered include rings of integers,
factorization in Dedekind domains, finiteness of the class group,
Dirichlet's unit theorem, p-adic numbers and p-adic analysis, and the
interplay between local and global fields.
We will illustrate these concepts with applications to
Diophantine equations and cryptography.
As time permits, we will also discuss the analytic theory of Dedekind zeta
functions and Dirichlet L-functions, and provide an introduction to Class
Field Theory.
Exams:
There will be no exams in this class.
Homework:
Homework assignments will be assigned periodically throughout the course,
and students are expected to turn in at least half of the assigned problems.
Grading Policy:
Students enrolled in the class will be
encouraged to give a talk in an informal seminar accompanying the course,
and will be required to complete a 6-10 page final paper
on a topic which builds on material learned in the course.
Some suggestions for final paper topics can be found
here.
Grades will be based on homework, class attendance, and the final paper.
Collaboration:
On the homework sets, collaboration is encouraged.
However, you must write up your own solutions.
This page was last modified on December 27, 2006 by
Matt Baker.