Math 514: Algebraic Number Theory
Fall Semester, 2005
Instructor:
Jeremy Teitelbaum
Office: SEO 421
Phone: 312-996-2371
Office Hours:
Text:
We will follow
Milne's notes on Algebraic Number Theory
Hours: 3:00-3:50 p.m. TH 215
Call Number: 22687
Topics
This course is an introduction to algebraic number theory. Principal topics are:
Dedekind domains and prime decomposition; finiteness of the class group and finite
generation of the unit group in rings of algebraic integers.
Assorted Notes
Examples ( dvi ) ( ps ) ( pdf )
Some prime factorization data
Sample computation of Hermite Normal Form
Sample computation of Smith Normal Form
Computing the norm of an element using Maple
Simple computation of polynomial of integral dependence for
sqrt(2)+sqrt(3).
Computation of classgroup and fundamental
unit in the field given by root of x^3-2x^2+x-6=0.
Homework
Homework on Fermat's Last Theorem for 9/19/05
Finite dimensional k-algebras (homework) for 9/19/05
Grading
Grades will be based on homework problems assigned at regular intervals.
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Other References
Hardy, G.H. and Wright, E.M. An Introduction to the Theory of Numbers,
Fifth Edition. Oxford Science Publications, Oxford University Press, 1993.
Borevich, Z. I. and Shafarevich, I. R. Number Theory,
Academic Press, Orlando, 1966.
Lang, S. Algebraic Number Theory, Graduate Texts in Math 110, Springer-Verlag,
Berlin, 1994.
Marcus, D. A. Number Fields, Springer-Verlag, Berlin, 1977.
Serre, J.P. A course in arithmetic, Graduate Texts in Mathematics 7, Springer-Verlag, Berlin, 1973.
Copyright © 1999 Jeremy T. Teitelbaum.
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