Algebraic Number Theory (Math 525)

Dr. Mills' Math 525 (Algebraic Number Theory) Web Page

I am teaching Algebraic Number Theory in the Spring of 2005. We will meet MW from 3:00 to 4:15 in AG 152.

Lecture notes are now available online (see below).

Note to Students: As some of you have a 2:00 class in Quigley Hall (a fair distance from the Agricultural Building), we will usually start class at 3:05, thus finishing around 4:20. This should not pose problems for anyone, as our end time is unconventional.

Schedule for Week of 3/28/05:

Monday (3/28, 3:00-4:15): 2.5 (Revisiting Dirichlet's Unit Theorem -- Stein's presentation considered)
Tuesday (3/29): Homework for Section 2.4 Due by 5pm
Wednesday (3/30, 3:00-5:00): Student Presentations of HW Problems and Review for Exam #2
Friday (4/1, 3:00-5:00): Exam #2 (Sections 2.1-2.4)

OFFICE HOURS: MW 9am-noon

Links:

Syllabus (updated)

Lecture Notes (This is a work in progress. The notes for Chapter 1 and Sections 2.1-2.4, 2.6 are now available. I intend to post lecture notes at least one week in advance throughout the term.)

Answers to HW Problems (updated 2/24/05 to include all HW problems from Chapter 1)

Review Sheet for Exam #1 (posted 2/15/05)

Follow this link to Amazon.com's page for the course's primary text (Algebraic Number Theory by R.A. Mollin). Here is a link to Mollin's errata page.

Here is a link to the course's secondary text (online algebraic number theory text written by W.A. Stein).

Deep results in algebraic number theory are used to prove Fermat's Last Theorem (FLT). Recently, a generalization of FLT, known as the Debarre-Klassen Conjecture, has been proposed. Click here to read a recent paper which addresses the conjecture for quadratic fields.

Papers to Read:

"Lucas sequences whose 12th or 9th term is a square" (deSouza)
"Power Bases for 2-Power Cyclotomic Fields" (Ghebremicael)
"Sums of Factorials in Binary Recurrence Sequences" (Marr)
"Markoff Numbers, Principal Ideals and Continued Fraction Expansions" (Schwartz)

Most recently updated on 03 May 05 at 5:10 p.m.
Contact Dr. Mills at dmills@math.siu.edu.

Comments: Donald D. Mills