Week 1: January 23 - 27
Monday:
Introduction. Pythagorean triples.
(
lecture,
tex file,
slides)
Wednesday:
Rings.
(
lecture,
tex file,
slides)
Friday:
Field extensions.
(
lecture,
tex file,
slides)
- Reading: Sections 1.3 and 2.1 (skip the proof of Theorem 2.2 for now).
Week 2: January 30 - February 3
Monday:
Modules and integral extensions.
(
lecture,
tex file,
slides)
- Reading: Sections 1.5 and 2.3. Skip the proofs in 2.3 the first time
through.
Wednesday:
Criterion for integrality. The algebraic integers form a ring.
(
lecture,
tex file,
slides)
- Reading: Section 2.3. Read the proofs of Lemma 2.8 and Theorem 2.9.
- We will have a short quiz at the beginning of class covering the
following: quiz topics. (The quiz covers material
from last week. In general, the quiz will cover the material from all
previous weeks, i.e., it will be cumulative.)
Friday:
Integers in a quadratic extension.
(
lecture,
tex file,
slides)
Week 3: February 6 - 10
Monday:
Discriminants I.
(
lecture,
tex file,
slides)
Wednesday:
Discriminants II.
(
lecture,
tex file,
slides)
- Reading: Section 2.2.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Bases for algebraic integers.
(
lecture,
tex file,
slides)
Week 4: February 13 - 17
Monday:
Norms and traces.
(
lecture,
tex file,
slides)
Wednesday:
Cyclotomic fields I.
(
lecture,
tex file,
slides)
- Reading: Section 3.2.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Cyclotomic fields II.
(
lecture,
tex file)
Week 5: February 20 - 24
Monday:
Noetherian modules.
(
lecture,
tex file,
slides)
Wednesday:
Hilbert Basis Theorem.
(
lecture,
tex file,
slides)
- Reading: Lecture notes.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Snow day.
Week 6: February 27 - March 3
Monday:
Catch-up day.
(
slides)
- Reading: Review lectures from last week.
Wednesday:
Unique factorization.
(
lecture,
tex file)
slides)
- Reading: Skim Sections 4.4–4.7.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Operations on ideals.
(
lecture,
tex file)
slides)
Week 7: March 6 - 10
Monday:
Midterm. The midterm will cover
this material.
Wednesday:
Dedekind domains.
(
lecture,
tex file)
slides)
Friday:
Fractional ideals.
(
lecture,
tex file)
slides)
Spring break: March 13 - 17
No classes this week.
Week 8: March 20 - 24
Monday:
Catch up. (Finish work from the week before break.)
(
slides)
Wednesday:
Smith normal form.
(
lecture,
tex file,
slides)
- Reading: Lecture notes.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Structure theorem for finitely generated abelian groups.
(
lecture,
tex file,
slides)
Week 9: March 27 - 31
Monday:
The norm of an ideal.
(
lecture,
tex file,
slides)
Wednesday:
Generators for ideals in a number ring.
(
lecture,
tex file,
slides)
- Reading: Sections 5.3 and 10.1. Lecture notes.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Group work factoring ideals in number rings
(
group problems,
tex file)
Week 10: April 3 - 7
Monday:
Catch up. Finish last Wednesday's work.
- Reading: Sections 5.3 and 10.1. Lecture notes.
Wednesday:
Minkowski's theorem.
(
lecture,
tex file)
slides)
- Reading: Sections 6.1 and 6.2.
- We will have a short quiz at the beginning of class covering the
following: quiz topics.
Friday:
Minkowski's theorem. Four squares theorem.
(
lecture,
tex file,
slides)
Week 11: April 10 - 14
Monday:
Lattices associated with number fields.
(
lecture,
tex file,
slides)
- Reading: Chapter 8 and Theorem 9.4.
Wednesday:
The class group I.
(
lecture,
tex file,
slides)
- Reading: Sections 9.1 and 9.3
- Turn in idea(s) for final project.
Friday:
The class group II.
(
lecture,
tex file,
slides)
Week 12: April 17 - 21
Monday:
Dirichlet's unit theorem.
(
lecture,
tex file,
slides)
Wednesday:
Project meetings
Friday:
Project meetings.
Week 13: April 24 - 28
Monday:
Presentations.
Wednesday:
Presentations.
Friday:
Presentations.
Here is a link to a
sample beamer tex
file. (It is based on the slides for Monday, Week 11.)
The \(\LaTeX\) document preparation system