| Date |
|
Section |
|
Topic |
| Thursday,
August 18 |
|
1.1 |
|
Uniqueness
of factorization |
| |
|
1.2 |
|
A
general problem |
| Tuesday,
August 23 |
|
1.3 |
|
The
Gaussian integers |
| |
|
2.1 |
|
Rational
and Gaussian primes |
| Thursday,
August 25 |
|
2.2 |
|
Congruences |
| |
|
2.3 |
|
Determination
of the Gaussian primes |
| Tuesday,
August 30 |
|
2.4 |
|
Fermat’s
theorem for Gaussian primes |
| |
|
3.1 |
|
The
ring of polynomials |
| Thursday,
September 01 |
|
3.2 |
|
The
Eisenstein irreducibility criterion |
| |
|
3.3 |
|
Symmetric
polynomials |
| Tuesday,
September 06 |
|
4.1 |
|
Numbers
algebraic over a field |
| Thursday,
September 08 |
|
4.2 |
|
Extensions
of a field |
| Tuesday,
September 13 |
|
|
|
Class Cancelled
|
| Thursday,
September 15 |
|
|
|
Class Cancelled |
| Tuesday,
September 20 |
|
4.3 |
|
Algebraic
and transcendental numbers |
| |
|
5.1 |
|
Bases
and finite extensions Notes |
| Thursday,
September 22 |
|
5.2 |
|
Properties
of finite extensions |
|
|
Test
1 |
| Tuesday,
September 27 |
|
5.3 |
|
Conjugates
and discriminants |
| |
|
5.4 |
|
The
cyclotomic field |
| Thursday,
September 29 |
|
6.1 |
|
Algebraic
integers Notes |
|
|
6.2 |
|
The
integers in a quadratic field |
| Tuesday,
October 04 |
|
6.3 |
|
Integral
bases |
|
|
6.4 |
|
Examples
of integral bases |
| Thursday,
October 06 |
|
Fall
Vacation |
|
|
| Tuesday,
October 11 |
|
7.1 |
|
Units
and primes |
|
|
7.2 |
|
Units
in a quadratic field |
| Thursday,
October 13 |
|
7.3 |
|
The
uniqueness of factorization |
| Tuesday,
October 18 |
|
7.4 |
|
Ideals
in an algebraic number field |
| Thursday,
October 20 |
|
8.1 |
|
Basic
properties of ideals Notes |
Tuesday,
October 25
|
|
8.1
|
|
|
| Thursday,
October 27 |
|
8.2 |
|
The
classical proof of the unique factorization theorem |
| Tuesday, November 01 |
|
8.2
|
|
|
|
|
9.1 |
|
The
highest common factor of two ideals |
| Thursday,
November 03 |
|
9.2 |
|
Unique
factorization of integers |
|
|
9.3 |
|
The
problem of ramification |
| Tuesday,
November 08 |
|
9.4 |
|
Congruences
and norms |
|
|
9.5 |
|
Further
properties of norms |
| |
|
Test
2 |
| Thursday,
November 10 |
|
10.1 |
|
Ideal
classes |
|
|
10.2 |
|
Class
numbers |
| Tuesday,
November 15 |
|
11.1 |
|
Pythagorean
triples |
| Thursday,
November 17 |
|
11.2 |
|
The
Fermat conjecture |
| Tuesday,
November 22 |
|
11.3 |
|
Units
in cyclotomic fields |
| Thursday,
November 24 |
|
Thanksgiving |
|
|
| Tuesday,
November 29 |
|
11.4 |
|
Kummer’s
theorem |
| Thursday,
December 01 |
|
Review |
|
|