## Honors Algebra III - Fall 2012

Monday, Wednesday, Friday 11:45 am - 12:35 pm, 119 Debartolo
Course website: nd.edu/~smapes1/HonAlgebra.html

#### Instructor:

Sonja Mapes
Email: smapes1 (at) nd.edu
Office: 228 (Hayes-Healey)
Tel: (574) 631-7586

#### Office hours:

Fridays 2pm-3pm
Or by appointment.

#### Textbook:

Michael Artin - Algebra, 2nd Edition.

#### Grading:

Homework 20%; Midterms 40% (20% each) each; Final 40%

#### Midterms:

There will be two midterm exams. The first will be in class on Friday September 21. The second will be a take home exam, and the date will be announced later but it will be after we complete the material from chapter 10.

#### Final:

The projected final exam date is Tuesday Dec 11 at 4:14-6:15 pm .

#### Homework:

There will be weekly written assignments which can be found below along with the due date and time.
• Late homework will not be accepted.
• The two lowest homework grades will be dropped.
• Please staple or paper clip your work.
• Don't forget to write your name on it!

#### Honesty:

This class follows the binding Code of Honor at Notre Dame. The graded work you do in this class must be your own. In the case where you collaborate on homework with other students make sure to fairly attribute their contribution to your project. For more information on the honor code see www.honorcode.nd.edu .

### Syllabus

This is a tentative syllabus and it is likely to change as the course progresses.

 Date Reading - sections in Artin Homework Aug. 22, 24 Prelimiaries; Laws of composition; Groups and subgroups sec. 2.1-2.3 Homework 1 due 8/27 in class Aug. 27, 29, 31 Cyclic groups; homomorphisms. sec. 2.4-2.5 Homework 2 due 9/3 in class Sept. 3, 5, 7 Equivalence relations, partitions, cosets. sec. 2.6-2.9 Homework 3 due 9/10 in class Sept. 10, 12, 14 Correspondence theorem, product groups, quotient groups. sec. 2.10-2.12 Homework 4 due 9/17 in class Sept. 17, 19 Abstract symmetry.sec. 6.7, 6.8, and some of 6.4 Homework 5 due 9/24 in class Sept. 21 Midterm. Sept. 24,26,28 The counting formula; the class equation. sec. 6.9-6.10, 7.1-7.2 Homework 6 due 10/1 in class Oct. 1, 3, 5 p-Groups, Icosahedral group, normalizers sec. 7.3, 7.4, 7.6 Homework 7 due 10/8 in class Oct. 8, 10, 12 Sylow theorems, groups of order 12. sec. 7.7, 7.8 Homework 8 Oct. 15, 17, 19 Fall break Oct. 22, 24, 26 Free groups; generators and relations. sec. 7.9, 7.10 Homework 9 due 10/29 in class Oct. 29, 31, Nov. 2 Rings, homomorphisms, ideals. sec. 11.1-11.3 Homework 10 due 11/5 in class Nov. 5, 7, 9 Quotient rings; Product rings. sec. 11.4-11.6 Homework 11 due 11/12 in class Nov. 12, 14, 16 Maximal ideals; introduction to algebraic geometry. sec. 11.7-11.9 Homework 12 due 11/19 in class Nov. 19 Factoring integers and unique factorization domains. sec. 12.1-12.2 Homework 13 due 11/26 in class Nov. 21, 23 Thanksgiving Nov. 26, 28, 30 Gauss' lemma; factoring integer polynomials; gauss primes. sec. 12.3-12.5 Homework 14 due 12/3 Dec. 3, 5 TBA