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.

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