Honors Algebra IV - Spring 2013

Monday, Wednesday, Friday 11:45 am - 12:35 pm, 201 O'Shaughnessy Hall
Course website: nd.edu/~smapes1/HonAlgebra4.html


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

Office hours:

Monday 4-5pm; Tuesday 1:30-2:30pm
Or by appointment.


Michael Artin - Algebra, 2nd Edition.


Homework 20%; Midterm 20%; Quizes 15%; Project 15%; Final 30%


There will be one midterm exam after the completion of the material in chapters 15 and 16. The expected date will be March 22.


There will be two in class quizzes each taking about 15 minutes. The objective of the quizzes will be to test you on important definitions and application of important theorems. The first quiz will be after the material from chapter 15 is completed so a tentative date is 2/15. The second quiz will cover the important definitions from chapter 14 and will tentatively be on 4/15. As the dates get closer, the exact dates of the quizzes will be announced a week in advance.


The project will consist of a written term paper and an oral presentation at the end of the semester. There will be a hand out with detailed information on the project including a list of potential topics. Important deadlines to know are:


The projected final exam date is Tuesday May 7 at 4:15 pm to 6:15 pm. .


There will be weekly written assignments which can be found below along with the due date.


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 .


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

Date Reading - sections in Artin Homework
Jan. 16,18 Review of ideas from ch 12.
sec. 12.1-12.3
Homework 1
due 1/23 in class
Jan. 21,23,25 Irreducible polynomials, fields and field extensions.
sec. 12.4, 15.1-15.2
Homework 2
due 1/30 in class
Jan. 28,30, Feb 1 Degrees of field extensions, compass and ruler constructions.
sec. 15.3-15.5
Homework 3
due 2/6 in class
Feb. 4,6,8 Adjoining roots, finite fields, and primitive elements.
sec. 15.6-15.8
Homework 4
due 2/13 in class
Feb. 11,13,15 Fundamental Theorem of Arithemetic, symmetric functions and the discriminant.
sec. 15.10, 16.1-16.2
Homework 5
due 2/20 in class
Feb. 18,20,22 Splitting fields, isomorphisms of field extensions, and fixed fields.
sec. 16.3-16.5
Homework 6
due 2/27 in class
Feb. 25,27, Mar. 1 Galois extensions, Fundamental theorem of Galois Theory.
sec. 16.6-16.7
Homework 7
due 3/8 in class
Mar. 4,6,8 Solving polynomial equations (degrees 3,4,5).
sec. 16.8-16.9
Homework 8
due 3/20 in class
Mar. 11,13,15 Spring break.
Mar. 18,20 Cyclotomic extensions and Kummer extensions.
sec. 16.10-16.11
Homework 9
due 3/27 in class
Mar. 22 Midterm.
Mar. 25,27 Modules.
sec. 14.1-14.2
Homework 10
due 4/3 in class
Mar. 29, April 1 Easter holiday (note this is a Friday and a Monday).
April 3,5 Diagonalization of integer matrices.
sec. 14.4
Homework 11
due 4/10 in class
April 8,10,12 Generators and relations, Noetherian rings.
sec. 14.5-14.6
Homework 12
due 4/17 in class
April 15,17,19 Structure Theorem for Abelian Groups, and Structure theorem for modules over F[t].
sec. 14.7-14.8
Homework 13
due 4/24 in class
April 22,24,26 Term paper presentations
April 29, May 1 Term paper presentations