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
Email: smapes1 (at) nd.edu
Office: 228 (Hayes-Healey)
Tel: (574) 631-7586
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:
- Jan. 31 - Topic choice due via email
- Feb. 27 - Outline due
- Mar. 27 - Rough draft due
- April 22 - Final draft due and presentations begin
- May 1 - Presentation feedback due
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.
- 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!
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.
|| Reading - sections in Artin
| Jan. 16,18
|| Review of ideas from ch 12.
| 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.
| Homework 3
due 2/6 in class
| Feb. 4,6,8
|| Adjoining roots, finite fields, and primitive elements.
| 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.
| Homework 6
due 2/27 in class
| Feb. 25,27, Mar. 1
|| Galois extensions, Fundamental theorem of Galois Theory.
| Homework 7
due 3/8 in class
| Mar. 4,6,8
|| Solving polynomial equations (degrees 3,4,5).
| Homework 8
due 3/20 in class
| Mar. 11,13,15
|| Spring break.
| Mar. 18,20
|| Cyclotomic extensions and Kummer extensions.
| Homework 9
due 3/27 in class
| Mar. 22
| Mar. 25,27
| 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.
| Homework 11
due 4/10 in class
| April 8,10,12
|| Generators and relations, Noetherian rings.
| Homework 12
due 4/17 in class
| April 15,17,19
|| Structure Theorem for Abelian Groups, and Structure theorem for modules over F[t].
| Homework 13
due 4/24 in class
| April 22,24,26
|| Term paper presentations
| April 29, May 1
|| Term paper presentations