Honors Algebra II - Spring 2014

Monday, Wednesday, Friday 10:30 am - 11:20 am, TBA
Course website: nd.edu/~smapes1/HonorsLinearAlgebra2.html


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

Office hours:

Or by appointment.


Linear Algebra Done Right (Third edition) by Sheldon Axler


Homework 15%; Midterms 30% (15% each); Quizes 10%; Term Paper 15%; Final 30%


There will be two midterm exams. The first is Friday Feb. 24 and the second is Friday April 7. The exams will cover the material up to the Friday before the exam. Announcements as to exactly what sections will be on the exam will be made closer to the exam date.


There will be in class quizzes roughly every three weeks on Mondays each taking about 20 minutes. The objective of the quizzes is for you to get direct feedback from me on your written work. Depending on the topics you should expect that each quiz will consist of one computational problem and one proof.

Term Paper:

This semester I will ask that each of you write a 5 to 10 page paper which will allow you to explore applications of linear algebra to other fields of mathematics or to some real life situations. There will be more resources on this for you as the semester goes on but roughly speaking I would like your topic to be chosen by spring break, and a first draft by April 10.


The projected final exam date is TBA .


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 textbook Homework
Jan. 18,20 Mini Course on Determinants
Homework 1
due 1/25 in class
Jan. 23,25,27 Generalized Eigenvectors, Decomposition of an Operator
sec. 8.A, 8.B
Homework 2
due 2/1 in class
Jan. 30, Feb 1,3 Characteristic Polynomials, Jordan Form Quiz 1.
sec. 8.C-8.D
Homework 3
due 2/8 in class
Feb. 6,8,10 Inner products and orthanormal bases
sec. 6.A-6.B
Homework 4
due 2/15 in class
Feb. 13,15,17 Orthogonal complements and self-adjoint operators
sec. 6.C-7.A
Homework 5
due 2/22 in class
Feb. 20,22,24 Spectral Theorem Midterm 1.
sec. 7.B
Homework 6
due 3/1 in class
Feb. 27, Mar 1,3 Positive operators and isometries, singular value decomposition
sec. 7.C - 7.D
Homework 7
due 3/8 in class
Mar. 6,8,10 Complexification, operators on real inner product spaces Quiz 2.
sec. 9.A-9.B
Homework 8
due 3/22 in class
Mar. 13,15,17 Spring break.
Mar. 20,22,24 Trace and Determinant
sec. 10.A-10.B
Homework 9
due 3/29 in class
Mar. 27,29,31 Multilinear functionals and tensor products
Homework 10
due 4/5 in class
Apr. 3,5,7 Symmetric algebra and exterior algebra .Midterm 2.
Homework 11
due 4/12 in class
April 10,12 Exterior algebra, connectin to trace and determinant Easter (no class on 14th).
Homework 11
due 4/19 in class
April 19,21 TBA Easter (no class on 17th).
Homework 12
due 4/26 in class
April 24,26,28 TBA Quiz 3.
Homework 13
due 4/3 in class
May 1,3 TBA