Honors Algebra I - Fall 2016

Monday, Wednesday, Friday 10:30 am - 11:20 am, Hayes Healy 125
Course website: nd.edu/~smapes1/HonorsLinearAlgebra1.html

Instructor:

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

Office hours:

TBA
Or by appointment.

Textbook:

Linear Algebra Done Right (Third Edition) by Sheldon Axler

Grading:

Homework 15%; Midterms 40% (20% each); Quizes 15%; Final 30%

Midterms:

There will be two midterm exams. The first is Friday Sept. 23 and the second is Friday Nov. 4. 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.

Quizes:

There will be in class quizzes roughly every other Friday 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.

Final:

The projected final exam date is TBA .

Homework:

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

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 textbook Homework
Aug. 24, 26 1st Course in Linear Algebra.
Homework 1
due 8/31 in class
Aug. 29, 31, Sept 2 Vector Spaces. Quiz 1.
sec. 1.A-1.C 		Homework 2
due 9/7 in class
Sept. 5,7,9 Span, Linear Independence, and Bases.
sec. 2.A-2.B 		Homework 3
due 9/14 in class
Sept. 12,14,16 Dimension and Linear Maps. Quiz 2.
sec. 2.C-3.A 		Homework 4
due 9/21 in class
Sept. 19,21,23 Null Spaces and Matrices. Midterm 1.
sec. 3.B-3.C 		Homework 5
due 9/28 in class
Sept. 26,28,30 Invertiblity, Products, and Quotients.
sec. 3.D-3.E 		Homework 6
due 10/5 in class
Oct. 3,5,7 Duality and Polynomials. Quiz 3.
sec. 3.F-4 		Homework 7
due 10/12 in class
Oct. 10,12,14 Invariant Subspaces.
sec. 5.A		 Homework 8
due 10/26 in class
Oct. 17,19,21 Fall break.
Oct. 24,26,28 Eigenvectors. Quiz 4.
sec. 5.B		 Homework 9
due 11/2 in class
Oct. 31, Nov. 2,4 Eigenspaces and Diagonal Matrices. Midterm 2.
sec. 5.C 		Homework 10
due 11/9 in class
Nov. 7,9,11 Inner products and orthonormal bases.
sec. 6.A-6.B 		Homework 11
due 11/16 in class
Nov. 14,16,18 Orthogonal Complements and Self-Adjoint operators. Quiz 5.
sec. 6.C-7.A 		Homework 11
due 11/28 in class (note this is a Monday)
Nov. 21, (23,25) Spectral Theorem. Thanksgiving (no class on 23rd or 25th).
sec. 7.B 		Homework 12
due 12/5 (*note this is a Monday) in class
Nov. 28, 30, Dec. 2 Positive Operators and Isometries. Quiz 6.
sec. 7.C 		Homework 13
due 12/5 in class
Dec. 5, 7 Singular Value Decomposition.
sec. 7.D