Linear Algebra - Spring 2016

Monday, Wednesday, Friday 8:20 am - 9:10 am, Hayes Healy 129
Course website:


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

Office hours:

Or by appointment.


Linear Algebra: A Geometric Approach by Shifrin and Adams, 2nd edition


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


There will be two midterm exams. The first is Friday Feb. 12 and the second is Wednesday April 6. 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 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.


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 .


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

Selected homework problems by each section.
Date Reading - sections in textbook Homework
Jan. 13,15 Vectors, dot products, and introduction to proofs.
sec. 1.1-1.2
Homework 1: 1.1,1.2
due 1/20 in class
Jan. 18,20,22 Hyperplanes and linear systems. Quiz 1.
sec. 1.3-1.4
Homework 2:
due 1/27 in class
Jan. 25,27,29 Theory of linear systems and some applications.
sec. 1.5-1.6
Homework 3
due 2/3 in class
Feb. 1,3,5 Matrix operations, linear transformations, and inverse matrices. Quiz 2.
sec. 2.1-2.3
Homework 4
due 2/10 in class
Feb. 8,10,12 Elementary matrices and transpose matrices. Midterm 1.
sec. 2.4-2.5
Homework 5
due 2/17 in class
Feb. 15,17,19 Subspaces of R^n, four fundamental subspaces, linear independence.
sec. 3.1-3.3
Homework 6
due 2/24 in class
Feb. 22,24,26 Dimension, abstract vector spaces. Quiz 3.
sec. 3.4-3.5
Homework 7
due 3/2 in class
Feb. 29, Mar. 2,4 Inconsistent systems and projection, orthogonal bases, linear transformations.
sec. 4.1-4.3
Homework 8
due 3/16 in class
Mar. 7,9,11 Spring break.
Mar. 14,16,18 Abstract linear transformations, determinants. Quiz 4.
sec. 4.4-5.1
Homework 9
due 3/23 in class
Mar. 21,23, (25) Cofactors and Cramer's rule, signed area and volumes. (Easter break)
sec. 5.2-5.3
Homework 10
due 3/30 in class
Mar. (28), 30, April 1 (Easter break) Characteristic polynomial, diagonalizability. Quiz 5
sec. 6.1-6.2
Homework 11
due 4/8 (note this is Friday) in class
April 4,6,8 Spectral theorem. Midterm 2.
sec. 6.4
Homework 11
due 4/13 in class
April 11,13,15 Complex eigenvalues and Jordan canonical form.
sec. 7.1
Homework 12
due 4/20 in class
April 18,20,22 Matrix exponentials and differential equations. Quiz 6.
sec. 7.3
Homework 13
due 4/27 in class
April 25,27 TBA/catch up