The main theme of this course is foundational linear algebra considered from a numerical viewpoint. We focus on solutions of linear systems of equations, eigenvalues and eigenvectors, and transformations. The course emphasizes and illustrates proof and numerical implementation using problems arising in applications. Multivariable calculus and linear algebra are prerequisites.
Lectures: 
M, W  3:30pm  4:45pm 
Cudahy 131 
Office Hours: 
Monday,  9:00am  10:00am 
Cudahy 307  Tuesday,  3:00pm  4:30pm 
Friday,  2:30pm  4:00pm  
and by appointment 
I recommend using Overleaf (free) to write your assignments in LaTeX. You can use this document as a basic template by cloning it to your own account.
I'm happy to help troubleshoot your LaTeX in office hours!
Jan 14  Classes begin 
Jan 21  Martin Luther King, Jr. Day, no classes 
Jan 22  Last day to add/drop classes or request CR/NC option 
March 48  Midterm exams 
March 1017  Spring break, no classes 
April 12  Last day to withdraw from classes 
April 1822  Easter break, no classes 
May 4  Last day of classes 
TBD  Math 6040 final exam 
#  Date  Topics  Homework & Announcements 

1  Mon, Jan 14 
Syllabus Start Lecture 1 (Linear Algebra Review) 
There will be no office hours on Tuesday, Jan 15 or Friday, Jan 18. Office hours will resume the following week. 
2  Wed, Jan 16  Continue Lecture 1 (Linear Algebra Review)  
Mon, Jan 21  Martin Luther King, Jr. Day — no class  
3  Wed, Jan 23  Finish Lecture 1 (Linear Algebra Review) 
Due Monday, January 28, by 11:59pm Must be submitted electronically on D2L

4  Mon, Jan 28  Lecture 2 (Orthogonal Vectors and Matrices) 
Due Friday, February 1, by 11:59pm Must be submitted electronically on D2L

5  Wed, Jan 30  Finish Lecture 2  
6  Mon, Feb 4  Lecture 3 (Norms) 
Due Monday, February 11, by 3:30pm Must be submitted electronically on D2L

7  Wed, Feb 6 
Lecture 4 (SVD, part 1) Matlab Matrix Tutorial Plotting Demo (created by Sarah Hamilton) 
Due Wednesday, February 13, by 3:30pm Must be submitted electronically on D2L

8  Mon, Feb 11  Lecture 5 (SVD, part 2) 
Due Monday, February 18, by 3:30pm Must be submitted electronically on D2L

9  Wed, Feb 13  Lecture 6 (Projectors)  No homework today! Spend a few minutes playing around in Matlab. 
10  Mon, Feb 18 
Finish Lecture 6 (Projectors) Lecture 7 (QR Decomposition) 
Due Monday, February 25, by 3:30pm Must be submitted electronically on D2L

11  Wed, Feb 20 
Finish Lecture 7 (QR Decomposition) Lecture 8 (GramSchmidt Orthogonalization) 
Due Wednesday, February 27, by 3:30pm Must be submitted electronically on D2L

12  Mon, Feb 25  Finish Lecture 8 (GramSchmidt Orthogonalization) 
Due Monday, March 4, by 3:30pm Must be submitted electronically on D2L

13  Wed, Feb 27  Lecture 11 (Least Squares Problems) 
Due Wednesday, March 6, by 3:30pm Must be submitted electronically on D2L

14  Mon, Mar 4  Lecture 12 (Conditioning and Condition Numbers)  No assignment. 
15  Wed, Mar 6 
Inclass Midterm Exam Takehome Exam Assigned Covers up to and including Lecture 11. 

Mon, Mar 11  Spring Break — no class  
Wed, Mar 13  Spring Break — no class  
16  Mon, Mar 18 
Finish Lecture 12 Lecture 13 (Floating Point Arithmetic) 
No assignment. 
17  Wed, Mar 20 
Takehome Exam Due Lecture 14 (Stability) Lecture 15 (More on Stability) 
No assignment. 
18  Mon, Mar 25 
Finish Lecture 15 Lecture 17 (Stability of Back Substitution) 
Due Monday, April 1, by 3:30pm Must be submitted electronically on D2L

19  Wed, Mar 27 
Finish Lecture 17 Lecture 18 (Conditioning of Least Squares Problems) 
No assignment. 
20  Mon, Apr 1 
Finish Lecture 18 Lecture 19 (Stability of Least Squares Problems) 
Due Monday, April 8, by 3:30pm Must be submitted electronically on D2L

21  Wed, Apr 3  Lecture 24 (Eigenvalue Problems) 
Due Wednesday, April 10, by 3:30pm Must be submitted electronically on D2L

22  Mon, Apr 8 
Finish Lecture 24 Lecture 25 (Overview of Eigenvalue Algorithms) 
Due Monday, April 15, by 3:30pm Must be submitted electronically on D2L

23  Wed, Apr 10  Lecture 26 (Reduction to Hessenberg or Tridiagonal Form) 
Due Wednesday, April 17, by 3:30pm Must be submitted electronically on D2L

24  Mon, Apr 15  Lecture 27 (Rayleigh Quotient, Inverse Iteration)  No assignment. 
25  Wed, Apr 17  Lecture 28 (QR Algorithm without Shifts)  No assignment. 
Mon, Apr 22  Easter Break — no class  
26  Wed, Apr 24 
Finish Lecture 28 Lecture 32 (Overview of Iterative Methods) 
No assignment. 
27  Mon, Apr 29  Lecture 33 (The Arnoldi Iteration)  No assignment. 
28  Wed, May 1  Lecture 34 (How Arnoldi Locates Eigenvalues)  No assignment. 