8/25-8/29

Linear systems and Gauss-Jordan elimination

Bretscher 1.1-1.2

I've added two things to the "files" section of the canvas page: a glossary of terms, and a copy of my class notes. My hope is to keep reposting these as they evolve. Neither document comes with a warranty, so feel free to point out anything that looks wrong.

It's official! As of this fall you can now minor in mathematics at Notre Dame. After linear algebra, it takes 4 more math coures to earn this minor.

8/29-9/3

Vectors and Matrices

Appendix A and 1.3

3Blue1Brown is an excellent Youtube channel for math. Among other things, it has a series of videos about linear algebra , including one about vectors. It also has a series about machine learning.

9/3-9/7

Linear transformations

2.1

9/7-12

Geometric transformations

2nd part of appendix A and 2.2

Here's a nice online app that helps visualize linear transformations from R² to R². Here's another featuring the Mona Lisa.

9/15-9/17

Matrix products

2.3

Fields Medalist (think `Math Nobel prize winner') James Maynard will give a public lecture The Magic of the Primes in Jordan 105 on Monday September 15. Everyone is welcome!

9/19-9/22

Matrix inverses

2.4

9/24-9/26

Image and kernel, spans and linear independence

3.1, 3.2

9/29-10/8

Subspaces, basis, dimension

3.2, 3.3

First midterm is Monday Oct 6. See the files section of Canvas for a review sheet. Also, instead of my usual office hrs on Oct 7/8. I'll be available Sunday Oct 5, 5-6:30 PM in Hayes-Healy 229 to discuss any material related to the exam.

10/8-10/13

Coordinates

3.4

10/13-10/17

Orthogonal projection and the Gram-Schmidt algorithm

5.1, 5.2

Note that I skipped over QR decomposition of matrices. Just not enough time...

10/27

Matrix Transposes

5.3

10/29-10/31

Least squares Solutions of Linear Systems

5.4

11/3-11/7

Determinants

6.1-6.2

My take on determinants--particularly the way I order my discussion--will be different than Bretscher's. I'll use his Theorem 6.2.3 and the relationship with volume as my starting point. And I'll skip his discussion of `patterns' in 6.1.

11/10

Volume and determinants revisited

6.3

I've decided to largely skip over Cramer's Rule. Again, not enough time...

11/12-19

Eigenvalues, eigenvectors and diagonalization

7.1-7.3

I poked around a bit for online linear algebra calculators and found this one . It allows you to enter matrices by name and then perform various operations on them. The interface seems fairly nice and intuitive. If you think you found a better such thing, please let me know.

11/21

Application of diagonalization: transition matrices

7.4

The second midterm takes place in class Monday November 24

12/1

Complex eigenvalues

7.5

12/3

Quick tour: the spectral theorem (data compression, preference modeling)

Chapter 8

Here's a nice online demonstration of image compression via singular value decomposition

12/8

Quick tour: vector spaces (Fourier series, signal processing)

Chapter 4

Here's a nice online demonstration of fourier approximation of periodic functions

12/10

Quick tour: linear approximation and non-linear systems of equations

The final exam takes placce Tuesday Dec 16, 8-10 AM in Debartolo 310