Computational Linear Algebra

Frequently Asked Questions
What Are the Prerequisites?

To enroll in my course, you’ll need to have taken a standard undergraduate course in linear algebra. I consider my course to be a second course in linear algebra. It will reinforce some of the key ideas of the subject and teach you many new ones. Additionally, I strongly recommend that you gain some computer programming experience before enrolling in my course. We will be coding for every assignment/activity that we undertake. More specifically, we will program in R. Prior experience in R is not necessary, as the first unit of the course will be an introduction to (or, if applicable, review of) some R basics.

Do I expect that you remember all of linear algebra perfectly? Do I expect that you are a software engineer? No to both. But to be able to complete the basics of this course and succeed in learning new material, you’ll need the background described above.

What Even Is Computational linear algebra?

Here’s the deal. Linear algebra is arguably THE most important part of modern applied mathematics. When solving real world applied mathematical problems using linear algebra, doing it with a pencil and paper usually doesn’t work because the problems are too big. Do you really want to try to do Gaussian elimination by hand on a 1,000,000 x 1,000,000 matrix? I DIDN’T THINK SO. We instead use computers to solve linear algebra problems algorithmically. As soon as we are solving problems by implementing algorithms on computers, though, we have to worry about things like “what kinds of errors am I introducing into the problem?” and “how long is my program going to take to solve this problem?” In short, this course is a mash up of linear algebra, computing, and applications in various areas.

How will this course happen, logistically speaking?

The course is remote, that is, completely online. We will make use of the scheduled class time but there is no moment during the entire term when the entire class will meet together. I make this choice because for me, it is not possible to have meaningful interactions with 20 students online all at once. I will be dividing students into small groups for the various course activities. You’ll meet with your group during class time and I will spend part of the time with each group. Oh, and guess what: almost all of your problem sets are going to be done collaboratively.

What Are We Actually Going To Do In This Course?

For a typical unit of this course, you will watch some videos, do reading, take some multiple choice questions to assess your basic understanding of key concepts, meet in groups with me, and work on a challenging and educational set of problems. The videos will often not be videos of me. Why? Learning science research suggests that if a lecture is clear, there is nothing special about whether or not it is your professor delivering it. You might be wondering, then, what is my job as a professor if not to lecture to you? Well, it’s for me to work with you in a highly individualized way, helping to address the material that you find most challenging, helping you to explore your own interests, and much more.

How Will I Be Graded?

This course is ungraded. The way I implement ungrading is that every so often, I will have you write a rather detailed self-reflection about your goals and progress in the course. I’ll also ask you to reflect on how group work is going for you and for your group-mates. None of the assignments you complete “count” towards a final grade. I focus on giving you substantial written/verbal feedback that aids your learning. At the end of the course, I will ask you to think about your self-reflections and assessment of yourself and tell me what grade to assign you. Then I will assign you that grade. The one restriction is that I will not assign an A+ grade. Please realize that if you ever ask me for a letter of recommendation, it will be based on my own assessment of your work and not on the grade you assign yourself.

What Do I Need to Ask Myself?

As you decide whether you want to follow through with taking this course, please ask yourself the following questions.

(1) Am I ok taking a class where the professor doesn’t lecture at all during class? This means I will need to prepare substantially before class time by reading and/or watching videos.

(2) Am I ok taking a class where coding in R plays a central role? Am I ok that this means debugging code will be a thing that I often need to do? Am I willing to view that as not detracting from my educational experience, but rather, being part of my educational experience? Also, am I ok taking a class where the first week and a half will largely be spent learning/reviewing R? For instance, if you already are an experienced programmer in R, you are going to be bored, and will want to work with me to get paired up to provide support for other students.

(3) Am I ok taking a class where the professor’s fundamental goal is to create a learning community in which each student takes responsibility not only for their own learning, but for every single other student’s learning as well?

(4) Am I ok taking a class that is extremely applied? This is generally NOT a proofs-based class. We focus on understanding useful ideas in linear algebra and implementing them computationally to solve problems.

(5) Am I ok taking a class where nearly every single assignment involves collaboration? There is very little individual work in this class, which is also reflective of how a lot of applied mathematical work takes place. If you are the type of person who envisions saying to yourself “I don’t understand why I can’t work on this course by myself” then this is absolutely, 100% not the course for you. You will not be happy.

What Is the Point, Chad?

Please think carefully about if this is a course that’s right for you. I design it in a purposeful way to comport with my reading of the research literature in learning science. Based on that reading, I believe you will learn more if you can motivate yourself to invest in the course without the extrinsic measure of grades, and if you tackle difficult, open ended work. However, if you believe you are the type of person who will only feel comfortable if I lecture to you, or will force yourself to invest time in the course only in order to avoid the threat of a low grade from a professor, this is not the course for you.