Tips for Students Taking Linear Algebra
In general, linear algebra can be tough when you first encounter it, because there’s a single big unifying idea that’s hard to see at first. So you find yourself doing a lot of little things that don’t make a lot of sense, and hopefully at some point you step back and say “oh, I see how these fit together”. And the problem is, it’s hard to get to that moment before the last couple weeks of class. When you’re taking the class, you want to try to find that big picture; but here are some things that might help you get there.
One that I think is great for perspective is this video on an application of linear algebra to analyzing real estate listings. It doesn’t really teach you linear algebra, though it discusses a few major concepts in passing, but it’s a really great illustration of a major application of linear algebra that contextualizes stuff. It’s very easy in a linear class to get a bit lost in terms of “I can tell what we’re doing, but why is this useful”; that video explains how a lot of the tools apply to understanding large and complicated datasets.
For explaining some of the concepts of linear algebra directly, I highly recommend Essence of Linear Algebra by 3Blue1Brown. He does really great videos visualizing and explaining math concepts, and he has a whole series on linear algebra that I recommend to my students when I teach it. There’s also a text-and pictures version. And this writeup is a good explanation of what’s going on with the basic linear algebra operations.
I recently found this online textbook which looks pretty good, and the intro is great for explaining the basic ideas of what’s going on. And also, you’re welcome to take a look at my notes and slides from last time I taught it if you think those would be helpful. I’ve taken down all the assignments, but the notes are still there.