Course: Linear Algebra – Foundations to Frontiers
Length: 12 weeks
Instructors: Maggie Myers, Robert van de Geijn
Quote:Students appreciate our unique approach to teaching linear algebra because:
• It’s visual.
• It connects hand calculations, mathematical abstractions,
and computer programming.
• It illustrates the development of mathematical theory.
• It’s applicable.
What you’ll learn:
• Connections between linear transformations, matrices,
and systems of linear equations
• Partitioned matrices and characteristics of special matrices
• Algorithms for matrix computations and solving systems of equations
• Vector spaces, subspaces, and characterizations of linear independence
• Orthogonality, linear least-squares, eigenvalues and eigenvectors
I’ve never taken a linear algebra course before, though I’ve had some very basic work on geometric vectors, working with matrices, and Gaussian elimination through a variety of algebra and precalcs. I was looking forward to this. But, as sometimes happens (especially with math), it didn’t quite work out.
In brief: The course is set up as a series of lectures with embedded exercises, an additional set of problems at the end of the week, and four exams scattered throughout. A temporary license for Matlab is included, ending when the course is over. Staff coverage of the forums was excellent. A PDF of some material is provided, but they presuppose viewing the videos, and as usual with any math course, the video transcripts aren’t all that helpful without the videos. Disclaimer: I only made it through the middle of Week 8.
I quite enjoyed, and seemed to be doing very well at, the first three or four weeks. I think I learned a lot about linear combinations and transformations, what they have to do with matrices, and I had a lot of fun smashing Timmy Two-Space all over his grid. I saw a little hint of another point of all this with a (very primitive) weather prediction system, and that was pretty exciting. But it went downhill from there. I gave up in week 8, about halfway through. It wasn’t impossibly hard, but as time went on it had grown impossibly tedious; I just got seriously bored with slicing and dicing matrices for purposes that weren’t all that clear to me. We did have the option to skip over the Matlab algorithm exercises, but I had trouble telling where they began and ended. I completely lost the thread of “what am I doing and why am I doing it?” as calculations – small calculations, just adding and multiplying really but the stuff of nightmares for me – took over my life. I know there was something I was missing, but I never really understood what.
Let me say that I have no doubt at all that the material is essential to those who need linear algebra, and that those who are more comfy with math and computer programming would probably find it a great course. If I want to get to the point where I “know” linear algebra, I’ll probably have to take it again, but it wasn’t the right entry point for me. Of course, how would I know, since I’m still a bit hazy on what linear algebra is for.
I think one of the problems for me was that this was taught by computer science instructors, with a view towards optimizing algorithms as well as teaching linear algebra. Hence, memops and flops (which I actually understand, but don’t care about). Loops and indices. If those sound like music to your ears, this is the course for you, but as for me, STFU and leave me alone.
I’ve been hearing so many mathy people talk about how cool linear algebra is, and the course description includes “It’s visual” as a selling point. Other than Timmy, and a brief graphical description of two-rotation transformations, the only visuals I saw were printouts of algorithms and matrices, endless matrices to partition, multiply, transform. Maybe it got more visual in week 8, but I just didn’t want to do any more.
The instructors were very involved on the forums, promptly answering questions with humor, warmth, and encouragement. Prof. Myers told me about a very cool children’s book about basic combinatorics, Socrates and the Three Little Pigs; why kids that young would be learning combinatorics, I don’t know, but I spent a couple of nice hours figuring out how to fit three pigs into five houses under various conditions. Her videos of detailed proofs and exercise solutions were very helpful. And a mysterious image turned out to be computer wallpaper made from a beautiful image of a stained glass window from Prof. van de Geijn’s grandfather’s house in the Netherlands. These are great people! So I’m kind of puzzled about this: they seem to have gone out of their way to strip all that humor and warmth out of the course material itself. As a result, it was a “I’m going to read a textbook to camera and you watch the low-contrast, slightly out-of-focus slides” kind of course.
I’ve never thought of myself as someone who needs to be entertained in order to engage, but maybe I am, more than I’d like to admit, at least where math is concerned. And I admit I am somewhat spoiled by the truly exceptional moocs I’ve been fortunate enough to take. It’s also possible I no longer have the attention span for a longer course, especially one that requires so much of my time and fully focused attention over an extended period, since I was quite content for several weeks. I can sometimes skim through a philosophy or history lecture, but I have to pay attention to every detail when it comes to math, and it’s hard to sustain, even when I’m into it. And, of course, it’s very possible that, contrary to the Howling Stanfordtoids and their growth mindset, I’m just stupider than I think I am.
Even though I chose not to complete the course, I did find it very worthwhile for initial material. I’m investigating several other linear algebra sources – 3Blue1Brown’s linear algebra playlist on Youtube (which takes visual to a whole other level), Pavel Grinfeld’s lemma unit on linear algebra, and a couple of OCWs (I have trouble with OCWs; I can never figure out how to navigate them, where all the pieces are), and I’m finding that the initial material from LAFF has helped enormously. And, by the way, I think I finally understand mathematical induction thanks to this course, or at least I understood its use in the cases encountered here. So I’m glad I did as much as I did, and I hope to some day pick it up again.