Linear Algebra was a course in the first semester of freshman year when I was in uni (this wasn't in the US or in an english speaking country). It was famous for being a "filter" course, that made a lot of people quit the degree and switch to a different degree next year.
It had a 94% failure rate, but I got to pass on the first attempt because Gil's free lectures of his LA course made me intuitively understand the stuff we were being taught in that course, which was very dry and IMO poorly explained, at least for freshmen. Don't think I would have dodged the bullet otherwise.
I have a feeling that the intellect gap at a lot of universities isn't as profound as one would expect and that one of the reasons that the students of the best unis do so well is because their educators can actually explain the course material. You can do more when you've got to spend less cognitive energy on trying to piece together the hieroglyphic puzzle that lesser professors throw at you because they believe they're too important to teach.
A lot of the top universities have majority of their profs caring almost exclusively about research though. I think MIT is (or at least was) a bit of an exception, where there was enough of a critical mass of profs that cared about teaching. Can't say the same for a couple other "top" unis I've spent time at.
i find that in general (not always) the smarter people are, the better they understand precisely what you don't know, and what you need to know to understand what they are trying to tell you
it's a bit like the old "the more I know, the more I know I don't know" but with an addition of "the more I know exactly what I know, and exactly what I don't" and it's then applied via theory-of-mind, "the more I know precisely what I can teach you"
I would have to agree with this. In all my time in school I've had terrible and amazing professors, the difference in the amount I learned was generally due to their ability to explain the subject in a way that was easy to understand. I also credit the MIT open courseware chemistry lectures for helping me through uni, because that professor was one of the not so great ones at my school
I had the same experience. I didn't understand the teaching from my university. Once I found his lectures it all clicked. I understood what we were doing. It was no longer wrote learning of algorithms to manipulate things with no meaning.
I took linear algebra about 20 years ago as a requirement for my CS degree. I had no clue whatsoever what it was for beyond just "solving systems of equations" - whatever that meant. The prof didn't impress upon us how it underpins all of machine learning (which, mind you, wasn't as much of a hot topic then that it is now). Our attempts at grokking its importance were largely met with a kind of "because it's important" dismissal.
I didn't do great in the course, and when it was done, I was pretty happy this useless subject was behind me.
It wasn't until several years into my profession that I learned how important linear algebra truly is. I now work very closely with tons of data scientists, and I still feel like I should go back and learn it better.
Same thing happened to me. Yes ml wasn't a hot area then (20 years ago) but computer graphics, linear regression (ie old school statistics used for supply chain), signal processing for audio and video were all got them but their applicability was never pointed out let alone emphasized. I was just lucky that I was interested in these areas on my own so the linkages thankfully "clicked". Is it me or did profs back then just do research and teaching in a bubble?
I agree with u on Strang, wonderful lectures. I always learned on books at least a decade or older, I was amazed even the 90s about his lasting legacy. He has been helping people with linear algebra for more than 50 years. I haven’t even been alive for that long.
Weeder courses shouldn’t exist, they are immoral. Glad you survived yours.
I had the privilege of taking one of Strang's classes a few years back. He is still incredibly sharp, and has a great sense of wit.
During one lecture, he was half way through solving a problem on the board when he jumped straight to the final answer. He then turned to us, and with a deadpan delivery said:
"We haven’t proved it, but that’s okay, we only live so long."
IDR which lecture it was but there's a timely Monica Lewinsky joke somewhere in here. Small things but I appreciate when profs are allowed to have fun. Obviously Strang is also just an amazing teacher.
I picked up his linear algebra book and watched his lectures last year as part of my journey into machine learning. He made me fall in love with math in a way that I never had before, not even during my physics degree. Truly an inspiring teacher and amazing person.
I still have his linear algebra book on my shelf from the 1980's. One of the great teachers of a topic that has been crucial to my career in computer graphics and vision.
Fully agreed. I would argue that there is no replacement for Strang, though many may try. My copy has only been around for ~20 years, well worn from when I struggled with the course.
Very sad to see him go. I am fully envious of those who will be in attendance.
Readit News
It had a 94% failure rate, but I got to pass on the first attempt because Gil's free lectures of his LA course made me intuitively understand the stuff we were being taught in that course, which was very dry and IMO poorly explained, at least for freshmen. Don't think I would have dodged the bullet otherwise.
Thanks Gil.
it's a bit like the old "the more I know, the more I know I don't know" but with an addition of "the more I know exactly what I know, and exactly what I don't" and it's then applied via theory-of-mind, "the more I know precisely what I can teach you"
I did very well in that paper.
I didn't do great in the course, and when it was done, I was pretty happy this useless subject was behind me.
It wasn't until several years into my profession that I learned how important linear algebra truly is. I now work very closely with tons of data scientists, and I still feel like I should go back and learn it better.
Weeder courses shouldn’t exist, they are immoral. Glad you survived yours.
Now that I am, it seems kinder to fail people early out of paths they are ill suited to follow, no?
At first only MIT students were lucky to learn from him, but then, as his videos became available online, so did the rest of world.
I've yet to meet anyone working in AI, ML, data science, signal processing, etc. who hasn't watched at least some of Strang's lectures.
I've also met multiple people working in these/related fields for whom Linear Algebra 'clicked' only after watching Strang's lectures.
He deserves the collective applause and giant thank-yous he's getting.
I hope MIT names something after him.
During one lecture, he was half way through solving a problem on the board when he jumped straight to the final answer. He then turned to us, and with a deadpan delivery said:
"We haven’t proved it, but that’s okay, we only live so long."
And then he moved on to the next problem.
I've quoted that line a lot since then.
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010...
Here's the video transcoded on YouTube for anybody else who's curious:
https://www.youtube.com/watch?v=nfY0lrdXar8
He's been a professor at MIT since 1962!
Very sad to see him go. I am fully envious of those who will be in attendance.