Ya know, I get what you're saying and I am somewhat sympathetic to this position. But I think you're being a bit harsh. It's easy to talk about "understand(ing) that this is an extremely important topic" when you already know. But how many high-school kids really know anything about Linear Algebra or understand much at all about how/where it's used? Heck, rewind time a bit and ask if you really understood that when you were first starting college. And if you did, realize that you are probably the exception.

From a university lecture in linear algebra, I expect that it carries me through as many important topics as possible while giving me the tools to form a good formal and intuitive understanding.

Sure and unless your goal is to do pure mathematics research, part of that is providing some motivation in terms of understanding applications. There's nothing wrong with a class on LA (or any other topic as far as that goes) spending some time motivating study of the topic by showing how it can be useful... even explaining how it might used to make millions or billions of dollars.

When I took math in college there was no motivating examples for nearly everything. I had to complete my CS courses to understand nearly a quarter of the actual applications of what I learned in my math class. The only reason that I even know more applications right now is the fact that I am trying to teach myself SMT solving and ML. Why can't we have a math book that has motivating examples applicable to everyone? Or if that is too hard then just one for Computer Science?

Right now in nearly every Math book that is bought by a College student or High School student has motivations in Phyaics. So a person could go through HS, get their Undergraduate degree in CS and then never figure out how math could be useful in their job at all. When students ask "when am I going to use this" you have already failed in teaching your students how to apply this.

Once they have reached this point either they will have a really bad impression of math and just give up OR they will believe whatever you say after words and get rewarded ten years down the line.

I don't think that the GP is advocating that we motivate students to study linear algebra by telling them it will make them rich. They were merely saying that this is a nice way to grab student's attention.

I really liked it when we went over PageRank in one my university lectures. It made me think "Wow, I can actually have an impact using the things I've learned here".

You are wrongly assuming most courses aren't taught by overworked professors or TAs who just speed run through problems with no background on the subject and more or less teach you to pass the exams. Not everyone gets ivy league lectures.

I don't see how adding another example why systems of linear equations are important would solve the speeding problem.

> Because if somebody is taking linear algebra in university and still didn't understand that this is an extremely important topic, then he should maybe go back to school or take a gap year or something to improve his general education.

Because not everyone professor romanticizes the subject or discusses its importance, not teaching anything other than surface details about problems.

> if somebody is taking linear algebra in university and still didn't understand that this is an extremely important topic, then he should maybe go back to school or take a gap year or something to improve his general education.

raises hand

I was that kid.

I had to take differential equations, linear algebra, and discrete systems for my CS undergrad. I loved math, and I did my best but I eventually got bogged down and lost interest.

Since then I’ve come to appreciate more why you would want that advanced math as a programmer, but my experience at the time was that I could brute force almost anything with enough for-loops.

It just didn’t occur to me that there were interesting problems that were too complex to brute force, or that brute force would lead to such tangled code in some cases that it wouldn’t be debuggable.

Frankly, I doubt more liberal arts would’ve convinced me. I needed to get knee deep in big bad code and domain specific problems before I’d realize what I missed.