I'm incredulous that a linear algebra course taught by mathematics faculty didn't have a lot of theorem proving.
Maybe that would be the case if the intended audience is engineering students. But for mathematics students, it would literally be setting them up for failure; a student that can't handle or haven't seen much theorem-proving in linear algebra is not going to go very far in coursework elsewhere. Theorem proving is an integral part of mathematics, in stretching and expanding tools and concepts for your own use.
Maybe the courses are structured so that mathematics students normally go on to take a different course. In that case, GP's point would still have been valid - the LA courses you took were indeed ones planned for engineering, not for those pursuing mathematics degrees. At my alma mater, it was indeed the case that physics students and engineering students were exposed to a different set of course material for foundational courses like linear algebra and complex analysis.
Just like compiler theory, if you don't write compilers maybe it's not that useful and you shouldn't be spending too much time on it, but it would be presumptuous to say that delivering a full compiler course is a fundamentally incorrect approach, because somebody has to make that sausage.
I can only speak to my own experiences, but the math courses were not customised for engineering students. I sat next to students who were planning to become mathematicians. Linear Algebra was an optional course for me.
Having said that, I’m sure theorem proving was part of it (this was many years ago), I just don’t recall it as being fundamental in any sense. I’m sure that has something more to do with the student than the course work. I liked (and like), maths, but I was there to build my tool chest. A different student, with a different emphasis, would have gotten different things out of the course.
But I think my viewpoint is prevalent in engineering, even from engineers who started with a math degree. The emphasis on “what can I do with this”, relegates theorem proving to annoying busywork.
Maybe that would be the case if the intended audience is engineering students. But for mathematics students, it would literally be setting them up for failure; a student that can't handle or haven't seen much theorem-proving in linear algebra is not going to go very far in coursework elsewhere. Theorem proving is an integral part of mathematics, in stretching and expanding tools and concepts for your own use.
Maybe the courses are structured so that mathematics students normally go on to take a different course. In that case, GP's point would still have been valid - the LA courses you took were indeed ones planned for engineering, not for those pursuing mathematics degrees. At my alma mater, it was indeed the case that physics students and engineering students were exposed to a different set of course material for foundational courses like linear algebra and complex analysis.
Just like compiler theory, if you don't write compilers maybe it's not that useful and you shouldn't be spending too much time on it, but it would be presumptuous to say that delivering a full compiler course is a fundamentally incorrect approach, because somebody has to make that sausage.