> Consider the availability of free resources like Khan Academy, Paul's Online Math Notes, hours and hours of Youtube videos from people like Professor Leonard, Gibert Strang, etc. One can also often find problem sets with solutions by just Googling around and finding previous years course websites for various courses that have been taught at universities all around the world.
As a university professor, given the availability of all these resources, I'm not sure why you'd want to take advantage of them and take a university course if you're not interested in the credentialling. Universities are a place to learn the deepest knowledge of content experts, and I don't want to downplay that; but these content experts are usually not pedagogical experts, and they often tend to be less skilled at teaching less advanced material. That's not to say that there are no good introductory-level teachers out there—there are lots, and they do heroic work—but that a random university professor, even a very good professor, probably won't be as good at teaching introductory material. (With that being said, I don't regard Linear Algebra as introductory material—but, then, I'm not teaching at Princeton.)
Certainly, if I were advising a non-math major who wanted to take an introductory math class, I would encourage them to think very carefully about an auto-didactic approach to see if they like it well enough to continue. If you want to learn lots of mathematics, then a university math department is the place for you; but, if you just want to dip your toe into it, then it may well not be, because so many of those courses are set up as 'service courses' for people who don't want to be there but have to be, and that inevitably shapes the tenor of those classes.
As a university professor, given the availability of all these resources, I'm not sure why you'd want to take advantage of them and take a university course if you're not interested in the credentialling.
Fair enough. FWIW, my post was written from the perspective of being targeted at someone who has already chosen to take a university class, for whatever reason. But I agree with your point, and that approach is, in fact, my own. I mean, yes, I took some university maths classes in the past. But now as I want to learn new maths or re-learn maths I've forgotten, I prefer to just study on my own using mostly the exact resources I called out above. I wouldn't go pay to take a university class at this point in my life.
As a university professor, given the availability of all these resources, I'm not sure why you'd want to take advantage of them and take a university course if you're not interested in the credentialling. Universities are a place to learn the deepest knowledge of content experts, and I don't want to downplay that; but these content experts are usually not pedagogical experts, and they often tend to be less skilled at teaching less advanced material. That's not to say that there are no good introductory-level teachers out there—there are lots, and they do heroic work—but that a random university professor, even a very good professor, probably won't be as good at teaching introductory material. (With that being said, I don't regard Linear Algebra as introductory material—but, then, I'm not teaching at Princeton.)
Certainly, if I were advising a non-math major who wanted to take an introductory math class, I would encourage them to think very carefully about an auto-didactic approach to see if they like it well enough to continue. If you want to learn lots of mathematics, then a university math department is the place for you; but, if you just want to dip your toe into it, then it may well not be, because so many of those courses are set up as 'service courses' for people who don't want to be there but have to be, and that inevitably shapes the tenor of those classes.