I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math.

But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm fuzzy feeling of having learnt something cool but in reality that warm fuzzy feeling was not good enough for solving actual exercises that come in textbooks or really deeply understand the material.

I've given up on these online learning media. Back to textbooks. The difference is like night and day.

Critically, you can read/listen to something and come away with the false impression you understand it. Sitting down and doing problem is .. not always fun.. but can be critical for the concepts to sink in. I think this is the main point of what you're saying

I could see in the future it being something like watching a video and then doing a programming exercise

If you want anything past Analysis 1 I think you'll find that universities guard their content.

Not so; there's an absolutely vast amount of freely available undergraduate mathematics resources available at all levels. Honestly, so much that it makes it confusing to choose and not get distracted by the options -- perhaps AI-mediated distillation could be helpful in the future.

I wanted to find good analysis video lectures from a real university complete with problem sets, homeworks and their solutions. I couldn’t. I think MIT OCW now has one analysis course like that, but it’s relatively “recent”.

http://therisingsea.org/post/mast30026/

They have videos as well as everything else. I'd love to study them with someone/some group of people one day.

But, you don't need videos if there are carefully-written course notes PDFs.

Try Oxford: https://courses.maths.ox.ac.uk/course/index.php

E.g. two random Analysis-related courses (second more advanced than first)

https://courses.maths.ox.ac.uk/course/view.php?id=65

https://courses.maths.ox.ac.uk/course/view.php?id=4988

And there are tons of others, but with videos is a bit harder.

Berkeley exam papers with solutions: https://tbp.berkeley.edu/courses/math/113/

Hmm. All the way back to when I was in college there was advanced content available from the Open University. You had to be awake at 2am and it was in black and white, but it was there.

Are there people who think this is an "either/or" choice, as opposed to a "use both" thing?? I ask, because it's pretty well established that learning is enhanced by use of multiple media types and it seems self-evident to me that books and videos are complementary.

Can't speak for others but for me it is more about efficient utilization of time rather than complementing multiple learning methods.

I've found that time spent in learning math from videos have poor return of investment. That time is better spent re-reading a chapter or that thing that I couldn't fully understand the first time and doing more exercises.

On the other hand, there's for instance Optics where you basically have to condense an encyclopaedia and there's always prettier pictures. Or Thermodynamics, Fluid Mechanics etc that can be taught in different ways depending on the curriculum.

There definitely should be pedagogical considerations in higher education, that's lacking because it's usually an afterthought. And it also should be very clear to people getting into higher education that at some later point pedagogy must end and you have to be capable of working your way through the material.

To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement

But sure.. Thermodynamics.. things could be worse :)

Sometimes things are just hard because they're complicated and you need to buckle down and learn your multiplication tables. But at least in my own life experience, the vast majority of the time things are a problem because their poorly explained - often by people that poorly understand it themselves.

Once you truly understand something inside and out - and look back on it - it all generally looks relatively simple. But it takes a special talent to be able to go back and reexplain it from the naiive perspective

That's probably true.

> To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement

In my view, that's probably false. I don't think the problem is masochism, gatekeeping, and people holding on to old textbooks. I think the problem is that classical mechanics is actually hard, at least for most people. If you come in to beginning classical mechanics wanting to have learned it, rather than wanting to learn it, no textbook can save you. And I think that many people come in that way. They want it out of the way as a prerequisite for something else, rather than really wanting to know it for itself.

I think you overestimate the capabilities of students entering university (even 20 years ago), and underestimate how poor high schools can be in preparing said students.

I went to a mediocre university. A 50-80% drop out rate was there for both physics and EE - I don't know how it compares to the other engineering. And I did not even consider it challenging. Almost all the classes were a breeze for someone like me who was well prepared going in. At least in that EE department, the teachers were very dedicated to teaching. They would allocate 3-9 hours a week for office hours, and the pace they taught as was slow (probably only covered 70-80% of the material that is covered in a top university).

Students were given lots of chances.

The reasons they drop out are:

- Poor preparation at the high school level

- Poor discipline. A lot of students didn't transition well to independence, and didn't have an authority figure (e.g. parent) controlling their schedule.

- Realizing too late what it means when courses are built on top of other courses. Thus you'd have people getting an A in Calculus I, but almost failing Calculus III because they didn't realize they needed Calculus I beyond the course.

- In high school you can get far with a cursory understanding of the material. At university, you could get a B, or even an A, with that approach for introductory courses, but that approach will start trending towards an F in junior/senior level courses.

Sure, I agree with you that pedagogy can be improved, but I expect that 80% would at best become 60% if all you focus on is pedagogy.

You can't realistically expect that there will always be someone up the ladder to explain things to you. I mean, who explains stuff to the professors if it worked like that?

Even at the research level we are not independent islands of learning and discovery. People collaborate, some pickup certain concepts better than others and vice versa. So we teach and aid each other.

It seems you're firmly against this notion? Or if not please clarify your position?

I think everyone should be capable of working alone as well, and that has been the general assumption around as far as I've noticed. Of course collaboration is usually way more productive and also unavoidable.

But we were talking about education. Theses are individual for a reason.

Yes, you have to shed the expectation that others will teach you, I agree with that. In the end, people slogged through by doing a bunch of reading from various sources. It is maybe the main lesson of university for everyone: you're not in high school anymore, you won't just learn whatever the guy says while talking to you. It's quite the shock if you had actually good teachers at school.

The thing is though, you can still demand good teaching materials. Textbooks have to explain things in the clearest way possible. They shouldn't be confusing, especially considering they end up being the main source for just about everything. In this modern world where there are online lectures and textbooks, there's no reason we can't all have the very best explanations of every relevant concept. Yes, of course as a student you still have to put in the time, but the materials ought to be the very best.

I strongly disagree. All the best math and CS books I have are old.

New books about old topics tend to be less informed about the context and core ideas that led to their development.

There is a study showing that you actually understand material better, if you use the most primitive methods: chalkboard and a lecture. Because you are forced to visualize the material yourself, instead of being presented with a ready-made animation.

It probably makes sense to use visual aids for students that just can't grasp the concept, but I believe this will only help in elementary math.

2. When I struggle with books it is because they do not present the motivation behind what they are doing. Videos and "more popular" articles can both provide the big-picture motivation and overview. Sometimes, you have to construct a motivation for yourself, based on what you read. That's hard. Maybe you even invent something new in order to understand a concept better. This approach is slow, though. It's easier if someone explains to you why a certain concept is "hard" or a point of view from which the concept is "easy".

3. I think students who build on a partial understanding are not going to have a better time with videos. They are in greater need of learning how to learn something than they are of facts, but school does not teach that skill (afaik).

And do the homework problems. You'll never understand the material without doing the problem sets.