I'd like more math professors to make recordings of their courses. E.g. here is a pure gem [1]. This is a recording of a real analysis course from Rudin's principles of mathematical analysis (aka Baby Rudin aka the architect of many beginning mathematics students' misery). Anyone that's worked through this book knows the world of pain you're about to enter. I'd love if there was a similar recording for say, Charles Pugh's real mathematical analysis. I mean he's still alive, dunno if he still lectures from his book, but why not record one of those? It would be game changing for those who self-study.
Here's another request: Terrence Tao does a recording of a measure theory course.
Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle.
> Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle.
Sorry, but what?
You'd be hard pressed to find any single person, in the past 10 years, that has ushered more people into STEM by providing a solid fundamental education, than Salman Khan.
I understand that you're wanting more rigorous math, on a higher-level, but still - to blow off KA, 3B1, etc. as a waste of time sounds more ignorant than anything. Of the millions and millions that have seen these those guys, I'm sure a certain % have gotten their "Aha!" moments there, which have helped them tackle on much more comprehensive topics / fields.
edit: Just to clarify, I do not think these vids are any replacement for a solid book, just in the way I do not think lectures or tutorials are a replacement. But they can be fantastic aids for your learning.
Interactive websites are IMO vastly more efficient at conveying information, compared to static pages (like books, for example).
The value in good mathematical books is mostly the exercises. Like Spivak, Rudin and Pugh. Struggling through those is vastly more valuable than any video or hand holding. I mean most of those problems would take hours or even days to solve. I suppose Khan videos (or at least the ones I’ve watched) are useful but it’s no substitute for active thought. What I like about videos from a real course is that you can “see” how a real mathematician thinks about attacking a problem.
Err, uh, where do you get the idea that Khan academy "has ushered more people into STEM than any single person"? Seriously. I don't even know how you would measure something that.
Ok, so it's a very bold claim from my side - but he's done a phenomenal job making fundamental math (and science) lectures accessible, and more so, he does have a teaching style which works for a lot of people. It has been much faster paced, and more concentrated.
As for pure numbers, his videos have a total 1,806,946,640 views and 6M subscribes.
(Sure, there are scientists and inventors that have inspired magnitudes more people to enter STEM over the years)
Here's another request: Terrence Tao does a recording of a measure theory course.
Personally I find the Khan Academy, 3B1brown stuff to be a waste of time. It's too elementary and cutesy. That is not anything like what I've experienced real mathematics to be like. It is a continuous painful struggle.
[1] https://www.youtube.com/watch?v=ab41LEw9oiI&list=PLun8-Z_lTk...