During the 2020-2021 Covid-19 season, universities and colleges around the world made most of their math classes online over Zoom and many professors have their recorded lectures.

Most math lectures usually don't involve in-class discussions and for the most of the time, professors dominates the teaching. Oftentimes, excellent recorded lectures can be much better than live lectures in mathematics and other theoretical sciences. I have seen many students commenting under certain YouTube videos that those recorded lectures are much better than their professors'.

I wonder if we could possibly use those recorded videos (there are a lot of such videos modulo-necessary-editing during Covid-19 season. Building a system like (https://nptel.ac.in/) should be feasible) to free university math professors from repeatedly giving lectures on lower-division math classes like calculus, linear algebra or differential equations (but at the same time, asking them to hold discussion sessions and office hours to have more interactions with students and of course, grading homework assignments and exams), so that they could have more time on their research and teaching classes that are more relevant to their research? I believe this is particularly important for the early-career mathematicians. Many postdocs in math are assigned with lower division classes that are kind-of digressions to their research.

This seems to be a win-win strategy for both professors and students in terms of the mathematics. If this is good then maybe it should have been conducted already like https://nptel.ac.in/. What would be the potential challenges for doing so for higher education in United States and Europe?

  • I think this would most likely lead to greatly reduced sizes of math departments... Automated by playing those videos over and over. And, yes, many students might rightly be happier with good videos in comparison to dubious live lectures... – paul garrett Feb 23 at 21:51
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    @NoOne, I agree that "teaching calculus" is not the only function of mathematicians, but from an all-too-common viewpoint of university administrations, a way to reduce costs of "covering" calculus would be highly desirable. The other parts are toooo intangible. :) – paul garrett Feb 23 at 21:54
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    Among other things, teaching gives you additional insight into your subject. Efficiency and effectiveness are not friends here. – Buffy Feb 23 at 22:07
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    @Buffy "Among other things, teaching gives you additional insight into your subject. Efficiency and effectiveness are not friends here." Yes, but as an algebraic geometer or number theorist , a person may want to spend more time teaching algebraic geometry, algebraic number theory or at least abstract algebra, rather than calculus and linear algebra... – No One Feb 23 at 22:13
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    "Then it would be the government's duty..." Ha. Good luck with that. – Buffy Feb 23 at 22:37

Yes, you absolutely can!

The win-win is very unlikely though. Students won't see lower tuition or anything, and will have no opportunity to interact with anyone at the faculty level (so no letters of recommendation, no research jobs, etc). Professor lines will be closed on retirement (or through layoffs) because who needs them, we've got McGraw-Hill eLectures.

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    Yes, I'm afraid this is probably an accurate assessment, given my own experience with university administrations. – paul garrett Feb 23 at 22:12
  • "and will have no opportunity to interact with anyone at the faculty level ".... I did add some sentences about this issue (paragraph #3). Professors will hold discussion sessions and offices hours to increase their interactions with students. University administrations can make it a policy that students must go to discussion sessions as attendance requirement ... – No One Feb 23 at 22:18
  • That's a nice idea. A grad student TA is cheaper. We can even get the students to pay for the course kit though a textbook code. Guess what wins between nice and cheap? – user133933 Feb 23 at 22:24
  • @Libor This will be another issue that worths another question "why tuition and fees in U.S is so expensive" (which is not the case in many other countries, though) – No One Feb 23 at 22:26
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    Your question isn't but every administration is - so this thing you're suggesting is happening, will only grow, and will not be in any way designed or implemented as you hope. – user133933 Feb 23 at 22:50

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