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Future way of learning mathematics (towards graduate level)

Mathematics Educators Asked by Nothing on September 6, 2021

Recently, there is an idea sparkling out from my mind due to the COVID-19 outbreak. In the past, we typically attend a course, complete homework and assignment, then finish the semester with a final exam. This takes around 4 courses per semester and 4 years for a whole degree. But I feel we can speed up this process with the aids of the online lecture, as provided from Quality of Videos Lectures and Lectures vs Textbooks. Scott Young had successfully done this by completing a 4-year computer science degree through his MIT Challenge. Thus, I believe online lectures are beneficial for the following reasons.

It helps people to accumulate the background to do research as fast as possible. As we know, mathematics is becoming more and more structured and complicated. To overcome this, we have to learn much faster and more effectively. Typically, online lectures are around 30 hours where people can watch all of them in a week (with note-taking and understanding). The best thing is we can always rewatch the part we don’t understand and search for appropriate reference (using Google) to understand the idea better. Then we take another week to complete exercises and do final revision using Feynman techniques (teaching to yourself). We can complete a course ideally in two weeks.

Now let’s see how many courses do we need minimally to be able to read research materials in mathematics. We need Analysis I, Analysis II, Linear Algebra, Abstract Algebra, Point Set Topology, Measure Theory, Complex Analysis, Functional Analysis, Commutative Algebra, Algebraic Topology, Algebraic Curves, Differential Geometry, Representation Theory… Let say around 20 courses to reach the level. Then we only need 40 weeks for the whole program. To be more relaxing, one year is sufficient for us to have the background to do research, of course with the aids of online lectures.

Here is my central idea:
Self-studying by watching online lectures and then supplementing with exercises and textbook is much more effective than to read the textbook from pages to pages. It’s like playing a new board game. Online lecturers (people who know board game) give the main idea of study (game) and then the students (players) do the exercises (play the games) after listening to the main rules. If there is any problem, they consult the reference book (player guide).

What do you guys think about this? Is learning online a better option for the future? I feel this is an interesting topic to discuss and I hope to get some opinions on this.

$textbf{Edit}:$ I have to mention that doing this way only gives sufficient background to pursue research faster, but to consolidate the knowledge, the students have to read research papers, read more references, do more exercises on that particular research topic. For instance, people doing algebraic geometry should nevertheless do all the exercises in Hartshorne, read more advanced topics etc. When they face any difficulties, go back to the relevant prerequisites and consolidate them. (It should be easy to trace back since they have completed all courses)

2 Answers

It's so unclear. I cannot follow what your idea is. I understand what you're saying the result of your idea might be, learning the material better even when there's so much to learn in a limited amount of time. I am unable to figure out what your idea is that you think might lead to that result. In theory, I could try to learn more about the things you discussed; Quality of Videos Lectures; Lectures vs Textbooks; and Feymann techniques from the web pages I got by Googling them; https://www.tandfonline.com/doi/full/10.1080/10872981.2018.1555434; https://academia.stackexchange.com/questions/52678/what-is-the-point-of-a-lecture-when-you-have-a-textbook; and https://fs.blog/2012/04/feynman-technique/ and then see if I can figure out an answer to your question after studying them carefully that probably wasn't stated directly. However, I don't think my mind is going to be on that long enough to bother with. There may be some Stack Exchange users who when ever they encounter a question they deem not to have a satisfactory answer, focus only on answering the one question and take a really long time to give up on answering that question and will not move onto another question until they're either answered it or given up. Maybe attention to this question from 1 Stack Exchange user who takes a month to give up could do a better job of answering this question than attention from 30 Stack Exchange users who give up after a day, similar to my tendencies. Hopefully, you'll get an answer from somebody who focuses on one question at a time and takes a really long time to give up on that question.

I know the question is an idea of how to adapt to the situation of being flooded with so much material, not a question of whether we should be flooded with so much material. However, I cannot answer that and am not sure the idea would even work anyway so I'll instead answer how I think it doesn't have to be this way, imposing mountains of material on us in a limited amount of time. I read on the internet that Finland has the best education system in the world. I also saw a YouTube video explaining how Finland teaches less material and explores it in more depth. Students were struggling to learn all the material even before COVID-19. I think it's better if the world makes a coordinated change where a lot of the material is moved to job specific training and jobs no longer rely on people having learned what they couldn't learn in school. It's better to have extra people able to do jobs.

Answered by Timothy on September 6, 2021

If you are pushing videos so hard, you haven't even read Scott's story carefully. He says a textbook with problems is far more important than online lectures (which are not that much needed).

https://www.scotthyoung.com/blog/2012/11/13/why-lectures/

As far as the "who will check the work" comment (below OP's question), the answer is to use books with answers for the drill so you can check your self for mistakes.

There: two changes that fundamentally reduce the demand for math educators. Now we won't have to pay them all double six figures. (Oops.) ;-)

Answered by guest on September 6, 2021

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