Undergrad New Video Course on General Topology on YouTube

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A new YouTube channel has launched a series on General Topology, aiming to provide a comprehensive course with visual aids and rigorous proofs. The creator has previously uploaded courses on Linear Algebra, Real Analysis, and Math Olympiad preparation, with a focus on starting each lecture with practice problems. Suggestions were made to enhance video quality using the Manim library, known for its effective mathematical animations. The creator expressed challenges with Manim's complexity but remains open to using it in the future as coding skills improve. The content is designed to be engaging and beneficial for learners interested in advanced mathematics.
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Hello Everyone!
I created a YouTube channel (here's the link) a few years ago in which I post detailed lectures in mathematics.
I just started a series on General Topology. Following is a snapshot from a video.
2024-01-21_20-44.png

I mean to deliver a comprehensive course with a lot of pictures and intuition and rigorous proofs.

Apart from that, so far I have uploaded
  • A complete course in Linear Algebra.
  • A Kickstart series as a bridge between high school and college math.
  • A course on Real Analysis (which I am currently renovating).
  • Some material for preparation of Math Olympiads.
  • I am also converting my videos to have a light background.
  • Some other courses (like group theory) which require renovation.
Almost every lecture starts with problems for practice.
I hope that the people here would find the content useful and interesting.
 
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Thanks for sharing your work here. I'm always interested in learning new math and this should be a treat. Thank you. :-)

In case you interested in modernizing your videos even more:

Several math youtubers have been using the python-based Manim library for their animation work. The library was developed and first used by 3brown1blue math creator (Grant Sanderson) for his math videos.

https://www.manim.community/

and docs related to running and installing it:

https://docs.manim.community/en/stable/

On Github you can find Grant's personal Manim code that he develops independently of the community edition of the Manin community:

https://github.com/3b1b/manim
 
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jedishrfu said:
Thanks for sharing your work here. I'm always interested in learning new math and this should be a treat. Thank you. :-)

In case you interested in modernizing your videos even more:

Several math youtubers have been using the python-based Manim library for their animation work. The library was developed and first used by 3brown1blue math creator (Grant Sanderson) for his math videos.

https://www.manim.community/

and docs related to running and installing it:

https://docs.manim.community/en/stable/

On Github you can find Grant's personal Manim code that he develops independently of the community edition of the Manin community:

https://github.com/3b1b/manim
Thank you for the suggestion.
I tried Manim for a bit but found that the time it takes to make one video using manim is way more than what I can do in the handwritten style.
Maybe when my coding skills improve Manim would be an option.
 
We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.

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