I New Video Course on General Topology on YouTube

caffeinemachine
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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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Likes WWGD and PeroK
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.
 
A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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