Summary: an example covering ALL group theory concepts!! | Essence of Group Theory

The summary of the entire video series! After a quick recap on all the important concepts covered in the series, we see a very interesting, yet a bit involved example to see how these concepts can be applied to prove an interesting result.

The concepts that we used are:
(1) The correspondence between action and homomorphism (where symmetric group comes in)
(2) The three statements of isomorphism theorem
(3) Lagrange's theorem

But as an aside, the group in the example is actually the group of rotational symmetries of a regular icosahedron (and dodecahedron, because they are dual to each other and has the same symmetry groups), and one can use Orbit-stabiliser theorem to verify that this group has 60 elements, and the intuition of conjugation to see that it is a simple group. I haven't filled up the details in the video, so leave a comment for the proof!

I could not promise when the next video will be out, but hopefully it will be out in a few weeks (?), and I don't really want to give a time frame for that. Currently, the plan is to have the next video to be about the current epidemic, but there might be some other videos that get in the way as well.

Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:

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If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!

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See you next time!

[mathemaniac]

The next video will finally be about coronavirus, but this is a very nice summary of the entire video series!

[craigtonlian]

This series is invaluable to building my intuition on Group Theory. I have never left a comment on a video before, but the amount of effort put into this series is truly commendable! Keep up the awesome work. We really appreciate it.

[anitsh]

I was on the path to understand Burnside's Lemma and Pólya Enumeration Theorem. I realized that those concepts requires deeper understanding of Group Theory and the series has been extremely helpful in understanding of Group Theory. I would like to thank the channel for the effort put into it. Wish you all the very best!

[aniksamiurrahman]

Thank you. Your group theory series feels the same way to 3b1b's linear albebra series.

[asdfghqwerty]

Thanks, i see all playlist. I study math and u clarify this concepts :)

[usermlgbzzcnm]

ain't Ker(phi)=H?
Edit: Oh, it's Ker(phi)<=H

[gbeziuk]

Everybody is praising the series in the comments. I don't want to seem ungrateful, but I won't join the choir here.
Obviously, you tried to follow in the footsteps of Grant Sanderson's Essence of Calculus and Essence of Linear Algebra brilliant courses, which are amazing in utilizing video medium capacities in order to build visual intuition for the named topics. Group Theory itself has a lot of geometric illustrations, so it's clearly possible to repeat the approach and the success here. However, what you do kinda defeats the purpose of the video medium: instead of graphics, you are using the formal language as your primary instrument, which doesn't help to build the intuition (compared to reading a textbook) at all. And here we go with the summary: it's totally formal, there's no picture seen even in the definition of the problem, not to mention the proof itself. Sorry, man, it's not 3blue1brown level yet =( The effort is precious, though.