An Introduction To Group Theory

I hope you enjoyed this brief introduction to group theory and abstract algebra.
If you'd like to learn more about undergraduate maths and physics make sure to subscribe!

[ohebfbq]

This chap managed to cram 3 whole chapters of Further Mathematics in A Level in less than 11 minutes. This is what I call QUALITY video!

[riyaraizada]

You managed to make me understand something in 10 min that I couldn't in 70 mins thank you so so much. You're a legend.

[muhammadhassaan]

wow you've just summarized my professor's two weeks lectures, waiting for future videos on Group theory

[austincarter]

This video is amazing. What’s so surprising to me is how often the distributive property shows up in every area of mathematics

[UtsavMunendra]

You are making really amazing videos, kind of like a mash up of Khan Academy and 3Blue1Brown. Keep it up.

[mistsu]

Damn, now I understood why 3Blue1Brown once said the matrices are transformations. By multiplying with the matrices, we indeed rotate / flip the image around!

[ankk]

You are truly amazing.
You should make more videos.
You dont just have knowledge but you can also explain it to the others.

[kerrickfanning]

This was so good, it was an college-lecture like introduction with good sound quality and great visual examples! It was exactly what I was looking for

[maowtm]

Well made! You presented the ideas concretely unlike some other group theory video I came across, and your video definitely helped me understand some key things.

[mumbaicarnaticmusic]

At 6:58, you say we conclude our set is closed by observing every element of our set appears exactly once in each row and column. Why do we need that? Don't we just need every element of the Cayley table to be an element of our set?

[dantong]

Sometimes, a more rigorous definition of "binary operation" is used (S x S --> S) and it implies that groups must be closed. So sometimes you won't see the "closure" property as a group axiom, but rather just "a set with a binary operation, blah blah" with the rest of the axioms

[cameronspalding]

@8:32 one can prove that the set of symmetries on an equilateral triangle is associative by using the matrix representations

[anirudhr]

When you defined X1 and X2, I think you meant to use it as a rotation along axis tilted 30deg from the horizontal and not 45deg...

[maarirs]

What a wonderful video! Thank u very much!

[oo]

Welcome back
Please talk about ai somnium

[badwolf]

sounds like data types in programming... this is cool

[krishnasomasundaram]

When I came to the part with matrices I tried to apply concepts from 3b1b series of linear transformation and kind of realized that each 2D array represent the exact same transformation that he described for the equilateral triangle

[seanchan]

in your definition set S doesn't contain the Identity element I, so how does it satisfy the identity axiom? Shouldn't the underlying set be S:{I, Q, R, Y, X1, X2}? Thanks

[aaaa-hjvv]

Some of the drawings are hard to see, but other than that it's a great video. Thanks for making these.

[numerouslogins]

@5:17 These aren't going to be a "y=x' or "y=-x" axes, they need to be at 30°, not 45°. "y=(1/√3)x" and the same with a minus sign would do the trick, if I'm correct.

God bless from Poland!