@kevon217
Can’t thank you enough for this series. These concepts are finally starting to click for me.
@birdbrid9391
i can hardly wait for the next subjects!
@jneal4154
I look forward to seeing your videos as much as I look forward to videos from 3Blue1Brown and StandUpMaths. Excellence work! Please keep making awesome maths content! (If you ever felt up to making videos about homotopic type theory, category theory, or geometric algebra, I would welcome them wholeheartedly, too. 😁 )
@jeanchristophe15
Thank you for making the video! For ring, the multiplication does not form a monoid, because it does not need to have the identity. The unital ring needs to have the identity.
@EvanMildenberger
I love how it's obviously MS paint from 6:00 onwards haha. But seriously, it's great that you provide so many visuals along with your detailed voice narration, even if the visuals are not super fancy. They're clear enough to explain the point but probably simple enough it allows you to produce your videos fast enough.
@alegian7934
the zero proof is craaazy 🤯🤯
@GedasSarpis
This has been fantastic series, as a particle physicist, I dream you extended this to group decomposition, Young Tableaux and weight diagrams... Those things scare me
@naterthot
You are doing an incredible job, great work!
@robin1826
Thank you!
@superdummboy
this is good fucking stuff
@EvanMildenberger
20:10 I wonder how this relates to the generalized Stokes' theorem: which written in LaTeX is ```(\int_{\partial \Omega} \omega = \int_{\Omega} d\omega)```. It essentially says that in Calculus on smooth manifolds, the boundary is the opposite of the interior, and if you know one, you can figure out the other.
@NicolasMiari
I think that the fact that you can "know" the internals of a group from its homomorphisms isn't so magic once you realize it's the groups own internal structure the determines which homorphisms are possible from it to other groups.
@jonny__b
I found this series incredibly easy to follow, so thank you, but I always find it difficult to understand the "why" of group theory. With e.g. calculus or linear algebra, I can really intuit why it's useful from its applications - but with group theory I'm not sure what its applications are. Were the pioneers of group theory trying to solve a certain class of problems that demanded the theory? Or is this form of abstraction more about trying to understand the fundamentals of something? I'm not trying to impose an application of the theory if its not merited, but I always find it hard to motivate myself to learn more when I can't see them clearly. Thanks again!
@alegian7934
Is homomorphism the same as morphism? or do they mean different things
@misericorde6336
Sorry for the bother but, would it be feasible for you to provide proper subtitling? Asking since the autogenerated ones often fail to transcribe what was said properly, or just drops entire sentences, and consequently I'm forced to try to reconstruct what might have been said based on what the visuals are and what remains of the text, if any of it does.
@nanamacapagal8342
I noticed: you said matrix multiplication isn't commutative, then later at the end of the video you said linear transformations and matrices act like homomorphisms for vector spaces. Does this imply that homomorphisms are not commutative, in the case of monoids and groups?
@DeathSugar
Is there any math structures above the rings where you add extra N binary operation with new identity element and the identity element of n-1 binop becomes void for nth binop?
@DKFX1
video seems to lack geometry.
@CognitiveOffense