Chapter 5: Quotient groups | Essence of Group Theory

[@mathemaniac]

Thanks for all your support in the previous video! I have never thought it would reach such a wide audience. I really like the comment section on the previous video, which involves some in-depth discussion about the model and the data I used. This is simply a continuation of the group theory video series. Most of you just subscribed, so I would highly suggest you to watch the entire video series from the start because I referenced quite a few previous videos. If you find this video series useful, consider sharing this video and subscribe if you haven’t already. You can help me create better videos with better pacing and suitable math levels by logging your math levels in this Google form: forms.gle/QJ29hocF9uQAyZyH6

[@keeleynorman2943]

So helpful! I wish there were more animated explanations like this on KZbin

[@mathemaniac]

Thanks so much for the appreciation!

[@monojitchatterjee3185]

This is actually pretty awesome! You're a good teacher.

[@mathemaniac]

Wow, thanks!

[@ThefamousMrcroissant]

Very high quality! Great script, and of course good use of Manim.

[@PunmasterSTP]

Quotient groups? More like "Quite useful and dope." These videos are awesome!

[@inshashah2578]

Cannot thank you enough for this one.

[@mathemaniac]

Glad to help!

[@carlosraventosprieto2065]

this was amazing!! thank you so much for these videos

[@Joel-fs5zh]

i love you channel. thank you so much for what you do. I think about math all the time.

[@steveschwartzm.d.7362]

Your conjugate intuition is brilliant!! And your relative perspective view is brilliant!! Why isn't group theory being used in QCD in physics? It seems they know all about the components, the eight fold way and other factors including shift operators and hyper charge conservation. In algebra we solve for unknowns. Maybe someone can write some software that can tell us using group theory how everything really is working on the atomic and nuclear scale. We have quarks, kaons, pions, mesons and much much more. I wonder if this perspective capability of group theory to simplify relativistic quantum equations.

[@ultramadscientist]

Quantum chromodynamics was defined off group theory by Gell-mann. Yang Mills gauge theory is based off the special unitary group specifically SU(2) the quaternions. I'm not super well versed in it at the moment but you're somewhat on the right track

[@any13131]

Your explanation is brilliant 🤩

[@mathemaniac]

Glad you liked it

[@enderyu]

I think there should be a comment on how normality on H implies the cosets form a group by themselves (some demonstration or intuition). Also, is it a necessary condition as well or simply a sufficient one?

[@tomwellington4255]

Does this have any use for anything in engineering?

[@non_sense7441]

Awesome

[@mathemaniac]

Thanks!

[@alejrandom6592]

9:02 So every subgroup of an abelian group is normal?

[@BleachWizz]

On 4:30 I really think the axiom of choice should state you can choose any rule to pick elements from a group rather than any element from a group

[@zapazap]

A problem comes when we try to define the concept of 'rule' in a way that allows for uncountably many of them.

[@girishgarg2816]

Do you share code on github?

[@mathemaniac]

Sorry if this disappoints you, but I don't use coding to produce my videos. Will make a video on how I make videos in the future, though.

[@blacklistnr1]

I don't like the example at the end, or maybe I'm not understanding: The idea is to study the existing structure of e.g. a rubik's cube, but what you do in the example is you introduce some artificial structure by dividing by the arbitrary 12. I think a better example would be divinding Z into Z- and Z+: you study manipulating just the positive numbers to also understand the negative ones(1 + 2 = 3 => -1 + -2 = -3 ). Similar to how you would study solving a face on the rubik's cube to understand how to solve the others due to symmetry. There's also the patching of the discontinuities which I didn't hear: e.g. 1-2 takes you from Z+ to Z-. That would make it a lot more clear as how the smaller parts fit into the larger thing we're studying.

[@geraldpysniak6228]

to many terms

[@sinkingboat101]

What in God's name am I even watching here? xD

[@weighttan3675]

Meh

[@ke9tv]

Just getting caught up here. I've a pretty decent understanding of algebra, Things like the proof that PSL[n](F[q]) is simple except when n=1 or n=2 and q