Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)
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- Опубліковано 19 бер 2017
- Lagrange’s Theorem places a strong restriction on the size of subgroups. By using a device called “cosets,” we will prove Lagrange’s Theorem and give some examples of its power.
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Dummit & Foote, Abstract Algebra 3rd Edition
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Milne, Algebra Course Notes (available free online)
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While Mathologer, Numberphile and other UA-cam channels present entertaining aspects of math, this channel -- IMHO -- does the best jobs of *teaching* math, while still doing so in an entertaining way. Thanks, and keep up the great work!
I can't agree more, it is indeed a very professional, talented, and entertaining way, ...
That's what I was going to write, you cited great channels but here it was much more clear and easy to understand, very well explained
This video (I haven't seen others on this channel yet) does PURE teaching. Mathologer is very educational, while also paying attention to being entertaining. Numberphile is lighter on the education side, but still informative.
You can learn a lot from Mathologer videos. But it's true that, taken together, they don't make a course.
@@NuisanceManmathologer videos are nice, but they're less approachable
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she deserves an oscar for her wonderful and refreshing rendering of dry and abstract topic
Couldn't agree more...
More like "for proving that abstract algebra isn't as dry as some professors"
True
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intimating@@Shubham-ic5tx
"The proof of Lagrange's Theorem is definitely going to be on your next exam" [which is tomorrow]. thank you!
[In 1 hour]
how can you know
Q; What's purple and commutes?
A: An Abelian grape.
You don't get the point, do you?
It's a joke
I thought it was bonzai buddy
I'm only 19 but I laughed at this so I figured that I have fatherly instincts 😂😂
Purple?
"Don't get overly excited about LaGrange's Theorem..."
BECAUSE IT IS NOT A BICONDITIONAL!!! It's not that powerful folks!
It'll be hard bit I'll do my best
If you want an important result about the converse, then look at the First Sylow Theorem
Damn! And here I was all set to go out on the town, womanizing and carousing with LaGrange's Theorem...
She didn't even mention how it could be used to derive Fermat's little theorem and Euler's theorem
Took me a couple of minutes to figure out who this Cosets guy is.
It's pronounced _ko-say_
@@sb-jo2ch yeah its french!
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how was the final?
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That sound effect when we hit a contradiction at 5:31 haha
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I've been confused of Lagrange's theorem until this clever explication
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Thank you for your kind comment! We'll keep making more videos!
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It will be great if you guys have video on normal subgroup and quotient group. Your videos have been very helpful so far:)
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Thank you! I found the pictorials rather helpful. Once I realized we were only using elements of G not in H, and likewise elements of G not in subsequent cosets of H, then all the pieces started to fall in place.
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Very Helpful Video for cosets and langrange theorem. Cleared my doubts. Thank you
Excellent concise treatment.
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I learned something from your teaching on Cosets. Brilliant lady, you are the queen of Abstract Algebra!
How far down the rabbit hole are you going to go? Sylow theorems , normal series ....?
Thank you.
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3:35 : "This is the cautionary TALE on the limitation of Lagrange's Theorem" , n the background music, giving that wild west vibe. Just mesmerizing. Thank you for this amazing lecture.
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Thank you, Ms.Liliana
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and also analysis
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Best explanation of cosets and lagrange's theorem ever
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I got super confused by the proof for the size of the cosets. But then I just remembered that each coset is basically just a shifted version of H that can’t have duplicates because of that proof
Thank you so much! Your comment helped me, I got stuck on that part aswell and I couldn't figure it out.
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Thank you so much! I have abstract algebra in my second year and this really helped solidify lagrange's theorem:)
That's so great to hear!! We wish you good luck. 💜🦉
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