Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)
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- čas přidán 19. 03. 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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Milne, Algebra Course Notes (available free online)
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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
Ohhh what? I found abstract algebra intimating
intimating@@Shubham-ic5tx
While Mathologer, Numberphile and other CZcams 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
Absolutely. I devour alphanumeric puzzles and came to learn the proper fundamentals of discrete mathematics .
"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!
That sound effect when we hit a contradiction at 5:31 haha
These videos are absolutely fantastic. FINALLY a series of serious mathematics videos that TEACHES material well. Please keep making great upper-level math videos such as these! SO much better at explaining concepts/proofs than my professors.
I love good pedagogy that get's deep into the subject! Great video!
Thank you for not dumbing your content down.
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We're so glad you've found us!! Good luck on your Final tomorrow!! We're rooting for you!! :) :)
how was the final?
THANK YOU!!!! The way you present such abstract topics make them easy to digest and understand. I'll have to give you credit on my coming exam period!
These videos are so clear, thorough, and concise! I'm taking an algebra course right now, and although the lectures and textbook are quite good, I get an even better understanding of the material after watching your videos. Thank you!
I have to admit that I often need to replay some bits in this abstract algebra series... However, it's hard to imagine that the subject could be presented even more clearly. really high quality content and excellent teacher/host! Brilliant!
Thank You so much Socratica. Your tutorials were/are awesome!! Let me wait for the results now ☺
Yup, this is starting to remind me of my Modern Algebra class several years ago.
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I have learing dificulties and find it hard to understand dry complex books so this is a blessing, Thank you
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I appreciate this effort socratica. Its really educating, and simple to understand.
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I wish I had had professors when I attended college who can explain an abstract theory in such an entertaining yet rigorous way. You are a great teacher!
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Thank you for your kind comment! We'll keep making more videos!
It would be a huge help if you would share our videos with your friends or on Twitter/ Reddit etc. That will really help us grow! :)
literally you made me fall in love with the concept . Thx to u for helping in this crucial exam time by keeping video short and effective .
Your illustrations make it very clear, thanks.
Thank you so much for making these videos on Abstract Algebra they helped me a lot in my studies.
Never disappoints.
Very interesting and helpful video!
I've been confused of Lagrange's theorem until this clever explication
Wonderful!!! Beautifully explained. The concept is very clear. Thank you
Wow why did I not know this channel when I was an undergrad. Very well put compact lessons.
Thank you so much for providing such concise summaries of Group Theory topics!
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Awesome video, really appreciate your work and the way you present it.
I love your videos, thanks to you I got 78% on the last Abstract Algebra test I wrote! Keep up the good work.
Topology please! I love this kind of videos.
Yes, I would love to see topology. The way they break things down is so clear.
and also analysis
It's been a year. I'd still love to see Tpology
It's been another year. And I'd still love to see Topology, too!
It’s been a month and I’d love to see topology
Very well done! Superb exposition and explanation.
It will be great if you guys have video on normal subgroup and quotient group. Your videos have been very helpful so far:)
I'm french, and this video helps me a lot to get the big picture. Now i can understand my maths course in french. Thx alot
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How far down the rabbit hole are you going to go? Sylow theorems , normal series ....?
Thank you.
Very Helpful Video for cosets and langrange theorem. Cleared my doubts. Thank you
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I learned something from your teaching on Cosets. Brilliant lady, you are the queen of Abstract Algebra!
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Best explanation I found online (and also much better than what my university showed us)
You're the greatest! Thanks for this clear demo
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Excellent concise treatment.
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your style of explanation is great...Please made More Videos on Pure mathematics
This was very helpful! Thank you!!!
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You are a cool teacher who does not wish to present abstract algebra in an abstract way like some professors here.They come to class without a book or any reference material and pour their content on us.Teaching and learning doesn't have to be arrogant.If I must trail without loss of direction algebra routes
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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.
The best explanation of groups theory.
Thank you, Ms.Liliana
too impressed to comment with words.Watching your videos is an overwhelming experience.
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.
This made my understanding concrete, thank you!
I love your videos. I am currently in my final year of my undergrad and your videos have helped me understand the material I am being introduced too. Thank you so much for the work youre doing. I wish i could donate money to show my support.
Nate, we are so happy you are finding our videos helpful! This makes us really excited to make more videos. :)
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Thank you so much for this video. It helped me a lot to understand about cosets
Thank you so much. can you please make videos for real and complex analysis
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Well explained. Thanks!
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Good luck-we're rooting for you! 💜🦉
Best explanation of cosets and lagrange's theorem ever
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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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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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