Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)

[@Socratica]

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[@GlenMacDonald]

While Mathologer, Numberphile and other KZbin 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!

[@adeljasmin4214]

I can't agree more, it is indeed a very professional, talented, and entertaining way, ...

[@geogeo14000]

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

[@RadicalCaveman]

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.

[@fahrenheit2101]

​@@RadicalCavemanmathologer videos are nice, but they're less approachable

[@Dr.JudeAEMasonMD]

Absolutely. I devour alphanumeric puzzles and came to learn the proper fundamentals of discrete mathematics .

[@walidnouh1747]

she deserves an oscar for her wonderful and refreshing rendering of dry and abstract topic

[@viveknsharma]

Couldn't agree more...

[@ccgarciab]

More like "for proving that abstract algebra isn't as dry as some professors"

[@luyombojonathan7715]

True

[@Shubham-ic5tx]

Ohhh what? I found abstract algebra intimating

[@handledav]

intimating@@Shubham-ic5tx

[@rmb706]

"The proof of Lagrange's Theorem is definitely going to be on your next exam" [which is tomorrow]. thank you!

[@someone7752]

[In 1 hour]

[@Ali-1_0_1]

how can you know

[@tharagleb]

Q; What's purple and commutes? A: An Abelian grape.

[@obinnanwakwue5735]

You don't get the point, do you?

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It's a joke

[@wdai03]

I thought it was bonzai buddy

[@emmymatt]

I'm only 19 but I laughed at this so I figured that I have fatherly instincts 😂😂

[@chynxyune3546]

Purple?

[@andrewmoeller4538]

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.

[@melm5189]

WHY AREN'T YOU MY TEACHER?!?!? This is amazing, you present this in a way that someone who's never taken higher level math might even be able to understand. You're also very engaging, clear and your thought process is very organized. Will be watching more of your videos tonight to help me with my Algebra final tomorrow afternoon :) Thanks so much for doing these videos!!!!!

[@Socratica]

We're so glad you've found us!! Good luck on your Final tomorrow!! We're rooting for you!! :) :)

[@pqb0]

how was the final?

[@TheNomadic69]

"Don't get overly excited about LaGrange's Theorem..."

[@theproofessayist8441]

BECAUSE IT IS NOT A BICONDITIONAL!!! It's not that powerful folks!

[@gatoradeee]

It'll be hard bit I'll do my best

[@lucasm4299]

If you want an important result about the converse, then look at the First Sylow Theorem

[@RadicalCaveman]

Damn! And here I was all set to go out on the town, womanizing and carousing with LaGrange's Theorem...

[@Onoesmahpie]

She didn't even mention how it could be used to derive Fermat's little theorem and Euler's theorem

[@pathagas]

I love good pedagogy that get's deep into the subject! Great video!

[@autodidactusplaysjrpgs7614]

Thank you for not dumbing your content down.

[@gghelis]

Took me a couple of minutes to figure out who this Cosets guy is.

[@sb-jo2ch]

It's pronounced _ko-say_

[@Nonyabisness-12]

@@sb-jo2ch yeah its french!

[@claudefazio]

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!

[@naturesbliss2456]

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.

[@dragonslayer31415900]

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!

[@MrOvipare]

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!

[@barend4285]

I love your videos, thanks to you I got 78% on the last Abstract Algebra test I wrote! Keep up the good work.

[@AsaNole]

That sound effect when we hit a contradiction at 5:31 haha

[@hftconsultancy]

I have learing dificulties and find it hard to understand dry complex books so this is a blessing, Thank you

[@Beingaspirant-h4r]

You're best teacher in mathematics.. So good mam

[@viveknsharma]

I don't remember when I enjoyed Algebra last time... You all are REALLY REALLY SOCRATIC...

[@alexman97412]

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

[@pranjalshastry9113]

u r the best teacher u help me a lot in my studies thanx

[@escobasingracia962]

Topology please! I love this kind of videos.

[@vecter]

Yes, I would love to see topology. The way they break things down is so clear.

[@michaelnovak9412]

and also analysis

[@genericperson8238]

It's been a year. I'd still love to see Tpology

[@weinihao3632]

It's been another year. And I'd still love to see Topology, too!

[@gregoriousmaths266]

It’s been a month and I’d love to see topology

[@terryendicott2939]

How far down the rabbit hole are you going to go? Sylow theorems , normal series ....? Thank you.

[@rikenm]

Never disappoints.

[@115-ananda4]

Your presentation level so amazing and interesting.

[@a.b.c.d.e...]

Best explanation I found online (and also much better than what my university showed us)

[@partialorder5596]

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!

[@danievanwyk3975]

I think you also need to to confirm that k

[@antonionanni6683]

I think it follows from the rule of the construction -- you construct the coset one element of G\H [G\H is the set of the elements of G not in H] at a time. Let |G\H| = m. I believe it follows from the construction that m < k. BTW, this is valid also for trivial groups. If H == {e}, m = n-1 < n; if H == H, m = 0 < n [any group has at least one element {e}]. Again in the case of finite groups/sets!

[@antonionanni6683]

Sorry, you also need to observe that |Hg1| >= 1, which follows again from the fact that any sub-group will have 1 or more elements

[@emersonrico6061]

Very well explained! This channel deserves my tuition fee than the course I currently enrolled.

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Thank you very much for your work! Even though there're not so many subscribers yet, it helps a lot!

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Wow why did I not know this channel when I was an undergrad. Very well put compact lessons.

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Socratica makes the best videos ever in the history of the internet. True fact.

[@Socratica]

You're the nicest. Thanks for this today. 💜🦉

[@evansokosodo2791]

I learned something from your teaching on Cosets. Brilliant lady, you are the queen of Abstract Algebra!

[@samuelbenson201]

I appreciate this effort socratica. Its really educating, and simple to understand.

[@marinamaher8211]

Your illustrations make it very clear, thanks.

[@jamesdean3352]

I'm studying English and I like how clear your enunciation is.

[@Uejji]

Yup, this is starting to remind me of my Modern Algebra class several years ago.

[@kipkoechchepkwony6948]

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 then i must follow you shoulder by shoulder.Thank you so much.

[@nolwazizakwe9231]

Thank you so much. can you please make videos for real and complex analysis

[@miguelcerna7406]

3:25 please explain how you calculated your orders. I am having trouble understanding why the Order of 6 is zero.

[@roomcard1989]

Even I was confused. Later I understood that it is a whole different topic. Here is it. If you open the video below link then it explains how. m.kzbin.info/www/bejne/bKSycoyKhtN-gq8

[@undergraduateMath]

You're one of the best hv ever seen in life... Don't stop..

[@carlosmendes7]

In 6:51, the "n" in g(_n)H doesn't refer to the order of G, though they used the same symbol (like in 3:45). Probably, using g(_k-1)H would be better, as later they define k as the number of cosets!

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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.

[@Socratica]

Nate, we are so happy you are finding our videos helpful! This makes us really excited to make more videos. :) Please don't worry that you can't donate right now. Focus on school and work hard and we will help as much as we can! If you share our videos with your friends and on Twitter and Reddit and other places, that is a bigger help than you can even imagine. We hear from a lot of viewers that they are just now finding our channel - so the more you can get the word out the better! Thanks again for your inspiring comment. :)

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Best mathematical teacher on utube

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YOU'RE SAVING MY CAREER, THANK YOU SO MUCH FOR EXISTING !

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This is the only channel that I have ever subscribed on this planet. Your ways of explaining gave me interest in WRATH(S) of MATH for the first time. I won't appreciate since those are lies and tend to pull aback. Loved it ;)

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You're honestly hilarious. Your comments at the end of videos get me every time 😂😂😂

[@jeanchrist1085]

i want to cry , you save my life with this amazing video

[@michaelc.4321]

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

[@dynamo58]

Thank you so much! Your comment helped me, I got stuck on that part aswell and I couldn't figure it out.

[@keroroxx520]

AWESOME! It's my first time understand "coset".

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too impressed to comment with words.Watching your videos is an overwhelming experience.

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omg, this channel is amazing

[@JoopWilkens]

Very well done! Superb exposition and explanation.

[@noorameera26]

It will be great if you guys have video on normal subgroup and quotient group. Your videos have been very helpful so far:)

[@pauleugenio5914]

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.

[@bibekmandal7707]

I am from India.This KZbin channel is very helpful for Bsc Mathematics students.

[@Socratica]

Hello to our friends in India! Wishing you safe and well. 💜🦉

[@athame7206]

This was very helpful! Thank you!!!

[@devesh819]

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 .

[@theflaggeddragon9472]

YES TOPOLOGY!! Thank you so much for these videos but please upload more often!!

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Honorable madam, Socratica; first of all I really appreciate you indeed with a little bit comments that it is very important if your videos are in series or consecutive with identification number means that may be 1, 2, 3 .... or what else as you want just to follow your tutorials accordingly.

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I wish you existed when I was in school. They just threw algebra at us and expected us to get it. Your'e a god-send and very much apricated. Thanks xo

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LITERALLY YOU ARE ONE OF THE GREATEST ,KEEP GOING

[@realngure254]

Thank You so much Socratica. Your tutorials were/are awesome!! Let me wait for the results now ☺

[@ankitpandeynitdurgapur9813]

Very Helpful Video for cosets and langrange theorem. Cleared my doubts. Thank you

[@rishant5645]

We wish we had professors like you

[@obinnanwakwue5735]

8:38-9:07- Now that was really abstract there.

[@achievers2001]

Best explanation of cosets and lagrange's theorem ever LOVE FROM INDIA❤️❤️❤️

[@tiowu]

That's some fine acting at the outro! Very cool.

[@kquat7899]

Excellent concise treatment.

[@quantumgamer388]

Saving me in uni maths one video at a time, thank you

[@theboombody]

Even as a math major I think abstract algebra may be the most boring subject in the world. SO many definitions before you can do anything at all with them. What the heck do we have to learn a magma for? I don't plan on using anything without an inverse function. That said, I sure appreciate this channel for uploading content about it. Because it is WAY less dry than books on the subject would be.

[@radfordmcawesome7947]

abstract algebra is so powerful in software engineering. when you need to model a problem, if you can define your "elements" and "operators" in the right way, then you get (without having to reason about it) all the theorems that tell you how your constructs behave when combined in complex ways. likewise relational algebra for databases, lambda calculus for computation, category theory for types. AA may be boring for people doing pure math, but as a SW engineer, im thankful that y'all have done all the tedious work so i can just use it

[@GyanendroLoitongbamgyanendrol9]

Nice lecture... @3:33 I'm confused on how O(6) get 0... How is alternating group calculated? Please post video on alternating group too...

[@kevinjyh]

I had same question about this part. But seems nobody knows?

[@ChaudharyAteeq440]

your style of explanation is great...Please made More Videos on Pure mathematics

[@daisyorcine856]

Thank you so much for making these videos on Abstract Algebra they helped me a lot in my studies.

[@siyuanchen659]

Fix a typo: 5:48 Should be "pick g2∈G not in both H and g1H" (Note: this typo is only in slide). This explanation of cosets is more intuitive than the standard definition, since there are duplicate cosets in standard definition (Of course, duplicate cosets can be eliminated by set theory). Thanks.

[@lukaszr8834]

Very interesting and helpful video! I've been confused of Lagrange's theorem until this clever explication

[@paulyu6334]

this series is amazing

[@rachanacrasta9352]

Wonderful!!! Beautifully explained. The concept is very clear. Thank you

[@FactsandfiguresKing]

I love this site because of this great teacher

[@juanreza4500]

I am learning about the many classifications offered by abstract algebra. However, I am waiting for an application of any of the theorems and classifications to something, other than more abstract algebra. For example, calculus is applicable to many problems such as calculating varying velocities, distances, mass, and energies of actual *things" in the real world. Other than the rotations of repeating flower petals and molecules, which are easily done without recourse to abstract algebra.

[@fahrenheit2101]

It's weirdly effective to get an actress to play the role of a teacher, rather than using a plain old teacher. Is she just following a script a lot of the time, or does she actually know the math, too. Her wiki just credits her as an actress, and 'teaching assistant at Socratica', and this video was 'written and directed by Michael Harrison' Do y'all just get clueless actors to do this lol? Not complaining btw - it WORKS. Anyways, another very clear video - thanks to whoever's responsible for coming up with these nice explanations, and to Liliana for conveying the math in a friendly fashion.

[@Tyler-rh8mu]

Your channel is giving me a fighting change on my final today thank you so much.

[@Socratica]

Good luck-we're rooting for you! 💜🦉

[@arijitmajumder2638]

I love this channel because of this type of video

[@imrankhan8123]

Abstract algebra was not easy like this for me. Thanks for making abstract algebra as easy as possible.

[@luyombojonathan7715]

Great content !!! Cheers

[@karlmax61]

The best explanation of groups theory. Thank you, Ms.Liliana

[@infernal314]

Nice video, though there is one slightly problematic thing. The picture at about 6:58 illustrates a partition of a group G, which suggests there are n cosets (actually n+1 including H...), in place of k. I know how it is meant but it might be quite confusing. What I think is missing here is the equivalence relation, which might have been introduced. So when we construct the sets g_i*H, where i=1..n, we group them into k equivalence classes, the cosets, that form a disjoint and complete set on G. Loosely speaking, cosets are to groups what a base is to a linear space.

[@Socratica]

Sign up to our email list to be notified when we release more Abstract Algebra content: snu.socratica.com/abstract-algebra

[@roushankumar-lu2ov]

Direct and informative.Got the thing without getting into dumb explainations

[@totoplopp6630]

Super pedagogical!! helped me out a lot with the discrete math course I'm doing

[@stevesayers2601]

Hello, just wanted to say how perfectly aligned your videos in Abstract Algebra are for the High school International Baccalaureate Higher level math optional topic. Unfortunately, this is the last year they are offering the topic, as their curriculum changed. Boo! I've really enjoyed teaching the topic, and I sure appreciate the effort and level of sophistication. It is SO hard to find material that is appropriate for willing high school students.

[@Socratica]

This was wonderful to read - thank you so much for sharing our videos with your students! We hope it planted some seeds so we'll see them again when they're in college! 💜🦉

[@kelvinpage4647]

This video is so great! Hope for more videos like this.

[@ricardomarino8554]

Finaly a Higher math video without an indian explaining. I like indian people but the english is not my first language and i don't understand them for them english accent. Long live to this channel!!!! :)

[@err3088]

This video is GOLD

[@letsimage]

but I didn't get why there is no subgroupd of order 6 3:30

[@certifiedsmartass4122]

Well explained. Thanks!

[@AnjaliSharma06]

This made my understanding concrete, thank you!

[@mueezadam8438]

Thank you so much for providing such concise summaries of Group Theory topics!