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

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.

Be sure to subscribe so you don't miss new lessons from Socratica:

♦♦♦♦♦♦♦♦♦♦

We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

♦♦♦♦♦♦♦♦♦♦

Ways to support our channel:

► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9

Thank you!

♦♦♦♦♦♦♦♦♦♦

Connect with us!

♦♦♦♦♦♦♦♦♦♦

Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

♦♦♦♦♦♦♦♦♦♦

[GlenMacDonald]

While Mathologer, Numberphile and other YouTube 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!

[walidnouh]

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

[rmb]

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

[tharagleb]

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

[TheNomadic]

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

[melm]

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

[andrewmoeller]

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.

[pathagas]

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

[autodidactusplaysjrpgs]

Thank you for not dumbing your content down.

[AsaNole]

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

[dragonslayer]

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!

[gghelis]

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

[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!

[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!

[escobasingracia]

Topology please! I love this kind of videos.

[richardm]

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

[barend]

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

[alexman]

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

[partialorder]

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!

[pranjalshastry]

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