Lagrange's theorem - Basic abstract algebra pt. 15

This is a video series about basic abstract algebra and group theory. We will keep it basic so that anyone can follow the videos.

Music: The Planets - Contradanza

This is the fifteenth video in the series. We prove Lagrange's theorem.

Category:

Education

Tags:

• basic
• abstract
• algebra
• group
• number
• theory
• mathematics
• Abel
• math
• theorem
• prove
• proof
• science
• axioms
• subgroup
• abel
• abelian
• division
• algorithm
• modulo
• divisible
• coset
• factor
• groups
• Gauss
• Lagrange
• Lagrange's
• beautiful

[colverjustin]

I don't quite understand the logic behind the last proof, saying that gh = gh' , then h=h' . How does this translate to every coset having the same number of elements as H? You said think about it... didn't work for me sorry!

[VeritySeeker]

@colverjustin Because if h is not equal to h', then gh and gh' are two different elements in the coset. The contrapositive argument.

[interted]

The whole series was a *group* of digestible *pieces* of knowledge *operating* prefectly with each other to give a final revelation in this video. Thumbs up, and please keep the good work because maths need it.

[VeritySeeker]

Thanks a lot! There will be more videos when I get the time. I am very happy they are useful for some people out there.

[TheBlackwaterDemon]

Ah, very interesting and informative. Keep up the great work, man - nobody else on YouTube is doing stuff like this!

[kautilya33]

This proves that if a teacher knows the in and out of what he is talking about, he can communicate it to any motivated high school student in the most entertaining fashion. It does not matter the subject is Langrange's theorem or it is Cantor's cardinal.

[Elly720]

I think you just saved my life. I felt so lost and was so busy panicking that I couldn't grasp/understand anything. You've help develop a good foundation for me. Thank you

[Emperorlawson]

I seriously stayed up late on a weekend night to watch part of this series (lots of time spent playing with a small dry erase board trying to follow along/understand). You have a motivational talent.

[THEmikemook33]

What the hell does this shit mean?

[pocketsizednerd]

I was struggling to get my head round my notes on this and your video has helped a lot thanks =D

[Ezzyman17]

Very useful for me, thanks!

[nerioneinthehood]

you should make more videos like this. can you make videos about the next courses of abstract algebra? Thank you for these valuable videos :)

[mrfediuk]

This is probably my favorite video on Youtube

[LINGFERNANDO]

Great stuff. Is there anything about ring and field? Please keep doing. Thanks a lot.