Lagrange's theorem - Basic abstract algebra pt. 15

[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.

[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.

[seniorbooboojuice1]

I am 17 and a junior in high school and i love mathematics and let me say i really appreciate your videos. I've learned so much from them and seen so many beautiful aspects of math from them. I've taken faithful notes lol. Even tho its gonna be a while before im studying this haha thank you very much. :)

[iidxzeus]

I hope you decide to make more videos. I would like to review some advanced calculus (much harder, I know), or maybe more abstract algebra. Thanks for the videos!

[dagln0x0]

Next video you should prove Euler's (and then Fermat's) theorem as an interesting application of Lagrange's theorem :)

[Drregaleagle]

If only this could be manipulated for infinite sets somehow...then the continuum hypothesis could be disproven because it would require a subgroup of the group of all real numbers to have a cardinality greater than that of the integers.

[shalomdody]

these are really helpful please continue ....

i been sitting in front of my book reading it and i felt i a dumb person but reading these , is even better than being in class.... please put more examples in it cause then we could relate what we learned and understand it better!!!

thank YOU sooo much

[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.

[magestaff567]

Keep making videos!  Thumbs up!

[xinliw]

Please talk about Galois theory next time!!! I'm totally confused now about it! I love you way of delivering group theory. thanks!

[omarjnc]

¡Qué buena realización de un trabajo de divulgación!

Greetings from Uruguay!

[TheGroupKernel]

Excellent video! Is this the last part (15)? Will you have more classes on kernels / images / conjugacy classes and more examples of homomorphisms from complex to real numbers? Thank you!

[crtx2]

Good job, Sir! I remember Lagrange's theorem sending a shiver down my spine the first time I saw it! It was one of those moments where one suddenly realizes something deep about the very nature of existence :o

[Phanu9000]

I love the music you put in your video series. It makes Abstract Algebra even more exciting then it already is.

[TheGroupKernel]

Is this Vanessa Mae? Sounds like her style of playing?

[theboombody]

What's a group again? How's it different than a set?

[x1101011x]

A group is a set paired with a binary operation such that:

1) The operation is closed (redundant but emphasized).

2) The operation is associative: a(bc) = (ab)c for all a,b,c in the set.

3) There is an identity element e such that ex = xe = e for all x in the set.

4) For every x in the set, there exists an inverse y in the set such that xy = yx = e.

[x1101011x]

#3 above should read:

3) There is an identity element e in the set such that ex = xe = x for all x in the set.

Unfortunately, YouTube doesn't have a comment editing feature, and it also won't allow the comment to be deleted and reposted.

[VeritySeeker]

See the first videos in the series.

[theboombody]

Oh, it's a series? Darn.

Good thing I asked. Appreciate it.

[VeritySeeker]

Hope you'll enjoy... :)

[bosseyedbill]

the ordinary chav peasant in the street dosnt have a clue what beauty the purity of thought is.i spose there was a minor improvement in the music. whats next ?

[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.

[TheBlackwaterDemon]

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