@donovinrussell: In this video we start talking about a theorem of Galois theory which states that the Galois group of the splitting field of the m-th cyclonic polynomial is isomorphic to the multiplicative group of unit integers mod m. #math #algebra #abstractalgebra #galoistheory

lasmatesdefer :

The video is very, very good, but the music on the background distracts a lot, man.

Kamil Houari :

Insane galois discovered all this by 20 😭😭😭

mr.rabbit :

Finally! Galois theory! Yeeeeaaaah!

grisha :

I don’t see why the only two automorphisms that fix Q are the identity and conjugation. Can you prove it? Can’t you shift the sqrt(2) axis? I took abstract algebra for group theory (for physics) and have had to put off Galois theory for the moment, but I’d really like to study it soon.

petar :

you could be saying anything

Alex :

I showed this to my toddler and he started to cry. Was my mistake showing it to him at home instead of on a street? 😂 (But I think I mostly understood your explanation - thanks!)

seb7895 :

Maths is basically not knowing how to solve something on earth then taking it to mars and then bringing all mars itself to earth

turgutmakbak :

An isomorphism is a nice-o-morphism

Vampyrix :

is the notation in the question "Gal(K/Q)" equivalent to your notation "Gal(K:Q)"?

Xavi :

By the way, K-automorphism is an automorphism of a larger field L that fixes K. In your example you called the elements of the group Gal(K/Q) K-automorphisms but these are actually Q-automorphisms.

Pablo :

Will K necessarily contain Q?

me.probably.idk :

Is the toddler’s name Galois? (I miss algebra)

ProfOmarMath :

Teaching Galois Theory this semester, fun vid

aamari :

Algebra gave me grey hairs

mspessoa :

hey, isn't there an automorphism that sends a +b√2 to a + 2b√2? or to a+nb√2, for that matter?

Daaarrrreeennn :

first time I've seen this topic explained so clearly 🙏

x :

Great video as always

Joshua :

I miss Abstract Algebra 😭

Aarni :

huh?

j :

LFG we did it

lucas :

real dog :

very helpful thank youuuu

Emmanuel Olaye :

It takes me back wow. Completely forgot all that

romans :

I am speechless so anything that contains numbers can be split up and anything that is a field can be manipulated I feel that is just an assumption being made and that proof would make me ask questions till the end of time

Zahan :

What…