These lectures are marvellous. I studied group theory many years ago but fro a more abstract point of view: axiom, theorem, proof. Here we have discovery driven by example where the theorems just pop out, well motivated. Enjoying this immensely, thank you. Great lecturing style combining talk and text with real enthusiasm for the subject.
Bro didn't explain why the equivalence class of a is a+nZ, just kinda brushed past it. If I'm understanding it right, it's because a-b is in nZ, and a-bar is every b, so a minus a-bar = nZ, but since a is equivalent to a-bar, it also holds that a-bar minus a = nZ. Then if you add a to both sides you get a-bar = a+nZ, right?
a is not equivalent to a-bar. a is an element of a-bar. I think the reasoning is a bit complicated put like that. The equivalence class of a is a+nZ because if you take x in a+Zn, there exists some k in Z such that x=a+n*k (by definition of being an element of a+Zn). thus a-x = -n*k which is an element of nZ.
Even is dual to odd. Equivalence or similarity (conjugate) = duality! The number 2 implies duality and the integers or real numbers are self dual:- th-cam.com/video/AxPwhJTHxSg/w-d-xo.html Duality:- two equivalent descriptions of the same thing -- Leonard Susskind, physicist. Points are dual to lines -- the principle of duality in geometry. "Always two there are" -- Yoda.
I love the way he gets mad at the people talking in the back haha
I like Peter, but he seems a little stressed sometimes...
This is how everyone behaves when they're not used to being in front of a class
These lectures are marvellous. I studied group theory many years ago but fro a more abstract point of view: axiom, theorem, proof. Here we have discovery driven by example where the theorems just pop out, well motivated. Enjoying this immensely, thank you. Great lecturing style combining talk and text with real enthusiasm for the subject.
I admire his composure after scolding the talkers...but he's out of breath for like 30 secs afterward. Not DRILL SARGENT MATERIAL!!! LOL
Bro didn't explain why the equivalence class of a is a+nZ, just kinda brushed past it.
If I'm understanding it right, it's because a-b is in nZ, and a-bar is every b, so a minus a-bar = nZ, but since a is equivalent to a-bar, it also holds that a-bar minus a = nZ. Then if you add a to both sides you get a-bar = a+nZ, right?
a is not equivalent to a-bar. a is an element of a-bar.
I think the reasoning is a bit complicated put like that. The equivalence class of a is a+nZ because if you take x in a+Zn, there exists some k in Z such that x=a+n*k (by definition of being an element of a+Zn). thus a-x = -n*k which is an element of nZ.
the lecturer looks like papa franku
Can you please give the list of problems for HW?
Thank you.
Do all the problems in the book just to be safe.
it's better that peter takes all the lectures. he is precise and clear .
wew why the racism
Oh hell no!
But so is Gross.
It would be gross!
This reply section tho
fml.. this guy again
What a dikhed lecturer... Important result oout of thin air
Even is dual to odd.
Equivalence or similarity (conjugate) = duality!
The number 2 implies duality and the integers or real numbers are self dual:-
th-cam.com/video/AxPwhJTHxSg/w-d-xo.html
Duality:- two equivalent descriptions of the same thing -- Leonard Susskind, physicist.
Points are dual to lines -- the principle of duality in geometry.
"Always two there are" -- Yoda.