17:23 Good 35:22 I have to say I really enjoy this series. That reminds me the first months of my computer science degree.
@qzwxecrvtbynumi256
2 жыл бұрын
Bruh for some reason always thought you were a high school student
@Alex_Deam
2 жыл бұрын
Am I the only one that saw the word "good" flash up on the screen at 17:23 or am I going mad?
@goodplacetostop2973
2 жыл бұрын
@@Alex_Deam You’re not mad
@AndyGoth111
2 жыл бұрын
32:45 Nice
@Karatemaci
2 жыл бұрын
At 15:05 (12)(23) is the correct transposition series.
@AndyGoth111
2 жыл бұрын
I'm surely missing something, but how is this not (12)(23)(31)? Really new to transposition series, so please don't bite my head off if I'm being dense here.
@PersonaRandomNumbers
2 жыл бұрын
@@AndyGoth111 Well, consider where 1 goes in your transposition series -- (12)(23)(31) first takes 1 to 3, which gets taken to 2, which gets taken to 1 again. Compare (123), which only takes 1 to 2, and you can see that they're not equivalent.
@AndyGoth111
2 жыл бұрын
@@PersonaRandomNumbers The part I'm missing is what happens to 3. Doesn't (123) take 3 to 1? Am I just making that up?
@ratandmonkey2982
2 жыл бұрын
@@AndyGoth111 in the composition of (12)(23) , you act from the right transposition first. 3 goes to 2 by the right transposition, then 2 is acted on by the left transposition to be taken to 1. So overall, 3 goes to 1 by passing through both transpositions (first the right, then the left).
@kevinnguyen4055
2 жыл бұрын
This is a correct alternative but the one Penn wrote is good as well
@lexinwonderland5741
2 жыл бұрын
YES!! I'm so glad to see this channel get rolling! I can't wait for more abstract algebra concepts, especially if we can get into more generalized algebraic structures and/or how it connects with topology!
@kuberannaganathan5244
Жыл бұрын
Thanks!
@sciencewithali4916
2 жыл бұрын
Thank you very much for those amazing format ! It is very helpful and well explained !
@noumanegaou3227
2 жыл бұрын
You forget a condition in subgroup test set is not empty
@overheadpresschannel440
5 ай бұрын
if the set is empty then it doesn't have the identity and is not a subgroup
@MrRyanroberson1
2 жыл бұрын
Question: what about a subgroup in which the identity is not an element yet there exists some element such that for all THOSE elements it acts as an identity? This can occur when a set has idempotent elements, and I'm not sure whether such sets formally qualify as groups, but try the tricomplex numbers and you'll see. Let i^2=j, i^3=1, associative and commutative, notice (i-j)/sqrt(3) = z satisfies: z^4 = -z^2; z^(4n+k) = z^k for n,k natural numbers.
@synaestheziac
2 жыл бұрын
Loving the group theory. For the last homework problem, I thought that we had only defined the exponent notation for positive exponents so far (x^n is x operated with itself n times). I assume the definition of negative exponents is just x^-n = (x^-1)^n, where n > 0-is that right?
@schweinmachtbree1013
2 жыл бұрын
that's right. you could also do (x^n)^-1 as (x^-1)^n = (x^n)^-1.
@lachenmann
2 жыл бұрын
We all need closure at some point in our lives.
@abrahammekonnen
2 жыл бұрын
15:04 Isn't that (1 2)(2 3). Edit: Got rid of the commas.
@abrahammekonnen
2 жыл бұрын
Wait no I'm wrong dammit. its (1 2)(1 3)
@aaronharrell12
2 жыл бұрын
I am just waiting to when we really get into the meat of things.
@mathmajor
2 жыл бұрын
Video 6 will introduce vector spaces over an arbitrary field. All of this "set-up" allows us to look at vector spaces over an arbitrary field at a lower level than is standard.
@artificialresearching4437
2 жыл бұрын
I might be wrong, but this could work: kzitem.info/news/bejne/sayL2JamrIqLf4o P.S. A piece of advice: make video 1.5 times faster, I speak very slowly)
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