#serious-discussion

1 messages · Page 261 of 1

velvet dagger
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But yeah based on that I get a few vibes. I think the internet has made it much less rough to be a nerd nowadays

timid bronze
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No thats diff

junior veldt
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i mean for me I think they were just overly masculine in a way I couldn’t relate to (which looking back was obviously dysphoria but I didn’t know at the time)

timid bronze
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school sports teams ppl

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and like

latent edge
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oh my god

velvet dagger
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If you were in elementary school in the early-mid 2000s, being called a nerd was the catalyst for bullying

timid bronze
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the more popular ones

latent edge
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I hate that

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i have a lot of traumas from school sports to the point I just stopped doing sports altogether

timid bronze
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o yea the ones in my hs were hardcore racists icl

velvet dagger
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And I think this was true for a good block of the late 20th century as well

junior veldt
timid bronze
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even the POC were racist to themselves

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and their ppl

latent edge
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I gotta love playing soccer just to see the kids kicking and smashing your head and the ball is like 3 meters away waiting to be kicked

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cuz the ball is your head not the ball itself

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jesus

velvet dagger
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LMAO the send and delete, that was funny

latent edge
junior veldt
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Yes

latent edge
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why do i feel like im behind now

junior veldt
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huh…?

quaint spoke
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how old are you Deltoid?

timid bronze
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hes 13

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hes rly young

latent edge
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21

quaint spoke
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lol

velvet dagger
quaint spoke
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I'm 34

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you're ahead of me

timid bronze
junior veldt
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I mean I guess you’re younger than me if that’s what you mean

velvet dagger
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Yeah I think behind in the race to reach 50 years old first

junior veldt
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you are indeed behind in the race to the grave

timid bronze
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daily reminder dami is 8 years older than me and he dms me the corniest jokes in dms

latent edge
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no it just seems like i got to uni pretty late

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i mean i did

velvet dagger
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I mean when I was in NY there was less of that tbh but that's because we were split up by academic level starting from 1st grade

junior veldt
latent edge
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rising 3rd

junior veldt
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rising…?

velvet dagger
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But elementary school in Texas? I was definitely othered somewhat hard for being academically inclined

latent edge
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next sem i will be in 3rd

junior veldt
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Ah ok cool

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Seems fine idk

velvet dagger
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I'M NOT A SIMP THAT'S A NORMAL THING TO SAY

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Ah, sorry about that fam

junior veldt
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yeah that really sucks :((

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I had to do my PhD remotely for a few months cause of depression stuff recently

velvet dagger
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I mean you're not particularly behind even so for what it's worth. If you hadn't said anything about being behind and just told me your age and where you're at, instinctually I would've said "Yeah that sounds right"

junior veldt
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mhm mhm

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also u know waaaay more maths than me lol

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who’s behind here exactly :P

quaint spoke
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why are you all worried about this so much at your age

latent edge
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idk i just feel like out of place sometimes in uni

junior veldt
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yeah that really sucks :((

quaint spoke
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you have so much time ahead of you

junior veldt
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I know the feeling

latent edge
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well around students, not around profs

junior veldt
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I felt v behind in uni

velvet dagger
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Darn. I mean yeah I will say, globally you're definitely in the typical age range

junior veldt
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not just maths-wise but, like, life-wise

velvet dagger
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Like with how many people start school at age 6, either because their parents waited a bit or because their birthday falls in a certain part of the year

junior veldt
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mhm, yeah

velvet dagger
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Or with how many people take some time off

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Etc

latent edge
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well ig you could say it is definitely better now in uni since people with all sort of ages come here

junior veldt
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yep

velvet dagger
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But yeah 20-21 is the super typical zone I expect for third year undergrads

And then on top of that I don't think people really bat much of an eye if someone's even a fair bit older than that age range

latent edge
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one time my prof asked me why i knew all of these math when im so young and i was like "i never felt young in my life lol" then he was like blobwg

junior veldt
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oh no…

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I think I’ve felt young all my life

latent edge
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but fair enough ig

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thanks for letting me know

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i appreciate it

velvet dagger
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I think I alternate. As a kid I often felt older, now I feel younger

novel shell
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I used to feel fairly young until i stopped being a teen

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And i feel like i should become more adult now

latent edge
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btw how do u guys feel about essays in schools

junior veldt
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i found them very difficult

velvet dagger
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Hmm... I think a lot of people don't really write in that format afterwards

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But there are some skills that you learn from that which are hard to replicate

junior veldt
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mhm, true

novel shell
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Ugh hated them

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Fine yes it is important to learn how to express ypurself in paper

velvet dagger
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Maybe specifically the 5 paragraph format is a bit of a meme. And probably most people after uni never really write very many formal written defenses of a given position

latent edge
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I didn't like them mainly because the topics weren't interesting. They say the topics are supposed to be interesting for students but I didn't find them interesting at all lol. It was the same story with my peers

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Yeah the 5 paragraph format is a meme

velvet dagger
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But the ability to make claims and support them with evidence, consider and rebut counterclaims

quaint spoke
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schools impose a lot of stupid crap and they teach you very little about how to think or learn

velvet dagger
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That feels valuable

latent edge
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The topics I was required to write about NOW seem interesting to think about

velvet dagger
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The issue is that they try too much to make it algorithmic/industrial yeah

novel shell
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I felt like the requirements were stupid, it has to be this length it has to include this and this and everything must be formatted correctly

latent edge
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Do maybe the target audience was university students LMAO

novel shell
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Gave me much anxiety

velvet dagger
latent edge
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Yeah lmao

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The topics were too political. I get it politics is important but it's too much lol

velvet dagger
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Oh it wasn't like that for me tbh

novel shell
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Funny thing is i liked writing my english essays way more than my finnish ones

quaint spoke
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"your paper had extremely fallacious arguments and dehumanizing reasoning but you get an A because you followed the structure. timmy's paper was epistemologically sound but his extended eight paragraph argument had to be given a C because he didn't follow the rules"

latent edge
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Sounds about right

novel shell
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I liked philosophy bc we often got to have discussions about topics

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And defend the arguments

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And learn to think

velvet dagger
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I found a paper of mine from 8th grade LMAO

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"the master of Gothic writing" ffs 13 year old Dami why are you like this

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Oh my God this is actually so corny

quaint spoke
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I learned philosophy mostly through trauma processing lmao

velvet dagger
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Barely even saying anything

junior veldt
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my philosophy enrichment class was awful

velvet dagger
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Just a lot of yapping

junior veldt
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it turned me off from philosophy for years

novel shell
velvet dagger
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That's unfortunate. My first encounter with philosophy was a tiny bit of it in my "theory of knowledge" class during the IB program last couple years of high school

novel shell
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Maybe better to not see it actually opencry

velvet dagger
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Honestly that started to get me interested already. It was more of a glorified critical thinking class than it was an epistemology class but still

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Thinking about things like that was fun

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Then my humanities course first year of college was absolutely incredible

junior veldt
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glad you had a better experience of philosophy than me :)

novel shell
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Yes

velvet dagger
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As was social science second year, though humanities first year def left a stronger impact by far

quaint spoke
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you both had it better than me

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I promise you

latent edge
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I looked at my old writings vs now. The ones I got A in it are so cringe I wanna die

novel shell
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Philosophy should be more about critical thinking

velvet dagger
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It's just

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Idk I feel like I'm just saying a few things

novel shell
velvet dagger
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Like wow the setting in which you write things is important

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Whodathunkit

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This author does this with setting and sets this mood

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That author does that

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Kbye

quaint spoke
velvet dagger
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Like wtf kinda point was I trying to make

quaint spoke
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epistemology is extremely important

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to everyone

velvet dagger
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I agree

quaint spoke
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btw Daminark idk if I screwed up my roles, I'm tired and discord was acting weird about the access so I had to redo it a couple times before it started working properly

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I did want postgrad access but also undergrad cause I need to brush up on that

velvet dagger
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So typically you don't have both roles. If you qualify for post grad you have access to the undergrad roles implicitly, even without the undergrad role

quaint spoke
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that's fine

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I don't care about the role just the channels

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it just didn't show up properly at first

velvet dagger
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Ah okay. I will say to get postgrad there is an application process to determine if your math level is at least approaching that of a math graduate

quaint spoke
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I got a dm survey that had three questions

velvet dagger
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Yee exactly

quaint spoke
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I didn't really talk about my math coursework but it was extensive

velvet dagger
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Your answers to that survey will be evaluated and that decides whether you get the post grad role

quaint spoke
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I can clarify stuff if needed

velvet dagger
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That would be ideal actually

quaint spoke
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I had multivariable calc, diffeq, linear algebra, prob&stat, bayesian stats, discrete math, some AI/ML theory, computational complexity, computability... uh other stuff I don't think I need to be exhaustive

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cryptographic theory

velvet dagger
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I guess from discrete if nothing else, you've done some proof-based math?

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Any algebra or analysis?

quaint spoke
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yeah and in complexity, computability, cryptography

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ummm I know what a fourier transform is

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that's part of analysis right

velvet dagger
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Oh I missed computability and wasn't sure if the other classes were proofsy or not

velvet dagger
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Or what a Cauchy sequence is

quaint spoke
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I guess not

velvet dagger
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Hmm, I'd probably hesitate to say postgrad in that case, more undergrad

quaint spoke
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but you put that in the advanced category

velvet dagger
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Advanced vs early uni is kind of a different classification system than undergrad vs postgrad is the thing

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Wait but

quaint spoke
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I'm not in here for a math degree

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I want to study physics

velvet dagger
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I think undergrad role gives access to those channels

quaint spoke
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why do you need to be so restrictive with access anyway

velvet dagger
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Well, the only thing that's really gatekeep is that pre-uni isn't supposed to type in the advanced section

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And that's because if we don't do that

quaint spoke
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oh

velvet dagger
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The advanced algebra channel gets a ton of people doing high school algebra 2

quaint spoke
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so this isn't even channel access

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this is just a role?

vivid halo
velvet dagger
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Undergrad and postgrad give access to all the math channels

quaint spoke
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ooohhhhhhh okay

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I didn't understand that

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I don't care about the role

velvet dagger
#

Postgrad has access to some channels which are meant to be limited strictly to graduate level math.

Yeah they're divided differently from roles just to make it easier for people to navigate where they're interested

quaint spoke
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I'm not studying for a math graduate degree lol I'm kinda trying for like a self-taught demonstration that I can do a physics phd

velvet dagger
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Eg some people will just mute and collapse the pre-uni category because they care to talk about first year calculus

quaint spoke
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but like some of those things I named ofc fall under theoretical cs, so I could contribute there

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maybe. I'm not that versed in it

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if someone asks a really basic question lol

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it's also been like 8 years since I graduated

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I need to relearn a bunch of undergrad stuff I forgot anyway

velvet dagger
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Yeah I mean, the line is of course not sharp. But rest assured you will be able to have the undergrad role at minimum and have access to the advanced math channels

quaint spoke
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are there people doing structured self teaching here?

velvet dagger
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Some perhaps? There are a lot of people who self-study in some capacity or other, but "structured" may be the operative word here. Eg I can name quite a few who are perhaps early and self-studying later topics

quaint spoke
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idk what I mean by structured anyway

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I guess just planned

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goal oriented

velvet dagger
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Hmm so, I guess what I'll say is, a lot of people pick certain topics and self-study them, say via reading groups and such, outside of their classes

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The reason I hesitated to give a firm yes at first is that I wasn't sure how extensive you had in mind. So eg one specific topic as a supplement to classes vs a significant percentage of a degree

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Regardless yeah self-studying is definitely a thing here

verbal quest
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Dami, I see you underestimated your patiencecat_thonk
Basic Math for Adult Students Night School Sitcom
is back on the table

quaint spoke
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does that have something to do with what I said

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or is that just an inside joke

verbal quest
#

I was joking about something from yesterday
self education is great, dw

quaint spoke
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so I'm looking at probably a two year plan at least

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I think it's my best chance of getting into a decent program

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instead of trying to scrape together some means of getting noticed sooner

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this will demonstrate that I'd not only be capable of doing it but likely a good investment

velvet dagger
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That makes sense for sure

quaint spoke
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frankly my aspiration is to do quantum gravity research

velvet dagger
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I taught remedial algebra some time ago and I have had my fill of that kind of thing

quaint spoke
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I have profoundly deep intuition for physics and many other things

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so I think I can

velvet dagger
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I mean yeah go for it! You got this

quaint spoke
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thanks 🙂

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I only recently realized that I could think like this

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I've had an interesting life trajectory lmao

velvet dagger
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Oh huh

quaint spoke
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I was pretty smart all my life but more recently I became way smarter

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it's a combination of factors

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can I ask if the colors in your username have a specific meaning

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you don't have to answer that

velvet dagger
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Oh that's just the color set for senior mods

quaint spoke
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oh ok

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often see patterns that don't exist too

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like all people ofc

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I mean, really

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patterns don't exist

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patterns are simultaneously the entire basis of human cognition, and they don't exist

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not absent of something to perceive or interpret them

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patterns only exist relative to pattern-matching structures

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structures are ofc patterns themselves

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so here's the thing, my intuitive understanding often exceeds my symbolic understanding of a system, but ofc that means I might ask dumb questions without the formalism, is that something that will be okay here

velvet dagger
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Hmm, there might be some variance in people's willingness to indulge that sort of thing?

fast ivy
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It's always ok to ask dumb questions in any scenario... u just might hear some slurs directed back at u tho opencry

quaint spoke
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slurs?

velvet dagger
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Because people would rather you just learn the relevant definitions and the basic theorems to ask more precise questions

velvet dagger
quaint spoke
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I get that it was a joke but it wasn't a funny one

fast ivy
quaint spoke
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I will give you the benefit of the doubt

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I'm kinda hypersensitive to certain things

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which is partially why I'm so good at seeing patterns

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if you don't know what I'm talking about then you don't have to worry about it

velvet dagger
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I think Mister was exaggerating that there's a risk people will respond somewhat critically if they get the vibe that you're musing about things when they think you should just learn the standard stuff first. Which may or may not happen, depends on how that stuff pans out in each situation

Saying slurs wasn't great though, we don't wanna give the vibe that that kinda behavior is tolerated here

quaint spoke
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I'm not easily offended on a personal level

quaint spoke
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I don't think it was meant maliciously

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but yeah the word "slur" has a very specific meaning, it's not the same thing as an insult

velvet dagger
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Not malicious just... Was trying to simultaneously bring to light the embedded point, comment on its validity, and indicate to him that he was unnecessarily crass

quaint spoke
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I was more saying that I don't attribute malice, personally

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expressing my feelings about it

fast ivy
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I always used them synonymously

velvet dagger
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Oh

fast ivy
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English is not my native language

velvet dagger
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I thought you were exaggerating. Yeah nah slur is much heavier

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Stuff like n word and all

quaint spoke
# fast ivy Hm

in american english anyways a slur is a word with history of being used in hatred and violence towards marginalized people

velvet dagger
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^

quaint spoke
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and I get called slurs online pretty frequently when I openly express certain things about my identity

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I know that's against policy here

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I'm still vigilant about it

fast ivy
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Aight I gotta sleep

quaint spoke
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you're good

fast ivy
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It's 5am bking

quaint spoke
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have a good night

quaint spoke
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sorry nvm

fast ivy
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South America

quaint spoke
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ah ok. my brain forgets that your continent extends a bit further east

mint canopy
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Nuked

reef carbon
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oh lmao thank you

velvet dagger
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I'll delete your messages so the word isn't floating but yeah it's been taken care of

reef carbon
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ok sure

keen stirrup
neat lintel
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There is this different feeling of being stared at with baggy eyes

left void
old oak
#

@junior veldt Angela Collier's latest video talks about books she's read recently, and one of those is Stanisław Lem's "Futurological Congress", which I can confirm is a great book (and I'm not just saying that because I'm Polish; some of Lem's books are quite bad, but that one is not among them)

junior veldt
#

are you recommending it to me?

old oak
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I mean, depends what you're into, but I just thought of you because of Angela

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Whom we've discussed recently

junior veldt
#

Mhm!

granite scaffold
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dead

true zinc
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hey outsider, pseudo, aeoeoe

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and darknessnights

junior veldt
scarlet thistle
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How do bayseans reply to the swimming objection?

leaden mirage
#

Why are most discord servers nothing but social experiments?

deep mango
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hmm... yes...

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bird..

quaint spoke
leaden mirage
timid bronze
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Best group tn

velvet dagger
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Yay

scarlet siren
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How do I get help with roles, I lost my advanced math role and now I can't ask my field question

velvet dagger
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Get one of the university-level roles, e.g. undergrad or smth

scarlet siren
velvet dagger
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Postgrad needs an application

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Have you submitted it?

scarlet siren
agile fiber
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it seems you do not currently have the postgrad pending role, make sure to self-assign that

velvet dagger
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Read the full instructions on that page

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It tells you how

latent edge
agile fiber
scarlet siren
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The info bot wasn't working, the channels and roles one appears to have given me the pending role at least

scarlet siren
leaden mirage
scarlet siren
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I've previously had the role for like 2 years too

velvet dagger
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I saw you gave yourself the pending postgrad role at 10:35PM CST

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So something had worked

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But okay tell me now what's your background in math

scarlet siren
velvet dagger
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Do you know e.g. real analysis, complex analysis, abstract algebra?

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(Unless you're more applied, I'm less good at evaluating what constitutes grad level there)

scarlet siren
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Our uni doesn't do complex analysis but yes to the other two

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my field is matroids btw

velvet dagger
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Alright, what's a book or paper you've read recently?

scarlet siren
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I have Matroid Theory second edition by oxley right next to me

jagged forge
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conducting a postgrad interview in the field, dami’s a veteran

timid bronze
velvet dagger
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(I'm being a bit more... thorough, I suppose, than the usual application, but since there's a glitch I'd be unilaterally giving you postgrad, instead of the usual process, so I'm giving myself a higher threshold to circumvent the process)

scarlet siren
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I can whip out my thesis cites should you need, though you could probably guess my supervisor from that

velvet dagger
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Yeah no need for that

scarlet siren
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I mean I like my thesis topic so I'm happy to yap lmao

velvet dagger
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I'll just ask some questions about the topics you know, basic ones to get your vibe, but my inclination is already a yes for what it's worth

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Alright for algebra, here's a question

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Hmm okay this might be not immediately obvious so don't worry if you don't get it, but I wanna hear you think out loud I suppose. I'll have some other questions as well

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Let's say G is a simple group, and H is a proper subgroup. Show that |G| divides (|G|/|H|)!

latent edge
scarlet siren
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Oh I definitely remember my group theory

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don't mind me double checking the definitions, I took group theory in 2022

leaden mirage
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my dumb ass thinks that absolute values are always positive, and any group divides any proper subgroup

velvet dagger
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What

scarlet siren
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Oh yea I know |G| means order

raven plaza
#

||factorial||

velvet dagger
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No need to even spoiler that part haha

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It's just clarifying notation :P

raven plaza
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To avoid confusion one should put both factorial and exclamation mark

agile fiber
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calculate 5!❗

scarlet siren
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Oh there's a dumb bedmas joke with 5! being the answer

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I know that one

scarlet siren
velvet dagger
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Ah okay fair. I'll tell you how that goes then

leaden mirage
#

when touched by order/simple groups, Lie back and think of England

velvet dagger
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If H is a subgroup of G, you have an action of G on the coset space G/H by left multiplication

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So a non-trivial homomorphism G -> Sym(G/H)

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Can't have a kernel since G is simple

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So this is an injection

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First iso gives |G| divides |Sym(G/H)| = (|G|/|H|)!

scarlet siren
leaden mirage
scarlet siren
leaden mirage
scarlet siren
leaden mirage
#

In group theory, factorials appear most prominently when dealing with permutation groups and quotient groups. Factorials represent the number of ways to arrange a set of distinct objects, which is crucial when considering permutations (arrangements) of group elements. Additionally, the concept of a quotient group (or factor group) involves "factoring out" certain elements of a group, which can be related to factorials in combinatorial contexts

velvet dagger
velvet dagger
#

Take G = A_5

leaden mirage
velvet dagger
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Pick any subgroup

leaden mirage
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so (A_, _5) are subgroups?

velvet dagger
scarlet siren
jagged forge
#

damn is A5 the smallest non cyclic simple group

velvet dagger
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Yes

jagged forge
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o well could be a lot worse

velvet dagger
leaden mirage
#

yeah it could be .... in Aminor

(Kendrick song playing)

velvet dagger
#

It's also where I got the problem from, Lemma 4.5

velvet dagger
jagged forge
#

oh it’s literally the next theorem after that lmao

velvet dagger
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But yeah you can do a lot of Sylow counting stuff to get that A_5 is the smallest non-abelian simple group

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If you know Feit-Thompson it's of course easier but uh

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Feit-Thompson ain't easy

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Or wait no

leaden mirage
velvet dagger
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That's not what I'm thinking of

leaden mirage
#

is an instance within a group considered a subgroup?

fathom swallowBOT
#

Sloth King Daminark

leaden mirage
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A and _ and 5

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I parsed it lexically

velvet dagger
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I can't tell if this is next-level trolling or if you just don't know tex and algebra

leaden mirage
velvet dagger
#

Okay so A_5 lexically, which group does that even mean?

leaden mirage
#

it means each of those are characters on the computer screen

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there's three of them

velvet dagger
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Do you know what a group is?

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Define it for me

leaden mirage
#

@jagged forge said "damn is A5 the smallest non cyclic simple group" which makes sense if each character is an element of the group of three items, containing "A" "_" and "5" as given 🙂

velvet dagger
#

Okay you don't know what a group is

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You're thinking of a set

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A group is a thing in algebra

leaden mirage
#

yes you are correct

velvet dagger
#

Abstract algebra not y = mx + b algebra

leaden mirage
#

thanks for correctly categorizing my wrongness

velvet dagger
#

And yeah you don't know enough about that for me to explain what's going on here

leaden mirage
#

no I do not know algebra. I thought this was the offtopic place

velvet dagger
#

Yeah you're not required to know algebra to be here

leaden mirage
#

ill shut up now

velvet dagger
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But my point is you asked for an illustration of what I wrote above

jagged forge
#

i mean, no worries

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we were all just very confused for a minute lol

velvet dagger
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But from what I see, you don't quite have the background to understand such an illustration

leaden mirage
#

you are right

velvet dagger
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So yeah sadly I can't quite help there. But you should learn algebra one day

leaden mirage
#

I thought group members were actual transformations

velvet dagger
#

They often are

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A priori a group is just some set with a notion of "multiplication"

leaden mirage
#

like on a set of numbers, or a geometrical object, like rotate-translate

jagged forge
#

the second thing i did on this server was say something wrong about groups in front of a mod, i think

velvet dagger
#

Which might be multiplication of numbers, matrices, composition of functions

jagged forge
#

in an advanced channel too

velvet dagger
#

But it turns out, there's this notion called a group action

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Where you can manifest a given group as a group of transformations of a set

timid bronze
#

Guys

velvet dagger
#

Hi Ally!

timid bronze
#

i havea required training module due in 2 hours

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But im lazh

#

Do i do it

velvet dagger
#

Yes

#

Do it or you're gonna be broke

timid bronze
timid bronze
leaden mirage
timid bronze
#

can u give me toxic harsh motivation

leaden mirage
#

I'm ok with getting banned from math server for being dumb about math

jagged forge
#

no one is going to ban u for being bad at math

timid bronze
#

can i get banned for being bad at math

#

pls

jagged forge
#

if we did that we’d have banned everyone here fr

leaden mirage
#

@jagged forge my good sir, that emoji is art

timid bronze
velvet dagger
# timid bronze can u give me toxic harsh motivation

You wanna be some lazy broke bum? You literally signed up for this job and then you're gonna not complete the training module in time and signal to your employers that you have no sense of commitment? In this world excellence is required to succeed. Not less than the bare minimum

jagged forge
leaden mirage
#

"Yields falsehoods when preceeded by its quotation" yields falsehoods when preceeded by its quotation .

scarlet siren
ocean robin
#

i'm waiting

velvet dagger
#

Ally training module

#

Tabby if you distract Ally imma teach you real analysis

scarlet siren
#

I wanna make the ysis joke every single time

#

Like a child

velvet dagger
#

Oh right Starvin yeah okay lemme give you an analysis question

#

How far'd you get in real analysis?

timid bronze
#

they kicking

jagged forge
#

wtf

velvet dagger
jagged forge
#

thanx dami

scarlet siren
timid bronze
#

wait but he’s pregnant hes birthing his furries

#

ugh fine

velvet dagger
ocean robin
scarlet siren
#

I didn't do real analysis until my fourth year because non-american uni just has math major requirements being take enough math courses at various levels lol

velvet dagger
#

Tbh American unis are highly non-uniform in their requirements

ocean robin
#

i wish it was more uniform

jagged forge
velvet dagger
#

Tabby walked right into that

#

Uniformly, even

scarlet siren
#

The rest are take your pick

#

And I just picked the discrete side of things until postgrad courses started requiring PDEs :c

ocean robin
jagged forge
#

for the record i have NO such thing

velvet dagger
#

(What's your discrete math background btw?)

ocean robin
#

mmhm

scarlet siren
#

I mean, again, matroids

#

Which is like if linear algebra and graph theory made furry fanart together

sharp mulch
velvet dagger
#

Do you know "ordinary" spectral graph theory?

scarlet siren
#

The word spectral is scary

velvet dagger
#

I just mean studying adjacency matrices of graphs

#

Which I guess might be a different angle than matroid stuff

#

Tbh I only know there's some "top-heavy conjecture" for matroids that was solved using some fancy algebraic topology/singular space shenanigans

scarlet siren
#

I mean its not far off

#

I'm in like, kurwatowski's theorem for matroids area

scarlet siren
velvet dagger
#

Okay so I'll give a general linear algebra question since for some reason I'm blanking on suitable analysis questions at this moment (suitable means not just annoying drudgery but also not too fancy since I'm just trying to test what you know rather than what you can creatively come up with on the spot)

#

This will mix algebra and Hilbert spaces a little bit:
(a) Let's say T is a linear operator on some finite dimensional vector space V. Show that T is injective if and only if it's surjective
(b) Find an example in an infinite-dimensional Hilbert space where this is not true

ocean robin
#

hilbruh

scarlet siren
#

Thats an assignment ahh question if I've ever seen one

velvet dagger
#

Yeah I couldn't think of a good "on the spot" question that was also exciting

#

I have some exciting questions but I don't wanna make your postgrad test sneaky

scarlet siren
#

Time to whip out the massive whiteboard I use to do fuck around math

jagged forge
#

why haven’t i bought a whiteboard yet as an adult

#

this feels like a major oversight

velvet dagger
#

Here's another cute question if you'd like to answer: Given a random permutation pi in S_n, what's the expected number of fixed poitns?

timid bronze
#

Ugh this module is actually annoying

ocean robin
#

i want like a big one that rolls

timid bronze
#

These videos r shit i learned ab basic digital protection in hs 💀

velvet dagger
jagged forge
velvet dagger
ocean robin
#

ally dont get distracted dami is gonna teach me real analysis

#

i do not want that.

scarlet siren
#

So starting with injective -> surjective, suppose for contradiction we got a w which T doesn't map to. Then we've got the subspace fw for f in F that T doesn't map to by linearity

timid bronze
ocean robin
#

i want to distract but i cannot

#

im too scared of dami

tall badge
#

sloths arent scary

scarlet siren
ocean robin
#

rocket jump, i like that name

jagged forge
#

OH

#

so THAT’S what that is

ocean robin
#

roketto janpu

ocean robin
tall badge
#

youve been here 2 years and didnt once think to google translate my name

scarlet siren
#

or close to

tall badge
latent edge
#

rokettojampu eeveekawaii

velvet dagger
scarlet siren
#

Yea I'm not remembering all my theorems but that do sound like one lol

#

Mind went to spectral theorem

velvet dagger
#

Not quite, we didn't say anything about symmetric operators or even assumed V was an inner product space

timid bronze
#

Dami r u still avail for vc

velvet dagger
#

I will say, we're not assuming V is even over R or C. This works over a finite field

velvet dagger
timid bronze
latent edge
#

meow

ocean robin
#

mrow

timid bronze
#

U both r cats

scarlet siren
#

Its fucking rank nullity theorem

ocean robin
#

omg i love that theorem

scarlet siren
#

I have not seen that fella in over 3.5 years

ocean robin
scarlet siren
#

yes

latent edge
scarlet siren
fringe summit
fringe summit
velvet dagger
latent edge
scarlet siren
#

my guess on the counterexample hilbert space is (\mathcal{L}^2[a,b])

fathom swallowBOT
#

StarvinPig

velvet dagger
#

Well, we'd need a Hilbert space and a linear operator

scarlet siren
#

I am aware

velvet dagger
#

My hint is, try to find an operator on l^2(N)

scarlet siren
#

That is also one I was thinking of

#

I am pretty sure I've seen one on an exam or something that would work

timid bronze
#

@velvet dagger

#

W H E N

ocean robin
latent edge
#

meow

velvet dagger
timid bronze
ocean robin
#

mrrp

timid bronze
#

Me need change

velvet dagger
#

Yeah for sure!

#

In the meantime looking for good Indian food in the area

timid bronze
#

Me still wearing cable knit sweater rn so me change to smth comfy

timid bronze
velvet dagger
#

Yes I will!!!

fringe summit
fresh comet
#

I never got the night walk photos sad

median knot
#

How ya all doing?

scarlet siren
#

btw @velvet dagger I am still suffering over here

fresh comet
#

all things considered, fairly well, but my sides hurt for some reason thonkg

#

on the inside

scarlet siren
#

I know the moment you tell me the operator Ima feel like a right doof

fresh comet
#

how're you? EB_EeveeHappy

fringe summit
scarlet siren
#

It's analysis so there's a trick I'm missing

fringe summit
velvet dagger
#

You don't really need the analysis for this one

#

Can replace Hilbert space with infinite-dimensional vector space, in principle over any field (not even R/C, but finite field works etc)

fringe summit
#

Rank nullity is essentially “image + complement of image = whole set” in cardinality

scarlet siren
#

I know but its in that field

fringe summit
#

So, L^2 is kinda the N of this world

#

What’s an injective map N -> N that isn’t surjective

ocean robin
#

ur mom

fringe summit
#

Rank nullity is kinda just “yeah replace things with their dimension” in these nice cases tbh

median knot
median knot
timid bronze
timid bronze
#

one sec

#

dms

ocean robin
#

sharpie :3

fresh comet
ocean robin
#

i love putting off sleep

fresh comet
#

this is a typical reminder for me to go to bed :p

velvet dagger
ocean robin
#

its 3 hrs past my bedtime

timid bronze
#

No dami u dk where i go

#

Pls stop Dox me

scarlet siren
fresh comet
median knot
fresh comet
#

maybe in a couple of hrs :p

fresh comet
#

yippee lisayay

#

enjoy the vacation!! EB_EeveeHappy

scarlet siren
#

Is it really ((v_1,v_1,v_3,v_2,v_5,v_3,...))

fathom swallowBOT
#

StarvinPig

median knot
#

😭😭

fresh comet
#

why sleep when I can do more math PaimonProud

scarlet siren
#

Its only 5pm here I don't have that excuser

fresh comet
#

it's okay if I look sleep deprived if the math is being solved frfr

fringe summit
fringe summit
fringe summit
fringe summit
fresh comet
#

ello Sharp, sufficient c:

#

ello Deltoid

fringe summit
median knot
fringe summit
#

And every injective but not surjective map N -> N gives an example

#

(But not every example is necessarily of this form)

velvet dagger
#

Also just

fresh comet
velvet dagger
#

(v_1,v_2,...) -> (0, v_1, v_2, ...)

fresh comet
#

she had a reputation of being strict

#

but I think she was a great teacher

#

just high expectations

velvet dagger
#

Here's one which might be your style, I might've been cruel with my choice of subject

median knot
# fresh comet just high expectations

Does are really the teachers you can go to if you have a question, they are actually passionate about teaching, my chemistry teacher is such a person every other teacher is ehrmmm alright 😭😭🥲

velvet dagger
#

@scarlet siren Show that a graph is bipartite if and only if it contains no odd length cycles

fresh comet
#

I visit my physics teacher every so often

fresh comet
#

I happened to be her favourite student too

#

so we get along very well

velvet dagger
#

Actually answer any of the following
Graph theory:
Show that a graph is bipartite if and only if it contains no odd-length cycles

Algebra/probability:
What's the expected number of fixed points of permutation in S_n picked uniformly at random?

Real analysis:
Show that a monotone function f:R->R has at most countably many discontinuities

fresh comet
#

I have trauma from bipartite graphs

median knot
latent edge
#

are you claiming they are equivalent Dami?

timid bronze
#

GUYS

fresh comet
#

Hall's marriage theorem was cool though

timid bronze
#

SAY HAPPY BIRTHDAY TO DAMI

timid bronze
#

STOP TALKING

latent edge
#

I used Hall's marriage theorem in my research last week

#

it was so cool

fresh comet
median knot
#

Happy Birthday Dami!!! 🥳🥳

fresh comet
scarlet siren
#

Assume bipartite, assume for contradiction we have an odd length cycle (e_1....e_{2n+1})

fathom swallowBOT
#

StarvinPig

fresh comet
#

Dani is a different moderator >.<

velvet dagger
median knot
#

My auto correct is fkin irritating 😭😭😭

timid bronze
#

so u dont count

median knot
#

I ment dami

velvet dagger
#

Thanks NatxxD

fresh comet
#

I'm a fraud

scarlet siren
#

If our partition is ((A,B)) then WLOG (e_1) goes from (A) to (B)

fresh comet
fathom swallowBOT
#

StarvinPig

fresh comet
#

because somebody has a birthday in Pacific time

scarlet siren
#

Then repeat for (v_i), we'll end up with (v_{2n + 1}) going from (A) to (B) so our start and end vertices aren't the same

fathom swallowBOT
#

StarvinPig

wise bloom
#

higher!

#

Bro

fresh comet
#

howdy

scarlet siren
#

Contradiction, go away

median knot
fresh comet
wise bloom
#

Bro I need some help from you to validate my math

#

I would be grateful if you could

velvet dagger
fresh comet
#

I'm afraid that I'm not in the mood to assist you at the moment MiniheraBow

wise bloom
#

ok no problem

fresh comet
#

you can ask in a help channel if you would like

wise bloom
#

See ya have a nice say

#

say*

#

Lmao

fresh comet
#

you too!

wise bloom
#

Day*

#

higher!

twin lance
#

hi @fresh comet

wise bloom
#

Can you suggest what event we can do

#

Like I made a meta suggestion regarding this

scarlet siren
#

For graph with no odd length cycles, we're just gonna pick a (v_1) and work from there and path out:

fathom swallowBOT
#

StarvinPig

fresh comet
#

I cannot

twin lance
wise bloom
#

Oh

median knot
fresh comet
#

I happen to know a few people on this server giggle

twin lance
scarlet siren
#
  • If (v_1) is isolated, you can throw it in whatever side so WLOG let it be in (A) and pick another vertex
  • If (v_1) is not isolated, throw every vertex adjcacent to(v_1) in (B) with (v_1) in (A)
  • repeat for all vertices adjacent to (v_1), alternating back and forth
fathom swallowBOT
#

StarvinPig

median knot
scarlet siren
#

The only problem we're gonna have is if we have some (v_j) adjacent to some previous (v_i) where (i,j) are the same polarity

fresh comet
#

you flatter me kongouderp

fathom swallowBOT
#

StarvinPig

median knot
velvet dagger
#

You have the gist of it yeah Starvin

scarlet siren
#

And that

#

's only gonna happen if triangle which contradiction

fresh comet
#

I just do the best I can to demonstrate kindness to others EB_EspeonLove

velvet dagger
#

Well, not triangle exactly but odd cycle

#

Like assume connected WLOG

#

Pick v_0

#

Let vertices you get to in an odd number of steps by L

fresh comet
#

I think more people deserve a bit of extra kindness to their lives

velvet dagger
#

Even number R

#

And if this isn't well-defined

#

That gets an odd cycle

fresh comet
#

I try my best to add a tiny bit to that, even if I'm an internet stranger

#

it makes me happy to see others happy c:

median knot
#

That’s soo nice of you 😭🫶

#

I also want to be kind to everyone

#

And only try to come to a conclusion when I get almost all perspectives

fresh comet
#

it's good to be open minded 🤍

#

I've been practicing that a lot in the past couple of years

fresh comet
velvet dagger
median knot
fresh comet
#

I don't know what the latter is kongouderp

velvet dagger
#

LMFAO

#

NatxxD is peak

fresh comet
#

I'm not well versed in Korean culture ded

latent edge
#

wtf is hongdae

median knot
#

Erhmm

fresh comet
#

is it bad? kongouderp

median knot
#

Ehrmmm

latent edge
#

just seems like a place

median knot
#

It depends on what kind of personality and mentality you have…. 😂😂

velvet dagger
#

There's this tiktok meme where some guy named Sean doesn't like guys in Hongdae and makes skits about "Hongdae guys" who are basically players

jaunty ibex
#

Higher stop being AI please...

median knot
#

😭

fresh comet
solid yarrow
#

Vero and Deltoid :3

#

Hewwo

velvet dagger
#

So they go to foreign girls and try to convince them to engage in the hanky panky

jaunty ibex
#

Don't group me with Deltoid. I don't like Deltoid

median knot
solid yarrow
velvet dagger
#

"Excuse me! You seem very... Open minded 😏 Put your number in my iPhone 16 Pro Max"

solid yarrow
fresh comet
#

oh, maybe I was better off not knowing

solid yarrow
median knot
fresh comet
jaunty ibex
fresh comet
#

initiating memory wipe...

#

.<

#

.<

#

.<

#

...

solid yarrow
fresh comet
#

memory wiped! EB_EeveeHappy

median knot
#

😭

fresh comet
#

hi NatxxD nachoWaves

median knot
#

Hellooo

timid bronze
#

Higher /10 how open minded do u think i am

solid yarrow
fresh comet
#

how's your day going? EB_EeveeExcited

solid yarrow
fresh comet
#

ello f0xy, Deltoid, Dami, ally Loves

timid bronze
#

10 too open minded 1 not at all

jaunty ibex
fresh comet
#

ello Vero

solid yarrow
jaunty ibex
jaunty ibex
median knot
fresh comet
jaunty ibex
#

I feel like incredibly dumb in grad school

fresh comet
solid yarrow
solid yarrow
twin flicker
#

hi ally

velvet dagger
#

You're pretty open minded imo Ally!

timid bronze
timid bronze
#

Imagine being told ur hard headed

median knot
jaunty ibex
#

It all boiled down to studying the current state of art of what is going on with Severi varieties

fresh comet
# timid bronze yes

in general, I feel like you've consistently been very tolerant of others' perspectives, so I'll give it a 9.1/10

fresh comet
velvet dagger
#

Yeah that sounds about right

solid yarrow
jaunty ibex
#

Foxy is really kind...

jaunty ibex
#

I feel like Foxy is the kindest person here

fresh comet
#

f0xy is very kind eeveekawaii

solid yarrow
#

What is happening

median knot
#

🤩

solid yarrow
#

Why am I thr topic now

median knot
#

We ar just saying your kind 🤩

solid yarrow
jaunty ibex
#

cuz ur kind duh

#

Higher is AI

solid yarrow
jaunty ibex
#

I'm mostly teasing btw dont take it seriously

fresh comet
#

why am I always the AI sad

solid yarrow
#

I know i know np worries

velvet dagger
#

Higher is the only person I've seen get called AI a noticeable percentage of the number of times I get called that

solid yarrow
fresh comet
#

I must be at a 100 instances now

#

where somebody has assumed that I'm a discord bot

jaunty ibex
#

Dami is scary and goofy

fresh comet
jaunty ibex
#

He's a good mod lowkey

solid yarrow
#

Lmao

median knot
velvet dagger
#

😎

solid yarrow
#

Dami is goofy, but I like him :3

velvet dagger
#

Hyuk

solid yarrow
#

Bless you?

jaunty ibex
#

Ahahaha

solid yarrow
jaunty ibex
#

What are you guys up to

fresh comet
#

computing pushforwards ded

solid yarrow
#

Drinkikg coffee before going to uni

jaunty ibex
#

I'm just watching YT

median knot
#

Just got up 😭

solid yarrow
fresh comet
#

or rather, I was

#

but I got bored of doing that

twin flicker
fresh comet
solid yarrow
jaunty ibex
#

EST?

tidal shoal
#

hi discussion 2!

solid yarrow
#

,ti

fathom swallowBOT
#

The current time for f0xy.exe is 07:34 AM (CEST) on Fri, 27/06/2025.

median knot
jaunty ibex
#

huh

#

Germany?

twin flicker
solid yarrow
#

Yeah?

jaunty ibex
#

German?

fresh comet
solid yarrow
solid yarrow
fresh comet
#

f0xy is the German fox PaimonProud

jaunty ibex
#

I didn't know that lol

solid yarrow
jaunty ibex
#

I might have forgotten I'm not sure

solid yarrow
#

No worries

#

Nothing too relevant tbh

twin flicker
jaunty ibex
#

I might do my phd in Germany

twin flicker
#

im almost out of bread and potatoes so i need to buy more tmr

solid yarrow
twin flicker
solid yarrow
jaunty ibex
solid yarrow
twin flicker
#

my personall limit is 700-800

jaunty ibex
#

You guys have great beer bars there

latent edge
#

Now we know who is alcoholic

solid yarrow
solid yarrow
jaunty ibex
timid bronze
solid yarrow
#

Why did you ping me then sadcat

fresh comet
#

I hope I can meet you one day too Loves

#

and Dami too

velvet dagger
#

Yes I would also like to meet you both! :)

timid bronze
fresh comet
#

but it's a little hard for me to go to the US atm giggle

solid yarrow
#

ok sadcatthumbsup

jaunty ibex
#

Brutal

#

Dw Foxy I will meet u

fresh comet
#

maybe if I go there for grad school, I can meet you two pandawow

timid bronze
#

Sorry f0xy idk u much

solid yarrow
fresh comet
#

but I think the grad school prospects there are also a little challenging at this time

timid bronze
fresh comet
solid yarrow
timid bronze
#

may not even live in the US after school

latent edge
#

unironically grad school in europe is the move

velvet dagger
timid bronze
#

Im not doing grad school

solid yarrow
timid bronze
#

Unless ChemE doesnt accept me and i have to do my backup Chemistry

fresh comet
timid bronze
#

😂

solid yarrow
latent edge
#

for the record im not in US

verbal quest
velvet dagger
#

Chemistry is still quite good as well!

solid yarrow
timid bronze
twin flicker
latent edge
#

Canaduh

timid bronze
#

Im not saying it as if im expecitng it

latent edge
#

Close enough

twin flicker
#

if its spaced out then not really

velvet dagger
#

I foresee joy and success in your future regardless of where you go after finishing college

timid bronze
#

i have the required gpa (Unless physics kills it next semester)

solid yarrow
#

Ahhhhh... i remember

median knot
timid bronze
#

Anything except biology in life

jaunty ibex
velvet dagger
solid yarrow
#

Me need to finish my coffee in 4 min. Because then I need to go tp uni :(. Not even halfway through

twin flicker
timid bronze
latent edge
latent edge
#

Newtonian?

fresh comet
velvet dagger
fresh comet
#

it's actually really well taught at my uni, all things considered

#

I hear very good things about the chem dept here

timid bronze
#

since im needing that most

latent edge
#

makes sense yeah

fresh comet
#

I unfortunately know zero thermo

solid yarrow
#

quantum mechanics

#

Ahhhh

latent edge
#

I only know how to relate thermo with NT

median knot
latent edge
#

That's good enough for me

timid bronze
#

Come to me for thermo in chemistry!

median knot
#

I’m still in high school donno about uni yet 😂

fresh comet
velvet dagger
#

Only thing I remember from chem thermo is PV = nRT
And the fact that reactions have activation energy

timid bronze
#

NOT THERMO IN PHYSICS PLEASE

#

THEM DIAGRAMS PISS ME OFF

median knot
agile fiber
#

i took eng thermo so all i can tell you is that a refrigerator is nearly the same as a steam engine ran in reverse

velvet dagger
#

From physics I vaguely remember this notion of adiabatic stuff

latent edge
#

I learned the advanced version of PV=nRT and said "no im gonna go back to pervert equation"

velvet dagger
#

Or maybe that also was in chemistry?

fresh comet
timid bronze
fresh comet
#

I hope it's better than in NA KEK

velvet dagger
#

Oh right exothermic and endothermic reactions are a thing too