how do u read this expression?
#serious-discussion
vivid halo
they kinda can, provided they are doing other work
papers that length do come out not uncommonly
median zinc
True, I think most people are just struggling and working on a few things though
sleek wing
how do u read this expression?
the tensor product of FG with respect to FH and V is isomorphic to the induced module V arrow G
is how I'd read it
toxic schooner
true
sleek wing
I dare not post my proof... just in case 
sleek wing
group theory, lin algebra
and by lin algebra I mean fuckin lin algebra
none of this row-echelon bullshit
that's for the rep theory I'm doing anyway
toxic schooner
and by lin algebra I mean fuckin lin algebra
so tensor stuff
sleek wing
for anything more advanced you'll probably need ring theory and maybe even algebraic topology if you're doing lie group shenanigans
sleek wing
so tensor stuff
tensor stuff, abstract inner product spaces, and other nonsense
toxic schooner
for anything more advanced you'll probably need ring theory and maybe even algeb...
😵💫
sleek wing
OH and a very small amount of field theory
you just need to know how to exploit algebraic closure basically
spice storm
toxic schooner
you just need to know how to exploit algebraic closure basically
gonna learn that someday
frail sail
♾️
toxic schooner
sick burrow
wait no
this does't make sense if the thing I think is a typo is actually a typo
however
toxic schooner
sick burrow
it also doesn't make sense the way the paper is written 
toxic schooner
fallow whale
hello chat
sick burrow
ok I think I'm just going to email them
fair mural
ok I think I'm just going to email them
time to surrender
tender musk
hollow sundial
nah, just reopen or open a new help channel
brave garden
kk
cyan goblet
starting undergraduate college soon this fall, planning on doing a major in physics and a minor in CS
career goal is to do some form of quantum computing research
two questions:
- how useful would a math major/minor be along with physics major?
- how many math classes would overlap between physics/math requirements? Until what year would they start to differ?
asking here and not in the physics server because as a wise person once said in #chill ,
also i just really love math
so if i did a math minor, would i still get to do all the rigorous fun higher-level classes as a math major
for reference im currently doing calculus 3 so i may be able to test out of calc 1-3, depending if the school will let me
limber thunder
asking here and not in the physics server because as a wise person once said in ...
wise blo
cyan goblet
agreed
limber thunder
starting undergraduate college soon this fall, planning on doing a major in phys...
I feel like phys major/CS minor is a good combo if your goal is quantum computing research, the few people I know that did math/phys double major or similar ended up in mathematical physics though I'm not sure how much that overlaps with QC
certainly you'll get a better understanding of the (mathematical) fundamentals of QC if you've already taken higher-level math courses
cyan goblet
ye
high oxide
👍
cyan goblet
i just kinda want to take higher level courses in math just out of enjoyment tho
so not necessarily for the end goal of a degree in math or anything but purely just because "wow this is cool and fun"
at which point would it be worth to go for a math major/minor too?
limber thunder
i just kinda want to take higher level courses in math just out of enjoyment tho
yeah I get that and it's a good reason if it's something you can do
I feel like a CS minor would be obvs more useful (algorithms)
cyan goblet
ye, i think CS minor will be there regardless of math major/minor or no math major/minor
limber thunder
while a math minor/major would be a nice plus but not sure if worth it
cyan goblet
just a question of whether it's worth to take on that third course path
limber thunder
maybe it'd be better to hear from someone actually into QC lol
cyan goblet
mm true
im just wondering like
how much extra course load im looking at if i did Physics + CS + Math instead of just Physics + CS
limber thunder
all of these would require the basic calc+linalg sequence , so probably only as much load as the respective minors require you to take
I feel like the three don't really overlap in undergrad but have the same prereqs
like, if you wanted to do real analysis, algorithms and something like analytic mechanics on the same semester, these have pretty much no overlap except in that they all assume you know calculus
limber thunder
maybe it'd be better to hear from someone actually into QC lol
still 
cyan goblet
ye, i will probably reach out to respective professors and whatnot depending on the school i commit to
limber thunder
wooden flax
What is a good method to speedrun hard books?
cyan goblet
What is a good method to speedrun hard books?
sick burrow
blackbox all the results
and all the proofs
don't do any exercises
(in case it is unclear, this is bad advice)
modest rune
What is a good method to speedrun hard books?
dont without good reason
good reason = need it for a research paper but only have to cite it and get the gist
cyan goblet
does good reason also include cramming last minute for a test
modest rune
no
cyan goblet
shit
serene rover
Lmao
sick burrow
stressed because need to work on applications, hard to work on applications because stressed
dense belfry
vast surge
What is a good method to speedrun hard books?
Please don't
What does speedrunning a textbook look like try to do all the exercises as quickly as possible?
charred mortar
Yeah it’s weird
vast surge
Actually that sounds fun I wonder if speedrun.com has a category for Dummit & Foote
charred mortar
I guess if all you care about is the exam then just focus on what’s relevant
wooden flax
What does speedrunning a textbook look like try to do all the exercises as quick...
like perhaps skip certain sections
idk
charred mortar
Actually that sounds fun I wonder if speedrun.com has a category for Dummit & Fo...
How would you even define the rules though
Like if you’ve done all the material before it becomes a question of how fast you can write stuff down
vast surge
like perhaps skip certain sections
Wait does anyone actually read textbooks cover-to-cover? I've almost only ever read sections relevant to classes and personal interests, or sometimes the first third-to-half of a book if it's for a course.
brave hollow
what time do you think you can get rn zorn for any% DnF?
wooden flax
Wait does anyone actually read textbooks cover-to-cover? I've almost only ever r...
I do
i thought that was the only way to read a textbook
maybe thats why it takes me so much time
i read like every word
charred mortar
I have read a few from cover to maybe 90%
vast surge
Dude textbooks will often put in "here's what chapters you can use to structure a course and what you can skip"
wooden flax
i always ignore that lmao
charred mortar
It’s mostly just for texts that are of general interest
charred mortar
I mean the extra info may be useful
wooden flax
yeah of course
vast surge
It’s mostly just for texts that are of general interest
Yeah because texts that aren't of general interest if you know enough to read them you know enough to sort through to find what you need and are interested in
wooden flax
but its like when i read some parts which were pretty boring and were so irrelavent that ive forgotten about
vast surge
what time do you think you can get rn zorn for any% DnF?
100% DnF is the speedrun to go for. I think I can get it in a month, if I can find a way to not need to sleep
wooden flax
dnf = df?
dense belfry
This is really silly and counterproductive
vast surge
It's an objectively terrible idea. That's why I'm entertaining it instead of doing my invariant theory homework
dense belfry
Ah makes sense
brave hollow
counterproductive is my second name
dense belfry
I took you seriously lol
vast surge
Yeah I've been crunching for like 5 hours at this point and I still have a bit that I want to do tonight I'm just goofing off because goddamn I need a break
vast surge
I have seriously considered it. The only reason I haven't is that the coke where I live is often cut with fentonyl and I know some guys who ODed and died from that shit.
charred mortar
Remember to also use variables to refer to people
wooden flax
I have seriously considered it. The only reason I haven't is that the coke where...
i cant tell if youre being sarcastic or not rn
vast surge
Do you have ADHD?
Maybe. I was diagnosed with autism when I was young and I've heard it's often comorbid, and you're not the first one to suggest I might have adhd.
vast surge
i cant tell if youre being sarcastic or not rn
3 guys on the floor of my dormitory freshman year. One of them was dating my best friend. It wasn't a fun time.
charred mortar
Yeah unless prescribed by a medical professional
dense belfry
Lol I'm fairly sure I have autism, I've been putting off getting diagnosed
wooden flax
3 guys on the floor of my dormitory freshman year. One of them was dating my bes...
sorry for your loss
vast surge
sorry for your loss
Eh he was an abusive shithead anyway
dense belfry
I scored well within the range on the raads-r recently
I was also diagnosed with ADHD like last week lol
charred mortar
I think I have some form of anxiety issues
vast surge
Actually wait maybe he's alive and was just hospitalized and expelled for misconduct, I actually didn't care enough to check in on him
dense belfry
Also I was diagnosed with general anxiety, social anxiety, and major depression
vast surge
Anyway don't do drugs and if you do make sure you only buy drugs from a reputable drug dealer and for the love of god test your stuff before you do it to make sure it doesn't kill you
dense belfry
vast surge
Anyway back into the invariant trenches I go, which actually requires a fair bit of representation theory actually wait maybe I should try to learn representation theory at some point that sounds fun
wooden flax
the sad thing about math is like "wow a looks super cool" then a has prerequisite b which has prereq c which has prereq d which is something horribly boring
static loom
what you mean I can't just learn all math from numberphile and 3b1b!!!
dense belfry
vast surge
the sad thing about math is like "wow a looks super cool" then a has prerequisit...
"Commalg is dry and boring but alg nt and alg geo are super fun" is one I've heard a bunch but I actually really like commalg (at least what I know of it so far). I think it's just a matter of making sure it's well-motivated enough.
jovial ember
:)
vast surge
what you mean I can't just learn all math from numberphile and 3b1b!!!
Honestly it works through highschool
static loom
applications in getting lost in the forest and then further getting lost within a tree in the forest
wooden flax
what you mean I can't just learn all math from numberphile and 3b1b!!!
lmao fax
dense belfry
As bookkeeping devices go trees are pretty based
wooden flax
i mean more like im learning analysis rn for complex analysis for something that i forgot
but analysis is not boring at all tbf
dense belfry
Also posets of finite partial functions on the naturals are good
wooden flax
combinatorics based
dense belfry
Lol
vast surge
i mean more like im learning analysis rn for complex analysis for something that...
Eh just skip to smooth manifolds you can fill in the basics as you go
static loom
I think naturally your taste of what you thought was boring can eventually become fun or interesting over time so I sorta go that route
vast surge
Wait maybe I'm getting manifolds and riemann surfaces mixed up. I do that sometimes
brave hollow
I took the raads-r test
vast surge
Wait maybe I'm getting manifolds and riemann surfaces mixed up. I do that someti...
Yeah that's what happened. Not sure why I keep conflating them, but I meant riemann surfaces and not smooth manifolds.
dense belfry
Attitudes around self diagnosis are really weird
vast surge
On the one hand I fucking hate psychologists and psychiatrists almost as a rule and actively discourage people from seeking "mental health professionals" who only make things worse, on the other hand lots of people will use a self-diagnosis of Asperger's Syndrome as a justification for just being an asshole.
dense belfry
I was talking to someone recently who claimed to have did, and I really wasn't sure whether to believe them or not, they were self diagnosed and also they changed the story they were telling me quite often
And it seemed like they were recycling some stuff that I said into their story
vast surge
Sometimes I pretend to have Munchausen Syndrome to get attention
dense belfry
At the end of the conversation they had an episode where they acted like they were being one of their alters, and it really freaked me out
sick burrow
Bannanachair why did you add me
vast surge
sick burrow
WAIT
brave hollow
idk how autism diagnosis helps but I am most probably autistic looking at this score 😕
dense belfry
I mean it helps with understanding yourself
vast surge
I do not know what tf2 is but I should probably change my pfp then.
dense belfry
I actually had munchausen as a kid lol
vast surge
Oh I guess it's some videogame from the 1990s according to google?
dense belfry
It was really bad
sick burrow
Oh I guess it's some videogame from the 1990s according to google?
from 2008
wait no
2007
vast surge
Wait I see what happened it's saying tf1 is from the 90s and tf2 is the sequel
Still old by videogame standards I thought
dense belfry
I faked being sick for a month and actually spent a week in a hospital at the end of it
static loom
I faked being sick so that I wouldn't have to go to school for several months in highschool
vast surge
I don't know how to respond to that. I'm debating internally between something weird and witty and something more heartfelt but can't pull off either correctly.
static loom
so I could stay home and play runescape
dense belfry
I hated school so much lol
static loom
yeah I considered it mostly a waste of time
dense belfry
Well in my case they forced us to learn hebrew studies for 5 hours a day
static loom
gag
vast surge
Until university school is at best glorified babysitting
dense belfry
And I was constantly verbally harassed and physically bullied
static loom
that's worse
dense belfry
I feel really weird going to doctors now, like I'm always afraid I'm making shit up or something
static loom
haha
dense belfry
Whenever I fill out a form about myself I'm always afraid I'm lying
static loom
I've had some really dumb doctors visits
I don't even want to think about it but, you know when you are paranoid about something but turns out to be nothing
I guess better to be safe than sorry
dense belfry
Yeah I've had that, I think that's fine though
static loom
there's worse but I don't want to mention it haha too embarassing
sick burrow
I have so many weird health concerns
static loom
I am currently long overdue to go to the doctor, eye doctor, and dentist
dense belfry
I'm overdue for eye doctor and dentist
static loom
just meaning I need to get better glasses
sick burrow
thankfully I am able to rationally recognize that I worry about health shit for no reason so I haven't gone to the doctor about them.
But I think I just hold a lot of tension in my body and then worry about it.
dense belfry
I don't worry about health shit at all for the most part
static loom
me either, that's what makes avoiding going so easy
dense belfry
Except for when I worried about something for like 2 years and avoided going and when I did it turned out to be nothing
sick burrow
thankfully I am able to rationally recognize that I worry about health shit for ...
actually this is not entirely true. I asked my doctor about a weird thing where I was feeling my heartbeat in my stomach/diaphragm area
dense belfry
I don't even ever take pain medication lol
sick burrow
was worried it was some strange palpitation thing
but it turned out to be nothing of concern
dense belfry
I've been smelling cat poop for like an hour
I just moved the cat trash can away lol
It was like a foot from me
static loom
actually this is not entirely true. I asked my doctor about a weird thing where ...
I had something similar, my doctor was slightly worried and had me get an ultrasound to check it out to be sure, but was nothing
when I was a kid
dense belfry
That's good
sick burrow
I'm honestly starting to seriously think the ultimate source of all this stress/tension/anxiety is dysphoria
static loom
they said it was just normal if you're tall and skinny
dense belfry
I feel like I can never be definitively sure about anything and people acting in bad faith are going to exploit that all the time
sick burrow
because enby + no desire for hrt or surgeries
it's stupid though
the idea of trenders that is
dense belfry
It's not if you already have your beliefs and you need ideas to justify them
sick burrow
ok yeah stupid in an abstract philosophical sense
dense belfry
I hate my family so much lol
sick burrow
it's a very effective way of justifying transphobia in a way that's difficult to easily shut down
dense belfry
It's just unfalsifiable and sounds good
sick burrow
is it unfalsifiable?
sour pecan
now i can take a deep breath and exhale - that i have math buddies who help
sick burrow
I think with a few reasonable assumptions you could falsify it pretty easily
dense belfry
The same rhetoric has been used with slight variation for basically every LGBTQ group
sick burrow
and I think some people already sorta have?
what's annoying is when trans people unironically believe in the trender shit
like bru
h
dense belfry
Yeah that's because trans people are transphobic
Well a lot of them are
Sorry I'm saying that in a too general way
Should I go into detail about what I mean or do you understand
dense belfry
Well in my case I just wouldn't let myself think about any trans concepts at all
And I made a lot of assumptions and didn't bother actually confirming any of them
sick burrow
I had such a basic understanding of trans stuff for so long
like I legit
5+ years ago
remember thinking
"damn it would be really cool if I could be neither a man nor a woman. Shame that's not possible though"
dense belfry
I thought the same thing when I was 15 but just for women
sick burrow
and like I vaguely knew enby was a thing, I just didn't know anything about it
dense belfry
Lol I read this book called treason when I was like 11 and it made me feel so good
In it a male main character has a birth defect where he grows a bunch of body parts and he passes as a woman for a while
It's actually by Orson Scott Card lol
dense belfry
Yeah
sick burrow
or am I thinking of someone else
dense belfry
He's a Mormon
sick burrow
what is it with Mormons being really good but problematic fiction authors
like isn't Brandon Sanderson also a Mormon
sick burrow
less so now
dense belfry
Why was he problematic
sick burrow
but Mistborn eras 1 and 2 has some questionably written female characters
dense belfry
I feel like that's not a good reason to view someone as problematic
sick burrow
like there's a character who's an 18 year old girl whose only purpose in the story seems to be seducing a 36 year old guy
which leads to absolutely no plot relevance later down the line
dense belfry
Oh right her
sick burrow
Didn't she actually like breeze though?
I think so?
but it's weird because the age gap
which also keeps being brought up
maybe problematic is slightly to strong a word for Brando Sando
dense belfry
I mean it's weird but I don't think it's inherently problematic
Yeah I think it's too strong
sick burrow
just maybe a bit questionable
oh my god Marasi though
from era 2
like strictly speaking there's nothing wrong or problematic with the character
but also
the amount of times he wrote "Marasi blushed" is slightly obscene
sick burrow
it was fun
dense belfry
Ah okay
sick burrow
really I just don't read anywhere near as much as I should
dense belfry
I am reading bell hooks the will to change rn
I'm insanely bad at reading nonfiction
Especially stuff where there's room for me to say "but I don't know if this is actually true"
The ambiguity kills me every time
sick burrow
the issue for me is the stuff I want to read is extremely dense
but I don't have that much of a capacity for dense reading
sick burrow
but I had a period over last Winter break where I got into reading fiction again
dense belfry
Well if it's scientifically backed I can
But if it's something that can't be shown conclusively I can't deal with it
It's just a mess
My dad took advantage of this when I confronted him about my childhood stuff
sick burrow
see this is why I like math and philosophy
dense belfry
But he literally was like "you can't disprove the existence of magic"
I'm not joking there
He actually said that
sick burrow
you don't need much evidence besides what is inherently contained within the statements.
dense belfry
Because he believes in magic and that he can do magic
dense belfry
Yeah that's a big reason that I like math too
sour pecan
Yeah that's a big reason that I like math too
emma are you a logician or a horse
dense belfry
So my dad used to do a thing where he would pull money out of a hat and act like he materialized it out of thin air
And that the act of doing so hurt him
So he was literally hurting himself physically to provide for our family
dense belfry
emma are you a logician or a horse
I am both
dire sandal
hey stinkies hows it hangin
dense belfry
Anyway my mom actually believed him, and it seems like she still believes him
sour pecan
<#488120190538743810>
about antilog
dire sandal
about antilog
what is antilog
sick burrow
wait so Emma
did your dad honestly think
that his magician act
was him actually doing magic
dense belfry
Yeah so it seems so
dense belfry
But he actually raised us to believe that he could do magic
sick burrow
since you're, you know, doing it
dense belfry
Like this is a long term thing
He has consistently said he can do things, he and my mom have told us stories of him doing magical things, other people that they know who also believe in magic have said that he can do things
So it's very hard for me to definitively say that he can't
Even though he obviously can't
It's a really weird situation
This is one of the ways that he gets to act like he's incredibly special even though he's a total failure in every aspect of his life
My little brother fully believes that my dad can do magic, and actually it seems like he believes he can too now
It's very strange
dense belfry
But yeah with respect to the hat thing, I personally didn't see it but he apparently showed an empty hat to my mom and then pulled money out of it
Yeah that's the thing
sick burrow
but that doesn't ultimately really matter
dense belfry
But it does if you want to hold someone accountable and they won't accept that they did anything wrong
sick burrow
right I'm saying that it doesn't ultimately matter that you can't definitively prove anything
dense belfry
I know
sick burrow
because for all intents and purposes you absolutely can
dense belfry
The thing is that I was raised on beliefs that are incredibly marginal
sick burrow
magic, at least of the form that would allow you to create money in an empty hat, pretty clearly doesn't exist
dense belfry
Like rejecting things because they are implausible is at total odds with my fundamentalist education
sick burrow
indoctrination moment
dense belfry
And also it removes any plausible deniability I can give to my family for their harmful beliefs
sour pecan
i pray god i get the power of you guys in socializing
dense belfry
So yeah, I'm kinda at an impasse where I have to accept a bunch of beliefs as plausible even though they obviously aren't, or I have to actually try to reject beliefs that I've been trained to think are plausible for a ton of years
And obviously the second one is the better option but it's really hard and it makes me feel like shit all the time
sick burrow
religion is weird
dense belfry
And there are real world consequences in how I can act around people in my family
Yeah I know
sick burrow
my prof said in class today that he talked to some leading Catholic theologian who basically said "yeah obviously Hell doesn't exist"
sick burrow
and that the concept of Hell was basically just a lie you tell ignorant people because they're not sophisticated enough to understand the truth
sick burrow
that the real punishment for not loving God is being forever denied his presence
not Hell
dense belfry
Oh lol
sick burrow
or at least according to this person
dense belfry
Sounds like this person really believes in what he's saying
sick burrow
I actually forget if this is what the person believed or if that is what they thought the correct interpretation of Catholic thought was
dense belfry
That is so fucking funny actually
sick burrow
also I think they were a she?
sick burrow
women don't exist
dense belfry
I did notice that I had assumed but didn't care enough to correct and just hoped I was right lol
Anyway yeah so my mental health is pretty bad rn
But hopefully eventually it will be better
dense belfry
I proved a thing my advisor gave me as a mini project and it ended up being trivial modulo reading some papers
I do have a much better grasp on the topic now though, but I feel shitty because I feel like I didn't do anything
It turns out that I wasn't appreciating the difference between viewing things internally to a larger Computable thing vs externally enough
And my advisor gave me a bunch of problems that made me appreciate this, and that appreciation made me able to see what I needed to do for this mini problem
So that's good I guess
But I still feel like I haven't accomplished anything
sick burrow
I've basically finished reading one
sick burrow
modulo understanding a few details on some of the proofs
an REU
I made the short list so now they want to get a sense of how I approach mathematical reading
dense belfry
Lol I'd like to know how to approach mathematical reading
I just read things and once I get excited I know what to do
humble solar
My approach is very analogous to bashing my head against a brick wall repeatedly
not sure if that's optimal
vast surge
Every time I get assigned like 10 pages of homework a week in one class I realize I'm getting my revenge on the professors by turning it in at the last minute and forcing them to do 10 pages worth of grading each week
vast surge
Anyway it only took me another hour but I'm done with this homework for tonight which means I don't get a new problemset in this class until tomorrow
Which is today it's 1AM and I have class in the morning (not this one) bye
vast surge
Yes
dense belfry
Lol I don't want to though
vast surge
Rip off the bandaid, get it over with
sick burrow
oh also
dense belfry
I think I'll go to sleep and do it in the morning
sick burrow
I'm pretty sure the paper I'm reading is like a preprint or something
since the wording is kinda at times
see my rant earlier today about it pulling two functions out of its ass for a proof without definition
dense belfry
I wonder if my advisor will let me see the paper he's working on about Hilbert's 10th problem for generic fields
I should ask him
He hasn't even posted a preprint yet
He proved that for generic subfields of \bar Q Hilbert's 10th problem for that field is equivalent to the field itself
But that assumes you have an embedding into \bar Q, which is basically the same thing as assuming you have a root algorithm or an algorithm to tell is a polynomial over the field is irreducible
If you don't then be showed there are generic fields with no algorithm to tell if the field is irreducible
Huh I guess you can probably show that Hilbert's 10th for those fields are low relative to the atomic diagram of the field
I guess that's cool
Probably he proved that sort of thing in his paper that he hasn't shown me
But that's just a trivial observation from knowing that there is a low embedding of your generic field into \bar Q
I guess that isn't really the result I expected for Hilbert's 10th for generic fields but that's still nice
Oh he literally says this in the slides I was looking at
Smh
I am incapable of reading things sometimes
frail sail
have u been literally chatting with urself?
compact tartan
you don't?
echo adder
Is there a way to trace an intersection point in desmos?
Currently I have the variables change in time and it's drawing out a nice curve but I want to see it move on it
@me
vast surge
i talk to beatles
Tell Ringo I say hello
frail sail
Ringo’s out
neat lintel
Anyone wanna help me with this assignment?
https://i.imgur.com/u4DSnXc.png
I will be providing you with a set of questions to answer.
neat lintel
I'm an adult trying to learn math. I don't want to go the textbook/youtube route. I think I would learn much better if I had an actual teacher I could do lessons with. Is that a thing nowadays?
stray kite
what'd be the most cited papers in maths
devout nacelle
I'm an adult trying to learn math. I don't want to go the textbook/youtube route...
If it's feasible for you, you could enroll in something like a community college that offers math classes?
Private tutoring is also an option but you'll probably have to lay out a concrete goal beforehand then
neat lintel
If it's feasible for you, you could enroll in something like a community college...
I've thought about that, but it looks like college classes are just in person lectures with homework, rather than a personal teacher i get to ask a lot of questions to
like the youtube/textbook route in real life.
devout nacelle
I think instructors can often be really supportive and answer your questions after class hours. Plus learning with peers seems like an advantage for many people, it even helps in productive discussions.
rancid meadow
what'd be the most cited papers in maths
there are probably books with a bajillion citations
harthsorne or something
google says its this though
if u follow a reasonable definition of math paper
atomic hornet
C. E. Shannon, A mathematical theory of communication, has 72774 citations
not a paper but still thats a lot of citations
atomic hornet
harthsorne or something
yep
jovial ember
Says mr jane street
rancid meadow
you know this ivy league loser could get jane street in his sleep
neat lintel
Hi friend jesse. How do I get jane street. I like money
neat lintel
🤑
rancid meadow
🤑
chm is kidding i dont work at jane steret
i have a less prestigious internship
neat lintel
Wall street?
rancid meadow
No, software
jovial ember
Wait
I legit thought you were interning at Jane steeet or something isomorphic this summer
rancid meadow
fwiw I don't think it's actually that difficult to get a job at a lower ranked HFT place if you are good at maf
citadel/jane street/2sigma are omega hard cuz of the name
but like HRT/SIG hire from "lower" ranked schools pretty often
like i get their OA's everytime I apply
No Chm I'm at a sofware company 
rancid meadow
@atomic hornet im sorry for being mean
thank u for the... information
get it. cause Shannon
rancid meadow
Maybe you should learn some history ..
that was rude shin
I'm sorry
It's because Claude Shannon was a founder of the field of Information theory
I was making a pun
:)
neat lintel
And the homalg book
Very cool. Why though? What motivates you? Any particular problem/theorem?
odd narwhal
I'm gonna be doing algebra research next sem with a homological algebraist
And I find the theory cool
It was the nost enjoyable part of AT for me
Granted I haven't gone far
deft turret
is trategy not a word why not
it sounds like to describe something trategic, like a bad thing
tall badge
see 'tragedy'
fair mural
it’s a tragedy that you forgot that word
sick burrow
ancient flame
does it make any sense at all to write:
$$\lim_{n \to \infty} \bZ_n = \bZ$$
fathom swallowBOT
gmod [gmod gang]
ancient flame
oh true
calm rampart
anyone got any tips on how to get a grade 9 in gcse's, im currently working at a 7/8
ancient flame
ok so then N
deep mango
**gmod [gmod gang]**
sleek wing
does it make any sense at all to write:
$$\lim_{n \to \infty} \bZ_n = \bZ$$
kinda reminds me of a completion
deep mango
No
sleek wing
a completely ill defined completion
deep mango
There are a few notions of limits of groups
deep mango
But
ancient flame
kinda reminds me of a completion
totally know what that means
deep mango
Idk if any of them make sense here
calm rampart
ignored
sleek wing
what relationship
ancient flame
idk what that is lol
sleek wing
Look into how the p adics are a limit though
#serious-discussion message I'm gonna cry
just a little though
sleek wing
how could I describe the relationship then
the relationship between Z/nZ and Z is that Z/nZ is a quotient of Z
boooommm
fair mural
shed a tear
ancient flame
lmao
lavish sorrel
shed a tear
hey uh what can i do for this question?
fair mural
you can go to #❓how-to-get-help
twin sparrow
frozen merlin
anyone got any tips on how to get a grade 9 in gcse's, im currently working at a...
practice papers
frozen merlin
does it make any sense at all to write:
$$\lim_{n \to \infty} \bZ_n = \bZ$$
i'm really just guessing, but since $n\bZ$ ``tends to'' ${0}$ (in the loose sense that $k \neq 0$ is eventually never in $n \bZ$), if anything you'd have $$\lim_{n \to \infty} \frac{\bZ}{n\bZ} = \frac{\bZ}{{0}} \cong \bZ$$
fathom swallowBOT
∧res
frozen merlin
so probably? idk
fair mural
is there easy simple way to say what \cong means
frozen merlin
"it's the same thing, you're just relabelling the elements"
like, elements of Z/{0} are really cosets that look like n + {0}
but you can identify them with n
frozen merlin
is there easy simple way to say what \cong means
but if you're looking for a word, it's isomorphic
frozen merlin
you'll see isomorphism defined in a technical way, like 'a bijective homomorphism', but it's probably one of the most natural ideas in maths
so e.g. there's an isomorphism between {the integers with addition, written using arabic numerals} and {the integers with addition, written using roman numerals}
or for a more useful example, an isomorphism between the groups Z and Z defined by sending every number to its negative
because if you take the number line and flip it around, addition still looks the same
tiny marten
yeah
isomorphism is so natural that it's like the one thing everyone knows exactly what it means
you start to get a feel for stuff instead of just identifying by name
this naturalness is basically reflected in stuff like category theory which is pretty interesting
isomorphisms, unless defined in an unusual way, are fundamental to how objects of theories sit together on the level of categories
like, "actual" isomorphisms and not just things someone misleadingly named that
so in the category of topologies the isomorphisms are homeomorphisms, because otherwise it isnt what we want to mean by isomorphism really
which is that it carries some qualities of the objects of topology
in the category of sets we need them to only be a bijection
though there may be like, category of ordered sets idk
you first learn about it really in abstract algebra but its a general sort of term
in abstract algebra it just needs to be bijective and preserve some operations, tho we have theorems that make it nicer to prove
vague lion
isomorphism is like. 'these things act the same way'
tiny marten
yeah
"in this situation they are the same"
identity is like being isomorphic in every way, it's the strongest form of equivalence
well in regular math
zfc stuff you do by hand
frozen merlin
well in regular math
what an ominous statement
there's models where equality isn't the strongest equivalence?
maybe models isn't the right word technically but
tiny marten
well maybe not that but that equality isnt always given as readily
and may have to be shown in weird ways, idk it's all this automated proving stuff
we kinda think of it as basic and acting nice i suppose
when it's not so clear when you loosen some notions up or dont take some things as given
sort of like negation elimination in intuitionistic logic
not being in it, that is
i am sure there is also mathematics where equality is very weird
beyond any tricky automated proof program
you probably dont even have to get into any meme math either
summer widget
Hehehe
ancient flame
lol
summer widget
Is there a guide for commands?
tiny marten
what's not how what works
long matrix
but isomorphisms dont work too
tiny marten
tbh i wish i knew more about the logic than "idk some things arent as nice sometimes"
tiny marten
it's more an issue of proof methods than the actual equality i guess
but you can almost certainly even change that, probably to awful effects lol
i believe the issue is that equality isnt always reflexive, and you may need two different "paths" to get to each direction of an equality
reflexive in terms of how its proof is validated
long matrix
That sounds strange
tiny marten
something like that can sound strange, and i am explaining it poorly i am sure, but we do get two very different proofs for two directions of a relation others times too
tiny marten
well so, i should be more careful
it probably isnt an issue with equality itself but proving the equaliy
equality
long matrix
If we're talking normal numbers
or even sets/other stuff
The equality certainly is bidirectional
Your proof writes
a=b
=c
=d
=e
tiny marten
it will end up being true, but is not given for free
so you need two different ways to validate something we tend to take for free in the usual math
long matrix
Ok ok, I see.
tiny marten
but it's an issue about what things we can take for free, so here is a historical example
in usual problem solving logic and first order logic we take that if a statement like "A is false" and find that the statement is false, then A is true
so it has to be either false or true
so "A is false" is false, means A is true
in intuitionistic logic you cant assume this
humble solar
???
long matrix
I see - the concepts are getting deeper than what I know
tiny marten
i am shittily explaining issues of logic, and i believe flubbed that part
i was trying to explain paths as in hott without actually talking about homotopy
as an idea of where rules of inference arent as generally nice
humble solar
Identity in hott is still an equivalence relation
tiny marten
yeah i meant that it is true, but that you may need to show it in a different way than "reverse the steps"
it is possible that i am the one confused on the issue
humble solar
You go backwards along the path
tiny marten
is it that paths are not unique?
humble solar
That much is true (in general)
tiny marten
yeah but isnt there a specific issue of hott that has to do with the non-interchangeability of paths?
so in classical math we generally take readily that once equality is shown once there is no more issues
humble solar
That's because classical math isn't proof relevant
In classical mathematics, your system "forgets" the proof used to prove whatever theorem you care about. In hott, proofs are kept around and themselves are considered mathematical objects.
This isn't really my field though so I someone like clerk or mniip could explain better
humble solar
It's also because you keep your proofs around that hott's identity isn't actually a weakening of equality (where it would be in a more traditional framework).
tiny marten
that shows up in a bunch of whacky classical stuff
like when doing complex analysis to prove the various properties of the riemann zeta function
well, to expand out certain things
iirc
it's a pretty nice constant that seems to show up near complex analysis infinite products
empty stratus
that shows up in a bunch of whacky classical stuff
Replace "whacky" with "beautiful", and this is true.
tiny marten
it is very beautiful and good stuff to read as you get thinking about more advanced stuff
empty stratus
Really, though, it offends me that we haven't proven its irrationality yet.
tiny marten
but some of it is also magic, kind of amazing when you are like an undergrad
empty stratus
Someone needs to go tell the algebraic/arithmetic geometers "You don't get to play around with the Langlands program until you've helped the rest of us prove macaroni's irrationality".
"Eat your vegetables"
tiny marten
lol
convert all mathematical resources to macaroni constant
it will be like the covid medical science programs in scale but for math and this one thing
when i first read about the riemann zeta function for reals it was a classical complex analysis book
the latest edition was like 1920
but i think the earliest was 1800s
empty stratus
Awesome.
tiny marten
and i think that was a good thing to read because you dont get this impression with a class book
empty stratus
Whittaker and Watson, perchance?
empty stratus
A classic.
tiny marten
that was it
it's a little tough to work through at times but it also presents material in this different way
velvet dagger
Wait did someone say Langlands
tiny marten
it's interesting because some content is presented as a named result like the keyhole domain (i cant remember whose name is associated with it in the book)
now it's generally just "keyhole domain" or something similarly bland
empty stratus
Wait did someone say Langlands
Yes.
Algebra folks shouldn't be allowed to do anything with Langlands until they've helped the rest of us prove macaroni irrationality.
jovial ember
Why should I care about Euler’s macaroni 
I just want to play with schemes
empty stratus
Why should I care about Euler’s macaroni <:monkey:651816857153699840> I just wan...
...
This is why we can't have nice things.
tiny marten
sorry, we need to tie this loose end of math
jovial ember
I can have nice things by not concerning myself with hard problems I don’t have the toolset to solve
I just deal with the stuff I like and have a nice time
empty stratus
I can have nice things by not concerning myself with hard problems I don’t have ...
I'm exactly the opposite.
Whenever I see something I don't have the toolset to understand, I get FOMO.
velvet dagger
Lol I'm approaching Langlands more from the analysis pov
velvet dagger
Kinda
Like I've been doing analysis of automorphic forms
What's your shtick mathematically?
empty stratus
I'm an oddball.
I do analysis, but not PDEs/Probability.
I like generating functions, complex analysis, integral transforms, harmonic analysis, and, lately, non-archimedean / p-adic analysis.
I've been obsessed with Collatz for the past five years.
empty stratus
What's your shtick mathematically?
And am finishing up my dissertation on it.
And I suck at algebra.
velvet dagger
Interesting
Dissertation on Collatz? Or more generally on the analysis you've been doing?
(I ask because the order messages suggests Collatz but I've been under the impression that it's the kinda thing most people don't attempt until they already have a career going)
burnt kettle
Come join voice chat if u want to help me make logic puzzle problems, not necessarily about math!
velvet dagger
@burnt kettle don't spam
burnt kettle
I guess so
ripe wasp
is this a valid proof of the definite integral of cosx
i feel really happy rn i think i finally get how this works
first time actually (maybe even successfully) proving a definite integral rigorously after being stuck on this for like a week
compact tartan
first time actually (maybe even successfully) proving a definite integral rigoro...
have you covered FTC?
this seems needlessly complicated
ripe wasp
have you covered FTC?
not yet, my book covers integral first and it goes through it rigorously so i have to stick with these kinds of definitions
for now
compact tartan
?
ionic shadow
compact tartan
?
I think the inequality you want to write here is for step functions not these series
seeing as the series aren't functions of x
ripe wasp
uhh im not too sure but i was building it off a definition my textbook introduced and proved
ripe wasp
?
which is this inequality
what i tried to do is use this definition
and this already proved inequality
oh yeah i should have mentioned
i forgot to mention "let P be a partition of [0,a] such that it is divided into n equal subintervals"
ripe wasp
yeah, oh well i feel like im learning like real math
toxic schooner
i would have gone if i had to do it all this way from the start
ripe wasp
might prepare me better for like harder subjects like LA
toxic schooner
wet glade
Sean, what year are you in?
ripe wasp
i mean i had like 1 run through of calc from limits ot derivatives from stewart
ripe wasp
Sean, what year are you in?
im freshman hs
wet glade
What is that
ripe wasp
9th grade
ripe wasp
idk man i have no life and i like math LMAO
toxic schooner
You're in 9th grade learning that!?
wet glade
Im speechless
toxic schooner
i was struggling with geometry proofs in 9th grade
wet glade
idk man i have no life and i like math LMAO
Same, what's that topic that you've studied
That complex sheet with no numbers
ripe wasp
its just calculus but done kinda in a kind of intro to analysis way
wet glade
What country are you from
ripe wasp
im in korea
wet glade
That explains it all
toxic schooner
ripe wasp
but i lived a long time in australia
toxic schooner
how so?
wet glade
but i lived a long time in australia
Oh wow same
ripe wasp
nah im not really like those tryhard korean kids ik the types of ppl ur talking about
wet glade
Asian people
ripe wasp
i dont have like academies from the second school ends til 2 am
i mostly only self study except a physics tutor i go once a week
ripe wasp
nah i like textbooks
wet glade
So um :]... Can I have the download link :3
ripe wasp
i always get distracted when watching yt videos or i just like zone out sometimes
wet glade
I want to learn calc too at my own paste
ripe wasp
sure, dm
though the textbook im using might not be that good for a beginner
its not the usual intro to calc
toxic schooner
definitely not usual from what it seems like 
turbid epoch
bruh 9th grader doing real analysis here
toxic schooner
turbid epoch
maybe I shouldn't have come back /s
maiden bear
people who unironically use sound indicators exist?
turbid epoch
people who unironically use sound indicators exist?
/s is almost a necessity sometimes, it's the only one worth using imo.
waxen lily
before i knew about that i thought they meant per second LOL
limber thunder
/s is almost a necessity sometimes, it's the only one worth using imo.
yeah you can't read tone and subtext over the internet
toxic schooner
same lmao
charred mortar
I just kinda assume everyone is sarcastic
dense glen
Hey 
leaden skiff
/s is almost a necessity sometimes, it's the only one worth using imo.
/hj and /srs are useful
deep mango
handjob??
sick burrow
oh eryc
deep mango
Hello
sick burrow
half jerk
sick burrow
like when you're half joking
sleek wing
it's from reddit terminology ryc
sick burrow
since I see it in circlejerk subs
sleek wing
which makes it an affront to god
deep mango
what's wrong with reddit terminology?
maiden bear
rotund steppe
Reddit
sick burrow
circejerk subs are the only good part of reddit
calm rampart
reddit > discord👀
stray kite
is there mathcirclejerk
calm rampart
yes
dawn bridge
reddit > discord👀
get out
rare harbor
What is more important and fundamental: undecidability of the halting problem or Godel's incompleteness theorem?
sick burrow
These are the same picture
tiny marten
yeah they are both seminal works that are fundamentally similar results
you need to adapt either very slightly to be equivalent i think
halting problem has probably been cited more
velvet dagger
I'm under the impression that incompleteness is noticeably harder than halting problem tbh
tiny marten
it took me a lot longer to learn the incompleteness theorems
deep mango
i think that even though the ideas are similar, it's a bit harder to make the incompleteness theorem work properly
in terms of the proofs
sick burrow
Is the proof of incomplentess even hard
tiny marten
i wont deny that
velvet dagger
My impression is that it's on the longer end
sick burrow
Or is it just that you need a lot of logic to formalize it
tiny marten
yes it is much harder than halting problem
velvet dagger
The idea seems to basically be that if you have a system that can code arithmetic
deep mango
you need to do a lot of work
sick burrow
Like I remember seeing a proof in set theory last year
velvet dagger
Then you can assign these things called "Godel numbers" to statements
tiny marten
you could do a whole course on the incompleteness theorems pretty easily
and a large part would be studying the constructions
sick burrow
And it was basically just "this theorem can't be proven"
Oh wow you can't prove that true or false
But then you need a lot of background to formalize that
velvet dagger
Yeah, the point being that you need the system to be able to express that statement
And I think that's where the Godel number idea kicks in
sick burrow
Godel numbering is not that complex of an idea though right
tiny marten
i thought the hardest part was after that
when you start pumping the recursive functions
i had a hard time with it at the time (like 3 years ago)
and the prof had to help me
sick burrow
It's just there are countably many formulas and countably many positive integers
So you can find a bijection
velvet dagger
Worst Geometer: you don't wanna just define any bijection I feel
I feel like the content would then be nothing more than countability
You prob wanna find some mapping you can actually do things with
sick burrow
Do you
velvet dagger
You're first off using the fact that your system contains Peano
And you want a way to prove that your "This theorem can't be proven" statement is actually expressible by the system
Anyway I know literally 0 logic and this is mostly hearsay so I'm not gonna talk out of my ass much here
sick burrow
I mean you can say "this theorem" with godel numbering
sick burrow
velvet dagger
Exactly
tiny marten
the way you do this is pretty clever
and it makes the halting problem seem straightforward
sick burrow
You can find an explicit bijection between formulas and natural numbers
If you want to do this the dumb way write out a formula in your favorite text editor and take the file's binary
I don't give a shit what the function is
Just that it exists and can be computed
And then you can define a formula that checks if a proof is valid or not
Since every line of a proof is either an axiom (and you can tell if something is an axiom since your axioms are recursively enumerable) or follows from previous lines
tiny marten
idk maybe ultraproduct or obyaeg knows best
i just remember it being non-trivial at the time, i am sure it isnt so bad now
velvet dagger
Sure, the key point is that you have some finite list of things and string them together to create symbols. All I'm saying is that the devil's gonna be in the details here
sick burrow
Is it?
velvet dagger
https://web.yonsei.ac.kr/bkim/goedel.pdf here's a proof
sick burrow
Why do I give a shit about the details
velvet dagger
Is the proof of incomplentess even hard
.
tiny marten
lol
velvet dagger
Don't try to get sassy lmfao
sick burrow
Writing down an explicit first order formula that returns true if a proof (written as an ordered list of Godel numbers) is valid seems like a nightmare