serious-discussion

[charred mortar]

Yeah this server is gud

[bright hill]

it honestly helped me immensely

(shoutout to twice for basically carrying me through rudin lol)

[charred mortar]

Pretty direct feedback and you don’t have all the pedants on stackexchange yelling at you for posting something that’s slightly similar to another Q

[bright hill]

lmao

[olive kayak]

and maybe I should learn to convince myself

cuz I think I'll need it when i go to graduate school

which I hope for

[bright hill]

that comes naturally the more proofs you do

so dw about it

focus on asking good questions

that's really important

[errant ridge]

having both is better

[errant ridge]

how do I do that

[bright hill]

try to identify what you're really confused about

[errant ridge]

hm

okay

[bright hill]

ask precise (short if possible) questions

[errant ridge]

like asking myself "do you really understand it? or do you just think you understand it?"?

[bright hill]

and include as much context as necessary

[bright hill]

exactly

that's how you identify gaps in your understanding

also, and this is really important, try to answer your own questions before asking others

[arctic grove]

[bright hill]

only give up after spending some effort on answering them

[errant ridge]

shyshu are you preparing for physiks?

[arctic grove]

neamesis, u might want to not focus on maths for a little while

[arctic grove]

i am

kinda

[errant ridge]

i've recently just realized that :●

[arctic grove]

this is very imp

pondering upon topics u just read is imp

[errant ridge]

but... this is so interesting

[arctic grove]

whats this

[errant ridge]

I'm finally starting to kinda get how to intrinsically define a tangent vector on a manifold

[arctic grove]

[errant ridge]

that's defining it in R^n but the concept is the same

[arctic grove]

u are studying manifolds?

[arctic grove]

oh lmao

[errant ridge]

super basic differential geoemtry

[arctic grove]

locally flat and homeomorphic goes brrr

which book is this

[errant ridge]

intro to manifolds by loring tu

[arctic grove]

ah

[errant ridge]

it's really good

[arctic grove]

i wanted to read that

i read one page

then had to stop

it was too exciting

[errant ridge]

lmao ikr

[arctic grove]

cant get distracted

😭

[errant ridge]

math addiction 😭

why is math so addictive

[waxen lily]

math addiction 🚬

[errant ridge]

[errant ridge]

lol it's treating R^n as a manifold and defining vectors tangent to the space R^n

[arctic grove]

yeah i got that

for a second i was like why are u doing diff geo mid exams

[errant ridge]

lmao

it's the best field of math ever and anyone who says otherwise can fight me

I'll seperate them into two different manifolds

[arctic grove]

[errant ridge]

[arctic grove]

bold of u to say that when u dont know any maths

[errant ridge]

true 😭

me = dumb

[bright hill]

no me

[arctic grove]

no thats me

no shut up darq

[errant ridge]

no me

[bright hill]

fuck u shyshu

I said it first

[arctic grove]

fuck u darq

[errant ridge]

fuck you both i said it first

[arctic grove]

i have been saying it longer

[errant ridge]

doesnt matter, i said it first here

[bright hill]

I've been saying it better

[errant ridge]

I've been saying it louder

[arctic grove]

i have been saying it stronger

[errant ridge]

alright back to the methematics grind

[waxen lily]

when you tell a bunch of competitive people youre dumber

[errant ridge]

see you guys later!

[arctic grove]

cya

[bright hill]

bye

[bright hill]

this meme is dumb

[limber thunder]

imagine being competitive

[waxen lily]

imagine using your imagination

[velvet dagger]

I'm even less competitive than you tbh

[arctic grove]

but dami

u are very competitive

dont u remember?

[deep mango]

[dense belfry]

Hey shyshu

[swift sinew]

Yesterday Captain America graduated

[neat frost]

Bout time

Isn’t he like a hundred years old? Smh

[arctic grove]

hello emma

[arctic grove]

based

i will do this

[dire mulch]

Final grades for this semester has been published for my classes. A, A, B, B. Funny thing is I got an A in my hardest English course I ever took.

I would have had an A in my database course if I didn’t miss 1 homework.

[deep mango]

Nice

[still lance]

I've been watching and taking notes on math youtube videos, but I noticed that I have a problem that I would try to take notes on everything and this could led a 10 minute video taking me up to 30 minutes or even longer at times. I know that writing things down have helped my memory, but I feel like I've taken it somewhat to an extreme. I guess I like the way it looks in my notebook and that I would have the ability to reference it later. I don't have this issue when it comes to textbooks, but I've started to become aware of it with youtube videos.

[leaden torrent]

it's almost like youtube videos are actually a pretty poor format for learning math.

[mortal igloo]

What kind of math youtube videos are only 10 minutes long? Gimme a slice

[still lance]

usually they are longer it's just an example

[mortal igloo]

Nowadays stating one definition in a math talk takes 10 minutes

[still lance]

What makes you think that?
Also I'm using them as supplemental materials?

[mortal igloo]

There's been several discussions about math youtube videos and their educational quality in this server in the past

Generally I observe that what someone gets out of a video is not much different from what they already knew going in

[leaden torrent]

it's the same problem that online lectures have, but worse

it's a lecture where the lecturer can't adjust their pace or exposition based on student reactions

and where the contents of the lecture isnt tailored to student needs, common mistakes theyve seen in homework, or whatever

except unlike an online lecture, you cant even ask questions

[still lance]

I've found stuff like the 3blu1brown series helpful for gaining intuition. I've been using them recently to learn to write proofs and I've been working through How to Prove It.

[modest rune]

Idk if I'd call 3b1b a good source for writing proofs

but I think youtube videos can certainly be helpful for intuition

[mortal igloo]

Wait did 3b1b have a proof writing course?

[modest rune]

they have less pressure to be "exactly right" than a lecture does

[still lance]

not 3blu1brown a few other youtube channels like michael penn and some others

[modest rune]

ah

yeah I mean I think for most things books and lectures are strictly better

[still lance]

I just remember 3blu1brown series on calculus being helpful on gaining intution for it

[still lance]

yeah I'm pairing it with textbooks

I'm not trying to learn solely through youtube

[modest rune]

yeah nothing wrong w that

there is a lot of like, mediocre math content on youtube though

[still lance]

that's what i thought
i just became more aware that i try to write everything down when i'm watching a video
i'm not really sure when the behavior began but was wondering how to address it and it leads me to pause the video and take much longer
it's not that i don't understand the video and usually it makes sense but this behavior causes me to spend a lot more time on it

[modest rune]

I'm not sure its worth picking apart videos in that level of detail

[sick burrow]

I wonder if part of it is the mindset people have when watching a youtube video

[modest rune]

if youre looking for details

you might as well be reading

[sick burrow]

like learning math requires putting in a good deal of work but videos aren't generally as fun when you have to put in a lot of work to understand them

[clever knot]

Is this the one you were talking about hating and how the prof wanted to give you even more work

[dire mulch]

Yep.

I stuck with it and remained diligent and I passed.

[clever knot]

Did they update your grade going into finals or did you still have no clue

I recall you mentioning not having grades or something for the class but maybe I was confused

[dire mulch]

Yeah, he took a while to grade the midterms and first paper.

I got it back like 3 weeks ago.

I got a B for the first paper and midterms.

[ancient flame]

I realized that the $\rightarrow$ symbol acts like an equal sign in the way that it follows certain algebraic properties, like how $x \rightarrow y \iff x-y \rightarrow 0$ or $x \rightarrow y \iff \frac xy \rightarrow 1$ etc

[fathom swallow]

gmod

[ancient flame]

and the right arrow in this context means "approaches" such as when used in limits

[neat frost]

I thought you meant implies and I was confuzzled

[ancient flame]

are there interesting ideas that arise from my observations?

lol

[neat frost]

Uh well

Well firstly, do you mean x is a series and y is a constant?

[ancient flame]

I mean sure I guess

I was thinking of x as a variable

but it could be like a sequence as well

[neat frost]

Variable like function?

[modest rune]

I mean you can see some of this as like

[ancient flame]

variable as "it can change"

[neat frost]

[modest rune]

Reflected in the fact that Cauchy sequences of rational numbers form a field

Like this is how you prove the operations work

[ancient flame]

idk what cauchy sequences are

[ancient flame]

I see

[modest rune]

Things that approach other things nicely

[ancient flame]

ah

[bright hill]

if ${a_n}$ is a cauchy sequence then the larger n is the closer the terms of the sequence get

[fathom swallow]

DarQ

[ancient flame]

oh ok

[bright hill]

i.e., if n is very very large then $a_n$ and say $a_{n+50}$ are basically the same

[fathom swallow]

DarQ

[ancient flame]

so 1/n is a cauchy sewuence

[bright hill]

ye

[ancient flame]

oh ok

epic

[bright hill]

every convergent sequence is a cauchy sequence

[deep mango]

[bright hill]

what now?

[deep mango]

every convergent sequence in a metric space is a cauchy sequence

[ancient flame]

shut up

[deep mango]

let me troll darq

[bright hill]

[ancient flame]

pain!

[deep mango]

oh yeah i'm being a meanie today

oops

i forgot

sorry

ur explanation is correct

[bright hill]

it's fine lel

[ancient flame]

ryc is wrong!!!

[bright hill]

you don't have to appologise

[ancient flame]

blasphemy!

[deep mango]

i know i wasn't being sincere

[bright hill]

oh

anyways

the continuity chapter was such a breeze

I covered most of the stuff already so it was kinda nice to just relax and casually review

[neat frost]

Cauchy

Integrals

Cauchy has something about integrals

Ah yes

Improper integrals

Cauchy

[cold needle]

cauchy has a good number of things involving integrals

😵‍💫

[tall badge]

cauchy has a good number of things period

[wild lantern]

Cauchy's residue theorem always sounds like Cauchy got some kind of horrendous slime everywhere.

[errant ridge]

because he used to be an engineer

[deep mango]

[brittle socket]

Hi Chalk bird

[deep mango]

Hello grass.

[errant ridge]

lol chalk bird

ryc you're an analyst right?

do you have to sometimes do integrals? like computing indefinite integrals and finding closed form solutions

[brittle socket]

His PhD is on DEs I think

The first thing I thought of when I saw analyst was stats

[deep mango]

[deep mango]

yeah sometimes?

but they're usually like

rote

not super interesting

also they're basically all definite

[errant ridge]

i see

i just wanted to know how to get really good at finding closed form solutions for indefinite integrals, like yk those guys on math stack exchange who solve super crazy integrals and use esoteric stuff like i dont even know lol all kinds if specisal functions and stuff

yes i know i get that good by practicing for years

but what exactly? lol are there books or something for this?

[deep mango]

I did research on that in undergrad, it's not related to my phd research

[torn willow]

Oh mb

What's your PhD research on?

[deep mango]

Uhh

undetermined as of this moment, it's my first year in a 5 year program which will have me getting a masters in the middle

But most likely partial differential equations + probability stuff.

I'm looking to learn more about random dynamics and SPDEs.

[errant ridge]

ryc's gonna finish his PhD in 2 years

[deep mango]

definitely not

lol

there are people who could

[errant ridge]

ryc?

[deep mango]

i have no idea

[errant ridge]

I wanna do it by hand

[deep mango]

my friend read the book "inside interesting integrals" and liked it

well

ok

let's go back

actually no this is a public space so i'm just gonna stick with what i said

[errant ridge]

Lol

i mean i know it's not that useful, but i would just like to have that skill

[deep mango]

except that i will change the word "friend" to "acquaintance"

[errant ridge]

Lol alright

[errant ridge]

yeah i've seen that book it's pretty cool im planning on getting it

[deep mango]

anyway this is definitely not useful at all, so only do it if you think it sounds fun

like half the integrals i do these days are just "it's a gaussian integral but you have to complete the square in the exponent"

[errant ridge]

well i wanna go into theoretical physics so at least a little useful

[deep mango]

i guess so

[errant ridge]

Lol and then u-sub?

[deep mango]

yes

[arctic grove]

are u talking about people using contour integrals to solve weird integrals?

even i would want to know how to do those

lol

[arctic grove]

tell me if u find something

[stark charm]

Yeah its funny computations

[bright hill]

Bruh, slurp

You're time zone is even more advanced than mine

[neat lintel]

hello Shysu

[arctic grove]

hello mrlol22

[neat frost]

,ti DarQ

[fathom swallow]

The current time for DarQ is 10:35, 14/05/2022.
Slurp is 2 hours ahead, at 12:35, 14/05/2022.

[neat frost]

Oh it is inchresting

[neat frost]

Why the sully old man?

[bright hill]

ok, wtf

you were awake by 4am?

[neat frost]

Yesh

[bright hill]

and you're alive now?

[neat frost]

Yesh

I was reading webtoons

[bright hill]

[neat frost]

I got like 8 hours of sleep

That’s more than i usually get so I’m good rn

[bright hill]

lel

what were you reading?

[neat frost]

Uriah

[bright hill]

[neat frost]

I looked up horror webtoons, that was listed. It’s not a horror webtoon tho

[bright hill]

it's not one of those weird ones, is it?

[neat frost]

It’s pretty highly rated acshually

[bright hill]

I actually need something to read in my pomo breaks

do you have any recs?

I never read a webtoon

[long epoch]

webtoons 🤢

manga>

[bright hill]

manga can suck too

[long epoch]

well yes

[bright hill]

I'm looking at you slam dunk, you absolute waiste of time

[long epoch]

never read slam dunk

[neat frost]

1984

[long epoch]

but apparently its goated

[bright hill]

lmao

[bright hill]

it isn't

[long epoch]

you're the one person i've been told by that its not

[neat frost]

It’s not

Slam dunk is kinda shit

[bright hill]

it's super shit

[long epoch]

oh well

[bright hill]

just realized I wrote waste as waiste

[neat frost]

[bright hill]

don't you love reading your messages and seeing they were in engrish?

[neat frost]

Renrgish

[long epoch]

mine aren't necessarily in engrish, more like "can't-grammar-english"

[neat lintel]

[deep mango]

Cauchy sequences, Cauchy principal value (what you were talking about), Cauchy's theorem x3, Cauchy's integral formula, Cauchy-Riemann equations, Cauchy problem, Cauchy Hadamard theorem, ...

If u think the word "integral" when you see Cauchy I've got news for you

[neat frost]

I thought the word integral because we just proved his theorem about integrals last lecture

It was totally justified, old man

[deep mango]

Which of his 7 theorems about integrals

[neat frost]

The one on the existence of improper integrals

Like it exists iff for large enough values the integral between those values gets arbitrarily small

[flat harbor]

was gonna reply to this one with a sassy comment but discussion died 2 hrs ago

[bright hill]

rip

[deep mango]

We can talk more about cauchy principal value. I have a lot of thoughts on it

[flat harbor]

shame!

[wooden turret]

Any of you are familiar with probability?

im not good at it

a friend of mine need help with it

[bright hill]

they can read #❓how-to-get-help and then open a help channel for any question might they have

[wooden turret]

no one is replying to them :/

[bright hill]

just be patient

you really can't (and shouldn't) do much else

[charred mortar]

it's free help

[harsh fiber]

.

[winged saddle]

@harsh fiber

[harsh fiber]

Hello wac good good

[harsh fiber]

Ok so I need you to red #❓how-to-get-help

[harsh fiber]

If the helpers take too long to help you, then just wait until the bot notifies you. Don’t spam the questions and don’t spam questions in several different channels. Stay in one channel for help, and make sure its unoccupied.

[shrewd lily]

Hi. Is it right to say that the multiplication operation is just shorten for the addition?

[deep mango]

Not really

It's short for repeated addition only when one of the factors in your product is a whole number

[leaden torrent]

π * e is just adding e to itself π times

what's so hard about that

[brittle socket]

[prisma swallow]

How would you describe multiplication on the reals if not as repeated addition?

Maybe as the area generated by two sides of two lengths.

[rose dock]

well in order to define the multiplication for the reals, you first define multiplication for rational numbers, and then extend that to the reals, which are limits of rational numbers, by taking the limit of products of rational numbers.

[deep mango]

Continuous extension of the multiplication function on rationals

Yes

[bright hill]

good question

[deep mango]

Or just do it directly on cauchy sequences of rationals

[prisma swallow]

Yeah, I suspected something like that.

[deep mango]

Thats how reals are defined anyway

[prisma swallow]

That would be real analysis?

[deep mango]

Yes

[prisma swallow]

🔥

[bright hill]

I skipped dedekind's cuts tbh 😅

I should really come back to those

[deep mango]

They're kind of irrelevant

The cauchy sequences of rationals definition is better

Since it generalizes to metric space completions

Though dedekind cuts can complete ordered spaces I guess.

Idk anything about that

[cyan goblet]

dedekind cuts my not beloved

[rose dock]

regardless of which definition, I don't necessarily think going through an explicit construction of the reals is super helpful for learning real analysis

[deep mango]

Yeah

Its just helpful to know facts around completions of metric spaces

I extend uniformly continuous functions uniquely to completions of metric spaces like 3 times a week

Id better know why it works

[burnt kettle]

no you dont

[deep mango]

I could prove it right now

[cyan goblet]

why dont you prove that you're a hawk and not a pidgeon rn

pigeon

feels weird that pigeon doesnt have a d

[hushed turret]

what does this mean?

is that in reference to the fact that a uniformly continuous function is determined uniquely by its values on a dense subset of its domain

[deep mango]

A lot of times in analysis you show things are well defined on simple objects, and then take limits of those simple objects to get the definition on all objects.

[deep mango]

Yes. A metric space is dense in its completion and a dense subset of a complete metric space completes to the original metric space.

So it's the same thing here.

[hushed turret]

oki

[hushed turret]

wait is uniform cont even necessary here i can't remember

[deep mango]

Yes. The easiest example would be, say, 1/x on R\{0}

Or the function on Q which is 0 when x < pi and 1 when x > pi.

These are continuous but not uniformly continuous.

[hushed turret]

well that shows uniform cont is necessary for existence of a continuous extension, but if an extension exists is continuity sufficient for uniqueness

[deep mango]

Idk. That's interesting

Uhh

[hushed turret]

i think it probably is?

[deep mango]

I think no

Or

I mean I think that continuity is sufficient

Since limits are unique in metric spaces

[hushed turret]

okay yeah

i think it would be relatively simple to prove or disprove if i think abt it

[hushed turret]

oh wait that's all you need isn't it

[rose dock]

and the sequential characterization of a limit

although in general topological spaces I think you can replace sequence with net and get the same result

[hushed turret]

do you not need the space to be hausdorff?

idk enough topology to say that with certainty but i remember asking about this a while ago

[rose dock]

only the codomain has to be a hausdorff space

because you only need unique limits in the codomain

I was assuming real-valued functions though

[hushed turret]

oh, right. i thought you meant functions between topological spaces

anyways, it's a cool fact

[wooden flax]

Stupid question but I know you say $Gau\ss$ for gauss but do you say $Gaussian$ or $Gau{\ss}ian$?

[fathom swallow]

Invictus

[leaden torrent]

adding "-ian" to words is an english construction

not a german one

so it makes most sense to use the english spelling

Gaussian

[surreal sapphire]

Gaußsche

[leaden torrent]

yeah

the german equivalent is Gaußsche

[wooden flax]

oh ok

thanks

[limber isle]

Yo

I need help

And not with a maths question

[torn willow]

No you can't date the female guards

[limber isle]

Anyone here who consistently gets 90%+ on maths examinations, how do you maintain full concentration throughout the whole exam?

I’ve got a 3 hour mechanics exam coming up in 2 weeks. When I do practice papers (all the questions are of equal difficulty throughout the whole paper,) I get full marks until 60% through the paper where my mind starts to fade and I make incredibly stupid mistakes.

[mellow estuary]

do meditation

[limber thunder]

I don't

[mellow estuary]

thats the cure

[limber thunder]

but yeah you could try that

definitely make sure to sleep and rest well

[mellow estuary]

I only sleep for 4 hrs a day

i still am alive

kids don't try at home

[limber isle]

I could be more mindful to be fair

I’ll keep that in mind

Besides meditation is there anything else?

I tend to sleep well

And eat and exercise plenty

[limber thunder]

another factor could be just anxiety during exams, I had some serious trouble with that when I first started uni

[mellow estuary]

try to control emotions

[limber isle]

Yes yes I am in the middle of an anxiety diagnosis

And ADHD

And will probably be medicated

But I won’t get my meds till then

[limber thunder]

what works for one person doesn't necessarily work for another, but I managed to surpass that by convincing myself it's no big deal if I fail or whatever

as well as just getting better at studying and summarizing stuff

[limber thunder]

I see

[mellow estuary]

true af

[limber thunder]

I'm probably undiagnosed but yeah that's a thing

[limber isle]

Thanks for the ideas

[limber thunder]

it usually takes some weeks to get used to the meds too, keep that in mind

[limber isle]

I like this approach

Easier said than don’t

But good idea

[limber isle]

Yes yes I will

[limber thunder]

that's true of most advice

[limber isle]

I wasn’t clear: I am getting medicated after the exam

So I won’t have meds

[limber isle]

Word

[limber thunder]

yep I understood that

best of luck with your exam

try to review/exercise often (daily?) but don't overwork or strain yourself

especially like, the day before the exam

[limber thunder]

also 3 hours is a lot, any sane person would break concentration even for a while in the middle of it

[limber isle]

Thank you 🙂

I won’t, it’s just such a beefy exam

And I have so much to practice

And mechanics is awful in the sense that the question are like essays

[neat frost]

SAME

[mellow estuary]

you came here that mean you wanna ler=arn it somehow

okay I was the same but with patience I started solving problems and I became good at math

[frigid lark]

Didn't know randomized algorithm lecture can be interesting. First hw exercise was an interesting protocol, where you can distribute the information of a binary word of size n among t people. And do it like that, that a coalition of even t-1 people cannot reconstruct any bit of information.

[patent sphinx]

Hilbert was responsible for propelling the careers of brilliant students such as Emmy Noether, Bernard Riemann, and John Von Neuman
WHAT?
Is this a different Riemann? Bc the guy who came up with riemann hypothesis was much older than hilbert IIRC and his doc advisor was gauss right?

[leaden torrent]

that sentence just seems wrong.

[hushed turret]

i think this is incorrect information

https://anagrath.medium.com/david-hilbert-a-mathematics-mainstay-38aa85af3f2f

[patent sphinx]

Right?

[hushed turret]

if this is what you're reading from i wouldn't trust it

[leaden torrent]

medium article

lmao

[patent sphinx]

Is medium not that well reputed?

[hushed turret]

lol

[leaden torrent]

literally anyone can write a medium article

its a glorified blogging website

[hushed turret]

it's not reputed

[patent sphinx]

Is there a better place to read stuff like this

[hushed turret]

wikipedia is definitively better

https://mathshistory.st-andrews.ac.uk/Biographies/Hilbert/
this is also a good source i think

[leaden torrent]

or an encyclopedia like britannica

[neat lintel]

lol

[wooden turret]

Yo!

Infinite hotel

[leaden torrent]

imagine being the most influential mathematician of the 20th century and your legacy is some thought experiment you made up once to demonstrate a triviality

[wooden turret]

still a very fun thought experiment

if you really think about it

[vivid halo]

it's really not that deep

nor is it physically meaningful

[wooden turret]

still fun

[open latch]

j

j

j

j

[errant ridge]

nah his lecagy is HUGE

[wooden turret]

yea i can agree on that

[errant ridge]

hilbert space

[wooden turret]

hilbert hotel

the infinite hotel

[errant ridge]

hilbert space filling curve

[harsh fiber]

😂

oh god

I think i found my nightmare for the month

[fierce eagle]

[mortal igloo]

Finally I get to and the same message

[dense belfry]

Hilbert's legacy is him btfo'ing Brouwer and setting math back 100 years

[errant ridge]

emmy noether wanted to become a sort of a professor at a university

and they said "she's a woman we can't do that"

hilbert said

"I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bathhouse."

chadbert

[torn willow]

Also wasn't that nazi era

[errant ridge]

it was around 1910 or something

[torn willow]

Ok pre Nazis

[plush kestrel]

https://media.discordapp.net/attachments/960974834010042418/971108547293245460/09E98F95-34A4-475E-BA45-449A7F464FE0.gif

[iron mulch]

Hello ! I just arrived on the server and now I would like to understand how to learn math stuff around here and actually how does the server work ! Are there lessons or things like that ?
Thank you very much for your time ^^

[charred mortar]

Most of it is for homework help

You can discuss math stuff here too

Just not homework-specific stuff

[iron mulch]

Okay ! Thanks

[neat lintel]

We mostly just discuss math, no lessons or anything like that. Maybe a presentation sometimes

and of course there's the "homework help" part of the server

where people usually post really basic things they need help with for school

[iron mulch]

I see ! Seems pretty cool ^^

[neat lintel]

there's also people just talking to each other here
mostly young people, so nothing serious (uninteresting from my perspective)

[iron mulch]

Yes that's what I thought, I fastly understood that the really interesting stuff was in the "Advanced saloons"
Sadly I am currently far from the level needed to access to this places

[neat lintel]

there's also people that can point you in directions if you want to learn math on your own

or, continue learning it

[iron mulch]

That seems very interesting too ! I am in fond of analysis and topology, but it is so....humongous ! Hard to know where you could start by your own

[neat lintel]

are you learning something already

I mean, do you have like a book you read or something

[iron mulch]

I found some lessons on the internet
I read a few papers on the topic and thought that I understood pretty good ! However when the time for exercises came...Madre mia

And it was only basic stuff (topological spaces, compacts...)

[neat lintel]

I wouldn't advise learning from videos, maybe complementing with them

It's a good way to learn a lot of things fast (assuming that the one lecturing is good), but to learn something efficiently, you want to look at the definition in a book and stare at it, convince yourself that you understand it completely

words don't convey as much meaning as writing does

besides people in this type of videos often may simplify things, which is good on short term, but bad in general

[iron mulch]

I see ! Thank you for the advices ! Do you think that prerequisites are needed to learn topology ?

[neat lintel]

Basic set notation, some basic analysis for understanding what continuous function is etc., you don't need to know more advanced set theory but it's good to know what cardinals and ordinals is, since a lot illustrative examples of general topological spaces use ordinals (and why cardinals are important should be obvious)

[iron mulch]

Okay I see !

I was mostly surprised by the beauty of the proofs they use, it is so different from other - let's say "more common" - theories

[neat lintel]

A lot of definitions in topology are also motivated by example of metric spaces, but any good general topology book should include those (although maybe introducing topological spaces much before metric spaces)

but don't get the wrong idea, albeit metric spaces are intuitive, they can get pretty wild

[iron mulch]

Yes you are right ! I have seen none of them without an introduction to metric spaces

[iron mulch]

Really ? I am quite disappointed, that's exactly the idea i had

I basically saw metric spaces like spaces where you get sufficient axioms to measure stuff

[neat lintel]

well, yes

but there's nothing that bounds the "size" of a metric space

so there can be some weird metric spaces out there

[iron mulch]

What are you implying sir ? Are there things that usually "bound the size" of other spaces ?

[neat lintel]

well yes, there is whole field of set theoretical topology that deals with set theoretical notions of topological spaces

one of those are cardinal functions

to each topological space we can assign multiple quantities (that is cardinals) which measure its size in different ways

one of them is literally the cardinality of the underlying space

that's not a very good way to measure size of a topological space though (at least in my opinion)

there's a cardinal function called weight, which tells you from how many open sets can you get all other open sets by taking (arbitrary) unions of those

that is the least size of a basis of a space

for a metric space to have good properties you ideally want its weight to be at most countable

this is not really a problem, most metric spaces considered pretty much anywhere have countable weight

such spaces are called second countable

[iron mulch]

Well, all of this is highly interesting ! Thank you a lot you are motivating me to continue my studies !

[neat lintel]

this gives you the family of separable metric spaces, which are one of the most nicest classes of spaces you can work with

separable means something else than second countable, but for metric spaces that's one and the same thing

[iron mulch]

Separable...I guess I already saw this somewhere...Maybe in the definition ot compact spaces ? They respect Borel-Lebesgue condition and are separable if I remember well

[deep mango]

Compact metric spaces are separable

[wooden turret]

you still need help?

and maybe go to a help channel

[neat lintel]

yeah. This might be probably the biggest reason for why to consider separable metric spaces. If a space isn't separable metric, then it can't possibly be contained in any compact metric space

but any separable metric space can be contained in a compact metric space (it can be compactified - made compact in a most efficient way possible)

in fact, any separable metric space can be embedded into the Hilbert cube, a countable product of intervals [0, 1]

[iron mulch]

Compactify...what for ? Maybe for some properties of the compacts that would make us happier to work with them rather than with other spaces ?

[deep mango]

Absolutely

Compact spaces have lots of great properties.

[iron mulch]

Any ? From any dimension ?

[deep mango]

One big one is that any continuous function from a compact space to R attains its maximum and its minimum. This is super useful. Another big one is that continuous functions on compact spaces are uniformly continuous.

[neat lintel]

this is part of the so called Urysohn metrization theorem, which tells you conditions for a topological space to be separable metric space

[iron mulch]

Ow yes, seems really powerful

[neat lintel]

well there's no dimension in play here

[deep mango]

Somehow separable spaces can't be too too big. This doesnt exactly make sense, but separability presents you from being "uncountably dimensional"

This isnt a real thing

Like blitz said there's no dimension here

[iron mulch]

i will take a look !

[neat lintel]

well there's a good notion of dimension for separable metric spaces, but it doesn't matter here

[deep mango]

But the examples of nonseparability feel uncountably dimensional in a way.

[iron mulch]

A lot to consider !

[deep mango]

(and sometimes actually are, if you're in the field of functional analysis).

[neat lintel]

that's also part of the reason why to consider them over metric spaces

[iron mulch]

So when we talk about compact spaces it is a kind of non sense to talk about dimension ?

[neat lintel]

it makes sense to talk about dimension of a compact metric space

it makes sense to talk about dimension of a many spaces, just not all of them need to agree, and they don't all enjoy comfortable properties

we have three usual concepts of dimension, and they all agree for separable metric spaces

we deal with dimension in so called dimension theory, which is a subfield of topology

[iron mulch]

I am stun, so much to learn !

Mathematics are truly the school of humility

[stark charm]

I am humiliated

[iron mulch]

That's a nice one

[fair estuary]

I have a question about infinite sums

If I have a convergent series that I write as an infinite sum, is every number in that sum considered to be part of $\mathbf{R}$?

[fathom swallow]

TheDirtyHandsome

[fair estuary]

For example $\sum_{1}^{\infty}\dfrac{1}{(n)^2}$

[fathom swallow]

TheDirtyHandsome

[fair estuary]

Is every 1/n^2 term in the infinite series a real number?

[neat lintel]

wdym

1/n^2 is a rational number for any n

[deep mango]

These are all real numbers but you can also have infinite series of other things.

Like complex numbers or functions.

[fair estuary]

At some point you get a number for 1/n^2 = 0

Is that number part of the real numbers?

[cyan goblet]

well

it approaches 0

[deep mango]

In the most general you can have infinite series where the terms are elements from a topological abelian group. Usually you just look at infinite series in normed vector spaces.

[cyan goblet]

it does not hit 0

also 0 is in R yes

[deep mango]

That never happens

[cyan goblet]

lim 1/n^2 as n to infty = 0 sure

but you will never get a 1/n^2 = 0

[fair estuary]

Then how does the infinite sum end?

[deep mango]

It doesn't

It's infinite

Infinitely long

[fair estuary]

But then how do you get the convergent sum?

[deep mango]

Not infinite in value

[fair estuary]

That's the epsilon value or something

The infinitesimal thing

[deep mango]

You take a limit of the sequence of partial sums. Each partial sum is just the finite sum up to some endpoint.

Then it's the limit of a sequence.

That we know how to do, using the epsilon-N definition of sequence limits.

[fair estuary]

So is epsilon a real number?

[deep mango]

There is no epsilon, the sum doesn't end

I mean

idk

some people do "infinitessimal calculus" with this epsilon

But that isn't the endpoint of this sum

Every term in this sum comes from a particular integer n

[cyan goblet]

convergence of sum doesn't mean that the sum will reach that value

it just means that as we sum more and more values, we approach that convergent sum

and the sum cannot go above that convergent value

iirc at least

[fair estuary]

Follow up question. If you have an infinite sum in real numbers like the one I posted. Is the sum of the infinite series the same if you calculate that infinite sum inside of the surreal numbers?

There should be more numbers in that same sequence of the infinite series in surreal numbers, but does it change the sum at all?

[hushed turret]

well, it could if your sum has negative terms

[cyan goblet]

true

[stark charm]

you can just say if you go on for infinity the sum reaches that value

[vivid halo]

literally nobody uses the surreal numbers

[stark charm]

going on for infinity meaning you can take larger and larger numbers and they approach the value

[fair estuary]

Is infinity a real number?

[stark charm]

no

[tender tulip]

“Epsilon” is a variable that you can use to represent infinitesimality but isn’t explicitly infinitely small itself

[fair estuary]

Then how you continue it till infinity?

[stark charm]

going on for infinity meaning you can take larger and larger numbers and they approach the value

[tender tulip]

Infinity by most definitions is a notion, like the concept of inertia, bruhaps

[hushed turret]

take an intro analysis course, i think I you're missing some fundamental understanding of limits and series

[stark charm]

ill give you an example

imagine an infinite sequence 1/n

[fair estuary]

Do you know someone here who can use them? I'm interested in finding the answer to that question.

[stark charm]

so it looks like 1,1/2,1/3,…

[vivid halo]

no, the point is that nobody actually uses surreal numbers to answer questions like this. They aren't a useful construction

so it's just not a very useful question to ask

[fair estuary]

If people never use them because they don't think it's useful, then it will prevent something useful from coming out of them.

[stark charm]

sure

whatever helps you sleep at night

[vivid halo]

no

[fair estuary]

It's a self fulfilling prophecy

[vivid halo]

they've been studied, they come up in combinatorial game theory but that's about it. They don't play any kind of role in analysis.

[stark charm]

bang your head against a table 100 times. if you dont do it the 101th time you wont see god

[tender tulip]

Infinity essentially is the notion that “there is always another one”. For a natural number, there’s always a greater natural number.

[odd narwhal]

Popmath content mills should stop introducing genpop to funny sounding number systems

[stark charm]

genpop?

general population?

[odd narwhal]

General population

Yes

[stark charm]

i disagree

[tender tulip]

p-adics

[stark charm]

you need cringe for popularity sake

it would be a shame if math fell into obscurity

[fair estuary]

You guys don't have any curiosity to know if an infinite sum in surreal numbers has the same or a different value to the same sum in real numbers?

[stark charm]

i dont know if i would discourage the questions

[fair estuary]

:(

[odd narwhal]

Math isn't going to fall into obscurity because susan from the grocery store didn't go on discord.gg/math and ask what is the ultrapower construction of the hyperreals

[stark charm]

thats precisely my point

[vivid halo]

no, because I already know that the surreals aren't a very good construction to consider

[odd narwhal]

If that's your point you've made it badly

Because you communicated exactly the opposite

[stark charm]

what should pop math be communicating then?

[vivid halo]

quanta does a fairly good job with pop math articles

[stark charm]

just remove “funny sounding” names?

[vivid halo]

for the most part

[mortal igloo]

What should be the goal of pop math anyway?

[tender tulip]

Look up p-adics

[stark charm]

its just advertising and outreach

[tender tulip]

Or just, niche entertainment I guess

[stark charm]

entertainment for some people?

but i feel like the majority is outreach

[tender tulip]

Yeah,

To get to the “entertaining” part of math often you have to go through a fuckton of boring shit that people aren’t willing to put up with

[fair estuary]

That's a different number system though

[tender tulip]

Look up metric spaces

[neat lintel]

I will get to take linear algebra with Thomas Hales in the fall 😧😧😧😧😧

[odd narwhal]

Who

[neat lintel]

He’s famous for the honeycomb proof

The only downside is it’s the more difficult linear of the bunch and will prolly have 30+ hours of homework each week

[fresh oriole]

Sounds like an upside to me

[prisma swallow]

What is the entertaining part of math?

[surreal sapphire]

when you solve the problem

[fair estuary]

Wasn't he the person who did the sphere packing proof?

[neat lintel]

Yes he did

But I’m in quite a dilemma rn honestly cause I feel like if I do take the difficult linear course my workload would implode

[candid oak]

hey everyone, it's been a while

would you mind telling me where can I find a tutorial of how to create a model predicting the existence of potato late blight from scratch?

[keen tulip]

math is good

like good soup

[candid oak]

yep it is.Do you have, by any chance, some experience with neural networks?

[untold sapphire]

tau

[odd narwhal]

Tau moment

[sleek wing]

popmaths content mills should stop

[keen tulip]

I don't even know what that is

[neat lintel]

Thomas Hales

HGoly crap

[neat lintel]

Well it would suck if good soup isn’t good.

[keen tulip]

it's good, by definition

[neat frost]

Is 3b1b popmath content mill? Because if so I have to disagree. I need Grant. He is my light

[sleek wing]

yes but 3b1b is the best out of them

[neat frost]

[cinder zephyr]

I wouldn't call him a mill

He doesn't post too much content and what he does post is extremely high quality

[neat frost]

He mills my love and affection

[tender tulip]

Videos barely showing modular forms using those contour maps that use pretty colors

I mean, all I know about those functions is that they sorta “encode” the Z^2, Z[i] (additive group) isomorphism and SL(2,Z)-action-automorphism shit into C using lattices

A scaled modular form can be phrased as
f(x,y) [x, y in C such that x/y is not real]
f(ax,ay) * a^n = f(x,y)

and the action of SL(2,Z) on the transformed Z[i] through conjugation of the isomorphism

not Z[i]

Is there a symbol used for lattices in C?

Eh, any Lattice in C^2 is isomorphic to Z^2

I mean technically every Lattice in C is isomorphic to other C-lattices or R^2-lattices because C and R^2 are themselves isomorphic under their additive groups

Pardon my dumbass description, didn’t consider that

[vivid halo]

depends on what you mean by isomorphism here

they're all isomorphic to Z^2 as Abelian groups sure

but there's another sense in which two (framed) lattices in C are isomorphic iff they are in the same SL_2(Z) orbit

[tender tulip]

good point

[mortal igloo]

@tender tulip What video?

[tender tulip]

I’d have to find it

[mortal igloo]

Also, I can't parse "and the action of SL(2,Z) on the transformed Z[i] through conjugation of the isomorphism"

[errant ridge]

nope they get kids interested in math

[charred mortar]

Low-quality ones should stop, but that’s a given for any subject

High-quality ones can be useful

[arctic grove]

true

well

nothing should happen to 3b1b

if anything does, i will not be quiet

lol

[neat frost]

Yesh…. ma bb gurl

[arctic grove]

[errant ridge]

[arctic grove]

[errant ridge]

[arctic grove]

[errant ridge]

lol i've stopped learning QM

[arctic grove]

[errant ridge]

im gonna learn all that stuff once every exam is over

[arctic grove]

relatable pain

but the wait makes it even more exciting to learn

[errant ridge]

lol i guess

back to the sigma grind

[arctic grove]

im grinding formulae today

of physics and chem

[errant ridge]

Lol nice

[arctic grove]

its annoying

[errant ridge]

veryy

normally we can derive formulas when we need

but jee sucks ass

[arctic grove]

kvpy is in 5 days

im losing my shit

[errant ridge]

lol dont worry you have the cmi exam too

anyway im gonna go do that now lol see ya

[arctic grove]

that only adds to my worry

😭

[errant ridge]

[arctic grove]

[ancient flame]

I graduate today!!!!!

👨‍🎓

[deep mango]

Yay!

[neat frost]

Happy day!

Be sure to flip off your teachers!

[ancient flame]

but I liked most of my teachers tbh

and also

I don't even get my diploma until tmr

[neat frost]

O

Shame

[ancient flame]

since I have an even tmr

[neat frost]

Teacher’s pet.

[ancient flame]

so if I do smth stupid during the ceremony they could still revoke my diploma

[ancient flame]

during middle school I was but not during high school

I mostly had decent teachers

there are two that I fucking hate though

plus another two more but they aren't at the school anymore

[arctic grove]

go to their homes

and then flip them off

and flip off the ones in school as well

ez claps

[ancient flame]

oh

[frail sail]

I have achieved a wpm = 150

only thats in raw wpm

[neat lintel]

me too

yet the passage is too short

only contains 2 lines

[delicate knoll]

why?

[sick burrow]

is there a good way to figure out in advance what good restaurants are near an REU you're going to be doing

like a way to get the opinion of the student body

maybe I'm overthinking things and I should just search on Google maps...

[neat lintel]

[sick burrow]

if I'm going to be living on a school's campus for the summer I want to know how to orient myself on said campus and the area around it

[mortal igloo]

You could visit each one once during the first week or something

[sick burrow]

logically the people who would know this best are the students

nonono I've committed to a program

I just want to start researching food in advance

mostly because I'm bored

[mortal igloo]

I did mean each visiting each restaurant in the area once

[sick burrow]

the main think I'm after is how to figure all this out from my ass at home

[mortal igloo]

I don't have any other specialized advice for more focused ways to choose restuarants

[sick burrow]

since the program hasn't started yet

see what I really want is like a prospective student discord

(I am aware this entire endeavor is somewhere from silly to very silly)

[fast ivy]

[sick burrow]

ok so google maps turned out to be sufficient

and this place looks lit af

lots of good restaurants in the area and we have to buy our own dining plans so eating out won't even end up being much more expensive

[mortal igloo]

Do you get funded?

[sick burrow]

yeah the program is funded, the funding just doesn't include a dining plan

like they let you take money out of the stipend to pay for the dining plan, but how many meals you get seems largely up to you

like the base plan they recommend is nowhere near enough to cover an entire summer's worth of meals.

[mortal igloo]

Hmmm

[sick burrow]

you can buy additional swipes, but the math works out such that it's not that much more expensive to just eat out

[river spire]

I'm going to see Charli XCX tomorrow with Yeule opening

[delicate knoll]

@sick burrow do you like geometry?

[sick burrow]

what would you guess

[wild lantern]

tsundere geometry lover

[cyan goblet]

what’s the motivation for reading multiple textbooks over the same topic?

other than comparing how two authors teach something

[delicate knoll]

dunno, i dont know you and your personality

[delicate knoll]

to master the topic, maybe?

[neat lintel]

Makes you understand the whole topic in greater detail imo

It’s good to have different explanations of the same thing

[vivid halo]

usually when you get to more advanced topics, different textbooks will cover different subsets of the topic, so you have to go to read multiple books to get multiple perspectives on the topic

[cyan goblet]

ah i see

[velvet dagger]

@vivid halo thankfully no need for that in automorphic forms ofc

[vivid halo]

I like reading multiple books on automorphic forms because 3 books will use 5 different sets of notation

[bronze pelican]

Each book only takes 5 years to read

[mortal igloo]

Story of my third to fifth years of grad school

[sterile hare]

how long do you think you can go without doing math before u forget everything?

really would like to take a 4month break this summer if possible

[charred mortar]

I think that seems fine

Worse-case scenario you’d need to revise when you get back, and that shouldn’t take too long for a second pass through the material

[sterile hare]

relearning tons of theory is like the worst case scenario, would like to avoid that if possible. but also need time to relax been grind for like 9 months straight lol

[torn willow]

5 years ig

Atleast 2 years

[waxen lily]

5 seconds

[jovial yew]

Anybody can help with programming homework?

[sterile hare]

create a help channel

[sterile hare]

lmao 5 years

[waxen lily]

did you know 2 out of 3 americans choose not to use a help channel even after being directed to #❓how-to-get-help ?

[waxen lily]

i dont see why it would

[dusty idol]

Wait wrong server

[naive bolt]

What algorithm do CNC machines use to plan the most efficient path? Travelling Salesman on a discretized grid would take ages so its making me curious

[leaden torrent]

might be easier to find answers in an engineering or robotics server

i dont think it'd necessarily take ages though, you dont need an optimal solution

"close" solutions to travelling salesman are very fast

[naive bolt]

Yeah there's probably a lot more factors and heuristics that go into it besides minimum travel distance

still though at the tolerances that mills run at I feel like there'd be tens of thousands of vertices to hit but again theres probably a lot more that goes into it

[steel bronze]

@strong sphinx Look at what my friend had to say about the book you recommended lmao

[arctic grove]

here here

[deep mango]

Today is my last day

[arctic grove]

what

[deep mango]

I am giving a talk at 11

It is 6

Then I am done

With the semester

[arctic grove]

with life..?

oh semester

lmao

[deep mango]

Wtf...

[arctic grove]

complete ur messages man

u scared me

[deep mango]

Well I'm glad you care

Anyway im like

So mad

[arctic grove]

[deep mango]

Cause I did it again

[arctic grove]

why is that

[deep mango]

Went to sleep at 12

,ti

[fathom swallow]

The current time for ranyakumoschalkboard is 06:07 AM (EDT) on Tue, 17/05/2022.

[arctic grove]

[deep mango]

And I really tried to go back to sleep this morning

[arctic grove]

the more u try

the less sleepy u feel

[deep mango]

My head got super loud with like

Very very quick frantic thoughts

Weird

[arctic grove]

indeed

[deep mango]

I feel like that rarely happens except in the morning when I try to go back to sleep

[arctic grove]

[deep mango]

Anyway i will just get a cofe before my talk and let that do the job today

Last night once i'd given it fully once, the second practice run I was like

So active and emotive

I hope I can bring that energy again

I really like giving talks

[arctic grove]

you will, dw 😌

do u not feel nervous about them?

[deep mango]

Its so weird

I used to get so so so nervous in HS

Then one time it just flipped

And I went to loving them

[arctic grove]

flipped?

hmm

i think i would love to give talks

but im just too nervous about everything

[deep mango]

And I dont really get nervous anymore

Well

As long as ive practiced

[arctic grove]

"will it go well? will i do soemthing stupid?"

stuff like that

[deep mango]

If I hadnt practiced and just had my slides / notes it would be awful

[arctic grove]

whom do u practice with?

[deep mango]

But once ive practiced twice, there's basically no thinking and I'm just going through the motions

Just to myself with a timer

Or like

Sometimes people practice here in vc

[arctic grove]

Ooo

[deep mango]

But i dont really care about that. For me it's just about feeling out different ways to describe things

[arctic grove]

hmmm i see

(ping me the next time you give a practice talk in vc here)

[deep mango]

Sure

Oh

I'm gonna let you in obsidian

There you go

That would usually happen in adv math vc or obsidian

[arctic grove]

[deep mango]

OH

LOOOL

[arctic grove]

?

what lol

[deep mango]

Darq doesnt have acces to this channe

[arctic grove]

what?

why?

[strong sphinx]

I'm the one man army shilling this book haha. xD

[odd narwhal]

which book

[brittle socket]

LMAO what did i just see

[neat lintel]

Hey

I just read the def. of limit points but its not very clear to me. Is it correct to say that (informally) if you cut a closed interval out of R, then the set of all elements of this interval does not contain isolated points?

By cut out an interval out of R i mean just take every real number within a closed interval

Like leave no real number out

Then everythings a limit point right?

[leaden torrent]

yes

you dont need to use the wording "cut out a closed interval" though

just say "every member of a closed interval in ℝ is a limit point of that interval"

[neat lintel]

Ohh ok

Ohh yeah

Interval is not set

Ofc

[leaden torrent]

an interval is a set

[neat lintel]

Yeah yeah

Yeahh

Ah yeah

[leaden torrent]

there is the following fact:

a set S is closed iff it contains all its limit points

[neat lintel]

Noice

I’ll read up on the basic topology of R section

[leaden torrent]

a slight generalization: the closure of a set is the disjoint union of its limit points and isolated points.

[neat lintel]

I thought lemme skip it but nah ig i’ll tackle it

[olive kayak]

are there any resources for iterated/multiple sigmas?

[neat lintel]

Anyway thank u namington for respondingg