serious-discussion

[smoky plover]

I only took mathematics for 2 years

it was more or less "up until" polynomials

not a word of 3d geometry

[solid snow]

Khan academy is a great resource for catching up on high school math

[smoky plover]

I studied a bit of algebra over there, but I liked the idea of studying a book better

because it's easier to go back in a book and confirm my knowledge, than to go back through pages of unsorted notes

but yeah, this topic of Isometries just has me going mad!

should I maybe push on and not look back that much

and turn back in a future time, when I maybe need to solve other exercises?

or is it really so required to study other topics of geometry?

[sand moth]

What are theorems 1 and 2?

[smoky plover]

hmm, I cant send images here

[smoky plover]

Theorem 1. Let F be an isometry. The image of a line segment under F
is a line segment. In fact, the image of the line segment PQ under F is the
line segment between F(P) and F(Q).

Theorem 2. Let F be an isometry. Let P , Q be two distinct points in try
plane. Assume that they are fixed points, in other words

F(P) = P and  F(Q) = Q.

Then every point on the line through P 9 Q is a fixed point of F.

for example, I couldn't prove these myself

but looking at the proofs, they clicked

[sand moth]

How much experience do you have with proving things

[smoky plover]

160 pages of Serge Lang's Basic Mathematics

so 3-4 months at most

there were almost no proofs in my mathematics courses in high school

Turkish education emphasises the "getting results" part more than "knowing how you got those results" part

[neat lintel]

Anyone got Discrete and Combinatorial Mathematics", by Ralph P. Grimaldi

[ocean harbor]

#book-recommendations

[lavish kayak]

you will always forget things unfortunately so my take is to try to develop a healthy approach to it

but im just a first year really, the grads here probably really know how to deal with this issue.

[smoky plover]

hmm, I understand

this is just a side-hobby kind of thing for me, so I don't want to be allocating too much time

as a side question would I need to study any chemistry alongside physics in the future

[neat lintel]

my pleasure to get to know you mr beethoven

lol

[mental stratus]

transfinite induction

[tiny saddle]

Idek how that works but hey its nice

[jagged forge]

<@&268886789983436800>

don’t ping everyone

also i don’t want to see that shit, but also just don’t ping everyone

[storm sage]

yeah don't ping everyone

it's also offtopic for this channel, maybe try #chill

it's also pretty gross, so just don't post stuff like this here

nvm just banned them

[jagged forge]

yeah no way that wasn’t a troll lol

[storm sage]

they posted a bunch of nsfw stuff in #chill

so uh

yeah

[jagged forge]

oh…

[rotund steppe]

anytime someone uses :kurisugoodjob: I think rokettojanpu is back

good old days

[jagged forge]

sounds like rokettojanpu was based for using :kurisugoodjob:

[fair mural]

best mod

[zealous garden]

wait, RJ is gone?

[rotund steppe]

Not seen for a good 2 months

[neat lintel]

what is advanced role

[zealous garden]

Deeply saddening

[raven plaza]

U learning uni math

Math major math

[fierce abyss]

@tardy berry
Do you know Jensen’s inequality, and AM-GM?
Anyway you use AM-GM (reciprocal version) to show b/a+c/b+a/c<=3, then consider function f(x)=1/(1+2x) to apply Jensen’s inequality

[neat lintel]

what is Jensen's inequality

[fierce abyss]

f”(x)>=0 (<=0), f(Σ a_i x_i) <=(>=) Σ a_i f( x_i ) for non-negative a_i satisfying Σ a_i =1

[neat lintel]

nah i cant comprehend this

it aint like am-gm

[fierce abyss]

You can search it. I just commonly use it to prove inequalities similar to his question, 9 out of 10 times I use Jensen

[mental stratus]

[tiny saddle]

[mental stratus]

B is basis for vector space R over Q

[tardy berry]

got it, thank you so much!

[fierce abyss]

Np

[sudden spade]

hi

[long matrix]

hiss

[hallow thistle]

bzzzzzzzzzzzzzz

[neat lintel]

How can I stop being afraid of hard maths that I cant solve

[long matrix]

let fear become strength as you face it head on

[neat lintel]

🤑

[ripe bone]

Hello

Pls help me

Tmrw I have to give speech on any maths topic not from book in front of class . I am looking for good topic I am in class 9

[quasi jetty]

Please read #❓how-to-get-help

[vale trench]

nvm

[jade crane]

probability stuff

[slow rose]

High school, undergraduate or graduate? I think the topics may differ A LOT.

[glossy crescent]

Hello

[tight comet]

[jade crane]

i like to share the pain

[native ibex]

how to find height using only the angles of two positions and the distance between the two positions

[pallid shell]

pythagoras' theorem

and trig ratios

[neat lintel]

https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/double-integrals-a/v/polar-coordinates-1

[robust elbow]

trigs

sine law or cosine law

you decide

[ocean harbor]

first assignment for java...

the struggle became real

[solar hawk]

i like java

whats the assignment

[ocean harbor]

it won't me upload an image here still lol

[ocean harbor]

it's about basic java

[solar hawk]

dm?

im curious

[ocean harbor]

okay sure

[neat lintel]

if its big #/lil # its +infinity right? and if its lil #/ big # then limit is 0?

for limits

[tame egret]

?

[neat lintel]

1/infinity is 0 and infininty/1 is inifinity

the limits of them

correct?

what they approach

[tame egret]

lim (1/x)
x->∞

is that it

[neat lintel]

yes

[neat lintel]

HUH

[ocean harbor]

what

fuck java

[neat lintel]

java easy

[ocean harbor]

hard*

[bronze jetty]

sup guys ?

[sonic field]

sup psi

[bronze jetty]

not bad Jay

J of z or what ?

(:

[neat lintel]

Combinatorics.

Nothing beats it's elegance

[regal barn]

im just coding a pseudo class schedule maker lol

[mental stratus]

yuuhuu

[deep mango]

0d would correspond to individual points. there's no mathematical definition of negative dimensions.

you might be interested in looking into "fractional dimensions" though, which are used for fractals

https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

[deep mango]

yeah in math "dimension" loosely means "the number of variables you need to describe stuff" so it's pretty hard to make sense of it outside of whole numbers

[scarlet merlin]

is anyone good at probability? i need help in #probability-statistics

[neat lintel]

hm

[storm sage]

!noadvert

[quasi jetty]

Please do not advertise your help channel or thread in other parts of the server. There are many people who need help, and no one person can be prioritized over other people, so please patiently wait. Anyone who chooses to help you is a volunteer who is doing so out of their own kindness.

[neat lintel]

Is anyone good at life? I want to take yours

[sick shuttle]

sounds really cool

[surreal sapphire]

i think there is some insane framework (stacks?) where you can make sense of negative dimension, though thats really abusing the word "dimension"

probably not in the spirit of the question, but 0d is totally possible the same way that 1, 2, ... d is possible

[azure matrix]

Hi there. I'm struggling with the concept of variable, substitution, zero and other non-natural numbers( Can I ask here? Or should I go to math-discussion or prealg-and-algebra?

[meager sonnet]

spectra and classifying stacks both have some concept of negative dimension

classifying stack for a group scheme has a dimension that's the negative of the group scheme's dimension

[solar hawk]

Hi

[neat lintel]

Who understands this?

[solar hawk]

Sequences and series?

[neat lintel]

i'm the best at this

[fringe summit]

Why

[quick beacon]

@steel crater if you're still around: #help-11 message

you can put the equals sign before a minus sign if you consider the minus sign to be representing the negation operation

(i.e. -1 + -1 = -2)

similarly, it can go directly before a plus sign.

where 1 = +1

so conceivably your equation could be something like 2 + 4 = -2 + 8

[vivid halo]

there is no mathematical definition of negative dimension
There is, but nobody is ready for this conversation

[meager sonnet]

I already mentioned spectra and stacks smh!!!

[vivid halo]

Sorry I can’t read

[meager sonnet]

we're so alike

[smoky umbra]

P (P (κ^ℵκ^ωκ) = 2) = 2 the power sets on here make no sense to me😵‍💫

How could it equal 2 using aleph numbers

[jagged forge]

makes no sense to me either because I can’t read that

how can you take the power set of x = 2

P(x = 2)

[smoky umbra]

I'm not a mathematician🗣️

I literally know almost nothing

But I learned to figure out some other atuff

[jagged forge]

where did you see that equation

[smoky umbra]

Somebody posted it

I don't understand it, so I've been trying to figure it out

[jagged forge]

can you show me where they posted it

[smoky umbra]

It was kinda by itself, not on a meme server or anything

No context to it, it was just posted

[jagged forge]

i just wanted to see if maybe the original post was different

[smoky umbra]

Nah I copied it one to one

[fringe summit]

No contact you claim but still where

[regal barn]

Hi

I just got out of school

[night canyon]

wassup

[solar hawk]

Nice

[night canyon]

its 12:30 am and im here doing math again

i should really study chemistry instead

[regal barn]

mb I think I won’t still be able to help you with the algebra (I don’t think I understand it)

[night canyon]

its not that this time lol

althought that never got answered

[regal barn]

I finished highschool chemistry

last year

[night canyon]

my chemistry does qualify for a bit more than AP chem but im not sure how much more

[regal barn]

It’s probably different from the US

[night canyon]

yeah A level chem

but i think

what i have rn should be taught in the US as far as im sure ill send you what i have but you tell me if you know what it is

[solar hawk]

What algebra

[night canyon]

an algebra question i asked before that never got answered

[solar hawk]

What was it?

[night canyon]

something along the lines of, when im taking inequalities of curves with asymptotes, how do i know multiplying to the other side isnt negative therefore flips the sign

for linear numerators and denominators i can square both sides but

for quadratic i cant really

since i dont know trinomial expansion

[solar hawk]

O

Can’t you just treat the first two terms as one ?

I mean Iv never tried it

But (x + y + z)^n = ((x + y) + z)^n

[night canyon]

well it looks like theres a different formula but its not expected of us since its not taught

another question where, when you're finding the range of a curve with no vertical asymptotes, one of the boundaries you can find with |x|->infinity, and therefore when you use the determinant method, you can find out whether or not to use > or >=

but

the other boundary

theres nothing indicating whether it should be > or >=

how do i figure that out/ test that boundary

also the question im asking now is a vector question but

nno answers

its about to be half an hour

anyway none of those got answered i dont expect this to be answered either

kind of sad

[solar hawk]

o_o

[night canyon]

so yeah i dunno, this is literally the maths server where else am i supposed to ask

self studying further maths, my teacher cant help with this,

[solar hawk]

me too

idk

i cant focus hard enough to read it all

[solar hawk]

wdym multiplying to the other side

multiplying by what

[night canyon]

like a curve without asymtotes but a fixed range is a fraction

so if like (x+2)/(x-1) = y where y>3

then you gotta multiply x-1 to the side of 3

but x-1 might be negative unkless i draw the graph

[solar hawk]

oh

ye i see wat ur saying

uh

maybe.. cases?

like in a proof

i guess you would do cases

i would do cases

like

|x|=4

x=4

x=-4

or

lim_{x\to \infty} e^ax

[night canyon]

i mean test cases i can do

but

damn

theres no other wya?

just manually

[bronze jetty]

so I was reading a little about Hilbert axiomatic system and it was complete madness

I guess I'll be shocked when I enter the godall part

@storm sage are u from Iran ?

[storm sage]

No, just sympathetic to the situation

It's absolutely disgusting what's going on >.<

[bronze jetty]

thanks how ever

[storm sage]

are you iranian?

[bronze jetty]

I'm from Iran

[storm sage]

I hope your country finds its way out of this

[bronze jetty]

I hope too

we are experiencing the worst period of history of our country

[crystal coral]

whats happening there

[neat lintel]

The same thing that happens in every country the US invades

[crystal coral]

a power vacuum? wym

[neat lintel]

Death and destruction ( to everything but the energy sector )

[crystal coral]

damn guessing because of sanctions right?

[storm sage]

tbf it's not just the US's fault

although the US and UK screwed Iran over

[crystal coral]

i mean i wouldnt blame them for sanctioning lmao

[storm sage]

the "morality police" beat a woman to death almost a year ago for not wearing her hijab

this sparked mass protests which led to the government brutally repressing every form of dissent

https://www.reuters.com/world/middle-east/what-has-changed-iran-one-year-since-mahsa-amini-protests-erupted-2023-09-11/

[neat lintel]

The US overthrew a democratically elected country and let islamic fundamentalist take over

[storm sage]

no, the US and UK overthrew the leader of Iran and installed a monarch there to protect their oil interests https://en.wikipedia.org/wiki/1953_Iranian_coup_d'état

[crystal coral]

yeah i know about this

[storm sage]

yeah I mean the US clearly is not in the right here, I'm just saying it's too reductive to say the current situation is just because of the US

[crystal coral]

i know the history

i just havent been keeping up to date

[crystal coral]

which country are u talking about

[storm sage]

iran

[neat lintel]

Too many

The US has done the same thing to multiple countries

[storm sage]

yeah the US also screwed up the entirety of central america and latin america

as well as southeast asia

[crystal coral]

the us has taken a position of liberal hegemeny where they feel justified to topple any regime that goes against their ideology

[storm sage]

usually to "fend off communism" or something similar, even if the leader was democratically elected

[crystal coral]

which u can argue whether or not thats justified

the war in iraq was def a huge mistake

or mishandled i guess

saddams regime wasnt exactly democratic

[storm sage]

I find it hard to justify the propping up of politically repressive dictators all over south america, plus the us-backed genocide in east timor, plus all sorts of other atrocities

also the US's stated reason for invading iraq under george w bush was completely false, which really raises the question of how so many people greenlighted it

[jagged forge]

my dad was an intelligence officer in the army, and he said bush was told that invading iraq was a bad idea and would destabilize the region

kinda sounds like it was not a good idea no matter how you slice it

(moreover that they should have known that beforehand)

[storm sage]

but it was useful for uh... flips notes... continuing george hw bush's legacy?

[gritty gate]

The bigger clowns are those that laughed

[solid snow]

Bro his conscience lmaooo

[neat lintel]

I hate jobs

[jagged forge]

i prefer them to school

[neat lintel]

$0 = \emptyset$

[fathom swallow]

Replaced by new brandon H

[neat lintel]

$1 = {\emptyset}$

[fathom swallow]

Replaced by new brandon H

[neat lintel]

${\emptyset} \cup \emptyset = {\emptyset} = 1$

[fathom swallow]

Replaced by new brandon H

[neat lintel]

@neat lintel

[jagged forge]

that would be max(0, 1) but that works out somehow

$n+1=S(n)=n\cup {n}$

[fathom swallow]

suremark

[jagged forge]

oh wait no im dumb

@neat lintel you’re 100% right

i’m a fraud

(what i said is the same thing as what you said)

[storm sage]

please don't troll here

[flint sluice]

does anyone know if there's a difference in grad schools' eyes between taking the math subject gre online vs at a test center? like do they prefer scores from in person tests or it doesn't matter?

[neat lintel]

It probably depends on the university

[flint basin]

I think most schools nowadays (at least from what I've seen) don't even really care about the GREs anymore

[flint sluice]

yea ik that most dont, but some recommend it including some uc's

guess ill ask around more

[vernal vapor]

Hey guys

[thick zealot]

Tips for studying munkres topology?

[mental stratus]

umm idk try not to get too bored lol

munkres can really bore you

[small dust]

i know how to fix that

[mental stratus]

how

[small dust]

no further comment

[mental stratus]

tell me layla

i need to know

[small dust]

you already know

[mental stratus]

do i

[small dust]

yes

[flint basin]

Don't

[echo tundra]

[echo tundra]

What do you recommend

(please don't say nothing 😭)

[flint basin]

https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf
I just find Munkres to be a bit... boring? Idk good alternatives tho (unless you are okay with categories, in which case I recomment "Topology: A Categorical Approach". You don't even need much category theory background, they just use a few terms from it). I don't recomment "Topology through Inquity"

[chilly hull]

i have been told bredon is good

[echo tundra]

Bredon is pretty terse from what I remember

[fast ivy]

Munkres is hella boring

[dense belfry]

I know the authors of topology: a categorical approach

[flint basin]

:o

[fast ivy]

Tbh Lee's "Introduction to Topological Manifolds" might be the best intro to topology

[echo tundra]

How about Viro's topology book?

[fast ivy]

Even it focuses more on those topics relevant to differential topology and algebraic topology

[echo tundra]

I think Yamin recommended it to me

[dense belfry]

Yamin knows viro

[fast ivy]

and doesn't go in much detail about some topics which are useful in analysis

[dense belfry]

That book looks cool, haven't actually used it though. Tbh I really liked munkres

But I also like point set

Or at least used to

I also read it 6 years ago

[echo tundra]

Stockholm syndrome

[dense belfry]

Probably tbh

[flint basin]

point-set is decently fun

[fast ivy]

i mostly learned it through other topics anyway

it's obviously important

but I myself see it mostly as a tool to study more interesting things lmao

[fast ivy]

I found nets and filters to be really cool

thinking about convergence in general

quotient topology is also really cool

[tiny saddle]

[bronze pelican]

I read that

Its an exercise textbook

Bringing back memories

Lol

[echo tundra]

Ik cause you recommended it to me my man

[bronze pelican]

Like 4 years ago mayby?

Holy shit, time passes

I read it in second year of undergrad

Now I am in 3rd year of phd

[mental crane]

hows phd life

is it difficult

[flint basin]

a phd is well known to be the easiest part of your life /s

[echo tundra]

[bronze wedge]

Nah

[flint basin]

L

[bronze wedge]

nets are just shitty sequences

[flint basin]

That's why filters are better

[bronze wedge]

fine, I'll give you that

[neat lintel]

the only topological spaces worth studying are the ones where sequences work

[chilly hull]

hausdorff spaces

[zealous garden]

Hey it's mister system!!

[long matrix]

so 1st countable

?

[fringe summit]

Or quotients of em

[zealous garden]

Oh crap it's VMM!

[zealous garden]

Are you really him

[bronze wedge]

indeed

[bronze wedge]

literally this

[zealous garden]

Based VMM

I'm glad you're back, I missed you

[mint patio]

So like

What are the downfalls of Lagrangian mechanics?

Because in every application I've seen it in, it is superior to Newtonian mechanics

Using only scalars is so freaking sexy

[jagged forge]

it does not work for all systems i think

you can do weird hacks for things like friction

[zealous garden]

That doesn't sound sexy to me

[mint patio]

Bro what the fuck did my professor just do

Can one of you people that know linear algebra explain why/how this is valid

So we have the system Ku = f, K is a 3x3 singular matrix

Due to the boundary conditions, we know that the first component of u is zero, and the latter two components of f are equal to a constant P

So u = [0 u2 u3] and f = [F1 P P]

So the professor's argument was

u1 multiplies the first column of K, but u1 is 0, so we can "ignore" the first column of K (which he denoted by just crossing it out)

[fringe summit]

Ok that’s sensible?

[mint patio]

And then since we don't know what F1 is right now, he blackboxed the first row of K and crossed it out again, denoting the crossed out equation by (1)

So now he has a 2x2 system

that's no longer singular

in the variables u2 u3 with constants P, P

[fringe summit]

F1 = a u2 + b u2 and a 2x2 with the Ps

[mint patio]

Yes but why is it valid to just like

Cross out our columns and write out 3x3 as a 2x2 and solve the 2x2

[zealous garden]

Because u=u1e2+u2e3 is a 2D vector?

[mint patio]

I've never seen that done before

It's 3D

The first coordinate is 0 though

[fringe summit]

Idk if you’ll always get a solution necessarily, but any solution is gonna have to satisfy it

[mint patio]

That doesn't make it 2D does it?

[neat lintel]

i wanna become a sound engineer

[zealous garden]

Which means it's 2D

2 degrees of freedom

That is all

[mint patio]

Then he solved the system to get u2 u3 then plugged those into (1) to solve for F1

[mint patio]

[solar hawk]

hi

[mint patio]

I guess

[zealous garden]

A matrix is a linear map between vectorspaces

[mint patio]

I guess it's just weird becuase I've never seen a system solved this way lol

Then again I also don't think I"ve ever seen a singular system that wasn't just a contrived example

[solid snow]

Describe the xy plane in 3d space with the span of (1,0,0) , (0,1,0)

[granite linden]

can i just start with topology whenever i feel like it or are there higher prerequisits than highschool algebra and calculus

[mint patio]

Ah ic

[zealous garden]

This matrix has as input the vector u

[mint patio]

You want elementary set theory ofc

[zealous garden]

The vector u belongs to a 2D subspace

[mint patio]

And practice with proofs

[solid snow]

Definitely an exposure to proofs

[zealous garden]

So the matrix only maps from this 2D space

[mint patio]

Yeah okay I see it now

[solid snow]

I feel like topology would feel unmotivated without at least a bit of analysis

[mint patio]

I agree

[solid snow]

Or any reason to care really

[mint patio]

Analysis is a good gateway to maths and transitions naturally from calculus too

[granite linden]

what does unmotivated mean in this sense?

[fringe summit]

“Why?”

[solar hawk]

fr

what 3b1b does well

[mint patio]

Well upper level math is really abstract right

And the way a lot of math is introduced is just

Defn -> Theorem -> Defn -> Theorem (sometimes examples)

All in a super abstract space

This is pretty dry and you can easily just get lost in a sea of super general definitions in super abstract spaces

It can be hard to care about them

You just wonder wtf it's all for

[jade crane]

Sometimes the machinery is just a necessary evil

Especially in applied topics (but still advanced)

[mint patio]

Yeah, sometimes there is no motivation besides "it helps us establish a result in the future that is motivated"

But a lot of stuff are just motivated by their own unique applications too

And so when you see reasons and purposes for the things you learn, when you get more concrete scenarios in which these definitions and concepts arise naturally, you see the reason to care

Makes it a lot easier to stck with the subject imo

And it also makes it make more intuitive sense when you're in a familiar setting

Like the real line with standard metric is very familiar to you and when you put all those abstract topological definitions you're gonna learn to R, they're gonna suddenly click a whole lot better and make moer sense when you abstract them to more general spaces

[jade crane]

R is love

[mint patio]

R is life

[granite linden]

fair, thank you for taking the time to explain

[mental stratus]

Theorem -> lemma -> proof of lemma -> (maybe a corollary of the theorem ) -> proof of that theorem -> corollary

thoughts?

[mint patio]

(See Rudin as textbook example)

[jade crane]

Theorem 1 2 3 4 (prove yourselves at home) after this lecture to verify and we use them this lecture

Painful class

And he says to not read the book for guidance since people who read books don’t tend to last long

[mint patio]

what

least based professor on the planet wtf?

[jade crane]

he’s good tho

Abel prize winner just that we (the class) are nowhere as brilliant as him

Lol

[mint patio]

LOL

[jade crane]

He’s usually like I probably lost everyone right? Make sure you understand before next lecture

But he’s always willing to help at office hours so

[fringe summit]

Well there’s also papers and notes and such

But

What did he mean by this

[mental stratus]

who's that

[mint patio]

The Weeknd

Abel

You don't know him?

[mental stratus]

he says not to read the book for guidance since people who read books don’t tend to last long

no the prof

[fringe summit]

Hope this helps 👍

[mental stratus]

abel prize is pretty huge is it not

i might agree with people simply reading books struggling long term

[tame egret]

🤮

[mint patio]

You don't like The Weeknd?

[mental stratus]

like you're spsed to figure stuff out yourself a fair bit so simply looking up the way some stuff youre meant to solve in one text is done in another text can hamper learning

i know the people in abbott rg are using multiple books

[noble osprey]

Hey, Gangster mathematician here

🤙

[mental stratus]

so say abbott may have the decimal expansion of reals as an exercise but they might end up simply reading it from those other books which simply beats the purpose of using a book like abbott

[little vine]

The Understanding Analysis author?

[mental stratus]

yea

[mint patio]

Yasssss

[jade crane]

queen

[chilly hull]

[neat lintel]

For what purpose

[jade crane]

I met 60% goals of my day today but i cba anymore goodbye

[thick zealot]

I would like to learn topology on my own, that's why I was asking for munkres.

[flint basin]

like munkres is fine, it's just not the best (boring, as a few of us called it). Try out some of the other texts people mentioned around there and see how you like them

[thick zealot]

I don't consider myself very good at demonstrations, to be honest...That's why I was asking

[deep mango]

Munkres is basically popsci for nerds

[long matrix]

quack

[deep mango]

I miss when we had funny pasta

When's the most recent pasta

[long matrix]

[jade crane]

I don’t find spaghetti funny at all

[long matrix]

who dis

[haughty apex]

What’s this mean

[thick zealot]

So, which book should I start with?

[willow patio]

is there a name for the branch of mathematics related to what im seeing when I color code a times table by cells divisable by a number?

certain very interesting patterns show up at specific numbers lol

if you take a times table, and color code the cells divisible by any product of twin primes, you see a wave interference pattern

its kinda cool, i just dont know why im seeing it lol

[thick zealot]

Theory of numbers?

[long matrix]

or just

number theory

[willow patio]

maybe theres not even a specific name for this tbh

its probably a subset of number theory

ill do what mathematicians do and explore it and then name it after myself

[zealous garden]

You don't name it after yourself

At most, you leave it unnamed and someone else names it after you

[long matrix]

just use an alt

[zealous garden]

I should get one

[primal swan]

"sussy baka uwu"

[jade crane]

If I ever get something named after me, it’s gonna be the sussy baka conjecture

Or the uwu-owo lemma

[primal swan]

Xd

I havent thought about names if i do get something i get to name

[long matrix]

umu

[primal swan]

But its gonna be wierder than that

[long matrix]

[willow patio]

the Sussy Baka Theorem, ah yes

[long matrix]

,w sussy

[fathom swallow]

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[proud olive]

,w cox zucker machine

[fathom swallow]

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[smoky plover]

So alright, I completed Part II from Serge Lang's Basic Mathematics

and I've got to say, I remember jack shit from all the proofs

should I need all those for the rest of the book, or can I complete the rest and return back to Part II with isometries?

[hidden isle]

,w calculate toe

[fathom swallow]

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[hidden isle]

,w differentiate toe

[fathom swallow]

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[tiny saddle]

,w integrate your mom

[fathom swallow]

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[zealous garden]

,w integrate yotsuba koiwai

[fathom swallow]

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[burnt ledge]

,w yotsuba curve

[fathom swallow]

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[burnt ledge]

😁

[zealous garden]

You haven't seen the good ones harper san

,w yotsuba like curve squared

[fathom swallow]

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[zealous garden]

,w yotsuba like curve square root

[fathom swallow]

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[burnt ledge]

AHHAHAA id seen squared but not sqaure root

root is awesome

How do you square root an image?

[chilly hull]

,w cat curve

[fathom swallow]

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[elfin ridge]

,w sqrt cat curve

[fathom swallow]

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[storm sage]

alright y'all, #bots

[neat lintel]

Thicc

[tiny saddle]

While going through some proofs book (currently on relations) I started feeling overwhelmed. I'd be wondering "is this distributive? Associative? What properties hold? Inclusion, exclusion" and with more stuff like these in the exercises. I think I can work around such proofs, but.... I have this weird feeling that I'll forget smth abt them that's important and end up suffering in the long term. I tried looking for a wiki page since knowing that there's one usually gives me some form of relief: that there's somewhere to reference and tell myself it's fine, and I don't need to remember nor prove all these properties again since wiki alr has it. Furthermore, the logic manipulation (givens-shows stuff) get annoying and repetitive with compositions of relations and a lot of set operations on them

and as if that's not enough, even while working so much math gets to my head things like "how would I prove the set-related theroems which see in the book with ZFC?" "Dayummm cardinals and ordinals" and "Number theory? Cryptography? Sickkkk", "Wait how'd I prove euclidean division? What about doing it for the reals? polynomials? How about showing that any number base representation is unique?" "Real analysis ring theory group theory abstract algebra random BS goooo" and then it becomes... hard to concentrate. And sometimes often the emotions of stupidity and weakness creeps in, making it hard to focus on working through my immediate problems (mainly going through the book and latexing notes for it).

Ahem ahem kinda inconsiderate for me to treat this like my personal dumping ground for issues I'm struggling with but I'm really not quite sure where else to go to sry for this.

[raven plaza]

You will encounter basic set theory and logic a lot in uni math textbooks

In fact so much that they will become intuition

Very quickly

[echo tundra]

Forgetting is pretty much the part of experience, our mind is made to forget things that it doesn't consider important. You can't learn everything in one go, it takes time. You'll need to revise a lot or do various exercise questions that use the proof or theorem.

Also I don't understand the associative, commutative thing. Are you talking about binary operations?

Also most people do not bother about ZFC

[raven plaza]

so much math gets to my head
May not be a bad thing

[tiny saddle]

Yeah. Like I'd be thinking "is (A n B) compose C a subset of (A n C) compose (B n C)"

[tiny saddle]

well its nice to thonk abt stuff at times ig

[raven plaza]

Exposure is always pog

[echo tundra]

You can easily check these visually using venn diagrams

[tiny saddle]

I saw a strand of grass die when I read that

[tiny saddle]

Oh r i g h t.

Geez and all this time I was doing the givens shows thing

[echo tundra]

[tiny saddle]

A good thing to do to get hands dirty

But like

After a while it becomes

😭💀

[raven plaza]

It's normal to wonder about lots of stuff

[vocal vessel]

No it’s not

[echo tundra]

Plus don't focus on learning or doing too much, your end goal is to focus on high level things unless you're trying to be a teacher I guess

[raven plaza]

I find concepts stick much better when I've previously seen bits of it from random exposure

[tiny saddle]

N o

(also yeah exactly I wanna get this stuff cleared and under my belt )

[tiny saddle]

Ohhh true....

That did help me now and then now that I think abt it

[raven plaza]

E.g. scrolling in #get-advanced-access and googling stuff

[tiny saddle]

Relatable

[raven plaza]

Maybe you see a conversation that makes no sense whatever

[burnt ledge]

Btw how do you compose sets

[raven plaza]

And months later when you learn the stuff you randomly remember the conversation

[echo tundra]

Wdym by composing sets?

[raven plaza]

^

[burnt ledge]

whatever he meant

[mental stratus]

set-related theorems using ZFC? dayumm cardinals and ordinals

insert 20 year old prover meme

[tame egret]

wdym

[tiny saddle]

Let S be a relation from A to B and R a relation from B to C. S composed with R = S ° R = {(a,c) in A×C: exists b in B such that (a,b) in R and (b,c) in S}

Not sets, relations

[tiny saddle]

Indeed

[mental stratus]

regarding set identities just use indicators

[tiny saddle]

Indicators?

[raven plaza]

Domain and codomains are a good sanity check

[burnt ledge]

Oh yea, i knew that, but i never considered that relations could be intersected as well so i got a bit confused; thanks for clearing it up for me

[tiny saddle]

True

[tiny saddle]

Thanks guys. Geez, overthinking as usual just gotta get doing and less malding

[solar hawk]

Huh

[tiny saddle]

Nothing, just read above if you're rlly curious

[solar hawk]

Ok

[ocean harbor]

Java test next week

[tame egret]

Java test?

is that good or bad?

anyways good luck!!

[ocean harbor]

it's bad yea

each question has 10 marks lol

only 2 questions so 20

[jagged forge]

man schools really like java don't they

[ocean harbor]

yeah

most school teaches python and java

I went to two different high school

the old school was python and this im in rn is java

should have stayed in old school lmao

oh my days

[jagged forge]

yeah my high school taught java too

and my uni taught c++

they like them because of OOP i guess

[ocean harbor]

I was taught c++ in grade 11 cs and my class said it was python

do you think c++ is harder than python?

[jagged forge]

they said c++ is python?

they are like polar opposites

lol

python is easy to get into, good for beginners

C++ is a monstrosity

much harder than python

[long matrix]

does cpp even have oop

[jagged forge]

just ask @solar hawk lol

yeah it does

[long matrix]

oh ok.

[jagged forge]

it is…. complicated in c++

if you have a std::vector<Base> for some base class with virtual methods, and you insert a derived object, you will get corruption

you have to have a std::vector<Base*> (replace * with your smart pointer of choice) to make a heterogeneous vector

[river moon]

c++ oop is perfect

[jagged forge]

(which is what every language does to implement OOP, you just don’t see it)

i was into c++ for awhile, now i’m a rust programmer

[solar hawk]

Most definitely

That’s like the main thing

It used to be called “C with classes”

Obviously that’s not true e

It’s more like C with classes and fucking pain

[fringe summit]

std::vector<std::vector<Base**>*>

I don’t know the modern tricks or deep lore

[jagged forge]

that type signature could indicate like 5 different things

lol

[fringe summit]

[jagged forge]

c++ has had so much shit grafted onto it

and it is only getting more

as far as i know

[fringe summit]

Schizophrenic non computable parsing

Iirc it’s just literally not computable as specified or something

[river moon]

I've written this once recently

[solar hawk]

What In the

[jagged forge]

oh well that’s not bad

[fringe summit]

double[]

[solar hawk]

Java

[jagged forge]

i want to know wtf is std::vector<Base**>* doing in his code lol

[river moon]

I need to store a bunch of arrays that could potentially be of different length, can't be bothered to use double[] and figure out indexing

[fringe summit]

double[comically large number]

[jagged forge]

i mean that’s how matrices are stored

[fringe summit]

It’s all just integers all the way down

[jagged forge]

but matrices have fixed lengths for each row/column

[river moon]

no matrices are double[m*n]

it's just one long thing

[jagged forge]

right, that’s what sharp said

except m*n might be small

i am not sure if you could store a vector of vectors in one vector sanely

unless you just zero padded every row

[ocean harbor]

yeah i was taught cpp in my old school

and the new school were taught python

in old school I was taught cpp in gr 11 and gr 12 was python

now the new one they said it was python in gr 11 and in gr12 is java

[solar hawk]

We do Java in grade 9 and then python in 10+

I wish we did cpp :(

Fuckin ell

[ocean harbor]

cpp was fine for me

it was quite easy too

speaking for "basic stuff" btw lmao

[rotund steppe]

sheesh

[solar hawk]

fish

[storm sage]

how old are you

[jagged forge]

10 (in base four)

[storm sage]

Sorry only people who are 13 or older can use Discord

[jagged forge]

damn

eric hit him with the trap card

[solar hawk]

isnt that 16?

or is that supposed to be read left to right

er wait

right to left

idk

negative to positive

[jagged forge]

16 in base four is… not a number

[solar hawk]

wdym

[jagged forge]

6 is not a digit in base four

your digits are 0 1 2 3

[solar hawk]

yeah

16 in base 10.. i mean

01 -> 16

[solar hawk]

ykwim

turns out it is not.

100 is

[jagged forge]

10 in base four is 4

[solar hawk]

16

[solar hawk]

yeah ik

i read it shifted

instead of the first digit being 1s i thoght it was 4 idk why.

[solar hawk]

@sonic field

hello

https://en.wikipedia.org/wiki/S-expression ok

[sonic field]

no.

[solar hawk]

please

mathdiscussion is so boring

it fine doe

if u understand it

ill wait for someone to come and say smthn like "what the hell is this"

and then ill have a companion

[jagged forge]

what are you doing with s-expressions

are you making a lisp?

[solar hawk]

i wanna parse them properly

[solar hawk]

yah

whys it called a lisp?

[jagged forge]

lisp is the family of programming languages that are famous for their use of s-expressions

[solar hawk]

right except

my thing isnt gonna be like them

its gonna be procedural

not functional

and maybe OOP if i have time

[jagged forge]

alrighty

[solar hawk]

idk what it is called then

like its classification

ykwim

can i still claim it a lisp?

no i dont think so

[jagged forge]

probably not

[solar hawk]

it has nothing to do w lists

the parsing is just supposed to be convenient

[jagged forge]

well lists in lisp are s-expressions

but anyway

[solar hawk]

righ eigh

[jagged forge]

you are trying to parse s-expressions, what’s wrong

[solar hawk]

wdym wats wrong

its weird

like before

TYPE WORD ASSIGN {EXPRESSION};
int x = 2y;

it was pretty easy

to like

match that

(var int x (2y))

is kinda waht im goin for now

[jagged forge]

ok, so… where are you having trouble

[solar hawk]

well

i dont wanna say

well

i dont know ware ot start

i dont wanna say smthn like

if the first token is o-paren and ...

cuz thats just a bad idea

[sonic field]

this mofo thought I COULD HELP HIM WITH THIS.

[solar hawk]

yeah u could

its just algorithm

there no coding

maybe u couldnt

but it would still be fun to crack at it

thats what i was going for

[jagged forge]

well, sit down and take a crack at it

[sonic field]

no fun until I finish my topology hw

[jagged forge]

i am not sure what you are asking of me at this point

[sonic field]

have fun. tata

[solar hawk]

how do you think im supposed to approach it

without just

lots of if statements

is there a way ur supposed to parse these things

[jagged forge]

do you know about approaches to parsing?

[solar hawk]

eh

not really

i just usually wing it

[jagged forge]

you should learn about recursive descent parsing

it’s a simple approach that is widely used

[solar hawk]

ok

[jagged forge]

the recursive descent parser for s-expressions is about as simple as you can get

so that seems like a good starting point

[solar hawk]

ok

[jagged forge]

you can hand write one

or you can use a parser generator

and specify your grammar declaratively

[solar hawk]

:o

[jagged forge]

(there are many kinds of parser generators, not just for recursive descent-style parsers too)

[solar hawk]

And they output a parser?

[jagged forge]

this is a subject you study in cs btw

yeah

[solar hawk]

:o

Like wait

Like they give you the files for a parser

[jagged forge]

yeah i just used one for the first time awhile ago

[solar hawk]

Or just act as it

[jagged forge]

they are pretty awesome

[solar hawk]

Which one did u use

[jagged forge]

a rust library called pest

it has a website too

https://pest.rs/

[solar hawk]

So like

It’s a cli tool that outputs a rust program

Which yoy include

Or it’s an api

[jagged forge]

no it’s a macro technically

it generates parser code at compile time

based on the parser grammar you provide

but that’s kind of irrelevant I guess

some parser generators are cli’s

i used a typescript one that was a cli

[solar hawk]

O

And it made a parser in ts

That’s cool

So

Does rust work well w cpp or nah

Should I just find a cpp parser generator

Or do you think I could make that one work

[jagged forge]

rust does not work well with c++

you should find a c++ one, i am sure there are many available

[solar hawk]

Oh ok

What if I compile them both and just link the object files tho

Would that

Be a traumatizing experience ?

[jagged forge]

compile the parser generator?

[solar hawk]

Idk

[jagged forge]

oh compile the rust

[solar hawk]

Ye

[jagged forge]

and link it to the c++

[solar hawk]

Ye

[jagged forge]

no that’s going to be traumatizing, they have communicate through a C FFI

i have been there and do not recommend it

[solar hawk]

Lol

[jagged forge]

i am virtually certain there are excellent native c++ parser generators

[solar hawk]

Prolly

Alr tanks

Lol

[silent sun]

Say the apocalypse happened but some humans survived. Do you think they would die out because we have like modern ideals or understandings?

And we would try to enforce those or stick to those but they might not work in a world without technology

Like if we're shunted back to the stone age practically

[neat lintel]

https://www.youtube.com/watch?v=AYdC60Hvxow

[long matrix]

[mental stratus]

[sonic sentinel]

did some tests apparently i know around 15k, 4k, and 3k words in English, Hungarian, and Arabic respectively

last two results were only from a list of 5000 words idk how much more it would be if i used a larger set

first was just an online test

also also arabic list was MSA

i don't think i would have many more words in any dialect though

[sonic sentinel]

i did some more data points (100) for arabic and i got [2281, 2916] with 80% confidence

[north sun]

https://www.youtube.com/watch?v=k5lJ_dxvNHw

[tight birch]

nnn

[last turret]

tips on dealing with homesickness 'cause seriously 2000kms away from home with non-existent social skills

[vale trench]

ask chatgpt

[last turret]

of course

[vale trench]

[echo tundra]

I read that as homelessness and was gonna suggest, "just wait till they deport your ass"

[neat lintel]

go home

[little vine]

Wow chat

https://tenor.com/view/target-clap-slowclap-applause-goodjob-gif-10321174

[zealous garden]

Excellent work discussy

[little vine]

Homie wants a sympathetic ear and just gets shit on

[little vine]

Are a university student? What's your sitch

[storm sage]

🫂 are you part of any groups/clubs where you might be able to meet people

[rocky shuttle]

so what's the sitch?

[zealous garden]

The Kim possible theme song is possibly one of the greatest songs of all time

[neat lintel]

Khan academy has live tutoring https://schoolhouse.world/?ref=u-z28apru2l4xai

@frozen schooner

[timid portal]

If you're taking a (drawn, representation of a) graph, and you're moving the vertices around to change its spatial appearance, would you denote this with a function?

[wooden flax]

Out of Arabic, Chinese, Koran, Persian, Russian, and Turkish which is the most useful for math?

[jagged forge]

maybe russian since I heard they are good at math, idk

[wooden flax]

I think it is russian

[storm sage]

by Koran do you mean Korean

also yes, definitely Russian

[wooden flax]

yep

I am applying for a summer language program and I think russian is best choice

However, I am not sure about 1) safety and 2) how it will look on college applications given the war

[storm sage]

what do you mean safety?

I'm confused

if you want to learn russian, go for it

I see no reason why the war would be relevant here

[fresh stag]

unless you’re going to russia to learn russian

[wooden flax]

irl in russia-adjacent country

the war isnt there yet

[storm sage]

wait I thought you were american

[wooden flax]

i am lol

this is a study abroad kinda program

[fresh stag]

don’t travel to eastern europe rn

[wooden flax]

they say that the program will either be in molodva/estonia/latvia

a google search says all 3 are safe, but im not sure lol

[storm sage]

I don't think there are any safety concerns from any of those three countries, yeah

but my knowledge of eastern europe is pretty limited

[wooden flax]

right, emphasis on yet though

[last turret]

wow, wish they could but 2000kms still happens to be inside my home country. Can't deport me from my own country now can they? :')

[echo tundra]

My bad dude, I am sorry

[last turret]

funny

[last turret]

nah, iss cool

[echo tundra]

Tbh I can't really think of anything cause I didn't had much homesickness. Uni was straight out much better than home.

[last turret]

yep, funny part I have been here for a year and had some peeps to hang out with but now that I am on bad terms with them I suddenly feel homesick. Weird shit seriously.

[last turret]

oh yea true, uni was cool just the last week had been quite shit

[echo tundra]

[last turret]

I guess I should hear out chatgpt afterall

XD

[storm sage]

that sucks man, I'm sorry

[last turret]

nah dw, I am feeling better than yesterday already. I'd just find a different set of people eventually.

and focus on workload 'cause goddamn

[storm sage]

🫂 how much work

[last turret]

7hrs of extra lectures on top of 6quizzes and several assignments last week.

one is due on monday

yikes

[echo tundra]

Boiiii

That hurts

Is this 1st year?

[last turret]

nah 2nd

[jade crane]

so many lol

most of my classes are like 2 quizzes + 1 or 2 exams

with the quizzes being reality checks to tell you if you belong in class or not

[last turret]

oh I meant 6 quizzes as in one each class

[jade crane]

oh ok

makes sense

still hurts if theyre all together

[last turret]

oh yea I had 2 quizzes on day with 4 lectures with 1 extra class one of those days

Don't wanna relive that shit again

[last turret]

have you ever messed up a quiz on a course that you did better on later?

[jade crane]

yea but it doesn't really count

the TA running the quiz mixed up the undergrad and grad class's quizz lol

so the score didnt count

[last turret]

damn

[jade crane]

they were pretty similar though

[last turret]

that once happened with our seniors once

[jade crane]

since the grad class was for students not studying math but still needed analysis & related

[last turret]

the class median was 5/30

[jade crane]

😂

[last turret]

ahh makes sense

[jade crane]

I wouldn't be surprised if that happens for this probability class

Prof gives an exam on his research area on what he thinks is "obvious" and fails everyone

[last turret]

I have effed up a few quizzes here and there but still got As somehow

all thanks to relative grading I suppose

[last turret]

damn, that's what our Group theory prof is def planning

[jade crane]

maybe, anyways i gtg nice talking to you!

[last turret]

legit said, "The midsem won't be as...kind. You know what I mean."

[last turret]

yea, nice talking to you

[echo tundra]

Reminds me of my complex analysis class

The mid sem exam median was 2

Out of 30

[last turret]

bruh

that bad?

[echo tundra]

Yeah, half of us got preciously 0

[last turret]

oh my god XD

I was planning to take it next sem

[echo tundra]

Yeah, the guy was so shocked, flabbergasted even that he tried helping us to the point of overdoing the help

The next quiz was embarrassingly easy

[last turret]

ah that happened once with the prof who had to deal with 5/30 over here

he gave pretty easy exams to us

[last turret]

reminds me of several of our profs tbh, people are reeling from the hectic schedule atm

except for the group theory prof def

def gonna fail half of us

[echo tundra]

True, he was a nice guy but him having an accent didn't help with the class and that his class was immediately after lunch

I remember my friend sleeping in his class with mouth open lmfao

[last turret]

reminds me of this friend of mine, he perfected the skill of sleeping with eyes open

the prof used to get super conscious of him 'cause he looked like he was seriously scrutinizing what he said

he'd over-compensate somehow

[echo tundra]

Daaamn

[solar hawk]

You didn’t put anything in it?

At our school we would salt a lemon or put salt water in his mouth

Tell him we pissed in there a bit

That’s actually messed up tho

[last turret]

yea lmfao