serious-discussion

[fast moat]

https://tenor.com/view/mrbeast-ytpmv-rap-battle-squid-game-squid-game-vs-mrbeast-gif-25491394

[cold needle]

funnily enough over the summer for my reu we read out of cox little and schenck for toric varieties :3

[hearty berry]

hello

[amber orbit]

what would be funny is if you weren't even reading cox little o'shea and just chose an arbitrary book and were like 'ok ill solve an exercise from this book' without having read it

[ripe wasp]

cox little is a funny name

[void tundra]

cox-zucker machine

[devout nacelle]

Yes, mostly because sometimes when I'm too lazy to actually start working on my assignment, I just copy the problems to kickstart the effort

[silver perch]

By the way afaik I can draw graphs with TeX right?

[neat lintel]

I think you need some extensions

Also, why not latex instead of just plain tex

Who hurt you?

[silver perch]

i'm researching the difference between tex and latex now

i just wanna mess around but idk which one to choose

ig latex is better

[neat lintel]

None

Katex is the future

[silver perch]

huh?

lemme google now

wait is this available for usage now?

i wanna try

[neat lintel]

Figure it out

[silver perch]

hm nice i'm sent to google again

okay

[vast surge]

tikZ makes it a lot easier

[midnight crystal]

i have a math textbook that i purchased and it was printed in 1911

on the first page somebody wrote their name "George W. Elg"

and I was just thinking how cool it is that even though that person is probably dead, they never would think that in a hundred years from when they owned the book that a person would see their name and get curious about who they were

[radiant gazelle]

does anyone have recommendations for a good intro to signals analysis textbook. I already took the class but basically learned nothing cause so much of the math was glossed over (engineering classes :D) so I want to review it again with more rigor (but still be useful)

[mint canopy]

LaTeX is TeX + some libraries. Using plain TeX is unadvisable since you have to define lots of things in order to use it. Just use LaTeX. KaTeX is a program that lets you type a subset of LaTeX on the web; it is not comparable to either TeX or LaTeX, but it is similar to MathJaX.

[silver perch]

Thanks for explaining me everything so throughroughly

[mint canopy]

It just annoyed me that someone had said something so misleading lmao

[silver perch]

Lol I see

[tall minnow]

you have to use latex because that's what most journals and other authors work with in maths

[torn willow]

Pretty interesting
https://josephg.com/blog/3-tribes/

[neat lintel]

You should learn to read asm tho

Knowing what your compiler produces is kinda useful

Don't write asm altho, unless you have to for whatever reason

[torn willow]

True

[tall minnow]

I know quite a few applied math people whose jobs revolve around optimizing algorithms for performance. They mainly code in C++. They don't really care about hardware much though.

[torn willow]

I feel like "by applied math" the guy means "people who do FP research"

I guess type 2 would be performance and/or control oriented(the latter is what they tried to imply by saying hardware I suppose)

Actually the 3rd type is very vague

[alpine stone]

anyone know what type of math we learn in 8th

[neat lintel]

hey i am taking AIME I in a little less than a week internationally. i have some quesitons about how scores r graded for ppl internationally and how the testing format will look. please dm me if ur taking AIME I internationally.

[alpine stone]

anyone here know what math we learn in 8th

[wraith whale]

probably pre-algebra

[alpine stone]

ok thanks

[wraith whale]

not really sure though, i would ask your teacher

i do remember doing stuff with money

[neat lintel]

https://www.youtube.com/watch?v=IP4rhdPIbZs good or bad

[neat lintel]

I found this really cool function: f(x)=sqrt(a-x)
(f^infinity(a)+1)^2=4a+1 for all a’s that are integers over 1 i’ve seen

did i just discover something that has a name again

but basically it’s taking sqrt(2-sqrt(2-sqrt(2-sqrt(2-…)))) and (that +1) squared =9

obviously that’s simple but 3 becomes 13, 4 becomes 17, and 5 becomes 21

[river moon]

you just discovered sequences

[neat lintel]

oh yeah i did

oops

nested radicals yeah

[river moon]

this is one of the exercises in calculus books

prove convergence of x_n and compute limit x_n as n->infinity

(for positive a)

[neat lintel]

none of the cube roots seem particularly special

[supple lance]

help 🥺🥺🥺🥺

🥺🥺🥺🥺🥺🥺

[neat lintel]

i think you should probably go to the math help channel but u should probably either translate or go to an indonesian server

either way this isn’t the right channel

[supple lance]

how

oh

Ok

sorry

[neat lintel]

it’s fine nothing wrong! i came across a little rude i apologize

okok new question (doubling down): prove that for any integer root greater than 2, (let’s say b) and any integer value for a, the resulting value of [bth]root(a-[bth]root(a-…)) (is transcendental and) cannot be expressed in terms of algebraic equations that may also include pi and e

terrible conjecture 0/10

if i was on my computer i could actually set theory it but i’m not

[brittle socket]

Set theory it?

[neat lintel]

purposely dumb way of saying use correct symbols and notation

[brittle socket]

[neat lintel]

The Mathematics of Signal Processing by Damelin and Miller Jr

[midnight prairie]

I need help differentiating e^2 ln x

[brittle socket]

!help

[quasi jetty]

Please read #❓how-to-get-help

[brittle socket]

#calculus

[uneven roost]

I need help on how I can explain to someone a scenario in poker probability when they refuse to understand it correctly. lol

[neat lintel]

just don't

[uneven roost]

Lmfao but I don't have the ability to let things go

and we talk all the time about poker and study it together

[lavish kayak]

Usually making a simpler case that exhibits the same concept works

[uneven roost]

Yeah but I do that and he just basically says: no but counter "argument"

[lavish kayak]

Put it to the math

[uneven roost]

idk he is literally running an experiment with actual cards, the result is going to support what i am saying, and he is going to interpret it wrong, lmfao

[lavish kayak]

Is this something complicated with spread-of-cards probabilities

[uneven roost]

i can explain the actual scenario if you like, but would probably have to be a call, as its way too much to explain in msg

its like

the chance of opponent having X hand

based on your cards making it more/less likely

[lavish kayak]

Is this blind or in the turns

[uneven roost]

on the river haha

[lavish kayak]

I'm not good at poker math but perhaps I can help

[uneven roost]

the stages of the game are called preflop, flop, turn and river

preflop is before the middle cards come out, flop is the 3 cards, turn is the 4th and river is the 5th

[lavish kayak]

O that's hard. Probability of his cards are only reliant on the way you bet, not your cards

[uneven roost]

both

[lavish kayak]

Because he is guessing your cards based on your bets

Well yeah

For replacement cards

[uneven roost]

what we are talking about is a scenario where at the end of the hand, the opponent makes a big bet

and for this particular opponent it means either he has a very good hand, and you lose

or he is bluffing, and you win

so there is a thing in poker math called combinations (comes from the general math term), and you work out all the combinations of hands the opponent can have

[lavish kayak]

Or you fold, and loss less

[uneven roost]

and if you have certain cards in your hands, it makes it more or less likely that your opponent has stuff

because maybe you are worried about the opponent having KQ, for example, and you have a K

now its less likely he has KQ

but if you have TT, and his bluff might need to have a T, you make it more likely he has KQ, and less likely he is bluffing

in effect

[lavish kayak]

Yeah

[uneven roost]

so basically, he misunderstands when his cards make an impact on his opponents hand

[sudden shard]

can someone help me with probability

[uneven roost]

probably... hehe

[sudden shard]

prob of winning is 2/23 prob of losing is 7/23 how many games were not played

[lavish kayak]

What does he think? That there are 5 kings in a deck?

What you're talking about is 101, no offense intended

[lavish kayak]

!help

[quasi jetty]

Please read #❓how-to-get-help

[uneven roost]

Nah, its like say opponents bluffs are exactly 88 or 99 (so if he has those you should call) and his value hands are like KQ/KJ/KT where both are diamonds

He thinks that if he has King spade + King heart, it makes it less likely the opponent has for example KQ of diamonds

because he has kings in his hand it makes it less likely for opponent to have a king

[lavish kayak]

It doesn't, if you calculate for king of diamonds

[uneven roost]

but he doesnt understand that opponent having exactly the king of diamonds is independent to the opponent having the king of spades/hearts for example

in other scenarios where you want to worry if the opponent has any KQ, then you have KK affects that chance, but not the chance he has the King of diamonds specifically

[lavish kayak]

Ask him if having a jack lessens the chance of having a queen

[uneven roost]

and i have explained to this a hundred different ways but he doesnt get it

my other version was lets say i have the 2 of diamonds

and I am worrying the other guy has a diamonds flush

[lavish kayak]

When he says no, say, "but a jack and a queen are face cards, so he has less chances for a face cards"

[uneven roost]

but I know he never plays with a 2 of diamonds (cuz he would have folded)

does this impact his chance of having a flush

and he is like no

and im like face=palm

[uneven roost]

lmfao ill try that

[lavish kayak]

Your friend doesn't understand independence

[uneven roost]

yes

[lavish kayak]

Well the only way I know to fix that is to explain it more formally but that doesn't sound like it'll work

Try stuff like

[uneven roost]

what i did was show him the probability of som eone having the king of diamonds in there hand

[lavish kayak]

If I have 10 balls, and 5 of them are red

The balls are in a jar

[uneven roost]

and we did it twice - when I have KK and when i have AA

and the chance is (Obviously) the same

[lavish kayak]

My analogy doesn't work nvm

[uneven roost]

but because in example where we hold KK the total number of kings the player would have was twice as many in example where we hold AA, he incorrectly follows that through to the King of diamonds independently

[lavish kayak]

Have patience

Probability is almost hard wired into our brain and in the wrong way

Mistakes like his are apparently common

[uneven roost]

He is running a live "simulation" where he gives himself KK (black kings) and then deals in 8 people and records how often a king comes up and how often the exact king of diamonds comes up

then repeating it with AA

[lavish kayak]

Let him work the numbers again and again till he understands

[uneven roost]

and its going to be identical % for both for Kd (give or take variance)

but he is going to then say (and I am certain this is coming) that but since they have kings half the time when I have KK, the chance he has the Kd is less

its two fold - he is misunderstanding independence AND he is incorrectly assuming that because the total number of hands the opponent has before the hand starts impacts his hands at the end

The second misundertanding is like

Say the opponent could make a flush with KdKc or KdKs or KdKh. Then obviously us holding KsKh impacts opponents chance of having those Kd combinations. However, if the opponent has played such that it is impossible (or extremely unlikely) that he holds pocket kings himself, this does not matter at all. And though he understands that concept in general, he is basically passing that on to the Kd combos when he says "its less likely he gets dealt a king, so even though the kd chance is the same in THEORY, he doesnt have it very often in practice" and im like bro theory = practice #mathsisalwaysright lol

[lavish kayak]

So tell him that he run the numbers already. If his understanding is at odds with reality, he needs to fix it

Or he can just lose money on the table. Other player will be glad

[uneven roost]

Lol

[lavish kayak]

I don't understand

If you ruled out kk by playing then there are no kk

Ah I understand

He's mixing two different scenarios

[uneven roost]

Yeah

Like in total there are 6 ways to make KK out of the four kings

If I have KK now there is only one way

These “ways” are called combos

So if I hold KK and I think opponent might have KK or some other hand

I can count his one combo of KK and then his other hands

And this tells me (fairly accurately) the chance he has each hand

[lavish kayak]

Yes

[uneven roost]

But he is basically assuming him@having KsKh further affects the opponents ability of having Kd8c, or Kd9h for example, because it includes a K

[lavish kayak]

Well look it's taken us thousands of years of gambling to get past this stuff. People used to think 66 is as likely as 1 5 in dices and my brain keeps telling me 3 4 is more common than 1 5

You've got an unique advantage in that you can tell him that the table doesn't care and that he run the numbers already

[rustic vale]

Is learning R programming worth it

[barren anchor]

yeah probably, it's good for a lot of analytical tasks

I'd lean that way over python if I were starting out in STEM and not focusing on programming for non-math purposes, in which case I might lean towards python and supplement with pandas (which is like a less-convenient OO version of a data frame).

learning one once you know any programming language* is trivial. They're not very big as core libraries.

[rustic vale]

@barren anchor

So focus on R over python for math purposes?

[long matrix]

[torn willow]

No? numpy is pretty good

[bright hill]

prolly python

if you get good enough at programming, it won't matter

if you stick with one you'll pick up the other fairly quickly

so when in doubt, just pick python coz it's way more useful

and makes up for a good competitor to R when we're talking purely about analytical tasks

[rustic vale]

I see. Thanks for the advice, man.

[bright hill]

[old fox]

Agnes: "I have 5 clue sentences."
Ramon: "I also have 5 clue sentences."
Set: "Ramon doesn't have 5 clue sentences."
In a game, Agnes, Ramon, and Set each gave one clue sentence to Insi. Among the three, one person gave the wrong clue sentence. If Insi can guess who gave the correct clue sentence, then Insi wins. Who gave the correct clue sentence?

also, is this math related?

if so, what branch of math deals with this kinda questions?

[barren anchor]

yeah, that's what I'd recomend

I don't see eye to eye with darq here. I'd say pick up python first only if you're unsure of your field(like software engineering or cs vs maths or applied sciences).

[barren anchor]

well, if one person gave the wrong clue sentence, two must have given the correct clue sentence. If insi needs to guess who gave the correct clue sentence, and each sentence is different, then there is no one correct clue sentence, it's a contradiction, and the problem isn't consistent. Discrete math

[long matrix]

I wouldn't recommend R to anybody as a first language

[barren anchor]

why?

it's way more straightforward than OO languages, imo

[long matrix]

If you're planning to use R and only R for the rest of your life, perhaps, but really?

[barren anchor]

I dunno man. It's the de facto standard for statistical & time series analysis afaik.

the reasons are numerous.

I don't think anybody will be able to avoid learning both, if they're in applied sciences, because of the package ecosystems having slightly different emphases, but you gotta start with one.

[long matrix]

In terms of learning support, I think python has much more

Stuck? SE can solve it 99% of the time

[barren anchor]

that is probably true. I don't think it necessarily has more learning support targeting deeper applications.

from a bioinformatics background, biostars had many more useful discussions than SO.

or SE.

and within those discussions, R package use was predominant.

[teal lion]

@deep mango

oh wow

[haughty lintel]

Just a bit curious, but is anyone good at mental math and knows techniques for it? I heard mental abacus is pretty good but idk if it’s outdated. I’m tired of always using a calculator for basic stuff nowadays haha

[neat lintel]

for data science i like python

[tall minnow]

learn both

they are straightforward anyway

mathematicians don't have to master them
but if you know the principles of a programming language already (like C) then any language is just pressing F1 or reading the docs to get used to

[torn willow]

If you are not doing FP, that is

[barren anchor]

yeah I mean it seems to me that all data science, unless being done by an amateur, is best done by a functional approach. R's default approach is functional, Python's is OO.

some python libraries try to shoe-horn the OO baked into the language - list comprehensions, pandas, subsets of numpy - into functional paradigms. But it's not like the design of the language was meant to economize using those libraries' functions.

[tall minnow]

the real constraint isn't often about best (preference) but popularity

and what other mathematicians use

[barren anchor]

I guess I'd say that's domain specific

[tall minnow]

python could be suboptimal as heck for a problem but if it's about communication with mathematicians then usually people pick something others can understand like python

or even matlab, since most mathematicians know matlab

[barren anchor]

I duno, I figure if you boxed up octave and matlab common concepts alone you'd have a much greater correspondence to R than python.

in fact, learning R once you know octave or matlab is much easier than learning python's OO bs

[neat lintel]

R isn't hard to learn

[barren anchor]

yeha I was surprised to hear that

I find it much easier to communicate how to do any analytical tasks' details, if details are required to be communicated, in terms of R

the syntax is great and it doesn't continually push an object layer over everything

at least not from the user's perspective. It hides those details and allows functional* access to whatever data you need.

[neat lintel]

what do you guys think of julia? i was thinking about learning that

[shell oar]

I can't handle 1 college class, let alone 5

I hate myself

I can't do math

[stone ferry]

also there is so much stuff on the internet for python

Like, most of my work has been in fairly well-documented and supported languages

then I pick up Raku (perl6) and suddenly it is very hard to find good resources

or libraries

But something like python, you will find a library for anything you need

[jovial kiln]

@flint island hello how do you do

[flint island]

oh henlooo. I'm existing

[woven whale]

@flint island cat pic?

[flint island]

floof

[woven whale]

aww

[coarse agate]

So cute ❤️

[neat lintel]

awwww]

[flint island]

he baby

[sacred arch]

So I was playing around in desmos, and was thinking about music theory a bit. We use a 12-tone system, where there are 12 equally spaced (logarithmically) notes between the unison and octave. Out of curiosity, I did some desmos magic to get a graph of how many cents off the closest note to the perfect fifth is given how many tones are in your system, and ended up with... This.

desmos.com/calculator/v2vzlw8o0m

(Link copied by hand from computer on phone, may be incorrect tell me if it is)

Does anyone have any idea where these patterns come from?

desmos.com/calculator/v2vzlw8o0m

[storm sage]

it looks neat

That's all I can say

[sacred arch]

Fair enough

I think it makes sense for the maximum to relate to logC(2^1/x) and it almost looks close, but it looks a bit more restrictive

Might be 1/2 * logC(2^1/x)

That seems about right, and I guess that makes sense. Idk why it's 1/2 though.

Ok, a bit of derivation shows that this is equal to 1/x * ln(2)/2*ln(C)

Interestingly that means that it's equal to its inverse, so to calculate how many tones to be guaranteed to be within a given accuracy is the same as the minimum accuracy when using a given amount of tones... Assuming the conjecture's correct and it doesn't just happen to fit it perfectly

[neat lintel]

Why is the fourier space (sines and cosines) important for classifying images using machine learning? Nothing about pixels on an image naively to me seem to be relevant to periodic functions

[storm sage]

Do you know about convolutions

[neat lintel]

Yes

[storm sage]

Okay do you understand why those are important

Or should I explain

[neat lintel]

Not within the context of pixels

[storm sage]

Ah okay

So basically, convolution just means you're taking some filter and you apply it to a set of pixels, then you move it over by one and then apply it again, then you move it over, etc

So for example blurring is a form of convolution

[neat lintel]

Ya

[storm sage]

It's just convolution with the filter that's 1 in every position like

0 0 0 0 0
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
0 0 0 0 0```

Similarly you can do edge detection via convolution

And all sorts of other things too

And the human retina system kinda does that

[neat lintel]

And how is this relevant to sinusoids?

[storm sage]

The key is that when you're doing convolution, you have to compute a messy integral/sum

However, when you do convolution in the Fourier space, then convolution is just multiplication

[odd brook]

Computer scientists deal a lot more with the discrete variants of the FT right

[storm sage]

So what you do is you convert your signal to Fourier space, multiply by your filter, and then convert it back

[storm sage]

Yeah the FFT

[odd brook]

ah right

[storm sage]

Also I think this would fall under more of an image processing, electrical engineering, computer vision, etc thing

So it's not strictly CS

[storm sage]

To elaborate more, sinusoidals are the nice functions that serve as the eigenfunctions of your system

[odd brook]

my CS is so bad which is why I like learning how people there think of fourier analysis and so on

[storm sage]

When you have what's called a linear shift-invariant system and you apply it to a sinusoidal, what you get is just another sinusoidal

So analyzing how stuff behaves w.r.t. sinusoidals is really easy

While the problem is difficult in general

That's why you convert everything to sinusoidals and then back

[neat lintel]

@storm sage In my book it says
"Wavelets are most applicable when
the input values live on a regular lattice, such as the successive time points in a temporal sequence, or the pixels in an image."

I don't know what a regular lattice is but do you know if/how that information is relevant to what you are talking about?

[storm sage]

I think regular lattice just means they're evenly spaced apart

Like the pixels in an image just go (1,1) (1,2) (1,3) etc

[neat lintel]

@storm sage
I assumed it was this
https://encyclopediaofmath.org/wiki/Regular_lattice but maybe im wrong

[odd brook]

ah you're reading about wavelets

if you give me a couple days I can get back to you on this stuff lol someone recommended a book to read through and I've only just started looking at it

[dapper current]

to get the disjoint union of two sets, dont you have to assume there is a background physics with time and dynamics and stuff to make it possible?

otherwise wouldn't everything be static

[neat lintel]

What?

[neat lintel]

Like do you mean in order to consider the disjoint union of two sets you need to have a brain that exists and follows the laws of physics?

[dapper current]

in a sense

it kinda seems like there are 'presumed' axioms that are most of the time 'too simple to consider'

[neat lintel]

Thats exactly correct

[dapper current]

but yet we go super simplistic with stuff like the successor function

[neat lintel]

Im guessing that the motivation or the big idea of the purpose of set theory or logic may be at the heart of your question.
You are intentionally choosing as simple ideas or properties as possible in order to have a foundation to start reasoning. Deductive reasoning requires antecedents. 'if it is raining then you will get wet outside'. this sentence has the constraint of 'it is raining' in order to say something meaningful. These constraints or antecedents to 'if then statements' or implications are the axioms or first principles.

[dapper current]

yeah

'if you wish to make an apple pie from scratch you must first invent the universe'

[neat lintel]

Yes exactly

[dapper current]

just it can seem like shaky ground a bit when we 'know' we can never reach the bottom, so we have to make the best version of it we can

[neat lintel]

What you are reading about right now is the process of 'inventing the universe'

[neat lintel]

Yes this is a fundamental issue of epistemology and language

[neat lintel]

https://en.m.wikipedia.org/wiki/Problem_of_the_criterion

[dapper current]

but then should we worry about time in set theory or not?

to 'do' or combine anything it needs to be more than a freeze frame, unless its just implied, and often it doesnt seem to be written that way

what if there were time traveling sets?

[static loom]

Theres that one set that only visits on Wednesday

[dapper current]

time traveling monoid

[neat lintel]

In short - you don't need to worry about time when developing the primitive notions required to discuss mathematics. In my opinion, math is inherently connected with language.
We are developing a 'formal' language alphabet and grammar in order to start discussion.
The formal language can be studied using set theory, called proof theory, which does discuss the implicit understandings that textbooks assume when developing set theory but you need to start somewhere.

[static loom]

We've just been doing set theory at our local bit of space-time where time can be neglected

We need relativistic set theory

Damn auto correct

[alpine kindle]

quantum type theory

[dapper current]

i did hear someone saying they (sort of) use QFT as part of foundations for math who was some fancy category theorist, dont remember where i read it

[alpine kindle]

what i just said was a joke

[dapper current]

turns out not entirely

[alpine kindle]

people are not going to use qft in foundations

they might use something also used in qft in foundations

[dapper current]

youre gonna make me want to google it and idk if i have time to find it tonight

it was more of an offhand comment in an interview also

[alpine kindle]

i think qft uses some category theory so like

I'm not surprised there's a small connection

[dapper current]

i agree, the language thing is an interesting aspect

[neat lintel]

@dapper current @alpine kindle maybe i should have instead said "historically during the development of set theory to solve the mathematical foundations issue of the early 1900s they didn't think that time was an important piece of data fundamental to what they were developing nor did people of the time think it was necessary to track or talk about time in order to solve the specific issue of the foundations problem of the early 1900s"

[dapper current]

but i just wonder if it could be now

[neat lintel]

That I have no idea

[dapper current]

but gtg soon, gn, maybe can continue another day.. or discuss other things

[violet coral]

isn’t it so nice out?

[vale oar]

What's a little frost among friends?

[violet coral]

Whats the temperature like where you guys are ?

[violet coral]

This is Massachusetts

[worthy shell]

-21C

feels like i mean

warm weather

well it depends on what part of the world you're in obviously... i live in canada so not that -20C temps in winter are normal

[violet coral]

celsius ??

[worthy shell]

yeah

[violet coral]

oh that’s -5°F

[worthy shell]

actually i assumed you meant C as well until you said massachusetts

[violet coral]

yea no

[worthy shell]

and then i realized it had to be F

[violet coral]

-30°C

[worthy shell]

it's actually way warmer here than it used to be

like the fact that we had days in january where it was only -5C is astounding

[violet coral]

Is canada as nice as it appears ?

Can you convert C to F in your brain?

[worthy shell]

few years back you'd walk out in jan with it being -25C at least lmfao

[neat lintel]

it hasn't been this cold in a while

[worthy shell]

nah i can never remember the formula

[violet coral]

-15°f

i don’t either im converting on google lol

[worthy shell]

isn't it like

[violet coral]

how’s canada like ?

[worthy shell]

5/9(C-32) or smth

[neat lintel]

canada is alright

[violet coral]

maybe

[neat lintel]

(i am canadian)

[violet coral]

no idea

[worthy shell]

i mean i guess it's good

[violet coral]

ik kelvin is like +273😂

Is it like all the hype

[worthy shell]

haven't been anywhere else so i don't have anything to compare it to

[neat lintel]

is canada hyped up?

[violet coral]

From an american standpoint yea

[worthy shell]

yeah well

[violet coral]

how do you guys view us😂

fat asses

[worthy shell]

guns

[violet coral]

Yea

[worthy shell]

nah jk

[violet coral]

big gun problem

gun

[neat lintel]

guns and funny politics (but we're just as guilty of the latter)

canadians love to clown on americans for having goofy politics but holy shit we're not that great either

[violet coral]

Trump & biden bruh

What’s y’all’s political situations

idk much about canada beside the stereotypes

maple syrup
everyone’s really nice

😂

[worthy shell]

honestly i might be the only canadian who thinks maple syrup is overrated

[neat lintel]

you are not

[violet coral]

It is lol

[worthy shell]

thank you!

[violet coral]

well i’ve never had real maple syrup

[worthy shell]

not so sure about the nice part

[violet coral]

i’ve had the sugared down american syrup

[worthy shell]

seeing as i again haven't been anywhere else

[neat lintel]

i will always reference trudeau doing blackface that one time

[violet coral]

who’s trudeau

[worthy shell]

prime minister here

[violet coral]

i assumed so

prime minister is kindve the same as a president correct ?

jusf like the leader

swear i know nothing about other countries

[deep mango]

vermont maple syrup > canadian maple syrup

sorry not sorry

[worthy shell]

i'm not the politics person but yeah

[violet coral]

does vermont have a specific brand ?

[deep mango]

no

[violet coral]

do they get sap from like a certain type of tree ?

[deep mango]

i have no idea

i just eat a lot of it

[worthy shell]

is syrup something you eat or drink?

[violet coral]

with what

neither you don’t

[deep mango]

pancakes, waffles

[violet coral]

it’s a topping no?

Yea

french toast

[worthy shell]

yes

just a rhetorical question lol

[violet coral]

just making sure because “i eat a lot of it” sounds like you just make a plate of it 🤣

[worthy shell]

chugging syrup...

[violet coral]

i’d say drink

you don’t chew it

so

it’s just a thick drink

https://tenor.com/view/maple-syrup-syrup-chug-gif-13638315

that’s so gross

[worthy shell]

oh god

[violet coral]

what’s ur favorite food for syrup

pancakes waffles or french toast

[worthy shell]

waffles

pancakes are mid

[violet coral]

pancakes

no

[worthy shell]

yes

[violet coral]

will i get in trouble for saying that 😂

[worthy shell]

maybe

[violet coral]

Pancakes made well

are so good

[worthy shell]

waffles are better

[violet coral]

i don’t like how waffles have rough aspects

the divots never have an even number of syrup / butter/ batter ratio

Pancakes a good fluffy stack 😩

[worthy shell]

pancakes just feel bland

even with the syrup

[violet coral]

Bad take

choco chip pancakes can spice it up

[worthy shell]

i forgot those existed

i take back everything i said

[violet coral]

LMAOO

[worthy shell]

is your pfp a unit circle?

[violet coral]

yes it is

i thought it would fit considering it’s a math discord

[worthy shell]

i haven't done trig in so long

[violet coral]

😭

how old r u ?

[worthy shell]

hm, not sure if i want to say

actually, i don't really care, i'm 14

[violet coral]

i’m 16 lol

You’ve already gone through trig ?

[worthy shell]

i started self studying math last year, i started with trig

[violet coral]

Oh

Very cool

like clep stuff ?

if you know what that is

[worthy shell]

i'm currently doing lin alg and i've basically started multivariable and complex analysis

[violet coral]

You don’t go to like high school ?

[worthy shell]

oh i do

self studying

[violet coral]

Just on the side

You guys have the sat in canada ?

[worthy shell]

i'm gonna be honest, i genuinely have no idea

google says yes, but no one here has mentioned it once

[violet coral]

It’s just a standardized test

if you did you would be taking the psat right now

[worthy shell]

i mean i've seen sat problems

pretty easy

[violet coral]

yea it’s an easier test in comparison to like AP classes

i’m heading to bed but it was good talking to you mate

[worthy shell]

gn!

[neat lintel]

the calculus 2 experience

[worthy shell]

oof

teachers are annoying like that

[neat lintel]

good ol' crowdmark exams

get +0.5 for the correct answer

/2

[vale oar]

It's mean for your teacher to deduct points for small details

[neat lintel]

if i was building a bridge, and i forgot my +C

I would be responsible for the deaths of millions

[vale oar]

Well in that case you'd probably solve for C or solve a definite integral

But you knew the bounds of integration would change after your skillful use of u-sub, you just didnt write them down till you needed them

[solid snow]

deducting points for no dx is so dumb lol

[burnt dune]

This is so stupid

Sorry ur going through tbis bro

[vast creek]

hi

[zealous garden]

Honestly, I think the dx deductions are fair

[long matrix]

agreed.

[zealous garden]

The small details are the ones you forget when you step away from a problem (or work more generally) and come back, so if you left them out you're setting yourself up for failure.

I'd argue leaving out a +C is about as egregious as getting a sign wrong

Which can have tremendous consequences

[long matrix]

It may look minor now, but you will have no clue whats going on in some more complicated problems if u miss it

same for dx

[long matrix]

Points are pretty meaningless - the important thing is the learning process

[torn willow]

Yea let's say you ignore +C in something like ln y= x + C
then you get y=A e^x for some constant A which is very very different than y=e^x

[dapper vigil]

Just ran into the fact that mathematicians don't have an agreed upon definition of Natural Numbers in my Discrete Maths homework... oh boy. I want to love maths, but when you have 2 logically and algebraically equivalent equations and one is solvable but the other isn't... now I learn this... sheeeeesh.

[violet wraith]

isn't it great!

[dapper vigil]

😢

I watched my Calc 2 professor, do some digusting alchemical algebra to the function f(x) = x^x
to transform it to f(x) = e^(xln(x))
Eventually it satisfied the requirements for L'Hopitals rule, that kind of broke me inside.

[static loom]

good

[ripe wasp]

isnt that pretty standard

[static loom]

it's like building muscle

[dapper vigil]

The more I learn about maths, the more I realise, it is all made up and isn't fully logically consistent.

[cinder zephyr]

it is all made up
very philosophical question
isn't fully logically consistent.
wut

[bronze wedge]

No (?)

[dapper vigil]

Though I'm also realising that high level maths actually excites me, unlike algebra. Discrete maths is challenging but actually kind of fun.

[bronze wedge]

There is high level algebra

[cinder zephyr]

algebra has many meanings yea

high school algebra is very dry yea

but builds good foundations, and doesn't have to be dry

abstract algebra is beautiful though

and yea discrete math is cool

first introduction to many cool structures in math

and probably your first introduction to proofs?

[bronze wedge]

What is beautiful about it lmao

[cinder zephyr]

proofs >> mundane calculations

[cinder zephyr]

1st: ouch
2nd: lemme guess you prefer analysis?
3rd: (now I'll be serious) I find the study of these structures to be cool. The theorems are satisfying and certain ideas like exact sequences (which I'm learning about right now) and the parallels between R-modules and categories is fun to study.

groups pop up in many places and some algebraic flavors of other fields (algebraic complexity theory, algebraic number theory, or algebraic combinatorics) provide neat perspectives

[brittle socket]

I rmb last time I tried Rosen it bored the shit outta me

Then I have been doing Enderton since

[brittle socket]

[neat lintel]

Abstract Algebra proofs are beautiful

Analysis proofs are too, but... seldom

[bronze wedge]

Implying you haven't seen the good ones yet

[neat lintel]

What is a good one?

[bronze wedge]

Grothendieck's generalization of the Schwartz kernel theorem comes to mind

[neat lintel]

Thanks, maybe I need to dive deeper

[deep mango]

Algebra proofs are contrived exercises in rewriting

Analysis proofs are explorations of a wildnerness

[bronze wedge]

Algebra proofs are done via definitions, analysis proofs are done via techniques

[fading zealot]

I'm reading about substitution cipher, and I thought “Can I represent all substitution ciphers as combining chunks of shift ciphers with different keys?”, then try to categorize all base-26 monoalphabet substitution ciphers and found that some of such combinations are not possible, for example the case where the first 13 letters are shifted 0 and the rest 13 letters are shifted 1, doesn't make a proper cipher because A and Z are both mapped to A

[torn willow]

algebra proofs can be cool

[fading zealot]

That sounds less remarkable when I wrote it out

[torn willow]

all substitution ciphers can be represented by a 26 degree polynomial in Z/26

well ig it's atmost 25 actually?

[static loom]

I think you can do smaller

[fading zealot]

So basically I am convinced that no substitution cipher is the combination of exactly two shift ciphers, regardless of the base

Don't know how to prove it formally though

[static loom]

1-x^12 is an indicator for 0 mod 13 and 1-x is an indicator for 0 mod 2, so f(x)=2(1-(x-a)^12) + 13(1-(x-a)) should be an indicator for a mod 26

then do a linear combination of these

[split oak]

The trivial substitution cipher is, though.

[static loom]

by indicator I mean an indicator function 1 at the number, 0 otherwise

[fading zealot]

The trivial one is shift 0 isn't it

[split oak]

Basically map each element to itself

[fading zealot]

So it's exactly one shift cipher

[split oak]

This can be represented as the combination of two opposite shifts

No, one substitution is the combination of two shifts

[static loom]

basically since 26 is composite and not prime, the power is lower cause we're not using fermat's little theorem anymore and we're using the chinese remainder theorem to patch our polynomials together

[split oak]

What does indicator mean here?

[static loom]

@split oak

[split oak]

Ah ok missed that

[torn willow]

can we get a indicator of degree less than 12 for Z/13

[static loom]

$$f(x) = \sum_{a=0}^{25} f(a) [2^{12}(1-(x-a)^{12}) + 13(1-(x-a)) ]$$

just to try to be clear what I mean specifically, f(a) is just whatever you want it to be

err actually I have a minor issue, I could fix it by raising 2^12 though

[fathom swallow]

Merosity

[static loom]

to have the reduction mod 13 clean

[static loom]

well since the indicator f(x) satisfies that f(x)=0 for x != 0 that means it already has (x-1)(x-2)...(x-p-1) =x^{p-1}-1 as a factor since it's a field

it might be possible that we only need lower powers though to represent certain types of ciphers

[torn willow]

yea true

[static loom]

so maybe that's worth thinking about too

like obviously shift ciphers are linear

[torn willow]

caesar cipher is just x+5

[static loom]

or yeah that one, or idk the names of these things lol

I just guessed shift cipher is the one where you just move the letter a little lol

[torn willow]

I wonder how caesar cipher was considered a good cipher in ancient Greece

[static loom]

we have at least phi(26)*26 invertible linear ciphers

[torn willow]

Can't anyone who can read just decipher it

[static loom]

lol I guess people couldn't read back then

[static loom]

I guess this is a drop in the bucket compared to the 26! invertible maps that need to be accounted for, we might be able to pigeonhole principle show that we need degree 12 polynomials

[torn willow]

yea absolutely

[static loom]

26^13 > 26! I guess

[torn willow]

That seems ineffective

 Even as late as 1915, the Caesar cipher was in use: the Russian army employed it as a replacement for more complicated ciphers which had proved to be too difficult for their troops to master; German and Austrian cryptanalysts had little difficulty in decrypting their messages

[static loom]

that looks wrong to me

am I counting wrong, there are 26! bijective functions from a set with 26 elements to itself and there are 26^13 degree 12 polynomials with coefficients in Z/26Z

[static loom]

lmao damn

[torn willow]

well aren't coefficients constrained to be in a certain way in our solution

[undone wren]

If you could read back then and had a lot of experience in combat you could be elegible as a centurion for the roman empire millitary

[static loom]

yeah, but it's an upper bound even when you overcount

[torn willow]

It's a very inaccurate one

[static loom]

but it's wrong even with over counting

so something's not right

[split oak]

n^(n/2) < n! for n>2

[static loom]

yeah so what's wrong here

supposedly:
|{degree 12 polynomials mod 26}| > |{bijective functions on set of 26 elements}|

[torn willow]

yea

because the first represents all functions

[static loom]

however 26^13 < 26! lol

[static loom]

is there some reason the CRT stuff I said doesn't work, is my life a lie rn lol

I see why this can't work I think

reduction mod 13 will give f(a) and f(a+13)

well that's in the garbage

on the flip side, I know we can find an integer valued polynomial in Q[x] of degree at most 25

[bronze pelican]

Yes I agree

[static loom]

I don't think we can guarantee that it'll have integer coefficients though, which would be equivalent to saying their denominators are not divisible by 2 or 13, since all other denominators d can be cleared by multiplying through by d^12

[topaz trout]

Is it normal if youtube math videos make me understand the material better

[static loom]

I guess as sorta a heuristic, f(n) = n(n+1)/2 mod 4 represents a bijection on Z/4Z

[bronze pelican]

Yes

[static loom]

try representing this with a polynomial that doesn't have 2 in the denominator

[topaz trout]

Im not saying im a calc student but there would be no shame is lets say a calc 3 student watches a yt video on a subject

[static loom]

do whatever works

no shame in that to an extent

[topaz trout]

But it seems like every calc student who uses youtube watches the organic chemistry tutor or professor leonard

[static loom]

but I think it's a mature thing to try to get accustomed to other forms of learning as well, since often times you don't have control over the form of the source of the thing you might want to learn

[topaz trout]

Isnt n(n+1)/2 the partial sum formula for arithmetic series

[static loom]

coincidentally yep

it's also the number of ways to pick two items from a box of n+1 items

[topaz trout]

I would not learn anything in an online school but being there physically and interacting with teacher is what most likely makes me learn better

[static loom]

yeah that's what I mean about not having control over it

[fading zealot]

I found a counterexample:
0,1,2,3 maps to 0,3,2,1 with shifts 0,2,0,2

But the structure of n,n,n,…n,x,…x,x,x should still be impossible, as well as n,n+1,n,n+1…

[void tundra]

a substitution cipher is really just a permutation yeah?

[fading zealot]

Yes

But you can also think of it as combinations of different shift ciphers

[void tundra]

i mean permutations are bijective

so

[fading zealot]

To be clear what I'm doing is recreational

[void tundra]

and S_26 is a group anyway

not sure what "combination" here means

if you mean one composed on top of another

then that's not true because you can just compose the trivial identity permutation on it

[fading zealot]

No, just concatenations of fragments of different shift ciphers

[torn willow]

All permutations can be decomposed as a product of transpositions. Maybe that's what you want?

[fading zealot]

Sounds like it

[torn willow]

Wdym by fragments of ciphers

Like you make your custom cipher as "f(x)=x+5 for x=2 and f(x)= x otherwise"?

[fading zealot]

Yes

[torn willow]

Ok that's exactly this

[fading zealot]

Everytime I learn something new in mathematics I feel like a kid opening a new box of toys. That's probably a good thing.

[torn willow]

So a transposition (a,b) can be represented as "f(x)=x+b-a if x=a and x otherwise"

Now decompose into transpositions and you have your chain of custom ciphers

[void tundra]

is this just all permutations can be written as the product of 2-cycles

because yes that's true

[torn willow]

Same thing

[fading zealot]

What is a 2-cycle?

[torn willow]

A permutation that fixes everything except for 2 elements

So f(2)=3, f(3)=2 ,f(x) =x for all other x is a 2-cycle

[fading zealot]

One more useful terminology learned today

[torn willow]

Well the 2 comes from there being 2 elements in the cycle notation

[torn willow]

This would be (2,3)

[void tundra]

or just (23) lmao

you can decompose everything into 2 cycles like

(12345) = (12)(13)(14)(15)

[fading zealot]

Is this from graph theory?

[void tundra]

no group theory

[fading zealot]

Got it. It reminds me of cycles in graphs, because you map one to another and it would look lile a cycle on a graph

Well, I guess all other elements are mapped to themselves so they're all cycles

[void tundra]

oh sorry my decomposition was wrong

[fading zealot]

But this cycle has two nodes in (on?) it

[void tundra]

it's more like

(15)(14)(13)(12)

[torn willow]

There's a very simple way to decompose any arbitrary permutation like this

[fading zealot]

On further examination, in case of n,x,n,x… , only n,n+2,n,n+2… seems to work

[torn willow]

Decompose into disjoint cycles. Now let's say a cycle is
(a_1,a_2...a_n). A decomposition is (a_1,a_n)(a_1,a_{n-1})...(a_1,a_3)(a_1,a_2)

[void tundra]

[composing permutations right to left]

[pine pebble]

If a and b are real numbers, what is the possible range for this expression

sus

[craggy steppe]

This looks very familiar

[split oak]

Simplify the given expression, following which it would be trivial to compute the range

[craggy steppe]

Looks like the argment of Z

Or something like it

[pine pebble]

What are the integers that satisfy a, b, and p for the expression

[craggy steppe]

Calm down. Are we going to do all your homework XD

[pine pebble]

no its not homework XD

[craggy steppe]

Jk

[split oak]

Use the Sophie Germain identity

[pine pebble]

NO I SAW THAT

how to solve

[void tundra]

!help

[quasi jetty]

Please read #❓how-to-get-help

[viral sluice]

How does this work?
If x+y+z=xyz, then x=tanα,y=tanβ,z=tanγ(α+β+γ=π)

[void tundra]

!help

[quasi jetty]

Please read #❓how-to-get-help

[loud bane]

Could anyone help me with a math question? It’s in the nunya help channel, I’ve been waiting for quite some time

[brittle socket]

!help

[quasi jetty]

Please read #❓how-to-get-help

[brittle socket]

Don't advertise your help channel

Especially not in multiple unrelated channels

[void tundra]

grass for mod

[brittle socket]

no

[void tundra]

i sully your sully

[brittle socket]

My sully is bigger tho

[long matrix]

blue grass

[brittle socket]

Blue Shuri

[long matrix]

[winged token]

does anyone have experience applying for NSERC USRA

[woven whale]

have you tried RTNSC KRSLAN

[winged token]

?

[long matrix]

hes trolling.

[woven whale]

what does NSERC USRA mean

it's just a bunch of acronyms

[winged token]

its a undergrad student award for canada unis

the girls who get it, get it, the girl who dont, dont.

[long matrix]

[void tundra]

[silk pilot]

[leaden torrent]

with all due respect, this is easily googled.

though the fact that you dont understand the acronym also means the question clearly doesnt apply to you

so you coudlve just ignored it

rather than being an asshole

[woven whale]

ok

[tight comet]

dam illum being schooled

[frigid matrix]

dont belittle them because we were all immature at some point

[velvet dagger]

Speak 4 urself

[vast surge]

Unfortunately, I am not Canadian (though I do live almost directly on the border just a couple hours out from Niagara Falls, and there is a Tim Horton's in my town, so it's hard to tell sometimes...). Best of luck with your application though!

[neat lintel]

what do you think is a good place to find mathematical articles ?

[vast surge]

Ask professors for something accessible. Or browse ArXiV and struggle.

[neat lintel]

what do you think about the articles on arxiv?

[vast surge]

"the articles on arxiv" is just, every single paper someone's tried to publish in the past 30 years

[bright hill]

[neat lintel]

tim hortons does not make you canadian (anymore)

every single person i know hates tims

and i live in canada

the place has gotten so bad

[hot bridge]

what would you do if you keep doubting your proof even though it's right?

[neat lintel]

come back later

and then read it as if someone else had written it

[exotic carbon]

Someone posted this on a server I'm on

He also claimed to have solved climate change and world hunger

[woven whale]

why are these just a bunch of photos of some drawn stuff

[harsh linden]

interesting

asking the real questions here

[worthy shell]

i've seen some very interesting stuff in that queries spot

one time i saw something related to my little pony

[void tundra]

[mint patio]

@deep mango Sorry to ping but you seem like the right resource to ask, do you know of any fluid simulators that are "simple"?

Simple to use rather, and free for students

[deep mango]

i do not, sorry

[mint patio]

I'm having trouble visualizing the velocity field created by a rotating body

[deep mango]

i dont know anything about fluid numerics yet

[mint patio]

Would you mind checking my thinking for a conceptual problem then?

(The one I'm trying to model)

[deep mango]

maybe in a bit, but im busy rn

[mint patio]

No problem, take your time. Mind if I DM you it?

Oh shit never mind I found a YouTube video on it 💀

Thank you for responding though!

[deep mango]

[near talon]

There's this one person in our grade that has a sister who did BC calculus in 7th grade

It's completely insane

[sharp cave]

You can find quite many resources if you have matlab (your university might have free subscription) and search for related matlab scripts. An example is this: https://www.youtube.com/watch?v=lbTTGiM6zJQ (it gives a link for the script in the description).

[mint patio]

Yep, I get free MATLAB

But I want to try and derive it myself/see an explanation for the derivation

I'm trying to find the velocity field generated by a right cone rotating in a fluid

Having trouble visualizing it in my head

[rustic wyvern]

What's the usual undergrad math progression? I assume something like Calc, linear algebra, real analysis, diff eqs, complex analysis?

(In order that the average math major would take)

[devout nacelle]

Real analysis almost always goes before complex

Calculus would usually go before real analysis (or there won't be a "calculus" course at all)

Linear algebra would go early up but doesn't have much to do with analysis, proof-based linear algebra can often go a bit later depending on the program

Differential equations seems to be optional at most places, but at places where it is mandatory, it will usually go after calculus (and possibly linear algebra)

[rustic wyvern]

Thanks!

[neat lintel]

hey, i wanna learn math like from scratch
where should i start?

[exotic carbon]

We talking arithmetics like plus, minus and stuff?

[surreal sapphire]

probably start with khanacademy

[pure herald]

I can be taking you mathematics

[neat lintel]

no no haha, I'm an undergrad second year of college

something a bit more than that i guess

[neat lintel]

you teach meth?

[onyx pagoda]

percentages? Ratios and rates?

[neat lintel]

no

more than tha

I know calc, algebra, combinatorics, prob, stat

and some other stuff

but still I want to start everything from the basic

yk

[exotic carbon]

Khan academy

[neat lintel]

hmm thanks

[trim vessel]

Hi hi

[pure herald]

Yes

[noble zephyr]

where would number theory fall in that progression?

[neat lintel]

what iss taylor seriees?

what is an euler

[devout nacelle]

Hmm, one would generally pick up some elementary number theory as a part of abstract algebra classes, but number theory classes in themselves are largely optional from what I know

It's a more specialised domain in a way, although elementary number theory classes are often used as a springboard to proof based mathematics

[neat lintel]

seriously though.

why/when/where do we use it

$$\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^n$$ according to ahh. Wikipedia. I am reading about it

[fathom swallow]

The W

[bright hill]

It's a way to approximate a function using polynomials (which might be way more easily studied)

[neat lintel]

👍

[bright hill]

It's conceptually very intuitive and in some cases, letting the sum go to infinity would approximate the function perfectly

A good way of thinking about it is it's a stronger theorem than the mean value theorem

(indeed, for n=1, the two theorems coincide)

[bright hill]

This isn't Taylor's theorem that I'm talking about btw, the sum can go to infinity only if the function is infinitely differentiable

[fast ivy]

there are infinitely differentiable functions that do not have a taylor series expansion tho

C^infinity and analiticity are different concepts

[bright hill]

I see

I was just trying to hint at the fact this sum might not even make sense for all functions

[bright hill]

I answered the why

But when and where I can only say "in analysis"

More specifically perhaps "real and complex analysis"

[woven whale]

"in math"

[bright hill]

Possibly more broadly

Albeit rarely

[woven whale]

does mvt imply ivt

[bright hill]

No

[woven whale]

ivt is the only useful thing

[bright hill]

mvt applies when the function is differentiable on an interval

Since ivt is for all continuous functions and not all continuous functions are differentiable, the mvt can't possibly imply ivt

(without mentioning the fact that there exists continuous everywhere, differentiable no where functions )

[void tundra]

ah yes that one fourier series

[bright hill]

I just saw weiestrass' function yesterday actually

Twas cool

Very sleek argument

[fast ivy]

the set of differentiable everywhere functions is meagre in the set of continuous functions

painful

[flat harbor]

connected spaces and locally path connected spaces

[alpine cargo]

whats possible research topic related to magic squares?

[devout nacelle]

I think combinatorial design is a related field to look into

[alpine cargo]

thank you im having a hard time deciding wether to choose magic squares or schur triple theorem

[devout nacelle]

Choosing for?

[alpine cargo]

undergraduate mathematical research

[devout nacelle]

Ah, okay

Both sound interesting, I have been recently reading about BIBDs as a part of a class

They're also very cool

[alpine cargo]

whats BIBDs?

[alpine cargo]

yea and im kinda stuck rn

[neat lintel]

so true

[devout nacelle]

Balanced incomplete block designs, they are "combinatorial structures", like graphs/magic squares, etc.

Just like for magic squares you have a collection of objects (generally numbers) and some constraints on how you want to arrange those numbers, block designs are concerned with building families of subsets of a given set

That satisfy certain constraints (how many subsets should each element appear in/how many subsets should every pair of elements appear together in/how many elements should be contained in each subsets)

Then the problem generally is about determining if for a given value of these parameters, a corresponding family of subsets exists or not

And if it does, how one would go about constructing it

I haven't learnt a lot about it, but this is the broad theme from what I've picked up

[devout nacelle]

Might help to discuss this with a thesis advisor or someone working in a related area at your institute, imo

[alpine cargo]

currently searching it up, looks interesting

[alpine cargo]

i wish i can do that, we have to come up with a topic proposal first before we get to talk to any advisor

[devout nacelle]

Ah ooof

[stone ferry]

Hold on there's a better way to write this

[devout nacelle]

Would it be possible to reach out to potential advisors beforehand?

[stone ferry]

$$e^{\frac{d}{dx}}f(x)$$

[fathom swallow]

nHail

[stone ferry]

Then you expand that as a power series

[alpine cargo]

inside my institute its not possible

[devout nacelle]

Well, I guess you really have to make a call then

See what you find most interesting

To me it seems all of these are pretty interesting ideas for an undergrad thesis

You can ask for more opinions in #combinatorial-structures since that seems to be your primary interest area

[alpine cargo]

thank you so much, are u still a student?

[devout nacelle]

Yeah

[alpine cargo]

cool whats your course if u dont mind

[devout nacelle]

Undergraduate in mathematics, B.Sc in Mathematics specifically

[alpine cargo]

ohh same what year?

[devout nacelle]

3rd and the last

[alpine cargo]

cool, ig you’re having fun taking the course

[devout nacelle]

Yeah, it's an interesting class so far

BIBDs will not be taking up a large part of it though

After BIBDs it will move on to some coding theory

Followed by some random assortment of topics

Mostly about special matrices and groups with a view towards applications

[alpine cargo]

is conducting mathematical research also one of the requirements finishing the course? if yes do u have any ideas that you’re interested in doing

[surreal sapphire]

manan coding theory arc?

[fervent notch]

I know this will sound a bit crazy but please entertain the idea for a second. It looks like I have a polynomial-time algorithm for listing all maximal cliques of a undirected graph, which constitutes a constructive proof for P = NP. I'm almost certainly wrong for reasons I cannot yet see, I'm sure many people have thought they've had something before. What would you say is a good approach for getting peer review? You can't just publish something like that. On the off-chance that it's not mumbo-jumbo, it would have severe implications on cryptography, etc. Just entertain the idea for me and I'll eventually find the error or be proven wrong by peers.

And nevermind my nickname, I know it's ironic given what I'm saying but I actually want a serious discussion.

The problem is an NP-complete one, as you probably know.

So far, I have been unable to find bad outputs but testing continues.

[barren anchor]

lol maybe

[static loom]

what was the major insight that led to this discovery

in laymans terms

[barren anchor]

you get it peer reviewed by just talk to a professor

or your boss

are you in a STEM position professionally? or a student?

a professor or boss you trust

[static loom]

by this I just mean so you can say it lazily without revealing anything for us to scoop u 🍨

[barren anchor]

I had two professors to tell me not to tell anybody else some ideas they liked

I think that's a good confirmation

one literally said "don't give that one away"

[static loom]

meh I don't think there's much point in secrecy around ideas most of the time

[barren anchor]

yeah most of the time

lol

when you're having your once in a lifetime flash of brilliance I dunno

but the only way you can know it is that is by sharing it with trusted peers

you cannot be objective

[static loom]

make a youtube video explaining it, post it to multiple social media sites so that it's time stamped, and then you have proof you thought of it first if someone publishes after the fact

[barren anchor]

yeah how do you wanna capitalize? my end-run was get a biotech incubator going on, but due to disease I missed it

like just go apply. There are people who will take 5% but give you a million dollars

I agree with merosity but not about the youtube video

send yourself and trusted associates documentary evidence

or just yourself, I don't think multiplicity is necessary

the sad truth is there might be somebody out there who thought the same thing but they don't know it's important yet

they see your youtube video with 1 mil views

[static loom]

only one? you need to have an abundance mindset 😎

[barren anchor]

they then officiate before you do

I'd scam the patent off a dog

yeah, I probably should. It freaks me out though, I've had wiser superiors be like seriously guard that.

in fact, I do

I'm like whatever man everybody has done everything 5 million years ago

a dinosaur expressed that patent with a dance

I got my last job simply by scaring my employer

by like knowing exactly what he wanted to do

I think you should force anybody else who has the idea to join your company

[mint patio]

Wait I'm confusion

So an observer in an inertial frame of reference sees an objecte moving in a rotating frame of reference due to the Coriolis force right

https://en.wikipedia.org/wiki/File:Corioliskraftanimation.gif

Oh I think I'm misinterpreting the image?

If you're on the red ball, the black ball looks like it's going straight

BUt if you're outside of that system you can see it's clearly moving in a curved pattern

[barren anchor]

yeah

wait what

super wrong

if you're looking from outside the rotating frame of reference, it looks like it's going straight

I wouldn't use words so much for that one, I'd just think about it.

[mint patio]

Oh

What's the path it's actually moving on? Or does that depend on your perspective?

Like is it going in a straight line or curved? But depending on where you are you see it differently

[barren anchor]

I think the whole point is the effect is about the perceived path

usually demonstrated with an objectively straight path

and a changing frame of reference

there is a singular, actual path. Don't be confused by that. It's just that to define that path requires a frame of reference.

it's one of those mind blowers like wait we define words with other words? where does it end? and the endpoint is the same: you make something arbitrary up

then you agree to stick to it during reasoning, because consistency within the system is all you need, you don't actually require an objective frame for anything

this clearly implies God

[mint patio]

This is a great way to put it

[barren anchor]

but not this?

[fervent notch]

Software engineer. Obviously some background in CS.

There would be that about shining, sure, entertaining the thought. But how would you ethically even announce it?

You can't just say "Hey, banks, I'm publishing something in one year, trust me. You must change all of your security."

[mint patio]

I do not believe in God, no

[fervent notch]

Again, we are just entertaining this fantasy.

[mint patio]

You are welcome to your opinion though

[barren anchor]

change it to what?

I think the actual end result of your proof would be the total collapse of security forever

I'm just saying show your boss and peers

if you don't have people you respect who respect you, then make those people

[fervent notch]

Well, there are ways around it --- not all ciphers are based on the assumption that P!=NP.

[barren anchor]

which are those?

if you're talking one time keys etc it's fine

but if you're talking algorithmic hashes of the type that afaik comprise all modern security protocols, what?

[fervent notch]

The most obvious one would be the OTP, which secure stream ciphers are trying to immitate in a more convenient way. But there are others as well.

[barren anchor]

not even a hash- any algorithmic system

that's a one time key

[fervent notch]

It is.

[barren anchor]

like you said otp

just a heads up that's what I meant

THIS MAN'S A GENIUS

and yeah man that'd be the one

we'd literally be one time key forever

I'd appreciate that, I think

bigass kkeys

nah not even that big, collisions would be practically never

[fervent notch]

I believe there are a few alternatives but I have not looked into it. My background is not in crypto even if I'm not completely oblivious to it.

People usually say "most cipherps would be broken" but I have not looked into it further.

[barren anchor]

not-obliviously solving a problem i myself am satisfied is insoluble

[fervent notch]

I expect it probably is. I do not have any confidence in this result as of yet.

[barren anchor]

I have decent reasoning

that what you think you have is not that

on the basis of the actual problem

[fervent notch]

But I have to puruse it nonetheless for the time being even if to disprove it.

[barren anchor]

man who doesn't?

I wrote a shitty compression algorithm as an undergrad that I was certain would revolutionize

I think you are brave and honestly quite bright simply for taking the tact which you are

i.e. find a counter-example

you think it works, and the most reasonable response isn't "this is now a premise"

it's try to kill it

honestly and genuinely

[fervent notch]

I mean I don't want to be delusional. 🙂

[barren anchor]

some people super do!

but yeah. Just hang onto it until you've got someone you trust who can work through it with you.

I sought out those people.

[fervent notch]

Even so --- suppose despite all odds there's something there. What would even be a normal step into publishing this? Can't just publish it and wait for some terrible consequences.

[barren anchor]

bro publishing is not something you do before peer review

and you do not generally peer review before doing your actual serious peer review, which is like colleague / inner group review

and I agree, ethics

[fervent notch]

Well, no. But suppose my colleagues would agree and it would be time for peer review. That means publishing. While everyone's figuring stuff out, some evil programmer somewhere uses it. Or some government. Or whatever.

I'm not saying this is the real world. But in this pretend world.

[barren anchor]

I'll tell everyone I knew you

the man who broke P

[fervent notch]

Probably not 🙂

[barren anchor]

I'll call you Big P

Big P The Ethical

[fervent notch]

At any rate, if someone had something, they couldn't just put it up on arXiv or whatever.

[barren anchor]

some people would abandon the pursuit entirely and never bother to confirm or deny their hypothesis

[fervent notch]

Because the very next day, something bad would probably happen.

[barren anchor]

I think ethically it's dicy, because if it's out there, somebody else might crack it

who? who knows. Perhaps an ultra-orthodox terrorist

perhaps an insane child prodigy

[fervent notch]

On the other hand, the person who had this shouldn't NOT publish it either since apparently protein folding is NP-complete and is an important component in developing a cure for cancer.

So it's a weird situation to be in for this hypothetical person.

[barren anchor]

things would just be different. I have no idea what would happen if somebody declared security over.

immediately subsaharan africans would have nuclear fission etc

[fervent notch]

All economy and national security revolves around it.