serious-discussion

[alpine comet]

US layout is different from UK, which is different from German one iirc

[fresh comet]

eh?

what layout does the UK use?

[alpine comet]

idk, but I remember some keys are at different places

I usually type without looking, so it was really annoying

[vernal token]

It's the German layout, for example there is z instead of y next to t

[fresh comet]

QWERTZ layout?

[vernal token]

Yes

[alpine comet]

maybe that's why

[vernal token]

But it still says "Alt" on the Alt key on the picture

So that should be the same

[fresh comet]

you’re in France, is that right?

don’t they use AZERTY over there?

[vernal token]

[alpine comet]

yes, my keyboard has AZERTY labels

but I remember QWERT by heart

[fresh comet]

I think having the A where the Q is would throw me for a loop lmao

[alpine comet]

just don't look at the keyboard when you type

[fresh comet]

I don’t look

That’s the issue

lmao

I would just start typing nonsense bc of diff layout

[vernal token]

I think Megumi means still having QWERT

[alpine comet]

it literally takes 1 second to switch between two layouts

[vernal token]

Just the labels being different

[fresh comet]

I see

huh. I didn’t know you can switch like that

damn

[vernal token]

I want to be able to write \forall and \geq and \exists with my keyboard now

[alpine comet]

it was an issue when we participated in a programming competition 2 months ago. One teammate only knows how to type in QWERTY, and another only knows how to type in AZERTY

and of course, we only had one computer

[fresh comet]

[alpine comet]

we ranked quite high at the end, by some miracles

[latent edge]

We need a latex keyboard now fr

Without using external bots

[storm sage]

infinity is Compose+8+8 for me, \ge is Compose+>+= for me

I also have a latex layout keyboard, but those two I don't type using it because using the regular keyboard is more convenient

[storm sage]

forall I type with \forall in my latex keyboard, exists with \exists

I don't have alt-codes, that's a windows thing

In my computer it's control-shift-u and then you can type in a code, but I never use it because memorizing unicode code points is dumb

[vernal token]

What's a latex keyboard?

[storm sage]

you know how you can switch between different language keyboards?

like english, spanish, german, arabic, etc

you can just install a latex one too

or at least I can, idk what OS you're using

[cinder zephyr]

I can on Android

https://github.com/DenverCoder1/latex-gboard-dictionary

this is what I use iirc

[storm sage]

I think this is the one I use, I downloaded both the IPA and LaTeX keyboards from here https://github.com/moebiuscurve/ibus-table-others

[ocean harbor]

∫

it works lol

[cinder zephyr]

indeed

[ocean harbor]

thanks for this

[woven basalt]

woah that's cool

[latent edge]

The way I write Σ or ∫ is not with my English keyboard

I literally just write せき and ∫ pops up immediately

Same thing with Σ

[ocean harbor]

[surreal bison]

\sum is a keyboard shortcut on my phone

[fast hawk]

привет

[empty stratus]

You're japanese?

[latent edge]

No but I speak it

[random rover]

ooh kinda cool

are u in any sorte of way an otaku

[latent edge]

Did I stutter?

[random rover]

no maybe coz ur just written down things from ur comp or smt

[neat lintel]

D-did i s-stutter?

[tawdry pecan]

https://media.discordapp.net/attachments/383656402159403011/1195954000399446066/The_sigma_fem-1745904174628557248.gif

[neat lintel]

rocket catz

[clear fox]

What’s you guys’ favorite number?

[hexed hull]

42

[barren anchor]

man brilliant already seems to suck

anybody know something similar but better?

tryna find stuff for my half siblings who are about to be knee deep in college

some next gen stuff, not a textbook

[neat lintel]

I’d say that reading textbooks is a mandatory skill in college

[barren anchor]

yeah it's a really ineffective skill I guess

compared to say going to see a tutor or office hours tas

definitely wouldn't call it mandatory. At least in the case of basic maths

e.g. calc, diffeq, la

[neat lintel]

The ability to read textbooks includes the ability to summarize paragraphs and develop a new perspective regarding the topic the book is talking about.

[barren anchor]

bro I'm talking about math

[neat lintel]

I should’ve said the ability to read and understand math textbooks

[barren anchor]

what are you talking about, history of architecture?

I am pretty sure they can read and summarize topics from new perspectives, they're high school graduates

[neat lintel]

You won’t survive in college, the saharan desert, or Texas without textbook comprehension skill

[neat lintel]

Math textbooks are much harder to read and understand effectively

New gen resources are often subpar compared to them imo

[barren anchor]

absolutely true, which is why I don't recommend learning via them

yeah that's kinda ridiculous to me. I've had textbooks which had like, one simple trick that a TA was like nah dude it's like this

that I would've bashed my head against for 3 hours otherwise

so, any recs on topic or just a little opining to go around about?

[solid snow]

khan academy or youtube

pauls online notes

you can essentially just google around for the topics youve described since theres like infinite resources on them

[barren anchor]

you gotta be kidding me dog those are what I used like six years ago when I was an undergrad

I don't think that really answers my question though does it

[solid snow]

ok...?

[barren anchor]

I am looking for some next gen stuff

like brilliant

like a duolingo for maths

I'm tryna be cool cause you didn't read my question but I also know you kinda suck so

let me just say, maybe read up first sometimes

[solid snow]

khan academy is pretty much that

[barren anchor]

good rec though. I'm getting caught on tiny things in the presentation but it's definitely better than paul's online math notes.

miniscule things, like saying a function is defined for all real numbers except x= <a number> but never clearly stating that the function is of x

[carmine kindle]

I am happy to report that I have done the last required Imagine Math course

All 36 of them

[lost crater]

bad

[wary rapids]

yo

can anyone help me self study bc\

i am beheind

[odd narwhal]

That wouldn't really be self study then

Would it

[proven knoll]

69420

[sweet vortex]

is Tame Impala the greatest artist of our time?

[burnt ledge]

One of my favourite bands

[sweet vortex]

fun fact, its technically not a band

but it also is

[neat lintel]

isnt tame impala just 1 person

[deep mango]

Hes very close at this point...

Even rihanna wants to be him

[deep mango]

You can be a 1 person band

[lavish kayak]

i really liked the one with the purple cover

like most people I suppouse

[deep mango]

all his albums are quite good i think!

especially slow rush

[austere trail]

Guys, did I waste my time learning stuff that I'm not gonna use in the future? Seriously whats the point of learning things that aren't gonna be used.

[ocean harbor]

what kind of stuff?

[austere trail]

Everything, math ofc, but also history, geography, science, etc.

like bro what is knowing the timeline of ww2 gonna do for me

[peak tide]

”what’s the point of not being ignorant”?

[austere trail]

no point because i feel like i could've spent the time on doing things like exercising or learning stuff that actually matters

[river moon]

just because you didn't find that knowledge useful to you, doesn't mean there are no people for which it is useful

[austere trail]

Ok

[deep mango]

IMO learning lots of different kinds of things trains you to think and problem solve more efficiently. like you learn lots of different ways of considering problems and organizing information, and since you use those methods on lots of different kinds of information (whether historical, linguistic, logical, etc), you get really used to these abstract mental manipulations

and then you use them all the time subconsciously when making decisions or analyzing situations in pretty much any job

i dont really like the "someone else might use it" argument because i think it undersells the value of these 'soft academic skills' and seems to pretend that the value of academics is exclusively in the pure content

everyone uses it, and if you don't... you could be! someone else is and they'll leave you in the dust for it

[lost crater]

vulfmon

[neat lintel]

If you learn more things, you’ll comprehend and appreciate the world in a much deeper scale

[austere trail]

Wow... I never knew there was subconscious benefits to learning. That makes me feel a lot better about spending so much time watching educational YT vids cause I really thought that I wasted my life learning that stuff which doesn't matter.

Also if that's the case, does that mean any knowledge is useful? What about knowledge about stuff in video games like Minecraft speedrun tips? Did I waste my time playing video games or not?

Although I really hope this isn't some propaganda that teachers use to make students more happy with learning or something... lol

Srry just have a lot of thoughts cause this is weird :/

[deep mango]

eh i think it depends, as long as its balanced i think any kind of learning is healthy. i definitely improved a lot of my problem solving / visualization / coordiation skills from the types of games ive played

but i would say if you left people to their own devices they'll usually just focus on improving on the kinds of learning that they're already good at, since you'll have successes faster and that feels more rewarding

so school is good for forcing people to balance that out

[austere trail]

instant gratification going wild

ok, ty for the info

fr i was depressed cuz i thought i wasted my life, ty for helping

[quiet geode]

https://youtu.be/omDK2Cm2mwo

Ryoji Ikeda is not even the greatest of our time and yet he did this

[neat lintel]

guys

i was watching an interview with the director/writer of "bird box" i think

and he said the monster in the movie was inspired by things like infinity? cuz its so unknown?

he also said smth along the lines of "infinity could be sitting on the swing outside "

what the fuck does that even mean bro

this is what happens when people watch numberphile

[solid snow]

let the non maths ramble

[random rover]

real

[neat lintel]

okay i may have been too harsh

what he actually said is hes inspired by it cuz its unknown

and smth unknown personified is scary

i just thought its a bit funny

[fair mural]

no

[fair mural]

lol ryc there is no greatest artist of our time, trying to define one is entirely subjective so i don't really see the point

for example, i always see people in the comment section of songs calling it one of the best songs ever, and i'm just thinking, really? they can't ALL be one of the best songs ever

[fervent pebble]

quantum ur forgetting abt me

my singing is so top tier

[fair mural]

[deep mango]

Ok ur mad

[fair mural]

huh

[deep mango]

yeah its only one and its The Less I Know The Better

[fair mural]

so true

[deep mango]

its not lagtrain or "i am so kawaii cute" or scalp ripper or whatever

[fair mural]

what necessarily makes that song better than all of the other "one of the best songs ever"

like, i can see when a song is good and stuff, but calling it that is always too far

even for songs that i actually feel things about

[deep mango]

it has to have a good amount of depth to the lyrics without being so deep as to be unrelatable. it has to have a crunchy, satisfying, earworm start riff that gets in your head but that quickly transitions away into something more layered and substantial, it needs to flow in and out of the bridge delicately so as to trick the listener into forgetting the song is nearly over

i thought of other things it needs to have but tame impala is bad at those things so i didnt say them

[fair mural]

what about music without lyrics or guitar then?

i assume riff implies guitar

[deep mango]

Riff could be any melody

A hook

Music without lyrics could be the best

idk

i used to think it was

[river moon]

idk I like songs that start a bit slow, so that it takes 20 seconds to a minute getting to actual song

if it starts with something that should get into your head instantly it feels cheap

https://www.youtube.com/watch?v=bL557Ujzng8

[dense wraith]

lol (i dont think anyone can answer that question because it is entirely subjective)

[fair mural]

ryc has the correct view on things that matter but once they don’t matter his opinions go down the drain

[limber stratus]

Can i ask yall if you have a math degree what job did you get. Im currently an applied math major and trying to see what i can expect or shoot for

[glass peak]

Your uni most likely has a career service which you could visit

[limber stratus]

They do, but i wanta see the possibilties

[ripe needle]

Majority of my math peeps that graduated have a job title similiar to "Data Analyst", 70-120k/year

[limber stratus]

I have a new question.. what do yall do when something says " closely related field"

[vivid halo]

what

[limber stratus]

Like this is for data analyst in my area. "Bachelor's degree in Computer Sciences, Information Technology/Systems, Business Administration or a directly related field,"

[fickle holly]

Hi, im an undergrad physics&stats student and am looking to take a math class. Should i take discrete math or number theory? I dont have much knowledge in either classes, but am slightly leaning towards number theory since ive seen some interesting conjectures etc. would anyone like to share their thoughts please

[quiet geode]

isnt everyone a data analyst

why would you need to kill yourself with a math degree

[quiet geode]

meowwwwww

why is the server owner a furry

[quiet geode]

wouldnt it be lovely if Algebra didnt exist

rather itd be lovely to have a Algebra deactivation button

ill just press it in math class just to see what my math prof gonna teach

[tawdry pecan]

yeah actually i dont like the moving numbers around part of math, its not neat or cool or rewarding at all

[quiet geode]

its alright if its just a part of it

[mystic ivy]

it fucking sucks

[tawdry pecan]

ur just wrong sorry

what other part of math is cool to you then?? like...

[mystic ivy]

uhm,,,,,

counting sheep

[tawdry pecan]

understandable

[quiet geode]

everything outside of Algebra is really COOL

algebra too is allowed to be cool sometimes

but it can quickly get really redundant

[tawdry pecan]

ur probably thinking of the formula part

[quiet geode]

all of Algebra

[tawdry pecan]

the actual algebra part is the technnique of solving equations

zamn

[quiet geode]

zamn indeed

Algebra gets obvious sometimes, also its not something that really needs attention to the point where all you do in a class is Algebra

use the time to build familiarity with the new objects

[tawdry pecan]

if its obvious do it in ur head then

but i agree w the class part

[quiet geode]

people will build the algebra as a result of it

imagine being subjected to 3 hours straight of the professor trying to explain how they got from one part to the other

everyday of the week outside of weekends

why is a remainder theorem Chinese

[bold pumice]

No more hesitation

[lost crater]

the question first appeared in a Chinese text

[lost crater]

since you are a Phys stat guy I recommend probability theory

[fervent pebble]

the first place the statement/a similar was written down was in a chinese text ~500 AD iirc. the first proof/algo was given in the 6th century by an indian mathematician. it later showed up in fibonacci's famous work, and the first generalization and complete solution was given a few years after liber abaci in a chinese work that i forget the exact name of but had something to do w the number 9.

source: i wrote an essay on the history and mathematics of the crt and showcased 2 proofs two or three years ago for a math class

[lost crater]

My source is Wikipedia

I hate finite group theory!

[quiet geode]

was a rhetorical question lol

[alpine kindle]

funny I+J = 1 implies R/IJ = R/I × R/J

[lunar python]

We just did CRT (cough cough sun tzu’s theorem) last week in number theory

[errant ridge]

Cathode Ray Tube

@old oak are you still a prof at your uni?

[old oak]

Inasmuch as I teach 4 hours per week

Why?

[errant ridge]

No I mean like

the job title

are you an assistant prof? associate prof? something like that

[old oak]

adiunkt dydaktyczny 🇵🇱

No idea what it translates to in some kind of international framework.

Probably some kind of senior lecturer

In my language I definitely couldn't be called "professor" because it's the highest-ranking and most prestigious title in Poland.

[errant ridge]

Let me translate it

"Adjunct Daculty"

[errant ridge]

arent there different levels of "prof"

[old oak]

Just two in Poland, but they're both above what I am

[tender tulip]

Now prove it for rings

[neat lintel]

anyone knows anything about SIR-modelling and how to visualize it in a graph?

[burnt ledge]

thats that pandemic stuff right

isnt there a set of pretty simple equations for it

Just plug and chug surely

[tender tulip]

it’s actually the same proof don’t bother lol

[lunar python]

bash proof is crazy

[proven wadi]

hrlp pl,s

[sick kite]

sounds like adjunct professor in english. professor is a catchall term here with the adjective that comes before giving the rank

[arctic osprey]

It might be reasonable to define 1/(1/0) = 0 right?

[neat lintel]

sure

so then 1/0 = 1/0

[arctic osprey]

yup, as a fraction I write it

[neat lintel]

however

now set a = b

now a^2 = b^2

[arctic osprey]

you are going to "proof" that 1=0 right?

[neat lintel]

2=1 but yeah

[arctic osprey]

I think I actually solved that with division by a-b!, but its a bit unstable, as division by zero is to expect

[neat lintel]

NICE

i’ll be back in like 20 ill scroll up in discussion 2 then to find it gtg

[arctic osprey]

go! Bye! and Sell!

[solid snow]

no

You have to make a bunch of contrivances SPECIFICALLY for 1/0

That in turn make your structure boring

[neat lintel]

im back

finally

[neat lintel]

alright explain

[neat lintel]

So 1/0 is its own number?

It’s like a nonstandard number system where we appoint a value ‘a’ to 1/0 then

[orchid badger]

why we always ignore the base of log while calculating the log

[ionic heart]

do we

[neat lintel]

You cannot ignore

[mystic ivy]

people who write log instead of ln need to be killed (in minecraft)

[real field]

log is base 10 though

Also ln is french and cool and awesome

[mystic ivy]

lg is base 10

log is just an arbitrary base

[real field]

<@&268886789983436800> they're harassing me

[mystic ivy]

i got harassed first

wtf

[real field]

Also wdym i didn't say anything

[mystic ivy]

....

[real field]

You're tripping

[mystic ivy]

you know tampering with evidence is a crime in the us?

in fact, i didnt say anything either

what were we talking about?

[split island]

Don’t ping mods for jokes. I don’t know what happened here, but cool off

[lone gust]

honestly

[mystic ivy]

Wait until you hear about audit logs

Wait i shouldnt have said that

ill incriminate myself

goddammit

[neat lintel]

Wrong!

[mystic ivy]

dont look at the audit logs

[split island]

You’re probably fine, just don’t feed the trolls

[neat lintel]

You said earlier that people are animal so hunt something

That’s almost admitting to zoophilia

Remove the almost

[orchid badger]

that means that by taking 10 we are taking each one in general so
if the log of something with the base power of 10 can also be calculated with log of something which is relate to 10
more like of a sdiscrete maths logic

but waht if the base value is 3

[neat lintel]

hi

[pulsar karma]

What did he say

[neat lintel]

I view humans are animals in term of sexual preference or something like that

[weak ruin]

ihh

d

hi

hi

hi

hi

hi

hi

[keen grail]

Helo

[weak ruin]

anyone ther ??

oh

[keen grail]

Wadap

[weak ruin]

what you mean ?

[keen grail]

Wassup

[weak ruin]

Hey, not a lot. What's going on with you?

and im new to this server

[keen grail]

Nothing much either

[keen grail]

Same kind of, joined it a while ago but nevr talked

Mostly cuz most discussions idrk alot abt so its more comfortable to read other peoples'

[pulsar karma]

Helo

[stable sentinel]

Are there any servers like this for social sciences?

I saw that this is part of a science network, but I'm not sure if there's social science servers

[faint hare]

I am posting this assuming that the Venn diagram of gamers and people who are into math would be high here and I am looking for likeminded people in that regard.

I am in the very early stages of making a math game for high-school and possibly early university math. The ambition for the game is to feel like a real game. Therefore, I keep the math optional, so that players self-motivate to use math (vs. virtually all math games, I am aware of, where not doing the math stops the gameplay). In line with George Polya's view on guessing being fundamental to math problem solving, you can always get around the math through guessing. To keep it short, take a look here: https://baugarten.game/

Good games are built on feedback. So let me know what you think and tell me about other places with likeminded people I can go to for feedback.

[inland elk]

anybody here from cambridge??

[spiral saffron]

Hello!

Are there people that want to study undergraduate maths with me 1h a week at least for fun ?

(doing some exercices, learning the history of the concepts) etc

[rich acorn]

Hey is anyone here from Sweden or has been to Sweden? I’m in my final year of an undergraduate math degree in New Zealand and am thinking about Gothenburg University for a Masters in Logic. Would love to hear from you if you have any thoughts or if I could ask you questions 🙂 🩷🌸✨

[orchid badger]

why 1/x turns into or equals to x^-1

[ocean harbor]

if you ever learned how negative exponent works then you can get it

[quick beacon]

Exponent rules, x^m * x^n = x^(m+n), someone said what if negative numbers, so if we do x^n * x^(-1) we get x^(n-1) which is the same thing as if we divided by x.

[tawdry pecan]

zoop

[loud snow]

The science network didnt start off with social sciences. If you join one of the servers there should be a link in the networking channel of one of them

This is old information though, so dont take my word and try and find it through joining the other servers

[neat lintel]

Because that's how it's defined

[loud snow]

x^-1 existing means x* x^-1 =1

What times x equals 1? Well 1/x of course

[stable sentinel]

Did or didn’t start off with social sciences? Because you said didn’t and now I’m confused

[loud snow]

Didnt start with social sciences. Each of the servers had a network channel which added other servers gradually

One of those servers added was a social science

[stable sentinel]

Ohh

I don’t see it in this server’s network channel- which server has it?

I love math and social science and this server was easier to find

[loud snow]

I cant tell you because this is old info

Its likely inactive eitherway

[loud snow]

What about social science?

Like economics?

Idk if that counts

[orchid badger]

wow
this dude would be genious at discrete maths

hey
btw i got a very interesting qus
how the hell someone came with the product rule of differentiation

[solid snow]

notice a pattern in computing the derivative of products of functions from the definition

[loud snow]

Thanks for the compliment and I think there are other brilliant members on the server that could help you with discrete math than me

[loud snow]

The product rule comes straight from limit definition of derivative

But there are other ways to interpret it

Wikipedia has this famous picture

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

[stable sentinel]

I just want a server like this one but for social science

[loud snow]

Yeah I meant what specific social science

There are plenty of servers that talk about philosophy or sociology or economics as examples

Idk if these all count as social sciences

But idk if you are likely to find a channel that talks about all of these

[stable sentinel]

Ah sociology or anthropology are my focuses

[sly rivet]

y=-9(|x^2-0.5|)+2 Does anyone know how to describe this transformation?

[leaden torrent]

#❓how-to-get-help

[ocean apex]

hi

[timber flame]

where can I download this book :Cambridge IGCSE™ and O Level Additional Mathematics Worked Solutions Manual with Digital Version (2 Years' Access)
3rd Edition

tried to buy it online but it says no shipping method

[orchid badger]

what tricks you usually do to understand and solve discrete maths

[rough bluff]

@orchid badger
こんにちは

[solid snow]

understanding the material?

Writing coherent proofs

[orchid badger]

so the more you study the better you become

its not like how you do it

[orchid badger]

hey

its just my name is in kanji

but am not japanise

[rough bluff]

where are you from?

[primal spruce]

ここって英語だけだと思います

[vocal vessel]

“Your name” is Hayao Miyazaki but you’re not Japanese…? I don’t buy it.

[neat lintel]

なんか突然日本語で草

[wary lintel]

Thinking about buying a used Macbook for studies. I have two options:

1. A MacBook Pro 2020 w/an Intel processor and 16gb of ram
2. A MacBook Air 2020 w/an M1 processor and 8gb of ram

Which should I get? I really want an Apple Silicon processor, but also want 16gb of rams.

[vocal vessel]

M1. Sooo much better than intel.

[wary lintel]

I know, but the 16gb of ram is recommended by the university i'll be applying to next year or year after

I will more than likely apply for the Mathematics undergrad program, do you think the 8gb would suffice? I've heard 16gb are essentially the standard minimum nowadays

[vocal vessel]

🤷‍♂️

[wary lintel]

mane

[bright hill]

m1.

m1 for sure

[bright hill]

I think 8 gigs would serve you fine

especially if you're doing math

[wary lintel]

Okay, thanks :)

[wary lintel]

Hopefully

[neat lintel]

Is this the better of the 2 discussion rooms?

[shut ermine]

I think 1gb of ram is fine

pcsx2 runs fine

but the other one is a macbook pro

even the intel pro better than m1

[jagged forge]

apple charging $200 for 16gb ram

i just bought an extra 64gb for the same amount

[mystic ivy]

its apple, what do you expect

[jagged forge]

indeed

the apple tax is real

(i am typing this from my macbook )

[mystic ivy]

how tall are you

in cm

[jagged forge]

uhhhhhhh

178cm

y

[mystic ivy]

🐑

[limpid spindle]

This might be a stretch but can someone write me a letter of rec 😭
It's for an internship and my school is on spring break 😭😭😭

[velvet dagger]

Nobody here knows you enough to reasonably write you one

(Or maybe someone does but not the generic person)

It'd be fraudulent

[fervent pebble]

why not email a teacher?

[neat lintel]

Maybe you can get a friend or relative to write you one?

[neat lintel]

i got you

[solar hawk]

U HAVE A MACBOOK

CAN U HIRE ME AS UR PERSONAL INTERN

[solid snow]

???

[limpid spindle]

For real?

[ocean harbor]

no he's trolling

[orchid badger]

how come tanhx function is one to one function if it gets to one after a time

like
after a specific x we al get the same value of tanhx

[river moon]

it doesn't get to 1

[neat lintel]

On caseoh

[neat lintel]

wut

[orchid badger]

I mean

What kind of fun ring it is where there is one y value for more than one x domain

[jagged forge]

alright @fringe summit @fervent pebble i can explain how continuous time markov chains are related to pdes now

$$\frac{\partial}{\partial t} \mathrm{E}i[s^{X(t)}]=\sum_j \mathrm{Pr}i(X(t)=j)\sum{k}g{jk}s^k$$

in finite dim this is the same as
$$\frac{\partial}{\partial t}\mathbf{P}_t=\mathbf{P}_tG$$

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

where $(\mathbf{P}_t)_ij=\mathrm{Pr}(X(t)=j,|,X(0)=i)$

[fathom swallow]

suremark MSC2020 60G40

[neat lintel]

wtf

[jagged forge]

and $\mathrm{E}_i$ is just conditional expectation on $X(0)=i$

[fathom swallow]

suremark MSC2020 60G40

suremark MSC2020 60G40

[jagged forge]

then you get an equation like this

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

anyway

[fathom swallow]

suremark MSC2020 60G40

suremark MSC2020 60G40

suremark MSC2020 60G40

[jagged forge]

uhhhh hopefully that didn't mess my whole explanation up

@storm sage u might find this interesting unless u already know it

[storm sage]

it is long

😭

[jagged forge]

yeah idk how to make it shorter......

generating functions are brutal

[storm sage]

it is hard to read when split across lots of messages

[jagged forge]

hmm

off to #latex-testing i go i guess

[storm sage]

we showed in class that probability densities for brownian motion follow the heat equation 🥰

[jagged forge]

epic

brownian motion is in like

a couple chapters for me

can't wait

[fervent pebble]

i have this saved to look at later when im in a probability mood

tyyy

[jagged forge]

wait heres the condensed version

[fathom swallow]

suremark MSC2020 60G40

[fervent pebble]

lmfao i love the closing line

[jagged forge]

lol

just thought i'd make it extra clear

in case anyone got overwhelmed

[fervent pebble]

it's pretty readable imo

so good job!

[jagged forge]

thanks!

[jagged forge]

@storm sage hopefully this is better

yesterday i mixed up the forward equation with the backward equation and i got confused for 2 hours

[storm sage]

yayy

[fathom swallow]

suremark MSC2020 60G40

[storm sage]

very clear

[jagged forge]

cool, thx for making me improve it

[storm sage]

so continuous time markov chain = discrete number of states, but time is continuous?

[jagged forge]

yeah exactly

[storm sage]

ahh

[jagged forge]

it's basically a regular markov chain, but each state is separated by intervals of exponential distribution

[storm sage]

very cool

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

at least that's how my book notates it

[storm sage]

neat

[jagged forge]

the only edge case is continuous time chains can explode

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

which they call explosion

[neat lintel]

https://tenor.com/view/oppenheimer-oppenheimer-meme-oppenheimer-cringe-cringe-my-fault-gif-12609035039633063158

[jagged forge]

damn u oppenheimer

[storm sage]

what happens to the markov chain after that then

it just goes through like infinitely many states in a finite time?

[jagged forge]

i guess so yeah.... i need to do more problems with them

[fathom swallow]

suremark MSC2020 60G40

[jagged forge]

to make it non-exploding

[tender tulip]

@neat lintel you still here, sorry I got distracted

[latent edge]

ok let me spread anaNT propaganda again

[fresh comet]

preparing myself to see logs and sums

[errant ridge]

stock exchange moment

[neat lintel]

Who here deadlifts 200kg?

[vivid halo]

your mom when she stands up

[quick beacon]

I used to do weights, but I never did for 1 rep max, so I have no idea if I could have done 200kg. My highest deadlift weight attempted and finished is 7 sets of 7 reps of 85kg with 30s rest between sets, close stance.

If I were doing wide stance, 1 rep max, I might have been in striking distance, back then, but I've been mostly training running recently, so definitely not now.

[sudden thicket]

guys can someone help me post something on reddit. i have a new account so it will get removed but its important

[orchid badger]

i have a questionwhen we say that a set is antisymetrric

is antisymettric same as reflexive

[burnt dune]

me

205kg

conventional

have a video of it

S:200kg B:132kg D:205kg

88kg

[acoustic remnant]

My head hurts

[neat lintel]

Sorry I slept, it's alright

[neat lintel]

Amazing, how long have you been working out? How many calories per day?

[glass peak]

This must be a joke

This isn’t like for credit or anything but the combination of TeX gore, the ordering of the answers and the subjectivity of the question is certainly something

[quick beacon]

85 kg isn't my 7rm

It's my 7x7 rm

If you really you can do nearly 50 reps in a little under 7 minutes at 75% of your 1 rep max, then hats off to you. I have no idea how you do it.

[hardy python]

Hey guys. I just made a YouTube video, and I would really like some feedback on it. Here's the link: https://www.youtube.com/watch?v=Q2p4prE7PAQ

[bronze pelican]

@vast wraith @dapper badge

[dapper badge]

Nice, I wanted to learn some of that stuff in relation to geometry of moduli space of curves

[bronze pelican]

Me too

[vast wraith]

the approach described in the paper i linked in #math-discussion seems to be the simplest to constructing the figure for the automorphism group of the klein quartic… but i’m still stumbling over me simply not having been exposed to rather introductory stuffs before

[bronze pelican]

Have you seen that Harrer Zagier paper of the euler characteristic of the moduli space of curves? @dapper badge

[dapper badge]

Yeah, that's something I want to read at some point

[bronze pelican]

Me too

[dapper badge]

We should read it together

I haven't actually looked at it so idk what kind of math it uses

[bronze pelican]

There are many descriptions of Klein quartic

[vast wraith]

i have noticed haha

[bronze pelican]

I havnt read that paper, but the classical constructions are pretty understandable to me.

[bronze pelican]

Combinatorics

[dapper badge]

Coloring polygon

[vast wraith]

problem is i’m not really familiar with the theory of riemann surfaces

[bronze pelican]

I'm down

[bronze pelican]

Check out the book by Girondo Gonzalez-Diez.

They talk about Klein quartic in detail there

[vast wraith]

really all i have to go on is the figure in klein’s original paper, and the description in terms of the locus in CP2

[vast wraith]

oooh

amazing, i certainly will

[dapper badge]

Is this something you'd want to do this semester or maybe next semester? I'm also free for most of May I think, but June and July are probably busy for me

[bronze pelican]

We could do it in may

[dapper badge]

Ok that sounds good to me

[bronze pelican]

Can you explain to me how teichmuller space mod mapping class group gives moduli space of curves

[dapper badge]

So do you understand how the mapping class group acts on teichmuller space

[bronze pelican]

I don't know what teichmuller space is

[dapper badge]

Oh ok. So lets say you fix some Riemann surface of genus g, call it S

I'm using S essentially as a reference point for complex structures on surfaces of genus g. So any other genus g surface X can be given a complex structure via a diffeomorphism f: S -> X. Now I'll call two complex structures (X_1, f_1) and (X_2, f_2) homotopic if there's a map g: X_1 -> X_2 such that g o f_1 is homotopic to f_2

The set of complex structures modulo this homotopy equivalence relation is the Teichmuller space of S. The key point is that for g >= 2, it's homeomorphic to a ball of dimension 6g - 6 (and in particular, contractible).

Now the mapping class group of S acts on Teichmuller space as follows. Say I have an element of the mapping class group [g] and a complex structure [(X, f)]. Then I get a new complex structure via [(X, f o g^-1)], where I've applied a representative g^-1 of [g]^-1 to the surface S

Then the orbit of [(X, f)] is all of the points [(X, h)] where h ranges over all homotopy classes of diffeomorphisms S -> X

You can sort of define the moduli space of curves to be the quotient by this action, but the point is that in the quotient space, you've now forgotten the homotopy class of the map. So points are just isomorphism classes of curves of genus g

I think that's how it goes, I'm still learning this stuff too

[bronze pelican]

I'm confused because isn't that the entire teichmuller space, the way you defined it?

[dapper badge]

Not quite. Let's use the specific example of the torus (even though it's genus 1, things still work out). So we'll fix S to be C / <1, i>. A homotopy class of complex structure on the torus is uniquely determined by a lattice in C modulo scaling and rotation. Idk if that's obvious, but I think it's illustrated better by example. So like if I have an ordered basis for a lattice in C (which is how every torus is constructed), then it's isomorphic to the lattice generated by <1, tau> where tau in the upper half plane after I rotated and scaled my lattice appropriately. The corresponding complex structures on the resulting tori are homotopic via that scaling and rotation. So Teich(T^2) is the upper half plane.

Now the mapping class group of the torus is SL(2, Z) because any homotopy class of diffeomorphism is uniquely determined by action on generators of pi_1 (that's not immediately obvious but it's true). Then the action of mapping class group on Teich(S^2) is given by fractional linear transformation. You can see this by fixing a point [(X, f)] corresponding to the lattice <1, tau>. Then the matrix (1 1 \ 0 1) takes <1, i> to < 1, 1 + i>. Since f takes <1, i> to <1, tau>, it takes <1, 1 + i> to <1, 1 + tau>. Similarly for (1 0 \ 1 1) except now you have to pass through the equivalence of any one lattice <lambda_1, lambda_2> with the lattice <1, tau> so it's a little more annoying.

Anyway, the resulting quotient is the standard fundamental domain you know for SL(2, Z).

I guess maybe the other way to think about Teichmuller space is in terms of surfaces with markings, i.e. surfaces S with a homotopy class of generators for pi_1. It's also not obvious that these give the same construction, but now when you mod out by the action of mapping class group, the orbits are just biholomorphism classes of Riemann surfaces of genus g

Yeah ok maybe this is the better way to think of it. So a marked Riemann surface of genus g is a Riemann surface of genus g, say X, along with a choice of generators C for pi_1(X). Then (X, C) is equivalent to (X', C') if there's a biholomorphism f: X -> X' such that the curves f(C) are homotopic to the curves C'. These equivalence classes give you the points of Teichmuller space of genus g surface. Then when you quotient out by mapping class group, you forget about the markings so you only care about X up to biholomorphism.

Oh, I guess I didn't mention how the biholomorphisms play into the original description, oops

[dapper badge]

Hmm maybe I'm confused because in Bers' paper it's all just homeomorphsims up to being homotopic to identity. I guess it's true that a conformal homeomorphism homotopic to the identity is necessarily the identity map so maybe these are equivalent constructions

[mystic ivy]

thats funny as fuck

[naive grove]

ping me in #discussion

[ocean harbor]

no

[dreamy ore]

oops extra dollar sign lmao

[neat lintel]

Lmfao

[neat lintel]

hi, can all classical geometry/ synthetic geometry be stated in a way that uses algebra , real number, or something similar to set theory?
(such as similarity of triangles and bisector theorem)

I mean , all these problems in geometry that should be proved with Euclid style be proved with modern mathematics?

[ocean pewter]

So can euclid’s axioms be stated in terms of set theory?

[leaden torrent]

yes

the statement may not be particularly elegant though

the axioms of ZF (or indeed a much weaker system than ZF) are sufficent to encode turing machines, and therefore any finite computation, including determining whether an argument from Euclid's axioms is valid

to more directly address the question

there exist axiomatizations of Euclidean geometry in the style of modern mathematics, yes

the most famous is Tarski's axiomatization https://en.wikipedia.org/wiki/Tarski's_axioms

(which is what proved that Euclidean geometry is decidable, a fact that I used implicitly in my above argument about Turing machines)

Tarski's axioms explicitly avoid set theory though

i am not aware of an elegant construction based on set theory

you can do "bad" constructions based on set theory by doing what i did above, or any other standard way to build up mathematics from set axioms

but as for "nice" constructions, i would not be able to tell you

[wild lantern]

Does the construction of R, R^2 and so on count?

[leaden torrent]

those are euclidean spaces but not euclidean geometry in the classical sense

[wild lantern]

If you're willing to accept that, then the usual way lines and planes are dealt with doesn't seem so far off.

[leaden torrent]

as they have a notion of a metric and stuff

and generally dont care about constructibility

like you can very easily square the circle in ℝ²

which you famously cannot do in euclidean geometry

[wild lantern]

The euclidean axioms vs constructability via ruler and compass are different things though?

[leaden torrent]

the euclidean axioms are about constructibility.

[wild lantern]

Idk, I get that they are meant to mimic constructibility.

But something like "between any two points there is a line" seems easy to deal with set theoretically.

[leaden torrent]

you can use ℝ² as a basis on which to construct euclidean geometry

but the construction of ℝ² itself does not suffice

its too strong (well, actually too weak before you have a notion of metric, and then too strong as soon as you imbue it with one)

[wild lantern]

My point was not that R^2 by itself sufficed

[visual breach]

Seems only constructables are dealt with in euclidean geo

[wild lantern]

.

[leaden torrent]

that's how i interpreted this

[visual breach]

Unless you introduce some given length

[wild lantern]

Your message was interleaved between the two. Weird timing.

First comment was meant to be like "well if you get over how annoying constructing R is ..."

[leaden torrent]

¯_(ツ)_/¯

then yeah you can just embed any axiomatization of euclidean geometry into ℝ²

by just fixing a particular line as length 1

this is why we call the metric on ℝ² the euclidean metric

it's the metric by which we relate ℝ² to euclidean geometry

(in a sense...)

[dire glen]

hey

i've seen the ^ on top of the vectors to indicate unit vectors

but i'm not sure if i can use it for any unit vector, or only for the bases

what's the convention?

and a related questin , a direction vector is also meant to be of unit length?

[wispy heath]

Hey. In my university they usually use the hat convention for unit vectors in general (but only in physics classes)

[neat lintel]

r-hats are used to indicate unit vectors

[neat lintel]

Yeah

[wispy heath]

Not an expert, but I don't think so. They represent a direction in the sense than you can scale them as much as you want (to get a line) so I guess it doesn't really change that much if they have a different length

[neat lintel]

Unit vectors are used to indicate the direction of a vector. They are also called direction vectors and are of unit length. You can scale them sure, but on their own they represent unit length in a specific direction

[wispy heath]

Makes sense, at least as a concept

[dire glen]

why to form a circle, the basis vectors needs to be orthogonal? example Acos(t) + Bsin(t) where A and B are the basis vectors

if A and B are not orthogonal i get a stretched circle

my justification, after seeing the result on graph, would be that sin and cos are "meant" to work on orthogonal basis to form a circle. by changing the bases i am deforming the space, and the circle and anything in there with it

but.. i would not have expected that without graphing it.

[raven plaza]

A linear transform preserves the unit circle iff it preserves the inner product

So the transform taking standard basis to A, B preserves the unit circle iff A, B are unit and orthogonal

[dire glen]

so if i have Acos(t) + Bsin(t) the only way i have to check if the path is a circle is checking orthogonality of A and B?

and constant radius

[raven plaza]

Yea

[dire glen]

is there a way to see the circle is not a circle withtout checking orthogonality of A and B ?

i'm kinda repeating the same question i guess, from another perspective

i think i am doing that.

just trying to see the problem from different perspectives

[raven plaza]

Either A, B have different lengths or they're not orthogonal

I think any method will be equivalent to checking that

[dire glen]

could be a mix? having different length and not orthogonal results in a circle?

cause now i'm using unit vectors

[raven plaza]

No since t = 0 and t = π/2 will yield different lengths

[raven plaza]

Ig for the 2d case the check is easier, you just have to check whether one of them is the other rotated 90°, which is easy to compute in 2d

[dire glen]

ohhh ok. this fact i think highlight another thing for me: t=0 and t=pi/2 will be on the basis, and have the length of the basis in those points. nice

[dire glen]

this would check the lenght, right? not orthogonality

[raven plaza]

This gets both length and orthogonality

[dire glen]

but i have to do that for all points ok, not just t= 0 and pi/2

[raven plaza]

I meant check whether A rotated 90° is B

[raven plaza]

Since the only way to get an orthogonal vector with the same length in 2d is to rotate 90° clockwise or counterclockwise

[dire glen]

means add pi/2 offset, correct?

[raven plaza]

As in, rotating A around the origin in the usual manner

[dire glen]

i understand this graphically

but how do i check this with math?

well no worries anyway, i'll do some tests and ill figure it out

i'm a bit hazy at the moment, need to try

[raven plaza]

If A = (x, y), then rotated 90° ccw and cw are (-y, x) and (y, -x) respectively

[dire glen]

thanky you!!

[north topaz]

<@&268886789983436800>

[raven plaza]

'Twas but a heart 😔

[dreamy ridge]

is learning the basics of number theory enough to learn modular arithmetic

[river moon]

you only need to know what is a fraction and what is division to learn modular arithmetic

[dreamy ridge]

like, the general fraction and division or are we talking about some post-calc/university stuff

[river moon]

fractions and division as taught in 6th grade

[dreamy ridge]

ok ok good.

[dreamy ridge]

bc i tried learning the game theory or knot theory and it was god awful i didnt understand shit

[river moon]

well of course because both of these have a ton of pre-requisites

knot theory isn't even taught in university

[dreamy ridge]

well now i will try to learn modular arithmetic and hopefully know stuff to solve problems

[dreamy ridge]

whoever put that shit on "ideas for your extended essay" is a menace

[vernal token]

Do you even need to know fractions to learn modular arithmetic?

[river moon]

at this point I don't think it matters

if you don't know fractions you should probably learn them first anyway

[vernal token]

Yeah. But I think in theory you could learn modular arithmetic with only knowing multiplication and subtraction, lol

[neat lintel]

Wassap losers

[ripe needle]

@drowsy talon did you get some math reading done during spring back? Or just relax?

[drowsy talon]

I did a little bit of math reading. Looked through some of the books you recommended before. Finished a novel and started another one. Mostly relaxed. Did you have Spring Break too?

[ripe needle]

Yes but I was busy at work. I think spring break as actually my least productive week of 2024 so far lol

[ripe needle]

Any math books you have liked so far or disliked?

[drowsy talon]

Uh oh. Thats not good. Do you do mathy type stuff for work?

I like all of them. They're easy to understand and read through. I like to read textbooks like novels too. I'm nerdy. 🤓

[ripe needle]

I won't go into specifics but no it's not math-related.

John Stillwell has a few good books, I feel he writes very novel-like.

He has a few geometry books, one on number theory, there's Mathematics and Its History

If you want to learn more about abstract algebra. Like fields and groups and stuff, but you want a nice easy read and introduction instead of a heavy rigorous math-major textbook.

He has two books that are supposed to be read together (in either order)

Elements of Number Theory and Elements of Algebra

[drowsy talon]

Just curious. You seem very knowledgeable in math. Oh thanks. I'll check those out. Just don't want a dry math book that is all about history. Found a few of those before and they were very boring.

[ripe needle]

This is a career change for me it's easier to learn something when you're interested in it vs a timecrunch and pressure to get a degree

Yeah I personally didn't care about his mathematical history one but others have liked it. I enjoy his other books though.

[alpine comet]

In theory you can learn everything about foundation/logic theory/category theory/set theory without knowing what's multiplication

Doesn't mean your should

[vernal token]

You'd need multiplication sometimes (atleast if you want to want to do stuff like determining the cardinality of the cartesian product of two finite sets, ...) but yeah, true

[drowsy talon]

Do you read novels too or mostly math stuff? What is your favorite math subject or topic?

[ripe needle]

Nope, my little free time is devoted just to math. Right now I wouldn't say I have a favorite or non-favorite. It's all interesting and useful.

[drowsy talon]

Do you read alot of material on one subject and then move to another one? Or do you read alot about everything all at the same time?

[cunning plaza]

Hey fellow career changer. Same!

[drowsy talon]

Are you a math major too? @cunning plaza

[cunning plaza]

Yep.

[drowsy talon]

Oh nice. I'm not. I just like to read and study various math topics. 🤓

[cunning plaza]

It is a fun topic as you go higher up

[dire glen]

anyone knows if it's possible to pan the view in desmos3d ?

it is always centered at the origin

[gleaming panther]

If you click the gear in the top right you can adjust the x,y,z bounds to move over the view

[upbeat fractal]

hi! im doing a project for my stats class and need answers for a survey, the answers are anonymous! i would appreciate if some of u could fill it out :D
https://forms.gle/EjTqKPUzkNRKhDdz5

[ocean harbor]

done

[upbeat fractal]

ty!

[magic meteor]

ey

what's the most interesting for yall in differential geometry

[tame dawn]

i need to show proof for the triangle inqeuality thm for a>= 0, b<0, and a+b>=0

i said that |a|=a, |b|=-b, and |a+b|=a+b
then i said a+b<=a-b since b<0
then i substituted everything in leaving |a+b|<=|a|+|b|

does this proof work?

the answer key shows a different proof, so that is why i am curious

[leaden torrent]

seems fine to me, "then i said a+b<=a-b since b<0" might need another sentence of justification though

(namely, use b < 0 < -b and add a to both sides)

[neat lintel]

Why do calculus

$

$\sum_{n=1}^\infty (-1)^n a_n$ and not $\lim_{k \to \infty } \sum_{n=1}^k (-1)^n a_n$

[fathom swallow]

determinate

[solid snow]

the former is notation for the latter

[tame dawn]

yeah make sense, you mean subtract a from both sides though right?

[leaden torrent]

i mean add to both sides

b < -b implies b + a < -b + a

which is equivalent (by commutativity) to a + b < a + (-b)

[tame dawn]

oh nvm i thought you meant add a both sides to a+b<=a-b

[bronze warren]

how do I get image perms?

[surreal sapphire]

why do you need them?

[neat lintel]

You have to complete a dare given to you by eric

[valid lance]

hlu!

[ocean harbor]

https://tenor.com/view/epix-image-perms-gif-20444679

[bronze warren]

https://tenor.com/view/discord-no-image-perms-image-perms-image-perm-flex-gif-25321823

repost if no image perms

[ocean harbor]

https://tenor.com/view/thinking-space-epic-mbed-fail-gif-21266064

[south rapids]

Guys , are the calculus and similar courses on Khan academy fully complete to applies them in more advanced things ?

[ocean harbor]

yes

[neat lintel]

If fog(x) = 6x+5 and gof(x)= 6x then find g(x) or f(x)

[turbid ocean]

It looks like there exist linear g and f that satisfy the system of equations

Id have to check

[burnt ledge]

g=ax+b, f=cx+d
fog=c(ax+b)+d = acx + bc+d
gof=a(cx+d)+b = acx + ad+b
1)ac = 6,
2)bc+d=5
3)ad+b=0
sub 3 into 2,
-adc+d=5
-6d+d=5
d=-1
so a=b
g=ax+a, f=(6x-a)/a

[turbid ocean]

Yep

You need to solve a bunch of linear equations

[north topaz]

#help-15 message

Another approach

[mystic tartan]

gm

[dreamy ore]

chimpanzees can drink out of bottles?

[ocean harbor]

lol

[dreamy ore]

i guess i dont see why they cant

just never thought

that was smth they just knew how to do

i guess they couldve also been taught how to do it

[mint patio]

HOw do I clarify to the reader that I'm plotting my plot using polar coordinates "for ease of viewing"? Idk how to write it right lol

If I just plot it as y = f(theta) it looks uggy and like a sine wave with a very high frequency (which makes it hard to read) but if I plot it as r = f(theta) it's so much easier to read

y = ...

r = ...

:D

[mint patio]

Oh I just said "for visual clarity", that works

[jagged forge]

well i mean you could also just change the scale

[mint patio]

I like the radial plot better

[jagged forge]

also why is the radial plot smooth if it’s high frequency

maybe i’m just misunderstanding lol

shouldn’t it also be super spiky

[mint patio]

Idk it's just the scale that makes it look high frequency I guess

I think it's not high frequency I'm just an engineer who lost all math ability

[burnt ledge]

yea i think itd probably be better to just change the scale on the x-axis, if youre trying to show the relationship between two variables y and x

but, if your trying to show a shape, that really does look like the radial graph,then its better to plot that

@mint patio on desmos if you click settings you can change the x-axis limits

[mint patio]

Yeah I could change the scale but I like the radial plot a lot more 💀

Like this looks so clean and tells you everything you need to know

Just to be clear the plot is with respect to an angle so we're not losing information

at 0 rad E = 6 GPa, at pi/2 rad E = 6 GPa, E is maximized at pi/4 rad

[solar hawk]

HS GPAs suck ass

[mint patio]

Yeah 6 gigspascals is pretty low

[burnt ledge]

this is allowed then

pretty cool even

[neat lintel]

Is this on desmos/geogebra? And how do you get that circular graph?

[mint patio]

It's on Desmos, you can get polar plots using r(theta) = some function of theta

For example mine was r(theta) = I1 + I2 + R1cos(2theta) + R2cos(4theta), where I1, I2, R1, R2 are constants

[neat lintel]

I am not familiar with this stuff so

[mint patio]

You can make the coordinate system polar by clicking on the wrench in the top right

It will change the grid so it's radial and angular like in mine

[neat lintel]

Btw, do you think it's a good idea to start learning calculus fully until 2025? I am 15

Well, by fully I don't mean like very deeply, just become good at integration and derivates

[mint patio]

Go for it

I expect you’ll struggle though

[neat lintel]

Doesn't matter

It will be worth it

[neat lintel]

Should only take two weeks

[ocean harbor]

if you smart enough then go for it

[neat lintel]

I am also learning olympiad mathematics, so calculus shouldn't be harder

[fervent pebble]

calculus is just a trig and algebra check

you'll be fine as long as you're decent at that

[jagged forge]

well theres the occasional limit

[fervent pebble]

any limit you'll see in calc can either be done geometrically, with properties of e, or w lhop

or taylor series

[jagged forge]

ah, l'hopital, the hammer that keeps on giving

[neat lintel]

Are proofs in textbooks actually useful?

Like, I see them but. Do the actually expect me to care or remember them?

I'm not supposed to remember this proof right?

[rocky shuttle]

I think Theorem 10 is more important here, 11 is just a corollary

[wet mortar]

thanks zanarcane

💙

[silver prawn]

By the time you get gud you should be able to come up with proofs for things like that off the top of your head

[ocean harbor]

that's good

[leaden torrent]

proofs are understanding

if you understand this without the proof then you do not need to read the proof per se

[meager sonnet]

I don't know about explicitly remembering this exact proof but not understanding the argument behind this is basically just not understanding linalg itself

[leaden torrent]

although the way you phrased your message makes me think you dont understand it

since its utterly trivial.

[late mountain]

Yes. They expect you to care. If you can't reconstruct the proof, you don't understand the theorem statement.

[leaden torrent]

its not something you need to "remember"

[meager sonnet]

TL;DR yes?!?!

[leaden torrent]

nah theyre something added by Big Textbook Publishing to justify their $100 price tags

freely-distributed textbooks like Rising Sea famously have 0 proofs

[bleak hull]

https://www.youtube.com/watch?v=_Sh1vMg1qEQ

been listening to this shit on repeat

(my bad if links are not allowed)

[ocean harbor]

nah you're fine

as long it is not a scam link

[final idol]

Hey, does anyone want to correspond about data science stuff?

[slow jewel]

If I go from a community college to a university, and then I apply for grad school, will they care/look at what grades I got in community college?

[wild lantern]

For places I applied most wanted all transcripts, but some put a cap on how far back they cared about.

For the place I got accepted, even though they capped it off so that I never ended up having to submit all my cc transcripts to apply, after getting accepted they still wanted everything.

I'd say more wanted everything than not for the actual application.

[slow jewel]

got it

so would you say it is worth it to get a good gpa for humanities courses in community college, at the expense of more time spent on my math courses?

[solid snow]

huh?

are you trying to go to do math for grad school?

Oh like the required ones

[slow jewel]

math/cs

[slow jewel]

I have required humanities courses I have to take

[solid snow]

I mean theres really no reason to not get good grades in those

[slow jewel]

because they are in community college, not in stat uni, I was wondering if it was fine to not get good grades in them, but dooter said that grad programs look at the grades

[solid snow]

Humanities courses are kinda free for the most part

[slow jewel]

💀

thanks josemom2

[solid snow]

Intro I should say

[slow jewel]

intros give me composition credits

not arts&humanities credits (for english classes)

[solid snow]

Obviously they get more in depth and people start to care more once you delve deeper into subjects

[slow jewel]

and I'm not doing dance classes to get my humanity credits lol

[solid snow]

Why not?

Could be fun

[orchid badger]

what you peeps think of cantors diagonisation argument

[keen sinew]

It gives me nightmares

(I know nothing about it if you were wondering)

[pine dirge]

hi

[sly flint]

pretty cool

[orchid badger]

I mean

Explain your cool

[orchid badger]

I couldn’t get what it means

[neat lintel]

Hello

[sly flint]

cantor's argument or my cool?

hi american

[orchid badger]

Cantors argument

[orchid badger]

Am not

[neat lintel]

Hello

[neat lintel]

He was talking abt me

[orchid badger]

Oh

[sly flint]

Okay so essentially, cantor says that if (0,1) is countable then there is a bijection from N->(0,1), so he assumes this fact to work on a proof by contradiction. Since each number in (0,1) has a unique decimal expansion we can make a table like this (see image) where a_mn is a digit in the decimal expansion

Now the crux of his argument was that the number with digits highlighted in bold, ie the number in the diagonal, doesn't have a n in N such that f(n)= that number, hence a bijection wouldn't exist.

[neat lintel]

why isn't terminology in math consistent?

or atleast in liner algebra

One thing can have five different names

[north topaz]

It is consistent, there is just more than one way of looking at the same concept

[mental stratus]

what thing

[sonic sentinel]

I wake up at 7:15 and come back home from school at 14:20 (its shorter because of Ramadan)

I did the math and I only spend 280 minutes of those 7 hours in class

,w 280/(7*60)

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by alshfik

[sonic sentinel]

Two-thirds

And I don't have recess and I have after school class, which if I didn't would make the percentage even lower.

But that's crazy

an entire THIRD of the time I take out of my day now for school is spent on morning routine, transportation, and breaks between classes

(Actually there are some other causes but their contribution is negligible)

[distant heron]

This chat dead?

[ocean harbor]

no

this chat is usually better than other one

[jagged forge]

even silence is better than discussy 1

[fresh comet]

sotrue

[ocean harbor]

[deep dirge]

Why does this channel exist anyway?

Sending messages here is like one of those chess games where you get hours/days to make a move.

[fresh comet]

for when discussion gets too hectic

[deep dirge]

Does it ever

[fresh comet]

it does

sometimes there’s 3 convos going on at once and people will move here to continue

[deep dirge]

I always thought why thesw discussion/chill channels don't have the chat slowdown feature.

But I guess it never gets that hectic does it

[neat lintel]

i've seen more math discussions here than a normal convo

[deep dirge]

Yeah this one smells like business.

[jagged forge]

the cs people used to take refuge here

but now we have #1213610885277421588

[latent edge]

yes that's where I rant about economy

sotrue

[distant heron]

lmao

[distant heron]

ok lol

[neat lintel]

I need to talk to my teachers so they can be a reference for my REU applications

I have nothing to talk to them about, am i screwed?

Networking is so awful

[ocean harbor]

https://cdn.discordapp.com/emojis/1112022027847606383.gif?size=48&quality=lossless&name=catcombing

[orchid badger]

do you peeps calculus complicated or hard or something you can do with a bit of practice
like puzzles
they can be solved with a bit of effort and are also interesting.

[autumn jungle]

what is 35^214 + 124^4577?

what is 35^214 + 124^4577?

[ember marsh]

I'm acc abt to do an optimization question rn

It's the worst tbh but that's cuz I lack doing application questions, but taking derivatives from different rules and such are nice

I liked just taking the derivatives, now it's more 😭

[autumn jungle]

what is 35^214 + 124^4577?'

[crisp blade]

Y'all know geomags? I have a question about some of the mathematics of it but I'm unsure which channel to ask in

If y'all don't know what geomags are, they're a toy with magnetic sticks and steel balls

[ocean harbor]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[minor current]

,w 35^214 + 124^4577

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by xbz24

[sage mulch]

7-11 near my place finally carries the strawberry monster energy drink. this is so swag

[neat lintel]

there's strawberry monster?

must be an interesting drink indeed

[jagged forge]

my favorite drink is GGF9000

[sage mulch]

yes

its brand new (in my part of canada) but i think its been around in the states for a while

[vivid halo]

strawberry monster is so good

[sage mulch]

sipping it rn

this shit is heavenly

had it for the first time a couple weeks ago and ive been fiending for it since

now i have 3 in my fridge mwahaha (that will last me 2 days)

[surreal bison]

my favorite drink is diet coke

my second favorite is a blend of arsenic, mercury, and wine.

[neat lintel]

that's a name of a drink?? 😭

[fresh comet]

no wonder you aren't calm, collected, or sane

[surreal bison]

my body requires certain materials to run at top form

cobalt is an example

[fresh comet]

are you sure you're a human

[surreal bison]

ing

we've been over this

[fresh comet]

we have??

[surreal bison]

did me explaining that the language center of me is an llm exit your context window?

[fresh comet]

I completely forgot about that convo

[surreal bison]

surely it then becomes a natural conclusion that there are Q-learning models modelling and controlling various hierarchies of actions

maybe one day you'll understand smh.

but the mainstream is still using adam of all things

thankfully our in house method is vastly superior

"our" being the secret organization i run, of course

[surreal bison]

yeah, my point exactly

perhaps somebody should actually implement retrieval augmented generation on your end, huh?

at this point you are being outperformed by claude

[jagged forge]

https://gamersupps.gg/products/guacamole-gamer-fart-9000-by-russianbadger-100-servings

[fresh comet]

[neat lintel]

oh lmaoo

[surreal bison]

https://twitter.com/alexalbert__/status/1764722513014329620

Alex (@alexalbert__) on X

Fun story from our internal testing on Claude 3 Opus. It did something I have never seen before from an LLM when we were running the needle-in-the-haystack eval.

For background, this tests a model’s recall ability by inserting a target sentence (the "needle") into a corpus of…

Twitter · Mar 4, 2024, 6:40 PM

[fair mural]

gamer supps no way

[keen sinew]

someone help quick cries derivative question

how tf would I derive f(x) = (cos(2x))^-3

BRAIN IS FARTING

[jagged forge]

what

you mean take the deriative of

[keen sinew]

yea mb

[jagged forge]

use the chain rule

[keen sinew]

yea but thats where my brain farts how in the fuck does that happen again

im integrating and thats what im setting as u

[old sierra]

did you solve it

[clear fox]

What hobbies do you guys have?

[vernal token]

What do you think Apart from math, nothing much

[loud snow]

Progress of grimmmet?

[jagged forge]

dawg i literally just got out of bed 2 seconds ago

also let me do this meeting in a couple mins first

[distant heron]

😡

[jagged forge]

i finished the (100-page) chapter on markov chains

and by finished i mean i skipped the last section and the final 50-problem set they do in every chapter

i will go back and do the problem set at some point

[clear fox]

I don’t have hobbies other than math

And I was looking for new ones

[vernal token]

Same

[loud snow]

Holy crap i didnt know its that long

[jagged forge]

yes it was fucking brutal

[jagged forge]

110 pages

[latent edge]

What book is that

[jagged forge]

grimmett and stirzaker

[latent edge]

I'll read it after sieve methods

[jagged forge]

based

[latent edge]

mfw author of my book leaving the proof of GPY sieve as an exercise to the reader

leave cutting edge stuff as an exercise

real

[jagged forge]

do i dare ask what this is

[latent edge]

A sieve used to prove stuff about gaps between primes

GPY (Goldston Pintz Yildirim) btw

I mean I get the philosophy of the author that I need to do exercises but some of these are just crazy

[jagged forge]

who, grimmett & stirzaker?

[latent edge]

No I'm talking about sieve theory

[jagged forge]

ah. well grimmett and stirzaker share the same philosophy lol