serious-discussion

[frozen venture]

Could be finding ways to make the world a better place

I don't know

Like doing research in some altruistic field like medicine or climate or something

Stuff like that

[wicked ore]

Yeah for sure

Those fields need statisticians or data analysts

[frozen venture]

I want to help people without having to be a teacher

[wicked ore]

But it depends on what you’re willing to consider math

Is data science math? It involves math but it’s also coding

[frozen venture]

Hmm so data analysis/statistics seems like the way to go

I like coding also

Is the math in data analysis interesting?

[torn willow]

Well,if you do research it is ig

[wicked ore]

It’s not original or anything

[torn willow]

Then don't do a pedagogy degree

[wicked ore]

But don’t take my word for it I’m not a data scientist lol

[torn willow]

Just do a math degree

[wicked ore]

They didn’t, I think they phrased the question oddly

[torn willow]

mb

[frozen venture]

Yeah sorry I'm a bit sleepy

[torn willow]

Well, Your degree doesn't restrict your actions

[wicked ore]

I believe biology is making use of topological constructs

[torn willow]

Math is a toolset

You can use it to do stuff that are useful in other fields

Like you can probably do some analysis and design robots to do some specific thing

[wicked ore]

@frozen venture

Topology has been used to study various biological systems including molecules and nanostructure (e.g., membraneous objects[18]). In particular, circuit topology and knot theory have been extensively applied to classify and compare the topology of folded proteins and nucleic acids. Circuit topology classifies folded molecular chains based on the pairwise arrangement of their intra-chain contacts and chain crossings. Knot theory, a branch of topology, is used in biology to study the effects of certain enzymes on DNA. These enzymes cut, twist, and reconnect the DNA, causing knotting with observable effects such as slower electrophoresis.[19] Topology is also used in evolutionary biology to represent the relationship between phenotype and genotype.[20] Phenotypic forms that appear quite different can be separated by only a few mutations depending on how genetic changes map to phenotypic changes during development. In neuroscience, topological quantities like the Euler characteristic and Betti number have been used to measure the complexity of patterns of activity in neural networks.

[frozen venture]

How difficult is it to pivot into machine learning after graduating with a bachelor's in math?

[near fox]

Do you know any programming languages? If you have experience with programming the transition should be smooth.

But generally, it is a smooth transition. But "machine learning" also entails very different things for different people, so it depends what you intend to do in ML

If you just mean being a practitioner of ML (e.g. at a company), then the transition is very easy and mostly comes down to learning how to use the software tools and some of the common tricks and practices, and then convincing a company to hire you. There will be no intellectual barrier to learning those things.

But research in ML is just as difficult a field as any, and certainly far more competitive than most.

[neat lintel]

Why do universities expend so much effort silo-ing knowledge

[leaden torrent]

youre gonna have to be a bit more specific than that

what do you mean by 'universities'? admin? profs/researchers? publishing companies?

[neat lintel]

Mainly the structure of degree-granting programs

[leaden torrent]

what efforts are you referring to? knowledge in what fields?

[neat lintel]

Most universities, for example, don't offer post-bacc.

And when they do, it's primarily provided for people who want to get into medicine

[leaden torrent]

oh sure

part of that is funding incentives iirc

[neat lintel]

christ

[leaden torrent]

public unis get subsidies based on how many full degree students they have

so theyre not incentivized to take in others and usually charge more if they do

private unis dont suffer as much here but even then, things like uni ranking metrics like usnews

and scholarship requirements

still incentivize 4 year programs over anything else

[neat lintel]

I mean, I guess there is the GRE -- and if I'm really incensed take a year "sabbatical" and "do nothing"

I feel like universities should probably look at lateral movement in the sciences, because otherwise the knowledge creation aspect will just turn into humanities/doctrine crap

I mean, I would assume

[dawn forge]

Is there anyone good at math and physic the same time

[neat lintel]

lol

[fair mural]

physicists i would hope

[neat lintel]

i wonder if maths guys know how to make a hand-turkey

[dawn forge]

how do you called moved on a circle trajectory with the same speed?

[neat lintel]

uniform circular motion is what they probably call that

the acceleration is like $v^2 \over r$

[fathom swallow]

Lysh

[dawn forge]

so if i projected on the direction of Ox what is it called

[neat lintel]

tic-tac-toe? also... what?

[dawn forge]

harmonic oscillation?

like this bruhh

[neat lintel]

I don't know what "in the direction of Ox" means

[dawn forge]

Reference system

like Oxy

have u studied it in physic

[delicate knoll]

in that case there is not vector acceleration to change the velocity magnitude,only acceleration vector.
so they call it uniform circular movement.

[dawn forge]

okay

but

[delicate knoll]

do you mean ortogonal plane?

[dawn forge]

yeh bruh

finally

[delicate knoll]

so you wanna graph the result of the function?

[delicate knoll]

bruh, my brain´s ram is stuffed.

[dawn forge]

can you help me transle this on google because i m so stupid at eng

[delicate knoll]

please, could you rephrase you question, boy?

i´ll do my best to help understand it.

[dawn forge]

tks

[dawn forge]

ortogonal plane

là hình chiếu của chuyển động tròn đều lên trục Ox đúng không

like in this pic

[delicate knoll]

WHAT? please dont lemme think i am wasting time.

[dawn forge]

ortogonal plane is the projection of uniform circular movement on the Ox right?

and i dont understand why "ortogonal plane is the projection of uniform circular movement on the Ox" but ortogonal plane still have acceleration

[delicate knoll]

so, it is asking if the x´s coord of that yellow ball, has the projection on the x-axis.

[delicate knoll]

do you know what is ortogonal?

[delicate knoll]

he refering the x coord on the yellow ball in the x-axis.

[dawn forge]

it is a kind of movement that have a limit in space and repeat a lot of time around a balance point

is it the same definition as u

[delicate knoll]

what? i could wrong i thought orthogonal was just generalisation of parallelism.
that would be harmonic movement,a physica phenomenon

or could i be wrong?

[dawn forge]

bruh

sorry for wasting your time

but when i have got a better english

i will ask again

thank for your time

[delicate knoll]

hey waits, you english seems to be good.

what the question asking if the projection on x-axis is right.

[delicate knoll]

when it was talking about "ortogonal plane" he means the plane formed by two intersecting line with 90 degree angle

[dawn forge]

right

https://www.youtube.com/watch?v=bmGqhM-tUk4

this is what i want to ask about

[delicate knoll]

ah, so you wanna know about harmonic oscillating movements ...right...

[dawn forge]

bruhh i think ortogonal plane meant harmonic moviments

bad English

[delicate knoll]

what? that does make anysense.
orthogonal plane is from geometry!

oh

pardon, it was just mistake

little mistakes with communication. You´ve learned!

[compact tartan]

physics also ends here

all of physics is harmonic oscillators

[dawn forge]

in physic we use orthogonal plane to make different velocity into a line by using sin cos tan so we can easy to calculate bruh

[delicate knoll]

but that not means the orthogonal planes is a harmonic oscillator.

it a tool to help understand and graph the phenomena

[dawn forge]

like in this pic M1=cosMOM1*M

[delicate knoll]

quantum mechanics?

...

[dawn forge]

yeh

[compact tartan]

same by quantum harmonic oscillator

quantum field theory? imagine harmonic oscillators at every point in space

[dawn forge]

i gonna sleep thanks for help i will comebak tomorrow

[delicate knoll]

my god, you got me there. harmonic oscillators...

[dawn forge]

so tired

bad English + Physic = death

[delicate knoll]

no, it equals to the learning process

[dawn forge]

Add friend me bruh

How old re u

[delicate knoll]

welcome to my friend list.
i have tea and cake

(virtually...cake and tea,but well,you can grasp"

[delicate knoll]

19 years old

[dawn forge]

So now you re in college

[delicate knoll]

computer science.

i pass on the exams just one time. then got into uni.
i´ve need to make that exam again. it just first time.

i was bad only in history... man

[dawn forge]

that cool

So what is your job

Code?

[delicate knoll]

and the rest of humanities...

[dawn forge]

[delicate knoll]

but i got 720 on the redaction...

speaking about the Aristotle, a bit

[dawn forge]

Google translate don't know what is Arislotle

What is it

[delicate knoll]

i am IT technician(fancy name,hum?). do some computer hardware stuff recently.

and software too

and the clients got virus from unknown place.

or dont know how to boot up the computer the right way.

[dense sorrel]

I think most of them get viruses watching some questionable videos

[delicate knoll]

and he was that,humm, philosopher.https://en.wikipedia.org/wiki/Aristotle

[dawn forge]

Hmm so do you recommend any good virus scan app?

[delicate knoll]

my job not related that, but i do some C,C# and bit C++. i have this,humm, humble ascii engine.

[dense sorrel]

c++ was damn hard for me

[dawn forge]

I know a little bit c++

[dense sorrel]

i respect you for learning that

[dawn forge]

I used to study pascal but now pascal is old

[delicate knoll]

it was fun, C is fun and C++ is fun too. it makes me think more about algorithms
but my major language is C#

i have this ascii games in C#

now i am trying to create some fancy 3d

[dawn forge]

Wow

Where re u from dude

I'm from Vietnam

[delicate knoll]

well, normally, i would recommend to well "be you own app scam".
but , avast seems to be decent,on win10

[dense sorrel]

I'm from south korea

wait that wasn't a question for me

[dawn forge]

Nah i like South Korea

[delicate knoll]

from good old,Brazil

[dawn forge]

Nice i don't have win 10

[delicate knoll]

south korea? humm, you have the most internet speed.

[delicate knoll]

good ol´ win7?

[dense sorrel]

but internets censored here

[dawn forge]

Brazil

[delicate knoll]

it nice to meet you,dear

[dense sorrel]

and government sites require third party softwares to function

nice to meet you too

[dense sorrel]

i like vietnam too

i've actually travelled to hanoi a long time ago

[dawn forge]

Yeh

[delicate knoll]

Welcome to our math server. nice to meet you,dear!

[dawn forge]

[dense sorrel]

but I was like 6 back then so i really dont remember anything

[dawn forge]

Okay

Hmm

[delicate knoll]

i think there is still a version of avast for win7

[dawn forge]

I'm gonna sleep it is 11pm

[dense sorrel]

its 1 am here lol

and i have to wake up at 5

im screwed

[toxic schooner]

[dawn forge]

Me 5:30

[toxic schooner]

,ti mark

[fathom swallow]

User cancelled member selection.

Mar 29, 2022, 3:58 PM

[delicate knoll]

well,i think you brain would be fine-ish with 3 hours of sleep.
if you do that only rarely.

[toxic schooner]

,ti mark noel

[fathom swallow]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[dense sorrel]

hi

[toxic schooner]

hello 👋

[dense sorrel]

ti --set

[dawn forge]

Wah?

[toxic schooner]

the comma

[dawn forge]

3hour is enough?

[dense sorrel]

,ti --set

[toxic schooner]

3 hours of REM sleep

[dawn forge]

Hi

[delicate knoll]

sleep is good for the brain!
we humans so we need to rest;biological beings,anyways.

[fathom swallow]

Your timezone has been set to Asia/Seoul!
Your current time is 12:59 AM (KST) on Wed, 30/03/2022.

[toxic schooner]

not just 3 hours of sleep

[toxic schooner]

hi

[toxic schooner]

oof

probably should go sleep

[dense sorrel]

im currently doing military service

[toxic schooner]

lol

[dense sorrel]

but not in the army

[toxic schooner]

u too?

[delicate knoll]

if he manager to get in this stage,if this little time, so the brain could still do some cleanup.

[dense sorrel]

yep

[toxic schooner]

(im not doing service, coz im not in SK)

[toxic schooner]

true

[dense sorrel]

tbh military draft is one of the worst aspects of south korea

[toxic schooner]

but its not easy to get into REM sleep instantly

[dense sorrel]

though I have been extremely lucky and got a easy job

[delicate knoll]

man, if the general knows you are wake, what he would do?

[toxic schooner]

u have how much time left in service?

[dense sorrel]

it ends next november

got a long time

[toxic schooner]

ur in uni?

[dense sorrel]

ye

p

[toxic schooner]

2nd year?

[dense sorrel]

yes

[toxic schooner]

damn i guessed that

[delicate knoll]

is south Korea dictatorship?
sorry i donk remember well some of the geography class

[dense sorrel]

I was a sophomore before leaving for military

[toxic schooner]

noice!

i see

im a HSer

[dawn forge]

How can you are wake bruh

[delicate knoll]

humm, at least it not communist...

dunno

[dawn forge]

I don't care about dictatorship but South Korea have good food

[dense sorrel]

which food do you like

[dawn forge]

Spicy noodle Black bean noodle spicy chicken

Spice food

[dense sorrel]

which type of spicy chicken?

one that is sticky and has sweet flavors on it?

[dawn forge]

Chicken feet with no bones

[dense sorrel]

oh

thats pretty interesting

so you like 닭발(dakbal)?

[dawn forge]

With cheese on it

[dense sorrel]

so you have pretty trendy tastebuds lol

[dawn forge]

Don't know how it called but i like it

[dense sorrel]

I like pho with a bunch of corriander in it

but koreans don't use corriander which is a shame

[dawn forge]

They just sold trendy food here not alot of type

[dawn forge]

Wah?

Idk that

[dense sorrel]

people say that it taste like soap

I am the only one who likes it among my family

[dawn forge]

Bruhh

Corriander here we have a lot of kind

and i don't like spring onion

[dawn forge]

But they put big spring onion on soup right

[dense sorrel]

dunno if it is spring onion or leek

but yes they do

leak

[dawn forge]

Baro onion?

[dense sorrel]

idk about that

[dawn forge]

[dense sorrel]

btw how did you get into learning mathematics

[dawn forge]

I'm studying physic and there are some math idk

So i try to find some server that i can ask

[dense sorrel]

i changed major from economics after taking a semester of math courses

i would like to learn physics but don't know where to start

some people say that I have to study high school physics before tackling university physics textbooks

others say that i should dive straight into college textbook

[dawn forge]

I'm in high school

[dense sorrel]

oh

high school is a good time

[toxic schooner]

not for me

[dawn forge]

Grade 10

[dense sorrel]

grade 12 was hell for me

competition was literally hellish

[dawn forge]

Hmm

I have school tomorrow so I'm gonna sleep

Bye

[dense sorrel]

bye

[dawn forge]

[toxic schooner]

it is hell for me as well

[delicate knoll]

classical mechanics...

[delicate knoll]

on, in korea culture, they seems to be get hard on people to study more and more?

[dense sorrel]

actually, they teach little concepts

[delicate knoll]

sorry, because i hear somewhere the korea parent tends to be very "hard to pleasant"

[dense sorrel]

but design test questions to get people wrong

[dense sorrel]

they are especially like that when the kid is little

but as they grow up parents realize the truth and become more lenient in most cases

but some parents are just insane/cruel

[delicate knoll]

but they tends to put pleasure to kids get into college, have the greatest grades...

[delicate knoll]

oh,my God.

[dense sorrel]

actually they got much more lenient compared to like 20~30 years ago

unemployment is high and house prices have soared too much

now parents know that studying doesnt equal to being successful and college isn't relaly that important

things started to change

[dawn forge]

That is scare for a teenager like me

[dense sorrel]

its even scarier for me as a college student

I have 4 years left till I have to jump to a hellish job market

[dawn forge]

The biggest thing make me worry is that when i finished my study i didn't have a direction to my life

[dense sorrel]

thats what happened to me

[dawn forge]

I don't know what's to do

[dense sorrel]

you have like 3 years

if you go to college, you get additional 4 years

[dawn forge]

That really scare

[dense sorrel]

you should enjoyu your life now

[dawn forge]

[dense sorrel]

you never get to enjoy life like now after getting into college

[dawn forge]

Undefined future

Now sleep and dream

[neat lintel]

In the future we'll probably teach the most fundamentally known, rather than the historical method

Like, momentum is some emergent property of standard model particles, we should teach that way, rather than; "this was obvious because we were trying to light each other on fire with trebuchets"

Modern schools all employ this historical hegemony that I think is badly informed.

Makes everything look disparate and unmemorable.

[karmic zealot]

friedberg's linear algebra book just straight up proves one of the exercises with the hint lol

section 2.1, exercise 39

but it doesnt sit right with me how

you're asked to prove that there's a function that's additive but not linear

but then you use a result which states there exists a linear transformation of a certain kind

and then claims that the linear transformation is the function we want

what??????

and this is exercise 34

[ancient flame]

those capital letters look weird af

they're like verdana font

[karmic zealot]

i know but look at the claim !!!!

that's the weirder thing

[ancient flame]

I don't understand it!!!

idk linalg

[karmic zealot]

you dont even need to

oh actually yea you do

[ancient flame]

lol

if I knew what a basis was I could understand it

[karmic zealot]

like what even is it trying to say, claiming a linear transformation exists and then saying it's not linear

[ancient flame]

oh

lol idk

[long matrix]

how much of lag do u know

[ancient flame]

I know what vectors and matrices are and I can work a bit with vector operations and such

[hushed turret]

isn't this just saying a linear transformation is uniquely determined by how it transforms the basis vectors

[long matrix]

matrix represents a linear transformation

yay or nay

[ancient flame]

I think so

[long matrix]

T : R^n -> R^m

T(x) = Ax

for some constant matrix that is m x n

[ancient flame]

mhm

[karmic zealot]

oh you're supposed to look at the pic above that, that one is just reference

[long matrix]

As said above, you can figure out what T does

if you know what T does to 'basis' vectors

[ancient flame]

I see

[long matrix]

So sticking to R^n euclidean space

[ancient flame]

what is a basis vector

[long matrix]

the 'standard' basis is

in R^3

(1, 0, 0)

(0, 1, 0)
(0, 0, 1)

[ancient flame]

oh ok

[long matrix]

ok? And this generalises to R^n

[ancient flame]

ohhhhhh

I see

[long matrix]

this is known as the standard basis for euclidean space

[ancient flame]

they're unit vectors

[long matrix]

well this is just the standard choice

[ancient flame]

oh

[long matrix]

This particular choice has unit orthogonal vectors

known as an orthonormal basis

[ancient flame]

what's orthogonal

[long matrix]

perpendicular

[ancient flame]

oh ok

[long matrix]

dot product of any pair = 0

[ancient flame]

yeah

[long matrix]

Anyways, lets stick with this

I will call the 3 basis vectors in R^3

e1, e2, e3

[ancient flame]

mhm

[long matrix]

Now, if we know what T(en) is for any n = 1, 2, 3

Our claim is we know what T(v) is

[ancient flame]

I see

[long matrix]

The special property of basis vectors is, any vector in your vector space can uniquely be written as a linear combination of the basis vectors

[ancient flame]

what is v?

a vector?

[long matrix]

So let v = (4, 2, 3)

[fair mural]

yes

[ancient flame]

ok

[long matrix]

v = 4e1 + 2e2 + 3e3

And

[ancient flame]

mhm

[long matrix]

T(v) = 4T(e1) + 2T(e2) + 3T(e3)

Because T is a linear transformation

[ancient flame]

alright

[long matrix]

So this generalises

[ancient flame]

I see

makes sense

[long matrix]

So one handy result is

The matrix A

which represents a linear transformation

The columns of it are exactly

[hushed turret]

oh, huh. that is dodgy.

[long matrix]

T(e1) | T(e2) | T(e3)

The columns are exactly the images of the basis vectors

[ancient flame]

I see

[long matrix]

glued together

[ancient flame]

ooooo

and the rows?

[karmic zealot]

yea it's confusing at the very least

[long matrix]

uh

the rows are the rows

[ancient flame]

oh

lol

but alright that makes sense

[long matrix]

This idea is for a matrix represented in the standard basis in R^3

But hmmm

T : R^n -> R^m
T(x) = Ax
A is m x n matrix
You can choose a basis for R^n (domain), and choose a basis for R^m (codomain)

And you can make your matrix A represented differently

[ancient flame]

oh

[long matrix]

This is a bit hard to explain without explicit example

[ancient flame]

lol

[long matrix]

Like in a standard basis, the transformation might be a shear

[ancient flame]

a what

[long matrix]

But viewed in other coordinates (basis), it might be a rotation

[hushed turret]

ohhhhh
huh
i think i kinda understand it? @karmic zealot

[ancient flame]

woaj

[long matrix]

The red -> blue is a shear

[ancient flame]

woah

[long matrix]

(this is a type of linear map for R^2 -> R^2)

[ancient flame]

oh I see

[karmic zealot]

also there's a result earlier in the book, exercise 37, stating that for every pair of vector spaces over Q, if there is an additive function between the two spaces, the function must also be homogenous. and we have here a R as a vector space over Q. so that doesn't work out either!

[hushed turret]

so T is linear when multiplied by any rational
but it's NOT linear for all reals

you only use 34) to show that T is additive

[long matrix]

In fact, there's a theorem which says any linear transformation can be made to look like a 'stretch'

[karmic zealot]

oh it could be that

[long matrix]

by choosing basis

[ancient flame]

ah

[karmic zealot]

thank you!

[long matrix]

This is related to eigenvectors

[hushed turret]

take that with a grain of salt tho i don't wanna mislead you

[ancient flame]

idk what those are

[long matrix]

T(x) = kx

for k a scalar

You are looking for solutions to this equation

for both k, x

T a linear transformation

[ancient flame]

oh

[long matrix]

k is known as the eigenvalue
The x which correspond to specific k are known as eigenvectors

[ancient flame]

oh interesting

[long matrix]

And choosing the eigenvectors to be our basis is a smart choice (when possible)

Because then our transformation matrix will be 0's everywhere except the main diagonal

[karmic zealot]

yea i think that 'c' term there isn't necessarily rational so it's just saying it's not linear over the reals. then it makes sense

[ancient flame]

oh ok

why exactly

[long matrix]

why which

[ancient flame]

why will the main diagonal be nonzero

[long matrix]

they can be 0

[hushed turret]

i guess that's why it's just a hint and not a full solution
doesn't specify what fields the numbers belong to

[long matrix]

The requirement is everything else is 0

[ancient flame]

but why can they be nonzero

[long matrix]

The diagonal can be whatever

uhhhh im handwaving , but lets plow on

[ancient flame]

alright lol

[long matrix]

$A = BDB^{-1}$

[long matrix]

Ok, so you have a transformation matrix A

represented in say the standard basis

[ancient flame]

mhm

[long matrix]

T : R^n -> R^n

T(x) = Ax

[karmic zealot]

ah so i was wrong to assume that it just straight up solved its own exercise lol

[long matrix]

Now we say A is diagonalisable

[long matrix]

If this is possible for some matrix B

[ancient flame]

cantor!

[long matrix]

Where D is a diagonal matrix

same name, doubt

[ancient flame]

oh lol

[long matrix]

To change basis in general, you can multiply a vector by the change of basis matrix

A change of basis can be viewed as a linear map on the basis vectors, basically

[ancient flame]

ah

[long matrix]

Say we have our standard basis (1, 0) and (0, 1)

We might want our new basis to be (1, 1) and (-1, 1)

[ancient flame]

alright so we multiply by those basis vectors

[long matrix]

eh

multiply by the change of basis matrix

[ancient flame]

oh

[long matrix]

I think I've reached the limit if not passed it already of what can be handwaved

[fair mural]

shuri trying to teach LA in 10 minutes

[ancient flame]

lmao

rip

[hushed turret]

sorry gmod, how much math do you know
in the least offensive way, i thought you probably knew lots of stuff because you've done talks in #events

[ancient flame]

nono ur good

[errant furnace]

gmod kinda smart ngl fr

[ancient flame]

I know calc 1 very well, calc 2 fairly well, and some calc 3

some set theory, some number theory

some topology

some real analysis

currently learning group theory

[hushed turret]

cool beans

[ancient flame]

hbu

[long matrix]

uve been fooled

gmod pretending to be phd

[errant furnace]

Dr gmod

[ancient flame]

lol

[long matrix]

if uve seen generators for groups, then basis vectors for vector spaces are kinda like that (except they have stricter requirements)

[ancient flame]

oh okay

makes sense

[long matrix]

The better analogy is

• generating set for group
• spanning set for vector space

[ancient flame]

since vector spaces are like stricter groups

oh ok

[long matrix]

Basis has the extra restriction that you can write every element uniquely

The underlying structure for a vector space is an abelian group (under the addition operation of the vector space)

On top of this a scalar multiplication is defined

But hmmm that analogy has its limits (spanning set for vector space is rarely a generating set for the underlying additive group)

[ancient flame]

I see

[hushed turret]

i am a small child and this is all self-studied so how much i "know" it is up for debate:

calc 1 and 2 im good i think
lin alg up to eigenvectors pretty much
calc 3 up to triple integrals
very little analysis i started reading rudin
a bit of number theory (richard borcherds has some banging lectures on yt)
and a tiny bit of group theory started reading artin
i think that's it

[ancient flame]

oh ok that's similar to me

[hushed turret]

and naturally i know random things from wikipedia.

[ancient flame]

same lol

[hushed turret]

and random things from this discord as well, i suppose

[karmic zealot]

oh wow same

i also know only a tiny bit of math

[hushed turret]

wheel algebras @ allyc

[karmic zealot]

and still only studying on my own

but no number theory

[hushed turret]

wikipedia binges are a common affliction

[karmic zealot]

because it's evil

[karmic zealot]

true

i dont like it because it makes me sound like i actually know more than i do

and i don't wanna be a pretentious fuck, not even unintentionally

[ancient flame]

guys I found a desert temple

[hushed turret]

eh, nothing wrong with indulging in curiosity.

though i do see where you're coming from

[hushed turret]

you what?

[ancient flame]

lol

[hushed turret]

the understanding you get from studying a textbook is defo worlds apart from reading wikipedia

i'd like to think i am aware of my own ignorance, but i suppose that's not for me to judge lol

[karmic zealot]

wise words

but sometimes i go on wikipedia just to get a better idea of things

it can be helpful especially because it's not written like a textbook

[hushed turret]

yeah. it's especially good for checking definitions of various things when you want a refresher

1000 times easier than finding the correct textbook page

[karmic zealot]

like not using concepts yet unintroduced to the reader

and sometimes i get to see things ahead and from a different angle i guess

[hushed turret]

yep

also (somewhat) good for trying to make sense of the conversations in #discussion

[karmic zealot]

true

almost like learnig a language as a child

we're switching channels often lol

[hushed turret]

you know how people talk about mathematical maturity?
i feel like a mathematical infant the majority of the time tbh

[karmic zealot]

i feel like a mathematical crawler

[hushed turret]

a large vocabulary (for my age), so to speak, from various sources but little fluency

[karmic zealot]

true

[hushed turret]

the edit lmao

[karmic zealot]

yea

i realised i dont know math

i can derive theorems in a textbook from definitions and axioms, that's about it. not so confident about my (nonexistent) ability to actually problem-solve though

[near fox]

This is a natural feeling to have

Out of undergrad I felt like I had been exposed to many things but understood very little

After grad school I felt like I was starting to understand stuff better, after seeing things again for the second, third, fourth time

And now years after that, I'm only starting to feel "oh hey I might be really fluent with some of this"

[hushed turret]

after grad school
so what you're telling me is i have about 10 years left till i feel somewhat confident in maths

[karmic zealot]

oh wow such a point exists??

[near fox]

Math is only worthwhile because it is about difficult concepts. If it were that easy to understand then it likely wouldn't be nearly as powerful

[karmic zealot]

thank you oh wise mip chunk

[near fox]

Also I sometimes still have dreams about not figuring out some math problem on an exam, even though I haven't been in school in a long time...

So I think that anxiety is still inside me

[hushed turret]

what are you doing now?

[karmic zealot]

i still dream about failing an exam even though i've been out of school for at least half a decade

[near fox]

I'm a mathematician, though I do applied work for industrial purposes

[hushed turret]

cool beans

[karmic zealot]

:o

[hushed turret]

wait what are you doing now

[karmic zealot]

waiting until i move out and go back to university some place else, maybe abroad

dropped out of physics because of mental health, decided to go back but covid hit, things came to a halt, and then some pretty big political stuff happened and uni still isnt operating again. has been that way for nearly 2 years now

[hushed turret]

oof

[karmic zealot]

and in that mean time, i thought hey math is kinda nice so i guess i'll do math instead

[hushed turret]

that sounds pretty rough for you but it's nice that you've found something to do

[karmic zealot]

i'm glad i found something to do as well

[worn garnet]

Does anyone know what a bridge program is ? https://math.virginia.edu/graduate/bridge/

Seems like its very similar in spirt to a TCC been looking into doing a bridge program before doing anything else

[bronze pelican]

Between undergrad and grad school usually

[worn garnet]

ahh kk makes sense I was talking to one of the graduate students and he recommended that I should do a bridge program get a wide mathematical background then go fro mthere

He mentioned that american undergrads don't get the chance to "seeee" everything or get a taste of what would be considered a wide range of math

[dense belfry]

I think it's otherwise called a postbacc

[bronze pelican]

Yeah cause some people are not prepared for grad school right out of undergrad, or they took a break from school and need something to catch up b4 grad school idk

[dense belfry]

but also some bridge programs have guaranteed admission to the phd program

if you do well enough

[frozen venture]

Anyone have any tips they'd like to share regarding REU applications?

[worn garnet]

Just apply and have an open mind maybe try doing something applied to get an idea of the kind of things that are going on that involve math but are outside of math

[worn garnet]

Do you know the history of bridge programs btw they seem like a recent thing in the US. Upon talking to that grad student I mentioned that was the first time hearing about them

[dense belfry]

no, I think they're pretty rare

I was looking at the upenn one when I was doing grad apps 3 years ago

[worn garnet]

I was told there good if you have a low overall gpa but a good math/technical background

[worn garnet]

But i'm considering the postbacc espcially at places like UoW where get exposed to a wide array of math

[devout nacelle]

This might be helpful: https://mathoverflow.net/questions/17209/consequences-of-the-riemann-hypothesis

[vivid halo]

there's a really impressive number of crank replies here

[devout nacelle]

The comments on the question?

[vivid halo]

yeah

[devout nacelle]

Some of them seemed to be really weird even to me, yeah

[vivid halo]

Riemann Hypothesis is the discrete version of Calabi-Yau theorem as solution of Ricci flat metric. You need to define suitable discrete Ricci curvature as Infinite sum of Riemann series. Then You need to develope discrete monge Ampère Equation. This must be the method for solving Riemann Hypothesis.

lol, lmao

[devout nacelle]

Hahaha

Yes, this is the one I found odd

I wouldn't have discarded it until I read the last line

[worn garnet]

Speaking of which is there any cs equivalent of the Riemann Hypothesis ?

[karmic zealot]

well, "cs-equivalent of the Riemann hypothesis" is a very vague phrase but https://en.wikipedia.org/wiki/Millennium_Prize_Problems?wprov=sfla1

[wicked ore]

Aren't there some primality tests that depend on the truth of the Riemann hypothesis?

[weary garnet]

is it just me or is strang's linear algebra course kinda... useless

it barely covers the theory about abstract vector spaces which made me overconfident when trying to study quantum mechanics

the concepts he emphasises i feel can be learnt in a few page long summary

[toxic schooner]

isnt strang a computational LA book

u should try friedberg

or LADW

[weary garnet]

yeah but i didn't know that beforehand lol

[toxic schooner]

they cover more theory

[toxic schooner]

eh, its alright

no harm has been done

[weary garnet]

but even for a computation based text

there's no way engineering or CS students can't handle slightly more theoretical linalg

strang is really slow paced and I've never had any linear algebra background

[toxic schooner]

CS students most definitely can i think

[toxic schooner]

Oof

[torn willow]

Strang's la,(both book and course) is for people who just want to rush through Linear algebra

It isn't supposed to teach people Linear Algebra but how to apply the algorithms that are useful in applied math

It's supposed to be "beginner friendly"

But it doesn't teach you anything like how to think or solve problems that aren't already solved

[fair mural]

Proof that a linearly independent set of vectors cannot have more than dimV vectors in it

Suppose dimV = n, then a basis for V looks something like v1,v2,…,vn and any vector v in V can be uniquely represented as v = a1v1+a2v2+…+anvn for some coefficients ak. Suppose we have a system of n+1 vectors a1v1+…anvn+a_{n+1}v_{n+1} for some v1,…,v_{n+1} in V. then v_{n+1} can be represented uniquely as b1v1+b2v2+…+bnvn for some coefficients bk. therefore the system a1v1+…anvn+a_{n+1}v_{n+1} is linearly dependent.

short proof i randomly thought of

could someone tell me if this proof works?

yes i know the “uniquely represented” part was probably unnecessary lol

[surreal sapphire]

you use the same variables for a basis and for your set of n+1 vectors?

[fair mural]

oops

Proof that a linearly independent set of vectors cannot have more than dimV vectors in it

Suppose dimV = n, then a basis for V looks something like v1,v2,…,vn and any vector v in V can be uniquely represented as v = a1v1+a2v2+…+anvn for some coefficients ak. Suppose we have a system of n+1 vectors b1v1+…bnvn+b_{n+1}v_{n+1} for some v1,…,v_{n+1} in V and coefficients bk. then v_{n+1} can be represented uniquely as c1v1+c2v2+…+cnvn for some coefficients ck. therefore the system b1v1+…bnvn+b_{n+1}v_{n+1} is linearly dependent.

shoot

@surreal sapphire how about now

many letters

[surreal sapphire]

did you change anything lmao

[fair mural]

yes the letters so the coefficients are different

for each system

that’s it though

[surreal sapphire]

my issue was you fix a basis {v_1, ..., v_n} and then you seem to choose arbitrary vectors v_1, ..., v_{n+1}

[fair mural]

i added another vector into the system to show that the new system can’t possibly be linearly independent

[surreal sapphire]

ok

ye, that works

[fair mural]

nice

[surreal sapphire]

the wording is a bit odd

[fair mural]

well i just typed it to get it out of my head and on paper really, didn’t think about the wording much

[flat harbor]

im not exactly sure what you mean by "system of n+1 vectors b1v1+...b1vn+b_(n+1)v_(n+1)"

[fair mural]

v1,…,vn are the same vectors from before, v_{n+1} is a new vector

[fair mural]

.

that’s about all i can say

[flat harbor]

then what youre showing is that adjoining a vector to a basis makes it a linearly dependent set

it doesnt make a statement about any arbitrary system of n+1 vectors

[fair mural]

ok never mind then

[flat harbor]

which is what i believe you want to start from

[fair mural]

i tried

[flat harbor]

its ok

[surreal sapphire]

ye, you can fix this with some words though

[fair mural]

like what

[surreal sapphire]

if they are already linear dependent, there is nothing to do, otherwise n of them are linearly independent thus form a basis ...

the thing is

the word basis already implies this right

[fair mural]

i guess so

[surreal sapphire]

so you show this when showing that dimension makes sense

[fair mural]

could i edit it a bit and resend in a minute

[surreal sapphire]

you have to show that finitely generated vector spaces have minimal generating sets of same cardinality

[fair mural]

ok that’s a lot of fancy words for me to digest if i gotta be honest

[surreal sapphire]

and then you show that if one of them satisfies a linear relation in the others, you can reduce the size of the generating set

this is what you did

ye, the wording becomes the main issue 😛

because if you say dimension n, you are already saying that any set of n+1 vectors must be linearly dependent

eh, kinda

at least if you think that a vector space cant have dimension n and n+1 at the same time

[fair mural]

ok never mind i thought i had something but i didn’t lol

[olive panther]

#help-7｜zen1thxyz

[long matrix]

#cats

[neat frost]

#❓how-to-get-help

[terse flax]

#help-2

[frigid lark]

If you guys write big articles in Latex, is it normal to have many warnings? Do you ignore them sometimes?

[fair mural]

i get warnings all the time in overleaf but i mostly ignore them

if it’s something big it would be noticeable without the warning anyways

[frigid lark]

If I make two line breaks with \ I get a underfull hbox badness 10000 warning. The warning is so pointless for me....

[fair mural]

yeah same

[surreal sapphire]

i deal with my warnings

[fair mural]

i do not

[surreal sapphire]

you shouldnt use \\ to break lines

[frigid lark]

whatelse?

[fair mural]

[surreal sapphire]

press return twice?

[frigid lark]

There is this "Einschub". Are you okay with that?

[surreal sapphire]

you can do \smallskip \medskip \bigskip for skipping

or adjust \parskip

\\ is only to be used in special environments (where it is fine)

additionally you can adjust the warnings themselves

if you have overfull hboxes a lot but you think they are fine

you can adjust the badness level or something

[gritty gazelle]

is 3.6 gpa good

[dense sorrel]

has anyone here used zorich's calculus

?

i mean analysis by zorich

[dense sorrel]

depends on univeristy/courses you've taken

[toxic schooner]

it looked interesting to me

i didnt try it

[dense sorrel]

I think that the textbook covers most out of all undergraduate analysis textbooks

[toxic schooner]

but i would probably do it for multivariate analysis

[fair mural]

are the exercises in ladr known to be hard? i feel like i’ve heard that they are

[dense sorrel]

tbh i didn't find it that challenging

tho i've only done some chapters

maybe cuz i did it for review tho

[toxic schooner]

people do say that

and also no determinants

so bad book

[dense sorrel]

i'd recommend another book though

[toxic schooner]

same

i would rec friedberg

[dense sorrel]

theres no need to put in too much effort for linear algebra

[toxic schooner]

this lol

[dense sorrel]

i don't meen that you should rush over it tho

[toxic schooner]

also this

[dense sorrel]

I think that spending a semester for theorems and a month for applications like svd is best

[toxic schooner]

svd?

[dense sorrel]

singular value decomposition

[fair mural]

i can’t tell if i’m not trying hard enough or if this book just doesn’t explain stuff well

@rotund steppe sadcat

[dense sorrel]

which book?

[fair mural]

ladw

[dense sorrel]

i don't recommend ladw tbh

just go for friedberg

especially if you are learning the subject for first time

[fair mural]

i’m this far and i don’t feel like switching

[dense sorrel]

nah

i don't think that you will take that much time in switching

[fair mural]

everything before diagonalization has been explained decently well

i’m gonna stay with it

[dense sorrel]

then you can skip those parts in friedberg

[ancient flame]

when you graph a complex number are you supposed to graph the point or the vector

[long matrix]

depends on the weather

[neat frost]

Don’t graph either

[surreal sapphire]

whats the difference

[ancient flame]

out of curiosity

[grave sable]

I have a question about finite state transducers and regular expressions encoding. Which channel would fit better to ask it?

[devout nacelle]

#foundations might be the best fit

@grave sable

[grave sable]

thanks!

[fervent pebble]

so say i wanted to go to college in europe, as an american student in the IB program

how would i go abt it?

just like

apply?

[surreal sapphire]

first of all good luck finding a bachelor degree offered in english

[fervent pebble]

fuck me i forgot abt other languages

hmmm

i'm taking german in school and am like

conversational

barely

hmm

[quasi zealot]

I wish i could take Japanese

[surreal sapphire]

american moment

[fervent pebble]

i'm bilingual i swear

[long matrix]

what other languages

english and weeb is all i know

[surreal sapphire]

Ja, natürlich

[long matrix]

[dire mulch]

I know igbo. Tho not sure if people know that language.

[fair mural]

cringe

[dire mulch]

quantum, I don’t know why but a quick glance at your pfp looks like someone’s face is melting off(maybe stretched out).

[fair mural]

,av

[fathom swallow]

quantum#6320's Avatar

Click here to view the GIF.

[velvet dagger]

Oh yeah I can see how the hair looks like melting skin at a distance

[deep mango]

[worn garnet]

I'm aware of P vs NP of course

[neat lintel]

https://www.sciencedirect.com/science/article/abs/pii/S2352673416300026

why would people say "a new phenomena" instead of "a new phenomenon"?

does it has meanings

since I have seen so many people say in this way

[toxic gale]

I mean, there's always the UK, right? Applying to the UK is really easy. There's just 1 single application and essay that is sent to all your choices via UCAS. IB is very recognised and shouldn't be an issue at all. Not sure about other parts of Europe.

[fervent pebble]

that's true but like

it's the uk

which is ew

no offense to any brits here

[toxic gale]

😂

They have some good unis though.

[fervent pebble]

i hear cambridge is good

although i'm probably too poor and have too shit grades to get there

[charred mortar]

Cambridge is very good lol

Although yeah super pricey without a scholarship

Imperial/UCL are also decent

Although again very pricey

[fervent pebble]

i also rly wanna go to nyu except i hate nyc

[charred mortar]

Lmao

[toxic gale]

Cambridge is one of top unis in the world for math, I think. Their entrance exam is also really damn hard.

And yeah, super duper expensive because the pound is too damn strong.

[stable patrol]

So the entrants get multi variable calculus?

[toxic gale]

No. The content isn't the hard part. It's the difficulty of the problem.

They only assume high school math, but they set university-style questions.

It you're curious, just go look up STEP past exam papers.

[stable patrol]

Alright

But first, I’ll have to finish my studies for this semester if I want to go beyond trig and probability

[neat lintel]

If someone can help with geometry proofs real quick can you dm me it shouldn’t take long

[neat lintel]

did anyone actually dm u?

Nope.

lol

[toxic gale]

You're probably more likely to get help by posting the question in one of the help channels than asking for people to DM you.

I'd like to think most people (including myself) keep their DMs only to talk with friends.

[neat lintel]

how do u know

[shadow glacier]

because in dms, people get gross and touchy

and are like can u do exam for me

or dm u at 1am asking for homework help

no one wants to become your dedicated answer generator

[neat lintel]

Any tips on how to re-learn Euclidian geometry? I can't make any sense out of what I was taught; especially the relationship of angles between different vertices

[toxic gale]

Exactly. When people DM you, they expect you to respond with an answer. When it's in the server, you can choose to respond. It's far less imposing.

That's why I've learnt just to keep DMs closed for any educational servers. 😂

[long matrix]

isnt that every uk uni - the pricey part

[charred mortar]

Yeah it prolly is

[neat lintel]

any? i am only in educational servers

[toxic gale]

Fair enough. I'm mostly in educational servers and servers for games I play.

[gritty gazelle]

Applying g to Australia is easier

U don’t need a essay

[toxic gale]

The person was asking about European universities.

Can't say I've tried applying to Australia. I don't think they have that many prestigious universities compared to the US and UK.

[ripe wasp]

i lived like 12 years in australia

and its hot af

[gritty gazelle]

uk obviously have oxbrdige but australia ione of the easiest unis tog et to

[charred mortar]

Australia unis are ok, but certainly not on the same level as the best of UK/USA

They’re a lot easier to get into indeed

[dense sorrel]

how about canadian ones

[charred mortar]

Also pricey for internationals too

I dunno about canadian

[dense sorrel]

oh okay

[toxic gale]

I mean, it depends on personal preference obviously, but I don't think being easy to get into is necessarily a good thing.

Top universities are hard to get into for good reason.

[gritty gazelle]

which uni did u go to

I go UNSW

its hard to get a 4.0 in australia

a lot of assessments

is 20 class test

20 class test

60 final

[gritty gazelle]

I'm from UNSW the courses there are hard as u could tell with our assessments

i want to apply for grad school

we dont get much opporutnity to write

publications as well only have honours project

[lime sorrel]

Uni here in Italy is so cheap

[old fox]

here too in Indonesia

even tho the best ranked one is this

[dense sorrel]

uni here in korea is fing expensive

i have to pay like 3000$ a semester

[toxic gale]

Uni here in Singapore is $9000 per year for citizens.

[dense sorrel]

oh

thats pretty brutal

do they offer loans or scholarship to compensate for that?

[toxic gale]

There's quite a few scholarships you can apply for.

I think universities here are fairly generous with giving out scholarships.

[dense sorrel]

hmm

[fervent pebble]

so does anyone know of any good math extracurriculars colleges would like that aren't competition math things?

[dense sorrel]

maybe research project?

[toxic gale]

Perhaps tutoring?

[frigid lark]

I pay 200euro per 6 months in Germany.

[outer vector]

it isnt math but how the heck do you determine which hemisphere is which is this image

[leaden torrent]

theyre labelled?

[outer vector]

yes

but

they are labeld on the line

so you could argue that its either way

[leaden torrent]

i assumed the line was the axial tilt

[outer vector]

it is

[leaden torrent]

not the hemisphere divider

[outer vector]

i am dum

welp

thank you lol

[outer vector]

thanks namin

[neat lintel]

can you help me with this question?

#help-21｜아리스킨충1

[long matrix]

#❓how-to-get-help tells you not to do this

[neat lintel]

ive pinged helpers

its been

30 minutes

[long matrix]

wow only 30 mins

[neat lintel]

yeah thats a long time

[long matrix]

ive seen people wait half a day for an answer

tough luck, buddy

[fervent pebble]

they also managed to wait half a day without pinging random ppl like four times

impressive, innit?

[bright hill]

I've once waited for days for an answer lmfao

those are rooky numbers

[outer vector]

Dude i am so sorry

I didnt keep the tab open becuasw i went outside

Do you still need helpm

[waxen lily]

get back inside 😡

[outer vector]

N-

NO

[vernal estuary]

Can anyone help me with a 2 geometry problems quickly.

[outer vector]

what grade level

[vernal estuary]

9th

[outer vector]

I can try, but its been awhile

Channel #

?

[vernal estuary]

Okay. I appreciate any help #help-19

[neat lintel]

no im fine

[elfin wigeon]

Why is the help system not working I put in a request and wait 3hours and then I get timed out and no one replies

[median zinc]

Find out what attracts people to reply.

[toxic gale]

It's working perfect fine. It just depends if people want to help. High quality questions tend to attract more help. Tell people what you tried and where exactly where you're stuck.

[fervent pebble]

help other ppl help you

have a good question, tell people what you've already done or tried

etc

[toxic gale]

Also I'd help, but geometry is beyond me.

[elfin wigeon]

Ok it just that I asked my cousin who did special maths in school and he couldn't help so I thought some one here could help

[elfin wigeon]

i can't really help as my math skills are only grade 9 and 10 so i won't be able to help as a lot of the questiosn are on complex topics

[fervent pebble]

that's not what i mean

[elfin wigeon]

what did you mean then

[cyan goblet]

help other ppl help you means like

be specific about your question

make your intention clear

[elfin wigeon]

ok

[fervent pebble]

i mean "provide as much information about your question as you can, so other people can help you better"

[cyan goblet]

tell them as much information as possible that's related to your question

[fervent pebble]

make it easier for them, basically

[elfin wigeon]

yeah thanks i worte everything i could think of

[toxic gale]

If you still don't get help, it could also mean that people don't know how to do the problem either. Maybe you can try posting in the more specific channels, like #geometry-and-trigonometry since I think people better at those topics tend to browse it more.

[elfin wigeon]

ok thats good advice i will try that

[normal sparrow]

why is epsilon of all symbols is used to mean infinitesimal?

whats so significant about the letter epsilon itself?

[pale orchid]

they use epsilon for error and delta for distance in some sense

but the letter itself is not important at all, you could use any other if you wanted

it's just standard practice

[normal sparrow]

ah that makes sense

just like how pi is chosen for what it is bcs it comes from the greek "perimetros"

[pale orchid]

i can't comment on that

[charred mortar]

You can swap the delta and epsilon if you want

It’s not recommended, but you can if you want

Oh wait I guess you’re moreso asking about perhaps the meaning behind the letter “epsilon” or something similr, in which case I’m not qualified either

[normal sparrow]

What exactly is multiplication if the two numbers are real numbers?

Its easy to see that multiplication is adding a number integer amount of times

[leaden torrent]

unique continuous extension of rational muliplication

[normal sparrow]

What is meant by unique

[neat lintel]

its just the multiplication derivied from how reals are made with rationals

unique because there is only one way to do it

you can think of multiplication as a function

Q x Q -> Q

on the rationals

you can extend this function’s domain and codomain in a unique way such that it equals rational multiplication on rational numbers

so if f:Q x Q -> Q is rational multiplication

we can say g: R x R -> R is the unique extension of this multiplication

and g(Q x Q)= f

[dense belfry]

Unique continuous extension

[neat lintel]

also for a useful notion

you can think of a change of basis

so how intger multiplication is repeated addition

you can think of rational multiplication in a similar way

so if you have a/b * c/d

it can be repeated addition of a/b , c*d times

but its not actually

because clearly that gives you the wrong numbers

so instead you can think of doing a coordinate transformation on one side of the input

and scale up by a denominator

and then the notion of repeated addition of a fraction still makes sense

alternatively you can just make this simpler and think of a/bd added c times

when this comes to real numbers you can convert multiplication by two reals into repeated addition if you want but its not very helpful for thinking about multiplication

its better to think in terms of areas

[near fox]

If you construct reals using Dedekind cuts then you don't need to invoke any sort of continuity to define multiplication (though of course it ends up being the same thing)

[shadow glacier]

bUt WhaT aBout rEaL ARithmeTic!!

yOu maDe thE reAls but YoU haVen't dEfiNed thE arIthMetic!

wHATZ e + π!!!!!!

[eager yarrow]

what they doin for dq today?

[normal sparrow]

What is the motivation behind the development of polynumbers?

[surreal sapphire]

what is a polynumber

[sleek urchin]

@bright condor Sorry for the ping as I cant reply in the channel anymore Dw, Im aware that my answer for number 1 is incorrect cause the correct answer wasn't in the choices soo I picked the one that's the closest~ I'll also approach my teacher regarding this. Thanks again

[delicate knoll]

today i thought i was hacked,because all my discord server icons is different

now i blue baby for helps

it all upside down, like another dimension