serious-discussion

[sleek wing]

average alliteration will not stop your defeat

[toxic schooner]

wew why did u do this

[fair mural]

WE’RE WINNING

[deep mango]

yep

too easy

i could even switch my vote and i bet we'd win again

[fair mural]

but then i’d have to… sully you

[toxic schooner]

yeah dont do that ryc

we need all the support we can have againt these blushy sulliers

[deep mango]

whoops, too late

[toxic schooner]

Noooooooooooooooooooo

[bronze pelican]

Get BLUSHYSULLIED on

[toxic schooner]

Fuck no

thats a monstrosity through and through

[simple raven]

http://math.univ-lille1.fr/~ramero/teaching.html

yeah

it seems very good

[deep mango]

cute

[toxic schooner]

what does this mean tho?

[neat lintel]

cum

[deep mango]

Digusting.

[neat lintel]

sperm

[deep mango]

[fair mural]

man i hope you get banned

[sleek wing]

Digusting

[toxic schooner]

[neat lintel]

i cant even say an opinion in 2022

[toxic schooner]

[limber thunder]

[vast surge]

So what do I put in my cv

I'm applying for reus and summer camps and don't know what to put in my resume. I don't have any research or publications, I'm an undergrad.

I TAed a little bit and took some math classes, but the math classes they'll see in my transcript I think if they need that

Do I just list books I read or something

[dawn bridge]

put that

also ur contact information

[vast surge]

Yeah I so far have my personal email and my school email.

Should I put my discord?

[dawn bridge]

skills u have
e.g. proficient in microsoft excel
languages if ur multilingual

anything that might be related to job

[dawn bridge]

probably not

discord is for like gamers

[limber thunder]

since it's for a REU I'd only put skills/achievements that are strictly relevant for a REU.

[dawn bridge]

unless you know the company actually uses discord i wouldnt put jt

[limber thunder]

like, not Excel but maybe programming languages if you know any

[dawn bridge]

idk what an reu is

but i see a ton of jobs that list excel under skill requirements

[limber thunder]

definitely do put TA experience, and not your whole transcript but maybe your GPA (?) up 'till now, and grad credit if you've taken any

[vast surge]

Research thing for undergrads

[dawn bridge]

oh

latex?? idk

[limber thunder]

yeah it's more like a summer camp thing offered by unis

[dawn bridge]

latex skills help?

[limber thunder]

[vast surge]

Yeah I'm doing my resume in latex and I'll try to also show off my tikz skills

[dawn bridge]

i want to TA

It seems fun

and get a certificate and money for it and meet ppl

but problem would be time

[vast surge]

Find a prof you like and bug them to let you TA a calc section it's a good job and sobriety isn't even necessary

[dawn bridge]

when im 2nd year i think ill have opporutnity to

be ta in some first year courses

[limber thunder]

I remember seeing some math SE guy who always brought whisky when grading papers lmao

but in all seriousness being a TA can be kinda fun

like don't expect everyone to fully appreciate it, but the one or two people that will really can bring a smile

[vast surge]

It's a rewarding experience in my experience, just helping people see how to do the calculus

Even if they're not super motivated to learn math for themselves (my school makes everyone take a math class to graduate), I still get a bit of satisfaction when they say "oh yeah that makes sense"

[dawn bridge]

intro to programming has like 20 2nd year TAs at my uni

i dont think i can TA math

i might be able to TA intro to programming

[prime plover]

TA math at my uni u need to be 3rd year with A+, usually just 4th years and above get it tho

[limber thunder]

pretty much the same in my uni

but we don't do TA for like engi or science calc courses, it's for the classes that math and phys majors take

[prime plover]

seems more competitive for math than other sciences

[limber thunder]

I've done TA for multivariable calc, ODE and real analysis that way

[prime plover]

ah same

[limber thunder]

that can be fun too, some physicist friends of mine have done TA for a similar course and it's a quite different experience since it's about code and all

[dawn bridge]

yeah i would want to im just not sure if ill have the time

[vast surge]

If I'm doing independent studies is it a good idea to elaborate on the contents of those in my cv

[dawn bridge]

cause i know the courses i will be taking are more likely to clash with ta times

but idk yet

so might not be able to

[dawn bridge]

i think so, why not

i imagine for an undergrad research internship they would interview you

you might be asked to talk about that

[vast surge]

I didn't get interviews last time but I also wasn't hired so

[limber thunder]

maybe as a small bullet point, then elaborate on your statement of purpose if it's relevant

this looks like a nice read: https://blogs.ams.org/mathmentoringnetwork/2021/01/20/advice-for-applying-to-reu-programs-from-recent-participants/

and here's two examples of CV, linked to in that article: https://drive.google.com/drive/folders/1dZdzTnPlKB0u1XhPdDLTQI5kd_6Blomg

[vast surge]

If I've read several textbooks not for class, is it good to mention that on my cv?

[jovial ember]

I think a CV is a bit of a weird place to put it

You could try to mention it in a personal statement or something, but I think the best thing is if someone like a professor can confirm that you have worked through it

This could be either like them having directly worked through it with you to some degree, or having conversations which indicate you know the material in the book

[vast surge]

Okay. I'll put brief descriptions of my independent studies though because I don't know where else to put it and on my transcript it just looks like "MATH 450: Independent Study" over and over again

[jovial ember]

Yeah, that’s a good habit

I tended to give a brief description because “Math 583: Topics” doesn’t really say much

[cinder flume]

CELLLLL COMPLEXESM

Mıtıvatoin of sel

[rotund steppe]

Are there supposed to be bubbles in my rice cooker

While it’s cooking…

Did I mess up

[deep mango]

yeah

no

[fair mural]

neko rice cooker reveal

[deep mango]

you didnt mess up

i get bubbles too

they go away

[rotund steppe]

Ok I just never watched it cook before lol

Ty

[deep mango]

idk what the bubbles are from

something in the rice i guess

[rotund steppe]

Yea

[dense knoll]

Starch bubbles. How many times did you wash the rice before cooking?

[rotund steppe]

2 times

[dense knoll]

That's good enough, you got a lot of bubbles for 2 washes haha. looks good

[deep mango]

,av

[fathom swallow]

ranyakumoschalkboard#7228's Avatar

Click here to view the image.

[deep mango]

lol

[jaunty gate]

surprised you saw my mistake i deleted that instantly

[neat lintel]

,av

[fathom swallow]

Gev#6676's Avatar

Click here to view the image.

[neat lintel]

best avatar

[sick burrow]

[odd narwhal]

Starch

[neat lintel]

its boiling water

also bubbles are a sign that the temperature is rising

the down side of rice cookers is that you cant control consistency as they make you believe

i also have oster brand

[uncut socket]

,av gev

[fathom swallow]

Gev#6676's Avatar

Click here to view the image.

[fathom swallow]

8 members found matching gev!

1.   AregevDev#6696 
2.   asgevorg#0866 
3.   framingeveryone#3956 
4.   orangev#8386 
5.   OrangeVanilla#6149 
6.   dodogevipert56#1243 
7.   Alex Langevin#4220 
8.   Gev#6676 ```
Please type the number corresponding to your selection, or type `c` now to cancel.

Member selection timed out.

Feb 13, 2022, 4:35 AM

[chilly hull]

idk where to go after studying multivar calc once i finish that when i get to uni

anyone got any good ideas

[ripe wasp]

probably linear algebra if u havent taken it then idk maybe differential equations or real analysis or smth depends

[stray kite]

how do you do multivar without la

[modest rune]

it is a common thing

despite being pedagogically questionable

[stray kite]

i see

[cold needle]

it happened to me

you kind of like

blackbox all of the linear algebra concepts and instead go for pictures and geometry

and basically only stick to 2d 3d euclidean space

[neat lintel]

how much of Dummit and Foote's abstract algebra text can one follow without knowing linear algebra (or very bare basics of linear algebra)

[leaden torrent]

most of the first few chapters

i say "most" since some arguments do require it, and furthermore, many definitions assume you at least know what a matrix is, what a determinant is, and the properties thereof

in theory you should be able to skip that stuff but, since GL(whatever) is the best early example of a nonabelian infinite (usually) group, i wouldnt advise it

[charred mortar]

maybe try Artin's Algebra instead? He does develop the requisite linear algebra

[toxic schooner]

based

[cinder flume]

Yeah be based and learn la in abstract alg

[sleek wing]

so funkin vased

[neat lintel]

thank you for the response
i do know matrices, determinants, some properties and some computational problems involving them

hmm ill try to make time to learn linear algebra

i find it a little dry

[alpine kindle]

maybe try knapp
he explains LA in the first few chapters before getting to groups

[toxic schooner]

artin takes an interesting approach u can say

firstly he does basic stuff like a lil nt and matrices

then he talks a bit about groups

then goes back to 2 chapters on LA

and then back to groups and then onto other stuff

[alpine kindle]

knapp does some basic NT, polynomial stuff, and matrix stuff
and then a few chapters of basic LA, then to basic groups (and rings and fields) and basic category theory, then back to another 2 chapters formalising linear algebra, then back to more groups and stuff

[toxic schooner]

Cat theory as well?

[cinder flume]

artin approach seems better than knapp approach

[toxic schooner]

yeah i agree nevzat

[cinder flume]

because la is less fun than group theory

[toxic schooner]

avoiding cat theory is always better

[cinder flume]

but Im still reading knapp

[toxic schooner]

[cinder flume]

because I only have it printed

sorry man

[toxic schooner]

tis alright

[inner finch]

my balls

[toxic schooner]

i am also doing apostol coz i had a hardcopy

mirza what

[inner finch]

testicles

[toxic schooner]

[inner finch]

i recently went undercover to this server

was really sad

it was like some self hating-ish lgbtq ppl

[toxic schooner]

went undercorver as in?

[alpine kindle]

where are you up to

and is it good

[cinder flume]

we talked this yesterda

im at multilinear alg

[cinder flume]

Its going well

sometimes the examples feel unnecessary

but the problem parts are really nice

[alpine kindle]

nice

does it get better as you go along

[cinder flume]

definitely yes

first chapters were really boring

[alpine kindle]

because I'm kind of getting tossed around with theorems I don't care about yet in ch1

[cinder flume]

yeah

the motivation is not well presented

in those chapters

[cinder flume]

its not a good place to learn los angeles probably

[alpine kindle]

hm

I'll do it anyway

I'm not prepared to do a whole course on los angeles

just for algebra

[sleek wing]

read that as "los angles"

and started wondering what a los angle was

[inner finch]

as in went undercover

[toxic schooner]

[alpine kindle]

put themselves under a literal cover

[toxic schooner]

or a topological one

[sleek wing]

do it got a finite subcover tho

[toxic schooner]

Probably

[sick burrow]

Fun fact: 3% of this server is mirza alts

[fair mural]

mirza has over 2.3k alts

[alpine kindle]

are you a mirza alt

[sick burrow]

Yes

I thought that was obvious

[toxic schooner]

we are all mirza alts

obviously

[cinder flume]

@alpine kindle

you know what?

[alpine kindle]

yes

[cinder flume]

you can countinue with godement algebra

I heard he does los angeles with modules

which is logical unlike vector spaces

[alpine kindle]

I'm enjoying knapp

well

hm

does he cover as much as knapp

[cinder flume]

I just heard

let me see

[alpine kindle]

because knapp basic has a ton of content

[cinder flume]

i just looked at godement and

its really amazing

it was the approach for algebra I believed to be right

how could la be understood with vector spaces

I dont know

but I made the mistake too

with modules the definitions make sense

[toxic schooner]

[agile heron]

What do we mean by pre-universitary math ?

Is it like 11th and 12th grade ?

Or things between High School and University ?

[devout nacelle]

Usually anything before uni, so it ends up including the final years of HS

It's an approximate call based on when one usually sees a topic, and need not be exact

[alpine kindle]

goddamn

[agile heron]

What do you mean by that ?

[devout nacelle]

Different learners may see the same topics at different stages of their education

[agile heron]

yes

so, basically it's HS last years

[devout nacelle]

Correct

Or more like

upto the last years of HS

For instance #prealg-and-algebra is kind of more middle school onwards in scope

[bronze pelican]

I'm a mirza alt

[tiny marten]

im an alt but you dont know the original so it's the perfect crime

[sleek wing]

the alt has become the main

[alpine kindle]

i know someone like that

[latent blade]

@gilded hare based on your graph I finally got to the thing I had in my head, I thought you might enjoy having a look

the shape is supposed to be a large chamber with a flat bottom and a dome such that the floor curves up at the edge and connects to the side of the dome

https://www.desmos.com/calculator/mnqrj39lza

basically a cookie

[gilded hare]

yea that looks super interesting

were you doing an area optimisation or something

cause thatd be pretty cool to figure out

[latent blade]

nothing that practical, I'm creating a scifi universe for fun and this is supposed to be a large underground chamber on an inhospitable planet which houses a city

[gilded hare]

thats so cool

[latent blade]

I felt like I needed to figure out the shape, just to satisfy my own need to express it mathematically

[gilded hare]

yea i can relate to that. im always trying to figure the stuff i see outside of math into it

my friends call it an illness lol

[latent blade]

well, you're not alone :)

I'm gonna go to bed now

thanks again for the help

before I go

do you know if there is some free to use software where I could graph this in 3D?

would be easy enough to get the equation, just add a variable

[gilded hare]

usually i use wolfram

but thats paid so not really

though i suppose desmos or geogebra could be sufficient

[fair mural]

should i be concerned if i can’t prove anywhere near everything in the proof book i’m reading

[sleek wing]

no lol

you ain't there yet

[fair mural]

i can prove maybe like 1/3 of everything

possibly

ok thanks wew

[sleek wing]

that's more than 0!-1

[fair mural]

[wooden flax]

Can there be multiple disjoint unions for this definition?

The disjoint union of sets $A$ and $B$ is the union of sets $C \cong A$ and $D \cong B$ where $C \cap D = 0$

[fathom swallow]

Invictus

[wooden flax]

($A \cong B \implies \text{There exists a bijection between A and B}$)

[fathom swallow]

Invictus

[neat lintel]

yes

but this definition lacks a lot of context

using definition by universal property is way more clear

[jade crane]

Wake up

@fair mural

[inner finch]

my balls

[waxen lily]

you're balls

[charred mortar]

All balls

[toxic schooner]

on this fine day we are all $B(x,r):= |x-a|<r$

[fathom swallow]

Shyshu of the Golden Flower✓

[sleek wing]

I would never

[tall badge]

we're all open

[toxic schooner]

[jade crane]

Math jokes are so funny

[stray kite]

what data analytics adjacent fields do you get to learn in a math undergrad course

[leaden torrent]

math

[median zinc]

data analytics is mostly vague, but in a pure math course you would study objects a lot more abstract and general than 'in real life'

The really relevant fundamentals would be Linear Algebra and Probability. Most of data analytics is applied statistics which is studied by a lot of people. Econometrics comes to mind in terms of related people

[stray kite]

just wondering what courses ill be needing to take for when i inevitably give up on pure maths

[charred mortar]

much of stats is really just applied linear algebra tbh, or at least what I've seen

linear regression in particular

if you're interested in the statistical theory some understanding of mathematical proofs would also be helpful as a starting point

[pale orchid]

linalg, multivar calc, some complex analysis, statistics, odes, optimization

those are more or less the basics for "data analytics"

how much you need varies from "none lol library goes brrrr" to "get a phd"

[median zinc]

Complex analysis does not come in IMO, unless your object of study is sufficiently advanced

[charred mortar]

yeah the phrase "data analytics" is really broad

[pale orchid]

not really. it's just that linalg and related topics show up a lot whenever working with multivariate stuff

so it's more that you need the two things at the same time

[stray kite]

i see

[last elbow]

Hey how would you prove that x < 2^x for all x >= 1?

[sleek wing]

induction

[deep mango]

you can do this with a notion of continuous induction actually

how does log help you

you then need to prove that log(x) < log(2) x

[last elbow]

Wouldn't it be that x < log_2(x)

[deep mango]

well, it would be x > log_2(x)

[last elbow]

Yeah

[deep mango]

but that's the same as

using the log base change identity

[last elbow]

I don't think sooooo?

[toxic schooner]

it is the same thing

[last elbow]

Ohhhhh

[deep mango]

yeah, log_2(x) = log(x)/log(2)

[last elbow]

I was bein dum

I forgot what log(x)'s base was

Right

[deep mango]

anyway i don't think this is necessarily easier (you still just take the derivative and see the inequality there)

[last elbow]

Yeah I was wondering how you would do it without the derivative specifically

I'm working a problem that should be possible to do without calc

[deep mango]

well what wew said works for integer x

[last elbow]

Someone was talking about continues induction

How would that work

[deep mango]

ummm

hmm

that's some fucked up analysis shit

yeah

i mean

[deep mango]

i basically want to use a bootstrap argument

no, i don't think this is helpful

[sleek wing]

consider a separate proof by induction on all the cosets in R/Z...

[deep mango]

im thinking though

actually true

well

you need to know it on [0, 1]

or

on [1, 2]

then you can prove it everywhere

using wew's cursed method

[sleek wing]

you sully me... and yet here we are

[deep mango]

ok you know what

it's actually fine this way

on [1, 2), x < 2^x because x < 2 but 2^x >= 2^1 = 2

so it's just true by monotonicity of 2^x

it can't get smaller than 2

then for x + n, x in [1, 2), if we have x + n - 1 < 2^(x + n - 1) then 2(x + n - 1) < 2^(x + n). but x + n =< 2(x + n - 1) when x >= 1 and n >= 1, since x + n > 2. so x + n < 2^(x + n). now use induction on n.

@last elbow here's your proof

not continuous induction but the thing floating around in my head was similar

[last elbow]

Cool

[deep mango]

I could write that induction proof better

It's kind of backwards

[last elbow]

I have a cleaner one

Because you assume x < 2 then if you prove 2 < 2^x then you imply x < 2^x

And 2 < 2^x is easy

Take log of both sides

[mint patio]

x = 1?

[last elbow]

If you take x > 1, this works

[mint patio]

Or 0

Mm okay

[last elbow]

Then you just fill in the required interval with the single case x=1

[deep mango]

True

Thats good

[sleek wing]

Proof by contra positive my beloved

[fair mural]

~Q->~P oh yes

[last elbow]

Huh?

[last elbow]

Enlighten me

[fair mural]

$P\implies Q$ is logically equivalent to $\lnot Q\implies\lnot P$

[fathom swallow]

quantum

[neat lintel]

wow, cool stuff

[last elbow]

Ok but how is that related to my proof or how would you use that to prove x < 2^x

[fair mural]

idk, i was just commenting on what wew said

@sleek wing explain i guess

[sleek wing]

You proved the contra positive of the original statement

[last elbow]

I did?

[last elbow]

How?

[neat lintel]

A folded napkin has a triangular cross section of sides x cm, (x+1)cm and (x+2)cm. If one of the angles of the triangle is 90 degrees, find the value of x.

[ripe wasp]

wait, $|f(x)|^2 = f^2(x)$ for all real functions right.. or am i having a mental blank

[fathom swallow]

sean

[ripe wasp]

where f^2(x) is just [f(x)]^2

[fair mural]

yeah

since the square of a real number is always positive

[ripe wasp]

yeah makes sense

weird

never wondered about that until now

[sleek wing]

0^2

Trolololololol

[fair mural]

since the square of a real number is always non negative

cringe

[ripe wasp]

... bruh that means i just wasted the last 30 mins splitting an integral into different parts for absolute values when there was literally no point......

this is why i shouldnt do math after midnight my eyes are barely open now

[sleek wing]

Gimme gimme gimme a math after midnight

[neat lintel]

A folded napkin has a triangular cross section of sides x cm, (x+1)cm and (x+1)cm. If one of the angles of the triangle is 90 degrees, find the value of x.

[last elbow]

Answer question grrrrr

What about my proof was contra positive

[sleek wing]

You negated both statements then flipped the implication

[last elbow]

No?

[sleek wing]

For example, you changed x >= 1 to x < 1

[last elbow]

I didn't

[fair mural]

#❓how-to-get-help

[last elbow]

I had a x < 2 in there somewhere

And I split the x >= 1 into x > 1 and x = 1

I dunno really though

I just have heard contra positive used a lot and I don't really understand what it means

[surreal sapphire]

i am looking to purchase a springer textbook

the site says this:

is there any reason to not buy the hardcover

[toxic schooner]

[surreal sapphire]

or does this just mean one version does not exist

and its the same

[toxic schooner]

The only thing i can think of is,
A thief can hit u in the head with a hardcover book really hard

[surreal sapphire]

i can throw it at intruders

the hardcover will prove very useful

[toxic schooner]

so true

A book that does math, and damages people

A smashing deal!

[surreal sapphire]

this is still very expensive but whatever

[toxic schooner]

yeah 60 euros is a lot

[surreal sapphire]

its so weird, the e-book is only 10€ cheaper

[toxic schooner]

5100 rupees, dayum

[toxic schooner]

[surreal sapphire]

guess i will get the hardcover 🤷

also those tags

ecotoxicology

[fair mural]

the outlier

[surreal sapphire]

glad that i can apparently transition into ecotoxicology if the math career doesnt work out

[toxic schooner]

[tiny marten]

Lolol

I wonder how they setup their mathematical theory of ecotoxicity

[surreal sapphire]

there is nothing of the such in this book, the auto tagging system is broken

calibre also tagged the pdf with "Environmental Science" for some reason

[last elbow]

Hey

Say I wanna use the transformation (x,y) -> (2x,2y) to transform the line y = x + 1

Why isn't the transformed line 2y = 2x + 1

Why is it the inverse

Why is it y/2 = x/2 + 1

Help I'm dying

[blazing pawn]

read #❓how-to-get-help

[last elbow]

I've read it this isn't that type of thing my dude

[blazing pawn]

But anyway the point is that if you have like, (2, 3) on this line or whatever then (4, 6) is not described by the equation 2y = 2x + 1

It sounds like a pretty standard intro linear algebra question

Lol

[last elbow]

I guess I shoulda asked it in linear algrebra then

[blazing pawn]

since (2, 3) has 3 = 2 + 1 we necessarily have 2 * 3/2 = 2 * 2/2 + 1

[last elbow]

Right this still doesn't make sense to me

[blazing pawn]

just like, plug in points and you should see why 2y = 2x + 1 doesnt make sense

equivalently

lets divide

[last elbow]

Why it ends up being the inverse

[blazing pawn]

2y = 2x + 1 is the same thing as y = x + 1/2

[last elbow]

Ok

[blazing pawn]

if y = x + 1 does 2y = 2x + 1/2

[last elbow]

No, but that's not the the thing, if anything it shouldn't

I'm asking the logic behind why using a transformation like (x,y) -> (2x,2y) does what it does to equations

[blazing pawn]

you have two lines, L and T(L)

where T(L) is the image of L under the transformation (x, y) -> (2x, 2y)

[last elbow]

Because from what I've seen, transforming a curve with that means subbing in x/2 for x and the same for y

[blazing pawn]

the equation y = x + 1 gives you a relationship between points in L

so given (x, y) in T(L) we know that T^{-1}(x, y) = (x/2, y/2) satisfies this relation

e.g y/2 = x/2 + 1

[last elbow]

Ummmm

Ok I still don't understand why it ends up being the inverse that you need

Satisfies what relation

[blazing pawn]

The definition of T(L) is that it consists of points whose preimage under T i.e whose image under T^-1 are in L, ie satisfy the equation y = x + 1

[last elbow]

What is T^-1?

[blazing pawn]

The preimage of (x, y) is (x/2, y/2) and so if (x, y) is in T(L), (x/2, y/2) is in L and y/2 = x/2 + 1

The inverse of T

[last elbow]

Sorry btw this is one of few knots in my brain related to math that ive had sitting their for so long

There are so many mental blocks in my brain rn

Trying to push them away

Why is that the definition of t(L)

[blazing pawn]

Thats what it means to take the image of the line L under T

Its the set of points of the form T(x, y) for (x, y) in L

[last elbow]

This sentence makes little sense to me

I can't even imagine what that set would look like

[blazing pawn]

What does the image of a line under a transformation mean to you

[last elbow]

"Of the form t(x,y) for (x,y)"?

[blazing pawn]

Yes, points in the image of T on L

[last elbow]

The image of T?

Oh man

[blazing pawn]

What does "the transformed line" mean to you

[last elbow]

The set of points under the transformation

[blazing pawn]

Yes

The image

Thats what the image means

[last elbow]

Ok wouldn't then you say the image of T(L)?

What would the image of T even mean

[blazing pawn]

T(L) meaning the image of L under T

You apply T to points of L

It consists of points T(x, y) for (x, y) in L

[last elbow]

Ohhhhhk

"Preimage"

[blazing pawn]

So a point (x, y) of T(L) has T^-1(x, y) in L

Preimage meaning image under inverse

[last elbow]

Ok

What do you mean "has"

"Has T^-1(x,y) in L"

[blazing pawn]

I mean that T^-1(x, y) is in L lol

If (x, y) is in T(L)

[last elbow]

Ok

[blazing pawn]

See this

Like read these msgs

See if they make sense now

[last elbow]

Ok I get it a little more

[last elbow]

Why would it need to satisfy the previous relation

Ok wait I got it a little more thanks sooooo much

[last elbow]

What if the transformation is like (x,y) -> (y, 2x)

Where it's switched

What would be then the inverse

[wanton shoal]

There’s a problem that’s been making up a lot of my thought and I can’t seem to get anywhere near solving it.

Find all integer solutions to $n^{2}=\left(2xy\left(2x-y\right)\right)^{2}+\left(z^{2}\left(x-y\right)\right)^{2}$

[fathom swallow]

Chixen

[wanton shoal]

I would ask a help channel but that’s usually for homework type stuff. This isn’t.

[last elbow]

Some one gets it lmfao

[fair mural]

it doesn’t matter if it’s for homework or not lol

you need help with a problem

that’s where these go

the help channels

[wanton shoal]

Yes, but this isn’t a problem I think people would know how to solve and teach me. This is a problem that I want to solve with people.

because i don’t think one person can solve it alone.

I’ve also been redirected here from a help channel before.

[neat lintel]

looks like fun problem

you can factorize more

[wanton shoal]

I can?

[neat lintel]

yeah

also all 0s is a solution

[wanton shoal]

true

but not all the solutions

[neat lintel]

is x=y then this becomes a simple problem

similarly if x=2y

[wanton shoal]

I know, there are many trivial solutions, but I’m looking for all.

[neat lintel]

mb i meant y=2x

[neat lintel]

go to help channels then lol

i just gave you direction

if you think it’s trivial then work it out yourself or go to help channel

also if you need any extra help there are these things called pythagorean triples

[wanton shoal]

it’s not trivial

I’m just saying that i’m looking for all solutions, not just trivial ones.

like (1,4,3) is a nontrivial solution. I’m looking for all nontrivial solutions.

[stray kite]

damn i encountered a diffeq that maxima cant solve

what will i do when even the gods have forsaken me

[vast surge]

So I asked this in one of the help channels but it's really not a help channel question; what is a personal statement and what sorts of things should I put in my personal statement?

I need to write one to apply to REUs for the summer, haven't started yet, and lots of applications are due tomorrow

[frigid lark]

Quantuuuum

[fair mural]

@frigid lark hi

[frigid lark]

How are you

[fair mural]

i’m good

i started mathematical induction today

pretty fun

how are you

[frigid lark]

😞Tired. Woke up early just to realize my exam was at evening. But exam was ok. Numerical Analysis second attempt.

[fair mural]

rip

i don’t really know anything about numerical analysis

might have to look it up

[frigid lark]

Not sure if english is the same word.

[fair mural]

it probably is

i’ve heard of it before

[frigid lark]

But topics are function approximation, interpolation, quadrature, error analysis, lu, qr, cholesky decomposition, iterative methods like Gauß Seidel, Jacobi, cg

Quadrature means integral approximation by different methods.

[empty stratus]

Quadrature is also an old-fashioned way of saying "(definite) integration".

[odd narwhal]

#❓how-to-get-help

[ancient flame]

would you guys consider concatenation to be part of number theory?

[tiny marten]

concatenation of what

there are concatenation arguments in number theory, probably some of the oldest

i would say that it is just a general symbolic idea and isnt native to one field

appearing in NT, CS, logic, and dynamics

dynamics and CS inherit a lot of notions from NT, even if it's not obvious

or at least NT influenced a lot of general math things that both use often now

[ancient flame]

just like

10 concatenated with 29 = 1029

[ancient flame]

but yeah I agree with this actually

[tiny marten]

i can see where you would get this idea but it is very general these days

there are old number theory arguments for decimal expansions and other things tho

[ancient flame]

ah

[tiny marten]

they actually feel kind of like a CS argument actually

[ancient flame]

interesting

[analog salmon]

Does anyone know of a larger tuple than this? I wanna see how big it goes

[bronze pelican]

https://youtu.be/VYfWfrk5P7w

[neat lintel]

Why is north korea below south korea?

how did that happen

[tiny marten]

prior political distributions of the population and america has a large navy so coming in from the south was feasible

the war fought back and forth across the modern day DMZ

oh whoops i misread that and took it seriously lol

[neat lintel]

yeah i thought north korea was below

google said it isnt

[deep mango]

omg im so excited for this

[dire sandal]

ill be impressed when i see parabolica

[deep mango]

oh shit on pi day

nice

we need parabolic geometry...

[dire sandal]

its just x^2 lol

easy mode

[deep mango]

[carmine geyser]

a basic question

diff between finite and countably finite

please

[tiny marten]

they are the same

finite are a subset of countable, so countable finite is finite

[carmine geyser]

sorry that was a mistake on my part

[neat lintel]

I require assistance from mathematics gods

[carmine geyser]

question is

diff between finite and countably infinite

[leaden torrent]

finite means your cardinality is equal to, well, a finite number $n$

[fathom swallow]

Namington

[leaden torrent]

countably infinite means your cardinality is equal to the cardinality of $\mathbb{N}$

[fathom swallow]

Namington

[leaden torrent]

so infinite but "the smallest possible infinite"

[tiny marten]

yeah

[carmine geyser]

what is n here?

[leaden torrent]

some natural number

0, 1, 2, 3, 4, ...

[carmine geyser]

like bijection with natural numbers ?

[leaden torrent]

yes

[tiny marten]

scandalous

[leaden torrent]

if you prefer, there's an alternate phrasing

[carmine geyser]

i am still confused, you said both are in bijection with natural numbers ?

[leaden torrent]

we call a set countable" if it injects into a subset of $\mathbb{N}$, and then a countable set is countably infinite" if it furthermore surjects into $\mathbb{N}$; otherwise it is finite

[tiny marten]

some people in the US make a big deal out of the 0 is a natural number thing

[leaden torrent]

no, a finite set is in bijection with {0, 1, 2, ... n} whereas a countably infinite set is in bijection with ℕ = {0, 1, 2, ...}

note that the former "ends"

the latter doesn't

[carmine geyser]

so countably infinite is bigger than finite ?

[fathom swallow]

Namington

[tiny marten]

yes

[leaden torrent]

yes, infinite is bigger than finite.

[tiny marten]

countably infinite is bigger than any finite

[carmine geyser]

thanks boys

[leaden torrent]

finite < countably infinite < all other infinite sizes

[carmine geyser]

🔥

[dire sandal]

$\aleph_{-1}$

dang

[carmine geyser]

was going thru diff between algebra and sigma algebra

[fathom swallow]

hiidostuff

[dire sandal]

cursed

[toxic schooner]

why do i wake up to such cursed things

[orchid hawk]

math is in minecraft

[neat lintel]

@obsidian jetty yeah it's vector geometry, and I'd say it's the fundamentals for sure

[obsidian jetty]

thanks man :)

[restive aurora]

I can be successful in math without doing competitions, right?

I don't like competitions, and the very nature of constantly comparing myself to others

it seems like a toxic thing to pursue

[calm rampart]

ofcourse

[leaden torrent]

though if you dont like constantly comparing yourself to others, academia at least might not be a good path

the structures of the system kind of demand it unfortunately

with how competitive everything is

[compact tartan]

most games involve at least a little bit of math relating to movement and hit detection

minecraft's is probably one of the simplest

[severe lagoon]

Hi

Terria

[vivid halo]

yeah absolutely

it's like, people who do really well in math competitions more often than not end up doing really well in mathematics, but also a lot of people who don't touch math competitions also end up doing really well in mathematics

[dawn bridge]

wdym by 'doing well'

when u see famous modern mathematicians it seems they often have olympiad golds

[blazing pawn]

They are also often famous specifically because they have olympiad golds and the media enjoys popularizing stories about young geniuses

But the correlation is also real in part because I think people who end up getting fields medals and stuff are probably talented, and if people can tell early they probably get encouraged to do competitions and stuff

[dawn bridge]

and isn't fame part of "doing well"

[vivid halo]

I mean yes more often than not the people who perform at the top level at olympiads will go on to become very good mathematicians

just out of sheer ability

[blazing pawn]

Im assuming by famous you mean

In the general population

e.g tao

[dawn bridge]

is it talent

like do these olympiad ppl train for it

[vivid halo]

at that level yes absolutely

[dawn bridge]

or do they just show up like hi whats an olympiad

[blazing pawn]

I dont think like 99.999% of people have any idea who the fuck quillen was

[dawn bridge]

oh nice i got a gold medal

[vivid halo]

they train a lot but it's also talent

[dawn bridge]

im so skill

[blazing pawn]

I dont really think being a successful or well regarded mathematician implies you have any fame at all outside of that circle

[vivid halo]

yeah lmfao

[dawn bridge]

well that depends on what u define successful to be

fame brings in a lot of opportunities

[blazing pawn]

This is also totally conjectural but I think that like, math problems that get big in the media tend to be more combinatorial or related to number theory and it does seem like a big proportion of comp math people go on to do combinatorial or number theoretic things

[vivid halo]

yeah maybe

[median zinc]

The simpler part of number theory is easier to understand, like for primes.

[dawn bridge]

cause normies can understand that stuff ig

yeah

[blazing pawn]

i dont think atiyah and singer proved the index theorem for attention from the media lol

[median zinc]

And I do not think it is possible to explain algebraic geometry more than drawing cubic curves

[dawn bridge]

like i dont even understand what navier stokes is

[median zinc]

You mean the problem or the equations

Wikipedia is quite comprehensive on it

[dawn bridge]

the problem

well im too lazy to read

[tiny marten]

To be fair you often dont need a lot of theory for this

It may be a reason they are popular in pop math and comp

[blazing pawn]

Kind of

[tiny marten]

They're not asking like, class field theory questions after all

[blazing pawn]

I think its more that like comp math people tend to develop "tastes" earlier than other people

[tiny marten]

Could be

[dawn bridge]

number theory is for the sake of itself rn rigt

while combinatorics is heavily linked with optimization

[tiny marten]

Combinatorics is often used in CS tho I would say it is definitely it's own pure math topic

[dawn bridge]

i mean number theory has its uses

but the new stuff u find doesnt

for now

[vivid halo]

[dawn bridge]

i guess

😂

thx for the sullies

[median zinc]

some part yes but I think many parts no

[tiny marten]

Trust me the new stuff in pure math can be hard to apply regardless of field, depends on the result

[dawn bridge]

is combinatorics synonymous with discrete maths

[dawn bridge]

i thought combinatorics was applied math

[devout nacelle]

Generally no afaik

[tiny marten]

It seems that way because how much CS people use it

Yeah

[dawn bridge]

there is no course at my university called "combinatorics"

but there is "discrete maths"

[vivid halo]

algebraic geometers: I study solutions to polynomial equations

[dawn bridge]

and the textbook for that is "introduction to combinatorics"

that is why i asked

[devout nacelle]

I think "discrete math" is actually identified at some places

Although I'm not sure what its scope is meant to be

[tiny marten]

We have combo in my unis math department but it's under mathematical computer science

Otherwise it is a CS class

But that's just like, undergrad

Which basically doesnt reflect the math community tbh

A bit ofc but not directly

I believe Terrence Tao has worked on pure combo for example

[blazing pawn]

Yes what else is Gal(Q)

[vivid halo]

[dawn bridge]

do maths researchers just read papers then sit in their room thinking

[vivid halo]

yes

[dawn bridge]

sounds fun

[vivid halo]

yeah it's a blast

[dawn bridge]

is undergraduate maths supposed to be easy

[vivid halo]

ehh

[dawn bridge]

for future phd students

like they just walk through it without trying

[vivid halo]

not necessarily, it's normal for it to be a little challenging here and there even for really good students

[charred mortar]

Depends on the person

And like there’s some overlap between undergrad and grad topics

[vivid halo]

it probably shouldn't be like, an absolute ordeal to get through the undergrad courses for future PhD students

[toxic schooner]

if u are me
yes its too challenging

[vivid halo]

but maybe not completely trivial

[surreal sapphire]

take harder classes :catKing:

[blazing pawn]

[blazing pawn]

They are especially easy to get through when you do not take them

[dawn bridge]

if i keep forgetting the proof of heine borel does that mean i never understood it in the first place

i have to learn all the proofs and be able to do them again right?

if i understand them

or is that wrong

[blazing pawn]

I dont think you need to be able to reproduce every result in a class

Lol

[neat lintel]

No famous mathematicians with important proofs have forgotten their own proofs

[dawn bridge]

i rmm someone in chat said being able to verify and understanding a proof is different

if i cant prove it from memory i never understood it

[devout nacelle]

This isn't true

Lots of proofs rely on very technical constructions

It's easy to trip on one detail or the other

Humans are still bound to make mistakes and forget things

[blazing pawn]

atiyah has 10 seconds to reprove the epimorphism version of the atiyah jones conjecture

[tiny marten]

andrew wiles can just write 100 pages of FLT's proof without stopping

[dawn bridge]

if im reading a textbook do i make an attempt to memorize proofs then

[neat lintel]

I agree with the idea that Proof validation is much more important than proof memorization

[tiny marten]

greatest party trick

[dawn bridge]

or just validate and move on

[blazing pawn]

Whats the point of memorizing the proof lol

you need to understand it

[dawn bridge]

understand = validate?

[tiny marten]

if you are telling me that set theorists memorize their proofs then i guess they really are the best

[toxic schooner]

[tiny marten]

deities among mathematicians

[neat lintel]

I agree with that

To me, some proofs require a lot of creativity inspired by ideas kind of like how an artist is inspired by ideas to make a painting. You will never know the exact ideas that inspired the creative solution, you only ever see the outcome. I believe that knowing the inspiring idea for a proof, or creative sections of a proof, would be incredible information to have. But in the absence of that, you can always come up with your own intuition for the solutions, and I believe the act of doing that is more important then memorizing each little detail of a proof.

[dawn bridge]

i c

thx

the creative process is hard to understand

even if i engage in it and come up with a creative solution to a new problem i often cant describe why

sometimes you just think of things and then stuff comes to you

[neat lintel]

I agree, it’s like fishing, sometimes you get lucky and catch a big one.

[mellow moon]

It depends on many things, your way of thinking about things, the kind of Maths you are doing, how many subfields does it cross etc.

The more you know and remember, the more material you have to play and think with

[neat lintel]

Agree for sure. Memory is a critical component.

[glossy bolt]

how do i compare which performs better?

[glossy bolt]

@foggy raft heres the image

[foggy raft]

what is being measured

[leaden torrent]

#❓how-to-get-help

[glossy bolt]

which student performs better

[foggy raft]

at what

[glossy bolt]

test marks

[foggy raft]

well you’ve kinda

wouldn’t you take an average

[glossy bolt]

nope, teacher said us to use measure of variability

otherwise i thought of average

[foggy raft]

well then like

i guess whoever varies less?

i mean it’s obviously edgar

[glossy bolt]

hmm alrr

tyyy!!

[foggy raft]

np

i could be wrong btw i don’t understand why you need to use variability for this LOL

[glossy bolt]

also yea, i know but i didnt had too complicated of a doubt just needed a opnion thats why i choose this

[glossy bolt]

same lmao

[glossy bolt]

abt that, yes we cant cause both the average is 93 lol

[foggy raft]

well then edgar still cause he has bigger numbers overall

[cyan goblet]

if average is equal then whoever has the least variability is the better student

(60, 100) and (79, 81) both average at 80, but the former varies more than the latter

[long matrix]

90-100 is an A
80-90 is a B
Problem solved? 😏

[dawn bridge]

unreasonable to assume lower variability is necessarily better

there are situations where high variability is preferred

the question is crap

[sleek wing]

I’d look at average and then compare minimums if they’re equal tbh

[dawn bridge]

id just cross out everything other than math

maveric is better, done

[sleek wing]

Me when I can solve linear equations but can’t spell my own name!

[toxic schooner]

Ok lets be a little inclusive and include science
marivic still is the better person

[sleek wing]

I’d just cross out everything and then write myself in an extra column(?!) with 100s in everything and claim superiority

[toxic schooner]

[sleek wing]

Hold on why are the names in the COLUMNS

[analog salmon]

this might be the least helpful definition I've ever read

[compact tartan]

makes sense to me

[mint patio]

https://tenor.com/view/siege-tales-russian-badger-floor-is-made-out-of-floor-rainbow-six-gif-21093443

[fair mural]

floor(floor)

[alpine kindle]

= floor

[mint patio]

god I hate engineering math classes

[sick burrow]

square root is defined to only take the positive value

since otherwise it wouldn't be a function

[deft hornet]

exactly so if its -5
sqrt((-5)^2) = 5 but if its equal to x and x is -5 so it will be equal to -5 therefore not true

[sick burrow]

y^2=x is not the same as y=sqrt(x)

that's why you write $y=\pm\sqrt{x}$

[fathom swallow]

Worst Geometer NA

[deft hornet]

if sqrt(x^2) = x and x = -5
then it says that sqrt(25) = x = -5

which is not true

[sick burrow]

I think you typed that wrong

[deft hornet]

so it should be -x if x <= 0

[sick burrow]

anyways

[foggy raft]

i mean

are they

[sick burrow]

just wait until you learn about the complex logarithm and branch cuts

[foggy raft]

whats being

happening

[deft hornet]

yeah

I meant that yeah "sqrt(x²)= |x|"

HAHA

not really

if x = -5
sqrt(25) = 5 and not -5

[cyan goblet]

sqrt(25) = -+ 5

your teacher is right lol

[deft hornet]

no

[cyan goblet]

you'll be using $\pm$ in square roots in math

[deft hornet]

it goes agianst the definition of square root

[fathom swallow]

anamono

[cyan goblet]

no it does not

[deft hornet]

square root is defined as the positive number no?

[cyan goblet]

no

,w square root

[fathom swallow]

Results provided by WolframAlpha

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

Requested by anamono#1010

[cyan goblet]

that's no use

the square root is simply a number which produces a specific quantity when multiplied by itself

got that def'n straight off google

-5 * -5 is 25

[deft hornet]

well but talking about principal square root

it is the absolute value of x

imo

[cyan goblet]

principal square root =/= square root

[deft hornet]

it doesn't exist

[cyan goblet]

the principal square root is the positive value

[deft hornet]

well it is commonly used like that

[cyan goblet]

the square root itself can be the positive or negative value

common does not mean definition

when finding extrema, you use -+

education system fails to explain the differences between principal square root and square root

[deft hornet]

I meant to say its not true

|x| =/= +- x

principal sqrt(x^2) = |x|

but when people say sqrt they commonly refer to principal square root ig

🥑

[frozen merlin]

if the class of lebesgue measurable functions is meant to be, in some sense, the `completion' of the riemann integrable functions

so philosophically why do we lose a bunch of riemann integrable functions like sin(x)/x ?

by integrable, i mean over R

not some bounded interval, where (I think?) everything riemann integrable is also lebesgue integrable

[odd narwhal]

The definition of lebesuge integration coincides with 'absolutely integrable'

Or absolutely convergent integrals

There might be a deeper answer but conditionally convergent functions aren't really integrable in a strong sense

[frozen merlin]

yeah, I guess it just seems weird that moving to a better/complete theory of integration doesn't strictly increase the class of functions you can integrate

[deep mango]

there is no such thing as "riemann integrable over R"

the only way to make sense of this is via improper integrals

where you integrate over compact sets and then take a limit

if you try to take an "improper lebesgue integral" of sin(x)/x you get the same thing as the improper riemann integral.

[frozen merlin]

hmm so

you can lebesgue integrate non integrable things?

[deep mango]

what i should have said here was "riemann integrable over R" does not mean the same thing as "riemann integrable over [0,1], but with [0,1] replaced with R"

whereas "lebesgue integrable over R" does mean the same thing as "lebesgue integrable over [0, 1], but with [0, 1] replaced with R"

[deep mango]

instead, this means "the improper integral exists"

[deep mango]

while this means "L^1 limit of simple integrable functions"

[deep mango]

you can take improper lebesgue integrals of nonintegrable things, yes. the convergence will be conditional. if you know riemann's rearrangement theorem, then you know why we want to avoid this at all costs.

especially in a theory which is totally focused around being able to break things into countable unions.

countable unions don't care about the order the sets are in, in the same way countable sums care about the order of the summands.

[frozen merlin]

yeah this makes a lot of sense

thanks for clearing that up

[odd narwhal]

That's Much better answer

[wanton tartan]

Is there no channel for geometric algebra?

Unfortunate

(not #algebraic-geometry)

[honest veldt]

does it deserve a dedicated channel

[little vine]

What's a problem in geometric algebra?

[wanton tartan]

Idk, it's not like I know all of it, or even close. From what I do know though, yeah seems like it

[wanton tartan]

Like give an example or?

[honest veldt]

I see, I don't know much about it myself, only read about it

wasn't it just clifford algebras? I feel like it's too narrow to warrant a dedicated channel

[wanton tartan]

Yeah I think it was 2 forms of the same thing or smth like that

[honest veldt]

I'm guessing it somehow fits into either the LA channel or the algebra channel

[wanton tartan]

tbh I just want to abolish cross product in favor of outer product

[little vine]

Yeah I'm just curious

[wanton tartan]

Uhhhhh

Find the geometric product of $2e_1-3e_2+e_3$ and $-4e_2_3+e_3_1+2e_1_2$

Something like that ig

Uhhh wait I'm bad at latex

[fathom swallow]

hiiistrex
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[wanton tartan]

It gave the right output so uhhh not bothering with the error lol

[ancient flame]

you can do $e_{31}$ instead of $e_3_1$ @wanton tartan

[fathom swallow]

gmod [gmod gang]
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[ancient flame]

then it won't have the error msg

[wanton tartan]

Yeah that makes sense

[vivid halo]

geometric algebra

lol

[wooden flax]

lmao

[solid stream]

finished my homework ty so much
@fluid rapids

[pallid reef]

hey everyone, my exams are coming in 10days and I am at my last leg of studies but i am getting stuck in some maths papers. Is there anybody who is good enough to solve IB Maths AA HL past papers especially trig with me….

We can have a private convo and daily till 2weeks solve questions together…please i really need some help…

my maths teachers rarely help me so idk where to go if i have a doubt in a step or question….mostly i can do everything but still need helpz…

[sterile hare]

why don't you solve past papers

and when u run into question u cant solve

upload question on help channel and learn to solve it

and repeat

[rotund steppe]

Pay for a proper tutor

[mystic lintel]

Anyone have an idea for an experiment I can do at home but it has to be an experiment which is not soo common or not too hard. I just want ideas on one experiment I can do at home on which I can also create a table for independent and dependent variables. I want to also measure my results but I don’t want it to be too hard.

[rotund steppe]

Dice

[mystic lintel]

What do you mean by that?

[long matrix]

,w series expansion 1/(1 - x^2) at 0

[fathom swallow]

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Requested by Shuri2060#9525

[long matrix]

Radius of convergence should be 1

|x| < 1

is wolfram being dummy or what?

[empty stratus]

You probably just typed something wrong.

[long matrix]

What.

[empty stratus]

Granted, WA freaks out at the drop of a hat.

[dire sandal]

unless ur an actuary then bank is now made

[empty stratus]

If you don't type it just right, anything can happen.

[long matrix]

Notice it should be 1 clearly, by considering geometric series fornula

????

Look, the input is completely fine

[empty stratus]

Maybe WA is just having a bad day.

[short pivot]

,w differentiate sum x^k for k = 0 to infinity

[fathom swallow]

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Requested by coycoy#4831

[short pivot]

...

WA? You good?

wait i goofed

[fathom swallow]

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Requested by slimvesus#9286

[toxic schooner]

[short pivot]

,w sum x^{2k} for k = 0 to infinity

[fathom swallow]

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Requested by coycoy#4831

[short pivot]

okay there we go

[long matrix]

wow

[short pivot]

am confusion

[long matrix]

much pain

ty

why wolfram dumb

smh

[empty stratus]

As I said, it's very, very finicky

[lilac prairie]

@open holly hello

Sup

[mint patio]

Can't stop laughing at this

[raven haven]

if you can get complex solution from real equations

is the real field not closed?

[modest rune]

the field of real numbers is not algebraicly closed

meaning that polynomials over R have solutions not in R

This is not true, for example, over the complex numbers

[raven haven]

what structures must be closed?

[modest rune]

?

[raven haven]

i think vector spaces hace to be closed to be vector spaces no?