ug-maths-physics

[vestal swift]

Wait u mean f(x)?

[tawdry gull]

so not all the area is positive

yes

f is f(x)

[vestal swift]

For antiderivative of |f(x)|

All positive area right?

[tawdry gull]

yeah

[vestal swift]

So this not correct ah

[wary sluice]

Yes

Sorry you can read this when u r done

[tawdry gull]

when u have -|A| < B < |A|, then |B|<|A|

thats exactly whats happening to the inequalities u see

[wary sluice]

I only have up to A Levels maths knowledge

n
E
i = 1

What does this mean

[vestal swift]

I mean if u put modulus on ∫ |f(x)| dx , then it becomes |∫ |f(x)| dx| n the outside modulus no effect?

[tawdry gull]

i dont see anything thats no effect

[tawdry gull]

oh

yeah it's unaffected

[tawdry gull]

it means u sum the terms up from i=1 to i=n

[wary sluice]

and what's i

Just like any value of x

[tawdry gull]

i is just a placeholder

[wary sluice]

Like how we used n for any value of x in a levels?

?

[tawdry gull]

in this case "i" is the summing term

that changes as u sum the terms up

[vestal swift]

like for i in range(1,n+1) that i right

[tawdry gull]

[vestal swift]

Ah ok thank u again math god 💪

[idle rain]

Gave +1 rep to The_Pierrot#1126

[tawdry gull]

🙏

[stark wave]

PERRIOT

[tawdry gull]

yez?

[stark wave]

i need help

[tawdry gull]

hmm?

[stark wave]

i have matrix analysis and i dont understand crap

[tawdry gull]

.........

[vestal swift]

I saw this meme

[stark wave]

the lecturer has such a strong french accent i cant understand her videos

[tawdry gull]

yes exactly lmaoo

[stark wave]

im relying on the lecture notes and they think things are very obvious

[vestal swift]

N I thought to myself: damn the coding side is so much easier

[tawdry gull]

so how can i help :')

[vestal swift]

Pierrot and Alex r carrying this channel

[verbal nova]

What about the none scary factorial symbol

Scariest code

[stark wave]

i have very many stupid questions

[tawdry gull]

[tawdry gull]

good fucking luck

[stark wave]

um how is the highlighted part make sense

[stark wave]

oh this is q1 from the background material

this isnt even actual content of the module

[tawdry gull]

bruhh

[stark wave]

:')

[tawdry gull]

wdym by make sense?

[vestal swift]

Fck if I'm gonna learn this as a math major I'm srsly considering dropping out 😭

[stark wave]

idgi how the coefficient of the char poly is related to the trace

[stark wave]

well its an option in third year

you dont need to go down lin alg

[tawdry gull]

it's more like, it happens to be related to the trace

u can try it out for 2x2 or 3x3 matrices

and u will see that the coefficient of t^(n-1) [which is the sum of eigenvalues] is equal to the trace

[vestal swift]

Is it like coz t^(n-1) then u do all possible combinations of choosing n-1 times of t and 1 time of a not t term n u get the trace

Ok idk what im sayin at this point imma head out

[tawdry gull]

😔

[rancid schooner]

Not Alex. Just Pierrot 😄

Do they have a matrix decommission where A = UWU*? 😄

[stark wave]

but how will i know that in an exam

[verbal nova]

Please don't say that again

[tawdry gull]

🤷‍♀️

memorized

https://math.stackexchange.com/questions/1425082/how-to-show-that-the-tracea-is-the-coefficient-of-the-xn-1-in-the-charact

heres a stackexchange for that

[stark wave]

NOOO

[tawdry gull]

it do be like that sometimes

[stark wave]

fuck this crap

i hate this so much

[wary sluice]

Oh thanks btw

[idle rain]

Gave +1 rep to The_Pierrot#1126

[stuck rapids]

Linear algebra... Calc

[vestal swift]

Real analysis next year and I still dk wtf is that

[stuck rapids]

Finished some real analysis hahahaa

Wanted to jump into the ocean

[rancid schooner]

Most of the maths at A-Levels is real analysis - calculus, etc

[vestal swift]

But RA is all proving right 😭

[rancid schooner]

All mathematics is about proving :)

[vestal swift]

Which is why I'm not well suited for math :)

[rancid schooner]

You seem to be doing well

[stuck rapids]

rlyyy HAHAHHA dont think i have touched any proving materials, i do know there is induction in fm

[rancid schooner]

Well it’s elementary real analysis. :)

[stuck rapids]

but i didnt take fm

HAHAHAH

[rancid schooner]

Just a flavour

You should. It’s fun.

[stuck rapids]

up up HAHAHHA

[rancid schooner]

Both of you will make good maths teachers 😄

[stuck rapids]

for add math yes i loved add maths in high school

but but uni maths is on the next level

[stuck rapids]

i should have taken it HAHAH..now that i regret

[rancid schooner]

You can still take it for fun 😄

[stuck rapids]

wht for

hahahhaa

[young marten]

i've never seen someone laugh as much as you LOL

[stuck rapids]

HHAHAHHA seems like i m going a bit crazy bc of school

[young marten]

look🤣

nonono

it's v good

[stuck rapids]

https://tenor.com/view/nice-gif-21458880

[rancid schooner]

What topics are you doing?

[stuck rapids]

a lot of maths this time also..but i finished linear algebra last sem xD

so multivariable calculus, probs and stats, financial mathematics

and financial reporting (similar to accounting)

[rancid schooner]

Nice. Please share some interesting questions.

[stuck rapids]

[vestal swift]

How can u tell

I'm barely surviving

[vestal swift]

Yea I loved further maths coz how standard the qs are (except further mec)

[vestal swift]

Pattern more than badminton sia😭😭

[rancid schooner]

Because handwriting still very neat :)

[vestal swift]

No correlation with good at maths or nah

My handwriting can be nice but I still suck af at maths ok😭

[stuck rapids]

same here mr alex

nice handwriting doesnt mean being good at maths

[stuck rapids]

uni is like..lemme put some magic..tada unexpected question

[vestal swift]

I had to retake one math mod, and NONE of my math mods got A+

🥹🥹🥲🥲

[rancid schooner]

Nice handwriting means you are not stressed :)

[stuck rapids]

i was very stressed

HAHAHAHA

[stuck rapids]

garyaooo

[rancid schooner]

Share your maths problems over a study session here

[vestal swift]

Invalid conclusion

[stuck rapids]

studies said those with bad handwriting has a faster brain

brain works faster compared to hand

[young marten]

or just a slow hand

[stuck rapids]

Yeppp

[long aurora]

me with bad handwriting all the time

[wary sluice]

He said that the numerator and denominator are both third degree polynomials so he just did 9/2 times 2

umm can someone explain how

I jumped from A levels maths to uni maths and I am confused

@rancid schooner

that's one way of tagging math helper

heh

[rancid schooner]

😄 just expand everything and it will become clear

[ebon rose]

hey can i post statics questions here?

[wary sluice]

uhh it did not

(n^2 + n) (2n+1)

2n^3 + n^2 + 2n^2 + n

[rancid schooner]

Then divide

[wary sluice]

2n cube + 3n squared + n

alright

individually?

2 + 1/n + 1/n squared

um

OH

so the fractions become 0 because of 1/ infinity

and 9/2 times 2

@rancid schooner Thank you so much

[idle rain]

Gave +1 rep to AlexV#1811

[wary sluice]

so this obviously looked like a cube thing above

do you think I should learn the polynomials that go above cubed?

[rancid schooner]

😊

[rancid schooner]

The principles are the same

[wary sluice]

umm sorry but that means ?

you mean if cubic above cubic below quadratic above quadratic below

[wary sluice]

One more thing. For a cubic should it always follow this sequence

the way 9/2 multiplies the third thing

Or am i overthinking and I should just expand till I get the hang of it?

[long plank]

anyone some help ?

[rancid schooner]

@tawdry gull can we used Green’s Theorem here to convert it into a line integral?

[tawdry gull]

I wouldnt wanna try that

[rancid schooner]

But in some cases it’s easier to do that.

[tawdry gull]

The path isn’t nice in the first place -_-

[vestal swift]

Discrete maths :’)

[tawdry gull]

it's from the IMO, wat do u expect...

i think that uses the pigeonhole principle

i'm not good with discrete maths personally

[vestal swift]

Yess but idk how HAHAH

[tawdry gull]

same

🙃

u can check the solution online tho

[rancid schooner]

Pigeonhole

If you have 8 pieces of cake and you finish them in one week then on at least one of the days you would eat at least 2 pieces of cake.

[vestal swift]

Yea but this advanced hahaha

[rancid schooner]

More pieces of cake

[vestal swift]

@math gods how to even prove this tf

isn't this an axiom T-T

[rancid schooner]

Still solving maths problems on CNY Eve?

[stuck rapids]

i m also studying hhahhaa

no choice at all :/

[tawdry gull]

it's not an axiom :v

what does the the + and x mean in this case btw?

direct sum and direct product?

[stark wave]

Usually sum and multiplication modulo

*modular arithmetic

[tawdry gull]

thats in group theory tho

[stark wave]

It can be used anywhere tho

[tawdry gull]

but how in vectors...

[rancid schooner]

You can calculate reunion dinner table combinatorics

[vestal swift]

Vector addition n scalar multiplication

[vestal swift]

Not going back Malaysia :')

[tawdry gull]

gong xi gong xi

[rancid schooner]

g(x)g(x)!

[vestal swift]

g(x)f(c)

[stuck rapids]

Nahhhh some probs

[rancid schooner]

@tawdry gull home for CNY?

[tawdry gull]

im alrdy home since december...

flying back at 1st of feb

[rancid schooner]

Nice. Enjoy CNY!

[vestal swift]

May your good luck be infinite like the number of elements in the span of a subspace

May your money in your bank account grow factorially like O(n!)

May u reach the top of class like a class variable and get that Dean's list 😤😤

[stuck rapids]

Wtf

HAHAHAHA

[verbal nova]

I need a lil bit of help for Linear Algebra plz

Reduced row echelon of A

And augmented reduced row echelon of A and u

Can someone plz explain a,b,c

[idle rain]

Help needed <@&597104882482413589>

[verbal nova]

My answers are
No, because the third column doesnt have a pivot
Yes, because system is consistent

[tawdry gull]

for a), if det=/=0 then it spans R3
for b), if matrix spans R3 then for sure the vector u is in the column space, otherwise you have to check it by urself using REF (I think u alrdy did from the third pic)
for c), just transpose the matrix and REF again

[rancid schooner]

There should be study sessions for this channel

[stuck rapids]

@rancid schooner u host one session

[vestal swift]

He always ask ppl host

Then ppl ask him host he say

"bOtS cAn'T hOLd sTuDy sESsiOn"

[vestal swift]

U can teamup with your bot friend chatGPT to host one :D

[verbal nova]

Ok so for c what do we do after Transpose and REF?

Our uni is speedruning linear algebra like as if we already done tbis shit

[tawdry gull]

c is basically u transpose then do the same thing as u did for b

[verbal nova]

Ahhhh alright, thank you

[idle rain]

Gave +1 rep to The_Pierrot#1126

[rancid schooner]

Others answer more maths problems here than I do.

[stuck rapids]

Nahh they don't

I see u answering most sir

[rancid schooner]

Only the easy ones.

πerrot answers (and also asks) difficult questions

[stark wave]

Welcome to uni

[stuck rapids]

That's true

[vestal swift]

Can somebody help me verify if this is true

Discrete maths fucking with my brain

😭😭

[tawdry gull]

nobody knows somebody means that no one knows a certain person, they may know others but not that one certain dude

what u drew is nobody knows anybody (or simply everybody knows nobody)

and also, does "know" means two-way or one-way here?

[vestal swift]

So same as somebody knows nobody?

[tawdry gull]

yeah

[vestal swift]

Uh actually in the context of the question it's mutual haha

[tawdry gull]

but depends on how u define "know"

it can be that i know u but u dont know me :b

[vestal swift]

But if according to english it's just one way right :truejoy:

[tawdry gull]

yap

[vestal swift]

Ok thank uu!!

[idle rain]

Gave +1 rep to The_Pierrot#1126

[tawdry gull]

just make sure u have a proper definition and ure good to go

👍

[rancid schooner]

Nice way to learn about mapping

Anyway there’s one more option

Everybody knows everybody and at the same time they don’t.
Like on Discord.

[stuck rapids]

My brain cell can't handle

[rancid schooner]

Discrete maths is fun

They should teach more of that at school and A-Levels.

Instead of calculus overdose

[verbal nova]

I love calc but I have no calc courses anymore :/

I wish AL math focused more on linear algebra

Especially Matrices

[rancid schooner]

So you have escaped the torture of epsilon delta 😄

[verbal nova]

Never did it 😎

I had one Multivariable calc course

Differentiation and shit

I can take Multivar calc 2 as an elective but nahhhh

[rancid schooner]

Discrete calculus

[verbal nova]

This is a contradiction

How can calculus be discrete

[rancid schooner]

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

[verbal nova]

Delete this shit

[rancid schooner]

😄

[stuck rapids]

That's the not the worst part yet

...

[rancid schooner]

What is?

[wary jungle]

https://tenor.com/view/moana-delete-maui-delete-this-gif-15101621

[stuck rapids]

Can't think of anything significant in mind now

[tawdry gull]

i'll be waiting

[minor schooner]

Agreed

[minor schooner]

Matrices isn't even there for standard A levels😭

[minor schooner]

So what's worse abt calculus?

[stuck rapids]

proving..so not just eplison delta

anything to do with theorems xD so in short calculus is not my thing hahha

[verbal nova]

plz plz help with a

[idle rain]

Help needed <@&597104882482413589>

[vestal swift]

O math gods

[rancid schooner]

Write a short Python code to simulate :)

[tawdry gull]

Make into matrix then rref it, the pivots indicates the useful vectors

[tawdry gull]

Thank god i dont have to do this

[vestal swift]

Yes ntu sucks

Hkust no discrete maths??

[tawdry gull]

Have but elective

Not required

I take pure maths i dont even have to do discrete maths if i want to lol

Compsci must

[vestal swift]

I'll ask chat gpt

[vestal swift]

But your calc super adv compared to mine lol

[tawdry gull]

Yesh we focus more on analysis here lol

& algebra

[vestal swift]

:')

Ours got some coding mods

[tawdry gull]

😔😔

We have coding too but not math requirement

[verbal nova]

Thank you 🙏🙏🙏

[idle rain]

Gave +1 rep to The_Pierrot#1126

[rancid schooner]

@tawdry gull

[vestal swift]

Oh math gods

Which book is better?

[rancid schooner]

What about Strang’s book?

[rancid schooner]

https://youtu.be/cGu0du5Q5mk
Features book on left

[vestal swift]

Nvr read that coz my lecturers dint use that book

LA1 lecturer used the Howard Anton one,
LA2 lecturer used the Sheldon Axler one :')

The pain when they don't stick to the same book 😭

[rancid schooner]

The story is the same. Just different storyteller.

[rancid schooner]

Perhaps someone can do a study session on basic undergrad linear algebra?

[tawdry gull]

LADR takes a more rigorous approach

Anton's is more to computation

[vestal swift]

But anton also got some proofs right :')

[vestal swift]

As in proofs more in-depth?or?

[tawdry gull]

LADR is for mathematicians
Anton is for engineers

thats the simple way to say it

LADR gives u more in depth stuff for ur understanding

what linear algebra is

[rancid schooner]

@tawdry gull used Strang?

[vestal swift]

Hmm but my LA1 lecturer is the head of pure maths and he used Anton lmao

[tawdry gull]

u can use anything technically lol

as long as the end u learn the requirements for it

[vestal swift]

Im dying in LA2 :(

My LA1 lecturer was better

Even tho he kinda snobbish :')

[tawdry gull]

ganbatte

[vestal swift]

Idk if I should take second major in data analytics :(

[tawdry gull]

if cannot just minor can right

[vestal swift]

Or specialize in stats or business analytics track

Coz our math track got 4 so

😭😭

[tawdry gull]

[rancid schooner]

Major and minox axes. Ellipse.

[rancid schooner]

They should just teach pure maths

[vestal swift]

Pls no

Us peasants will die

[rancid schooner]

Good to be pure

[tawdry gull]

👍

[rancid schooner]

😊

[stuck rapids]

wht pen is it @rancid schooner

[rancid schooner]

Faber-Castell Loom fountain pen. 😊

[stuck rapids]

Rm 120..?

Omg wht

[rancid schooner]

It was RM200 a few years ago but there was a 15% or 20% year end discount then.

It’s a nice pen though :)

[stuck rapids]

Owhhhhh

But a rm 200 pen

Fr hahahaha

[rancid schooner]

Can last quite a few years.

Anyway there are other pens which are even more expensive

[stuck rapids]

for example xd

[rancid schooner]

Those with gold nibs. This one is stainless steel. Although it writes very well.

[stuck rapids]

Owhhhhh

[rancid schooner]

Go get one 😄

[stuck rapids]

No money @rancid schooner

Maybe Mr Alex can sponsor me

Hahahaha

[rancid schooner]

Ask for one as a present for your brilliant results!

[stuck rapids]

for a levels?

[rancid schooner]

Yes 😄

[stuck rapids]

🤣 not an excuse dy for now

[tawdry gull]

interesting questions

[rancid schooner]

Looks fun!

What an enjoyable course you are doing 😄

[tawdry gull]

try doing them alex haha

[minor schooner]

Is this what awaits me if I major in math??

Damn

[tawdry gull]

if u take honors and have a prof that likes to give hard questions

maybe yeah

this is the first homework lol

and i didnt send the other 2 (3 if u include optional) questions

[rancid schooner]

What is meant by taking honours?

Does the university follow the Australian system?

[tawdry gull]

we have honors version courses which are harder than the usual course

[rancid schooner]

Congratulations! And best of luck!

Is there an easy maths degree anywhere in which they just give you fun problems to solve without too much of the dry theoretical stuff?

[tawdry gull]

Sadly not :)

Analysis is compulsory in math degrees

[stuck rapids]

Never knew maths can be considered as easy

Hahahahahhaa

[rancid schooner]

Well perhaps not easy but less dry 😄

[young marten]

the dry theoretical stuff doesn’t exist xD

[stuck rapids]

True true

Maths is indeed very dry

Especially calculus

[stuck rapids]

all these just to prove chain rule

[rancid schooner]

For πerrot’s enjoyment :)

[tawdry gull]

it's just like that :v

and also, notation bad there

actually more like typos

[rancid schooner]

Please circle in red

[tawdry gull]

can i do it in blue?

[stuck rapids]

i will send more proofs from my textbook then

HAHAHA

[rancid schooner]

Just send the whole textbook

[stuck rapids]

He is gonna correct every single thing in da book

Hahahaa

[rancid schooner]

Edited by πerrot

[tawdry gull]

What is ur textbook even

It’s got like 2 typos in that one single page 💀💀

[vestal swift]

Math gods ? 🥹

I'm stuck at the recurrence formula part bc I have something like a piecewise function 😭

[rancid schooner]

Think in terms of density

[rancid schooner]

||5f(n+1) = 3f(n)+4||

[rancid schooner]

Challenge: Can you derive a continuous form approximation?

On a different note I wonder if anyone here thinks it’s an abomination to mix tea and coffee.

[tawdry gull]

@rancid schooner if you would like to try ;)

[rancid schooner]

Please conduct a study session on the topic first 😄

[tawdry gull]

No need

[late frost]

WTF !

[rancid schooner]

Is that the correct answer?

[vestal swift]

Yessir

I interpreted the qs wrongly 😭

[vestal swift]

No sir I lack the brain cells

[rancid schooner]

😊

[rancid schooner]

Of course you can 😄

[vestal swift]

I have an op Ed due monday

I'm MATH

[rancid schooner]

How did you solve it?

[vestal swift]

And ntu expects me to be an all rounder 😭

[rancid schooner]

What op ed?

You’re writing an article?

[vestal swift]

Coz initially I interpreted it as pour 1L as one step then pour back as second step

[vestal swift]

Yea place, community in sg or writing habits

😭😭

[rancid schooner]

What are you writing on?

[vestal swift]

Place

Any humanities ppl here :')

[rancid schooner]

Show how you solved

[vestal swift]

I desperately need someone to proof read 😭

[rancid schooner]

Just post it here 😄

Did you write about the best place for a mathematician to hang out in Singapore?

[vestal swift]

No

Not math related so

[vestal swift]

Just the extended version of ur ans

f(n)=¾f(n-1) + 1/5 (4-f(n-1)+¼f(n-1))

Then simplify it to get ur ans

Idk if it's complete tho

[rancid schooner]

Nice

Is this under recurrence? Discrete maths?

[vestal swift]

Yessir

[rancid schooner]

Nice. Post more questions.

[vestal swift]

If my bacon fell to the floor in ntu canteen then I picked it up and ate it within 5 seconds, what is the probability that I'll get diarrhea?

[rancid schooner]

Is that under probability or discrete maths?

[tawdry gull]

I think it’s discrete maths, probability is under discrete maths right?

[vestal swift]

Maybe both

My LA2 lecturer is just

Idk man

"I'll be on reservist next week, so just watch the recordings that I uploaded"

The recordings: "Proof omitted", "Left as exercise", "Do it yourself"

[rancid schooner]

did he think of the bacon on the floor question?

[vestal swift]

Lmao no hahaha

[vestal swift]

This is what happened to me today :)

[rancid schooner]

Did you eat it?

[vestal swift]

funny how he only does the questions that I know how to do, the ones idk he omits them :')

[vestal swift]

Yessir

Hence the question

Still no diarrhea for now

[rancid schooner]

you need to define the timeframe for the diarrhoea to occur

[vestal swift]

i hope it doesn't :")

[rancid schooner]

Any diarrhoea?

[young marten]

out of context alex

[tawdry gull]

🙃 🙃 🙃

[rancid schooner]

Nice. Your favourite topic. Integrals.

[vestal swift]

@rancid schooner @tawdry gull

I'm too dumb for this

[tawdry gull]

I check later

[rancid schooner]

Exploit the symmetry

[vestal swift]

What symmetry

[late frost]

WTF

[late frost]

😨

[rancid schooner]

was tempted to post the solution but better to allow you to enjoy the fun of attempting it :)

[late frost]

@rancid schooner r u in uni bro?

[rancid schooner]

Alex is a bot trying to learn maths :)

[late frost]

:)

I wanna become like you

teach me

[rancid schooner]

You should aim to become like πerrot 😄

[late frost]

yes

[tawdry gull]

i am rubbish

dont become like me

[late frost]

oki

[vestal swift]

Wait so you replaced 2022 with 2u?

[vestal swift]

Why did you replace x with 2pi - x ah

[vestal swift]

Happy Valentine's, I have a confession ❤️
Dating is just trial and error in hopes of finding that partner but there are too many unknown parameters in life so the probability is undefined and ever fluctuating due to Bayesian probability or some shit 😌

[tawdry gull]

u = 2pi - x

[vestal swift]

But why 2pi :(

[rancid schooner]

It’s 2n not 2u

[rancid schooner]

2 π - x to exploit the symmetry

Actually it’s substituting u = 2 π - x. Then do all the usual stuff. Then replace u with x.

[vestal swift]

Why not pi-x tho?

[vestal swift]

Symmetry of graph or?

[rancid schooner]

Because of the limits

[rancid schooner]

Symmetry of function. And consequently graph.

[rancid schooner]

Try it and see then you’ll get a better understanding why it doesn’t work

[stuck rapids]

🤣

[rancid schooner]

Is it like Newton-Raphson search?

[stuck rapids]

Yes

It is

[mellow ether]

I need help with this. It's 2nd order ODEs(Variation of Parameters)

I can't figure out how to integrate u1' or is it me who made a mistake from the start

[rancid schooner]

@tawdry gull is this correct?

[verbal nova]

Dead chat but I have a question

lets say Vector V is a subspace of R2

is the vector <1,0> in the subspace of R2?

very dumb question, ik

[tawdry gull]

yes

[verbal nova]

Ok ok, thx

[idle rain]

Gave +1 rep to The_Pierrot#1126

[tawdry gull]

@rancid schooner

if you wanna try

[rancid schooner]

Nice. Looks more like STEP rather than undergrad maths?

[tawdry gull]

it's most likely taken from HKALE

Hong Kong A Levels

[rancid schooner]

Thought it’s been replaced by the school leaving diploma

[tawdry gull]

which unfortunately has stopped at 2012

[rancid schooner]

Yes

[tawdry gull]

yeah it has, DSE it's called

try it out 😄

[rancid schooner]

Is there an IGCSE replacement?

[tawdry gull]

im not sure

[rancid schooner]

When you say this it means the question must be quite tricky 😄

[tawdry gull]

quite haha

but maybe you can find some neat trick there

[rancid schooner]

Is the DSE more difficult than the HKALE?

[tawdry gull]

easier

[rancid schooner]

Apparently it’s multiple choice. Or at least parts of it.

[tawdry gull]

HKALE involves some current undergraduate materials

such as mean value theorem or even lagrange remainder formula

but DSE has deleted those

HKALE also got easier throughout the years

[rancid schooner]

Maybe more practical

[tawdry gull]

yeah

try the question out haha

[rancid schooner]

Maybe after dinner haha.

[tawdry gull]

suree

[rancid schooner]

Please post some nice HK food pics on #the-food-network

[rancid schooner]

It pairs nicely with its conjugate integral J_n with cos replaced by sin.

[tawdry gull]

how does it pair?

[tawdry gull]

ahh i see

[rancid schooner]

😊

Is that valid as a reduction formula?

[tawdry gull]

must only be in terms of I_n 😂

[tawdry gull]

yes thats right

[rancid schooner]

😊

The fact that I₂ is negative the reciprocal of the solution to the Basel problem is interesting :)

Maybe it might be easier to use the Maclaurin expansion of cos πx to integrate.

[rancid schooner]

@tawdry gull did you use that?

[tawdry gull]

Nope

[rancid schooner]

Don’t need Jn if you continue the IBP further until you get I(n-2).

[rancid schooner]

https://www.youtube.com/watch?v=MfI1gA910Cw

@tawdry gull should have been there 😄

[rancid schooner]

@tawdry gull doesn't seem to converge either on Excel or Python (shown here).

maybe they can't handle the precision... 🤔

[tawdry gull]

The limit converges actually haha

To -1

[rancid schooner]

Yes I know 😊

Just saying that it’s curious how commonly used computation tools can’t handle the precision required.

Usually it’s not a problem

But if you compute the integral directly for any large n using Desmos or Wolframalpha it converges.

[rancid schooner]

@tawdry gull do you take numerical computation as a subject?

[tawdry gull]

numerical analysis

[rancid schooner]

(c) is 1?

[rancid schooner]

Yes. Do you?

[tawdry gull]

yep

[tawdry gull]

i dont think im taking it

im not interested haha

[rancid schooner]

It would help explain why the recursion doesn’t seem to work numerically. And to help come up with adjustments to make it work.

[blazing wraith]

how to do this?

[idle rain]

Help needed <@&597104882482413589>

[blazing wraith]

is it just 50mm?

[rancid schooner]

Nice. Q4 is the famous Dalzell integral.

@tawdry gull

[vestal swift]

my tutor: "only 2 ppl in the entire cohort could do this q last yr" AND I AM NOT ONE OF THOSE TWO T-T

welp i am fucked for tmr's calc exam

[tawdry gull]

just x=1/u

let the original integral be I, after substitution you add them together to get the result

[rancid schooner]

looks like an A-level question

or STEP

[rancid schooner]

very nice. to exploit the symmetry.

[vestal swift]

How to get that intuition😭

[rancid schooner]

pretend to be πerrot 😄

[tawdry gull]

by experience...

and just like that, u r one of the two ppl in the cohort

[rancid schooner]

maybe she is one of the two who could answer another question

[vestal swift]

No way :(

If I could I would've gotten A+ for calc 1

😭

Y'all got more hard calc2 qs? :(

[vestal swift]

Nah ur just too smart 😭

[rancid schooner]

dQ planning to go into academia or teach maths after graduation?

[vestal swift]

dQ too dumb

sleeping on the streets

[rancid schooner]

not true

highly sought after graduate

do they have a maths society?

[vestal swift]

If u mean spms club then yea

But like not super math-y haha

[vestal swift]

Last time I checked data sci pay was the highest

[rancid schooner]

What is spms?

[tawdry gull]

school of physical and mathematical sciences

[rancid schooner]

Nice

[rancid schooner]

What do they do?

[vestal swift]

Like recently they sent those math puzzles similar to presh talwalker's mind your decisions

Apart from that it's like generic club stuff

And yea based on Devan's problems HKUST math is wayyyyyy harder than NTU math

AND IM ALR DYING IN NTU MATH😭

[long aurora]

what's NTU?

[rancid schooner]

they sent the primary school exam question?

so dQ joined other non-nerdy clubs at uni?

[vestal swift]

HAHAHAHAH some random sg uni 💀

[rancid schooner]

among the top in asia

[vestal swift]

Lmao is presh talwakers qs primary standard

[vestal swift]

Nah the rankings r fake

Quality wise hkust looks better HAHAHAH

[vestal swift]

Just for cca pts

[rancid schooner]

someone sent a PSLE question to him

[rancid schooner]

what clubs

[vestal swift]

Someone sent a spm qs also

Rotaract

[rancid schooner]

that was a few years ago haha

[vestal swift]

Ok ANY TEXTBOOK RECC for CALC 2?

I tried James stewart and did a bunch but still midterms one are harder than the book 😭

But not as difficult as hkust level 😭😭

[rancid schooner]

a charity club?

thought they would have many interesting clubs

[rancid schooner]

did you do that paper?

was it you who sent him the question?

[tawdry gull]

we simply have honors courses

im pretty sure NTU does too

this is the description of my current homework lol

[vestal swift]

Sort of ya

[vestal swift]

Yes but I dint send it HAHAH

[vestal swift]

Ya ours way ezier

Even tho still hard for me😢

[tawdry gull]

u picked the easier one or is there no harder one?

[vestal swift]

Y1 standard

Can't pick

Y2 onwards specialization

[tawdry gull]

oh so no like

[vestal swift]

But still hkust one is harder

[tawdry gull]

special math course for y1?

[vestal swift]

Got advanced calc

But nobody take

[tawdry gull]

as in honors version for y1

ooh

[vestal swift]

COz like 1 AU

But too much work

But even advanced calc is ezier than hkust standard

[tawdry gull]

our normal calc is easier than urs

[vestal swift]

Have to emphasize I'm still too dumb for it

[rancid schooner]

did you know that bourbaki (typo in question paper) is not one mathematician but several?

[vestal swift]

Send pic see

[tawdry gull]

yes i do lol

[rancid schooner]

😊

[tawdry gull]

ours is just like calculating stuff mostly

[rancid schooner]

i would like to belong to a club of mathematicians like that. they meet to discuss maths over lavish meals and fine wine.

[tawdry gull]

right now, their calculus 2 (i say their cuz im not taking it), are learning reduction formula

just like further maths A levels

[tawdry gull]

we have that in the math dept every friday 🤪

[rancid schooner]

hmmm teaching further maths at university

[rancid schooner]

nice! what food do they serve? send pic!

[tawdry gull]

i never joined though

i wasnt invited

[vestal swift]

Ours also

[tawdry gull]

maybe cuz im not in the math major yet

[rancid schooner]

form your own club

[vestal swift]

Until chap 3 is mostly fm a2

Apart from FTC

[tawdry gull]

this is a pic from my friend asking help from me

[vestal swift]

And Simpsons rule

[vestal swift]

And trapezium rule midpoint rule

[vestal swift]

Ch4 onwards is sequences

[rancid schooner]

so simple. maybe she just wants your attention :)

[tawdry gull]

it's a he....

[rancid schooner]

right. maybe he just wants your attention :) :)

[rancid schooner]

sequences nice. show questions.

[tawdry gull]

@vestal swift but honestly i think ur calc course is harder than our standard calc

just that we have honors courses

[vestal swift]

Not there yet haha midterm doesn't cover that

[vestal swift]

Send ur midterm then I'll send mine compare see see XD

Abt the same ig

[tawdry gull]

my midterm or their midterm?

so u want mine?

mine is honors :b

[vestal swift]

Lmao our tutorial q also got this q

Very similar

Just without the -5

[tawdry gull]

ooh

[rancid schooner]

how big is the tutorial class

[vestal swift]

NO HAHA REGULAR CALC IF GOT 😭💀

[tawdry gull]

i try find find

[rancid schooner]

did all maths majors do further maths at a-levels?

[tawdry gull]

if u talk abt mine, almost all didnt even do a levels at all :b

[rancid schooner]

haha asking dQ

but for HK do they have maths and further maths as two different subjects for their school diploma (what's it called?)?

[tawdry gull]

@vestal swift

[tawdry gull]

they do DSE

but im not sure if they have such thing as further maths

[rancid schooner]

so only one maths subject then

it's a good idea to have both

so those who are really interested can take further maths

but everyone else should take basic maths

[tawdry gull]

im asking my friend if there is such an equivalence

[rancid schooner]

Q1 is interesting. does it have to do with cryptography?

[tawdry gull]

validity of the exam paper

to be graded

[rancid schooner]

yes i mean something like a check digit

[tawdry gull]

yeah

they made different versions of the exam paper to prevent cheating

[rancid schooner]

nice. a lot of work though.

[vestal swift]

MCQ FOR MATHS?!?!

[tawdry gull]

yes

[vestal swift]

the only qs i am confident

Ntu standard

^this yr was harder coz diff lecturer i think

[tawdry gull]

LOL

i see first question

alrdy harder than our standard calculus

[vestal swift]

is ok haha the other yrs ezier

[tawdry gull]

this is equivalent to the course in between of our standard and honors

@rancid schooner

[rancid schooner]

so it's their version of maths and further maths

[tawdry gull]

https://www.edb.gov.hk/attachment/en/curriculum-development/kla/ma/curr/CA_2017_e.pdf

check pages 50-85

[long aurora]

i want to major in math but i dont take further maths

[tawdry gull]

it will be helpful if u take fmaths

[long aurora]

it's a lil too late tho

[tawdry gull]

oh damn

[long aurora]

my A2 exams are this may

[tawdry gull]

right

but u still can go into maths ofc

but the jump will just be a bit higher

no worries tho, they will teach from the beginning again to review

[long aurora]

i see

[tawdry gull]

and one thing about math major is that

analysis is compulsory, no matter which math u go to

so just a heads up cuz, for most, it's one of the most challenging courses in math

[rancid schooner]

Did @tawdry gull learn analysis all by himself before going to university?

Anyway spotted something interesting in a mall today. 😄

@tawdry gull

[tawdry gull]

im not sure if thats me

[rancid schooner]

😄

Well you are Pierrot and you are lucky to be so smart! 😄

[mild fulcrum]

triangle fancy

[tawdry gull]

proof without words of $\sum_{k=1}^n k = \binom{n+1}{2}$

[round siren]

The πerrot

[rancid schooner]

Nice animation and illustration of proof

Would be nice if there is a similar one for the sum of C(n+1,2) in 3D 😄

[tawdry gull]

@rancid schooner
Suppose there are k gas stations in a circular road, each gas station has a gas capacity such that when you take the sum of all k gas stations it will be 1 litre. You drive a car starting with no gas, if you drive past by a gas station you take all the gas they have. The journey to make a whole loop takes 1 litre.

Prove that there exists a gas station to start your journey such that you can complete a whole journey.

I hope you havent heard of this one before

[rancid schooner]

Haha dynamic programming

[tawdry gull]

if it will motivate you, it has a neat solution

:)

[vestal swift]

O math gods, is part (d) integral test?

[rancid schooner]

Seems reasonable

Summation starts from 3 so that’s a useful clue

[vestal swift]

Is there a shorter way?

Like limit comparison test

[rancid schooner]

But integrals are fun 😄

[vestal swift]

It's VERY LONG

[rancid schooner]

Wow so neat 👏🏻

You should get a prize for the best handwritten maths solution.

Shouldn’t the integral be of (ln(x-1))² / (x-1)³ since you want to show convergence rather than divergence?

[vestal swift]

Wait why tho

Neat but is it correct

[rancid schooner]

Here’s an even better one

Use ln n < √n and that reduces the comparable sum to the Basel problem summation converges 😊

[rancid schooner]

Because you want the integral to “cover” the summation bars. Draw graph and see.

[vestal swift]

No clue what is this

[rancid schooner]

It’s the infinite sum of the reciprocals of squares

Very famous problem

Solved by Euler

[tawdry gull]

ln(n) < sqrt(n) will get u 1/n^2 which converges by p series

[rancid schooner]

😊

[vestal swift]

Hmm but the prev examples in the lecture notes also follow the series tho 😭

[rancid schooner]

but that is to prove that it's divergent

[tawdry gull]

where the ^2 and the ^3?

[rancid schooner]

Is this related to Bertrand’s Ballot Problem?

[verbal nova]

You guys ever heard of Monte Carlo integration?

[rancid schooner]

There’s Monte Carlo simulation

[verbal nova]

There's an integration technique based on it

You take bunch of random samples from a to b, pass it through f(x), take its average and multiply by (b-a) to get an approximation

[idle axle]

hello

i hath been summoned

[tawdry gull]

hmm?

[rancid schooner]

name sounds familiar

[rancid schooner]

undergrad now? maths major?

[verbal nova]

[idle axle]

crying over latex alignment

[idle axle]

undergrad, aero eng (but i am maxing out my higher math courses), slay

guys how tf do i align my equations to the center, asking for help, genuinely, crying at 6.00am in the morning

apparently all the engineers are using word and im the only one using latex rip

[verbal nova]

MS word does have latex and math stuff too yeah

I just used it for my recent project

[tawdry gull]

linalg?

[tawdry gull]

which one is "not in the center" here?

[idle axle]

the x_1, x_2, and x_3 equation

[idle axle]

im trying to center them so like [ ] but allign at the = sign

rip

[tawdry gull]

LOL TEXIT

[idle axle]

bruh

not that removing

ive been whacking my head

for the past hour

tryning to center this shit

im literlaly done, but i cant centre

[tawdry gull]

hmmm

[idle axle]

latex guarantees my chances of getting 100%

[tawdry gull]

im more confused on why \begin{align} for u doesnt center it

[idle axle]

FOR REAL

[tawdry gull]

because mine does...

do u mind if u give me access to ur doc?

i have an overleaf acc

[idle axle]

i neede to give you my whole login id

can i give you my code?

[tawdry gull]

wait what

login id?

[tawdry gull]

yeah sure

but it's also possible to invite a person in overleaf

just like google docs

[idle axle]

ayo

[rancid schooner]

Nice. University in which country?

[verbal nova]

I think she's in Australia, not sure

[tawdry gull]

australia

unsw

[rancid schooner]

Nice. Clever girl.

[verbal nova]

Anyone here know how to do an ANOVA in stats?

[tawdry gull]

sadly not me...

[long aurora]

why is the circumference of a circle the derivative of its area?

i realized this while staring blankly at the sticky note on my wall

i searched it up but the explanations are too... complex for me?

[verbal nova]

Im gonna take a guess here and the Math Lords can say if im right or not

Circumference = derivative of Area
is same as
integral of circumference = Area

And integration means taking multiple small areas and adding them up

Lets say im taking the area of all these circles 2pi*r from r = [0 to n]
total area = pi*n^2

n being radius of the big circle

sum of all inner circles circumferences = area of outer circle
2pi*0.0001 + 2pi*0.0002 + 2pi*0.0003... + 2pi*r = pi*r^2

[tawdry gull]

basically like that yea

[rancid schooner]

Nice. Now try drawing a spiral.

[rancid schooner]

How did people know this (or did they?) before calculus was discovered/invented?

[verbal nova]

Hmm

[rancid schooner]

And also how did they know that the surface area of a sphere is four times the area of its great circle?

[finite spear]

Maybe it was this:
https://people.wku.edu/tom.richmond/PiR2b.gif

[vestal swift]

Hi math gods, can i ask what is the correct way to show this

Idk how to fix this 😭

[tawdry gull]

only worth 2 points no need so much working la

the center is at x=-3, it converges when x=-6 and diverges when x=1

distance from x=-3 to x=-6 is 3, while distance from x=-3 to x=1 is 4

since it converges when x=-6, the radius of convergence must be at least 3

since it diverges when x=1, the radius of convergence cannot exceed 4

hence 3 <= R <= 4

[vestal swift]

Oh lmao the reasoning is that simple ah

OK thankiew😭

[tawdry gull]

👍

[vestal swift]

Is this a valid proof 🥲 (the second b_k on second line got modulus oops)

To this: https://math.stackexchange.com/questions/3595657/sum-n-0-infty-a-k-converges-absolutely-and-sum-n-0-infty-b-k-converg

[tawdry gull]

|bk ak|/|ak| is limit comparison test?

[vestal swift]

yes

been doing power series whole day

my brain is not functioning

[tawdry gull]

limit comparison test works if the limiting result is >0

[vestal swift]

is there a shorter way

[tawdry gull]

u got 0 so thats invalid

[vestal swift]

for?

[tawdry gull]

the limit of the ratio must be >0

[vestal swift]

nani

this is our lect notes

[tawdry gull]

oh okay

then thats fine

[vestal swift]

hkust diff league T-T

[tawdry gull]

no lol i just took it from wikipedia 🗿

[vestal swift]

oh lmao

[vestal swift]

coz this stuff too basic for hkust AHHA

[tawdry gull]

🗿

[rancid schooner]

Maybe πerrot can do a study session for university maths

[rancid schooner]

Need to put this in a nice table

A truth table.

[rancid schooner]

It’s a strange way to phrase the question though. We know for sure that R >=3. We also know R must be less than 4. But we cannot actually claim that 3<=R<4 because we don’t have enough information about the upper bound. Eg we don’t know if eg R=3.9 is a valid radius.

[tawdry gull]

3.9 is valid because it ensures that x=-6 converges but x=1 diverges

So the answer is still 3 <= R <= 4

[rancid schooner]

Perhaps a better way of writing it would be to say that R cannot be less than 3 and cannot be greater than 4.

Which is not the same as saying that R lies between 3 and 4.

[tawdry gull]

Can’t be less than 3 & cant be greater than 4 is 3 <= R <= 4 right?

[rancid schooner]

Not exactly so. Slight difference logically.

[tawdry gull]

Negation of (R< 3 or R>4) = (R>= 3 and R<= 4) = 3 <= R <= 4

[rancid schooner]

I go to a cafe at 3pm one day and it is open.

I go to the same cafe at 4pm another day and it is closed.
Assume that the cafe has the same opening hours every day.
I can conclude that the opening time of the cafe cannot be later than 3pm, and the closing time cannot be later than 4pm.
But I cannot conclude that the opening hours of the cafe are 3pm to 4pm.

[tawdry gull]

Do you mean to say it should be 3<= R < 4?

[rancid schooner]

Nope.
I meant
R≮3 ∩ R ≯4

[tawdry gull]

So R>= 3 U R<= 4 ?

That would mean the whole real number line…

[rancid schooner]

Typo fixed :)

[tawdry gull]

Then that is still 3 <= R <= 4

[rancid schooner]

Refer to the cafe analogy.
Came up with it because I’m at a cafe right now haha.

[tawdry gull]

Hahaha i see

[rancid schooner]

Based on the information given, you know for certain that
R≮3 ∩ R ≯4.
But you do not have enough information to conclude for certain that
3 <= R < 4.

[tawdry gull]

the answer is 3<= R <= 4 right? why 3<= R < 4 ?

[rancid schooner]

So if your friend asks you “what are the opening times of the cafe?”, you cannot reply “3 to 4pm”.

[tawdry gull]

the point of R≮3 ∩ R ≯4. implies that it can only be 3<= R <= 4

cuz the question also asked "the largest and smallest possible values"

[tawdry gull]

so the right question for the cafe would be "what is the possibly largest duration of opening times of the cafe" if u were to match the context with the question

basically the most optimistic answer

although it is possible to say to have radius of conv of 3.2 <= R <= 3.8

but that is not what the question asks since they were asking for the largest and smallest possible values

[rancid schooner]

Not duration but opening and closing times.

[tawdry gull]

yeah u get the point 😂

[rancid schooner]

What I’m saying is that we cannot definitively say R is between two values.

A simple way to settle this is to say
3 <= possible R < 4.

[tawdry gull]

eh, isnt that the point?

[rancid schooner]

Yes but just emphasizing

[tawdry gull]

R has to be bounded by two values in order to satisfy the condition

so the possibilities of R is 3<= R <= 4

[rancid schooner]

So the answer for the cafe question should be
“the opening hours of the cafe could be 3pm to 4pm”
and not
“the opening hours of the cafe are 3pm to 4pm”

[tawdry gull]

yeah

[rancid schooner]

😊

Hmmm I’m the only one doing maths in this cafe.

[tawdry gull]

thats great 😄

[rancid schooner]

I should ask them what time they close 😄

[vestal swift]

Is it a maths cafe

I am vv confused

[rancid schooner]

I was in a real cafe :)

[formal compass]

Looks tasty xd.

[rancid schooner]

yes it was

😊

[formal compass]

Oo that's great!

[rancid schooner]

which inspired me to come up with the cafe opening/closing time analogy 😊

[vestal swift]

If i wanna show convergence for the series 1-cos(1/n) , is this ok? I know the alternative solution is shorter but I could only think of the inefficient one 🤡

[tawdry gull]

Sure thats ok

There is no point in saying 0 < 1/n < 1 tho

[rancid schooner]

nice. dQ learning all the convergence tricks.

[vestal swift]

HAHHA I'm extra

[vestal swift]

The limit proof is rigorous af

I won't know how to do this during the exam

Shit af

Isn't this like real analysis stuff 😭

[rancid schooner]

Back to delta-epsilon

Maybe you could change your name from dQ to δ ε 😄

[tawdry gull]

the intro actually

[vestal swift]

https://math.stackexchange.com/questions/2244339/prove-if-sum-a-n-converges-then-sum-frac1a-n-diverges

is there a rigorous way to prove this? (using precise definition of limit)

[tawdry gull]

using precise definition is too tedious i think

if u at least want to use some epsilon-N stuff

since a_n -> 0, then there exists N such that for all n>N => -1< a_n <1

so 1/a_n is >1 or <-1

implying divergence

[vestal swift]

this isnt precise def?

[tawdry gull]

no

precise def too hard

maybe not possible lol

[vestal swift]

so choose epsilon =1 or?

[tawdry gull]

yes

[vestal swift]

i suck at RA sry :')

[tawdry gull]

choose epsilon=1

[vestal swift]

ok thank u math god

[idle rain]

Gave +1 rep to The_Pierrot#5106

[vestal swift]

can donate some brain cells for my calc exam tmr ? :')