ug-maths-physics

[tawdry gull]

as much as possible

[little widget]

Proof : a + b = b + a
If a + b = b + a
a+b = b + a
QED

[rancid schooner]

@tawdry gull

[tawdry gull]

looking at this makes the question sounds so easy

[rancid schooner]

😊

Well they did give you a_n as a hint haha.

[tawdry gull]

how did the hint help you?

[rancid schooner]

Compute the first few values and find that they are the same as b_n.

[tawdry gull]

same as in?

[rancid schooner]

numerically equal

[tawdry gull]

ah i see

when i tried making progress

i found that $b_{n+2}=a_{n+1}-a_n$

[round siren]

The πerrot

[tawdry gull]

which was...

im not sure how to prove by induction haha

[tawdry gull]

for n=1,2,3...

[rancid schooner]

Oh I used a2 = 1 haha

[tawdry gull]

a2 = 4 right :'D

so technically an =/= bn

different initial conditions

[rancid schooner]

a’n = bn 😄

[tawdry gull]

haha

[tawdry gull]

does that mean your proof is wrong or... it doesnt matter?

[rancid schooner]

My proof should still be valid. Because in a proof you don't have to explain where you got your inspiration from.

[tawdry gull]

okay thats good then

haha

[rancid schooner]

haha i.e. you don't have to explain why you assumed b(n) = A b(n-1) + B b(n-2).

[tawdry gull]

yes ofc haha

[rancid schooner]

anyway from your earlier observation you can easily derive the same

[tawdry gull]

how so?

[rancid schooner]

$b_{n+2}\
=a_{n+1}-a_n\
= (4a_n-a_{n-1}) - (4a_{n-1}-a_{n-2})\
=4(a_n - a_{n-1}) - (a_{n-1}-a_{n-2})\
=4b_{n+1}-b_n$

[tawdry gull]

...

well

why didnt i think of that

[round siren]

AlexV

[tawdry gull]

that couldve been much easier

[rancid schooner]

😊

[tawdry gull]

alright thanks a lot alex for the insights

[rancid schooner]

a pleasure

anytime

[verbal nova]

Because im not a edexcel student

Todays class I 😴

[tawdry gull]

credit transfer?

[verbal nova]

Exemptions

[tawdry gull]

ah i see

[verbal nova]

What does φ : R -> R^2 mean

[tawdry gull]

function that maps an input a real number to a vector with 2 components

[verbal nova]

[verbal nova]

Thanks

[idle rain]

Gave +1 rep to The_Pierrot#7889

[tawdry gull]

no problem sir

no one saw anything

[rancid schooner]

in a server we are usually not allowed to ping everyone but what if we ping @verbal nova ?

[verbal nova]

I get pinged lol

[little widget]

Shut ur normie ass

U havent done epsilon delta definition of limit

Go back to calc 1

[verbal nova]

🤓

I have Alex and Pierrot

[rancid schooner]

@tawdry gull you should ask your lecturer this question: how can you tell if a recurrence relation can be expressed in linear form?

[tawdry gull]

next time when i have the chance haha

[tawdry gull]

@rancid schooner do spoiler if u have done a solution

haha

[rancid schooner]

Haha just when I thought I could relax 😄

Oh it’s a related problem.

[swift zinc]

2 questions in my number theory assignment i gotta solve

[rancid schooner]

I’ve already worked out the general case haha.

[tawdry gull]

oh thats amazing

[rancid schooner]

I did it yesterday as I was curious

After solving it

[tawdry gull]

do send here as a spoiler

i havent made an attempt yet

[tawdry gull]

number theory is not my passion 😩

[rancid schooner]

||b(n) = (c+2) b(n-1) - b(n-2)||

[swift zinc]

haha

[rancid schooner]

😊

[tawdry gull]

is this the solution or smth? haha

[rancid schooner]

See above.

This is the solution haha.

Not difficult. Same method.

[tawdry gull]

oke will try later

haha

[rancid schooner]

Have fun

[swift zinc]

figured out part c hehe

now only part b left

[tawdry gull]

@rancid schooner just attempted it on my own

I got it haha

[rancid schooner]

Nice 👏🏻😄

[rancid schooner]

||a(n) and b(n) are always of different parity||

||taking mod 2022 doesn’t alter parity||

[swift zinc]

I'm confused

[rancid schooner]

||when one is odd the other is even||

[swift zinc]

Ah

[rancid schooner]

Is this part of lectures on calculus or discrete maths?

[swift zinc]

Ok this makes a lot of sense

[rancid schooner]

||Proper argument:
5x+1 changes the parity of x. And taking mod 2022 doesn’t change the parity. Since a1 and b1 are of different parity, and their parity changes for each increment, an and bn will always be of different parity and therefore cannot be equal.||

[rancid schooner]

😊

[swift zinc]

Yeah this was the reasoning I was gonna go with after you explained the parity thing.

Thank you so much

[rancid schooner]

😊

[tawdry gull]

Wdym?

[rancid schooner]

the subject for the question on recurrence

[tawdry gull]

Not taught in lectures

But still have to do them

We were only taught abt sequences

But not solving recurrence in itself

So it’s all on us to study it

[rancid schooner]

under which subject?

[tawdry gull]

Honors calculus 1

Thats the only math class i have this semester

Others are just requirements

[rancid schooner]

discrete maths in a future semester?

[tawdry gull]

If i wanna take yes

[rancid schooner]

recurrence relations is probably more discrete maths than calculus

[tawdry gull]

It’s the convergence part that’s calculus

[rancid schooner]

everything converges to calculus 😄

[rancid schooner]

Do consider. Very interesting subject.

[tawdry gull]

Will see

[rancid schooner]

But maybe you’re more interested in continuous stuff haha.

Since you like difficult integrals.

[long aurora]

difficult integrals... in discrete math? 😃

[little widget]

No.

Difficult integrals

In calculus

And maybe physics but physics is lazy as fuck with integrals

Will call everything trivial

[swift zinc]

i also prefer continuous to an extent

tho discrete math is sort of interesting

unlike abstract algebra 🤮

[rancid schooner]

If you like both then you like concrete maths 😄

[swift zinc]

haha nice

[rancid schooner]

there's a book with that title

[tawdry gull]

@rancid schooner

what do you think?

the questions we did together are question 4 and optional question

[rancid schooner]

Wow looks very professional! 👍🏻😄

[tawdry gull]

all this for bonus points

haha

[rancid schooner]

Do they expect students to typeset homework beautifully in LaTeX like this?

[tawdry gull]

heres the explanation

[rancid schooner]

0.2 points. Well every point counts :)

[tawdry gull]

good practice too for LaTeX

so why not

good for future

[rancid schooner]

But it takes up a lot more time though

[tawdry gull]

yeah

[rancid schooner]

If it’s essay writing it’s understandable to require submission in typed up format in pdf rather than handwritten. But for maths homework it does take up a lot of time. TeX is primarily for writing papers, lecture notes, or maybe a special project.

Maybe you can find a software to convert handwriting to TeX :)

Anyway if I’m the lecturer I would use this as the sample solution for future students haha

[tawdry gull]

hahaha i see

[little widget]

It wasnt in TeX?

[rancid schooner]

?

[rancid schooner]

So you use a clear square rather than a black square or halmos to indicate end of proof

[tawdry gull]

its part of the package

which i couldnt (or just dont know how) change

[main topaz]

https://mathpix.com/

[tawdry gull]

ah thats nice

itll help a bit

[main topaz]

Have used this for small equations, not sure how it'll hold for larger text

[tawdry gull]

it will help for equations

which is nice

[rancid schooner]

$\text {...end of proof.} \blacksquare$

[round siren]

AlexV

[tawdry gull]

in the package

we are able to just simply write

\begin{proof}
...
\end{proof}

which will put the square automatically

[rancid schooner]

Nice :)

[rancid schooner]

That's quite convenient.

[tawdry gull]

yes it is haha

[rancid schooner]

What else does it do apart from adding the square?

[tawdry gull]

it adds "Proof." when you do \begin{proof}

and ends with the square when you do \end{proof}

thats a comparison

[rancid schooner]

nice

[main topaz]

Uhhh I know this will be destroying the uni math tempo but a lil help with 8 and 10 would be appreciated

[tawdry gull]

im particularly bad at this honestly

[rancid schooner]

that's not typeset in TeX :)

[tawdry gull]

not everything has to be in TeX :)

[rancid schooner]

Me too :)

[long aurora]

Where is this from?

[main topaz]

Not sure a friend sent it to me

[long aurora]

In q8, is it A?

[main topaz]

Yep

Could you please explain how?

[long aurora]

Well tbh i just used a calculator 😅

[main topaz]

...

[long aurora]

Maybe pierrot or alex can check it out

[rancid schooner]

For Q9, it's C, ie. 5.

Nice question.

Just find n where 12/(n+1) is an integer.

[rancid schooner]

For Q8 the midpoint i.e. 108°, and deviations from it.

[main topaz]

You mean 9?

[main topaz]

Ye got that

[main topaz]

Hmm will give this a go

[rancid schooner]

Yes Q9 :)

[rancid schooner]

Yes :)

It's 1/2, so 1+2=3

[main topaz]

You edited the wrong message lmao

[rancid schooner]

It's correct now 😄

[rancid schooner]

||It reduces to 2(cos 2𝜋/5 + cos 4𝜋/5)² = 2(-½)² = ½.||

[little widget]

I meant ur handwriting

[verbal nova]

Our sir is spending so much time explaining p -> q

He gave best example

If moon is made of green cheese, then I am richer than bill gates

[swift zinc]

We have an option to handwrite, type or use Latex here

I used to handwrite

But now I just solve it messily and then write it up in LaTeX

Because the LaTeX aesthetic is crazy good

So it's hard to go back to handwriting answers

[rancid schooner]

What are the other questions?

[main topaz]

Uhh dumb question but how did u get -½?

[rancid schooner]

Because the sum of cos (2nπ/5) for n = 0 to 4 is zero. And cos θ = cos (-θ).

Consider the real part of the sum of the fifth roots of unity.

1 + cos(2π/5) + cos(4π/5) + cos(6π/5) + cos(8π/5) = 0.
But cos(8π/5) = cos(2π/5)
and cos(6π/5) = cos(4π/5).
So 1 + 2(cos(2π/5) + cos(4π/5) = 0
cos(2π/5) + cos(4π/5) = -1/2.

[little widget]

@swift zinc

i need some advice for c and d

a was fine i managed to get rref and set up free var

b i imagine was jus using the free variable to calculate values for f1 f2 f3

i hope so.

[swift zinc]

I'm ngl I haven't solved a question like this before lmao

[little widget]

ripp

flows are jus like

whats entering is equal to

whats exiting

[swift zinc]

Right

[little widget]

so for example: f1 + f2 = 20

cant tell what it wants with min and max flows

fuck sake

i wonder if a certain @tawdry gull would know

hes in uni tho

[finite spear]

Let's start from A. If we assume all traffic flows along AB, the maximum value of f₁ would be 10 + 10 = 20. As a result, the minimum value of f₂ would be 0. This also means the minimum value of f₃ would be (20 + 5) - 20 = 5 and the maximum value of f₄ would be (15 + 15) - 5 = 25.

If we assume all traffic flows along AD instead, the maximum value of f₂ would be 10 + 10 = 20. As a result, the minimum value of f₁ would be 0. This also means the minimum value of f₄ would be (15 + 10) - 20 = 5 and the maximum value of f₃ would be (15 + 15) - 5 = 25.

[main topaz]

Oh yeah forgot about that

[little widget]

Uh huh

Aight i think i get it

Interesting way of looking at it

[rancid schooner]

Use Kirchoff’s Laws

Physics/Electrical Engineering does come in useful :)

[little widget]

Nah the first parts made sense

This textbook also mentioned those laws

It was jus getting the intuitive idea of c

[little widget]

@stuck rapids @swift zinc need to use matlab to confirm calculation that shows three vectors are in the span of R3

What would u do

I could jus confirm what the rref is but not sure if thats acceptable

[swift zinc]

I haven't learnt MATLAB yet

There should be some tutorial online that'll give you an idea of how to do that question specifically

[little widget]

I could use it

But it comes down to whether my teacher will allow it

The hints they give for homeworks is horrid

Completely unhelpful

Are they even lecturers man

[swift zinc]

Idk doesn't sound like it

Or they're people getting 6 figures and couldn't be bothered helping students

Can you complain to higher up?

[rancid schooner]

Lecturers earn so much?

[swift zinc]

In my uni they do

Depends on the subject

[stuck rapids]

i see money coming

HAHAHAHA

[little widget]

Q7 can go fuck itself for the homework

@swift zinc i cba

@swift zinc got a q in vectors and matrices to balance a chemical equation

Bruv

I DIDNT TAKE CHEM IN IGCSE

[rancid schooner]

What’s a question on chemistry doing in a maths course?

[stark wave]

I'm so confused

[stark wave]

I'm also confused how and why you would do that to yourself

[little widget]

everyone made it sound scary to naive hayzy back in the day

But what the fuck is chem doing here

[stark wave]

It's IG, very little about it is not doable

[little widget]

Im doing the bonus problems to make up for it

[stark wave]

Natural sciences shit no

[little widget]

Fuck the prof

[stark wave]

Just make sure you have equal numbers of atoms on both sides

[little widget]

I also have to state what the each compound is

[stark wave]

Google it

[little widget]

Na we make up for it with bonus problem 😎

[stark wave]

Oxygen, carbon dioxide, iron oxide, sulfur dioxide, iron sulfide for a start

The organic I cbf

[little widget]

I wanted to do sth else with a saturday ngl…

[stark wave]

C6H12O6 is glucose

[little widget]

Its only q 7 so

[stark wave]

You've started very early for a Saturday man

I haven't moved out of my bed yet

[little widget]

Idk i cant sleep

[stark wave]

But I'm 1h behind

[little widget]

As much nowadays

8 hours done and im up

[stark wave]

Aww

[little widget]

It gets cold so

For some reason have to take a piss

[stark wave]

Well I still woke up at 6 am like I would for work

[little widget]

The moment im outside

[stark wave]

And then went back to sleep

[little widget]

Thats jus trauma

[stark wave]

Oi

I also wake up cuz cold

[little widget]

Ah fairs

[stark wave]

Then I make it warmer and go sleep

[little widget]

Im lucky my roommate is sick

Noticed outside heaters werent working

Called maintenance 😎

[stark wave]

Wait you share a room?

Nice

[little widget]

No

Yes and no

[stark wave]

Ah cool

What

[little widget]

Not the way u said it

That sounded gay

[stark wave]

So you changed your answer to yes after you thought about the gay

[little widget]

🥴

@stark wave btw do yk how to find the span of 3 vectors in matlab

Or somehow verify the calculations for it using matlab

[stark wave]

No idea

Haven't done MATLAB before

[little widget]

Fuuuuuuck

[swift zinc]

I used to love these questions

They're so fun

[little widget]

MFER I HAVENT TAKEN CHEM

[swift zinc]

You don't need Chem💀

[little widget]

Man i was meant to solve 6 problems

I solved 7

[swift zinc]

You just need to understand where the numbers go

[little widget]

Should make up for the last one 🙏

Might look this up later

Dk why its in lin algebra

[swift zinc]

It's just an application of augmented matrices, like here is another way to solve balancing equations that might be cool and useful for some of you

[little widget]

Can gib hint?

[swift zinc]

Send me the question and I'll be able to solve it I think

[little widget]

Its q7

I posted it

[little widget]

.

[mellow ether]

I need help with q2(d) and (e)

[little widget]

@swift zinc more chemistry for you.

[tawdry gull]

@rancid schooner the new homework came out, it involves epsilon proofs

which im not sure if you like it or not haha

but its optional problem doesnt involve epsilon delta

[rancid schooner]

Haha that’s quite dry

[tawdry gull]

what can we do about it haha

[rancid schooner]

get used to it ;)

And wait for the course on discrete maths and probability

[tawdry gull]

i prefer doing analysis and algebra haha

https://prog-crs.hkust.edu.hk/ugcourse/2022-23/MATH

heres the full course catalog for my uni @rancid schooner

u can freely take a look

[long aurora]

my mom is telling me to go into computer science - data analysis since "it has lots of math" instead of majoring in math and cs

[long aurora]

i need external opinions on this

what exactly is data analysis and what sort of math is involved?

[tawdry gull]

i would say data science would involve more math, and its more in demand too

it involves lots of statistics surely

and some discrete math

but mostly statistics

especially when it comes to modelling data, finding general relationship etc

youll also learn to make algorithms, example is on data sorting

its almost a combination of cs + statistics

@long aurora

[swift zinc]

yep its basically this

thats almost exactly what im learning rn

[tawdry gull]

i hope i describe it well 🙏

[swift zinc]

you did haha

[long aurora]

yes i understand

i dont really like stats pls

[swift zinc]

theres also business domain knowledge that you learn with data science, coz businesses and industries are where you apply your data sci skills

[long aurora]

i see

[tawdry gull]

if youll do a double major in math and cs, youd probably learn math that wont be needed in cs

but ofc theres nothing wrong with it if u like it

[long aurora]

yea but my parents are so against the idea

[tawdry gull]

i see

why so?

[long aurora]

they think majoring in math would be useless and i would end up as a teacher

they want me to only study math that has practical applications

[tawdry gull]

eh, applied maths is a thing

and u dont be a teacher doing that

[long aurora]

yea i try explaining

[tawdry gull]

hmm

did they not listen?

:'D

[long aurora]

nope they didnt

they're deluding themselves into thinking im going to major in cs and get the bad

bag*

when i would rather choose math if i had to choose between it and cs

[rancid schooner]

Just do what you enjoy

[rancid schooner]

2343 looks interesting

[rancid schooner]

You can easily get free credit for 3900. :)

[tawdry gull]

I was planning to take that haha

But that is only for MATH students

Just fyi, first years do not get to pick their majors yet

So the earliest i could take it is when i have declared my major, which is next year

[rancid schooner]

Just submit your ZNotes notes and videos. Instant credit 😄

[tawdry gull]

Hahaha I’ll see

Who knows that could happen

[rancid schooner]

Do the students use textbooks or just rely on lecture notes?

[stark wave]

maths server be like

[finite spear]

The last two look like y = sin(cos(eˣ)) and y = sin(sin(eˣ)). Very cool.

[rancid schooner]

@tawdry gull is either Spivak or Apostol being used for Analysis?

[tawdry gull]

for?

last time i used bartle's

[little widget]

What the fuck is the hkust disc serv lol

[rancid schooner]

Prescribed text for analysis at university

[tawdry gull]

??

[little widget]

Saadman sommow 💀

[tawdry gull]

this is what they give for this course

and its just considered as additional reference

[rancid schooner]

Nice

[tawdry gull]

@rancid schooner

Thats the first homework, the one you did Q4 on

[rancid schooner]

Interesting questions

[tawdry gull]

Try them out if you feel like it

Here’s the 2nd one

[rancid schooner]

The optional problem looks interesting

Looks like one of Ramanujan’s radical identities.

[tawdry gull]

Haha yeah

It could be

[verbal nova]

Thank Allah I took fmath

[tawdry gull]

@rancid schooner what do you think about question 4 here?

in HW2

[rancid schooner]

Looks difficult!

[tawdry gull]

im more confused by part b

i can just make the sequence dependent on y then?

[rancid schooner]

So am I 😄

[tawdry gull]

hahaha

[verbal nova]

I luv my meth classes, but I hate hate discrete méthe

[swift zinc]

lol

[rancid schooner]

It’s good to be discrete :)

[little widget]

Do u have weekly hws that are graded

[little widget]

@rancid schooner @tawdry gull would u guys proof by contra this one

[rancid schooner]

Over to you @tawdry gull :)

[little widget]

FUCK

[little widget]

@swift zinc are my teachers braindead if they asked for matlab verification

For a fucking proof

[swift zinc]

They're really busting your ass huh

[tawdry gull]

Yes

[little widget]

Will i get a hint or a possible answer

For the q i sent

[tawdry gull]

The => shud be easy, cuz each column adds up to 1

[little widget]

Oh wait

Yea igwym

Will try to verify what i got once i get it on paper

[tawdry gull]

@rancid schooner can u try the optional problem in HW02?

[rancid schooner]

looks difficult! will try when i have some time.

[tawdry gull]

suree

[verbal nova]

REEEE

Life is good until it becomes discrete

[verbal nova]

∃x∃y(Love(x,y))
❤️ ❤️ ❤️ ❤️

[rancid schooner]

Have you done it? Quite interesting.

[tawdry gull]

haha yes i did it

have you?

[little widget]

This is such a sweet love story

Didnt know maths could be so passionate

[rancid schooner]

Haha yes

[tawdry gull]

whats ur solution?

[rancid schooner]

Haha will write it up neatly first

[tawdry gull]

well i have done it using LaTeX haha

[rancid schooner]

Haha I won’t look yet

[verbal nova]

How to solve part d?

[verbal nova]

Oh ma gawd

[idle rain]

Sniped!

Message by Dysto#3930

[verbal nova]

@rich wraith you were right!

I was confused why... v (¬p v q) opened to... v ¬p v q but realized its the assossicative law

@rich wraith thanks, idk why u deleted it tho

[idle rain]

Gave +1 rep to Dysto#3930

[rich wraith]

I thought I made a mistake lol

[tawdry gull]

@rancid schooner

updated version

[little widget]

@swift zinc day 50 of ranting about my shitty maths teachers

These fuckers left a note saying hint: (insert matlab func) and for some reason thats meant to mean USE THIS FUNC OR YOU LOSE A FUCKING MARK

[tawdry gull]

what can be done

[little widget]

Whichever dumb cunt made this course should reconsider teaching maths and quit

[little widget]

Nothing i cry for a few mins then i try not to be dumb again

[tawdry gull]

sometimes life is like that

[little widget]

Ig

I try anyway

[tawdry gull]

all those sentences are sarcastic btw 💀

well rhetorical for the first one

HAHAHAH

[little widget]

Suck my dick

[young marten]

yeah that's quite obvious tbh

[little widget]

Yeah nvm im good

She said its fine for this hw

[tawdry gull]

@rancid schooner the newest hw

[rancid schooner]

Nice. Continued fractions 😄

[tawdry gull]

Try doing them if ure interested

[verbal nova]

what does the highlighted sentence mean?

[swift zinc]

Bruh wtf do y'all do in math 💀

I have not seen this notation before

[verbal nova]

discrete math

[swift zinc]

Fuck

Istg

If I have this

And I haven't studied it

I'm failing Discrete math this sem

[verbal nova]

nah its alright, mostly

bruh wtf have you done so far

[swift zinc]

Uhh

It seems I'm 6 weeks behind now

[tawdry gull]

"i am gay" becomes "i am not gay"

"not" precedes (is behind) the predicate

[swift zinc]

LOL

[rancid schooner]

The meaning is not the same though

[tawdry gull]

it's what they mean abt negation right?

[rancid schooner]

It says transform so they want you to move the negation sign elsewhere but without changing the meaning. Or so that’s what it seems.

[tawdry gull]

hmm i see

[rancid schooner]

Maybe you could use De Morgan’s Laws for the first one.

[verbal nova]

Speaking my language now

[verbal nova]

So that just means that we have to negate the whole statement

Everyone is good
AxG(x)
~AxG(x)
Ex~G(x)
Some people are not good

[wooden imp]

I wonder how I could get the present value for this (problem revolves around annuity):

If money is worth 12% compounded quarterly, what is (a) the present value and (b) the amount of annuity of ₱4,332.50 payable at the end of each 3 months for 3 years and 6 months?

[little widget]

Go fuck yourself

You dumb piece of shit

How dare you integrate the summation symbol

[rancid schooner]

What’s that currency symbol?

[wooden imp]

philippine peso

[little widget]

I love filipino rupee

[rancid schooner]

It’s a geometric series with n = 42, R = 1/(1+r/4)

[verbal nova]

This is where the fun begins

[wary jungle]

Could you guys do this and show me your answer? Test is already over so no need to worry about me cheating

[little widget]

Well i) should jus be

Wait

Im gonna cry nvm i forgot all of this

[rancid schooner]

(i) ||∀x(P(x)→Q(x))|| ? And for (ii) just put a ¬ in front of (i)?

[verbal nova]

I am having a hard time translating sentences into logical propositions

specifically if a proposition is (p -> q) or (p * q)

anyone got any tips or resources to understand this?

[wary jungle]

0.0 you're correct

my dumbass did (ii) and (iii) together in (ii)

This is what I wrote on q3 hahhaa but I changed it last minute

I am probably fucked

I missed out the Ex at the left

I did this when there is 5 minutes left on the clock

[rancid schooner]

😊

[stark wave]

for any science nerds here (i assume this is a good place), there's a board game called search for planet X and it is absolutely fucking amazing, buy it if you see it!!

or find someone who has it

its probably the best game ive ever played

[rancid schooner]

The option part is very interesting

[tawdry gull]

@rancid schooner this one was released last friday

[rancid schooner]

Looks very theoretical 😄

[tawdry gull]

Try out question 2

[rancid schooner]

“Evil? :)” 😄

[tawdry gull]

try it out haha

[tawdry gull]

heres the hw which was released today

[rancid schooner]

Wow so much homework

And looks very formal

[little widget]

“Extended squeeze theorem”

[tawdry gull]

u wanna tussle?

[rancid schooner]

maybe πerrot can do a study session

[rancid schooner]

@tawdry gull did you enjoy the one on continued fractions?

[tawdry gull]

i did not do the optional problem

sadly because the induction was confusing

[rancid schooner]

@tawdry gull

[tawdry gull]

will check later

thank you

[rancid schooner]

Interesting question with a neat answer. Let me know if the solution looks right.

[tawdry gull]

it look correct to me

amazing

[little widget]

He complimented his own answer

Legend

[rancid schooner]

😊

[rancid schooner]

Thanks! Very kind of you. That made my day. 😊

[idle rain]

Gave +1 rep to The_Pierrot#7889

[tawdry gull]

🙏

[rancid schooner]

Haha if you read carefully I said the answer (meaning the final value) is neat, not the solution (which refers to the how the answer is derived) :)

[little widget]

Fair fair

[tawdry gull]

ya @little widget u dumbass

[little widget]

Go thirst over unattainable women

Burger flipper

[tawdry gull]

hey at least i got women

[stuck rapids]

So pro!

[idle rain]

Help needed <@&597104882482413589>

[blazing wraith]

hihihi can i ask does the inverse of this function exists?? cause if we combine 1/x and x into a single graph it doesn't exists however if we separate 1/x and x it exists

i need help plsss

this is calculus 1

[rich wraith]

this is what I got for f inv (x)
when x is greater than 2 any single input maps to 2 outputs so it cannot be a function

I think another way to do it is to state that f(x) is a many to one function in that domain so an inverse, which will be one to many, cannot exist (unless maybe the domain is restricted)

[blazing wraith]

ohhhh! so my other assumption is correct

so when there’s a piecewise function , it needs to look at both f(x) function together right

[rancid schooner]

Piecewise is when you eat a whole cake by yourself, one piece at a time

[vestal swift]

@rancid schooner curious to know what alternative approach u have for part b :)

This was the ans:

[rancid schooner]

Wow a rare DQ appears after long absence

[vestal swift]

Dying in Uni

Linear algebra and discrete maths midterms next week😭😭

[rancid schooner]

What fun 😄

Will take a look after dinner

[blazing wraith]

i seee

[little widget]

reads q “ this looks straightforward” reads sol

[rancid schooner]

no alternative approach but perhaps solving it backwards would be clearer :)

[vestal swift]

hmm why did you move the (1+X) to the RHS?

[rancid schooner]

Just to show what the inverse is

[vestal swift]

so the inverse can't be zero coz of the I term or?

oh nvm i think i kinda get it but also konfius :')

[rancid schooner]

Yes

[vestal swift]

also is there way to prove that a matrix with its # of rows greater than # of columns multiplied with another matrix with its # of columns greater than # of rows doesn't give an identity matrix?

my lecturer pointed it out in class but idk how to prove it :(

as in the first one has to be a "tall" matrix multiplied with a second "long" matrix on the right

like [3x1 matrix][1x3] matrix etc

[rancid schooner]

yes the dimension of the product can be determined easily by cancelling, e.g.
(axb)(bxc) = (axc)

[vestal swift]

what if it's mxn and nxm where n<m

[vestal swift]

how to prove that this doesn't give an identity matrix for all n and m

[rancid schooner]

hmmm if AB=I, then I⁻¹ = (AB)⁻¹ = B⁻¹A⁻¹, which is not possible, so AB≠I. ?

[vestal swift]

nani

as in non-square matrices have no inverse?

[rancid schooner]

Not a true inverse. ||But there’s the Moore-Penrose pseudoinverse.||

[vestal swift]

no idea what that is :')

but if m<n it works tho

[rancid schooner]

yes because you can just let the last (n-m) columns of A be zero etc

[rich wraith]

is this a valid "proof"?

[rancid schooner]

nice diagram

[rich wraith]

XD

[rich wraith]

B should be A transpose for the ones to be on the diagonal
idk other matrices which will produce the same effect

[tawdry gull]

proof idea yes

[vestal swift]

wdym by perpendicular?

[rich wraith]

their dot products being 0

[vestal swift]

like relate it to dot product or something?

[rich wraith]

yeah exactly

[vestal swift]

hmm then what about the 1 ?

[rich wraith]

dotting each row with each column

[rich wraith]

the unit vector dotted with itself

i think this only works for if B = A transpose tho

[vestal swift]

ah i think it makes sense haha still tryna digest it :")

[vestal swift]

so each row must be the same vector as the column right for the dot product to be 1

[vestal swift]

can't visualize this T-T

then does the last n-m rows of B be zero as well

[rich wraith]

yeah so if u.u = 1 but u. (any other vector in our matrix) = 0

[rich wraith]

I don't even know if i'm right💀

[vestal swift]

makes sense to me hahaha

[rich wraith]

if they are zero the last elements on the diagonal will be 0 so no identity matrix

[rancid schooner]

Consider the product of two square matrices S and T (pxp) which are inverses of each other, i.e. ST = I.
Stretch S to the right adding q new columns of zeros to create S' (px(p+k)).
Stretch T to downwards by adding q new rows (not necesarily zeros) to create T' ((p+k)xp).
Then S'T' gives I (pxp) because it is effectively ST.

[rancid schooner]

not necessarily. the zero columns in the first matrix will take care of that.

[vestal swift]

can it be the other way around

like the first one doesn't have to be column of zeros but the second one has to be

I don't think so but i cant exactly get why

[rancid schooner]

yes that's also possible

this method might be helpful in visualizing the other case as well.
start with two mxm matrices which are inverses of each other. then shrink insteadf of stretch.

[vestal swift]

so either row of zeros or column of zeros are fine?

[vestal swift]

I'll slowly think about this haha thanks :')

[idle rain]

Gave +1 rep to AlexV#1811

[vestal swift]

I can't prove Cramer's Rule and I'm struggling like shit :')

[rancid schooner]

yes. try it and see.

[rancid schooner]

good luck! 😊

[verbal nova]

Bonjour

remember me?

[rancid schooner]

cramer's rule is just instant gauss-jordan :)

[vestal swift]

Coz i dumb :(

i couldn't even visualize part a until i see the solution :')

haven't seen the solution for part b yet tho

[vestal swift]

yes you're Brave

[verbal nova]

got into uni?

[vestal swift]

got into but can't get out :')

the only way out is dropping out at this point😭

[rancid schooner]

Part (c) is easy. Just divide both sides by det(A) and make xⱼthe subject :)

[vestal swift]

yes lmao the fucking part b

:)

[stuck rapids]

Linear algebra 😭

[vestal swift]

is there a formal proof to show this ?

even tho i like the intuitive explanation

[vestal swift]

I DYING SIS :')

@rancid schooner btw u can try this if u wanna haha i gave up :')

[rancid schooner]

haha ok when i have some time.
try sketching the structure of the matrices - it might help visualization.
or use a small matrix as a numerical example.

[vestal swift]

sketched but still clueless af :')

[little widget]

Dude i fucking hate it

[little widget]

@rancid schooner in your opinion is it enough that i jus put the In and the identity matrix together in a matrix to show its inverse

or since thats just a method to compute an inverse it wont work?

cuz thats the easiest thing i can think of

one lined proof

[rancid schooner]

Just multiply with itself?

[verbal nova]

plz help, how do I translate (a) into a logical statement?

Can the "No visitor from Canada is from Asia" be ∀x ~(C(x) -> A(x))

[little widget]

Nah the trick u use where u put it in matrix form side by side

And u do ERO on LHS until it becomes identity matrix

[tawdry gull]

let C be the set of visitors from Canada
let A be people from Asia
for all c in C, then c is not in A

or simple
c in C => c not in A

[vestal swift]

Hi math senpais how to prove part (b)? Idk what method to use :(

[rancid schooner]

Hint: The reciprocal of an irrational number is also an irrational number.

[vestal swift]

Shd we use direct or indirect proof?

[rancid schooner]

Start with the “fact” provided in the question

[verbal nova]

i see, thanks

[idle rain]

Gave +1 rep to The_Pierrot#7889

[verbal nova]

I hate discrete meth

[tawdry gull]

discrete methametics

[vestal swift]

ye but there is no way to express an irrational number tho, so just use an arbitrary variable or something?

But isn't the fact something like the negation of the statement tho

[vestal swift]

I can't both :')

[rancid schooner]

Please share your solution

[vestal swift]

Should I do like let the irrational number be t or something 😭

Can't solve that's why I'm asking 🥲

[main topaz]

||Let a be a rational number and r an irrational number then:
a=a * r * 1/r

To prove a * r is irrational
a * r=c
r=c/a
Since a is rational c needs to be irrational for r to be irrational.
Therefore a * r is irrational

To prove 1/r is irrational
r=1/1/r
Since r is irrational and 1 is rational 1/r needs to be irrational.||
?

[rancid schooner]

Can be any variable. As long as it’s a rational choice. 😄

[vestal swift]

So acid's solution works?

I spent whole day failing at doing math proofs and the exam is on Fri 😞😞

[rancid schooner]

Start with the hint in the question. Then multiply both sides by the inverse of the irrational number that is multiplied with the rational number.

[tawdry gull]

if x is rational, let x=p/q (assume p and q are coprime), then p/q = p/r * r/q where r is irrational

note that r wont ever be 0 in the first place since r is irrational (0 is rational)

[vestal swift]

Is there more to the proof? Looks like it's done right? 🥲

[tawdry gull]

thats the idea yes

jsut formalize it a bit

[vestal swift]

Then just say since product of non zero rational number with an irrational number is irrational, so quotient of an irrational number with a rational number is irrational, so r/q is irrational?

Like what the hint said ?

Then wb for p/r tho

[tawdry gull]

also irrational la

integer divide by irrational is irrational

[vestal swift]

Yes but how to use the fact

Reciprocal?

[vestal swift]

So from here say reciprocal of irrational is irrational?

[tawdry gull]

yeah

1/r is for sure irrational

it's like saying p*1/r

[vestal swift]

If I write this in my proof it's ok right?

[tawdry gull]

yeah u can write that just to be safe

but even without it is also oke 👍

cuz reader shud alrdy understand

[vestal swift]

Ok thanks 😭

[idle rain]

Gave +1 rep to The_Pierrot#7889

[tawdry gull]

okei

[vestal swift]

How to be good at proofs :(

I'm dying 😭

[tawdry gull]

u dont have to use the hint is also okay u kno

[vestal swift]

Any alternatives tho :')

[tawdry gull]

oh wait nvm

the one in the question is a fact that u can use without proof, but at the same time it serves as a hint

the rational*irrational thing

[tawdry gull]

i like to imagine it as storytelling

when u do story telling, it has to be clear, make sense, and understandable

but this is maths, so add a few more

in proofs, u need to have those, but it also needs to be logically sound

[vestal swift]

So let qr = p,
q is rational,
the other 2 are irrational,
Then q = p/r = p × 1/r ?

[tawdry gull]

every statement should be precisely defined or logically sound

[vestal swift]

Yea but quite hard to tell which method to use for which q :(

[tawdry gull]

method to prove?

[vestal swift]

Yes

And some got combine different techniques 😞

[tawdry gull]

try to start by thinking of examples first

for example, ur question

try to think of two irrational numbers, that when u multiply become rational

[vestal swift]

Hmm so is this logically sound 😭

I rlly can't tell :(

Lol this one came out in finals :')

[tawdry gull]

well what can u conclude from this?

[rancid schooner]

Yes

[tawdry gull]

huh, for all integers a,b?

[vestal swift]

I didn't translate wrong right :')

[tawdry gull]

oh damn

yeah u didnt translate wrong

[vestal swift]

same paper :)

[tawdry gull]

this one isnt so bad i think

since n is composite, let n=mp (all are positive integers)

let p be such that p<=m

then we have $\sqrt{n}=\sqrt{mp}=\sqrt{m}\sqrt{p}\geq\sqrt{m}\sqrt{m}=m$

[vestal swift]

Solution they gave was q long :')

[tawdry gull]

oh really?

:'D

[vestal swift]

Ye

But urs is better hahahhaha

[tawdry gull]

eh wait i made a mistake

HAHAHHAHA

no no

wait

[vestal swift]

Oh :(

[tawdry gull]

let p be such that $p\geq m$
then we have $\sqrt{n}=\sqrt{mp}=\sqrt{m}\sqrt{p}\geq\sqrt{m}\sqrt{m}=m$

there u go

[round siren]

The πerrot

[tawdry gull]

too many typo 😔

[vestal swift]

Oh wait just like that ah

[tawdry gull]

i might be wrong

if the real solution is long

😂

[vestal swift]

NO IT MAKES SENSE LMAO

solution mf did proof by contradiction

🥲🥲

[tawdry gull]

bruh

[vestal swift]

Wanna see?

[tawdry gull]

sure HAHAHA

[vestal swift]

🥲

Oh wait shit forgot to mark as spoiler sorry :')

[tawdry gull]

i mean... this makes sense too

[vestal swift]

Hmm but for this there is also the possibility that n=m² right

^Then this one is obvious

Basically either n=pm or n=m² right, no other cases?

[tawdry gull]

thats why p>=m

p can be equal to m

[vestal swift]

Ohhh

Smart

[tawdry gull]

also since n is composite, we can choose both p and m to be >1

(otherwise it would be prime since prime can only be divided by itself and 1)

[vestal swift]

Ye haha idk how to prove the sqrt n part :')

[tawdry gull]

wdym?

from n=pm, just take sqrt

[vestal swift]

yes hahaha i meant idk how to prove that part before ur solution XD

[tawdry gull]

ooh

:'D

[vestal swift]

@rancid schooner sorry i know this has been posted q awhile but could u explain the "equivalent when swapped" part? :')

Oh nvm I get it now

[rancid schooner]

😊

[vestal swift]

Can I ask if my solution is doable or nah? I got stuck :’)

[rancid schooner]

Looks ok

[vestal swift]

How to proceed?

Can someone pls explain c to me 😔

I really can't understand what it's saying

[rancid schooner]

Plug the answer into RHS and show that it equals LHS 😄

[vestal swift]

How to plug 😭

[rancid schooner]

Just like the cube roots of unity

[rancid schooner]

Substitute 😄

[vestal swift]

Which one?

The tr or the summation thing

[rancid schooner]

A^T = B

[vestal swift]

Ohh but aren't I supposed to prove that

Isn't that like circular logic

[rancid schooner]

Well it doesn’t prove that it is the only answer. But it does prove that it is one of the answers. 😄

[rancid schooner]

So, if 𝜔 is the m-th root of unity, then A =𝜔I could be a possible solution.

[vestal swift]

Shit I forgot my complex 😔

Got a more basic solution? Coz imma basic bish

[rancid schooner]

But this is the most convenient solution :)

[vestal swift]

I don't understand :(

So A is ω x identity where ω is a scalar?

[rancid schooner]

oh wait. my solution gives A^m = I, not 0.

[vestal swift]

I don't even understand the question🥲

[rancid schooner]

ok I think I've got the answer.

A is the mxm matrix with upper right triangular elements equal to 1 and other elements zero.

So, for example, for m=4, it would be

A =        A² =       
0 1 1 1    0 0 1 2    
0 0 1 1    0 0 0 1    
0 0 0 1    0 0 0 0    
0 0 0 0    0 0 0 0    

A³ =       A⁴ =
0 0 0 1    0 0 0 0
0 0 0 0    0 0 0 0
0 0 0 0    0 0 0 0
0 0 0 0    0 0 0 0``````

[tawdry gull]

hint would be a matrix with det=0

[vestal swift]

Wait. m is the DIMENSION????

Not power????

[rancid schooner]

both

well in the question it is power (question doesn't state dimension) but in your answer you should specify A as an mxm matrix

[rancid schooner]

Oddly satisfying 😄

[vestal swift]

How to come up with this kind of intuition 😭

I would have never thought of that 😔

[rancid schooner]

😊

[vestal swift]

23 idk if I'm writing it correctly

:(

[rancid schooner]

It would be clearer to first show what the element c_ij is, where C = AA^T. Then sum c_ii for i = 1 to m.

[vestal swift]

Hmm as in before the summation?

For this one is true right, how to justify tho :')

Srry for spamming lmao my midterms r tmr

[rancid schooner]

Separately

[rancid schooner]

Use induction. And the fact that (AB)^T = B^T A^T

[vestal swift]

Ah shite

[vestal swift]

Ok thanks :')

[idle rain]

Gave +1 rep to AlexV#1811

[vestal swift]

My last min saviour 😩🙏

[rancid schooner]

😊

[vestal swift]

Since this is trace and we can do air ajr right, but if it's matrix multiplication instead of trace we can't do airajr, but have to do airarj coz the # of columns of the first matrix has to match the rows of the second one?

14 & 16🥺

14 is if C is invertible then C can be expressed as a product of elementary matrices?

[rancid schooner]

it's the trace of the product, which is a square matrix, even though A is not square

[vestal swift]

Which corresponds to elementary row operations that brings A to RREF?

Idk abt 16a) tho :')

[vestal swift]

Is it bc it's square then we can switch to from rj to jr?

[rancid schooner]

it's because of the transpose

a' is an element in A^T

[vestal swift]

Ye but I thought like the column of the first one has to always match the row of the second one :")

[rancid schooner]

see the diagram

[vestal swift]

Same logic as this?

Not me violating my uni's intellectual property pls dun sue me 🥺

[rancid schooner]

well it's more straightforward but similar

anyway gtg soon

good luck with your exam!

[vestal swift]

Thankiew😭

[vestal swift]

Stuck 😞

[little widget]

Omg step lecturer help im stuck

[little widget]

Man why the fuck is 14 even a proof

Fucking bullshit ITS OBVIOUS IF U TAKE A TRANSFORMATION THEN U TAKE ITS INVERSE YOU JUS GO BACK TO THE SAME PLACE AKA THE IDENTITY MATRIX WHICH IS IN RREF

[vestal swift]

Lecture: teaches row swap
Exam: asks to prove column swap

I can rot :')

4 marks GONE

[vestal swift]

@rancid schooner or any math gods? 🥺

[rancid schooner]

Nice question though. It’s about divisibility by 11 and by 3

[rancid schooner]

Adding both gives sum of digits of n which is divisible by 3 if n is divisible by 3, since 10^m = 1 mod 3.

Subtracting gives +/- alternating sign sum of digits which is divisible by 11 if n is divisible by 11, since 10^m = (-1)^m mod 11.

[rancid schooner]

So if
a = sum of odd digits
b = sun of even digits
(counting from LSD)
then we want
a+b = 3s
a-b = 11r
where r and a are integers.
Solving gives
a = 1.5s + 5.5r
b = 1.5s - 5.5r.

[vestal swift]

Yea so how to make use of this to get some expression divisible by 33?

[rancid schooner]

If it’s divisible by 3 and also divisible by 11, then it must be divisible by 33.

[vestal swift]

So how to proceed from here ah :(

[rancid schooner]

See explanation above

[vestal swift]

Ye but so far my expression no 11 :(

[vestal swift]

I thought of this too but idk how to make use of the r

[rancid schooner]

If n is divisible by 33, then it must be divisible by 3 as well as by 11.
For n to be divisible by 3, a+b = 3s
For n to be divisible by 11, a-b = 11r.
(see earlier posts for definitions and details).
Solving gives a = 1.5s + 5.5r, b = 1.5s - 5.5r.

[tawdry gull]

@rancid schooner another playtime for us

the optional problem is quite humorous

[rancid schooner]

Interesting! It’s the ham sandwich problem. https://en.m.wikipedia.org/wiki/Ham_sandwich_theorem

[tawdry gull]

yes it is haha

but proving it on our own is the challenge

[rancid schooner]

Or is it called the char siu bao problem in HK? 😄

[tawdry gull]

who knows 😂

[rancid schooner]

Now I feel like having a ham sandwich and a char siu bao.

[vestal swift]

Sorry for the late reply but I asked my lect :')

And umm

I failed my discrete math test

If I can't do math proofs

Am I even well suited to study math

[tawdry gull]

😭

[rancid schooner]

It’s ok, you’ll do better next time

[rancid schooner]

Was that the correct answer?

[vestal swift]

yeah something along those lines

[vestal swift]

this @anyone ?

[rancid schooner]

Or maybe they didn’t teach it well

[vestal swift]

Idk everyone couldn't do like one q, some can't do 2 but at least they wrote something

I couldnt do 3

And 2 i left completely blank :') the other one my solution was shit :')

[blazing wraith]

can someone use the most simple explanation to define span (in linear algebra)
perhaps with examples?

[idle rain]

Help needed <@&597104882482413589>

[tawdry gull]

i think ur well suited, but just not well adapted yet

[blazing wraith]

i just cant understand that term.

[tawdry gull]

the locations where u can reach using the given vectors

[blazing wraith]

what locations?

[tawdry gull]

points in the space

[blazing wraith]

space as in real numbers?

[tawdry gull]

space as in coordinates ofc

examples i have two vectors (1,0) and (0,1)

then i am able to touch (3,2)

cuz 3(1,0) + 2(0,1)=(3,2)

[blazing wraith]

ohhhhh

thanks ! @tawdry gull

[idle rain]

Gave +1 rep to The_Pierrot#7889

[tawdry gull]

okii

[rancid schooner]

Nice explanation

[vestal swift]

but i failed my proof mod :')

which is the ESSENCE of math :')

[vestal swift]

why y'all so sure hahah :')

[tawdry gull]

mod = module?

[little widget]

The set of vectors you can represent as linear combinations of the span/basis vectors

[little widget]

Proofs can go suck my ass

[vestal swift]

ye

[vestal swift]

i always hated stats but i'm thinking to specialize in stats if stats has less proving :')

[tawdry gull]

well it is ur first time too

[tawdry gull]

yeah it has less proving, doesnt mean theres completely none tho

[vestal swift]

and i'm failing

on top of that we have uselsss mods like eThICs

and a connect4 python project

i'm dying

[tawdry gull]

i mean, it's still fair that ur not well adapted to proofs yet

😭

[vestal swift]

everyone i know i s

how's meth life in hkust hahaha

[tawdry gull]

cuz they probably have a background in proofs

[tawdry gull]

its just fine ofc

[vestal swift]

coz u pro :D

[stuck rapids]

Sis u r well suited

[rancid schooner]

All three of you can do a study session here. And anyone else.

[vestal swift]

i failed my math mod :')

[vestal swift]

how u so sure sis :")

[stuck rapids]

U have passion for it + u have always been a smartieee

I think u haven't adapted to it yet la..

[vestal swift]

if i smart i wouldnt fail :)

B- hahah for ccmods

[stuck rapids]

But this is just the first sem la... Usually it is the phase where u r getting used to the pace and all

[vestal swift]

the worst part is that mod is prerequisite for other future mods so my math is just gonna get worse and worse if i don't get my foundations right :")

[stuck rapids]

how hard is the maths in ur uni? out of 10 in ur opinion

[vestal swift]

somewhere between 8 or 9

depends on the mod actually

tbh it would be more managable if we didnt have to take a bunch of shitty mods that has nothing to do w our major

[stuck rapids]

https://tenor.com/view/teletubbies-dipsy-running-away-scared-run-away-gif-25928776

[stuck rapids]

like cs or the programming one right

something wrong haihhh wtf

[vestal swift]

python connect 4 :)

[rancid schooner]

Do they have tutorials or small group study sessions?

[stuck rapids]

brain damage

haihhh

[vestal swift]

yea for math but it's not vv helpful

i only like the calc one hahahaha coz he's malaysian :)

and he gives supplement notes :)

[stuck rapids]

i like my calc lecturer the best also HAHAHA

[stuck rapids]

then calc da best xD?

[vestal swift]

yeah more manageable relative to other mods

but shit mods are making me falling behind in everything

why tf would u want a math major to study uTiLiTaRiAnIsM

[rancid schooner]

Ask your coursemates seniors. Or post here.

Well it’s to broaden your outlook.

[vestal swift]

yeah idm if it's pass fail but it's graded

[rancid schooner]

University graduates are supposed to have a world view.

[vestal swift]

sucks the joy in learning innit

[rancid schooner]

That’s life

[stuck rapids]

tf is this utilitbiqkqkq

[vestal swift]

yeah life sucks

[rancid schooner]

It says just be happy

[stuck rapids]

how did our genius bot survive uni