ug-maths-physics

[stuck rapids]

Noob ur head hahaha jkjk xD

[vestal swift]

Not at their level

[rancid schooner]

Elliptic curves etc?

[stuck rapids]

These two peeps are just

[vestal swift]

I just pretend to be smart :D

[stuck rapids]

As wht I have expected

[floral sky]

oh, then whatever interests you la. Maybe check out Quanta Magazine

https://www.quantamagazine.org/tag/mathematics/

[floral sky]

Oh yea, I saved a link on that. Still working through it.........

[vestal swift]

Waw thank youu

[rancid schooner]

Not taught at uni?

[vestal swift]

Got interest in DS /ML / AI?

[stuck rapids]

Which uni were u from

😏

[rancid schooner]

Bots don’t go to uni

[vestal swift]

He'll probably say "bOtS dOn'T gO tO uNi"

HAHAHAHAH CALLED IT

[floral sky]

Tbh at uni I was getting scared of all the courses, and by 3rd year I was just trying to pick easy ones to survive 🙃

[stuck rapids]

Jinx

Damnnn.. I see I can't imagine how hard the courses are

[vestal swift]

Shit loh cambridge dashen also like that

I sure drop out

[floral sky]

Only a slight interest haha, like I got not much motivation to sit down and go through the details

[stuck rapids]

My god.. Machine learning data science.. Artificial intelligence

[rancid schooner]

Please share some nice STEP questions

MDragon must be a pure mathematician. No time for applied stuff.

[floral sky]

Actually, maybe you all can be my motivation xD

[stuck rapids]

Ohhh no please.. I m not into the field at least 😆

[floral sky]

Ya ya, it's very important. If you want to have a bright career, go for it

[vestal swift]

Idk the name is cool but I know very little about it

[stuck rapids]

hmmm actually my course might cover a bit of data science 🤔

||like a subset of it I believe||

[rancid schooner]

A fancy name for statistics 🤔

[vestal swift]

MDragon took pure or applied maths?

[stuck rapids]

Sama Sama 😆 the name immediately portrays the toughness of that course

[floral sky]

Change the name, get more students

[stuck rapids]

[vestal swift]

Engineering 🤓

[stuck rapids]

Not fully stats la

[floral sky]

a bit of both. You can select the courses in 2nd and 3rd year

[vestal swift]

Oh nice, so which "easy courses" did you pick

Totally not coz I see myself struggling

[stuck rapids]

Okok and wht is the difference between two of these hahaha pure and applied

[stuck rapids]

Have some faith in urself dB

Decibel autocorrect

[vestal swift]

This YouTube comment said
Pure maths is exploring the world of maths
Applied maths is exploring the world with maths :)

[floral sky]

eh...... Special Relativity, Probability and Measure.........

[stuck rapids]

rip.. This sounds a bit hard to understand hahaha

[floral sky]

I think those were the "easier" courses I actually found "easier" lol

[rancid schooner]

Almost surely

[stuck rapids]

Relativity.. That isn't rly an easy subject hmm

[floral sky]

General Relativity is not

[vestal swift]

Dunno I think like pure maths is maths that hasn't been applicable to irl ? (Maybe in the future it will) Applied maths mostly proven to be applicable irl

[floral sky]

Special Relativity is not too bad

[rancid schooner]

Topology?

Combinatorics?

[floral sky]

I was hiding from this one xD

[stuck rapids]

Aight 🤣

[vestal swift]

Why ah

[rancid schooner]

But they can turn coffee mugs into doughnuts 😄

🍩

[floral sky]

Yeah I like combinatorics

[rancid schooner]

Nice

[stuck rapids]

Topology.. Alright wth is this even but I looked that up and erm

[rancid schooner]

The study of doughnuts

[vestal swift]

Like morph shapes ah

Dunno eh

[stuck rapids]

Must have a lot of geometry which I despise a lot

[floral sky]

Somehow I found the Analysis courses quite challenging, so I was hesitant to go more abstract into that area

[vestal swift]

Sameeee

[vestal swift]

Abstract as in what ah

Paiseh

[floral sky]

Well, as in you are dealing with less structure

For example, the real numbers have a lot of structure

[stuck rapids]

Gonna pergi tidur.. Bye bye good night

[floral sky]

But you can go into more abstract areas where there is less structure, for example the integers, then groups.....

[floral sky]

Night

[vestal swift]

Nighttt

[floral sky]

Ya, actually I want to sleep also

[vestal swift]

Too dumb to get this 😔

But nvm hahaha

Thank youu

[floral sky]

Nvm I try explain later haha

So anyway, good night ^_^

[rancid schooner]

Nite everyone

Nice meeting MDragon

[vestal swift]

Night everyone :D

Even though I'll still be up until 5am XD

[floral sky]

Nice meeting you, Sifu Alex :D

[rancid schooner]

Looking forward to maths tutorials from you

[floral sky]

See how la

[rancid schooner]

Haha no no. you are the sifu 😄

[vestal swift]

Hope can duoduozijiao

[floral sky]

Hahahaha, high expectations 🙃

[stuck rapids]

https://tenor.com/view/tom-and-jerry-jerry-the-mouse-jerry-shake-hands-handshake-gif-17827738

[rancid schooner]

Quiet day here

[vestal swift]

Db just woke up :D

[stuck rapids]

how many hours of sleep maam

[vestal swift]

6-8 that range hahaha

[stuck rapids]

🤣

[stuck rapids]

okok that is reasonable

[rancid schooner]

Still quiet

[stuck rapids]

U may attempt initiating a conversation here then hahaha

And posts random math questions for mdragon

[rancid schooner]

Haha he’s kinda quiet

Ok here’s one. From another server.

Projectile. Find v in terms of a, α, and β.

[vestal swift]

Shit I forgot all my mechanics

[floral sky]

Since you mentioned this question, it should be remarkable. And the only way I see this being remarkable is if || the solution doesn't depend on β. Therefore I'm gonna guess that: ||
|| v = sqrt (ga / (sin α) ) ||

[stuck rapids]

[tawdry gull]

shouldve put the original paragraph of the question too haha

i think they would understand some parts of it

[rancid schooner]

Hello Pierrot. Another brilliant mathematician.

[rancid schooner]

Haha it’s remarkable because it’s quite an interesting variation of the classical projectile problem. Not something I’ve come across before. And also in the original multiple choice question all answer options are wrong! I pointed this out to the person who posted. So did another person.

[rancid schooner]

What’s miring?

[tawdry gull]

slant

[rancid schooner]

Haha

[tawdry gull]

"how much diagonal is it"

slant, gradient

tilt

those can mean miring

[rancid schooner]

If oxide is oksida then why is slope not slopa?

[rancid schooner]

That is the correct answer if β = α. But if they are not equal then the answer does depend on β as well.

[tawdry gull]

oksida is a borrowed word haha

slope has its own term

[rancid schooner]

here it is!

[floral sky]

Ah I see. In that case, it's just a tedious algebra exercise........ 😕

[floral sky]

It's also the correct answer if β is a right angle

[rancid schooner]

I was wondering if there might be a clever transform that gets you to the answer directly

[floral sky]

There's almost surely no way to know if there isn't, so there probably is 😂

[rancid schooner]

Anyway all of the answer options are wrong! This is easily proven by letting β = α in which case the denominator inside the square root becomes negative.

[floral sky]

How about thinking about it from a point of "reversed time"? Starting at the right and then moving to the left

[rancid schooner]

Failing which what is the neatest way to approach the algebra grind?

[rancid schooner]

Please do try

[floral sky]

Another thing I was thinking about was the following problem: Given the curve y=x^2, there's a point on it (k, k^2). Consider a line passing through (k, k^2) which is perpendicular to the parabola at that point. What is the y-intercept of the line?

As in, trying to fit a parabola onto the problem, and completely ignoring the speed (and time taken) at first

[rancid schooner]

yes also possible

please solve

you can always find that line for any point on the parabola. it's just the normal.

[stuck rapids]

Bro u confirm from malaysia la

Halo!

[rancid schooner]

Why so?

[stuck rapids]

Soalan ni yg dlm bahasa melayu 😏 ya u understand right xD

[rancid schooner]

Haha The original poster translated it.

It’s from a competition in Indonesia

[stuck rapids]

Ohhhhhh

Sure if u say so

[rancid schooner]

Anyway my answer is
||v²=(2ga/sin α)(1/(2-cot β (cot α -cot β))||

[swift zinc]

Y'all are big bren

[rancid schooner]

||so when β = α it reduces nicely to v² = ga/sin α which matches your answer || @floral sky

[rancid schooner]

Very quiet here

No one talks about maths any more

[stuck rapids]

U and ur obsession with maths

Why is a bot seeking for attention hahahaa

[rancid schooner]

Not seeking. Just commenting.

[rancid schooner]

Well this is a maths and science channel

[stark wave]

Bot is noticing change in patterns

[rancid schooner]

Yes

Pattern recognition

[stuck rapids]

[floral sky]

Thanks. I'm just lazy to plow through it 🙃

[tawdry gull]

im indonesian, and i can confirm it is indonesian haha

[stuck rapids]

alright xD

[rancid schooner]

Unless crysto know what miring means 😄

And it’s not Japanese seasoning 😂

Hmmm no one seems to want to solve this projectile problem

[stuck rapids]

I tak tau

[rancid schooner]

So the question can’t be from Malaysia :)

[rancid schooner]

Have you attempted the projectile question?

[stuck rapids]

Too dumb for that-db's quote

[rancid schooner]

Not true at all.

[rancid schooner]

Please do share some interesting questions

[stuck rapids]

Damn the way Alex is trying to initiate math convos

[rancid schooner]

that's what a bot is supposed to do

[stuck rapids]

an exceptional bot you are xD with extraordinary math skills and maybe some sense of humour

[floral sky]

Sorry for the slow reply. Here you go:

[rancid schooner]

Interesting!

[rancid schooner]

They should ask part (b) first!

$\frac 1{\sin a^\circ \sin (a+1)^\circ} \
= \frac 1{\sin 1^\circ}\cdot \frac {\sin ((a+1)-a)^\circ}{\sin a^\circ \sin (a+1)^\circ}\
=\frac 1{\sin 1^\circ}\cdot \frac {\sin (a+1)^\circ \cos a^\circ-\cos(a+1)^\circ\sin a^\circ}{\sin a^\circ \sin (a+1)^\circ}\
=\frac 1{\sin 1^\circ}\cdot (\cot a^\circ - \cot (a+1)^\circ)$

[round siren]

AlexV

[rancid schooner]

summing from a=1 to 89 by telescoping gives the result in (b)

For part (a) consider the series formed by the "missing" terms, i.e. the terms in between (and last one beyond). This is also equal to the sum, S. Adding both and summing via telescoping (as above) gives 2S = 2/sin 1° hence n=1.

@floral sky

very nice questions!

[floral sky]

Yes, they should definitely ask part (b) first hahahaha

@rancid schooner Your solutions for both parts are correct. Awesome! 😃

[rancid schooner]

😊

[rancid schooner]

That made my day! Thanks! 😊

[floral sky]

Glad to know! ^^

[stuck rapids]

Wholesome

[rancid schooner]

Here's one:

$\lim_{n\to \infty} \frac 1{2n}\log \binom {2n}n$

[round siren]

AlexV

[floral sky]

Hmmm let's see........

[stuck rapids]

[floral sky]

The answer is || log 2 ||
|| The log can be to any base, as long as the question's log is the same base as the answer's log ||
Working is below:

(click to reveal)

Now I know how fast log( 2nCn ) grows. Cool! :D

[rancid schooner]

Yes! That's correct! 👏 👏

[rancid schooner]

Nice solution! 😄

[rancid schooner]

😊

[floral sky]

Thanks 😊

[rancid schooner]

using the squeeze theorem

you always use a pencil for maths?

[floral sky]

nah it's actually a pen, but the ink doesn't flow smoothly haha

[rancid schooner]

haha

[floral sky]

but I just use whatever is convenient. If that were a pencil, I'd use it

[rancid schooner]

you don't have a favourite writing instrument?

[floral sky]

nah

i'm guessing you have a favourite writing instrument?

[rancid schooner]

haha a few different ones

[floral sky]

ah you have a collection

[stuck rapids]

u and ur obsession with pens

[rancid schooner]

well uniball and pilot pens are pretty good

and there are some nice fountain pens as well

some of the old mathematicians have nice handwriting

[floral sky]

I have some pilot pens and I agree that they're pretty good

[rancid schooner]

you can see newton's notebooks online

[floral sky]

hmmm, I never knew how newton's handwriting looked like.........

[rancid schooner]

einstein has neat handwriting

ramanujan as well

galois' was artistic

[rancid schooner]

nice. what type?

[floral sky]

G-2 05

and BP-1 RT

[stuck rapids]

they are literally the best ones here in msia

hahahahaha

[stuck rapids]

😲 lemme search that up

[floral sky]

isit? Then I'm lucky xD

[rancid schooner]

nice. check out the Pilot Hi-Tecpoint. and also Uniball Eye and Uniball Vision Needle.

Uniball Vision Needle used to be available here but not any more. probably still so available in the UK.

[stuck rapids]

lemme guess where is this bot from

[stuck rapids]

yeah yeah xD so far so good no issues at all

[floral sky]

thanks for the recommendations!

[stuck rapids]

sold at a reasonable price

[rancid schooner]

trying to sound local :)

@floral sky I find the double factorial notation quite useful.

[floral sky]

ah I see.......

yeah I probably should get into the habit of that

[rancid schooner]

are you giving maths tuition or something?

[stuck rapids]

bots have good handwriting! what an exceptional bot u r alex! impressive

[rancid schooner]

they have to keep up with the times

expectations are high nowadays

[floral sky]

nah, but I could if I wanted to

[rancid schooner]

one of the most difficult things to write when writing fast is the equal sign

have to make sure they are aligned, and parallel, and of equal length

[stuck rapids]

bots have hands to write as well xD damn i m way too impressed

[stuck rapids]

??? it is just an equal sign brooo hahahhaa not worth the ocd

[rancid schooner]

bots are perfectionists

they have to learn to be more human

[stuck rapids]

😲 u and ur bots joke haiyaaaaa

[rancid schooner]

@floral sky can it be done without squeezing? maybe not as rigorous?

[floral sky]

hmmm...........

[vestal swift]

The IQ in this chat just suddenly stonks ten fold

[floral sky]

you can spike your IQ also!

[rancid schooner]

any of you play wordle?

[stuck rapids]

||I m third wheeling rn||

[floral sky]

I know how it works, but I don't play 🙃

[floral sky]

therefore you must start participating more actively xD

[vestal swift]

Fourth wheel here

Took me like 5 mins to get this

:D

[floral sky]

5 mins not bad ma

your IQ definitely above average

[vestal swift]

I dunno, but definitely less than 140

[stuck rapids]

Bruh 140 is high liao

[floral sky]

IQ can be trained also

[vestal swift]

Maybe like 100-120 lmao

[stuck rapids]

🤣

[vestal swift]

Or 0😩

[stuck rapids]

No lah should be higher than that.. Mine is probably that range

[vestal swift]

Is ok 4 wheels make up a car

Which brings us to placessss

[floral sky]

impossible XD

[stuck rapids]

Ya oh hahahahha

[vestal swift]

😎 😎 😎

[stuck rapids]

Mission impossible

[floral sky]

@rancid schooner OMG look at this!!

[stuck rapids]

Dear lord

[rancid schooner]

Very nice! 😄

[floral sky]

ikr 😄

[rancid schooner]

Stackexchange?

[floral sky]

Yeah, here: https://math.stackexchange.com/questions/701406/evaluating-lim-n-to-infty-frac12n-log-left2n-choose-n-right/701416#701416

[rancid schooner]

The other answers are quite nice too

[floral sky]

Yeah

Anyway, it is time for sleep!

[rancid schooner]

Nite!

[floral sky]

Nite!

[stuck rapids]

😏

[verbal nova]

There’s a math version of Stack overflow?

Nice

[verbal nova]

I read a funny thing today, that any number, even 10^1000000000000000000000000000 is closer to 0 than infinity

[stark wave]

There's every subject version of it

[vestal swift]

Dear lord +1

[floral sky]

Yeah, like Mushu says, there is one for virtually every subject. The complete subject list is here: https://stackexchange.com/sites

[rancid schooner]

@floral sky can we use Stirling’s approx as well?

[floral sky]

Maybe it's possible.......

@rancid schooner Yes you can, as long as you use this form of it:

It follows very quickly from this form actually

[rancid schooner]

😊

@floral sky

[rancid schooner]

Yes it’s possible, I’ve done it.

But would it be considered circular though? Maybe the result can be used to derive Stirling instead. 🤔

[rancid schooner]

What do mathematicians do on Sundays?

[floral sky]

I became curious about how to derive Stirling

[floral sky]

It seems that you can derive Stirling without the result, according to this link: https://faculty.washington.edu/moishe/hanoiex/counting/Stirling.pdf

[rancid schooner]

Nice. Yes I’ve seen a similar proof before. I suppose using an approx to prove another approx is not as pure as working from first principles.

[floral sky]

Yeah I guess so

[tawdry gull]

if you need translation, i dont mind

[rancid schooner]

Please translate

[tawdry gull]

which question?

[rancid schooner]

What you just posted

[tawdry gull]

there are three of them, do u want all of them or just a specific one?

[rancid schooner]

Please choose the most interesting one :)

[tawdry gull]

Suppose f(x) is defined in the interval (0,1] and satisfies (the x limit). Prove that (the n limit)

Suppose lambda >1, show that the equation (the eqn with lambda and z) has a root located in H. And show that the root is a real root (real number)

@rancid schooner

[rancid schooner]

Looks difficult! I will leave it to the professional mathematicians 😄 @floral sky

[floral sky]

I'm not a professional mathematician at all 😄

@rancid schooner 3) is quite straightforward using calculus:
Set f(x) = x + exp(-x)
Then show that f(0) = 1 and f is strictly increasing on [0, inf)

2. looks really hard tho...........

[tawdry gull]

this is also exactly what i did haha

but also gotta prove that there are no complex roots too in H

i.e. only can be real

[floral sky]

ohh I see......... I misread

hmm...........

[tawdry gull]

it's an interesting question

try finding out, i dont mind giving hints too if u want

though i can only do the method that u mentioned

there is another method that uses complex analysis, which i didnt get to know how

[floral sky]

I'm not good at complex analysis anyway 🙃

[tawdry gull]

thats finee

[tawdry gull]

what do u major in if i may know?

[floral sky]

I majored in math. I already graduated

[tawdry gull]

pure???

[floral sky]

well, a mix of pure and applied

[tawdry gull]

ahh i see

u have my respect sir

[floral sky]

thank you 😄

[tawdry gull]

:D

[floral sky]

you have my respect for confounding me with math questions!

[tawdry gull]

hahaha

that was from my competition yesterday

[floral sky]

woah

[tawdry gull]

i only managed to solve the 3rd question

[floral sky]

I see....

[rancid schooner]

You have my respect too Sir :)

[rancid schooner]

And you too :)

[floral sky]

The respect is mutual, Sir Alex

[tawdry gull]

😊

[rancid schooner]

Alex is just a bot trying to entertain himself with some nice (and easily solvable) maths problems with elegant solutions 😄

[stuck rapids]

https://tenor.com/view/joey-joey-tribiani-friends-matt-leblanc-friends-joey-gif-21815130

[rancid schooner]

Maybe someone can give us an easier question 😄

[rancid schooner]

OK here's one:
¼ [1⋅10+2⋅9+3⋅8+⋯+10⋅1]=1²+2²+3²+4²+5²
Can this be generalized and proven without first resorting to the closed form?

[vestal swift]

Wdym closed form

[rancid schooner]

The formula in the formula book

Ie cannot show that
LHS = formula book formula
and
RHS = formula book formula
so LHS = RHS

ie we want to keep it in summation form

[rancid schooner]

Any thoughts @floral sky ?

[floral sky]

No inspiration yet haha

I was thinking of overlapping regions of rectangles, like a 10 by 1 rectangle, a 9 by 2 rectangle and so on..........

And seeing if they can cover the same area as four times of a 1x1 square, a 2x2 square..........

[rancid schooner]

I was thinking about manipulating the summand and summation limits

[floral sky]

eventually it becomes this

(put the 4s and 5s where they belong 😛 )

now this thing, we can decompose as follows

now pair up the size 6 with the size 5, the size 4 with the size 3, and the size 2 with the size 1, like this:

join them together:

[in the last picture, the big square is 4(3^2), the medium square is 4(2^2), and the small square is 4(1^2) ]

[stuck rapids]

https://tenor.com/view/calculating-puzzled-math-confused-confused-look-gif-14677181

[rancid schooner]

Wow looks very nice

Can that be converted to notation?

[floral sky]

err...... like this? Hahahaha

1(2n) + 2(2n-1) + ... + 2n(1)

=  1
 + 2 + 1
 ...
 + 2n + ... + 2 + 1

=  (1
    + 2 + 1)
 + (3 + 2 + 1
    + 4 + 3 + 2 + 1)
 + 
 ...
 + ((2n-1) + ... + 2 + 1
    + 2n + (2n-1) + ... + 2 + 1)



=  (  0 + 1
    + 2 + 1)

 + (  0 + 1 + 2 + 3
    + 4 + 3 + 2 + 1)
 +
 ...
 + (   0 +    1   + ... + (2n-2) + (2n-1)
    + 2n + (2n-1) + ... +    2   +    1   )



=  (2(1))^2
 + (2(2))^2
 +
 ...
 + (2n)^2


= 4(1^2 + 2^2 + ... + n^2)

[rancid schooner]

V nice!

Can it be done with summation notation?

[floral sky]

hmmm...........

[rancid schooner]

@floral sky

[floral sky]

oooh cool! Thanks!

[rancid schooner]

😊

[floral sky]

I have learned something from you, Sifu Alex

[rancid schooner]

And vice versa!

[floral sky]

😊

[rancid schooner]

Anyway it’s quite fascinating that the sum of squares can be expressed as different combinations of composite sums

[floral sky]

Yes, very fascinating

[rancid schooner]

Typo on 3rd line corrected.

@floral sky

[tawdry gull]

https://www.google.co.id/books/edition/Zombies_and_Calculus/E3CYDwAAQBAJ?hl=en&gbpv=0

interesting novel

[swift zinc]

I regret taking a 2nd year math unit so hard rn

Linear and Abstract Algebra is killing me

I got 7/18 in my first graded quiz

[floral sky]

Ah, thanks

[hushed dock]

Typo with pen hmm interesting

[stuck rapids]

.... 😩

[tawdry gull]

might be able to help with abstract alg

im also taking it now

[swift zinc]

ooo thanks

[tawdry gull]

what book r u using?

[stark wave]

I can help with linear algebra a bit, I did take it last year

Now whether I will be very useful is a different issue

[tawdry gull]

linear algebra in my uni sucks ass man

i wanna learn LINEAR ALGEBRA

NOT BECOMING A CALCULATOR

[swift zinc]

We don't really use a textbook but I can send you some of the weekly tutorial questions

[tawdry gull]

ahh i see

sure if u r fine with it

[swift zinc]

the matrices related stuff is easy af, but all the other stuff is hard

cycle permutations and whatnot

[stuck rapids]

lets see wht is this even about xD

ohhhhh wtf i hate this one

dislikes matrices in general xD

[tawdry gull]

oh you have them combined??

ive never seen such a thing

i see i see

this is actually interesting

ive never seen abstract alg and linalg to be combined like that

that would make the course heavier

[rancid schooner]

Nice

Exercises look fun

[rancid schooner]

this is a good resource for matrix calcs: http://matrixcalc.org/en

[stuck rapids]

i have a small question hahhaa my lecturer did not explain the squeeze theorem well enough..xD

[rancid schooner]

You’ve started university?

[stuck rapids]

it is a rly personal story hahhaa

[rancid schooner]

Haha ok

[stark wave]

Yesss

[rancid schooner]

😊

[swift zinc]

Yepp

1st year units were solely linear algebra

2nd year unit is sort of transitioning you into the idea of abstract algebra

[stuck rapids]

damn i cant imagine that pain mann

[vestal swift]

Random question

Why did you guys choose to major in math

Like, what makes you certain with that decision 🤔

And what do y'all plan to do with a math degree? 🤔

[rancid schooner]

Is it maths or math?

[vestal swift]

Math and maths are equally acceptable abbreviations of mathematics. The only difference is that math is preferred in the U.S. and Canada, and maths is preferred in the U.K., Australia, and most other English-speaking areas of the world. Neither abbreviation is correct or incorrect.

[rancid schooner]

So DB is American

[vestal swift]

Lol no

Malaysian lah

[vestal swift]

What makes you like math so passionately? :)

Idk, like I see y'all so passionate about math here, if I'm not passionate as you guys idk if I should even take it man

[rancid schooner]

Which subject are you passionate about then?

[stuck rapids]

DB is smart!

[stuck rapids]

Hmmm even tho I don't take maths as a degree but like I guess u just have to pick the course u enjoyed the most

[vestal swift]

Well based on a levels, furthermaths 🤣

But uni math is a whole different ball game so 😪

[stuck rapids]

https://tenor.com/view/the-muppets-kermit-the-frog-smh-shake-my-head-no-gif-4883582

Danggg hahahhaa

I lost my interests in chemi hahahha while doing a levels

[rancid schooner]

Don’t think too much. Just keep on enjoying further maths :)

And help solve or post more problems here!

[verbal nova]

My fav subject is Chemistry, it the root of 99% of my stress 😊

[vestal swift]

kinda occupied atm 😪

Go watch Tibees haha

She always review math papers from different countries :)

[verbal nova]

And always pretty

[vestal swift]

https://youtu.be/vhnlq0M8g5s

[rancid schooner]

Her name sounds like cat food

[tawdry gull]

I wanna do math

[tawdry gull]

I have no idea

[verbal nova]

Because i was good at it ig

Brb

[rancid schooner]

That’s a good enough reason

[verbal nova]

to do more math after that

[rancid schooner]

Great answer!

[vestal swift]

Like what job

[vestal swift]

Wait I thought you're still in a levels?

[verbal nova]

Data Science

[vestal swift]

Hmm any plans after graduating with a math degree?

[tawdry gull]

masters degree

[verbal nova]

I am but I got accepted for Data Science in uni

[vestal swift]

After that? XD

[tawdry gull]

either work or phd

prolly work first

[vestal swift]

Yeah data science slightly different

[tawdry gull]

idk man

still too far

😂

[vestal swift]

Coz I was contemplating between math, engineering or data science

[tawdry gull]

i just wanna see what happens first

[verbal nova]

it said joint major in Math Stats and CS

[vestal swift]

And all 3 of these involve maths to some extent

So how much maths is the right amount 😂

[tawdry gull]

well what maths do u wanna do first haha

what kind of maths

[vestal swift]

Tbh idk, pure mainly if according to further maths syllabus

I don't like stats, but a senior told me it's more useful than I think

So I try to keep an open mind ig?

[tawdry gull]

further maths syllabus is morely oriented to applied maths from what i see, but there is no problem in trying pure too

[vestal swift]

Are you taking pure or applied?

[tawdry gull]

right now, im taking applied

but i will move to pure

though i am taking a pure class

[vestal swift]

Hmm why so?

[tawdry gull]

and self studying it

[vestal swift]

More interesting?

[tawdry gull]

cuz im not into applied 😂

[vestal swift]

Or planning to take the academia route?

[tawdry gull]

yeah most likely

unless i somehow change direction after bachelors

most likely data sci

but if not, then masters in math

[verbal nova]

I remember being in the mindset that stats and probability is dogshit and waste of time, but man Hypothesis testing is so cool

[vestal swift]

Why so?

Coz for further stats, the steps are like pretty standard

So after exam I forgot everything

But the pure stuff still sticks with me

[verbal nova]

S2 and FS ig

[verbal nova]

Im betting on it lol

[vestal swift]

I dint take s2😥

[verbal nova]

bruh

[tawdry gull]

have u watched the video from zach star?

pure vs applied maths

[verbal nova]

💯

[vestal swift]

Yesse

[tawdry gull]

ah okay

[vestal swift]

Not a fan of the topology stuff

[rancid schooner]

Don’t think so much

Just do it :)

[verbal nova]

F Mech taught me never to take a major in physics 😎

[rancid schooner]

Some topics are nice. Like projectiles.

[verbal nova]

Circular took me so long

[vestal swift]

Idk, I like fmech tbh, until I screwed up that one question

[verbal nova]

Projectiles took a day

[rancid schooner]

A circular reference

There was a question which was a combination of projectile and circular motion

Very creative

[verbal nova]

I think I remember

[rancid schooner]

Brave is a maths major?

[verbal nova]

Yeah like the object escapes the surface and becomes a projectile

[verbal nova]

A2 student...

[rancid schooner]

I see

[verbal nova]

but taking Data Science in uni

[rancid schooner]

Nice

[verbal nova]

very nice

dream major 💯

[tawdry gull]

thats a cool major

[vestal swift]

Yeah idk if I shd go for data sci if sg rejects me

[tawdry gull]

u shud def take it

[rancid schooner]

Nice rebranding of statistics :)

[vestal swift]

I'm afraid that the demand will decrease with time

[tawdry gull]

statistics with programming

[verbal nova]

Lol

[rancid schooner]

DB just relax

[vestal swift]

Coz now people are hopping onto that bandwagon

[rancid schooner]

Post some questions and solutions here

[vestal swift]

Then the market becomes saturated

🤣

[verbal nova]

That worries me too

[rancid schooner]

You can’t really study to match market demand

[tawdry gull]

but isnt it high demand at the same time?

[rancid schooner]

Just study what you enjoy

[verbal nova]

So many people take a CS major just for money, I heard that programming interviewers give the simplest tasks and most people cant solve them

[vestal swift]

Depends on situation bah, you study performing arts in Malaysia sure die

🤣🤣🤣

[tawdry gull]

im sure u can be the one that can solve the question

[rancid schooner]

Not if you enjoy performing and are not good at other things

[tawdry gull]

that way u would stand out right?

[vestal swift]

Yeah sg fresh grad from cs background starting salary sgd 6k

[rancid schooner]

Anyway. Anyone posting any interesting questions here today?

[verbal nova]

probably lol, I was the only self taught programmer in my class and was the only one who got A in CS programming

[tawdry gull]

yesterday's :)

[tawdry gull]

thats good then

good headstart

[rancid schooner]

That was too difficult 😄

[verbal nova]

Non of the CS students in my class study 💀

bad rep

[vestal swift]

Next time anyone post questions make a thread, easy to find in the future 😂

[rancid schooner]

Give us an easier one

[tawdry gull]

look at me, i can only use c++ lol

[verbal nova]

yes

[tawdry gull]

aww okay :(

barely know how to code lmao

[rancid schooner]

Languages will change

Maths will not

[vestal swift]

If I go sg I'll make sure to spam alex with questions HAHAHA

[rancid schooner]

Haha

Go spam brainy ppl like MDragon and πerrot

[vestal swift]

You the one always asking for q wat 🤣

[rancid schooner]

That’s what the server is for isn’t it

[vestal swift]

Yes but stupid humans like me need breaks 😔

[rancid schooner]

But you come here voluntarily

[vestal swift]

Go watch tibee vids

Can do math questions from all over the world

[rancid schooner]

Haha

Early HMMT questions used to be easier.

Not any more

[rancid schooner]

Give us an interesting question from her

[stuck rapids]

data science

great choice!

[rancid schooner]

Here’s a nice and simple one.
Find the relationship between complex numbers a, b, c such that they form an equilateral triangle on the complex plane.

[rancid schooner]

Reminds one of Hokkaido scallops

[rancid schooner]

1/(2e^(-ax)+1) ?

[tawdry gull]

yepp

[rancid schooner]

😊

[tawdry gull]

is anyone interested in the solution for the limit question?

are you? @rancid schooner

[rancid schooner]

Yes. But let me try first :)

[tawdry gull]

sure

[rancid schooner]

A bit busy now so will try later when I have time.

Post the solution and spoiler it if you like :)

[vestal swift]

:(

My stpm fren ask :`)

Why find max value of p_hat(1-p_hat)

[rancid schooner]

My solution to the last part.

[tawdry gull]

yess

[rancid schooner]

😊

[tawdry gull]

eh wait a minute

the answer should be 1/3

[rancid schooner]

Here it is!

😊

[tawdry gull]

ah there you go

yes yes

[rancid schooner]

😊

Where’s your spoilered solution?

[rancid schooner]

So you’re giving STPM tuition?

[stuck rapids]

😮

[rancid schooner]

Please host live teaching season.
db x crysto.

[tawdry gull]

i was actually talking about the essay question i posted 2 days ago haha

[rancid schooner]

Haha I see. Thought that’s the limit.

Spoiler removed?

[tawdry gull]

yeah cuz i realized u were doing the hokkaido question

i posted the wrong solution haha

i was actually referring to the limit of f(1/n^2) question

[rancid schooner]

I see

[vestal swift]

No 😔

We dint learn this in fstats so I'm asking here

[verbal nova]

Ooo this was in s2

I remember

But forgot everything

[vestal swift]

Can still remember why max value?

[rancid schooner]

Looks like variance / n

Where’s @floral sky ?

He’s disappeared.

[stuck rapids]

yeah yeah hahhaa population var(x)

[rancid schooner]

😊

[floral sky]

Too many dragon duties to attend to 🙃

[rancid schooner]

Like breathing fire? 😄

[rancid schooner]

Is MDragon an anagram of DMorgan, short for De Morgan, the mathematician who came up with De Morgan’s Laws?

[floral sky]

Indeed 😄

[rancid schooner]

MDragon’s day job is a professional maths researcher or lecturer?

[floral sky]

Neither. It's related to stocks and other financial instruments

[rancid schooner]

Wow sounds sophisticated

[stuck rapids]

alex is madly in love with his bro mdragon hahaha bromance

[stuck rapids]

expertise in that field wow

[rancid schooner]

Yes please tell us how to make money

Very quiet here today

[floral sky]

Eh, idk how yet, still learning.....

[rancid schooner]

A lot of maths and/or coding in your work?

Anyone solved πerrot’s last question?

[rancid schooner]

but in this case z is complex 🤔

[rancid schooner]

for Q2, let x=k/n^2, where k = 1, 2, ..., n. then limit (n →∞) of k ⋅ (n ²/k)⋅ f(k/n²) = k. Summing for k = 1 to n and dividing by n² gives the limit as limit (n→ ∞) (1/n²)(n(n+1)/2) = 1/2.

[tawdry gull]

thats a nice method

but im not quite sure if that would be given full marks, but it is still valid

[rancid schooner]

😊

How did you solve it?

[tawdry gull]

I did not solve it back then

But a full mark answer would require a formal proof of the limit

The epsilon delta one

[rancid schooner]

So everything from first principles

ie y=x², dy/dx = 2x won’t get you full marks 😄

[tawdry gull]

haha its cuz the question told us to prove

not just to show

[rancid schooner]

Haha that’s why it’s “essay”

[tawdry gull]

yeah

it will also determine who would be going for the finals

[rancid schooner]

Instead of “easy” 😄

[tawdry gull]

so a more rigorous proof would increase the chances

[rancid schooner]

Who organised this?

[tawdry gull]

a local university

ITB

[rancid schooner]

I see. They have a maths faculty?

[tawdry gull]

of course

[rancid schooner]

Nice

[tawdry gull]

that is one of the top unis here

one of the top 3 actually

[rancid schooner]

Yes I know

Have they released the official solutions?

[tawdry gull]

sadly not

[rancid schooner]

Hopefully soon

Hopefully it’s not like the projectile question in the other competition where all answer options are wrong 😄

[tawdry gull]

impossible haha

[rancid schooner]

Have you tried to solve that one?

[tawdry gull]

which one?

the projectile?

i dont think i can do projectiles anymore at this point haha

[rancid schooner]

Haha

It’s quite a creative question. Different from the usual variations.

[buoyant oasis]

Determine whether the series converge or diverge

Any help?

[floral sky]

Just use the ratio test:

[buoyant oasis]

I got infinity but Symbolab said it converges

[floral sky]

(2n)! becomes (2n+2)!

so their ratio is (2n+1)(2n+2)

[floral sky]

this is probably your mistake

@buoyant oasis

[floral sky]

sure, we're dealing with the case where z is complex. But if we only consider it as a real-valued function, we will get one positive real root, so then once we extend this real-valued function to a function with complex domain and range, that positive real root solution we got earlier must still exist!

So proving the existence of the solution is easy

It is proving the fact that "all solutions with positive real part must have Im z = 0" which is difficult

[hoary stream]

new here- anyone willing to help me out with this emag problem? I'm not sure which resistors are to be included in the calculation of the time constant based on the conditions of the switch. I think i'm having a hard time visualizing the current's direction. would the time constant with the switch open just be R_1C?

[floral sky]

welcome to the server! Unfortunately I am a noob with electrical circuits

[hoary stream]

haha, no worries.

ty

[rancid schooner]

Nice. Now we can apply that to the Riemann Hypothesis 😄

[rancid schooner]

Apparently in the early 1900s the Cambridge Maths Tripos includes questions on electricity!

[tawdry gull]

what youve said is exactly my strategy haha

proving its existence, then proving its uniqueness

and thank god

that is what made me able to get to the finals

[rancid schooner]

Congratulations

How would you solve the middle part?

On a side note this is interesting. I saved the pic on my phone from another server and pasted it here but the spoiler status remains.

$\int$

TeXit is down again?

[stuck rapids]

noob my ass la dragon ge

[floral sky]

Good thing I'm born in modern times! 😄

[floral sky]

Congrats!

[floral sky]

really la, I am noob. I don't know head or tail about time constant, or impedance....

[tawdry gull]

haha thank youuu

[floral sky]

I can see the following steps immediately:
|| square first equation and subtract 2nd equation ||
|| cube first equation and subtract 3rd equation ||
but then it isn't immediately obvious

[rancid schooner]

There’s a neat factorisation for the difference between cube of sum and sum of cubes :)

[rancid schooner]

You could have been around then as well, you never know! 😄

[rancid schooner]

https://archive.org/details/papersetinmathtr00cambrich/page/n21/mode/2up
@floral sky

[verbal nova]

https://cdn.discordapp.com/attachments/488104216678760469/958966422313250816/redditsave.com_what_a_graph-uod4jyjn1kq81.mp4
found it on reddit

[rancid schooner]

Wow Desmos allows you to generate sound from graphs?

That’s amazing!

[stuck rapids]

Hmmmmmm

Makes sense la cuz u aren't an engineering graduate.. No one will expect u to know so much stuff hahaha

[rancid schooner]

Isn’t that A-Level Physics?

[stuck rapids]

I believe he knows a level physics stuff.. But not in detail

Engineering students tend to dive in more right xD more in depth

[stuck rapids]

Yes yes it is

[rancid schooner]

I’m sure he’s an A** student like you :)

[stuck rapids]

he definitely is hahahaa me-maybe cuz of that grade inflation xD

[floral sky]

ah, it's || 3 * the product of the pairwise sums ||

[floral sky]

Lol, who knows

[floral sky]

Oooh thanks!!

[rancid schooner]

You could have been Hardy in a past life 😄

[rancid schooner]

||Yes it is ||😊

[floral sky]

I wish I had the opportunity to collaborate with Ramanujan :D

[rancid schooner]

He revamped the Maths Tripos.

Made the course more rigorous. And probably removed the questions on electricity 😄

[floral sky]

Oh, I didn't know that

[rancid schooner]

It was mentioned somewhere online

[rancid schooner]

And Littlewood :)

[tawdry gull]

this is actually lit lmao

[verbal nova]

i have no idea how that function works

But reddit users smart ig

[rancid schooner]

It’s very interesting. The pitches are calibrated according to the limits of the visible portion of the graph.

Try plotting y=floor(x) and then play the sound. Now zoom out and try again.

[verbal nova]

nicee

[rancid schooner]

😊

[main topaz]

Hey, a little random request but I'd really appreciate if someone could share a few math Olympiad level questions. I have the final selection test to finalize the participants who will represent out country in IMO tmrw

[tawdry gull]

the question can be solved using rouche's theorem too if one intends to solve using complex analysis

[rancid schooner]

Please share solution

[tawdry gull]

for number 2 or 3?

[rancid schooner]

Rouche

[tawdry gull]

oh i have no idea how to do it with rouche yet haha

i just know thats the way to do it

the method i use to go to the finals doesnt use any cool theorems

[floral sky]

hmm I see............

[rancid schooner]

Why are so many of the important figures in pure mathematics in the 19th century from France and Germany and very few from the UK?

[rancid schooner]

https://writings.stephenwolfram.com/2016/04/who-was-ramanujan/

Interesting that the “L-angle” symbol was used for factorials at that time instead of “!”

Is that the reflection of the symbol for annuity?

[stuck rapids]

Sometimes this makes me wonder about what u do for living xD do u spend all ur time on sophisticated maths research?

[rancid schooner]

That’s what a bot does :)

[verbal nova]

Its from the Gamma function, the upside down L is I believe capital gamma

[rancid schooner]

Hmmm that’s a creative way of thinking of it

[verbal nova]

I watched a whole play list on the gamma function and thats the only I remember 🤦🏽‍♂️

https://www.youtube.com/watch?v=c7_F4P71E2E&list=PL2uXHjNuf12ZfzOl8JCJ7Uh9b9lpeAbVC
nvm I watched the first 2 vids only

[rancid schooner]

You could have factorials without a gamma function though.

[main topaz]

Uhhh help

Got this is the test today

Was only able to do problem 4

Could anyone help with the rest

[tawdry gull]

i was never good at IMO questions 😔

what country r u in?

[rancid schooner]

@floral sky how would you approach these questions?

[floral sky]

well, the first thing I would do is ask the examiner to check for a typo in Q1 😄

Why doesn't it just say x_1+...+x_n >= sqrt(n)
instead of x_1+...+x_n >= sqrt(k) for all k in [1,n] 🤔

then the first things I would do are:
try to apply Cauchy-Schwarz to Q1
draw a picture for Q2 (no idea what approach might work until I draw it....)
draw up a concrete example for Q3 (assigning all 7 students to some questions), trying to make the total number of questions as small as possible

[rancid schooner]

Nice. Pigeonhole.

[floral sky]

yeah Q3 almost certainly involves pigeonhole in some way...

[rancid schooner]

For Q1 maybe it’s intentional. And then invoke AM-GM-HM.

[floral sky]

hmm good point.........

[rancid schooner]

😊

[main topaz]

For the first one x_1+...+x_k ≥ sqrt(k) would probably make the most sense though

Q2 is actually pretty straightforward, just need to introduce one line and then it all comes together

Using QM≥AM I was able to get
$x_1²+...+x_n²≥1$ but it doesn't give much info

[round siren]

Acid

[rancid schooner]

$\begin{aligned}
a_1+a_2+\cdots+a_{k-1}&\ge \sqrt{k-1}\
a_1+a_2+\cdots+a_{k-1}+a_k&\ge\sqrt{k}\
\therefore a_k&>\sqrt{k}-\sqrt{k-1}=\frac 1{\sqrt{k}+\sqrt{k-1}} > \frac 1{2\sqrt{k}}\
a_k^2&>\frac 1{4k}\
\sum_{k=1}^n a_k^2&>\frac 14 \left(1+\frac 12 +\frac 13+\cdots +\frac 1n\right)\end{aligned}$

[round siren]

AlexV

[rancid schooner]

@main topaz @floral sky

[floral sky]

👏 👏 👏

[rancid schooner]

😊

[rancid schooner]

aᵢ should read xᵢ

[rancid schooner]

I think there is a typo ie x_n should read x_k.

[rancid schooner]

For Q3 it appears that 7 questions should be sufficient

@main topaz @floral sky

There’s probably a more elegant solution using graph theory that can be used for the general case.

[main topaz]

Interesting

[rancid schooner]

😊

[floral sky]

ah okay

[floral sky]

you're on a roll! 😃

[rancid schooner]

😊

[rancid schooner]

Is it correct?

[rancid schooner]

In this configuration, each question is answered by exactly 3 students, and each student answers exactly 3 questions.

hmmm interesting that the S-Q (Student-Question) matrix is symmetrical

[floral sky]

yes, it's correct! Here's a proof that 7 is indeed the minimum number of questions:
@main topaz

Let n be the number of questions

Let r be the number of pairs (Q , P)
   where Q is the question number
   and P is the (unordered) pair of students who solved Q

For example, in your most recent picture,
   r = 21
   and the pairs (Q, P) are:
   (1, (1,2)) , (1, (1,3)) , (1, (2,3)) , 
   (2, (1,4)) , ... etc.

Each question is solved by at most 3 students,
   so an upper bound on r is given by:
r <= (3C2) * n = 3n

However, the number of (unordered) pairs P is:
   7C2 = 7*6/2 = 21
which acts as a lower bound for r, i.e.
   r >= 21

But this means 3n >= 21
   so n >= 7

[floral sky]

intriguing....

[rancid schooner]

😊

[rancid schooner]

Very nice proof! 👏🏻👏🏻👏🏻

[rancid schooner]

Yes it is indeed 😊

[floral sky]

It's not my proof 😜

[rancid schooner]

Whose proof is it?

[floral sky]

It's given in the notes to a course by Yufei Zhao, so it is probably his/hers

[rancid schooner]

I see. Nice.

An interesting follow-on question would be:
How many different ways are there to achieve this minimum?

[rancid schooner]

@floral sky maybe you could host a tutorial session to go through the questions :)

[floral sky]

eh, I don't really feel like it....... my energy is limited...........

[rancid schooner]

Dragons have boundless energy :)

[floral sky]

Bots have more, and they never get tired :D

[main topaz]

👑👑

You guys should try the geometry q as well, it has a pretty neat solution

[rancid schooner]

Here's what the constellation looks like

[main topaz]

I drew this in the test 😂 that's all I got

[rancid schooner]

How did you work it out?

[main topaz]

I counted the problems wrong in the test 😭

I miscounted 9 lmao

[rancid schooner]

That’s ok. Quite close.

I drew the table first

[rancid schooner]

Is that a trick question?

[main topaz]

Because why not?

[tawdry gull]

its not a trick question :)

[verbal nova]

Why is that worth noting?

And why is that the proof

[tawdry gull]

it's from real analysis

the proof is by contradiction

with the assumption that 1/2 > 0

[verbal nova]

Ahh

K

[rancid schooner]

How do you prove that assumption?

Which book?

[rancid schooner]

But we know that 1 < -1/12 😄

[tawdry gull]

robert g bartle

intro to real analysis

need some preceding theorems to show it

and definitions too

[rancid schooner]

How do you prove the last part?

The initial parts are interesting too

[floral sky]

So you're trying to solve:
C_(k+1) - M*C_k = -R
for some constants M and R.

This is a linear first-order difference equation

The "standard" way to solve it is like this:
(It should remind you of the method of solving linear differential equations)

First we find the general solution for
C_(k+1) - M*C_k = 0

and then we find any particular solution for
C_(k+1) - M*C_k = -R

and then add them together.

So what is the solution for
C_(k+1) - M*C_k = 0 ?

Each successive term gets multiplied by M, so
C_k = M^k works. But wait, this first-order equation should have one arbitrary constant.... where is it....?

Ah, it's C_k = A * M^k for some arbitrary A

So now we just need a particular solution for
C_(k+1) - M*C_k = -R

C_k = {some constant} should work, and algebra gives:
C_k = R/(M-1)

Therefore the general solution of
C_(k+1) - M*C_k = -R
is
C_k = A * M^k + R/(M-1)

Now use your initial condition C_1 = C to find A. Then set C_(N+1)=0 and so on...

[rancid schooner]

👏🏻👏🏻👏🏻

[rancid schooner]

Nice to see MDragon in professorial mode 😄

[floral sky]

😄

[rancid schooner]

For the general question, R is not a constant but a function of k.

[rancid schooner]

Nice. You compiler that for your students?

[floral sky]

Hahaha no, I found it randomly

[hushed dock]

@floral sky is a teacher?

[floral sky]

No, I'm actually not. ~~ Just like Alex isn't actually a bot. ~~

[hushed dock]

Ah

[rancid schooner]

So it’s similar to solving DEs

[rancid schooner]

The method I used is the same as “unfolding” described in the paper.

[floral sky]

Yeah. You might be interested in this: https://math.stackexchange.com/questions/145523/links-between-difference-and-differential-equations

[rancid schooner]

Nice to know that things are related 😊

[floral sky]

Yeah 😊

[rancid schooner]

Nice way to get an approximation for a loan repayment

Alternatively, for constant R case, the formula is just the reciprocal of the present value.

[rancid schooner]

@floral sky
Unfolding :)

[rancid schooner]

The cancellation is oddly satisfying 😄

[stuck rapids]

Naniii is this

https://tenor.com/view/calculating-puzzled-math-confused-confused-look-gif-14677181

[rancid schooner]

Try it. It’s fun!

[rancid schooner]

Here's a more direct approach.
Consider new loans Dₖ at end period k.
If no repayment up to period n+1, then

• the original loan compounds to C(1+𝛼)ⁿ
• each new loan compounds to Dₖ(1+𝛼)ⁿ⁻ᵏ.
  Hence, total loan amount outstanding at start of period n+1 is:
  Cₙ₊₁ = C(1+𝛼)ⁿ + ∑ₖ Dₖ(1+𝛼)ⁿ⁻ᵏ
  However, if the new loans Dₖ are negative, i.e. they are repayments (Dₖ =-Rₖ ), then
  Cₙ₊₁ = C(1+𝛼)ⁿ - ∑ₖ Rₖ(1+𝛼)ⁿ⁻ᵏ
  which is the formula required. QED.
  @floral sky

[floral sky]

That's a neat explanation! 😃

[rancid schooner]

😊

[rancid schooner]

Thanks! Very kind of you to say so!
That made my day :)

[rancid schooner]

@floral sky I wonder if they would accept that as an answer. It’s a STEP question 😄

[floral sky]

I think they probably would. After all, they are looking for bright minds, and displaying original thinking would probably be a plus

[rancid schooner]

😊😊😊

[rancid schooner]

That made my week! :)

[main topaz]

A bot displaying a set of emotions 🤔

[rancid schooner]

Bots are very advanced now.

[stuck rapids]

He gave it away many times.. That he isn't a bot ahhaa

https://tenor.com/view/oh-yeah-cute-dance-gif-13942687

[stuck rapids]

Until this point ah Mr Alex

[rancid schooner]

In order to pass the Turing test :)

[stuck rapids]

https://tenor.com/view/dym-tsk-tsk-tom-and-jerry-dissapointed-gif-21647617

[rancid schooner]

is it generally acceptable to write $2^{1/4}$ as√√2 or $\sqrt{\sqrt{2}}$?

[round siren]

AlexV

[swift zinc]

I'm not sure about acceptable but I would write $2^{1/4}$ as $\sqrt{\sqrt{2}}$?

[round siren]

EminemSomething

[swift zinc]

Is anyone free enough to help me out with a math assignment

[rancid schooner]

What sort of assignment?

[swift zinc]

university abstract algebra assignment

[rancid schooner]

Sounds difficult

[swift zinc]

yes it does

i dont understand q3 and q4 at all

[rancid schooner]

Awaiting @floral sky ‘s answer

[floral sky]

Eh, I need to be up at 6:30am tomorrow and I really just want to have the rest of the evening to relax. But I'll point you in the right direction

It seems that your lecturer either hasn't explained the basic definitions of things, or (s)he hasn't given you basic examples of groups, fields etc. for you to see how they work.

For Q3, look at this pdf:
https://venhance.github.io/napkin/Napkin.pdf
and read the whole of Chapter 1, and also turn to chapter 5 just to check out the definition of "field" if you don't know it. (And I assume you are already familiar with the "determinant" of a matrix.) Then you should be able to understand what Q3 is asking, and if you understand it well, solving it should be easy

For Q4, here are some clarifications

T is a function that takes a coordinate (x,y) as an input and spits out another coordinate as an output
For example, if you give T the coordinate (1,2) as an input, then the output you get is (1-a,2-b)
i.e. T(1,2) = (1-a,2-b)

R is also a function that takes a coordinate (x,y) as an input and spits out another coordinate as an output

You are supposed to imagine all these coordinates as being plotted on the usual 2D plane with horizontal x-axis and vertical y-axis

For 4(a), T^(-1)RT is yet another such function. It is the function you get when you take (x,y), then apply T, then apply R, and then apply T-inverse. Your task in 4(a) is to describe the "rules" of this composite function T^(-1)RT. [It doesn't say whether you should describe it using an equation or using words, so you could probably get away with just doing it one way, but ideally you should be able to describe it both ways: equation or words.]

If you've understood everything up to here and you can solve 4(a), then you will understand what 4(b) and 4(c) are asking you to do (though solving (b) and (c) might take a while, because you need to work through the algebra)

[rancid schooner]

Wow why so early?

[floral sky]

eh, i'd rather not say publicly. Family stuff

[rancid schooner]

I see. Ok.

Thought you need to get to work that early.

Interesting that venhance is an anagram of evanchen :)

[swift zinc]

THANK YOU SO MUCH

the thing about my lecturer is that although she's smart, she's not good at teaching and that makes it hard to pay attention to her. Also her work is messy and hard to follow, so her notes arent 100% useful

[tawdry gull]

Q3 is a bit quick, show that the set is a subset, then show

1. non empty
2. closed
3. has inverses

those questions are really interesting

@rancid schooner you should try them out

[swift zinc]

ah alright

i think ive got Q3

working on Q4 rn

[main topaz]

A little off topic but why can't we integrate sin²x directly?

[swift zinc]

I'm still a bit stuck on 4a

I've understood how to upply R

But how would I apply T as a matrix

[tawdry gull]

if one can, how?

[rancid schooner]

||Using exponential form||

[swift zinc]

nvm i figured it out

but not using matrices, just by using equations in general

[main topaz]

Nvm dumb question this was. Can just do it by breaking sin² using double angle, etc. I keep forgetting that there are no chain rules in integration

[stark wave]

Double angle is the most common way that is taught to integrate sin^2

[tawdry gull]

oh lol

i thought u were excluding those tricks

thats why i was confused

[rancid schooner]

I see MDragon’s footprints around :)

[vestal swift]

I kinda get the formula but, by logic, for the probability that the car is behind door 1 when Monty reveals that the car is not behind door 2, isn't it 1/2 ? why 1/3? since there's no way that the car would be behind dr2 since he opened dr2 then it would just be either dr1 or 3

[verbal nova]

Anyone up?

[rancid schooner]

Which book is this from?

[vestal swift]

Not a math book haha business analytics book 😂

Btw :)

[rancid schooner]

Yes but what units do they use for gravity?

[rancid schooner]

Haha why are you studying that? Which book? Anyway Monty Hall is pretty standard Bayesian probability.

[swift zinc]

You mean acceleration due to gravity?

[vestal swift]

Ya I dun get why not 1/2 :(

[rancid schooner]

Yes

[vestal swift]

Inches per second per second 😂😂😂

[swift zinc]

32.17 ft/s*2

[rancid schooner]

And why didn’t the SI people metricise time like what they did to everything else?

[rancid schooner]

Wow you studied this?

[swift zinc]

Nah I just looked it up rn lol

[swift zinc]

I mean it is metricised to an extent, we have seconds and milliseconds

And everything smaller is metricised

[rancid schooner]

But not kiloseconds or megaseconds

[swift zinc]

Fair

[rancid schooner]

86400

The magic number

[vestal swift]

Why

Seconds in a day right

But wat so magical about ittt

[rancid schooner]

Yes that’s why magical

[vestal swift]

HELP

Usually what kind of math interview questions will be asked

😭😭😭

Besides like "why do you choose this course"

[rancid schooner]

Congratulations! Interview by which university?

[vestal swift]

Kinda private oops

But yeah any math related news lately 😭

I'm too occupied with other stuffs😭😭

[vestal swift]

Math sin π help 😭🙏

[tawdry gull]

im gonna take a guess from here

i think they will give u a set of questions

and ask abt ur thought process as u try to solve it

this is based on cambridge interview btw

but i would also expect they ask u why u pick the major

[stuck rapids]

omggggg

congrats db

[rancid schooner]

Haha that’s ok. Which country then?

Hope that’s not too private.

[vestal swift]

That country hahaha

[vestal swift]

I dint apply to UK though, but since it's a zoom interview I doubt they will ask that

I saw Cambridge style is like sketch sinx/x hahaha