serious-discussion

[jagged forge]

do you know how to multiply matrices?

[fathom tendon]

no

all weve done so far basically is state that an augmented matrix is another way of writing a system of equations

[jagged forge]

sorry, maybe that’s thr wrong question. did they teach you how to apply a matrix to a vector

[neat lintel]

that doesn't need a proof?

It's just a matter of representation at this point

[fathom tendon]

yeah thats not the thing im trying to prove tho

im trying to prove an equality thingy

[fringe summit]

$\begin{bmatrix} x_1^2&x_1&1\x_2^2&x_2&1\x_3^2&x_3&1\end{bmatrix} \begin{bmatrix} a\b\c\end{bmatrix} = \begin{bmatrix}y_1\y_2\y_3\end{bmatrix}$

[fathom swallow]

Dragonslayer Sharp

[jagged forge]

if you apply the matrix to the vector, it is pretty straightforward to see

[neat lintel]

you have that
ax_1^2 + bx_1 + c = y_1
ax_2^2 + bx_2 + c = y_2
ax_3^2 + bx_3 + c = y_3

[fathom tendon]

? whats that mean

[jagged forge]

u just gotta calculate and expand it out

[neat lintel]

this is just another way of writing that

[fathom tendon]

oh

[neat lintel]

I don't see anything to prove here

[fathom tendon]

idk

[neat lintel]

you said that given a system of linear equations, you can write it as an augmented matrix

[fathom tendon]

Its what my textbook is asking me to do

yeah which i did

[neat lintel]

what do you wanna do next

[fathom tendon]

so like on my first row I have x_1^2 + x_1 + 1 = ax_1^2 + bx_1 + c

And I want to show that x_1 is equal to say a

[fathom tendon]

and basically repeat this for the next two lines

[fringe summit]

Are you sure that’s what you want

[fathom tendon]

I can't think of another way to state that the y expression coeffecients are solutions then showing that they can each correspond to one of the variables

[neat lintel]

the augmented matrix would be
x_1^2 x_1 1 | y_1
x_2^2 x_2 1 | y_2
x_3^2 x_3 1 | y_3

[fathom tendon]

My teacher and my textbook have no seperation between colums 3 and 4, is that just notational?

[neat lintel]

that's not what the first row represents

[fathom tendon]

oh

why not

[neat lintel]

the first row represents
ax_1^2 + bx_1 + c = y_1

[neat lintel]

it's a matter of definition

[fathom tendon]

I know this is true because thats from the parabola, but i feel like it just ignores the whole left side of the augmented matrix?

so i was subbing that in for y on the righr side of the matrix

[neat lintel]

this equation literally represents the first row of the augmented matrix

they tell you the same thing

no info is lost or gained

[fathom tendon]

The first row initially doesn't have any coeffecients on the left side though? And now this is introducing coeffecients that weren't initially there

so now the coeffecientless line ceases to exist?

[neat lintel]

the coefficients are encoded in the columns

first column represents a

second b and third c

4th just represents the right hand side of the equations

[fathom tendon]

Wait why do the columns represnt the letters

[neat lintel]

for now it's a matter of definition

you can't prove anything

[fathom tendon]

I guess I just missed that in class today somehow

[neat lintel]

there are 3 representions: systems of equations, vector equation and augmented matrix

And they are just different ways of representing the same thing as far as intro to linear algebra goes

[fathom tendon]

ok

Well I need to go and try to rush through the rest of my HW lol

Ill see what I can throw together tomorrow knowing that the columns represent each coefficient

[neat lintel]

I guess there's a 4th representation that involves matrix multiplication which someone has shown already

[native sorrel]

What do we use the equation E=mc(squared) for?

[neat lintel]

nukes

[native sorrel]

XD

wow

But for the mass part of the equation, where do we get the mass from

do we apply that equation to objects to find their potential energy?

[neat lintel]

it's not their potential energy

[native sorrel]

Is the equation just a statement?

[mental stratus]

black name

[zealous garden]

He got cohonorable

[echo tundra]

Looking at history, looks like he made some poor joke and got muted for 2 days by Eric

[long matrix]

cohonorable.

[glossy crescent]

I want a rank too 😦

[vale trench]

yeah, give my man the black role

[glossy crescent]

I want roles with bright color

How do I apply for Mod

[vale trench]

need to perform a ritual

[glossy crescent]

I will do anything

To achieve rank

[vale trench]

sacrifice all your belongings, and devote yourself to this server

that is the first step

[glossy crescent]

I've done that already

I even quit my job to apply

[vale trench]

the next steps are known only to the current holders of the title

ordinary humans get purged if they know the truth

[glossy crescent]

How does one apply for staff

[echo tundra]

[glossy crescent]

lmao

[echo tundra]

don't ping mods unnecessarily unless you wanna get muted

[glossy crescent]

wdym It's a general question

An "inquiry"

[echo tundra]

for general questions use modmail

[vale trench]

they are not here for answering general questions

[glossy crescent]

Oh?

Sorry for the ping

[surreal sapphire]

we arent looking

[glossy crescent]

Figured, such a large server to be looking for staff

[mental stratus]

are we

[indigo oriole]

what is 88+22

i dont wanna use a calculator

but im too dumb

jk

im bored

hi

uwuw

haja

heje

hehehe

kkakakak

[surreal sapphire]

come back tomorrow, this isnt your personal circus

[woven whale]

How do I apply for Janitor

[mental stratus]

you don't

[alpine comet]

get a PhD

https://gizmodo.com/there-are-5-000-janitors-in-the-u-s-with-phds-5671062

[latent remnant]

is that really true? 5000?

[dense belfry]

There are 300 million people in the us though

idk if 5000 is really that many considering that

[sly flint]

Well, 5000 janitors with a phd.

[latent remnant]

how many janitors are there total tho

[sly flint]

It doesn't really help the fact though.

Lol.

[sly flint]

Imagine studying for 7+ years only to become a janitor.

[dense belfry]

I feel like 5000 isn't that big a number though

[sly flint]

It's just the fact they have phds is concerning. By magnitude it's small.

[neat lintel]

was posted in 2010

[proven plinth]

damn

[sly flint]

damn

[proven plinth]

that name

[sly flint]

That's a lot of text.

[dense belfry]

Sounds like a skill issue

[sly flint]

Janitors in the US earn around ~$30000 annually, apparently.

[sly flint]

[dense belfry]

Most of them do but some make more

[sly flint]

I'm from a third world country so can't really relate lol.

[neat lintel]

This guy 100% sniffs the painted floors

[dense belfry]

Aight time for my orientation for my course I'm teaching

[sly flint]

Awesome. See ya!

[pearl moth]

one of the cooks I used to work with at pizza hut had a PhD

[long matrix]

we have phd janitors right here.

moderators cleaning up after you lot

[wet mortar]

tfw you lot

[long matrix]

yeah you lot, nuffin to do with me

[smoky lodge]

is "a living thing is a thing made out of living things" a good recursive definition?
could it be disproved?

[surreal sapphire]

its not a statement in the mathematical sense, so its "not even wrong"

i.e. cant be proven or disproven

[smoky lodge]

oh I see

[unborn ferry]

First off I would like to say that this definition can be proven bull

Because at the beginning of the FIRST LIFE FORM

it was made of nonliving things

And yes I do mean cyanobacteria

[smoky lodge]

could it possibly be infinite?

[unborn ferry]

Wdym

[smoky lodge]

could there be no first?

[unborn ferry]

There has to be or atleast a few

[smoky lodge]

I am weak at math so maybe it isnt posibble

[unborn ferry]

Idk how even the first life form came to be

[smoky lodge]

like the real numbers

there is not a first

[unborn ferry]

My theory was that elements were bumping into each other by solar energy and eventually and accidentally created cyanobacteria with dna

[unborn ferry]

I think there is

There is either what I just said above

Or aliens was like “hey this looks habitable lets pop in some bacteria so they can evolve”

[storm sage]

To answer the original question though, no it is not a good definition lol

It gives no info as to whether something is a living thing or not

[smoky lodge]

its a value which is true or false

do I have to give a way to find how why its that way?

[fringe summit]

Yes

[storm sage]

It's not even true or false

[fringe summit]

Or a way which gives a starting part

[storm sage]

Like

Does a human being satisfy this definition?

I literally have no idea lol

[fringe summit]

(It’s not recursive since there’s no base case, for one)

[smoky lodge]

oh yea

[fringe summit]

Also “made of”

[raven plaza]

e.g. nothing is a living thing doesn't contradict this definition

[fringe summit]

Are lungs living on their own?

What about salads?

[smoky lodge]

It sounds ok to me

I wanted to get to that actually

[smoky lodge]

yee I see

[raven plaza]

We are all electric signals in the matrix

[smoky lodge]

my defenation is bad

[smoky lodge]

cool

[solid yarrow]

Hm. What would have happened, if Neo took both pills in Matrix?

[raven plaza]

Splits into two people

[solid yarrow]

Splits the timeline

He's now in a superposition

[unborn ferry]

no

[mental stratus]

aight im pretty much all healed up by now

time to do math

[wet mortar]

https://tenor.com/view/goku-healing-dragonballs-anime-gif-11693908

[neat lintel]

Why can't someone who speaks english writes these questions

the veolocity vector $$\vec{v}$$. At t = 4.00 s,

[fathom swallow]

One person

[neat lintel]

but naw

it's actually

two sentences before

[burnt ledge]

this is written clearly and simply

[neat lintel]

at t = 0

[burnt ledge]

Do you know what a full stop / period means. Its basic english punctuation

[neat lintel]

😞

[burnt ledge]

It means the end of a sentence

Youre only allowed to complain about the lack of paragraphing here and even that is kind of justified

[fringe summit]

This is clearly written chief idk

[fringe summit]

Ruthless

[neat lintel]

English is super difficult

[flint basin]

brutal, but correct. This is pretty clearly written

[storm sage]

I agree, it's clearly written, and there's no fault here on the author of the question. Reading can be hard sometimes though.

[fringe summit]

$20 moment

[neat lintel]

It’s easy for me.

FYI I was born in the USA 😁

[neat lintel]

You know what is a hard language. Chinese

[neat lintel]

It's super difficult for me

Even Chinese people still need to learn a lot of characters they don’t know

[neat lintel]

Where you from?

[neat lintel]

中文也很难

[neat lintel]

Lol coincidence haha

[neat lintel]

usa

But it’s true tho. Be completely literate in Chinese is hard

[tame egret]

well american english will be easy for you but maybe not british english

[neat lintel]

I know hood British. Like Init and bruv

[neat lintel]

Neither are easy

[tame egret]

LOL

[tame egret]

IKR

[neat lintel]

I can talk to roadman from Birmingham

[tame egret]

lol

[neat lintel]

I’m gonna be carrying a kitchen knife. Those Brit are gonna be scared

Extra sharp too

Gordon Ramsey knife I got that

[tame egret]

so if a roadman asks: you want to get sheffed bruv?
you reply:

[neat lintel]

I wanna be a chef!

[neat lintel]

I say go back do your a levels bruv because idk wtf you talking about

[tame egret]

no it means do you want to get stabbed

[tame egret]

then you get sheffed bruv

[neat lintel]

Even if he stabbed me. I will keep dissing on his english

[tame egret]

lol

[storm sage]

yooo wait you do?

that's so hype

[neat lintel]

xD i just mean that would be my response if someone asked me if i wanna be cheffed

[storm sage]

Oh lol

[neat lintel]

Oh it’s the German philosopher dude

Hiya

[burnt ledge]

ello ello ello

[neat lintel]

@split pawn @solar hawk https://www.youtube.com/watch?v=7rqKcqx5WKs did you two make a submission?

[solar hawk]

Nah

Afaik

[neat lintel]

today is last day

oh

7 minutes

[warped cliff]

Wow

[solid yarrow]

Ok, so I've been digging into Linear Algebra Done Wrong (LADW) for some while now. I found that the book skips some parts in the chapters. This makes it difficult when doing the exercises. Does anybody have some alternative book recommendation?

[neat lintel]

Why is this book so bad https://socialsci.libretexts.org/Bookshelves/Education_and_Professional_Development/Foundations_of_Education_and_Instructional_Assessment_(Kidd_et_al.)/15%3A_Instructional_Assessment-Grading/15.03%3A_Should_teachers_allow_extra_credit

It talks aboout extra credit but doesn't mention any studies

just

"They said this"

and "this person also said this"

really low quality textbook.
Ohhh, It's written by first year college students. that mus be why

https://socialsci.libretexts.org/Bookshelves/Education_and_Professional_Development/Foundations_of_Education_and_Instructional_Assessment_(Kidd_et_al.)/15%3A_Instructional_Assessment-Grading/15.06%3A_Should_praise_be_given_to_students_or_not

[storm sage]

Wait, skips what?

I thought that book was generally really good

[solid yarrow]

Well, it may be for a combination with lectures.

Not for self-study.

[storm sage]

I think it is reasonably good for self study

I like that book a lot

But Linear Algebra Done Right is also a good linear algebra book

[solid yarrow]

You mean Axler?

Hm, heard he likes to skip determinants.

[storm sage]

Yes

[storm sage]

Yes, otherwise a great book

[solid yarrow]

Might give it a shot then

Another reason I might struggle with the book might be, that I struggle with self-learning. Who knows?

[storm sage]

It can definitely be difficult, but ask any questions you have in this server #linear-algebra :)

[drowsy ridge]

someone trying to help me with 11th grade math pls

[burnt ledge]

!help

[quasi jetty]

Please read #❓how-to-get-help

[storm sage]

If they're struggling with LADW though, I can't imagine they'd appreciate hoffman kunze

[sleek pagoda]

How do you prove that f(-infinty)=0 and F(-infinity)=0, if f(x) and F(x) are a pdf and cdf respectivly

or is this not true?

[storm sage]

I assume you mean the limit as x→-inf f(x) = 0

In which case

[sleek pagoda]

yes

[storm sage]

Let's say it's not zero, then what does it look like?

[sleek pagoda]

the area would be >1

[storm sage]

yeah it would have infinite area

[sleek pagoda]

IDk how to write that more formally

[storm sage]

Do you know about epsilons and deltas?

[sleek pagoda]

a little bit

[neat lintel]

How do i get better at writing math

[flint basin]

practice

[sleek pagoda]

If you want to learn how to write online, you can learn latex

[neat lintel]

$$\int u'v = uv - \int uv'$$

[fathom swallow]

One person

[neat lintel]

I know latex :(

[lean coyote]

I'm a current cs undergrad

I'm dodging more towards data analysis than web development

What should I do ?

How should I decide

To skill on ?

[loud snow]

Probably go to dats analysis if you want to and its not too much of a burden to move

[quick beacon]

There are big data frameworks you can look into, such as Hadoop, though I'm not sure what exactly is hip these days

[jagged forge]

arrow datafusion is hip :]

that’s not a serious recommendation btw

arrow by itself is pretty hip though

datafusion is a WIP

[lean coyote]

I think more ppl are heading towards web development or front end, ryt ? Best to go on data analysis ?

[jagged forge]

backend development jobs are plentiful, I’m not sure where you got that idea

[lean coyote]

I mean all the current students are heading that way

[jagged forge]

everyone needs engineers to manage their stuff that’s been deployed to the cloud

[lean coyote]

Cs

[loud snow]

Ultimately shouldnt matter if you are looking for money both are employable

[lean coyote]

My bad then

Not money, only experience

I didn't mention money

[loud snow]

You are mentioning popularity

[lean coyote]

I mean don't go towards a bigger crowd

Ryt?

[loud snow]

Why not?

Personally I like statistics

So I wouldn’t mind doing data analysis jobs

[lean coyote]

Have u graduated

[loud snow]

Yea

[lean coyote]

That's coool

Oh are u doing a full time job

[loud snow]

Yea

[lean coyote]

I wanted to learn freelancing but how can I study skills and my subjects and sleep

[final igloo]

Put ohone on airplane mode

[split pawn]

I'm sorry I'm late, I was busy

[sly flint]

https://www.desmos.com/calculator/ambdlq1a8i
I did the thing.

[split pawn]

That's cool!

I'm actually gonna take a break now

[sly flint]

I saw yours and tried to replicate it.

[split pawn]

Mhm

[sly flint]

Oh.

[sly flint]

Well, have a good break. I'll try to do stuff with desmos in my spare time.

[glossy crescent]

What's a good TPU for mathematical calculations?

[storm sage]

what's a TPU?

[glossy crescent]

Tensor Processing Unit

For AI machine/deep learning

[alpine kindle]

that's a thing?

[glossy crescent]

Apparently according to Google

The renowned Chat-GPT operates from H100 TPU

[modest moon]

Chatgpt is terrible at maths. I have even experienced it getting the order of operations incorrectly.

[glossy crescent]

and Physics

[pastel axle]

yeah

[glossy crescent]

But why think about it pessimistically

Technology are capable of ameliorating

[proven plinth]

Yea, it's not made for math

such a lousy argument against it

[tame egret]

hello

[split pawn]

Hi

[magic heron]

BOO!

[tame egret]

Li, I know you're reading this. Fuck you kys
why will you type that?

[magic heron]

Who even knows tbh

why you looking at my bio? ☠️

[abstract forge]

This server is awesome btw

[ripe dirge]

Yes

[sonic sentinel]

concept idea thingamabob
problem: i want a reliable prediction of the weather where i live
weird solution: i let people buy a prediction from me. if their prediction about the weather is false, they don't get back the money. if their prediction about the weather is true, i pay them a pre-agreed sum of money. predicting harder-to-predict events correctly gets you more money.
why: people who are able to predict the weather better I pay more, people who can't predict lose money by playing

[loud snow]

This exists

CME sells whether derivatives

The downside is that they are very expensive

[spark lance]

[echo tundra]

TPU's are only good are tensor operations

for general purpose maths calculations you need a CPU

[neat lintel]

HUH?

[loud snow]

I never heard of tpu

[neat lintel]

Can't you vectorize most math

[loud snow]

Is it same as gpu?

[echo tundra]

nope

I guess you can, I am not very sure actually

[loud snow]

Lol

Tpu is buzzwordy

Also no way of knowing much about them

They are proprietary

Actually they wrote blog posts about them

[jagged forge]

fuck cme 🖕 their data feeds are the most complicated mess I’ve ever had to write code for

[loud snow]

Its just a gpu but for higher volume matrix inputs is what the blog post is reading

[loud snow]

Can you explain more?

[echo tundra]

basically yeah

[loud snow]

And they have a unit for activation functions

Idk exactly how it works im still reading

[jagged forge]

their data feeds use some open source format they named Simple Binary Encoding or SBE. you can’t write a parser for it, it’s too complicated, so you have to find the xml schema definitions and plug those into their code generator

to get the xml files u have to access their ftp server, which also blocked me because I accessed too many pages too fast, so i had to access their ftp server through incognito mode and click around the blurred sections

[loud snow]

Sbe says its an encoding algorithm

/protocol

[jagged forge]

and their rust SBE code generator is like one of the worst things I ever had to work with. it was also somewhat new so maybe I’m being harsh. but it was like, astoundingly hard to work with

yeah they stream their live data encoded as SBE

[loud snow]

How much does it cost?

[loud snow]

Is it like a subscription service?

[jagged forge]

Idk the pricing details, someone at my company worked it out I guess

I didn’t buy it myself

[loud snow]

Thas cool

I havent done any programming related to streaming

[jagged forge]

the data is valuable but handling it was such a pain

[loud snow]

I want to work with streamed data );

Idk how to start either

[jagged forge]

maybe look for a data provider with a websocket endpoint

[loud snow]

Is this found on kaggle

[jagged forge]

Idk what kaggle is

[loud snow]

Website for stuff relating to handling data

[jagged forge]

maybe they have some material on websockets

websockets are high level so you don’t have to deal with sockets and IP packets and stuff

and usually websocket servers transmit json (though they can technically transmit anything)

[loud snow]

Im confused

[loud snow]

I want to deal with this

But then ig my goal becomes more complicated

[jagged forge]

yeah if you just want to handle data in real time you don’t need to deal with networking at that level

but it is fun if you need efficiency

then you can explore different settings and different ways to use the Linux networking stack

CME and other data feeds use UDP because they can transmit it via multicast, which is more efficient when transmitting one-to-many

also because of the ultra low latency requirements I guess

[neat lintel]

Praise efficiency not disdain

[jagged forge]

you can have efficiency without garbage like SBE

none of the other SIPs do what they do

they only use SBE because they have like a bazillion different feeds and they wanted a generalized approach

[sonic sentinel]

what are they actually selling? i went to the website and it has too much jargon for me to understand

chatgpt explains it as "its basically insurance against bad weather"

maybe chatgpt is wrong maybe not, but the core of my idea was buying information from anyone who can produce it

[mint canopy]

Do not trust ChatGPT, ever. Here is an actual explanation, found by something just as easy to do: googling. https://www.investopedia.com/terms/w/weather-insurance.asp#toc-weather-insurance-vs-weather-derivatives

[sonic sentinel]

what did you google

[mint canopy]

The words "what is a weather derivative." Hope that helps in the future.

[sonic sentinel]

oh right i saw the investopedia article for weather derivative

but like

it opened

"A weather derivative is a financial instrument used by companies or individuals to hedge against the risk of weather-related losses."

i already don't understand what that means

so i ignored the rest of the page

(because its presumably going to expand upon that idea)

[jagged forge]

do you understand what derivative instruments are? eg options and futures

[sonic sentinel]

i am SIXTEEN fucking years old

😭

[wet mortar]

answer the question

[jagged forge]

options and futures are not hard to understand

at least not the basic idea

[sonic sentinel]

no

[jagged forge]

the common example is a farmer purchases a contract with a buyer to sell their crop at a fixed price on a certain date. so if the price of the crop crashes, they can still sell at the original price. actually this is called a forward contract but futures are similar I think

[sonic sentinel]

ok forward contract

[jagged forge]

because this protects the farmer in the event of a market crash, the farmer has to pay an upfront cost for that protection. which is the cost of the contract

[sonic sentinel]

so you don't exactly know what future is but you're saying it is similar?

[sonic sentinel]

that makes ense

[jagged forge]

I know they are pretty similar, in that you enter a contract to buy or sell an asset at a certain price and you can’t back out (unlike options)

I think futures you can buy or sell at a range of dates, whereas forward contracts have a fixed date. but I skimmed that on Google 2 minutes ago so idk if it’s correct

[sonic sentinel]

oh OK

why is this information important

[jagged forge]

also futures are standardized and traded on exchanges unlike forward contracts

well, the main idea is hedging, which is what the farmer is doing

he is hedging the risk of adverse market conditions for his crops

[sonic sentinel]

hedging is what what what now

from conext i pick up that hedging is just any sort of contract to try and make revenue(right word?) more stable?

[jagged forge]

no, hedging is more like you offset the risk from one asset by purchasing another asset that moves in the opposite direction

[sonic sentinel]

moves?

[jagged forge]

sorry, I meant the price moves in the opposite direction

so if one asset falls, the other rises and your portfolio doesn’t get hurt as much

[sonic sentinel]

OK so in the farmer example the farmer owns crops that they can sell but they can also sell anti-crop weather

[jagged forge]

if there were an asset that was correlated to the weather, he could purchase that, so the weather asset would rise if the weather ended up being bad for the crops

so if his crops are harmed by weather, the weather asset makes back the money he lost from bad weather

[sonic sentinel]

ok "A weather derivative is a financial instrument used by companies or individuals to hedge against the risk of weather-related losses."

financial instrument

what is that

sounds abstract

[jagged forge]

just a fancy word for thing that is bought or sold by people in financial markets

it is a very broad term

it includes stocks, bonds, index funds, all kinds of derivative instruments (options, futures, etc) and a bunch more

[sonic sentinel]

does this relate to the "derivatives (finance)" that i looked up on wikipedia

or are they just named the same thing

[jagged forge]

yes that’s exactly what we’re talking about

derivative in finance just means some asset whose value is derived from the value of another asset in some way

so, the fair price of the farmer’s forward contract depends on the current price of his crop on the market as well as the terms of the contract (delivery date and agreed upon price, or delivery price)

eg if his crop goes down in value, suddenly the contract becomes a lot more valuable because it lets you sell at a higher price than the new market price after the drop

[sonic sentinel]

ok I don't understand how weather derivatives are related to derivatives

[jagged forge]

well, which part is confusing you?

[sonic sentinel]

iiuc, you purchase a weather-related asset whose worth has negative correlation with another asset you own, that weather-related asset is an example of a "derivative", why?

OH cause the price of the weather-related asset is derived from the asset you own

not price

value

[sonic sentinel]

right?

[jagged forge]

well you might not even own the underlying asset, but yeah more or less

and price = value, or at least price = someone’s opinion of the value

(plus some markup I guess)

[alpine comet]

Not just the price, but everything

It's an instrument built upon another

[sonic sentinel]

?

also this makes the word "derivative" always applicable (i.e. useless) to a financial instrument until you start talking about a particular context, right?

[jagged forge]

how would it be always applicable?

[sonic sentinel]

"derivative in finance just means some asset whose value is derived from the value of another asset in some way"

surely you see assets' values not being independent like alll.. the.. time????

[jagged forge]

that’s a good point, but you could argue those relationships are not always causal, and in any case usually the relationship is set in stone in a contract or deal of sorts

[prime adder]

Derivatives are instruments that let you profit from changes in the underlying asset without trading it directly. Typically involves the promise of future delivery of some commodity or set of cash flows at a set price

[long matrix]

hello quants

does anyone 'get' risk-neutral probabilities

im failing to pick up intuition

[jagged forge]

I implemented binomial options pricing model and I don’t get it either

[alpine comet]

I have a theory that the majority of quants don't get what they do, but do nonetheless

[jagged forge]

From the perspective of black scholes, I remember being confused that you can omit drift in the underlying from the calculation or just assume it’s the risk-free rate, but iirc the result doesn’t change

but idk how that generalizes to models besides the simple black scholes pricing formulas or the binomial options pricing model

[long matrix]

sigh.

i dont understand why i cant find a bloody intuitive explanation online

[jagged forge]

what is the homework problem you’re stuck on

[long matrix]

what.

[flint basin]

what

[jagged forge]

I assumed u were doing this for homework or something. nvm

[long matrix]

my homework is to make a few bucks

[loud snow]

Options and futures for things like cooling/heating degree days which measure how high or low the average temperature of the day deviates from a selected baseline from utility companies

So if I buy a hdd(heating degree day) future this means that at a certain day in the future when the contract matures I will either gain money because the temperature is hotter than the baseline that was set or lose money in that I wont get the money back after the bet. Usually these maturity dates are further into the future so they arent easy to predict and are used to hedge against smaller losses related to temperatures

An example cme mentions is if you expect to run cooling in a building more than expected you can buy cdd to hedge against the potential costs of cooling on those especially hot days

[loud snow]

I think the concept is to have a fair pricing( when taking into account investor risk preferences) for a derivative assuming no arbitrage exists

[loud snow]

This is most definitely false by the way

I have two friends working in the industry and they do have great imposter syndrome but they definitely understand the math behind the finance

Maybe they are exceptional but they arent frauds

Its kind of insulting when you work 50+ hours a week and you give up a lot of freedoms to try and do your best are your job and someone tells you that you are a fraud

[stuck hollow]

round 20994 to three significant figure

[fringe summit]

!help

[quasi jetty]

Please read #❓how-to-get-help

[mental stratus]

love

[next blade]

in a very rough intuitive sense, you can think of the risk neutral probability distribution as how market prices imply future price moves. we can look at this from multiple angles, with increasing complexity, but as a very simple example to start with, suppose you want to punt on some sports event.

for simplicity let's say there are only 2 possible outcomes (win/lose). you've done your analysis and estimate that A is going to win at 60% probability ("physical measure"). i am the bookie and deal 1/1 odds (implying a 50% "risk neutral" probability), so you obviously think im underpricing A's likelihood to win and make the bet, for $100. you then have 60% chance (based on your estimate of true probabilities of events) of making $100 and 40% of losing $100 (i.e. in the long term you'd expect $20, but either way, one or the other of the events is going to happen and you may well lose money).

am i, the bookie, the chump? as long as i can find as much money to bet for A and as for B, i just pass the money from one side to the other - perhaps someone else thought the probabilities the opposite direction and took the bet for B. ive taken no market risk, I don't care who wins, i am "risk neutral". and in reality id skew the probabilities so that the implied probabilities for both sides don't add up to 1 (that's the bid/offer spread and that to the bookie is a guaranteed profit). and if money to one side adds up too much, id move my offers around to attract the other side to balance the bets out, or if i had a view on the physical probability and thought the market pricing was off, i could leave some market risk in the book.

that came out longer than intended

[lilac steppe]

ah yes the Albanian group

the strongest algebraic structure

[teal tree]

well, not really

it's quite far from the "strongest algebraic structure"

[long matrix]

👍 thanks

I guess trying to convince myself the time continuous delta-hedge portfolio for an option gives me the same price as an option is 😵‍💫

and discrete is the way to understand it

[lilac steppe]

fields shake before the might of the albanian group 🇦🇱🇦🇱🇦🇱🇦🇱🇦🇱🇦🇱

[glossy crescent]

Wha..

[mental stratus]

switzerland

[jagged forge]

so as long as a perfect hedge exists and there’s no arbitrage, the risk neutral price is the one that is consistent with the market I suppose

[long matrix]

ngl this no arb assumption is pretty sketch in practice isnt it

fees whatever

and other stuff

[jagged forge]

yeah actually you routinely see option prices that are impossible

[long matrix]

[jagged forge]

especially for in the money options, oftentimes the bid is really low or the ask is really high, so much that it violates no-arbitrage bounds

though tbh those aren’t really real prices

[long matrix]

well no, thats alright

they act as price bounds

[jagged forge]

well if they’re price bounds the market doesn’t follow them lol

[long matrix]

I think the price wants to be higher in general due to collat requirements

usually

[wet mortar]

fuark

shuri tryna secure the bag?

[jagged forge]

that’s if you’re selling right

[long matrix]

well the seller has to put down collat unless its some centralized thingy

[jagged forge]

I think there are some formulas to calculate the additional fee based on the risk they have to carry

[long matrix]

and well id hope the centralized thingy would put aside collat regardless

[long matrix]

as in im viewing it both sides.

Naively, I feel like the 'fair value' options in practice should generally be overpriced due to collat

[jagged forge]

I assume a market maker would buy slightly below the fair price and charge slightly above the fair price

isn’t that how they make money

[long matrix]

ofc

but im just observing it makes more sense for the fair price to be above b-s

unless there are other factors u wanna throw in

but hmm call-put arb puts a limit on how much above it can be

[jagged forge]

I’m not that good at thinking like a trader, I mostly just shovel data around and do some basic calculations

[long matrix]

oh nvm it dont

me neither

I really wanna get a handle on bs and then see what other reasonable models u can come up with

weakening assumptions or whatever

[mental stratus]

why is there only an older version of okular for my ubuntu

the apt one is so old

and the one from snap is all shiny and new (yet older than the newest one)

[echo tundra]

just download the desired package version and install it locally

[next blade]

i mean the continuous case in terms of like formal math arguments goes very similar. you have some process V, you find a measure under which it (well, a deflated version of it) is a martingale, and ta-da you have V_t/B_t = E^Q(V_T/B_T | F_t) as per they must given martingale (i.e. the fundamental theorem of asset pricing). formally the m'gale representation theorem tells you there is a replication strategy

[long matrix]

In terms of making a simulation to convince myself b-s pricing isn't bullshit

I just uh

ack my brain ded, ill have a proper think later

[next blade]

i mean that's all pretty formal as a lot of this stuff is. really it's all due to PnL Taylor expansion coming out to be second order in the move of the underlying, giving rise to a parabolic PDE from which all these probability interpretations stem from

[jagged forge]

my friend recommended me a book, stochastic volatility by bergomi, and I think that is more or less what he did in chapter 1 when he was explaining black scholes

the idea of lending out all your assets or spending all your excess cash on risk-free assets (which I guess is like lending out your cash) is kind of foreign to me, but it all sort of makes sense

[next blade]

it's a fine book but def not where you should begin if you don't know stoch calc or b-s etc

[jagged forge]

yeah that’s why I’m backtracking and grinding my way through probability and random processes by grimmett and stirzaker

bergomi was too hard

someone gave me a list of books to work through so I’m just going to take my time and then revisit it when I’m ready

[next blade]

my no. 1 recommendation for the basics of fin math is baxter and rennie. it's very short, covers all the basic math (e.g. girsanov etc), but doesn't get bogged down in like formal definition land. if you want a version amped up in rigor, then id recommend shreve vol 2, but it's a much thicker book (skim through shreve vol 1, which is discrete time intro stuff, if you really want but it's not really a prerequisite esp if you've seen binary trees somewhere else). neither has any prereqs

[long matrix]

I'm currently disatisfied im not coming up with a eli5 intuition (that satisfies myself) to understanding the risk free aspect of bs without going into measure.
How do I put it. Its kindof rare this is the case for the math ive seen.

What uve said so far is great, but at the same time slightly beyond me and I have to think

[long matrix]

Like every other part of the price formula is very explainable to someone with an elementary math background

[next blade]

i mean, if it helps, in practice it's not like you use b-s in some sense to price an unknown option. you know the price of the option and you calibrate your b-s model (its volatility) to hit the price. what your b-s model will give you, then, is the delta (and by extension, the probability density function implied by the market prices you observe)

[long matrix]

Yeah

Im still thinking about this purely theoretically in my attempts to understand - assume the perfect model

[next blade]

that's a simplification, but is to highlight that you could invert my prices/odds to probabilities (though i quoted prices, not probability), and the same goes for call options

i mean if you have the perfect model in the sense that your physical measure is the same thing as the risk neutral one, then all your intuition about the prices predicting future prices is true

if then what confuses you is the bit about drift, don't think about options, think about forward contracts. think how you'd price a forward contract via replication (where your entire market only has two assets, a stock and a bank account)

[long matrix]

But this model 'works' if the forward rate is 0

forward = spot

[next blade]

well the relevant part is where you have a drift term roght

you estimate a drift of mu

[long matrix]

Alright.

[next blade]

same as you estimated a probability of A winning earlier to be 60% or whatever it was

[long matrix]

yes.

[next blade]

note that this is one's forecast of the future

and a drift doesn't guarantee that that's where the price will be right

so even if you can buy this thing cheaper (in drift) than your estimate of mu, is it a good buy?

you might make money, you might not

now, what's a sure-fire way to lock in money today (or what investment strategy cannot lose money in this simplified world with constant short rate etc)?

[long matrix]

So we're only thinking about forward

[next blade]

think it through, but this is why the no arbitrage condition has r in it, not mu and is stronger right

yes

[long matrix]

So buy the cheap forward

and then uh

loan & sell 1 asset per contract i think...

[next blade]

so lets say the spot is S, maturity is T, short rate is r

where should the zero cost strike be

i.e. the forward price of the structure

[long matrix]

F = S exp(rT) should be the price of the forward

[long matrix]

sell the loaned asset, then loan the money out at rfr / use it to purchase forwards

And thats locked in an arb

[next blade]

right

[long matrix]

ive ordered that awfully but yeah

[next blade]

good practice to go through each part of the thing systematically, like you buy the fwd contract with strike K, then what do you do with underlying and bank acct at t=0 and how do you deliver the contract at T

but yes

now, that's a guaranteed profit

[long matrix]

I understand the same situation occurs for options. Your delta hedging strategy replicates exactly the same portfolio as an option

[next blade]

playing with mu is not guaranteed, even if you knew mu

[long matrix]

But uhhh yeah, im trying to see this still I suppose

[next blade]

with my the play is law of large numbers, ie you make the same trade at many different time points and hope it averages out into profit

this arb pricing there's no such uncertainty, you make the profit

[long matrix]

I guess half the problem is figuring out the cost of continuous hedging makes no sense without doing the integrals

So in terms of a basic intuition I really do need to stick with a discrete model

[next blade]

the basic intuition was in suremark's screenshot. you choose your strategy (i.e. delta) so that there is no stochastic component to your PnL

[long matrix]

Right I do recall this cancellation

[next blade]

this way you'll end up with a PDE that has a probabilistic interpretation

(that being the black-scholes PDE)

and there's your risk neutral distribution, then

[long matrix]

👍 thanks ill have another go

[flint basin]

Thank you, Hairy Ball

[fringe summit]

“Thank you Wizard”

[mental stratus]

bairy hall

[proven plinth]

exactly

[mental stratus]

egg

[flint basin]

egg

[solid yarrow]

geg

[jagged forge]

gge

[solid yarrow]

love the vibe

[proven plinth]

[vast surge]

gregg

[solid yarrow]

gergg

[wild lantern]

gegrg

[latent edge]

Talking with engineers just makes my head hurt

"I'm working on insert deep math concepts
"Yeah I got that but what are the applications for that?"

[neat lintel]

yo

[neat lintel]

what's popping

bored

[latent edge]

Same

[flint basin]

egg

[storm sage]

Hey applications are fun

[ocean harbor]

[neat lintel]

Eric should be protected

Such wise words

[latent edge]

[neat lintel]

logloglogloglogloglog

[jovial ember]

log

Hey look at these monkeys

Cool guys

Not monkeys actually

Apes

[jagged forge]

if they only knew the power of the dark side

[ocean harbor]

the black monkey looks cute

[ocean harbor]

☠️ -

[jovial ember]

Me

[ocean harbor]

oh I like this one

[jovial ember]

That’s the last one I have

[ocean harbor]

[jovial ember]

[wooden flax]

1st day of college tmrw

[jagged forge]

who are you and what have you done with @flint basin

[wooden flax]

?

[velvet dagger]

Hmm so apparently real estate flippers are kinda the worst

And you shouldn't buy a property that's been flipped

[flint basin]

we were brothers but no longer

I am now 🥚

[velvet dagger]

Like this just isn't livable

[jagged forge]

…..

[velvet dagger]

I can just imagine the groan

[lavish kayak]

Chuckle

[storm sage]

#chill

[velvet dagger]

I'm giving advice smh

[jagged forge]

speaking of audible groaning

don’t go to main discussion rn

[flint basin]

average discussy moment

[quick bramble]

@fickle skiff Not sure if you got muted for longer, but I hope it's just shortly

[storm sage]

They got banned

[ocean harbor]

☠️

[quick bramble]

k, bc at least the reaction was rather induced by someone else

[zealous garden]

Orangutans are great apes

They are also Great Apes

I wonder what life is like through the eyes of an Orangutan

All of the Great Apes are so clearly highly intelligent

[neat lintel]

Monkey

🙈

[latent edge]

me having a stroke on should I say wraithlord or just yotsuba

[flint basin]

yotsuba

[loud snow]

Harambe is an example

[zealous garden]

Yes

No further comment your honor

I believe we could teach the other great apes our ways

[neat lintel]

My teacher does not seem okay

[peak tide]

what damned book is that?

[neat lintel]

https://socialsci.libretexts.org/Bookshelves/Political_Science_and_Civics/Texas_Government_(Teas_Jefferies_Shomaker_Watson_and_Gilmour)

They actually linked to the wrong book in the syllabus

[peak tide]

texas does have an interesting history, but are there really people in prison all around the world for espousing ideas about texas history? 😯

coincidentally i have a youtube video about the mexican-american war playing in the background

[mental stratus]

aaahhhhh topologyyyy

aaahhhhh linear algberaaaaa

[glossy crescent]

Cheer up mate

I have linear algebra next semester too :/

[mint oasis]

Hello y'all

How to do you guys overcome the fear of doing math homeworks and start enjoying doing math? What benefits does it have when you do them?

I hope this is the right place to ask

[alpine comet]

strangely I was never afraid of maths, least math homework

but I can say one would overcome that fear once they realised they could do it

[river moon]

the more homework you do the less you care about it

[alpine comet]

I mean, we only fear what we don't know

What benefits does it have when you do them?
it gets easier

[errant ridge]

This is why you should become a hobbyist house flipper, so that you can buy flipped properties and re-flip them yourself

Man I missed sotrue

[mental stratus]

i didn't

[neat lintel]

Anyone knows whether Russia rubel will get appreciated soon?

Or it would just go down...

Forever

[loud snow]

There are people in prison for less

I dont know how true it is that people are in prison for talking about Texas now

[flint basin]

Grr of course the morning I want to sleep in they are doing construction literally in front of my house

[burnt ledge]

Tell them to instead prove it by contradiction

[flint basin]

They reject classical logic in favor of constructivism

[burnt ledge]

why are there two ryx eggs!!?

[flint basin]

we have multiplied 🧑‍🤝‍🧑

[mental stratus]

your eggs just changed colors

[wet mortar]

it's cracking

[mental stratus]

f i neither studied enough linalg nor did i study enough topology today

[glossy crescent]

What's inside?

[flint basin]

We do not know yet

[flint basin]

F

[echo tundra]

Is it a reference to the egg story

[glossy crescent]

What I know is that, that thing's ending up in a frying pan

[flint basin]

What egg story

[glossy crescent]

Humpy Dumpy?

[neat lintel]

How to remember this

[flint basin]

determinants go brrr

[zealous garden]

Eww

I'm gonna vomit

[zealous garden]

Start from the properties on the basis vectors

Use linearity and anticommutativity to simplify

[neat lintel]

https://tenor.com/view/kel-kel-omori-omori-kel-omori-ily-kel-gif-24000739

[latent edge]

lol

[latent edge]

This is very ugly

[flint basin]

but it works

[zealous garden]

$x \times y = - y \times x$

$ax \times by = a(x \times by) = ab (x \times y)$

[flint basin]

And much easier to remember imo, when doing calculations at least

[fathom swallow]

wraithlord_kohonorable

[zealous garden]

Those come obviously from thinking of the cross product as the wedge product

Imagine the vectors form a parallelogram

[latent edge]

I agree tho

[flint basin]

(it's calculations, ofc it's ugly)

[zealous garden]

If you swap the order of the vectors, the parallelogram changes directions

If you take the special case of a square

The bilinearity is obvious

Using these two basic properties, take (ax +by + cz) × (ux + vy + wz)

Or no

a_i and b_i

To get the right labeling

[faint meteor]

https://tenor.com/view/square-prism-gif-13191186

i love not knowing what this is

[zealous garden]

A projection of a tesseract (hypercube) as it rotates in 4 dimensions

[flint basin]

[wet mortar]

$\det(A)=\br{\Lambda^{\mathrm{top}}A^{\mathrm{top}}}^{\wedge\top}$

[fathom swallow]

Daybroken🥭

[zealous garden]

$\underline A(\mathbf{I})=\det(A) \mathbf{I}$

[fathom swallow]

wraithlord_kohonorable

[zealous garden]

$\det(A) = \frac{\underline A(\mathbf{I})}{\mathbf{I}}$

[fathom swallow]

wraithlord_kohonorable

[zealous garden]

I have the best definition

[long matrix]

det(A) = A

no me.

[zealous garden]

Based

[zealous garden]

I have made quite a large assumption

No I didn't, that's definition, we're good

[mental stratus]

ryxi's egg hatched?

ok tomorrow def gonna finish this chapter

[flint basin]

I have come 🐣

[mental stratus]

pervert

[flint basin]

baseless accusation

🙃

[mental stratus]

first countable means every point has a countable nbhd base

second countable means topology has a countable base

[wet mortar]

yes

[burnt ledge]

Is there a third countable

[wet mortar]

no

[long matrix]

[glossy crescent]

[rocky shuttle]

of third kind

[neat lintel]

How hard really Ap stats is

Rate it out of 10

-/10 basically

[deep mango]

it was like a 4

well

5

[neat lintel]

I mean I’d it hard for a

11th grader to take

?

[glossy crescent]

Why take AP Stats

[neat lintel]

Cuz

[glossy crescent]

Take Calc BC instead

[neat lintel]

…

[deep mango]

i took it in 11th grade, it was probably my second easiest AP class out of all my APs but also im a mathematician now so

[neat lintel]

https://tenor.com/view/sweaty-speedrunner-epic-gamer-sweatyspeedrunner-gif-22461398

POV Ap calculus

I hate the fact I can’t send gifs

[glossy crescent]

AP Stats are just for boosting average AP score

[neat lintel]

Yeah that’s what I want

If it is easy I’m gonna try to take it in 11th

[deep mango]

it's a fine class

[neat lintel]

I mean what if, u hate word problems

[deep mango]

i think someone who really didn't like math at all would still have some trouble

well, the whole class is word problems

[neat lintel]

…

[deep mango]

but they're like

well written

and not ambiguous

[neat lintel]

Ohh

Aight

So u just need to know English

?

[deep mango]

but still, every problem is like a paragraph of reading and then figuring out what the heck to do with the numbers in it

[neat lintel]

I don’t like hate math but don’t love with

Math

[neat lintel]

Oh…

[deep mango]

so if you do not like that

it's not a fun class

[neat lintel]

Well I’ll most likely take it in 11th, if I pass algebra 1 without problems and take geometry for 1 month in summer and pass it’s test

We’ll see

Cause it’s like at least I know the teacher that teaches it, and it’s a really good teacher

That’s another pro for me

Can u take pre calculus and Ap stats the same time?

Both

Don’t u need to take pre calculus to take it too?

[deep mango]

That should be fine

[deep mango]

I don't think so necessarily

[flint basin]

aaaaah my forearm hurts to even type it hurts

[solar hawk]

oof

not developed yet, little chick

[flint basin]

[neat lintel]

:)

Me and my tutor are clueless

[storm sage]

about what?

[neat lintel]

What I should talk about

[storm sage]

Wait, talk about for what?

[neat lintel]

I pretty much knew everything I've read besides how to calculate tension

[velvet dagger]

If they knew what they were clueless about that'd be a clue

[storm sage]

Oh, like what to go over during your tutoring session?

[neat lintel]

Yeah

[storm sage]

Oh gotcha

I guess that's a good thing lol

[loud snow]

[flint basin]

[neat lintel]

In 1896 in Waco, Texas, William Crush parked two locomotives at opposite ends of a 6.4-km-long track, fired
them up, tied their throttles open, and then allowed them
to crash head-on at full speed (Fig. 7.1.1) in front of 30,000
spectators. Hundreds of people were hurt by flying debris;
several were killed

In the past, people were so smart!

[zealous garden]

Genius

[vivid halo]

Will Crush

[fringe summit]

As the prophecy foretold

Waco has had multiple standoff tragedies

[little vine]

Fire town

[fringe summit]

Why have a tutor

[peak tide]

fast forward 120 years and people are doing the tide pod challenge

[loud snow]

Very good learning

I want a tutor

You obv learn by yourself

[neat lintel]

Bruh why do they require us to take algebra 2 for AP stats

So annoying

Algebra 2 is already a pain

[loud snow]

Ur lucky ur in hs

[neat lintel]

?

Wdym

[loud snow]

You have a lot of opportunity rn

[neat lintel]

Wha

Do u not have Ap?

[loud snow]

I dint think so

[neat lintel]

Oh

[loud snow]

Im not in hs

[neat lintel]

Did u graduate

[loud snow]

Yeah im working

[neat lintel]

Wow

Is algebra 2 hard

Is it more harder than algebra 1

[loud snow]

When I was your age it was a hassle

[neat lintel]

Is it harder then algebra 1

[loud snow]

Jk it wasnt i just wanted to say when i was your age

[neat lintel]

Like how much difference

[flint basin]

not much

[loud snow]

If you are a low confidence math student dont worry this server will back you up

[neat lintel]

Ok

Ty

[loud snow]

If you are high confidence then no worries either

Just make sure to ask when you get stuck with things

Dont let misunderstandings pile up

[neat lintel]

(Bros dreaming of Ap stats but still in algebra 1 cause failed in 8th due to not caring)

[loud snow]

I understand

[neat lintel]

I had opportunity to take algebra 2 this year

[loud snow]

I was the same with my liberal arts classes with not caring

[neat lintel]

Oh

[loud snow]

Like english and social studies

[neat lintel]

Oh

[loud snow]

I got back on track when i was in like 10th grade

[neat lintel]

Well math is different

[loud snow]

Not really

[neat lintel]

I could literally

Take like 8 college courses

For math

If I had taken algebra 2 this year

Well

I do have a chance to take geometry over summer

[loud snow]

Wait

O

[neat lintel]

That’s my last chance

[loud snow]

What are you saying

APs dont have prerequisites?

[neat lintel]

Yes they do

[loud snow]

You can study and take the test if you know the content

If your school doesnt let you take the test you can register anywhere else and they are happy to take the money

[neat lintel]

The only pre…….. for Ap stats is algebra 2 and algebra 1 and geometry

Idk why but it says eligible grade: 12th

[loud snow]

Maybe im wrong or things have changed

[neat lintel]

But you can literally take it in 11th

Why does it says eligible grades: 12th

[loud snow]

Maybe its a school specific thing

Some schools let you take as many APs as you want

[neat lintel]

But can I take it in 11th?

[loud snow]

Try asking

[neat lintel]

If it says eligible grades 12th

[loud snow]

I was able to ask to skip pre calc and it worked

[neat lintel]

WOW

I’ll try that

Cause google say I might need to take pre calculus

To take Ap stats

[loud snow]

Why do you want to take AP stats so badly?

[neat lintel]

And it also says you can take pre cal and stats both

Google***

[neat lintel]

It’s

Ez

No need to worry about

8483&4&4&48;&:@:$202

Calculus harder

[loud snow]

Not rly

Imo stats is hard because its a lot of memorization for the answers

[neat lintel]

WHAT

[loud snow]

I remember having to memorize how to write out hypothesis test prompts

[neat lintel]

…

Well either way

I’m taking it

[loud snow]

And its pretty much remembering 3 sets of 6-8 sentences depending on the contezt

And then there are still other questions to do

[neat lintel]

calculus is quite easy

[neat lintel]

…

So it’s pretty much

[jagged forge]

what's the integral of sec x

[neat lintel]

Word problems

?

[flint basin]

easy

[neat lintel]

Are the word problems easy

In AP Stats.

Is that what u meant

[neat lintel]

let me see

$$ \int \sec(x) dx $$
$$ \int \frac{1}{cos(x)} dx$$

[fathom swallow]

᲼

[neat lintel]

Multiply top and bottom by cos(x):
$$\int \frac{cos(x)}{1-sin^2(x)} dx $$
$$ u = \sin(x)$$
$$ - \int \frac{1}{1-u^2} dx$$
$$ - \tanh(u) + C$$
$$ - tanh(sin(x)) + C$$

[fathom swallow]

᲼

[neat lintel]

wait

arctanh

uuuh

I umm

wait

[jagged forge]

hmmmm that seems right

idk i purged this stuff from my brain

u convinced me

[neat lintel]

It's not right

wait

it is

I keep messing up while checking my work