serious-discussion

[ocean harbor]

hmm how about changing the school then

[tame egret]

i like the school

but the teacher left

and there's a new one

hopefully he'd be good

series?

[neat lintel]

Yes ???

[tame egret]

wdym

[tame egret]

what do you mean series

sequences and series?

[neat lintel]

Is it a series, a coherent sum of points?

[tame egret]

I should be asking you bro

[ocean harbor]

#math-discussion

[ocean harbor]

hopefully

[tame egret]

yes

well talk to u after school

[ocean harbor]

oke

[neat lintel]

for example any sum $\sum_{i}^{\infty} f(x)$ It is a series?
What happens if $\sum^{\infty}- i$ ?

[fathom swallow]

Cristhian

[tame egret]

,ti @fathom swallow

[fathom swallow]

"Time is a storm in which we are all lost." -- William Carlos Williams

[ocean harbor]

there are a lot people can talk about this in math discussion

[fathom swallow]

This user hasn't set their timezone! Ask them to set it using ,ti --set.

[ocean harbor]

lmfao

[oak quest]

Well that's a divergent series

[neat lintel]

@oak quest Exactly, very good

[oak quest]

That has some flaws though

[neat lintel]

what defect?
define them?

[oak quest]

$\sum_{i=1}^{\infty}$ (-i) should be the correct way to put it ig

[fathom swallow]

Normed

[oak quest]

_i=1 was missing

[neat lintel]

Exactly, you are right. the series diverges at dim(i) . Do you know that it is a hypergeometric series?

[tame egret]

i guess school closes 2pm

[oak quest]

Why are you quizzing?
I've not learned about hypergeomtric series yet

[neat lintel]

you define it,
A hypergeometric series is a generality of convergent series

[ocean harbor]

3pm

I get home by 3pm and maybe I start studying at 6pm for me

,ti

[fathom swallow]

The current time for kensukeken is 02:27 PM (EDT) on Thu, 07/09/2023.

[tame egret]

mine used to end 3pm but after covid it 2pm

[ocean harbor]

I see

actually my old school ends at 2pm and new one is at 3pm

starts at 9am and ends at 3pm

[tame egret]

starts 7:45 am ends 2pm

[tame egret]

happy studying

[ocean harbor]

my old school was like that yeah

sometimes it's hard to get up at 6am

unless you have fixed your sleep schedule

[drowsy forum]

can anyone help me please

[ocean harbor]

#❓how-to-get-help

[oak quest]

That's the time I sleep

[ocean harbor]

bro

thats crazy

[oak quest]

Yeah should go up till 8

I can afford to do that coz my classes are in evening

[ocean harbor]

fix your sleep schedule fr

[neat lintel]

Religion was created to explain things no one could explain. It gave people hope and understanding of a world they did not know

But as the sciences came and explained things that once were unknown less and less people looked towards religion for their answers

Our society grows but our faith in god shrinks. At a time like this a man must ask himself.
"Has science gone too far?"

[long matrix]

[vivid halo]

[glossy crescent]

?

[lament path]

Sorry if you’ve seen this before, I am trying to collect as much data as possible

I am writing a 20 page text talking about the math major. It is intended for high school students or first year uni students going into a math major. I want to know what this demographic would like to see in such a text.

[full marlin]

Maybe it doesn’t have to be 20 pages or is that a thing

[supple bramble]

@mighty axle sorry, i am in class right, when i get home, can i text you?

[mighty axle]

uh im going to sleep

[supple bramble]

Okay, goodnight

[loud snow]

Highest form of naïveté

Religion was created to advocate for my awesomeness

[neat lintel]

which is better for math

• Conceptual Learning is the process of learning and reasoning from detailed facts to general principles.
• Content-based Learning is the process of learning and reasoning from general principles (concepts) to detailed facts.

[lament path]

Second one

Well maybe not

I mean I feel the first way is more frequently taught

[neat lintel]

YES

the education system priotizes concept based learning, math texts are like
Fact, formulas, differentiation ---> general principled (practice problems)

do u think is better? or the other way around

[loud snow]

@solid snow do you know context

Context was that most physics isnt obvious

[zealous garden]

I'll agree a lot of obvious questions are in no way obvious to answer

Fuck glass

[loud snow]

Bubble formation is another one

[solid snow]

I mean i find it astonishing that we're able to do anything with what I would consider extremely rough approximations of the natural world

[loud snow]

Energy in general is still confusing

[solid snow]

Even with all of our fancy math and computers

[zealous garden]

That's part of what I'm saying though

Extremely rough approximations

[solid snow]

Ig I'm just going off on my own tangent

[zealous garden]

Basic Newtonian mechanics is just, common sense and calculus

[loud snow]

Yeah

That isnt common sense

[solid snow]

Plus spamming the words 'square' 'proportional' 'inversely' 'distance' 'rate of change'

[tribal slate]

more like intuition

[solid snow]

Newtonian physics 101

[loud snow]

I dont think I would have thought of newtonian physics past some very basic equations about linear motion

And i def couldnt have invented calculus

[zealous garden]

I'm okay with that, intuition falls under "obvious"

[loud snow]

Not formally atleast

[zealous garden]

That's where I'm founding my argument

[loud snow]

But newton didnt do it formally either

[tribal slate]

intuiton fails at most physics no?

[zealous garden]

Not by our standards no, what about the standards of the time?

[tribal slate]

or is it just mine

[zealous garden]

As did newtonian mechanics!

[loud snow]

Well yeah

[solid snow]

I think we take for granted the amount of things that have to line up for progress in science and the humanities to occur

[zealous garden]

My point stands and is strengthened

[loud snow]

We obviously do

[zealous garden]

I don't, I was talking about it the other day

[loud snow]

Most of the things we learn about we dont know the history

Only roughly

[wild lantern]

I don't know if it makes sense to take things as obvious when you're viewing them in retrospect in this context.

[zealous garden]

If you take away everything but the discovery and its consequences, a number of these things become obvious, if you take away the backdrop then almost every one becomes quite the achievement

If you are given the calculus, I think newtonian mechanics is not far off from you surmising, if you're interested

But Newton also had to make his iteration of the calculus

Which changes everything

If you take away the experiment about light speed measured from different reference frames

Good luck ever finding SR

With that experiment, it's just the consequence of updating your notions

[solid snow]

Most of these things are beyond the scope of a human lifetime

We're ants in the grand scheme of things

[zealous garden]

We aren't meant to know

[tribal slate]

meant to know what

who is meaning this

[zealous garden]

Just like we aren't meant to exist

There is no meaning

[tribal slate]

what meaning?

[loud snow]

I agree

[wild lantern]

I am meant to exist

[tribal slate]

you guys talk about meaning and shi like its a thing

[zealous garden]

And so in spite of this we exist, create meaning, and find ways to know

[wild lantern]

I am a necessary being

[loud snow]

I will say math def makes understanding the natural world way easier

[zealous garden]

I was conceived on April Fools day

[loud snow]

The otherway around is cool too

But thats why I revere physicist

Using physics to elucidate math is cool

[zealous garden]

I agree

[topaz trout]

D.N.E

[loud snow]

Honestly if I was in some society -1000 years ago

Dream job would be toilet engineer

[zealous garden]

Dream job is to be an experimental particle physicist at CERN to shit on my friend that wants to do that

[loud snow]

I have a friend who did it for undergrad research

Super cool stuff id say

Physics engineering in general is cool

[zealous garden]

Nah it sounds fun but idk if I'd wanna do that

[loud snow]

There is nothing wrong with having no dream job

[zealous garden]

Who said I had no dream job

I want to make things

[loud snow]

You can as a toilet engineer

Or mcdonalds chef

[zealous garden]

Nein

Nyet

I want to create experiences

[loud snow]

Mcdonalds employees do that

Im half memeing

Besides pay I dont see much wrong working at franchise fast food places if it means I have no further aspirations

[solid snow]

Working with the public

[zealous garden]

I do better than I would there where I am

[topaz trout]

Don't you get free food too

[loud snow]

It isnt free if you are working

[zealous garden]

I'd like to write books and make games

Write books about, whatever the fuck I want. Make games about, whatever the fuck I want

[loud snow]

Why though?

[zealous garden]

Why not?

[loud snow]

Self expeession?

[zealous garden]

It's what I want to do

I want to use this ability I have

[loud snow]

Well yes but you have a reason

You can also run and jump why not beat marathon records?

[zealous garden]

Existence is a rare gift, understanding rarer yet, the ability to speak your understanding of the world rarer still.

[loud snow]

I disagree with this

[zealous garden]

How do you mean

[loud snow]

I think a lot of people have pretty good ability to express themselves

Like majority of people

Its just not always shit I care about

[zealous garden]

I don't.

As in I don't think so

The majority of people have some satisfactory method of self expression, being themselves, sure

[solid snow]

Hard disagree

[zealous garden]

The average person is terrible at making more complex facets of their experience understood by another

[topaz trout]

What if you're abnormal

[loud snow]

This is why I agree

[zealous garden]

It's a skill you can work on of course

People get better

[loud snow]

Complex facets stuff is partially BS

[solid snow]

Being on this server should be first-hand experience with the opposite of what you believe

Most people can't even ask a question about their schoolwork coherently

[loud snow]

Thats why I said self expression and not language

[zealous garden]

Yeah I mean language and art

Like visual art, linguistic art, musical art

[solid snow]

I still contend with that, a lot of people are pretty lousy at that too, not that it's a character flaw or anything

[storm sage]

I feel like opportunities to express your inner being to others come fairly seldom

[loud snow]

I mean self expression is broad

[storm sage]

It requires a somewhat intimate emotional connection

[zealous garden]

A lot of people aren't good at communicating in that format

[loud snow]

I disagree with that too

[zealous garden]

And it requires practice

[loud snow]

Self expression is evident in actions and ideas

You dont need to speak to someone to make assumptions about who they are

[zealous garden]

I don't really think there's anything to it that you can't acquire through practice or working on it some other way

[storm sage]

sure but your assumptions won't necessarily be right lol

[zealous garden]

Yeah sure, but that's not what I'm talking about doing

In talking about writing books and making other forms of media

[loud snow]

As in any situation ig

[zealous garden]

Thats a wholly separate thing

[loud snow]

It is seperate and wanting to be understood has never personally been a motivation of mine

[zealous garden]

I also mean in interpersonal communication, people are great at being misunderstood

Harder to drop the mis

[loud snow]

So im curious how it becomes peoples motivation for things

[zealous garden]

But wanting to be understood isn't my motivation

It's simple, I see the world in a way only I will ever see it

I want to, out of that, crystallize some things for others to see

So that they may see things I never can

[loud snow]

Well this is motivation for writing books and making games.

[zealous garden]

I also have the abilities necessary to crystallize some of these things

[minor current]

what do you guys think of the characteristics method for solving prtial diff eqs

[loud snow]

So wanting others to understand your viewpoint sounds like what you wanted

[storm sage]

best thing ever

[loud snow]

Actually

[zealous garden]

It'd be nice

[loud snow]

@minor current if you want to read erics thoughts just search

[minor current]

[minor current]

ty, will do

[zealous garden]

But if I'm not understood it's okay

The reason I mentioned existence is because I often think about how existence is the rare opportunity to leave a mark that rings out for eternity

I should invest time into mine

It doesn't matter if my work has its meaning through my name, through direct impact, here and now or in any proximity to my lifetime or family

I just know that it is the work I should do

Desu

[loud snow]

Idk if existence is rare tho

Kinda a bad qualifier

[zealous garden]

There are certainly more ways for you to not be here, than there are for you to be here

I could've been a stillbirth

Etc.

[loud snow]

Well now we will sound crazy

[zealous garden]

Sure, everything that exists exists

But that's quite a wild first step

Unjustifiable even

[loud snow]

Yeah and for that reason existence isnt rare

Imo

[zealous garden]

Terminology spat aside, do you understand me

[loud snow]

Yeah but I disagree

I dont think existence should be something thats valued

Not in every context atleast

To stick with the theme of writing

It will probably be possible to write every text that can be read in one human lifetime

I dont think any of those writings existing should be something that’s valued

Even if they mimic writings of something I care about

Maybe I didn’t express it properly

But I dont think sentimental values are that strong

Phrased it wrong again

But for example say you write the thing that you say is your most prized writing

If it gets destroyed I feel that you shouldn’t feel too strongly about it

[zealous garden]

I think I should

But that it's not a loss of the work

It simply changes the meaning that it will have

[loud snow]

I dont know any hypotheticals to make my point

But maybe say you had amnesia

What value would the work have if you don’t remember it

[zealous garden]

I created it, during that time my brain developed and changed, I developed

[loud snow]

I havent had amnesia but I would like to think some values I have aren’t completely related to memory

[zealous garden]

Even were I to lose all record and memory of it, its imprint exists in my thought patterns and abilities

[loud snow]

Yeah thats a benefit of it

[zealous garden]

Let's say writing it helped me process a trauma, as an example

Losing the work, I am still "healed"

And everything that I can do as a consequence of that, is a consequence of the work

[loud snow]

What if instead of writing it was addiction?

[zealous garden]

What do you mean

[loud snow]

Nevermind

I was going to say what differentiates doing writing from addiction as something you would want to do even after losing memory. I realized this defeats the original purpose of you wanting to do the writing though

Writing is cool but ive always thought speaking is a cooler avenue to go down as something I would want my job to involve

[zealous garden]

I don't like the idea of speaking and giving public speeches

[loud snow]

From a business perspective infrastructure is constantly changing so your writing will become obselete

Im sure you dont mean that entirely

[zealous garden]

I don't like the idea of being too close to the front of something as an actual person, presenting with unironic interest

[loud snow]

Well thats how most the world operates

And I would want to be pretty influential in the world

Not necessarily famous

But being impactful

Ive always seen writings as an aide

[zealous garden]

I can do that after I die

[loud snow]

Until you cant

[zealous garden]

Like Lovecraft or Confucius

Or Clifford

I just need my work to be true and good

If I've done my part then time will tell

[loud snow]

I’m sure in 1k years no one will know of them and their impact will be vague similar to how giving speeches all your life would go

[zealous garden]

I doubt it

[loud snow]

I do too

[zealous garden]

Confucius is already known for thousands isn't he

[loud snow]

1k is an example

But sooner

[thin smelt]

ahoy goys

[zealous garden]

And with the internet it seems less likely that an impact will be vaguely forgotten

[loud snow]

Prehistory is long

[solid snow]

We've got socrates and plato as the bedrock for western philosophy and they're millenia old

[zealous garden]

AI historians can read everything we've ever written and answer any question about us

[loud snow]

People just as mentally capable existed way longer

[solid snow]

Socrates didn't even write shit down

[zealous garden]

Socrates is remembered because he did his part

His part didn't include making a name for himself to last

[loud snow]

Who is to say society wont crumble?

[zealous garden]

It included inspiring a student to do it for him

[zealous garden]

It will.

[solid snow]

Most of what we know of socrates isn't entirely 100% factual of his life

[loud snow]

I dont think it will

[zealous garden]

It doesn't need to be.

[solid snow]

and a lot of it was tradition that kept the idea of "socrates" alive or as a mechanism for philosophy at the time and in the future

[zealous garden]

I'm always open to maybe conservation is just wrong, but everything collapses

[loud snow]

Its kinda hard to say what is factual when it comes to history

That isnt the point though

[zealous garden]

It's impossible really

And beside the point

What is factual has a chain of consequences that reaches to the end of time

[loud snow]

That’s pretty dramatic

[zealous garden]

It's reality

Life is very dramatic

[loud snow]

But it goes to my point Im trying to communicate

No one has a good concept of what consequences their long term actions have. So its moot to attempt to perform a perfect expression that will persist throughout time.

So writing a book for 20 years is an example

Im not entirely sure you said you would write because of the long term consequences it will have on society. But I dont really understand what you think writing will bring to others

[solid snow]

Ok this take is just not grounded in reality

[loud snow]

Im not saying its useless to write either, just thats its not something I can find passion in for reasons you mentioned

[solid snow]

I don't even see how you could start to ask the question of "what do you think writing will bring to others"

[loud snow]

Well there is context to this conversation

You are reading my sentence in isolation

[loud snow]

Honestly I could elaborate but I will just link you this

This reply was for josemom

[zealous garden]

I'm not aiming for anything

[solid snow]

Idk, this isn't your fault but I feel atm as if I don't have anythjing interesting to say about this. I usually would but I'm currently not in the best headspace right now and I've been through a really fucked up day

[loud snow]

Ok thats what I thought but wasnt sure

[solid snow]

I'm just fumbling around where I would usually be able to say something

[loud snow]

Spilled milk?

[solid snow]

No. Abusive household

[zealous garden]

Its something I feel as the core of my being tries to express itself, and in order to be the best wraithlord I can be, I have to figure out how to do that

The long term consequences, are beyond me. All that matters is that I do correctly what is in my hands

So I must be the best me, because I am grateful to existence for having me as a part of it

[loud snow]

I like writing sometimes too, but for purposes of perfecting self expression, speaking to people is my favorite way of going about this. I mostly feel this way because of memories of cooperating with others

[zealous garden]

And so the gifts existence has given me, must be used as existence has intended

If the specific goal is perfecting self expression, yes you must speak to people

[loud snow]

Bruh existence isn’t a person to me

[zealous garden]

No, it's the roll of the dice

Except, there aren't any dice

It's a set of logical consequences

Even if you don't know how or why, things make sense

So, I find myself with a set of abilities and proclivities, it is not an antisocial or otherwise morally repugnant or reprehensible act for me to fulfill these abilities and proclivities, and so it would be most harmonious with the waterfall of consequences of the universe for me to follow them.

It is not a given that acting in accordance with this is a good thing

But it is where I fall

The fire wants to burn, and when doing so it fulfills a function in the greater chain beyond its imagining

[loud snow]

I dont have better idea of why you want to write or make video games

It would be helpful to know what specific moment made you come to this decision

[zealous garden]

The childhood memory of a moment of realization that starts it is when I'm playing a video game and sit down and say to myself that I would like to do that growing up. To create a world with meaning in it for others to explore and take something home.

[loud snow]

Thats cool 😎

[zealous garden]

Sometimes I feel immobilized by the weight of what I dream to be capable of accomplishing. So I'm trying to focus on breathing and just doing my best to accomplish, something.

[storm sage]

I dunno if having your work being true or good is either sufficient or necessary for being well-known after you die

[loud snow]

It isnt

[zealous garden]

I don't care

[loud snow]

I didnt mention it because I knew it didnt matter to you

[storm sage]

I'm just saying that I don't think this is true

[zealous garden]

I acknowledge that proposition as a matter of faith

[storm sage]

I feel like random confluence of circumstance plays a large part here

[zealous garden]

Confluence of circumstance?

[loud snow]

Things coming together conveniently

[zealous garden]

Things come together conveniently quite often, but only because so many fail

[loud snow]

I used to be similar in that I really liked animals and wanted to do animal research later in life. Now that Im later in life I still want to do it but its not as important even if its very achievable. Most of my current aspirations including job stuff came from 2 years ago after I took a nap and woke up and felt pretty good about it. There really isnt much to explain about that moment but I it made me realize a lot of important things about life

I havent had a nap like that in a while and its not something I can chase either so thats why I think it is a pretty important part of my life

It probably sounds stupid though

[zealous garden]

I realized that time is very real

Everyone says time is an illusion

Because they are confused

now is an illusion

Absolutely

Time is very real

[loud snow]

Nah you arent making sense

[zealous garden]

Do you know any SR

Like relativity of simultaneity

[loud snow]

Concepts about time dialation?

[zealous garden]

It's related

[loud snow]

Space time and curvature

Yeah i know some concepts but nothing standard about it

[zealous garden]

Because of special relativity, relativistic speeds cause you to disagree on whether two events (with a spacelike separation) happen at the same time

For example, who shot first depends on how fast you're going and in what direction

[loud snow]

Are you trying to say instants of time dont exist?

[zealous garden]

Basically

It's a slice of spacetime

[loud snow]

I sorta disagree but I can see where you are coming from

As a concept it exists and for all its uses it is useful

So its reality imo

[zealous garden]

If you think of spacetime as instances of space stacked along a time axis

Changing reference frames corresponds to a Lorentz boost ("rotation")

I almost want to just link a video

But yes

The thing is the whole time part is real though

Causality is preserved

And outcomes are agreed upon

[loud snow]

I mean being pedantic about it time is just as real as money

[zealous garden]

But now, now disappears completely if you look through someone else's eyes

[loud snow]

Socially constructed idea that helps us make sense of the world vs people’s value

[zealous garden]

Time isn't socially constructed

[loud snow]

It is though

[zealous garden]

We have a lot of social constructs around time

I'm willing to accept that time may be constructed in the mind

But it isn't social

[loud snow]

Yeah it isnt social

It exists outside of society probably

[zealous garden]

Your concepts of time are social constructs, sure. Just like any concept

[fervent rapids]

Can someone help me calculate a future score?

[loud snow]

Yes

[zealous garden]

Nu uh

I'll admit that 3D spherical geometry is not immediately obvious

But I plan to play Hyperbolica in VR while studying Topological and Riemannian Manifolds to fix this issue

I will then return with a belittling argument as to why non Euclidean geometry is trivial

[loud snow]

Lol ok

[static loom]

it's locally euclidean, therefore trivial - saved you time you would have wasted playing silly VR games

[neat lintel]

First, formally define what a Riemann-manifold is.
A Riemann-manifold is a general class of projective-manifold of the form $\varphi{}: R^{n}\to{} R^{n+1}$ where in generality $\varphi{}$ is the part-proyective of the manifold .But a Riemann-manifold is endowed with local-symmetry, where its global-symmetry $\varphi{}=0$ as exemplo of zero funtion-nomal , but about a variety-Riemann and its symmetries-local in $\psi{}>0$

[fathom swallow]

Cristhian

[fresh heron]

is there any youtubers who cover calc 3 topics in depth/well? my prof isn’t that great this semester and i need a good supplement since organic chem tutor doesn’t have any

[peak portal]

Professor Leonard and Professor Dave Explains helped me through Calc 3

Org Chem Tutor also has some calc 3 topics and helped me as well

[primal swan]

watch bprp

good calc channel

[mental stratus]

https://en.wikipedia.org/wiki/Continuous_linear_extension

[vale plover]

does anyone here use a small wacom intuos? the dimensions are 7.87 x 6.3 x 0.35 inches. here's a link to the product: https://www.amazon.com/Wacom-Drawing-Software-Included-CTL4100/dp/B079HL9YSF?th=1. i was wondering whether it's worth getting. i type pretty much all of my homework in latex, but some homework assignments feel extremely tedious to complete solely with latex. i was hoping i could supplement latex with something like this.

[vale trench]

okie dokie

<@&268886789983436800>

[mental stratus]

👍

[remote hornet]

things change, things move around, the ability for things to change in an orderly fashion, that is time, we observe this through all our senses and with constructed measuring instruments, time is a real thing by the same standard that we consider anything to be real, now you could argue it is a social construct on a more deeper level and that other things that we consider to be real like water or chairs are also some kind of construct, but that is boring because we cant prove anything about whatever is real outside of our minds so there is no point in speculating about stuff like that

but yeah our intuitive notions of time are wrong, shown by SR as wraith said

but that doesnt make time an illusion

that the speed of light is constant turned out to be more real than the concept of simultaneity

"constant in all reference frames" is what contradicts with our intuitions

[solid snow]

I use one. It’s pretty handy for writing notes on PC if you don’t have one of those laptop tablet things with a pen. Takes a little getting used to, but it’s better than writing things out with a mouse like I did for a while.

Plus if you do Photoshop or graphic design in general it’ll be useful for that as well

[long matrix]

where the quants at

[ocean harbor]

[weak vector]

chonkey

[ocean harbor]

fr

[neat lintel]

I would avoid wacom at all cost

Had three of their tablets and they all broke in 1-2 weeks

[tame egret]

i get up 7am or 7:15 am. Fr

[tame egret]

?

[solar hawk]

I use huion

It’s pretty decent.

[dense belfry]

Has science gone too far???

[neat lintel]

math-2

[tame egret]

maf-2

[tame egret]

no,

[dense belfry]

[tame egret]

it hasn't gone too far

[ocean harbor]

I always get up at 6am

[sonic sentinel]

akira you're fluent in saudia arabia?!?!

[tame egret]

when do u sleep

[tame egret]

I get to school at 8 o'clock

although i prefer waking up 8 am

[tame egret]

do you feel it has

[ocean harbor]

9pm

[tame egret]

ohh

[ocean harbor]

Saudi Arabia is known as Arabia language ye

it's my 2nd language

and I'm fluent at it yes

[tame egret]

11 pm for me

[neat lintel]

ih

[tame egret]

hi

[tame egret]

: D

learn fr*nch

[ocean harbor]

ah I only sleep at that moment when I have a test or something

I wake up at 6am in school days but on weekend it's different

[neat lintel]

so i got flammed in a server for trying to make the argument that running through as many practice problems as you can is more effective than "understanding concepts", my reason being is that u see the pattern when u spam problems, and in a way understand the concept backwards

[tame egret]

I just do limits and implicit differentiation
and stuff

from 9 - 11

[neat lintel]

what do u guys think

[tame egret]

you're half wrong they are both important

[neat lintel]

if i have a test in an hour, which would allow me to do better on the test, "reading and understanding the textbook" or "doing as many practice problems as i can"

[ocean harbor]

nice

[dense belfry]

No

[tame egret]

ikr

[tame egret]

good

[dense belfry]

I think we are at the very beginning of science

[rotund steppe]

That’s on you for studying 1hour before a test

[dense belfry]

However I think socially science is complicated

In the way it is viewed

[tame egret]

ikr

[neat lintel]

ur not getting the point, the point is generally which is more effective for learning the most in the least amount of time

[rotund steppe]

Do you retain stuff?

Do you care about the theory?

[neat lintel]

i do yes

[oak quest]

not if the test is in a hour

[tame egret]

science will come to an end soon

[rotund steppe]

And what are you learning?

[neat lintel]

if i do 80 practice problems for 3 hours instead of trying to understand what the textbook. is saying for 3 hours, i retain from the practice problems more

[rotund steppe]

Computations that you can grind out in an hour? 😂

Oh

We can’t compare

Bruh

Ya no shit you have no theory to learn anyways

If you are doing 80 problems in 3 hours

Different math

[dense belfry]

I think science has no end

[neat lintel]

and also another argument is that textbook reading give u the most simple examples to understand how to do a problem, while exercise 55 could be like nothing you have seen in the reading, but runnning through exercise 55 helps be more aware of it

[dense belfry]

We are exploring the consequences of physical reality

[neat lintel]

argue that

[rotund steppe]

There’s no point in arguing we’re learning different things

[oak quest]

Lol pre-uni students do find their math not so utterly easy that you as a undergrad do

[neat lintel]

yes but im trying to argue for the most effective way to learn

[dense belfry]

And I think there will always be consequences we will have not found

[rotund steppe]

learn the math that YOU do

[neat lintel]

ok dont argue, but what do u guys think abt this point, tell me it doesnt apply to all levels of math

[rotund steppe]

Bruh

What is math to you

😂

[neat lintel]

being able to do a problem

correctly

[rotund steppe]

what type of problem

[neat lintel]

with the right answer

[rotund steppe]

What if you don’t even know that there’s a solution

[dense belfry]

I think humans will exist forever

[rotund steppe]

😂

[neat lintel]

an integral example say, whatever it can be anything

[dense belfry]

[oak quest]

prove or disprove

[tame egret]

thonk again

[dense belfry]

No

I am done thonking

No more thonk

[long matrix]

quants where

[tame egret]

,ti @long matrix

[fathom swallow]

The current time for shuri2060 is 08:09 PM (BST) on Fri, 08/09/2023, the same as ishigamisenku_!

[long matrix]

[tame egret]

,ti @ocean harbor

[fathom swallow]

The current time for kensukeken is 03:10 PM (EDT) on Fri, 08/09/2023.
ishigamisenku_ is 5 hours ahead, at 08:10 PM (WAT) on Fri, 08/09/2023.

[tame egret]

I'm done spamming now

[oak quest]

Brit*sh

[tame egret]

who

?

[neat lintel]

ok one finial question, i rly want yalls advice im taking calc 2, is reading the textbook crucial?

[tame egret]

what's calc 2 if i may ask

[neat lintel]

or should i jump straight into practice problems and learn from that?

[tame egret]

integration

[neat lintel]

yes

most of it

and sequences

[tame egret]

Then i can't advice I'm doing differentiation

but ik volume of donut

[neat lintel]

do u have an A in the class?

is it easy or hard for u

[long matrix]

wherezza quants

[neat lintel]

A or no A?

[river moon]

more often than not you see the pattern in specific problems that you're given, but not in the reasoning of why you're doing what you're doing

[river moon]

and no, trying to understand the theory in the book can be as challenging as solving exercises

[chilly hull]

oftentimes more

[ocean harbor]

I forgot it's Friday

sleep time

[vale plover]

what model huion do you use

[solar hawk]

Idk

I could check

I will in a bit

[tame egret]

we haven't learnt intro to differential calculus in school

but i have

[tame egret]

gn

nah you're not sleeping

rn

[ocean harbor]

ye

[tame egret]

dead chat XD

[tame egret]

you know java

: D

[ocean harbor]

im learning it at cs lmao

i mean im not good at it since it just new to me

tried to make one friend they also have no idea what to do

[untold trout]

Who knows Discrete Mathematics

[neat lintel]

Larry Gao

[vale plover]

@solar hawk re: huion model

?

[solar hawk]

It’s

H610PRO

idk

lol

[solar hawk]

It’s really big

It’s not one of those w a screen

[vale plover]

yeah i wasn't looking for one with a screen

good to know it's big

https://www.amazon.com/HUION-Inspiroy-Graphics-Battery-Free-Sensitivity/dp/B01FTE9HS2

i was looking into getting this tablet

[solar hawk]

Woah that one looks cool

[vale plover]

there are newer models but i hear this model is better than the newer huions

[solar hawk]

O

Definitely looks fire

[vale plover]

what pencils, erasers, and pens do you all use? for those that use mechanical pencils, what size lead do you use? do you prefer smaller or bigger leads?

[solar hawk]

Mechanical, medium size

Too small breaks easily

Too big is annoying asf

[river moon]

black gel pens ftw

[vale plover]

what counts as medium

like 0.7 mm?

[river moon]

I've used up like a 100 for the past two years

[vale plover]

https://www.amazon.com/Pilot-Retractable-Premium-Roller-31002/dp/B00006JNJ8?th=1

i think i have one of these

[solar hawk]

Yeah I think that’s what I use

There are these big massive white erasers

Too

And you can erase a whole ass book with them

And they don’t run out

[river moon]

I just use the cheapest ones out there, as long as you're able to find ones that work well

[solar hawk]

I had to trace over my pencil today in Spanish on a massive poster right and then I had to erase all the pencil under it and I used the eraser on the whole poster

And it was flawless

And barely scuffed

[dense wraith]

0.5 mm is good. If you have a decent mechanical pencil it won't break at all

[zealous garden]

Pens

I use the G2 pens

1.0 and 0.7

[lyric nimbus]

.38 is the only acceptable size

[zealous garden]

Disastrous taste

[rich rapids]

Vakil:

1.4.11. Joke. What do you call someone who reads a paper on category theory?
Answer: A coauthor.

[little vine]

How do you really hurt a category theorist? Kick them in the monads

[flint thunder]

I use this: https://uniballco.com/collections/207/products/207-gel-pens?variant=39362234810574

It has refills, which I don't see on that site. I haven't bought any new ones for years because I just get the refills.

[long matrix]

ask how their funding is doing

[neat lintel]

Monads

[neat lintel]

#latex-testing

[young quartz]

get an xp pen tablet

better drivers, good availability of nibs, good pricing, etc

[vale plover]

model?

[young quartz]

deco 01 is good

sadly I have a wacom and after I exhaust the nibs I will buy an an xp pen

wacom is absolutely cringe

they are selling pens, nibs, cables separately now

[vale plover]

https://digitalarttabletguides.wordpress.com/2019/08/01/my-screen-less-tablet-top-picks-august-2019/#contents3-4

i found reviews here

https://digitalarttabletguides.wordpress.com/2018/04/16/huion-inspiroy-h1060p-review/

i heard xp-pen tablets have a rougher surface, so their nibs also wear down faster

[wild plinth]

is there any math phd student here? I am curious that how people make friends/research partner? I think they could be colleges but.. anywhere else I can start to know people?

[mental stratus]

ask this in #advanced-lounge

[wild plinth]

ok

[mental stratus]

noone's joining it ffs

[echo tundra]

<@&268886789983436800> discord invite spam

[ocean harbor]

good morning chat

[mental stratus]

morn

[mental stratus]

~~

[jade crane]

discussy2dead

[ocean harbor]

indeed

[royal garnet]

what's up chat

[ocean harbor]

chat is dead but what's up

[sweet trout]

hey

[ocean harbor]

ive been pinged

who was it

[tame egret]

I accidentally sus reacted rn

😭

[ocean harbor]

bro

stop giving me ghost ping

[tame egret]

🤣

[ocean harbor]

why why why

[tame egret]

just 🧌ing

[ocean harbor]

die

do not do it again please and thanks

[tame egret]

...

*harsh

the first ping was an accident

[ocean harbor]

im joking chill :D

[tame egret]

[ocean harbor]

[tame egret]

I thought other wise 😂

so this is weird...

chat keeps on dying

[ocean harbor]

maybe if we both stopped chatting here

the chat can be alive by a few other people

[tame egret]

[ocean harbor]

i won't be chatting that much because it's my last year for being in high school

i think they call it addition year

so grade 13th

[tame egret]

aww

I am in 11th grade

[ocean harbor]

grade 11 was tough

because covid

[tame egret]

i don't have to do 13th ig

[ocean harbor]

well if you aren't new to school maybe just 4 years in high school

I think ive went three different high school

In my home high school was closed for two year during covid so i went to canada as half grade 10

[tame egret]

wait you're 15

[ocean harbor]

my age?

[tame egret]

ye

[ocean harbor]

im 18 sadly

just turned 18 last month so it's a new thing

it's time for adulthood uh

I know bunch people at my age are graduated this year and im still suck in high school ☠️

[tame egret]

oh, I'm sorry to hear that

[weak vector]

Is x=(6/6)-ω possible

[bitter talon]

quick question, does anyone know how much general ed requirements you need if you're studying mathematics?

[dull pilot]

it depends on what x and omega means in that context

[dull pilot]

depends on the college

[bitter talon]

in college ofc

[dull pilot]

for example mine, located in Europe, doesn't have any at all

[bitter talon]

I would go to france and try to study there, but I don't have the money, plus I don't speak french well enough

[tame egret]

dead chat in 3

2

1

dead

[bitter talon]

no

[tame egret]

ya

[sonic sentinel]

no

[tame egret]

yes

+yes

[neat lintel]

Go onto your college's website and look at the degree requirements

[glossy crescent]

Oooo college

[oblique oracle]

are algorithms for solving linear congruence systems something beginners are taught or you gotta reach the intermediate of number theory to learn them?

eg stuff like the chinese remainder theorem

[jagged forge]

you mean like the Euclidean algorithm? i would consider it basic, i did it in my discrete math class which is an introductory class

[oblique oracle]

oh no, i know that the ea is simple

and is enough for solving one linear congruence at a time

but as far as i know, it doesn’t work for systems and more complex algorithms are needed (or just guessing, in case it’s something simple)

by systems i mean problems like “you have x ≡3(mod 4) and 2x ≡5(mod 7), find x”

[jagged forge]

ah, yeah my bad, i did not make it far enough in school before dropping out to know when you learn the Chinese remainder theorem

but if it’s just one variable, CRT sounds exactly like what you want

[zealous garden]

I can never remember CRT

I never learned it

[zealous garden]

Certainly the solutions in Z are non-unique?

[rocky shuttle]

cathode-ray tube

[oblique oracle]

…english please-

[zealous garden]

Carly Rae Thomas (He called her)

[jagged forge]

i may have even learned multiple congruences in my discretemath class but it’s been so long I forgot

[rocky shuttle]

(maybe)

[zealous garden]

(Maybe)

[oblique oracle]

The reason I asked this is because I’m currently doing independent learning on like every branch of math, starting with the “elementary” stuff and since the CRT and all this stuff is hard, I was hoping that it’s considered intermediate and not elementary so that i could put off studying it

[jagged forge]

essentially it says if you have a bunch of equations $x\equiv a_i\mod n_i$ with $n_i$ coprime, then that gives you a unique solution to $x\mod n_1n_2\cdots n_k$

[fathom swallow]

suremark

[oblique oracle]

is it intermediate? 😭

[chilly hull]

smh not general enough

$R/(I_1\cap...I_n)$ is isomorphic to $R/I_1\times...R/I_n$ if we have that $I_i+I_j=R$ for all $1\leq i<j\leq n$

[fathom swallow]

C(hmonkey)at Bread

[chilly hull]

where R is a comm ring and I_n are ideals of R

[jagged forge]

personally i think if you can do extended Euclidean algorithm, there’s no reason to be afraid of CRT

[rocky shuttle]

i consider crt basic

[storm sage]

👀 did you solve the case of infinite ideals

[chilly hull]

it is untrue

observe Z

[storm sage]

why

[chilly hull]

and all the ideals are pZ where p is prime

the intersection of all of these ideals is 0

[storm sage]

this is true so far

[chilly hull]

so Z/(the intersection of all these ideals) is just Z

and therefore countable

[storm sage]

yes.... and then what

[chilly hull]

but the infinite product of Z/pZ is uncountable so we cannot possibly form a bijection

[storm sage]

ayyyyy :D

did you come up with that yourself

[chilly hull]

got some help with choosing the counterexample

but once i was told to try using Z i got it

[storm sage]

By the way the infinite product of all of the Z/pZ quotiented by a maximal ideal is an ||ultraproduct||

[jagged forge]

ngl i was tempted to sully you before realizing i was the one who needed to be sullied

[storm sage]

https://mathoverflow.net/questions/15151/product-of-all-f-p-p-prime

[jagged forge]

[storm sage]

happens

[chilly hull]

and by this logic CRT for integers is also false

[storm sage]

nice!

cat bread is become algebraist

[jagged forge]

also any integer n should have n = n mod p for p sufficiently large right

so like, you can’t just have any element of the direct product be an integer

[little vine]

Cat bread has gotten stronk in a short amount of time

[chilly hull]

https://cdn.discordapp.com/attachments/807809192537882647/1144757430375420086/IMG_9500.gif

[storm sage]

I don't think this prove that there is no isomorphism

just that the specific isomorphism you said of reducing the number mod each prime doesn't work

[jagged forge]

that’s true, but the Chinese remainder theorem is the statement that this specific map is an isomorphism, no?

[storm sage]

uhh I think it depends on how you state it

either way they're not isomorphic which is a stronger claim

[jagged forge]

right, i never meant to say those two statements are equivalent

[ocean harbor]

we go gym

[fringe summit]

I didn’t think about the containing Q’s algebraic closure bit

Wild

[storm sage]

it's a wild object

[midnight crystal]

whats the point of a generating function? I read on wikapedia "One can [use generating functions to] generalize to formal power series in more than one indeterminate, to encode information about infinite multi-dimensional arrays of numbers."

and that makes me think we are trying to get equations like e^x to find sequence coefficients

am i on the right track?

[solid snow]

Sure, they can transform problems where you want to know some info about, say a function, into a problem of finding coefficients of a power series

take for example moment generating functions for probability density functions

[storm sage]

it's a tool you can use to count things

[solid snow]

calculating moments* or moments centered about the mean $E(X^n) = \int_{-\infty}^{\infty} x^nf(x) \dd{x}$ can be a bit cumbersome or you don't have direct info on the pdf itself going in

[storm sage]

once you have a formula for a generating function for something, you can start manipulating it and doing algebra to it

[fathom swallow]

josemom2

[solid snow]

the moment generating function for a random (continuous) variable X defined as $M_X(t) = E(e^{tx}) = \int_A e^{tx}f(x) \dd{x}$ does something pretty neat

[midnight crystal]

oh so are they typically infinite?

[fathom swallow]

josemom2

[storm sage]

do you know the proof that there are the same amount of partitions of a number into odd parts vs into distinct parts? for example you can partition 5 as

• 5
• 4+1
• 3+2
• 3+1+1
• 2+2+1
• 2+1+1+1
• 1+1+1+1+1
  and then the partitions into odd parts are 5, 3+1+1, 1+1+1+1+1, meaning there are 3, and the partitions into distinct parts are 5, 4+1, 3+2, meaning there are also 3

[solid snow]

not necessarily

[storm sage]

this is a very cool application and also very basic application of generating functions

[storm sage]

they can be and often are

but yeah not necessarily

[midnight crystal]

i didnt know that

[solid snow]

the function $M_X(t)$ has the interesting property that $M_X^{(r)} (0) = E[X^R]$

[fathom swallow]

josemom2

[solid snow]

so knowing the coefficients in the maclaurin series expansion of M tells you direct information about the moments of X

[midnight crystal]

thats really cool actually

[storm sage]

the trick to proving it is writing the number of partitions into a generating function (euler did this)

[solid snow]

moments being used for things like: mean, variance, skewness, kurtosis, etc.

[midnight crystal]

im on a math rabbit hole rn cuz i was trying to read Claude Shannon's paper on information theory and like 3 pages in I got lost but i think im close to the bottom lol

[solid snow]

there's also a seemingly obvious fact waiting to be said here: that if the moment generating functions of two random variables are the same, then their cumulative frequency distribution is the same. (some technicalities omitted for brevity)

But yeah they're used for a bunch of stuff like this

another probability example is the factorial generating function $G_X(T) = E(t^X)$ and even $\Phi_X(t) = \ln(M_X(t))$ which is the cumulant generating function

[little vine]

MGF is very cool

[fathom swallow]

josemom2

[solid snow]

both of these have some uses which would make them preferable depending on the scenario

[midnight crystal]

woah

[solid snow]

there are many many more generating functions

[midnight crystal]

i feel like i have a lot of work to do to really understand them. I feel like my brain is working at max power when i try to understand what they are still

[solid snow]

i bet it feels that way at first for everyone

it certainly did for me lol

[midnight crystal]

i wonder how many people even know about them

it seems like wherever im at in my math learning journey i am lacking some serious knowledge on the "basics"

[solid snow]

these are not the basics i would say

they're a pretty intricate object

[midnight crystal]

true but i feel like a lot of textbooks assume people know what they are

[solid snow]

ah that does dependon the textbook

[midnight crystal]

textbooks assume people dont know set theory but then act like everything else doesn't need explaining lol

[neat lintel]

probability

MGFs are just next in the book i'm working through

seems fun

me and my homies love taylor series

[solid snow]

which book

[neat lintel]

casella and berger

i could have hit the ground running with a measure-theoretical treatment but i just didn't wanna lol

felt like it hit a nice balance between "hardcore analysis" and "we don't even assume you know what a set is"

[jagged forge]

i'm doing grimmett and stirzaker and they do a measure theory free approach

but my friends insist i ought to do measure theory

[solid snow]

over in #1136101521386389544 we're doing lee bain and engelhardt

[fierce abyss]

Let $A=\sum_{j}\binom{3n}{3j}, B=\sum_{j}\binom{3n}{3j+1}, C=\sum_{j}\binom{3n}{3j+2}$, you have
$\begin{pmatrix}1&1&1\1&w&w^{2}\1&w^{2}&w\end{pmatrix} \begin{pmatrix}A\B\C\end{pmatrix}=\begin{pmatrix}2^{3n}\u^{3n}\v^{3n}\end{pmatrix}$ where $w=-\frac{1}{2}+i\frac{\sqrt{3}}{2}, u=1+w, v=1+w^{2}$
Therefore $\frac{A}{2^{3n}}=\frac{1+(\frac{u}{2})^{3n}+(\frac{v}{2})^{3n}}{(w-1)(w^{2}-1)}$ the rest is clear

[fathom swallow]

Cogwheels of the mind

[storm sage]

good paper!

I don't think I've ever actually read it

Only heard it summarized many many times

[midnight crystal]

yea im excited to work through it. I've really wanted to read it as well as richard hammings algebraic coding theory

[fierce abyss]

This is for the user elrich… in help-10, but I can’t find his name to ping…. Someone reply to him for me?…. I can’t reply in help channels

[midnight crystal]

something about those topics is super interesting to me

[solid snow]

i wish i could read a measure theoretic probability text

but unfortunately i dont know measure theory lol

[midnight crystal]

i always wonder if you could just learn the ideas rather than how to prove stuff so you could learn the stuff you want

[solid snow]

eh

that works for somethings

probably useless if it's a text involving measure theory though

[midnight crystal]

maybe idek. Like you dont need to be able to solve an integral to understand whats happening

idk how that works in higher math

[solid snow]

things start to get a little more complicated and you need to be able to abstract

[midnight crystal]

true but i swear sometimes i will be solving problems without understanding but then i watch one animated youtube video and im like wow this is all i needed

[storm sage]

I thought we told you to stop giving away complete answers in the help channels?

[fierce abyss]

Yes, I didn’t give any details

[storm sage]

.<

[fierce abyss]

I just want him to know to use root of unity

[storm sage]

okay but do you get how this way of communicating is not helpful to the person who asked the question

[fierce abyss]

I didn’t solve A and the limit for him. If you think it’s not appropriate, tell me which step it is, I will further edit it

[fierce abyss]

I am not sure. I will further edit it. I didn’t solve that inverse matrix for him. Do you think I should omit expression of A/2^(3n) or something?

[storm sage]

I mean that when someone doesn't have any idea on how to approach a problem and they see a wall of symbols as a response, it's discouraging and also doesn't enlighten them as to how they could have come up with it themselves, or how to solve future problems.

The design of this place is different from places like stackexchange, where the purpose is to provide canned answers and long explanations

Rather the help channels are meant to be conversations between the helpers and people asking for help, centered around the thinking of the people asking for help

[fierce abyss]

Okay. I just saw he wasn’t replied for quite long… I haven’t answer him yet
Can someone answer him in the way you think is appropriate ….

[storm sage]

Well they're gone now anyways, but @uneven pebble do you still need help with the limit you were asking about?

[sick tiger]

Minecraft music is so good for studying or working on homework. No right being so cozy

[neat lintel]

Which analysis should i learn first?

[sick tiger]

Like between real and complex? Or like single or multivariable?

[zealous garden]

Harmonic

Wait

Geometric

[echo tundra]

Huh

[zealous garden]

Geometric Analysis

[pearl moth]

minecraft music gets on my nerves after a while

[remote hornet]

minecraft music reminds me of my mortality

[solid blade]

how long should i expect to wait for a response to modmails?

[remote hornet]

when the stars align

[shut stone]

I ate a block of cheese[swallow, small block,but not that small] and I vomited it out

[young geyser]

can someone please help me calculate interest I'm in grade 7

[tame egret]

!help

[quasi jetty]

Please read #❓how-to-get-help

[potent forum]

help?

[noble osprey]

Its ya boy the gangster mathematician 🤙

[rocky shuttle]

ya boy kongming

[little vine]

bang bang skeet skeet

[neat lintel]

Umm

I'm confused

[smoky plover]

So, I've got a question

I forget a lot when I'm studying mathematics

even in the previous chapter of the book I'm reading (Basic Mathematics), I can't prove some of the recent theorems

should I continue on to a different book, such as an Algebra when the book is complete, or should I try to repeat until I can remember most of what I've learnt?

[dim sparrow]

You should definitely reread chapters if you're forgetting whole proofs or whole theorems and not little details

Possibly take notes alongside each chapter

that helped me a lot for new concepts

[storm sage]

make sure to do exercises

[lavish kayak]

Are you stressed?
Try to take a few short moments, let your awareness expand a bit and see if the memory flickers in a bit

[zealous garden]

Yeah this

[cinder ledge]

Hello in the help section if i called the helpers and didnt respond

do i still wait ?

[rocky shuttle]

yes

[neat lintel]

Kill the helpers

[cinder ledge]

ive been waiting for awhile

an hour

[indigo storm]

mcm(16, 20) = 80?

[zealous garden]

Hey, that's me

Ping me next time

[glossy crescent]

Ping

Pong

Ping

[ocean harbor]

@upper loom revive

oops pinged someone

[crimson osprey]

how do i clean up dog vomit plus chunks of ham off the carpet

ill get the vacuum

[restive seal]

hello do you guys know other good math help discords?

[neat lintel]

Cut out the carpet and put a new patch in

[ocean harbor]

yes this server

loll

[neat lintel]

What should I do if I have a bullshit math teacher

[restive seal]

fair enough

[restive seal]

get better

[ocean harbor]

switch to a new school

[crimson osprey]

bro i have that aswelll

he's teaching how to multiply fractionsand im in eighth grade

[neat lintel]

That teacher makes me want to quit

[crimson osprey]

how so

[neat lintel]

She’s just terrible at teaching

I don’t really wanna do math as I have other interests

Science is good

[crimson osprey]

well depending on your future, if you need math over something else. i'd look to youtube or books or something to self-learn the materials needed

[neat lintel]

Read the textbook and ignore the teacher

You're there to receive a grade not to learn

[neat lintel]

You need math in science

[glossy crescent]

I need math in science

[crimson osprey]

math is the science of numbers and counting

right?

[neat lintel]

huh

[crimson osprey]

i dont know

[neat lintel]

?!?!?!?

[neat lintel]

not really

i mean

actually yeah

but like

science can be used but is not the best way

so kinda ig

[crimson osprey]

arez goto bed

[neat lintel]

real

[neat lintel]

ok

[crimson osprey]

okay

[fading zealot]

Just learnd about the empty function and it is now on the top of my list of most useless concepts in nathematics

Still made a note just in case I see it and don't know what it is because that would be embarrasing

[smoky plover]

I'm doing all of them. But when I return after a couple of week, I can't solve every single one.

[charred burrow]

Imo not being able to solve every single one of them is totally fine after like a week. It's normal to forget few concepts, although, you should still be able to solve some of them and recollect how you solved the remaining ones. You might even see a new solution pop up in your head for some problems.

[noble osprey]

Hey hey hey gangster mathematician here! 🤙

[sand moth]

no

if you look in any of the advanced channels, you’ll see more letters than numbers

[edgy basin]

the further you get they aren't even latin letters anymore

[teal lion]

Serge Lang’s Basic Mathematics is not meant as preparation for his Algebra.
That would be evil.

Instead, you should use his First Course in Calculus. It is very clean in terms of exposition. Lots of examples, no gimmicky full color nonsense.

If you want to get started with proof-based math, I’d start with Lang’s Undergraduate Algebra, which was the first math book I completed on my own.

[mental stratus]

https://www.youtube.com/watch?v=IreR69AY41k

[smoky plover]

My plan was to go through some of the books recommended here to me by others:

Serge Lang's Basic Mathematics
Tao's Analysis
Artin's Algebra

My goal with mathematics is to firstly have fun, then understand physics and then tuning systems in music

but I can only allocate an hour or so a day, and I do forget a lot of the proofs and exercises I've done

so, I'm not sure how that single hour is going to be sufficient

[echo tundra]

I'd recommend, NOT to try to go through some set in stone reading list

especially when you want to do some chill maths

[solid snow]

Use a bunch of different books foe the same topic

[smoky plover]

Wouldn't that take a lot of time?

Mathematics for me is a side hobby

[solid snow]

I mean you don’t have yo always read every part of them or do every exercise

But something like Abott’s Understanding Analysis may have something to say that makes more sense to you than the way tao says it

It also has pictures

And the exercises focus on some specific analysis problems too (same with bartle), whereas Tao mainly focuses on big results

[smoky plover]

hmm, I think I understand

[solid snow]

With something like analysis, it’s good to have a bunch of different viewpoints and exposure, at least in my experience

[smoky plover]

quite, I generally don't fully forget "topics", but some proofs or exercises fly out of my mind

[smoky plover]

I understand

Anaylsis was only recommended for me to study, so let me ask this

what even is analysis actually?

[solid snow]

the study of the triangle inequality

[smoky plover]

a follow-up question then

what on earth is a triangle inequality?

[rotund steppe]

Draw a triangle

[solid snow]

Jokes aside, think of things like limits, sequences, metric spaces, approximations, continuity, etc.. Analysis is the study of all these things and more in a formal setting. It arose after people started trying to precisely pin down the concepts of calculus and the evolution of some other fields like diff eq, etc.

[solid snow]

|a + b| <= |a| + |b|

[smoky plover]

I think I understand maybe some of it

so, I think I would need analysis?

[long matrix]

does this thing hold on earth hmmm

it should i think

[smoky plover]

again, my goal is to learn some calculus, learn some physics (nothing too advanced) and read a couple of books about tuning systems in music

and have a lot of fun doing it

[long matrix]

it might not hold in hyperbolic geometry???? no idea

[smoky plover]

I'm more a "humanities" guy, so mathematics is quite foreign and difficult to understand for me

[solid snow]

you should learn lots of analysis if you care about doing music theory mathematically or even look into things like harmonic analysis

It’s surprisingly… involved

[long matrix]

the triangle inequality says if you want to go from A to B. Then it is always going to be no slower going directly than visiting C first

[smoky plover]

For example, this is a question from Serge Lang's Basic Mathematics in the topics of Isometries. I studied the chapter, but I had no clue about the question:

6. Visualize 3-dimensional space. We also have the notion of distance in
space, satisfying the same basic properties as in a plane. We can therefore
define an isometry of 3-space in the same way that we defined an isometry
of the plane. It is a mapping of 3-space into itself which is distance
preserving. Are Theorems 1 and 2 valid in 3-space? How would you
formulate Theorem 3? (Consider the plane in which the three points
lie.) Now formulate a theorem in 3-space about an isometry being the
identity provided that it leaves enough points fixed. Describe a proof
for such a theorem, similar to the proof of Theorem 3. Make a list of
what you need to assume to make such a proof go through. Write all of
this up as if you were writing a book. Aside from learning mathematical
substance, you will also learn how to think more clearly, and how to
write mathematics in the process.

[smoky plover]

I'm actually planing to study musicology, but I want to become quite good at music theory also

[solid snow]

Serge lang kinda pisses me off

[smoky plover]

in fact, I'm uncertain if I want to major in musicology or music theory

[solid snow]

You can learn math formalisms and proofs in a book like hammack’s book of proof

[smoky plover]

hmm, I see

so, what should I do about this question, ignore it?

because god knows I can't solve it

[solid snow]

If you know highschool algebra 1+2 and precalc then book of proof is probably better for you

[smoky plover]

I didn't take algebra and precalc in high school