serious-discussion

[neat lintel]

Hi

Friends, I have a question, what if I say that I want to learn computer science completely, and I am only asking the question for discussion, what is the best source for obtaining information?

[mint canopy]

You want to learn the whole of computer science? I don't think such a thing is possible

[sick burrow]

isn't there an interesting thing going on here where Euclid's axioms give R^2 with the usual metric

[zealous garden]

it kinda just says that we live in a locally euclidean space

[neat lintel]

Why??!

[sick burrow]

locally?

[zealous garden]

why did God see fit to separate us from Euclid's Dream

[zealous garden]

see General Relativity

Even Special Relativity actually

Norms in Spacetime are cursed

[sick burrow]

is the geometry predicted by relativity Euclidian?

[zealous garden]

lightcone

[lavish kayak]

I think you're unaware of the size of that task.
However, there are certain subjects you're going to have to learn at the start, so you can start bit by bit and when the size of the journey is clearer to you you can decide if you want to keep on it

recently i've been thinking about this old chinese paradigm in this context a lot

"A thousand li journey starts under one's foot!"

[neat lintel]

First, thank you for your response. Second, I joined this community to help me open the way for me and make me think correctly

[velvet dagger]

Sounds like a skill issue to me

[mint canopy]

True tbh

[neat lintel]

I am thinking of learning computer science on my own, and I am one of the people who likes to read from books, but I have a question, is it enough to learn computer science from books and get enough information or not?

[zealous garden]

CS is easy, hasn't changed in like 100 years

[burnt dune]

yes ofc

you can learn anything

you want

[neat lintel]

This means that I do not need courses to learn computer science ?

[lavish kayak]

it's possible just not very efficient, atleast for most people

learning with people is easier

[burnt dune]

nope

[zealous garden]

There are a surprisingly large number of choices to make when learning, and it's just easier to have someone else make the choices

[velvet dagger]

Wraithlord is fairly correct here

This is the main difficulty with self studying, along with organization and the like

[neat lintel]

I want to know the source of information about courses in universities in the field of computer science, from where they can get it in order to teach it to other people?

[lavish kayak]

you can find a lot of textbooks suited for university students

most of the material taught in undergraduate years hasn't changed in decades

I recommend going on any university syllabus and checking the textbooks they list in 'additional readings' under the courses

[neat lintel]

My friend, your words are great, and I have done this before, but I was confused by some of the people I spoke to, and this makes me ask here

For example, I searched the syllabus of a university and found all the courses, but they did not put the books, so I started taking the name of the course and looking for a book in this field, for example, an introduction to computer science. Do you think my method is correct like this and does the book give me the information as in the course or not?

[lavish kayak]

yeah

intro. to cs tends to be a catch-all course of sorts

a bit of coding practice and so on

[neat lintel]

ok like I want to learning this

Fundamentals of computer science

What is the best book that makes me master this course?

[zealous garden]

Not sure but you're going to want to read TAOCP, and maybe Concrete Mathematics

[uncut socket]

@placid finch Look at #help-15, another example between $m \angle$ and just $\angle$

[fathom swallow]

dldh06
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[placid finch]

bruh ive literally never seen that notation being used

now its all appearing

[uncut socket]

Then your book is not normal because it's a normal notation

[placid finch]

possibly in the states

here in aus it is never used in the curriculum

[neat lintel]

solving a big problem without any mistakes on first try is so godly

[covert obsidian]

need help with a problem can somebody dm me please

[teal lion]

#❓how-to-get-help

[mint patio]

I'm trying to make a presentation to build intuition for what a derivative is and what the limit definition actually means

Any ideas for a presentation title?

[neat frost]

“Building intuition for what a derivative is and what the limit definition actually means”

[mint patio]

💀

That's so plain

LMFAO

[neat frost]

“Derivatives and why they make sense and are intuitive and also the limit definition and why it actually makes sense”

[mint patio]

thank you maybe I try that one

[neat frost]

[tall badge]

but what is a derivative?

rip off 3b1b

[mint patio]

LMFAO

[tall badge]

if its a short presentation

[mint patio]

I am planning to name one of my slides A Paradoxical Puzzle or something similar 😼

[tall badge]

then ‘derivatives tldr’

[neat frost]

Drvtvs

[tall badge]

i usually like disemvoweling but thats horrible

[bright hill]

[wooden flax]

how about "derivation of the derivative"

@mint patio

thank me later

[mint patio]

I uh

ok well they're high schoolers who don't know anything abt calculus

so I thought maybe they wouldn't find it too cringe

[bronze pelican]

Watch the history of calculus video

[mint patio]

so I put

"the language of the universe" (title)
"an introduction to calculus" (subtitle)
lol

[mint patio]

Yeah that's on my list

I have it saved

[bronze pelican]

This is the calculus they won't teach you by a well-rested dog

[mint patio]

Sure

Wait that's the vdieo I'm thinking of LOL

Yeah I still have to watch that

[bronze pelican]

He has a second channel called a sleep deprived dog where he posts minecraft amd tf2 vids

[tender tulip]

Okay so, I want to find a sequence of (real) quadratic extensions from Q to Q(cos(2pi/17)) and I really don't know how to go about it

Another method is through the 17th root of unity but I don't know how to "work around" the second extension

$\2cos(\frac{2 \pi}{17} has minimal polynomial: \
t^8 - t^7 - 7t^6 - 6t^5 + 15t^4 + 10t^3 - 10t^2 - 4t + 1. $

2cos(2π/17)'s conjugates are all of the form 2cos(2πn/17) for 2 ≤ n ≤ 8
And afaik, mapping x to 2T_n(x/2) [chebyschev polynomial] serves as an automorphism for 1 ≤ n ≤ 8, BUT i'm not sure if EVERY automorphism is of that form

[crystal topaz]

Wow so funny and original1!1!1!1!1!!1!1!

[dapper badge]

Not the best presentation because my bowl is too small, but pretty proud of dinnies tonight

Bell pepper + onion + egg atop rice noodles in a gochujang + soy sauce + whatever else I grabbed out of the pantry while the onions were starting to burn broth

[deep mango]

Delicious!

[bright hill]

that looks cozy

[limber thunder]

nice

I just made and ate some burgers after a long trip

[jovial ember]

Walter

[dapper badge]

walter

[neat frost]

Water

[neon silo]

Wafer

[neat lintel]

Bidmas moment

[woven whale]

?

[hearty berry]

What two irrational number add up to 2?

[mint canopy]

any irrational k and the irrational 2-k.

[woven whale]

sqrt(2) and 2-sqrt(2)

[open aspen]

I'm in too deep, chmonkey just popped up on my timeline

[bright hill]

migi very active

[open aspen]

Oh shit, my name is readable now so true

[gritty oak]

yo

[tender tulip]

i know the Galois group of cos(2pi/17) is isomorphic to Z/8Z but I can’t find a specific isomorphism

mapping cos (2pi/17 * m) to cos(2pi/17 * mn) is an automorphism

[odd narwhal]

what is the galois group of a number

you mean the galois group of its minimal polynomial over Q?

[tender tulip]

galois griup of it

yea

which I stated before

It’s conjugates are cos(2npi/17) where n = 1 to 8

Z/8Z is iso to (Z/17Z)*/<16> via (Z/16Z)/<8>

i think the isomorphism from Z/8Z is (-1)^s*k^n mod 17 where s is 1 if k^n mod 17 is greater than 8, 0 otherwise, and k is any of 3, 5, 6, 7, 10, 11, 12, 14

idk how else to define it

k^n mod 17 is the isomorphism from Z/16Z to (Z/17Z)*

but idk how to define the projection from (Z/17Z)* to it’s quotient by <16> w/o piecewise

eh it is what it is

but yeah, that’s the isomorphism

Z/8Z has subgroups Z/4Z and Z/2Z within that, so I’ll just create a sum of cosines invariant to multiplication by k^2, then solve for the quadratic with it’s coset-sums as roots

should leave me ultimately with the quadratics leading to cos(2pi/17)

[dusty wagon]

Wtf is that

[dapper badge]

Yummy tea to get started on work

Though I suppose it isn't much to look at

[little vine]

Chai?

Well

Chai means tea

[dapper badge]

yes, my attempt at chai

[little vine]

Nom

Is there an analogy to "nom " for a drink?

I love chai tea

[tender tulip]

schlurp

[little vine]

I like it

[tender tulip]

I fucking hate this problem

[little vine]

Ahahaha

Was it Gauss who wanted the 17 sided regular polygon on his tombstone

The tombstonist wouldn't do it because he said it was basically a circle

[tender tulip]

$Gal(\mathbb{Q}(\cos(\frac{2 \pi}{17}))/\mathbb{Q}) \ \cong (\mathbb{Z}/17 \mathbb{Z})^{\cross}/<16> \cong (\mathbb{Z}/16 \mathbb{Z})/<8> \ \cong
\mathbb{Z}/8 \mathbb{Z}$

[fathom swallow]

Mizalign

[tender tulip]

fuck

good enough, ignore the shitty latexing

Not even going to BOTHER with using primitive roots of unity mod 17 at this fucking point

I'm generating a Cayley table

[little vine]

Damn you went hard

That's good though

I understood

[tender tulip]

<[4]> is iso to Z/2Z

<[2]> is iso to Z/4Z

<[1]> has order 1
<[2]> has order 4
<[3]> has order 8
<[4]> has order 2
<[5]> has order 8
<[6]> has order 8
<[7]> has order 8
<[8]> has order 4

[dapper badge]

real

[tender tulip]

3 is the smallest prime root mod 17 so

[dapper badge]

I think I'd like to buy a nice tea set sometime

[wooden flax]

woah ded chat 2day

[deep mango]

Hi invitcus

[tender tulip]

i have no fucking clue what to do aaaa

<[3]> generates (Z/17Z)*/<16> and I am considering the set of cos(2npi/17) fixed by [3]^2 but there’s, none

[wooden flax]

Hi RYC

should i spice up chat with a Weibel problem

[tender tulip]

brainwave

[bright hill]

invictus!

[wooden flax]

DarQ!

[bright hill]

I'm about to be an aluffi fan as well

universal properties are sick!

[wooden flax]

very cool

pretty much everything satisfies a UP these days

[bright hill]

lel

[deep mango]

Whats a weibel problem

[bright hill]

a problem from the book by weibel, I assume

[deep mango]

Whats the weibel problem

[wooden flax]

1 sec

[tender tulip]

YOOO

I KNOW WHAT TO DOOO

i wonder if this general idea can be made into an algorithm for finding the extensions of any cos(2pi/n) via the isomorphism theorems and properties of (Z/nZ)*

[wooden flax]

Prove that Ext^1(-,Z) dosent vanish on flat abelian groups

my proof uses uni properties

[deep mango]

I dont know what that means

But thats ok

[wooden flax]

:(

ryc stop doing analysis

[vivid halo]

average algebra fan: 🤓
average PDE enjoyer:

[wooden flax]

https://tenor.com/view/reverse-card-uno-uno-cards-gif-13032597

the opposite

[vivid halo]

lmao nah

it's really like

average algebra fan: 🤓
average PDE enjoyer: 🤓

[wooden flax]

LOL

[zealous garden]

I had to revoke my react when I saw the self-react

[bright hill]

I like how they upvoted their own take

[vivid halo]

analysts: nOoO R is defined in terms of Dedekind cuts or Cauchy sequences
algebraists: Ext^1(Q,Z)=R

[wooden flax]

nG reacts to everything he posts within 0.00001 ms

mfw algebra applied math

[pure sun]

am i missing something? i dont htink thats true

[wooden flax]

its the real numbers as a group right

with operation as addition

[pure sun]

iirc Ext^1(Q,Z) is something like "finite adeles modulo diagonal embedding of Q"

[dapper badge]

group activity time!

[wooden flax]

you're probably right

[dapper badge]

lets compute it!

[wooden flax]

[dapper badge]

injective resolution moment!

0 -> Z -> Q -> Q/Z -> 0?

[zealous garden]

Do you know how to do calculus on the Rationals

[wooden flax]

why

[zealous garden]

what do you mean why

Rationals are based, that's why

they're a field and everything

[dapper badge]

Time to take Hom(Q, -)!

[pure sun]

yeah take hom of this, at some point yuou need to calculate Hom(Q, Q/Z), and then you write Q/Z as a sum of p-parts

[dapper badge]

dies

[pure sun]

and then each p-part will become like the Q_p part of the finite adeles

or something like that

[dapper badge]

sounds scary

[wooden flax]

yuh

[little vine]

Can you do calculus on an incomplete metric spaces?

[pure sun]

like Q/Z = \oplus Z/p^\infty

[dapper badge]

and not like R, but idk

[pure sun]

where the sum is over p prime

[wooden flax]

oh shit

yea

[bright hill]

well, I think calculus sortta implies you're working with R

but can you do anal on incomplete metric spaces?

yes

[little vine]

Oh ok

[zealous garden]

that felt pedantic even to me

[little vine]

Anal

[bright hill]

lmfao

I said anal and you thought that was pedantic?

[zealous garden]

probably because I use a different separator for calculus and anal personally

[tender tulip]

what in gods name is EXT

[little vine]

I figured they would have generalized calculus to other complete metric spaces

In the R sense

[pure sun]

don't.

[wooden flax]

LOL

sotrue

[tender tulip]

if it has anything to do with homomorphisms between structures

i am going to be afraid and cry

[pure sun]

i mean

everything is related to homomorphisms lmao

[tender tulip]

Functor of homsets I assume

[wooden flax]

think of it as a function that gives an abelian group

yea its a functor

[vivid halo]

you'll learn when you're older

at least Ext^1 is kinda explicit

[tender tulip]

I haven't seen many functors outside of like

the preimage functor

[vivid halo]

If you have two R-modules A and B you can talk about extensions, so short exact sequences

0->B->E->A->0

[orchid edge]

Learn now so you get a leg up in hom algebra

[vivid halo]

Ext^1_R(A,B) classifies such things up to some equivalence

[tender tulip]

fuck. no

[vivid halo]

the details are annoying and this is just Ext^1

like Ext^1_R(A,B) should be a group

[bright hill]

forgetful functor be like:

[vivid halo]

the 0 element is not so bad to describe:

[tender tulip]

I already had enough trouble with finding a practical example of a homology.

[vivid halo]

it's the trivial extension
0->B->A\oplus B->A->0

but the addition operation on Ext^1 is like

I mean it's not so bad

but it's still kinda annoying to write down

[tender tulip]

I'm gonna get back to what I was doing

[vivid halo]

[little vine]

Math discord is not real studying

[frozen current]

hell nah bruh ugly af 💀

[ancient flame]

what are some cursed latex/math symbols

lol

[fathom swallow]

washingbear

[ancient flame]

lmaoooo

[violet spade]

hmm I need a different font

the one where Xi is actually just 3 lines

[ancient flame]

lol

[fathom swallow]

washingbear

[bronze wedge]

New covid test just dropped

[gritty copper]

$UwU$

[fathom swallow]

Vijay

[tender tulip]

Kinda stuck

So essentially I considered the set of
$c(n) = \cos(\frac{2 \pi}{17}3^n)$ from $n = 0 to 7$

[fathom swallow]

Mizalign

[tender tulip]

and got a series of extensions to find the sums mod 2 or 4

but I can't actually find the original cos(2pi/17)

I can't sieve it out of the sums

nor find an algebraic relation for it in the past ones

even though I've exhausted the extensions I've been allocated

I didn't sieve 3^4 out of it, whoops

wo

so, because I'm insane

Lets say we're given some n

Can we create an algorithm to find the series of extensions from Q to Q(nth root of unity)

it's easy for 2p^k, p^k, 2 and 4 (p prime) cuz primitive roots and partitioning

I did my work with a variable so I assume the choice of primitive root is irrelivant

[sleek wing]

I agree with this statement

[fair mural]

i agree as well

[odd narwhal]

there is a nice thing where in the case of (abelian) groups if you fix an action the baer sum can be described by cocycles

iirc it's literally just a pointwise sum of 2-cocycles

[vivid halo]

Yeah but this was directed at Mizalign so please refrain from these words

[odd narwhal]

lmao

I just wanted to exposit a bit for anyone that's interested

(and isn't going to be annoying about it)

[grand night]

does anybody knows the answer to this equation i am afraid my dad would never come back

[manic ginkgo]

depends on if you've won the lottery or not

[grand night]

well you just told me the truth

fuck..

[arctic grove]

oh my god

[frozen merlin]

I have some correspondence between N and finite subsets of {1,2,4,8,...} given by summing the elements. which operator looks better? I was originally using \Sigma because I wanted to emphasis the fact that this is essentially a sum, and I'm worried that \sum looks too big, so the middle ground is \textstyle{\sum}

(the three options are on the bottom)

[mint canopy]

Purely my own opinion, but the middle ground you gave looks best to me.

[compact tartan]

note that \textstyle is a switch so it affects all text after it, not just the braces you added

you probably want {\textstyle\sum}

[frozen merlin]

yeah I did this when I made a macro

but ty

[ancient flame]

using latex for my econ assignment lol

[neat frost]

Lol

Empanadas per arepa

[ancient flame]

yes

[frozen merlin]

nice

[neat frost]

Tf is an arepa

[frozen merlin]

you might want to make the margins a bit thinner

[neat frost]

Make margins thinner and add some fancy lines and stuff to make it hella cute

[frozen merlin]

lines?

[neat frost]

Yeah

Rules

Squiggly lines

Colors

The works

[surreal sapphire]

so many indents

looks kinda weird

[frozen merlin]

yeah also the parskip package

[neat frost]

Lol I don’t think we should critique every piece of work someone posts

Sometimes ya gotta give some validation

[frozen merlin]

.

[neat frost]

Validation without criticism

[frozen merlin]

it's constructive!!

[neat frost]

I’ll construct your mom

[odd narwhal]

Maybe putting parentheses around the sets could look nice

Since it's a function

[tight comet]

Is the repetition really necessary?

[tall badge]

@desert adder thats inappropriate to post here

[desert adder]

I’m sorry

I just found it on TikTok

[fair mural]

[jovial ember]

Lmfao

[tender tulip]

Is there any complex valued function that is continuous but not differentiable over the entire plane?

[frozen merlin]

thanks for boldening, I would have pulled a chmonkey and not read it otherwise

anyway the answer is yes, but there's nothing special about the complex structure. you're really just asking whether a continuous\differentiable map exists from R^2 to R^2

right?

[tender tulip]

hm, good point

[bronze wedge]

In fact the even stronger result holds that the set of differentiable functions have measure zero

[tender tulip]

measure zero over ???

what sig

[bronze wedge]

Gaussian measure on C(C,C)

[tender tulip]

Measure theory is weird

[vivid halo]

this already exists for R->R, so it exists for C->C for the same reason

e.g. the Weierstrass function

[burnt dune]

no man its p easy

[echo talon]

.

[tender tulip]

The weierstrass function is the parameterization of the edge of the radius of convergence for the function that satisfies f(x^b) = a(x) + x or smth

it’s continuous otherwise

[velvet dagger]

What

Miz you gotta actually arrange the words in a way that make sense

[deep mango]

you can just add two weierstrass functions like f(x + iy) = h(x) + i h(y) where h is a weierstrass function R to R though

that will not have x or y partials at any point, but is certainly continuous.

[storm sage]

Oh shoot I've been messing it up this whole time

Sorry Chomsky I profaned your syntax trees

[dapper badge]

i love matcha so much

[jovial ember]

Bro I thought you were talking about me because ppl sometimes call me that

☠️

[neat lintel]

I hate matcha for some reason

[limber thunder]

I thought it was weird at first but learnt to appreciate it

the other day I had matcha Chai and damn 🔥

[mint canopy]

Matcha has such an interesting herbal flavour

I'm frankly not sure if I like it or not, but it's definitely different to what I'm used to

[tender tulip]

I realized my point is kinda ill-formed given what we usually specify as a complex mapping is continuous and differentiable satisfying reimann-cauchy

[inland raft]

Is this calc good?

Lol

I cant put the link

😐

[surreal sapphire]

its a calculator alright

[inland raft]

?

[surreal sapphire]

just check if it can do what you need

[inland raft]

It can

But maybe i can get a better one if this one is bad

[surreal sapphire]

you can get one that does more (i.e. graphing) but it will be a lot more expensive

maybe you need that for engineering, i dont know

[inland raft]

Hm

So this one basically has everything but graphing

[surreal sapphire]

i mean your phone can do all that

and more

so you should just get what you need for school or wtv

[mint canopy]

I'm in no way well-versed in calculators, but I really don't think you should stress too much about what calculator to get

They're all a bit awkward and annoying to use. The question is, does it do what you want it to, and is it reasonably priced

If you go into higher mathematics, you probably won't even use it much after high school

[inland raft]

Ok

I'll buy this one then

Thx guys

[manic ginkgo]

Is there some kind of music discord server any one knows of? Would really like some help transcribing a piece from a game

[little vine]

@manic ginkgo I'm in a good one

I can dm you an invite

It's a great time

Out of curiosity what piece is it?

[manic ginkgo]

Sure, would appreciate it! it’s this: https://m.youtube.com/watch?v=OD4WiyVOxpQ

[little vine]

You pretty advanced on dictation? It would take me a while to figure it out

[manic ginkgo]

Nah, I haven't had any lessons. Been trying to pick up stuff here and there by myself so still pretty much a total noob. I think I've figured out the beginning melody somewhat but that's about it tbh

[little vine]

Your skills will get stronk

Do you have a daw of some kind?

That'd make the process easier

Than sitting at the piano trying to bang it out on paper

[manic ginkgo]

hmm not exactly, I can try garageband or the free version of sibelius

[little vine]

Anything with a piano roll

[manic ginkgo]

hmmm not sure what you mean, I haven't actually done it yet but going to try plugging my keyboard in to garageband and see what comes of it

[little vine]

It's a convenient way of seeing/programming music

@manic ginkgo

You just draw the notes in, can move them around, etc

[manic ginkgo]

ah ok

I've usually tried just playing directly on the keyboard and getting the midi input

[little vine]

It'll be more convenient for you to transcribe the music if you use a program with a piano roll

[manic ginkgo]

thanks, I'll give it a go

[fading zealot]

If the Penrose tiling can tile 2D space without repeating itself, is there an equivalent that can tile the 1D space without repeats as well?

My instinct is no, but even then I don't know what changed between 1D and 2D to allow the Penrose tiling to happen

[open aspen]

WHY must my undergrads come to class if they're coughing every 10 seconds

Its not even the courtesy of not spreading whatever disease they caught. I simply cannot explain anything because they're coughing over me the whole dang time

Ffs, if you're sick, don't come. I won't even check to make sure you do the makeup work.

[chilly hull]

i mean when i caught covid months ago at first i thought i slept too little, turning on the AC while sleeping, or something else

then i was like "damn why does my body feel so cold"

"maybe it just isnt a good day"

i woke up tomorrow to realize that i had a fever and took a covid test

man

[little vine]

I have yet to get the vid

I ignore the "I woke up and wasn't feeling good" emails

[chilly hull]

i thought i just felt kinda bad that day and could go on

[little vine]

I understand

Huge inconvenience that your life halts

[uncut socket]

@loud rivet You became a helper now?

[loud rivet]

Yeah

Idk

My irl friend is also one so I was like "sure why not lol@

I did a funny thing tho so

It ain't too annoying

[tiny phoenix]

yo im new to college and Im using mymathlab for Introductory and Intermediate Algebra 6e and i need to find an access code for free

anyone know where i can find one?

[ancient flame]

that's like

illegal

[neat lintel]

@deep dirge

if u read second last line

in the pic that circle sent

it's stated that it's not square root exactly

[deep dirge]

#discussion

Lol.

[unkempt oasis]

yeah goodluck. been there. I couldnt find any

[ashen pike]

Is anyone on this server a good teacher/presenter?

I would like to ask a question regarding a maths presentation i I will hopefully be leading

[hushed turret]

you may want to ask in #math-pedagogy

[ashen pike]

but its kinda not really about the teaching aspect

[hushed turret]

well, what is the question?

[ashen pike]

The question is why do complex numbers feel like such a huge conceptual jump

for students

and if the naming convetion of imaginary is holding people back

[hushed turret]

the name certainly doesn't help

[arctic grove]

twice got honorable? awesome!

[ashen pike]

because rationals and integers are instantly applicable to real-life phenomena

[arctic grove]

coz they are quite literally that
its ur first intro to things that can feel extremely disconnected from reality

[hushed turret]

i am not an educator but i think for a lot of people they are told that square rooting negatives is something they "cannot do" or that it is against "the rules" or something equivalently prohibitive

[arctic grove]

Like, up until that point, the algebra you do, it all feels "applicable directly" to some extent

the numbers u see are real

but when you bring the name imaginary into it, people lose their shit

[ashen pike]

so where can you find imaginary numbers in real life?

[hushed turret]

they have to unlearn that "stigma". i'm not sure if that's the right word

[arctic grove]

anywhere there is a rotation

[ashen pike]

true

[arctic grove]

imaginary numbers represent rotations

[arctic grove]

stigma probably isnt

misconception would be more suitable ig

[ashen pike]

do you also think that all the previous steps between types of numbers can be linked nicely via basic operations

[hushed turret]

imaginary numbers are used for various things, but not in ways that are immediately visible

[ashen pike]

until you reach complex

like naturals to integers is extended by subtraction

[maiden bear]

well another thing is

[ashen pike]

integers to rationals uses division

and rationals to reals uses infinite sums

[arctic grove]

subtraction?

hows that

[ashen pike]

sorry

brainfart

[maiden bear]

actually nvm i am incapable of phrasing this properly

[arctic grove]

timo try

and if u cant

just talk about geometry

😌

[maiden bear]

i mean it feels like a conceptual jump because it's something you've never been told somehow exist or is even "allowed" to exist

[surreal sapphire]

historically that is what got complex numbers accepted

interpreting the arithmetic geometrically on the plane

[maiden bear]

taking the square root of a negative is illegal until a certain point

[surreal sapphire]

from a mathematical perspective the jump from rational to reals is much harder tbh

its just that you are intuitively used to real numbers all your life

[ashen pike]

exactly

[maiden bear]

yeah that kinda adds to what i mean

[arctic grove]

gabriels horn moment

[hushed turret]

i think students generally don't think about the reals as a whole that much in hs

you are generally occupied with algebraic numbers

and sometimes you use pi or whatever

[bright hill]

for HSers, $\bR$ is literally $\bQ\cup \sqrt[n]{\bQ}\cup \pi\bQ\cup e\bQ$

[fathom swallow]

DarQ (#bring_back_:akko_lewd:)

[arctic grove]

pi, e, and ln2

thats basically it

[bronze pelican]

Lol

Thats still a countable set

[hushed turret]

it is

[arctic grove]

it very well is

[wispy plover]

I once found a webpage that would allow you to merge pdfs and put bookmarks (in the sense that if you merged pdf1 and pdf2 (these are the names) you would have bookmarks pdf1 (at the beginning) and pdf2 (when pdf2 starts) online. However, I cannot find the page. Does anyone know of something similar?

[ancient flame]

$\bR=\bQ(\pi, e, {\ln(a):a\in\bZ},{b^{\frac1n}:b\in\bQ,n\in\bZ})$

[fathom swallow]

gmod

[deep mango]

[chilly hull]

isnt R just the set of all numbers you can plot on the real number line

[neat lintel]

R is just a letter

[chilly hull]

😡

[frozen merlin]

ln(-1) 😳

[ancient flame]

bruh

LMAO

[chilly hull]

sqrt(-1)

[frozen merlin]

behold, gmod's real line

[chilly hull]

not in R but in the other set

-1 is in Q and 2 is in Z

[neat lintel]

Mistakes pop out

[ancient flame]

lmao

I hate y'all

[chilly hull]

so therefore Q(sqrt(-1)) is a subset of that set

but it isnt a subset of R

[gaunt latch]

discussion-1 looked so bad so I left it

[gaunt latch]

noted

[chilly hull]

also what about sin(58pi/59)

[gaunt latch]

do you know you can fit a whole matrix inside a trig function?

[chilly hull]

what

how

[tender tulip]

yes, and the real number line is all the points that corrwspond to a real number

[gaunt latch]

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

[tender tulip]

differential equation solutions probably

[gaunt latch]

they provide an example with Pauli matrix

[tender tulip]

how do you define convergenceb

[gaunt latch]

and even cardinal trig functions, hyperbolic and inverse hyperbolic functions

[tender tulip]

How do we say the sequence converges

[gaunt latch]

If a sequence is bounded and monotonic, then it is convergent.

[chilly hull]

wait isnt that circular logic then

[tender tulip]

rhat’s the joke

[gaunt latch]

if you're talking in limits

[tender tulip]

i mean idk if the absolute value of the determinant is a suitable metric for GL(n,R)

[gaunt latch]

if there is some particular number to which it tends

you have many ways

[fast ivy]

Convergence in the space of n×n matrices?

Oh

That's an interesting question

First of all

Notice that M_n(R) and M_c(C) are respectively finite dimensional real and complex vector spaces of dim_R(M_n(R)) = n² and dim_C(M_n(C)) = n².

So in particular

We can induce in these spaces they topology they carry via the canonical isomorphism with R^n² and C^n² respectively.

So in particular

A sequence of matrices $(a_{ij}^{n}){n \in \mathbb{N})$ where for each fixed $n \in \mathbb{N}$ we have a matrix with entries $a{ij}^{n}, 1 \leq i n, 1 \leq j \leq n$ converges to a matrix $(b_{ij})$ iff for each pair $i,j$ we have that $a_{ij}^{n} \rightarrow b_{ij}$ in the standard topology of $\mathbb{R}$ or $\mathbb{C}$.

[fathom swallow]

MisterSystem
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fast ivy]

Another thing to have in mind is that on a finite dimensional real or complex vector spaces

the topologies induced by a norm are the same

so an equivalent way to work with convergence

is to endow this space of matrices with a norm

say the frobenius norm or the operator norm

and everything works just the same

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

And you define the matrix exponential as for a given matrix $X \in \mathcal{M}{n}(\mathbb{R})$, let:
$$
e^{X} = \sum\limits{k = 0}^{+ \infty} \dfrac{X^{k}}{k!}
$$
You can prove that for any matrix $X \in \mathcal{M}{n}(\mathbb{R})$ the series in the right hand side converges absolutely (wrt to any norm you put on $\mathcal{M}{n}(\mathbb{R})$). And analogously for absolutely convergent series of real numbers, we will have that $e^{X}$ also converges in the usual sense.

[fathom swallow]

MisterSystem

[fast ivy]

All of this still makes sense for any banach algebra btw

so talking about exponential of bounded operators makes sense, for example.

it also makes sense for lie algebras

and the exponential has an important place there too

Some examples of how this is defined in books.

[gray snow]

@fast ivy broo help

you done thesis right?

[bright hill]

please don't ping random individuals for help

[gray snow]

bro

i ned helpe

[neat lintel]

#❓how-to-get-help

[gray snow]

bro you got thesis?

[bright hill]

were you oblivious to all the "read #❓how-to-get-help " in your time here?

[gray snow]

ye bro

[bright hill]

why would you want someone who has specifically written a thesis?

[gray snow]

bro it not mathy questgion

[gray snow]

i have question about thesis

general one

[bright hill]

you can just ask

[gray snow]

ye bro what happen if you have factual/logic mistake in thesis

you get instantly fucked?

[bright hill]

well, you proabably have double checked with other experts and colleagues so the chances of that are low

[gray snow]

if no one check

before you turn it in

[bright hill]

that's not how it generally works

[gray snow]

it how it work for me

[bright hill]

you wrote a thesis?

[gray snow]

they do me dirty and dont give supervisor

[gray snow]

working on

so no one ever give feedback

so i scare i make stupid mistake with math

and get fail

math hard bro

already shit my pant over this

[bright hill]

ok

sigh

[prime adder]

What

[gray snow]

ye bro you read correct

[gray snow]

wdym sigh bro i major panic with this shit

@bright hill bro send help

• exblain

[neat lintel]

Gjorka open your own help channel #❓how-to-get-help, and post there the question clearly

[velvet dagger]

It's not really a math question for how to get help to make sense

What kinda thesis?

[neat lintel]

I don't even understand what he is saying

[velvet dagger]

It seems like what's happening is

He has a thesis to do. Not sure at what level

Maybe he's an undergrad and ever undergrad has to do a thesis

Somehow he wasn't given an advisor

So he's now worried that without someone to guide (and especially to look over, catch mistakes, and help revise) he'll submit a thesis with a fatal error

And that this will lead to some dire consequences

[manic ginkgo]

From what I gathered yesterday it’s an undergrad thesis on light transport theory related simulation on a gpu

[willow patio]

I'm working on a very simple maze AI and compactifying instructions to give the robot

i gotta think how to work wtf im even thinking, i always do this lmfao

[pliant nacelle]

i hate it when maths problems have a paragraph of context/story

just get to the point

[next schooner]

What do you mean?

[storm sage]

but flavor

[dapper badge]

proving minkowski's inequality for homework, can't fit the inequalities on one line 🙃

[burnt dune]

yoo

holders inequalitys proof turned out to be so easy

u just prove a little lemma

by calculus

yet holdeers is so much stronger

wtf math?

[dapper badge]

yeah it's pretty cool

[burnt dune]

lmfao yea

[dapper badge]

we like showing that our norms satisfy triangle inequality

[burnt dune]

yea triangle inequality is lit

math is just literally using one idea

lmao

[dapper badge]

there might be more than one, but don't quote me on that

[burnt dune]

p sure there arent

or like

its only 1 idea at a time

u build so much so much with 1 idea then ur finished and u go again with someething different

like hilbert spaces

literally the whole ( at my lvl ) theory of hilbert spaces is being developed using same 2-3 tricks 😠

cool

[fast ivy]

young's inequality?

[burnt dune]

idk its name

[fast ivy]

oh yeah lmao

[burnt dune]

a^lambda*b^(1-lambda) <= lambda *a + 1-lambda(b)

its like the first year math student forgetting the second part of thee chain rule

when differentiating with respect to lambda

thats how i remember it

[bronze wedge]

holders inequality is tbh easier to prove using jensens inequality

[burnt dune]

jensen the complex analysis one?

[bronze wedge]

https://en.wikipedia.org/wiki/Jensen's_inequality

use the most abstract measure theoretic formulation

(but it only works for prob measures)

[fast ivy]

oooh

[livid quiver]

I noticed in quantum mechanics, quantum states are represented in row or column vectors as bars and kets, does that mean that the operators that act on these states are also vectors ?

[bronze wedge]

They are vectors in some sense (members of hom(H,H))

[livid quiver]

I'm not sure what hom(H,H) is but from my understanding they're not vectors in the common sense they're just represented as vectors because it matches the calculations

[eager reef]

Whats a Vector in the „common sense“ for you

[prisma swallow]

Math is a hoax, it’s all made up.

[fading tusk]

hello

[gaunt latch]

what operators exactly? because for example the inner product of two state vectors is a scalar and in this case a complex number in general.

unless you mean operators like manipulating, projection, hermitian adjoint, matrix representation operators...

[livid quiver]

ah nvm I found that It's just a matrix

by operator I meant ones like the hamiltonian or the momentum or position operator

[gaunt latch]

An operator is a mathematical object that acts on the state vector of the system and produces another state vector. They're also used to represent the observables ( physical properties such as for example position, momentum, or energy that can be experimentally measured )

[livid quiver]

aha

so the state vector of a system or ket |S> is just a vector, what's the general form of that vector ?

I know it can have arbitrary number of dimensions

but what does each entry/element in that vector mean

like lets say you have the quantum state |e> of an electron you're studying, what would e[0][0] represent or mean

I looked into the bra-ket notation and these bras and kets could be vectors over R[n] but they could also be over C[n] and I assume that's the case in quantum mechanics since there are complex conjugates

but say the first entry in the state vector |e> is 5+4i, what does that say ?

[gaunt latch]

probability amplitudes are used to construct quantum states, and also to construct propagators that evolve one state to another. Complex numbers are used because particles are described as waves and also they're capable of making things easier involving the language of linear algebra.

[gaunt latch]

They could but what do you think applies the algebra here?

[livid quiver]

wdym applies ? like what makes the math work out ? if that's the case I think It's that representing quantum mechanics in the language of linear algebra is very effective because you can encode information about a quantum thing in a matrix and linear algebra deals with matrices

[livid quiver]

I heard that squaring the value of the wave function as a specific point gives you the probability of finding it there but I didn't know people approach this from the other way around

so you mean they get the probabilty first and take the square root to get the quantum state ?

I think I'm getting it wrong

[gaunt latch]

If you want to find the probability of something in quantum physics, you add up the “probability amplitudes” of every possible way that thing can happen, then take the magnitude (a generalized absolute value) and square it.
The probability amplitude is complex valued.

[livid quiver]

when I see something like this what I understand from it is that ψ is a vector of functions of x, ψ1(x) .... ψn(x) such that each function is an actual mathematical function like e^ix or something like that. and ψ altogether is the quantum state where you can apply operators to it etc..

am i right ?

[wide falcon]

physicist here

good enough

i dislike thinking of them as vectors because it implies choosing a basis

the bases usually preferred are not preferred by nature in any way i can observe

e.g. energy eigenstates

it's common to take the basis to be the energy eigenstates

it's arguable this led to interpretive biases which created the vacuum catastrophe prediction

the only reason an energy eigenstate's component would matter is if something happened to polarize the particle so it appears to have classical energy to its observers

in sum: waves wobble, and people like to break them into components which feel natural

the wobbles are discovered and the components are invented

better sum: people discover indivisible wobbles and invent components to break them down anyway

here enjoy some more rant

wave function collapse is just polarization
nothing actually collapses
there is simply harmony between experimenter and experiment
you are a wave
so is the experiment
look at this animation
https://www.shadertoy.com/results?query=quantum+harmonic+oscillator
this is a quantum harmonic oscillator
each part of your wave moves classically
if you were in a harmonic oscillator, you would move like a ball on a spring
the only thing different between quantum and classical is that you have an amplitude
and there are others nearby
those amplitudes bleed a little bit
okay so
since each part of the experiment wave moves classically
and each part of the experimenter wave moves classically
the only possible interaction an experimenter can undergo is classical
the quantum effects come from neighboring amplitudes bleeding about

[sleek wing]

psychosis in action

[tight hound]

after you left eath

you need more or less 151 * 10^3 km/h to leave the solar system

[wooden flax]

Lmfao

[livid quiver]

that's too big brain for me

certainly wanna know all that one day for sure

[errant ridge]

yea ever wonder why animals or fish dont discover math? it's always only humans

all of math is made up i swear

[prisma swallow]

So true

[fading tusk]

whales can do math

[dense belfry]

Not all of math is made up

https://plato.stanford.edu/entries/fictionalism-mathematics/

[errant ridge]

[fading tusk]

does anyone here have experience growing a lemon tree in a container?

plato means plate in my language

so it's a bit hard for me to take him seriously

[brave wraith]

My teacher asked me what to do when there is a tsunami, i need absurd answers from you guys

[zealous garden]

Swim

Prove generalized stokes theorem on manifolds with corners

Tire rotation

[brave wraith]

I mean if there will be a tsunami

so it hasn't happen

yet

[zealous garden]

Get a scuba suit

Dress up, get in the drive way and wait

[fading tusk]

when there is a tsunami u must donate

take blankets and canned goods

sir

[brave wraith]

when im about to get hit by a tsunami*

[fading tusk]

Oh i was confused

if a tsunami approaches u have to wave ur hands above ur head so u look bigger

and make loud noises

[brave wraith]

that'll scare away the tsunami ig

[fading tusk]

that does not work with polar tsunamis tho

[brave wraith]

Ima rephrase the question to avoid confusion
What should i do when I'm about to get hit by a tsunami soon? (absurd answers only)

[fading tusk]

if it is a polar tsunami or a grizzly u have to run opposite

[bright hill]

Thus, the idea is that sentences like ‘3 is prime’ are false, or untrue, for the same reason that, say, ‘The tooth fairy is generous’ is false or untrue
but all tooth fairies are obviously generous

[dense belfry]

That's their point

Lol

If they existed they would be generous, but they don't exist

They exist as a fiction in our heads

[bright hill]

yeah, I sorta figured after reading literally the next sentence

shouldn't've been so hasty

[dense belfry]

[errant ridge]

blushy sully = the worst emoji ever

[neat lintel]

do you guys just look at a math concept and go like, I wanna learn tbat, or the other way around saying, nope

[errant ridge]

I always say "I wanna learn that"

I never say never

[bright hill]

it's always like "I wish the knowledge of this thing has been transferred to my brain effortlessly in my sleep" or smth

[neat lintel]

relatable

[errant ridge]

no, I love putting in the effort

because I get rewarded for my efforts

[neat lintel]

you're really dedicated 👀

[errant ridge]

not enough though

[bronze wedge]

there are things i dont want to learn

[errant ridge]

like the entirety of physics (for you)

[bronze wedge]

I would say algebra as well

[neat lintel]

or chemistry

[bright hill]

why is dat?

[errant ridge]

finance people hate algebra

Noted

[bright hill]

algebra is literally all over pure math lmao

[errant ridge]

algebra is sick

[bronze wedge]

I can excuse algebra that is useful in analysis

nothing else

[tender tulip]

i mean algebra is what happens when you get two things and make another thing

[bright hill]

yeah, a lot of people learn algebra just because of how useful it is

[errant ridge]

I wanna learn it because it's fun

speaking of which, i should go do that

[neat lintel]

anything useful other than linear algebra?

[errant ridge]

,iam stu

[fathom swallow]

Gave you the studying! selfrole.

[bronze wedge]

useful for what exactly? the most "algebraic" thing ive ever used irl is C0 semigroup theory

[bright hill]

ofc

[bright hill]

for other areas in pure math lel

[bronze wedge]

and what is that useful in?

[bright hill]

well, you see

[bronze wedge]

(and maybe some functional analysis)

[bright hill]

not all of applied math has always been applied math, you know?

[light needle]

This is like very specifically the finance you do that you are talking about, algebra is useful in plenty of applied math

[bright hill]

also, cryptography mfs

[bronze wedge]

I can excuse math physoids, no one else

[light needle]

People use ag for algorithms of robots as an example

[neat lintel]

it came from pure first then became applied is what you mean?

[light needle]

Applied math uses tons of pure math

[bright hill]

some of applied math, I imagine

yes

[bronze wedge]

true i will admit

[bright hill]

some of it obviously also evolved with application in mind

[bronze wedge]

(and also note that supposedly applied things may never actually be used irl)

[neat lintel]

like what?

[river moon]

ellipsoid method moment

[bronze wedge]

heres a paper: https://arxiv.org/pdf/2203.11072.pdf

[neat lintel]

im gonna be honest im not used to reading a "math paper" yet, but what is it about if I can ask?

[river moon]

back in the 80s some soviet mathematician developed an algorithm to solve linear programming problems and proved that it solves them in polynomial time (which was the entire point of the algorithm), but the performance was so bad that everybody kept using simplex algorithm which was exponential time complexity in theory, but fast in practice

then smart people developed interior point methods which were proven polynomial time algorithms and worked really well

[bronze wedge]

its basically about comparing public info vs public info and some extra info on the occurrence of an event

problem is

no bank

no nothing

would every actually use this

[neat lintel]

oh?

[sick kite]

I have a question - when self-studying math, how can I be sure that what I'm doing (in exercises) and understanding from the textbook is "actually math" i.e. not crankery

How do I stop myself from becoming a crank when I'm the only person really holding myself responsible

[surreal sapphire]

stop being the only person

[sick kite]

in my current circumstance its a smidge difficult

[surreal sapphire]

in exercises you at least know the results are correct

but other than that, there is nothing you can do

[sick kite]

I have this discord, mathse and the exercises

oh lol

[surreal sapphire]

professional mathematicians talk with peers too

[sick kite]

Yeah ik

i don't have really any peers that I can turn to whenever like a prof or colleague or fellow student

because my teachers at high school either don't have a math degree or have forgotten a lot of it because it's been years

and I feel kinda bad asking people to check my work every single exercise on this server haha

but I also don't want to wait 2 years until I go to university to start learning, as that will leave me deeply unsatisfied and also will mean that I will have wasted a bunch of time, essentially

[golden pendant]

how can i change my color pleasse

i hate this blue

it sucks

[surreal sapphire]

i dont have any other tips

you also have to learn to not doubt yourself with certain things

but especially at the beginning its hard

[surreal sapphire]

i can give you white

[golden pendant]

is there any other? I am either a normie or this hideous color?

[sick kite]

Yeah, especially when I was first reading math textbooks it was quite hard, now it's a little easier and I feel like I understand way more, like before I didn't have a clue where to start with a lot of the exercises but now intuition is beginning to take over

[surreal sapphire]

i can make you helper

[sick kite]

and in the places where I have solutions, they match up (my intuition and solutions)

[golden pendant]

Looool fine i ll take hideous

not helper

Why is this the active color? green seems more appropriate i think

[bright hill]

it might not be as difficult as you think

I mean

you're here, aren't you?

[sick kite]

i feel bad pestering the people here a lot

especially when im wrong a lot

[bright hill]

then try to not be wrong as much as possible

and that's usually good enough

[sick kite]

aight

thats gonna be the strat

lmao

I'll just beg people to check my solutions and I'll pray they're right

[solid snow]

the people here are interested in mathematics!

[snow reef]

hello

[rich kestrel]

You need someone else to go over your arguments until you are able to judge the validity of an argument yourself

[wide falcon]

yeah the problem with that is mistake proofing usually involves independent checkers, and humans make mistakes

i have no doubt about the completeness of my ability to analyze an argument

my doubts are with regard to the reliability

that is why people ask

[lavish kayak]

What are you learning rn?

[vast surge]

Step 1. Be rich
Step 2. Hire private tutors

[zealous garden]

nope

We're blue, just like the very actives and the mods

blue

do you understand?

[lavish kayak]

Well @sick kite I'd like to start self learning some stuff myself and study groups are always a big help. Tell me what you're studying and maybe we learn together? I'm currently doing linear algebra and I'd welcome every year 1 or 2 subject unless I don't have the pre reqs for it

[bright hill]

<@&268886789983436800>

[gaunt latch]

Tada, I'll work here.

[gray snow]

Why calling polic

[velvet dagger]

The message that is replying to was deleted so probably it was inappropriate or something and the person got banned

[brittle socket]

Like me
I try to ask ppl here to help me check my solutions when self-studying, though I don't think I have been annoying or anything. E.g.: I don't spam.

[covert portal]

what was the message

[gray snow]

Ye only matter of time when fishkebab get same treatment

Scary bro

That why I would like know what considered inappropriate/bannable

Fishkebab is the fish in my pfp

[covert portal]

Dude... I could go for a fishkebab rn. But not if I'm getting banned

[teal lion]

hey dudes

[austere quartz]

This is just a test no need to respond $1+1=2$

[fathom swallow]

68 6F 77 3F

[storm sage]

use #latex-testing

[ripe wasp]

i think my group theory class teaching us field theory without any ring theory or linear algebra is fucking dumb

it's so hard to follow

[sick kite]

I'm doing a bit of la, a bit of real analysis and a bit of general maths stuff (currently looking at dedekind cuts, moving onto cardinality and general topology]

[ripe wasp]

linalg and real analysis ♥️

[deep grail]

Hi good morning guya

Guys

[shell junco]

Hello

[shell junco]

u watch aot?

[deep grail]

Yup

[shell junco]

same

[golden pendant]

what happens in the end

i never finished it

[deep grail]

Not ended yet

[golden pendant]

what

[deep grail]

But in manga eren died

[golden pendant]

when is it going to end?

i thought they were in part 2 season 4 a decade ago

[deep grail]

Next year

[golden pendant]

Ouffff

thats messed up

[deep grail]

Spoiler ||eren was killed by Mikasa||

[golden pendant]

niiice. That's good endings shit

[shell junco]

Spoiler ||zeke dies by levi, eren dies an ironic death after getting beheaded by Mikasa at the climax of the Paradis War arc, they all live in Marley after happy ending blah blah||

[shell junco]

yeah I liked it

[deep grail]

Yeah

[golden pendant]

I mean eren could have avoided death in a snap

this is annoying

but it's fine

mmaybe eren wanted to die

[shell junco]

yeah that’s actually exactly what he wanted lol

[deep grail]

But why Armin said that he killed errn

Eren

☠️💀

[golden pendant]

But he was under control of the attack titan?

[shell junco]

uhhh I kinda forgot haven’t read the manga in a while

[deep grail]

Nope

[golden pendant]

why did he want to die and eradicate half the world then

[shell junco]

Pretty sure it was to cover for mikasa running away with Eren’s head

or something like that

[deep grail]

Oo ha 😂

[shell junco]

lmao

also, armin was the commander of the scouts its most likely they wanted him to be the main peace negotiator and just said that

but like I said I haven’t read the manga in a while so take my words by a grain of salt lol

[deep grail]

😂😆

[echo tundra]

Anyone here played the natural numbers game?

[hushed turret]

yea

[echo tundra]

Have you completed it, I am stuck at a place and needed some help

[hushed turret]

uh idt i got through all of it but i can try

[echo tundra]

I am at Advanced Addition world last question

nvm, I did it

[hushed turret]

oh lol

im looking at what i did before and i do not understand it

[echo tundra]

But ngl, I find Lean more annoying than agda

[echo tundra]

Kinda makes sense, this is how I did it. A bit more convoluted, idk if I was supposed to do like this

[cyan goblet]

excuse my ignorance, but does a real analysis textbook usually cover Point Set Topology

eg Tao Analysis 1 and 2

i would check myself but im not quite sure what point set topo is, even after looking it up

[mint canopy]

I’ve seen a few that do, the most prominent one being Rudin ofc

[cyan goblet]

ic

[wide falcon]

enjoy more spam
the usual explanation is that x in int f(int x){ return 2 * x; } is the parameter of f and that 9 from 3*z in int z = 3; return f(3*z); is the argument of this call to f
parameter is associated with the definition
argument is associated with the call
the call is f(3*z)
this common distinction is limited, however
the argument of the call to f is 9
the operand of the call to f is 3*z
distinguishing the operand from the argument allows us to distinguish what happens at translation and what happens at evaluation
the operand is the expression in the call whose evaluation gives the argument
the parameter is the variable in the definition which receives the argument

[tender tulip]

how do we define differentiability of an R^n to R^m function via the R^m euclidean norm

[night thistle]

Is their a difference between (3)^2 and 3^2 I'm asking for a friend he just want quiet down about it. You know how they are

[surreal sapphire]

#❓how-to-get-help

[queen raft]

Here is a good question for yall: In your opinion, is trigonometry more about circles or more about triangles?

[zealous garden]

f(x + h) = f(x) + f'(x)h + r(h)

f is differentiable if |h| -> 0 implies r(h)/|h| -> 0

In other words, if the deviation from a linear approximation infinitesimally close to a point is infinitesimal even with respect to the offset

[open aspen]

Only 80% of my students even took the weekly quiz

Wth

Why not just at least guess answers

It's online!

[zealous garden]

Deadlines are hard

You have to remember and be responsible and stuff

[fast ivy]

The definition wraith gave for differentiability of functions f : R^n -> R^m makes sense for functions between any open subsets of banach spaces. @tender tulip

look up Fréchet-derivative for that

From Spivak's calculus on manifolds book.

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

[echo tundra]

Some Analysis 2 courses touch upon a bit of topology after doing metric spaces. I know A2 definitely does it in general you would wanna read Munkres or standard topology book for topology

[tender tulip]

So i have a question

that's kinda long

So

$GL(n,\mathbb{Q})$ has $SL(n,\mathbb{Z})$ as a subgroup

And two matricies generate the same lattice if they are in the same SL(2,Z) coset

well, what I wondered what happens if $M^{-T}$ the same coset as $M$

[fathom swallow]

Mizalign

[tender tulip]

Which means the lattice is self dual, aka unimodular

But for dimensions 1 to 7 there's only one unimodular lattice up to isomorphism, the integer one

for dimension 8

there's also the E8 lattice

which isomorphism in this case

is that they are in the same coset

I wonder if there's an algebraic way to interpret & prove this

[fathom swallow]

Mizalign

[torpid night]

Guys i need help. I have a math 1 exam in like 3 hours for 50 marks. I studied well but i have mever been able to finish in time or i have finished just as maam collects my paper please help and give tips

[limber thunder]

if possible try solving mock exams or just exercise sheets with a timer next time you study

for now since you've already studied well it's best to just rest and relax until the exam starts

maybe at most do some review but I wouldn't even do that

[wraith shuttle]

im asked a question in #help-27 if someone can take a look thanks

[deep grail]

Hey can someone dm me invite link of any Physics releted discord

[ancient flame]

#old-network @deep grail

[charred nest]

Guys, I want people to ask me what 7+8 is in base 12 modular arithmetics so I can say, oh it's 3 and so on.

[proud goblet]

whats 7+8 in base 12

[brittle socket]

Regular #chill chat

[charred nest]

Oh it's 3

[surreal sapphire]

hilarious i want the quality of this server to improve

[bright hill]

I dunno wtf is up the last few days

#discussion in particular has been insufferable

[neat lintel]

My b

[mint canopy]

Respectfully, when is it not

The last three things I remember from #discussion is someone being racist, some guy telling people he's better than everyone, and someone not understanding math + getting angry about it

[maiden bear]

It's usually bad yeah

but it really has been even worse the last week or so