serious-discussion

[clever knot]

i heard they have kinda hit limits somewhat in size

is that the case?

[untold sapphire]

verilog and vhdl are two known ones

[clever knot]

like stuff is getting kinda small

so is there like special machines that can read the code and print the boards

[untold sapphire]

oh yeah beyond 14nm across you start to have quantum tunneling problems. i mean transistors are little switches, computers run on 1's and 0's , on and off, so you have to be able to open and close the switches. there's a certain point where even when the switch is "open", the electrons can just quantum tunnel across the gap and so it doesn't look sufficiently different than a closed switch.

Another problem is that more transistors and a higher clock cycle simply require more electricity to run, which creates battery load problems. they have partially accounted this by working to lower the voltage thresholds necessary for a transistor to register a signal as a 0 or 1, maybe instead of 0 volts to 5 volts the range is like 0V to 3.3V

[clever knot]

interesting

how much does voltage control and all that impact this kinda stuff

[untold sapphire]

i don't know if the machines take VHDL code specifically, the code for hardware design languages is a bit more abstract than that. it tells you how the parts of the system fit together conceptually, not physically

[clever knot]

i must say

these cpus

are not very right to repiar

repair*

:/

1 transistor is dead

oof

[untold sapphire]

haha. they're very complicated, i don't think they're meant to be hard to repair by design they're just crazy small. i think the intel x86 has 18 parts of the pipeline

the toy model i studied in college only had like 5

to explain what i mean here

to make cpus more efficient

[clever knot]

they need to shrink the distance between stuff?

[untold sapphire]

you can think of each CPU instruction as having a couple different parts

and they have to be executed sequentially

like

"add two numbers" is like

1. first, move the numbers from the registers they are stored into the adder.
2. then, add the numbers
3. move the output to this register

so there are really three different parts but they're all using different hardware

what's more efficient is

the metaphor i learned is like a washer and dryer

doing the laundry involves both washing and drying

but you don't have to wait till the first load is done drying to put the second load into the wash

you can have a bunch of different instructions in the "pipeline" which are all working their way through the system at the same time at different stages of completion

so you should move new numbers into the adding machine at the same time as the output from the previous numbers are being removed, and so on

as people push for more efficient and faster CPU, the pipelines get longer and more complicated

[clever knot]

is this more so for single core performance

i mean i know you could slap more chips on something

but i guess that doesn't exactly improve certain applications

[untold sapphire]

all of what i'm describing is happening is in a single core

[clever knot]

i see

so is it possible to completely build a "computer ":... like wire by wire? Because it would be cool to understand a computer from the point of just some electrical power?

guess might really depend definition of computer and scope

[untold sapphire]

oh yeah, definitely, you can make a pretty simple one

i got a great book to recommend you that explains the process from the ground up

it's called "The Elements of Computing Systems" by Noam Nisan and Shimon Schocken

[clever knot]

when you say build does this mean using "prebuilt" chips of sorts

[rose dock]

I'm pretty sure someone did that

[clever knot]

well i have seen this

https://www.youtube.com/watch?v=z71h9XZbAWY

[untold sapphire]

oh no things are much easier today. i mean in those days, they still used vacuum tubes rather than transistors

transistors are extremely tiny

vacuum tubes are huge and need to be cooled

[clever knot]

http://www.megaprocessor.com/

i guess he built his using transistors

[untold sapphire]

nice

lmfao

this is very funny

it's a bit insane to me that he built a foot long adder instead of using a 23 cent off-the-shelf adding circuit

that's like

a bridge too far for me

it's a question of understanding how it works tho like

i have no trouble understanding how I could personally build an adder for transistors so it's not "cheating" for me to replace it with an off the shelf part

[clever knot]

but certainly 1 could step through the entire thing

and understand it

[untold sapphire]

right

[clever knot]

it is just more so impratical

to actually physically build it

[untold sapphire]

i recommend starting with digital logic / Boolean logic. NAND gates, D flip flops and JK latches and shit like that

[clever knot]

hmm

started a class on that

don't know how indepth it actually will be though

[untold sapphire]

yeah it won't go too far but you'll learn how to store bits in memory (these are what flip flops and latches are for)

[untold sapphire]

and it's not too much harder than that to figure out how to access a specific memory bank and pull a specific bit from it (or write to it)

[untold sapphire]

read the elements of computing systems book it goes much further

[clever knot]

probably should

the book for this course is

Digital Systems: Principles & Applications (12thEd.) 2016Tocci, Widmer & Moss; Prentice Hall. (ISBN # 978-0134220130)

[untold sapphire]

see look at week 12

you learn RAM, that's not nothing

[clever knot]

guess we will see

guess you can only do so much in a semester anyways

[timid spindle]

[maiden lily]

@clever knot I’m taking an intro to vhdl class this semester

In fact I’m in it rn

[clever knot]

nice

[maiden lily]

Neat class so far

Are you doing vhdl too

[white cliff]

If i have a main function and another 2-3 more function, how can i compare these and find out which one is the closest (using math)

Cross correlation is one my option but i wanna hear others aswell

[leaden torrent]

which one is the closest to... what?

like you mean the "main function"?

i guess it depends how you define "closest", my gut instinct assuming theyre integrable would be to take the integral of the difference

like if your main function is $f$ and your other functions are $g_1, g_2, g_3$ then minimize[
\int_{\text{domain}} \abs{f(x) - g_i(x)} \dd{x}
] and the $g_i$ that makes this minimal is the ``closest" function

[fathom swallow]

Namington

[leaden torrent]

this isnt quite the same measure as cross correlation mind

but its a bit simpler

cross correlation more compares the "shape" of functions rather than the "distance" between them

its more sensible for most applications

but i cant tell exactly what youre after

[warm crypt]

anybody got any advice on how i can get better at math's because i have started to like it and try to become better but there are certain questions where i cant find the solutions to

[white cliff]

Hi thanks for the reply:

I am doing a Math paper on the Elo Rating System from chess,

I have the theoretical function that plots the expected score with respect to the differences in the player's rating. I am creating right now another 2-3 experimental function that have slightly different factors from the databases, and I want to analyze how the experimental is different from the theoretical function and perhaps see which experimental function is closest to the theoretical one

I think integration is very simple and acceptable and i will use it if i struggle to understand the mathematical concepts of more advanced areas

[leaden torrent]

well its very imperfect

like consider

is the blue function or the green function "closer to" the white function?

my simple integral would probably call the green function "closer"

er wait

no it wouldnt because i was smart enough to take absolute values

...

ignore me

[white cliff]

ok lol

[leaden torrent]

namington of 5 minutes ago is way smarter than namington of right now

[white cliff]

What are some other areas

Other than cross correlation

that u feel is fit-able according to what i want

[clever knot]

no just basic intro to circuit stuff and some digital electronics course but i started doing some googling and ended up hearing about vhd and it being used for i guess making processors...

[uncut socket]

I'm learning VHDL currently

[maiden lily]

Same

I took digital logic last fall

Microprocessors last spring

[uncut socket]

Assembly is horribly difficult

[maiden lily]

I did a little in microprocessors but yeah

Fuck that

[uncut socket]

I don't know what microprocessor you used but I used the Motorola 68HC11

[maiden lily]

I used the TI MSP430

Well the microcontroller

I’m taking advanced microprocessors this semester and we are working with the msp432

With this robot gadget kit for the lab

[uncut socket]

I'm still using the Motorola 68HC11

[maiden lily]

You are taking a second course for microprocessors?

[uncut socket]

Yes

Still equally as horrible

[maiden lily]

Lol

Did you have to do a final project

[uncut socket]

Just started the course

[maiden lily]

For the first one

[uncut socket]

I did the first one already, just started the second

[maiden lily]

I know

Did you have a final project for the first one

[uncut socket]

Nope, not at all

[maiden lily]

Oh

Not even for the lab

[uncut socket]

Nope, we were given labs and was told to code

[maiden lily]

Yeah same but we had to do a final project on the microcontroller at the end

[uncut socket]

Are you a computer engineer?

[maiden lily]

Yes

Wbu

[uncut socket]

Electrical Engineering

[maiden lily]

Oh nice

[mint patio]

ODEs are so boring

[neat lintel]

[bronze pelican]

We used an ODE to prove the fundamental theorem of curves today

[clever knot]

if you don't mind me asking

what is the fundamental theorem of a curve

[leaden torrent]

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

[bronze pelican]

well we did the 2d version

then its just determined by curvature

[neat lintel]

[crystal stone]

@velvet dagger So basically in Pure Math undergrad at UCLA, most people get shafted and only the top 1 or 2 students get attention from faculty

In applied math they have a lot of research opportunities, so the applied math undergrads usually do very well

[velvet dagger]

Hmm, that surprises me a bit given the size

[crystal stone]

Like my algebra prof richard elman said he only gives out one A+

And that's the only person he can write a good letter of rec for

He told one of my friends, who was basically a prodigy in math that he wasn't good enough because his final score was like 184/270. Some kid in the class got 268/270. Before our year, the highest anyone got on his final was 170/270 for nearly 3 and a half decades

That friend gave up on algebra, devoted himself to analysis and got 3 REU papers in analysis before graduating from UCLA, and got lots of attention from Tao and Garnett

Got into every PhD program he applied to

Meanwhile in the applied math side of things, they hand out research projects and get papers out like it's candy

But if you go there and you are one of the super-star students you will get a lot of attention

[velvet dagger]

I mean is Elman a special case? I know a current student who seems fine

[crystal stone]

It could be Elman was a special case

But I had him for 5 classes

As a transfer student, that kinda hurt me a lot since

Y'know I'm no super star

So maybe it's heavily skewed based on that experience, but my experiences with Garnett were much better

[velvet dagger]

Yeah I think you just got unlucky there then

[crystal stone]

I'd recommend students to go to UCLA for applied math

or even math of computation

[velvet dagger]

Gotcha

[crystal stone]

For pure math I hear UCSD does a wonderful job of mentoring students

Everyone I know that transferred there and tried

Did well

[narrow rock]

this is probably the case moonbears

there are several people who are not in the "top 2"

who are doing very well

[crystal stone]

It also didn't help that I just had a string of bad post doc teachers my first year

And I was too much of a brainlet for Burt Totaro, and Gangbo was just awful at course structuring

My second year was much, much better at UCLA tbh

I think if I had a third or fourth year there my opinion would have changed drastically

But I was too poor for that

[narrow rock]

UCLA is fine, transfers tend to have a hard time as they only get 2 years

so just one year before getting rec letters

instead of 3

[crystal stone]

yeah, exactly

I fought so hard to get an A+ in 115AH

[narrow rock]

A+s are hard to get

[crystal stone]

I got an A only

[narrow rock]

"only an A"

[crystal stone]

I mean, it's one of my few As at UCLA

[narrow rock]

an A is great!

[crystal stone]

Lots of +'s in the B range lol

lots of Bs as well

If I had to do it all again I think what I'd do differently is

Take 131AH in the winter quarter

Take 110AH in the first fall quarter

And still do 115AH

Maybe try to take 225A first quarter

[narrow rock]

[crystal stone]

Shoulda woulda coulda

[narrow rock]

I know a couple of transfers who had pretty good strats

one of them did the departmental scholars thing and stayed an extra year

another one just took a gap year

[crystal stone]

I think that was the right move to make

[narrow rock]

and audited classes

both of them got recs from totaro

[crystal stone]

One of my friends whos still there is taking 215 now

He just did an REU in comm alg.

[narrow rock]

with gieseker?

[crystal stone]

I think so

[narrow rock]

the gieseker scommalg summer reu is pretty common

[crystal stone]

Oh no, not the REU summer with Gieseker

[narrow rock]

a lot of people do it after the 110 series

[crystal stone]

He did one at a different university that was actually funded

[narrow rock]

ah

[crystal stone]

John did an REU with Gieseker on Analytic Number Theory

[narrow rock]

the ucla reu is funded

500

[crystal stone]

It is now

[narrow rock]

[crystal stone]

They didn't start that until 2018

And nobody told me during that summer when I was doing an independent study w/ Garnett

Fkin' Connie

[narrow rock]

they usually send out an email around march

[crystal stone]

Oh I applied for the math department job opening

At the administration level at UCLA

[narrow rock]

noice

[crystal stone]

The payscale looks ridiculous

[narrow rock]

how's the texas thing going

[crystal stone]

Ok moving to dms

[light needle]

@fast ivy so meromorphic functions are just holo maps to CP^1

but yeah it tells you that given input you can always get given outputs

by some mero function

[fast ivy]

does foster cover riemann existence theorem?

[light needle]

yeah he proves it with cohomology

[velvet dagger]

How far along are you in Forster?

[light needle]

first section in ch 2

i.e finished section 13

[velvet dagger]

So it'll take me maybe 20 minutes to catch up is what I'm thinking?

jkjk

[light needle]

might like the first ch is like

a lot of AT review

[fast ivy]

aight, I will start reading foster too,

along with the lecture notes

[velvet dagger]

Forster reading group let's go

[light needle]

nice kek

[velvet dagger]

This time I'm gonna take it actually seriously

I need to learn something

[fast ivy]

I will read this first chapter this week

And I if I have any questions I will prolly ask here lol

but yeah, it looks like a big review of the theory of fundamental groups and covering spaces

[light needle]

yeah kinda, altho the sheaf stuff was somewhat new to me

[blazing pawn]

are the last 3 sections just riemann hilbert

[light needle]

i skipped section 11, but 9 and 10 are just defining differential forms and stuff

[velvet dagger]

Honestly can't hurt for me lol I am rusty on some deets on pi_1 and covering spaces

But yeah def soonish I'll be good with this material

And can catch up

[untold sapphire]

i'm in for the reading group on forster please tell me if there's a meeting plan

ping me

[atomic coral]

anyone doing aerospace engineering, and if so any tips for someone who is going into that path through the electrical engineering side pleading_face

🥺

[sharp hill]

Im doing aero engineering - or it's mechanical engineering with concentration in aerospace

[atomic coral]

are u a graduate?

[sharp hill]

undergrad

[atomic coral]

oh nice

wait how does concentrating in aerospace work

do u focus ur classes on

[sharp hill]

I have a close friend in EE grad school ,he says theres two main pathways: building circuits of actual computers or doing the E&M work of electronics

concenctration really just means "on top of"

so its ME with aerospace classses thrown in

[atomic coral]

oh danngggg

oh that does make sense

im a first year in electrical and i am a little unclear on the direction ill be taking

but taking aerospace classes is definitely something i plan on doing after covering my ge

do u have any tips - types of programs to join/ labs

[sharp hill]

You should change majors to aerospace then if possible

[atomic coral]

anything of that sort?

well i was going to, however when it comes to job search i was told itd b too focused of a major

and doing electrical/mechanical would give me room but also present me as one with a more rounded knowledge over specifically aerospace

[sharp hill]

I would explore your colleges clubs/projects, some may offer projects covering aerospace topics. For example my college offers a drone building club where you quite literally build a drone from scratch that competes against other schools. Another project is building a sattelite to launch into space, among many others

[atomic coral]

despite there being subcats within aero

[sharp hill]

see if your college has any of these types of projects within it's college of engineering

[sharp hill]

this is true, mechanical has the most "leeway", aerospace engineering will help you most get a job in aerospace (espeically airlines), electrical engineering is mainly building circuits OR programming

so if you wanna be the guy to code AI, or to build an RTX 3090 card with resistors, transisitors, semi conductors, etc, that is EE

[atomic coral]

oh that makes sense, that helps a lot honestly

i didnt rllt even know what to look for

tysm <33

and yes i was warned abt that - lucky early

[atomic coral]

yuhs 🥺🥺🥺 das actually sick so its def some im not opposed to studying

[sharp hill]

You have until your sophomore year to really decide, freshman year is mainly full of GE

[sharp hill]

yeah EE is the furthest from aero, unless you wanna like program the planes sensors etc. But EE doesn't design the plane, that is ME or Aero engineer

[atomic coral]

wait so when u say program, would that be the inner functions of a plan rather than the design of them and things of that sort

cries in lack of understanding

[sharp hill]

programming = coding

the literal if{}, then{} statements

like java, c, python, matlab, etc

[atomic coral]

ahhh yes makes sense . . .

[sharp hill]

good good, if you have any more questions about literally anyting in college just ping me

[atomic coral]

tysmmm!! can i friend u so i remember ur @

it was rlly nice talking, ill def come to ask for advice further along the line

[sharp hill]

Yeah for sure! I'll friend you as well

It was a pleasure, feel free to ask anything anytime

[atomic coral]

tysm 🥺 <3333333 too kind tt

[stone valve]

can someone explain why my answers are wrong

[brave hollow]

the wording is weird but apparently the week just started

and after he is done with the day

he just throws away the shirt and tie

in a pile

[stone valve]

its very weird

[brave hollow]

so you won't have that shirt ever again in that week

your choice of shirts decreases every day

also did discord change font?

[stone valve]

probably

i dislike it

i miss the old retro

[brave hollow]

this is fucking ugly man

[stone valve]

IKR

anyways can u explain a bit more

[brave hollow]

I thought I messed up zoom or something

sure I won't talk about the solution but the problem is literally saying that this guy is lazy so he does laundry at the end of his week he has 5 shirts and 5 ties with (shirt-tie) matching pairs, he goes to work and chooses a random shirt and a random tie and when he returns he throws it away in laundry pile, so next day he has 4 shirts and 4 ties to randomly choose from

[stone valve]

but doesn't part a

start out

fresh in the week

[brave hollow]

yeah

[stone valve]

oh wait

[brave hollow]

there's multiple possible pairs

[stone valve]

but they don't deepend on each other do they

[brave hollow]

you only considered 1

if you are confused about the solution and not the actual problem #❓how-to-get-help is better suited

[mild nebula]

Throw this in #help-6 we'll solve it up

[stone valve]

ok

[untold sapphire]

electrical engineering is a rich source of interesting problems for mathematics.

i would say that this is its primary value.

[neat lintel]

#❓how-to-get-help

[latent forge]

How do you get into these engineering fields as an ameture?

[untold sapphire]

Breadboarding is an easy way to start off with digital engineering.

If you want to make more advanced stuff, you'll have to read more and learn more

for example you could learn to make a PID controller and program it to control a very fine tuned physical movement

https://youtu.be/JFTJ2SS4xyA

i just found this guy from a random youtube search but there's a million amateurs online posting their constructions.

I recommend reading about signal processing and linear signals and systems as soon as you have the calculus background to understand it

[latent forge]

Ok thanks. I always felt that engineering was one of the topics thst needs lots of preparation

[untold sapphire]

there is a lot of advanced mathematics under the hood but you can get away with just learning the formulas and how to apply them in a lot of situations.

the important thing is to start getting hands on experience and playing with stuff

i think control theory is quite beautiful.

it's about applying the Laplace transform to study linear differential equations and use this to design feedback loops that cause a system to stabilize around a steady operating point

[thorn brook]

yooooo the seminar is fricking dope

it will be chill, no homework or nothing. The guy has also read Hatcher and he will be talking about algtop from a cat view there too

I'm so fricking hyped lesssgoooo

[fringe needle]

Sounds cool

[thorn brook]

yeeee it does

[odd narwhal]

there was a seminar this semester on higher homotopy theory

but I didn't have the prereq knowledge to go so I missed it

big oof

category theory and higher homotopy theory I think

[vale dawn]

hey can anyone tell what we do
after studying differential equations
like in high schools the last topic of calculus is differntiatial equation so what we do next if we have interest in calculus and want to study it deeper.

[fast ivy]

Real Analysis maybe?

But it really depends on what your interest in mathematics is.

In general

There's no such clear path

Of course you need to study some basic stuff to have the needed knowledge to advance

But you kind of make your own path in general

In general, people either take a real analysis course, linear algebra/abstract algebra course, basic point-set topology, complex analysis

These are all good starts

At least in my biased view

[magic meadow]

I'm not sure you actually study differential equations In high-school as in ODE's

[vale dawn]

yes bro there is a chapter named differntiatial equation in high school syllabus

in our school syllabus

[magic meadow]

Hmm OK interesting, thing is what did you like about calculus?@vale dawn

Was it the application, theory or proofs?

That will say alot about what type of math you enjoy

[vale dawn]

i think its a different field and a different
algebra is just a basic thing which we use in our daily life but calculus for me is an abstract like thing and it is also used in my favourite subject physics .

[magic meadow]

Makes sense

[frail lagoon]

you can also definitely learn much more about ODEs if you are so inclined, if it's anything like what we have in the uk

[vale dawn]

ya ur education system is much different from ours

[frail lagoon]

oh lol

[magic meadow]

Calculus is a great subject, because its not too abstract and not to hard to apply

But not all subjects are like that

[vale dawn]

i also want to learn because i want to learn physics of higher level which includes 80 prcnt calculus

[magic meadow]

Ok then you definitely need to learn differential equations

[frail lagoon]

for physics-related stuff, looking at linear algebra and more on differential equations would be a good idea

doing linear algebra opens up more on systems of differential equations for example and helps you generalise a lot of the ideas

[magic meadow]

Yup ^

[vale dawn]

specially that integral sign gives an awesome feel while making it

[magic meadow]

Lool🤣

[odd narwhal]

also vector calc

[frail lagoon]

yup

[magic meadow]

^

[odd narwhal]

linalg is also crucial to quantum

[frail lagoon]

lol just describing first year physics maths xd

oh yeah i mean it's crucial for most physics i guess

[vale dawn]

this is also in our highschool syllabus

[magic meadow]

Huh

What high-school do you go to🤣

[frail lagoon]

do you know gauss' theorem?

[vale dawn]

ya solving schrondiger equation for hydrogen like species
is using just maths like
Fourier transformation
lengendree polynomial
dirac delta notation
linear algebra
pde
etc......

[frail lagoon]

that feels like the maths behind undergraduate physics in a nutshell up to GR lol

[magic meadow]

Well anyways I'm sure physics students study real analysis anyways

So that's a good idea also

[vale dawn]

i dont know much about calculus just starting it

[frail lagoon]

lol in uk idk a single physics course that does real analysis

[magic meadow]

Oh..

[frail lagoon]

wait that means you haven't done vector calculus then lol if you haven't done much calculus

so yeah that's useful to learn too afterwards

[vale dawn]

just knowing basic formula using in kinematics 1d
now learning calculus for mathe

[magic meadow]

Differential equations in high-school don't always mean the same thing as ODEs e.t.c

Btw

[vale dawn]

i think ur saying right differntiatial equation are of different types maybe there is an easy one

but calculus is very interesting to explore because after highschool there are many topics to study like
multi variable calculus
PDE
complex calculus
etc .........

[magic meadow]

Ye

[vale dawn]

don't know why it feels very cool to study specially integration

gives the felling of real mathematics
and some more topics like complex no

[magic meadow]

Lol that's cool I didn't think it was that cool to study maths in hs

Haha

You need a good grounding in Calculus

[vale dawn]

basically linear algebra is about???

i dont know much about it

[pale orchid]

adding

[magic meadow]

Well oversimplified I guess

[odd narwhal]

and stretching

but that description isn't very descriptive

[magic meadow]

Deals with vectors

Also

[odd narwhal]

using 'vectors' with someone not very familiar with maths can be a bit misleading since people usually learn vectors are arrows in space

[vale dawn]

seeing the theorem it looks like matrix

[odd narwhal]

as in maths that's a much broader notion

matrices are one thing linear algebra deals with

[vale dawn]

lol we know vectors only this much a symbol with arrow is vector

[odd narwhal]

I don't think i've ever used an arrow symbol for a vector

and I refuse to ever do that

[neat lintel]

$\vec{f}$

[fathom swallow]

TTerra

[vale dawn]

thats necessary in physics
i studied it for 2d kinematics

[vale dawn]

first i thought it was a chapter of physics and used in it
then saw it in the maths syllabus

[odd narwhal]

it's really not necessary lol

it's just notation

[frail lagoon]

for physics i do not use arrow symbols lol

[toxic schooner]

all the physics we do uses an arrow for vectors

[odd narwhal]

gross

[toxic schooner]

in legit everything lmao

[neat lintel]

writing arrows gets tedious very quickly

[odd narwhal]

^

also time consuming when handwriting

[toxic schooner]

agreed

[odd narwhal]

most I do is an overbar but that's usually for elements of a sequence/product space

[frail lagoon]

just don't even underline/arrow them

[vale dawn]

everywhere we see arrows and arrows

[frail lagoon]

no need

[pale orchid]

we were required to underline and use squiggly lines here

pain in the ass

[vagrant kestrel]

just use certain letters for vectors omg

[vale dawn]

i just used in physics
now when i will use it in maths

i have a question
if anybody know any trick for solving those annoying trignometry proof questions.

[pale orchid]

$\underline{x}, ,, \underset{\sim}{A}$

[toxic schooner]

i have been trying to find that out myself

to no success

[fathom swallow]

Ebullient Descent of Daedalus ✓

[pale orchid]

that was painful, but there

[vale dawn]

ya thats a mystery for all of us thise are the most annoying trignometry question i have ever seen

its not pain in ass
its lava in your ass

[last oxide]

until meme geometers make them arrows in space again, except those arrows are derivations

[burnt dune]

@forest jackal hey sorry for the ping but can i ask a question? related to what you helped me with yesterday

the vitali theorem?

idk why the lebe measure is regular

if i know this then im done i understand the proof

[forest jackal]

it's a standard result, it will definitely be in your notes/book.

[burnt dune]

i cant seem to find it 😢

okay i will just google it then i didnt know it was important

[forest jackal]

what is your book?

[burnt dune]

papa rudin

i think he does this

mid proof

of the reizs

and i checked out another proof from another source

why does wikipedia have no proof*

[forest jackal]

The Lebesgue measure is introduced in Thm 2.20 of Rudin, and regularity is stated in property (b).

[burnt dune]

yea i couldnt follow much of this theorem

[forest jackal]

Because wikipedia is not a comprehensive textbook, plenty of things on it do not have proofs written there.

[burnt dune]

so i tried to read it out of royden

or the proof

okay maybe i will try again

[forest jackal]

regularity will be in royden too, any decent book will state it, as it is quite an important property.

[burnt dune]

whats with 2^-n in ?

is this an important idea too?

doing things with 2^-n idk i see it evrery major theorem proof

[forest jackal]

Royden section 2.4 is entirely about regularity of the Lebesgue measure for example.

well the point is in measure hteory we often build sets up as countable unions

if you are adding countably many errors together, you can't just take them smaller than epsilon and hope they converge

instead you take the k-th one to be smaller than epsilon/2^k, and then the sum of all the errors is going to be < epsilon

its important in a different way. one is a common technique in analysis proofs that is particularly useful in measure theory, the other is a fundamental property of the Lebesgue measure (and one that "decent" measures on general topological spaces should have).

[velvet dagger]

Alright you fucks

Time to join voice

https://arxiv.org/abs/2108.03750

We're going through p-adic Kakeya conjecture

[burnt dune]

you mean regularity here

the fundamental property

right?

[forest jackal]

yes

[burnt dune]

so like

lebesgue measure is a way we like

talk about measurable sets close to like open and closed compact stuff?

like approximationm

?

[forest jackal]

I don't understand the question in that sentence.

[burnt dune]

like is regularity why we can approximate some sets

with closed and ope nsets

some measurable sets*

[forest jackal]

yes, that is what regularity is.

[burnt dune]

okaay

i am going to try reading the proof for regularity from rudin

thank youu

[forest jackal]

👍

[burnt dune]

why is this functional the riemann integral

P_ns are the set of all xs with coordinates integer multiples of 2^-n

so f is uniformly continuous cuz of some theorem in chap 4 and then

you get that the sequence for f converges

now i dont see this remark its like suddenly this is the riemann integral idk how

[forest jackal]

Pretty much directly by it's definition. But no facts about it being the Riemann integral are being used subsequently, so there is no reason to get caught up on this.

[burnt dune]

okay good

[neat lintel]

does anyone here know game parity?

[neat lintel]

#❓how-to-get-help

[forest pawn]

I'm going to read baby Rudin

[neat lintel]

[mild nebula]

That book's gonna end this whole man's career

[forest pawn]

The first chapter of papa Rudin is possibly comprehendible

[mild nebula]

Jk it's definitely possible to read but a big shock for people who aren't used to the speed

[forest pawn]

I'm reading the first one

[vale dawn]

the every topics we study in which real no or variables are involved is real analysis or something different??

[surreal sapphire]

what

[fast ivy]

Idk

Is real algebraic geometry part of real analysis?

[leaden skiff]

it's not "why is it"

it's "is it that"

[odd narwhal]

only over R

[leaden skiff]

he's asking if stuff that just uses real numbers or variable is called real anal

i think

[leaden skiff]

wtf does this mean

[fast ivy]

[surreal sapphire]

real analysis is the study of functions that only differ by sets of measure zero

[fast ivy]

I think if he's asking if every field that deals with real numbers and real variables is called real analysis.

In that case, no.

[leaden skiff]

what if you have real analysis

but instead of studying R

you study R+i

or what if you study R*i 👀

imaginary analysis

[fast ivy]

And what about R[i]/(i^2+1) ?

What would that be?

[leaden skiff]

i always forget what that notaton means

what's R[a]/b

[fast ivy]

R[i] is a bad notation for R[x] which is the ring of one variable polynomials with real coefficients

(i^2+1) is the ideal generated by the polynomial i^2+1 in the ring R[i]

And the quotient R[i]/(i^2+1) is exactly the set of complex numbers

[leaden skiff]

i need to learn what ideals are

like understand them and not just get a definition i forget after an hour

[jovial ember]

They’re just stuff you quotient by

[leaden skiff]

yeah i don't get what quotienting is

[jovial ember]

It’s like a normal subgroup

Oh

[leaden skiff]

yeah i mean like i need to learn group theory lol

[jovial ember]

Well idk then you just need to spend more time with the stuff

[fast ivy]

Are you familiar with equivalence relations?

[leaden skiff]

yeah

oh i know you can divide by an equivelance relation

[deep mango]

Quotient = smush stuff together in a nice way

[leaden skiff]

is this like that?

[deep mango]

Yes

[fast ivy]

Yup

[deep mango]

Just like that

[leaden skiff]

wait really? how?

[fast ivy]

Yeah so

In the case of algebraic structures

[deep mango]

The question is just what the relation is

[leaden skiff]

x^2+1 isn't a relation

is it?

[deep mango]

Well, it gives one

By taking mod that

[fast ivy]

We don't quotient out by "bad behaved" equivalence relations, because we want the sets we are taking the quotient to still be an algebraic structure of the same "kind" after we impose this relation.

So for example

In group theory

The "right" way to quotient groups by

Is by normal subgroups

Because we can be sure

That after taking the quotient of this equivalence relation

We still get a group

In the case of rings and ideals too

The quotient has still a nice ring structure

Ninja, are you familiar with vector spaces?

[leaden skiff]

nope. not at all

[fast ivy]

I think quotient vector spaces are the easiest example.

[leaden skiff]

i think i just don't have enough pre req knowledge of algebra tbh

[fast ivy]

Ok, how would I say that in a grammatically correct way?

Or does that make any sense at all?

Lmao

[leaden skiff]

like i'm learning a lil group theory

and i just now got to normal subgroups

and i don't understand them really

it's a weird definition

[fast ivy]

Just think about them in the sense that

If we have a group G

And a subgroup H

[fringe needle]

i like to think of normal subgroups as a sort of pivot

[fast ivy]

We want to impose an equivalence relation in the following manner

[fringe needle]

a group is normal if it is equal to its conjugate for every g in G

so if you think of each g in G as "permuting" G by conjugation (in fact they act as automorphisms of G), the normal subgroups are the only invariant ones

[leaden skiff]

my problem is conjugation doesn't make any sense lol. feels like such a random definition

[fringe needle]

they are in some sense pivots of this rearrangement of elements of G

and quotienting by them gives you all the different ways in which we can pivot around the normal subgroup

[surreal sapphire]

the way normal subgroups were introduced to me is you want to define a group operation on cosets

[fringe needle]

conjugation is important because it is analogous to a change of basis in a vector space

[surreal sapphire]

there is really only one way to do that

and it only works if the subgroup was normal

[fringe needle]

by cayley's theorem every group is in fact a permutation group, and conjugating on a group is like changing the labelling of the set {1,...,n} that our group acts on

[leaden skiff]

yeah it did remind me of that. but i don't get the connection. probably just need to spend more time learning tbh

i thought it said every group is a subgroup of a permutation group?

[fringe needle]

every group is a subgroup of S_n

[fast ivy]

$\forall g,g' \in G, g \sim_{H} g' \iff g'
\cdot g^{-1} \in H$ where $\cdot$ is the group operation on $G$.
\
\
And with this equivalence relation in mind, we also want the following properties to hold:
\
\
We want $G/H$ to still be a group under the operation $\ast$ that satisfies $[g] \ast [g'] = [ g \cdot g']$.
\
\
And we also want that the following map:
\begin{align*}
\pi : G & \rightarrow G / H \
g \mapsto [g]
\end{align*}
To be a homomorphism of groups

[fringe needle]

a subgroup of S_n by definition is a permutation group

[fast ivy]

Hmmm bad typing lol

[fringe needle]

yes it's also nice to think of normal subgroups in terms of homomorphisms

[fast ivy]

Dammnit

[fringe needle]

in particular, every homomorphism from G to H induces a normal subgroup by its kernel

[fathom swallow]

MisterSystem

[fast ivy]

I think this is better now

[vale dawn]

real anal war

[fast ivy]

Yeah, the idea is that normal subgroups satisfy all these properties

And this is like

What we want from a quotient group to have

[g] • [g'] = [g • g'] is the most natural operation you could ask for

And with normal subgroups

You can do this and everything is well defined

[fringe needle]

to understand the use of a normal subgroup in a way you sort of have to first understand the use of a quotient group

if you know why a quotient group is useful, and what it represents, then you should see why a normal subgroup is useful

by what MisterSystem just said

[fast ivy]

I also had a bad time understanding its importance

Number theory helped me a bit with it

[leaden skiff]

i think i just need to learn more. cause this means very little to me

[fast ivy]

Because of Z/nZ

[fringe needle]

do you know what a quotient group represents

and why it's useful

[leaden skiff]

no i don't

[fringe needle]

then yeah maybe spend more time on it

examples always help, as MisterSystem pointed out Z/nZ is a great example

[fast ivy]

Have you seen modular arithmetic?

In the most basic sense

It identify integers up to how they behave under divisibility by n

If they leave the same remainder under division by n

Then we want them to be "the same"

We formalize this by imposing an equivalence relation

The nice thing is that you can still do arithmetic

Even under this equivalence relation

[leaden skiff]

yeah i know it

[fast ivy]

The idea is the same

But for general groups/rings/modules/vector spaces...

[leaden skiff]

is that what Z/nZ is?

[fast ivy]

Any algebraic structure that you are interested in

[leaden skiff]

Z_n?

[fringe needle]

looking at a quotient group in a sence is changing the resolution of our original gorup

[fast ivy]

Yup

The ring of integers modulo n

[fringe needle]

by looking at different resolutions of your group, you gain a lot of insight on its structure

[fast ivy]

The / makes it clear that we are taking a quotient

[fringe needle]

and since its quotient group may be simpler to study, it's always a good idea to look at it

where subgroups correspond to zooming into your group, quotients correspond to changing the lens with which you study the group

or projecting your group

[fast ivy]

Yeah, in a sense we are studying our group up to how they behave with respect to H

[fringe needle]

for example when you look at solvable groups, just figuring out that N and G/N are solvable tells you that G is solvable

[fast ivy]

In mathematics it is very common of you to hear "yeah consider ... up to some relation" or "this holds modulo something else"

[fringe needle]

so just by looking at G at a different resolution and the lens that changes that resolution, you get a whole lot of insight on the structure of G

[fringe needle]

a simple example of this in group theory is that we really only study groups up to isomorphism

and the relation of being isomorphic is an equivalence relation

like when working with numbers, you dont bother saying if what you're counting is apples or oranges

so in a sense as long as the number represents the same quantity, it is the same, even if they may be attached to different dimensions

this is a lot less true when working in physics

it's instructive to know that in the early days of mathematics numbers came with dimensions

you never worked with a length and the square of a length (an area) at the same time

and the only dimensionless quantities were ratios

[leaden skiff]

is there any like mathematical analysis of units and dimensions?

[fringe needle]

i dont think it's a field in itself but dimensional analysis is definitely a tool

[leaden skiff]

it feels like something someone would have studied lol. like relationships between different kinds of units or something

[leaden torrent]

units are defined precisely and very well understood

so im not sure quite what you mean

one could argue a lot of computational physics (e.g. intro kinematics) is just "relationships between different kinds of units"

[quiet geode]

This one? https://youtu.be/fo-alw2q-BU

[neat lintel]

"differential geometry is the study of topological manifolds"

[vivid halo]

pain

[leaden torrent]

topology is the study of general topological spaces which in practice are almost always spheres

[vivid halo]

how to learn pure mathematics on your own: a complete self-study guide (2913 hours of content)

[neat lintel]

insert one of those /sci/ reading guides

[vivid halo]

video 872: in this video we'll give some basic pointers about how to learn about equivariant derived categories; the next 8 videos will be about Springer theory

[leaden torrent]

topology: corners suck since now i have to do homology
analysis: corners rock since now i have less work to do

[vivid halo]

manifolds with corners

[leaden torrent]

exactly

[neat lintel]

they don't exist they don't exist they don't exist they don't exist they don't exist they don't exist

[blazing pawn]

if math isnt real please explain the incredibly success of mathematics in convergently evolving to S^n

Spheres are the crabs of math

[vivid halo]

thinking about the hell of defining conically stratified smooth manifolds

[leaden torrent]

i am convinced that no one really understands the visual intuition for gluing outside of trivial examples

they just collectively convince themselves that it makes sense

and that everyone else can visualize it so they have to to

as soon as we get past gluing cw complexes to wreaths of circles i'm fucked

[blazing pawn]

of sheaves?

Hurb

[leaden torrent]

this includes hatcher, there was lead in his water supply when he wrote his alg top book

[vivid halo]

how it started: vector fields on manifolds, actual geometry
how it's going: there are exactly 2880 different ways to map S^14 into S^4 up to deformation

[long epoch]

YHH, damn it was unlisted

[blazing pawn]

Nami what do you mean by gluing in this context

[leaden torrent]

quotients of topological spaces

[blazing pawn]

Oh

You just take the thing and you smack it on the other thing until they are one thing

[leaden torrent]

i know how its supposed to work and i can visualize all the examples from an intro course

but anything beyond that

???

[blazing pawn]

What even is the wreath of circles

[fast ivy]

I am having a hard time vizualizing quotient of sheaves :/

[leaden torrent]

moth have you never seen how cw complexes of genus g are constructed from a bunch of circles

take a "bundle" of 4g circles and glue a disc to them

[blazing pawn]

Oh is that called the wreath of circles

Yea ive seen the construction

[leaden torrent]

sometimes its called bouquet or whatever

or a rose

[blazing pawn]

isnt that just

the wedge sum of n circles

[leaden torrent]

sure

i dont care what the fuck you call it

you could call it The n-th Cotton Eye Joe Space

[blazing pawn]

im confused u can visualize gluing arbitrary CW complexes but not the wedge of n circles?

its just like. n circles connected at a point

[leaden torrent]

no

my point is that

i can visualize that stuff

and using that to construct cw complexes

but anything beyond that is ???

[blazing pawn]

Oh shit i see

you meant gluing complex onto them

[leaden torrent]

oh yeah i dont mean the construction of the bouquet itself lmao

i mean uhh

i have had a crippling fear of water droplets since i was a child

anything in that shape induces immediate panic in me

and so i have never been able to visualize a wedge sum of anything.

[blazing pawn]

Relatable content

[deep mango]

[blazing pawn]

rylatable content

[deep mango]

💦

[leaden torrent]

i accidentally sprayed my family dog with a hose once and ever since she was afraid of long green (or red) things

like we had a dark green ladder and she'd run from it

[deep mango]

Water droplets make namington sweat... But sweat creates water droplets...

[blazing pawn]

Its a vicious cycle

[leaden torrent]

🕷️

i wonder whether this emoji style can actually trigger peoples phobias

or if its too "cartoon-ified"

[neat lintel]

light mode users are the only one who could actually see that emoji and light mode users aren't afraid of anything

[leaden torrent]

🐍

why does this snake feel like its sassing me

[deep mango]

👨‍🏫

🦧

[leaden torrent]

[deep mango]

🤹‍♀️

[leaden torrent]

[vestal river]

[vagrant kestrel]

👯‍♂️

[leaden torrent]

Man in person classes is making my feet hurt so much

I didn't realize how underused they were during online learning

I'm not even taking proper classes, I'd hate to be a student walking around campus

[cold needle]

my feet hurt for the first week

and then they got better and now i am professional walker

i must learn more from the olympics speedwalking competition.

[summer nest]

Are bicycles allowed in your college?

[cold needle]

in mine they are

idk about namington

probably yes also

it would be weird otherwise

[summer nest]

Nice

[odd narwhal]

why would they not be

literally no good reason to ban bikes

[odd narwhal]

why is edd muted?

[summer nest]

I don't think bikes are allowed or even usable in our college

[vagrant kestrel]

he replied to someone without consent

[deep mango]

<@&268886789983436800>

[blazing pawn]

Hurb

[slim meadow]

what does hurb mean?

[stable oar]

i think it's like "bruh" but backwards

[blazing pawn]

Hurb

[bronze pelican]

Has anyone used a lightning bolt as a mathematical symbol?

[stable oar]

yeah, sometimes used as a "contradiction" symbol

[valid crystal]

i use it as a way to show harry potter fanboyism

[ember finch]

I think bourbaki uses a lightning bolt like thing to signify a hard section

[fast ivy]

You mean this?

[terse flax]

Z

[ember finch]

Yeah

[vale dawn]

why do we use Fourier transforms

[mild nebula]

Because there wasn't enough transforms before

[vale dawn]

nicely explained beyond mamths explaimnation

[mild nebula]

Actually though we use fourier transforms to do useful things. I could give some examples, but that won't convey what the transform actually is

Are you seeing an application of it in class?

[fast ivy]

They sort of where introduced historically to be a useful tool

Iirc

They emerged from a work related to the heat equation

[leaden torrent]

i argue fourier transforms are the only useful part of mathematics

everything else is useless

but fourier transforms are OP

[fast ivy]

The heat equation is just one of the many examples of applications of Fourier Analysis tho

[fast ivy]

[odd narwhal]

@light needle does DS stand for determined by spectrum by any chance?

[light needle]

nope

[odd narwhal]

What is it then

[light needle]

oh i went by John Doe Smith

and ppl called me JohnDS

so im JohnDS now

[odd narwhal]

Ah lol

[last oxide]

obv cause john is a nintendo fanboy

[chilly smelt]

Only losers put big math words or mathematicians in their name

[rose dock]

John DeeznutSacks

[terse flax]

boink

cone boink

[limber perch]

Jonathan Dee Snuts

[timid spindle]

hahah bonk

how did you make it?

damn you gonna be a good animator

[vale dawn]

https://c.tenor.com/R7ccqqtOlmYAAAAM/bonk.gif

well i didn't get the answer
what is real anal(ysis)

[vale dawn]

omk thamks

so the chapters here most are from real Analysis
Chapter 1 Sets
Chapter 2 Relations and Functions
Chapter 3 Trigonometric Functions
Chapter 4 Principle of Mathematical Induction
Chapter 5 Complex Numbers and Quadratic Equations
Chapter 6 Linear Inequalities
Chapter 7 Permutation and Combinations
Chapter 8 Binomial Theorem
Chapter 9 Sequences and Series
Chapter 10 Straight Lines Exercise
Chapter 11 Conic Sections
Chapter 12 Introduction to Three Dimensional Geometry
Chapter 13 Limits and Derivatives
Chapter 14 Mathematical Reasoning
Chapter 15 Statistics
Chapter 16 Probability

[surreal sapphire]

this looks more like a general intro to mathematics

[fast ivy]

Do you know about calculus yet?

[fringe needle]

what's "mathematical reasoning"

[fast ivy]

Real analysis is basically a rigorous study of functions $f : \mathcal{U} \subset \mathbb{R}^{n} \mapsto \mathbb{R}^{m}$ and as in calculus, we usually study properties of such functions as continuity, differentiability, analytic functions, integration (Riemann-Stieljes, Lebesgue and etc...)

[fathom swallow]

MisterSystem

[fast ivy]

I suppose like

Intro to proofs ?

[light needle]

doesnt work in math either

[fast ivy]

I have no idea if Gromov actually said that

But I find this funny af lmao

[nimble shuttle]

I like the omission of "splendid" in those memes

even though it would make more sense

[leaden skiff]

isn't this 10th grade cbse

no im pretty sure i had those exact chapters in 10th grade

wait no maybe 11th?

[leaden torrent]

That course layout is strange in any case

[leaden skiff]

yeah im dumb it's 11th

why's it strange?

it's like a mix of a bunch of different elementary topics

[neat lintel]

think so

[leaden torrent]

Its a "real analysis" course that does analysis for all of 1/16th

[leaden skiff]

that's not real analysis is it?

[leaden torrent]

Ie its title is just... Wrong

And no self respecting analysis course would introduce trig functions before calculus

[leaden skiff]

wdym mean by

so the chapters here most are from real Analysis

I learned those exact chapters in school lol. like in that order and with those names

so i don't think it's anal

[neat lintel]

same

[leaden torrent]

Yeh I would never call that an analysis course.

[neat lintel]

not even analysis

[leaden torrent]

It also just seems way more elementary

An entire chapter on "linear inequalities" lmao

[neat lintel]

that list of chapters is so sulliable tbh

[leaden torrent]

Linear inequalities are just linear equations with 1 extra rule

[leaden skiff]

well they're a lil bit more complex than that

[leaden torrent]

Well you introduce them as solutions to quadratics

And (handwavingly) note that C solved all polynomials whereas R doesn't

That's sensible if weirdly paced

It's how a reasonable complex analysis course does it

[leaden skiff]

this is what i was talking about

this was my 11th grade syllabus

[leaden torrent]

"we know going from Q to R lets us solve more polynomials, like x^2 = 2. Turns out going from R to C lets us solve even more, like x^2 = -2. As we will see later in this course, this is 'enough'; all polynomials in C can be solved in C"

Voila, there's your day 0 complex analysis motivation for C

[leaden skiff]

what about polynomials with quaternion coefficients

[leaden torrent]

Now note "constructing C is just matter of affixing an element i to R obeying i^2 = -1 and letting it obey all the other algebraic rules, like distributivity"

Voila

You can be more explicit and expand (a+bi)(c+di) or whatever

But that's the conceptual guide for complex numbers

(also cover polar form ofc)

[leaden skiff]

imo you need to teach the complex plane and not just use the vague algebraic explanation

[leaden skiff]

polar form isn't given the attention it deserves 😔

[leaden torrent]

Well sure, note that you can write complex numbers in the form a+bi for real a, b and then just represent that as an ordered pair (a, b)

[leaden skiff]

not in HS anyway

[leaden torrent]

And this motivates polar form

What attention does it deserve?

It's mostly a good visualization tool

[leaden skiff]

well i mean like complex numbers feel much more natural in polar form than the standard form

it's almost like that's how they're meant to exist

[surreal sapphire]

historically it gave "philosophical justification"

[leaden skiff]

it also makes it more clear why complex numbers are worth studying

they model rotation and oscillation really well

[leaden torrent]

Somehow I think modern students relate more to polynomials being solvable than exp being entire

But maybe that's just me

[leaden skiff]

well personally for me it didn't click until i understood how they worked in polar form. since that's where the intuition for multiplication and exponentiation is

and square roots. and basically everything else

[leaden torrent]

I mean I definitely think the "add the angles, multiply the magnitudes" slogan should be given

And it's clear from polar form and Euler's formula why that holds

[leaden skiff]

yeah, at least in my school that was glossed over

[leaden torrent]

But in fairness, proving Euler's formula isn't super easy

You could just define the complex exponential by it

And prove it agrees with the real exponential via trig identities

[leaden skiff]

you can give the intuitive explanation using derivatives

[leaden torrent]

This is elementary but tedious and not particularly insightful

[leaden skiff]

but at that point students havent learned differentiation

[leaden skiff]

also euler's formula specifically isn't necessary
I just want polar form to be given more importance and not just treated as a side thing you can use sometimes

[leaden torrent]

Wait how are you computing polar forms then

Without Euler's formula

[leaden skiff]

cos(x) + isin(x)

you can prove that via trig

[leaden torrent]

That's... Euler's formula

[leaden skiff]

you don't need to know that it's e^i*pi

[leaden torrent]

but that's the form you end up with?

[leaden skiff]

yeah

[leaden torrent]

What is polar form if not re^itheta

[leaden skiff]

i just meant you don't have to teach euler's formula specifically. and can just keep it with trig

and not bring in complex exponentiation

not until they learn calc anyway

[fast ivy]

Teach kids complex numbers via 2 × 2 matrices

[leaden torrent]

Teach it via group actions on roots of unity

Trust me this makes total sense

And isn't at all contrived

[fast ivy]

[last oxide]

complex numbers through algebraic closure

[leaden skiff]

teach it through solutions of certain cubics

since those are ones that have historically needed complex numbers to make sense

[leaden torrent]

This is what I recommend for mathematically mature students

It's both the historical and modern motivation

Besides dumb signal/wave stuff that uses C as R^2 in a fancy hat

[last oxide]

when will I be mathematically mature namington

[fast ivy]

DN theory

[last oxide]

only when you master original jokes

[leaden skiff]

that was candice

[last oxide]

then you got me

[fast ivy]

Deductive-nomological model

[leaden skiff]

Dr candice dick-fit-in-your-mouth PhD

[last oxide]

isnt nomenological a kantian term

[velvet dagger]

Lol what have I set off on this server

Actually I blame Chmonkey

[light needle]

I blame u

[fast ivy]

https://en.wikipedia.org/wiki/Deductive-nomological_model#:~:text=The DN model poses scientific,the phenomenon to be explained.

DN model

[last oxide]

DN was gonna arrive sooner or later irrespective of you, dami

[leaden skiff]

what is mathematical immaturity anyway?

[vagrant kestrel]

dont noe

[leaden skiff]

how do i go through mathematical puberty?

[last oxide]

better be careful with the mathematical weebs

[toxic schooner]

what ever i have

[last oxide]

if only von neumann was called don neumann

[leaden torrent]

Mathematical immaturity is when you spend hours arguing on math discord which notation is better

[last oxide]

are thoe hours cumulative?

[leaden torrent]

and not even bringing up Hom(•,•) the most versatile notation

[surreal sapphire]

but nami those people are WRONG and they need to KNOW

[last oxide]

prefer to take the L, nami

[leaden torrent]

Literally everything in mathematics can be interpreted as a set* of morphisms

*don't @ me foundations nerds

[last oxide]

too bad

ask mandelbrot

[fast ivy]

Oh no

[last oxide]

is he

dang

too bad

[toxic schooner]

im not a foundation nerd, so can i @ you?

[last oxide]

thats a sophism

[toxic schooner]

what is a sophism

thats a new term for me

[last oxide]

unless thats a question and not a conclusion

[toxic schooner]

it is both

[last oxide]

sophism is when you mess up syllogisms

[toxic schooner]

im just gonna google now

ah

i see

[leaden skiff]

hey do you guys think trig functions could have better notation

[leaden torrent]

Ahem