serious-discussion

[dense belfry]

Like you're talking about abuse coming from a largely voluntary service

Papers also

[bronze pelican]

I'm taking about how we communicate

[dense belfry]

Well that's a little different

[burnt juniper]

really if you feel a book uses too many immediates

move to another book or something simpler

[dense belfry]

I think you're talking about people at a different level than us

Probably

PT

[burnt juniper]

or if theres no more options then just go read the original papers

[bronze pelican]

We communicate mathematics by: 1. Writing textbooks, 2. Giving talks, 3. Writing papers 4. Teaching courses 5. Casual talks with close friends etc

[burnt juniper]

many times they are way more urgh

[swift sinew]

this is also a poor argument against the use of the word being wrong.
it's akin to saying "if you don't like uncle being racist, don't go to family events"

That doesn't change that the uncle is being harmful, just explaining how to possibly handle a shitty situation

[bronze pelican]

All of this is communication

[burnt juniper]

i disagree

it's literally

[dense belfry]

That's different alex

[burnt juniper]

a super different thing

[bronze pelican]

And when we communicate, we should be mindful of how our communication can be recieved

[dense belfry]

Saying "it's obvious" is not inherently harmful

[burnt juniper]

there are so many books written at various targetted levels

your job is to find what suits you

if your uncle is racist then whatever just break ties or something if it becomes too obnoxious lol

[bronze pelican]

Okay I'm done with this discussion

Bye

[dense belfry]

Bye

Sorry PT

[burnt juniper]

:petTheCat:

[dense belfry]

Damn I went full libertarian

[burnt juniper]

someday i need to write a script to send things as gifs instead of buying nitro

but im lazy

zzz

[dense belfry]

Same

[burnt juniper]

honestly

if it was easier to get paid to just

write better software out there or write better materials

[swift sinew]

I got a bit more energy to argue this point, so I'll continue.
Emma, having "obvious" be default as okay is harmful

[burnt juniper]

would be so much better

[dense belfry]

Hmm

If your book is targeted at grad students

[burnt juniper]

not as default, but as signalling what level you're aiming for

[dense belfry]

Then I am okay with obvious

[swift sinew]

Ari, I might be down to continue the "uncle" discussion later since it is a good thing to adress, however it would be hard to have two productive convos at once

[burnt juniper]

nah i also have no energy to deal with family members being obnoxious LOL

[dense belfry]

Because at that point they should be able to quit the book if they don't like the language

Same Ari

[burnt juniper]

yea

[dense belfry]

I cut ties with most of my family

[burnt juniper]

oH nO yOu CaNt HaVe A bOyFrIeNd UnTiL yOu GrAdUaTe UnI !!!!11!1!1!1!

tfw

[swift sinew]

Alright, so we're moving onto the "move onto another book" discussion
The problem with that argument is that very good information could be put in a shitty book
And if we just say that its okay to portray information in that manner, we make the community of math information less accessible

[burnt juniper]

honestly i feel like at undergrad level

there are books catering to all kinds of people

those who prefer a more verbose text

[dense belfry]

Yeah that's been blowing up

[burnt juniper]

and those who prefer a more succint text

[dense belfry]

For a while

[burnt juniper]

personally i prefer texts that uses more "clearly" instead of spelling out every damn detail

[burnt juniper]

ikr

[dense belfry]

Yes I actually can't read details

I usually intuit them

[burnt juniper]

details are annoying for me but essential for some

[burnt juniper]

same i jus skip bulk of the proof if it's all relatively straightforward

[dense belfry]

Like the way I read books is to read the narrative and fill in the gaps in my head

Yeah

[burnt juniper]

yee

[swift sinew]

Solid point. However, I think there are slight changes we can make to our vocabulary to make such books less repellent to those who don't like "clearly" but like terse language

[burnt juniper]

meanwhile my boyfriend needs me to spell out all the missing detail

[burnt juniper]

eh i feel like just need to make less "standardized undergrad textbooks" and more of "here are some options see what suits your style"

[dense belfry]

Fuck I just slammed the door on my hand

Wow

[burnt juniper]

rip

[swift sinew]

Fair point

[dense belfry]

But yeah for me I fill in all the gaps myself anyway and that's how I actually learn

[burnt juniper]

same i cant rlly learn by reading all the details

[dense belfry]

So I don't even notice when it says obvious

Because I don't look at the arguments usually

Lol

Yeah I guess I'm a bad case to generalize from

[burnt juniper]

we are like the one extreme lol

the kind of psychos that would read jacksons and call it "a bedtime storybook"

[swift sinew]

though an objection to this is that as a class, its often beneficial to all be following the same book. In such cases, the students wouldn't be able to pick a book they enjoy. Also, going out and finding which book you enjoy can waste time in a classroom setting

[burnt juniper]

tbf i havent actually attended math classes cuz i find lectures too boring LOL but i suppose so

[dense belfry]

Yeah same

I am very bad at going to class

This may be an ADHD/ASD thing for me tbh

The way I do math

[burnt juniper]

it's just sleep deprivation for me tbh 8am classes should be illegal

[dense belfry]

Lol

I agree

I taught at 9 am 2 years ago

Never again

I had to travel for 50 minutes to get there too

[burnt juniper]

waaaaa

shaks

that sounds like pain

[dense belfry]

It was

[burnt juniper]

so happy my work shift is

11-4

LOL

[dense belfry]

It was also teaching high schoolers who were taking a college class

So it was worse

[burnt juniper]

yikes

[dense belfry]

They played a couple of pranks on me

So bad

[burnt juniper]

[dense belfry]

It was my first semester teaching

What a nightmare

[burnt juniper]

honestly high sch low undergrad lvl is the hardest to teach

[dense belfry]

It gets worse

These kids were from a really good high school

[burnt juniper]

i personally prefer teaching people once their foundations has been built (for piano or for math)

[dense belfry]

And they were being made to take college algebra

[burnt juniper]

yikessss

[dense belfry]

In 12th grade

[burnt juniper]

honestly in theory possible

[dense belfry]

One of them had taken calculus previously

[burnt juniper]

but being made to do things as high school students

sounds like a disaster

[dense belfry]

All had done well in precalculus

So they didn't actually care about anything

In the class

[burnt juniper]

ahhh

sadge

[dense belfry]

Yeah

So many levels of shittyness

Also yeah I was going to sleep at like 3-4 am

[burnt juniper]

jus need to keep a mental note 24/7 "please do not scream at anyone keep a poker face sound nice AHHHHHHHHHHH"

[wicked ore]

@rose dock what did u get in for do you think

[rose dock]

I'm not gonna lie: I have no idea

[wicked ore]

Cause ppl with much better stats than me got rejected, idk what happened

Literally the valedictorian got waitlisted at UCSD and UCSB lol

[rose dock]

I had a 3.56 GPA at time of application, and since it was test-blind, my relatively better SAT wouldn't've helped me either

[wicked ore]

What rly that’s insane

Yeah my strong point was my ACT

But they didn’t look at that

So idk bruh

[rose dock]

might be the fact that my 10th and 11th grade performance was much stronger than my 9th grade performance

plus the number of APs I've taken

[wicked ore]

Ah

I mean I got a 5 on three out of six ap exams

That’s like, garbage compared to many other people

It’s just so weird

[rose dock]

I got a 5 on 9 out of 10 AP exams

[wicked ore]

Holy christ

[rose dock]

the valedictorian at my school got rejected too

[wicked ore]

That helped with your GPA for sure lol

Wow

[rose dock]

or, waitlisted

[ancient flame]

the valedictorian at my school is going go harvard

[rose dock]

so did a girl at around rank 5-10

[ancient flame]

p cool

[wicked ore]

Jeez

[rose dock]

and the valedictorians gf

[wicked ore]

Lol wow

[rose dock]

there's people who got into both Caltech and MIT at my school who got rejected

it's crazy

[ancient flame]

the salutatorian is going to a community college bc her bf is going there

[wicked ore]

Whattt

So it’s not just humanities kids

Wow

[wicked ore]

:(

[ancient flame]

yeahhhh

im #3 :)

[wicked ore]

What rly

[rose dock]

I'm #68 :husk:

[wicked ore]

R u a senior

[ancient flame]

yeah

[rose dock]

one away

[ancient flame]

im a senior

[wicked ore]

I’m #35

[ancient flame]

nice

[wicked ore]

Did u get in anywhere cool

[ancient flame]

UF

[rose dock]

68/619 or smth like that

[ancient flame]

University of Florida

[wicked ore]

Nice

[ancient flame]

yea

im gonna major in business

[wicked ore]

Ah

[rose dock]

I'm probably gonna do meth

[wicked ore]

Me too bro

[ancient flame]

I'll minor in meth

and/or CS

[rose dock]

I'll probably tack on either a CS or physics double major too

[ancient flame]

oof

[wicked ore]

Gl bruh

Have you seen what’s going on at berkeley

CS70, a prereq for many cs classes, is being barred from people who didn’t declare CS on their application

At least I think that’s what’s happening

[rose dock]

well I declared CS as 2nd choice I think

or maybe that was for UCLA

[wicked ore]

Oh

CS is also rly competitive there

[rose dock]

either berkeley or UCLA didn't have a 2nd choice

[wicked ore]

But I think that’s mostly at the engineering college

[rose dock]

whatever, I'm fine if I can't do CS

[wicked ore]

I want to try physics but it’s always been annoying when I take a class in it

The extent of the math is just remembering formulas

Most of it is labs and basic knowledge

[rose dock]

also can't math 55 substitute for eecs 70 if ur double majoring?

[wicked ore]

Not sure

[rose dock]

I think I saw that it can

but you have declare math major first

[wicked ore]

Ah

[rose dock]

I heard from a friend that some dude took like 202A and 250A freshman year

for math

I might want to try and copy that dude

[deep mango]

I know one such person

There is still plenty of time to do whatever you want if you do 202A and 250A in sophomore year

202A and 250A are hard

But then again repeating stuff is kind of silly. So that's up to you. I definitely recommend checking out 202A/250A but keeping your options open and being ready and willing to swap them out for less crazy classes

Ok, 250A is with borcherds so you can get a sense for how that will be from the various series on his youtube channel

202A is with rieffel and that class is pretty tough but doesn't move too quickly, which is good

The homeworks are really interesting but take a lot of thinking

[rose dock]

ye I saw some of the homework assignments already. I know a bit of measure theory already, so I think I should be somewhat prepared for 202A.

[deep mango]

It's probably fine

250A is the more grindy unpleasant class usually

[rose dock]

ye 250A is the one that I think I'll have more trouble with

[deep mango]

I never actually took 250A

It was a trainwreck in my sophomore year so I swapped it for something else at the same time

It conflicted with an important class in junior year

And then it conflicted with another important class in senior year, and was also a trainwreck that year (so I didn't keep up with recordings after a bit)

[deep mango]

This was with nadler

[rose dock]

is borcherds the only professor?

oh

[deep mango]

No it swaps around a lot

Borcherds was the professor the year it wasn't a trainwreck

He's good

he's just a bit fast

[rose dock]

ye main concern for me is actually getting into the classes

[deep mango]

Ribet was the other time it was a trainwreck

People drop these so I don't know if that's a huge issue

But

Hard to be sure

[rose dock]

ye also if I take 202A, will I still have to take like 104?

or would they substitute it

[deep mango]

They're typically pretty amenable about substitutions

Though I would talk to a math dept advisor about this stuff when you get there

They're usually very nice and helpful, and don't tell you to take it super easy or anything in my experience

(The L&S college advisors are very unhelpful in this regard)

[rose dock]

ye I'll definitely have to talk with an advisor, although I'm a bit intimidated cuz idk how any of the advisor/course selection stuff in college works

[wicked ore]

I want to take a class like this but I don’t want to die freshman year

[rose dock]

well I like pain

[deep mango]

You pretty much just drop into their offices on the 9th floor when they're around (most of the day mon-fri i think?) and introduce yourself and what your situation is. It's not very formal.

There might be a few people waiting before you at the beginning of the sem.

[rose dock]

would I have to email the professors to ask to get into the course?

or would just going thru the advisors be fine

[deep mango]

Umm, oftentimes for grad courses you do need to fill out a form to get permission to enroll.

Let me see

[wicked ore]

@rose dock what math do you already know

[rose dock]

uhhh

[deep mango]

https://docs.google.com/spreadsheets/d/1H8lQNQ8q6yUNzcuewxIkc1K6QwPILBCTfNMMdF5zxlY/edit#gid=254115028

Here

[deep mango]

I would angle towards not going crazy freshman year. I barely went crazy and I still basically ran out of classes I wanted to take by the end.

Ah here is the site I got that from

https://math.berkeley.edu/courses/enrollment/enrollment-scheduling

Sorry

That site has the link to the form

Under "if you are an undergrad and would like to take grad courses"

[rose dock]

like baby rudin chapters 1-7, a bit of measure theory, and a tiny bit of complex anal. Topology, I only really know what I picked up from analysis/diff geo. Algebra is a bit weaker, only group and ring theory.

[wicked ore]

Richard borcherds teaches at berkeley? Dude that is so hype oh my god

Wow nice

[rose dock]

I see, thanks

[deep mango]

So you don't need instructor permission for these courses.

[wicked ore]

Yeah my general idea is that I’ll take these courses a year later, when I’m actually ready for it, so why go through the pain

[deep mango]

202A and 250a.

[deep mango]

That is what I did

And I guess I did all the actual math major requirements except for math 53

(multivariable)

and math 54 (linear algebra)

I just had them count other stuff for those

[wicked ore]

I’m taking multivariable/diff eq rn, would they take that credit or nah

[rose dock]

I'm probably gonna do 54, cuz I'm considering double major with CS

[wicked ore]

@rose dock ryc suggested cs61a, apparently it’s really good

[rose dock]

ye I was planning on taking CS61A too

[deep mango]

The school will but for the purposes of the math major you will basically just tell them "this class subsumes the material from 53, so use it to fulfill that requirement)

61 series is great, I did it in sophomore year.

And 61c / 170 in junior (61c = computer architecture, 170 = advanced algorithms)

[rose dock]

have you taken the physics 5 series?

[deep mango]

Consider H54. If you don't know ANY linear algebra it might be a bit of a pain I guess.

I don't know

H54 is a much smaller class size. Peng Zhou is teaching it this fall who i've had, he's good.

[deep mango]

No. I just took Physics 137A (quantum mech)

I was gonna take 5a-c but they seem very unpleasant.

[rose dock]

oh I learned linear algebra from axler

[deep mango]

Oh

Well

[wicked ore]

Can you learn linear algebra from artin’s algebra text

[deep mango]

I'm not sure why you'd take 54

[rose dock]

idk what I could substitute for it

[deep mango]

I think you can just take EE16A/B right?

Idk

[rose dock]

ye, but I also heard 16A isn't that good

and that 16B is more interesting

[deep mango]

Well you need to take 16B

And either 54 or 16A

I think

[rose dock]

so I was planning on doing 54(H) -> 16B

[deep mango]

Do you know any EE stuff?

[rose dock]

not really

[deep mango]

This was also my plan (well, 110 -> 16B and then force them to accept 110) but then I changed my mind and didn't bother with the CS major.

[rose dock]

I guess I have knowledge of circuits at the level of AP Physics C

[deep mango]

That is also what I had

And they were like "see if you can do the 16A problem sets"

and I was like "I can't really, but whatever, it'll be fine"

So who knows how that would have turned out

[rose dock]

I see

actually it does seem like I should probably take 16A instead of 54H

what did you substitute for 53?

[sterile idol]

Hey, any ideas how to stress less before an important math exam?

[wicked ore]

The best thing would be to be super prepared cause then you’re confident and less nervous

[sterile idol]

The thing is that I am always super prepared, but still have somewhere in mind that I could do more :/

[uncut socket]

Honestly, if you study enough and provide all the necessary information that shows how you achieved that answer, you'll be fine

[wicked ore]

Have you taken practice tests and consistently done really well

In my experience that’s when I have the most confidence

The other way to not be nervous is to not care about the result of the test, but of course that’s probably not possible here lol

[sterile idol]

Yes, I did a mock test and got 95%

[wicked ore]

Then you’re good haha

I know me saying that is pointless but it’s true

[sterile idol]

My main problem is that the only mistakes I make are some small calculations ones

and beside that everything is fine

[wicked ore]

Oh I see

That’s annoying

[sterile idol]

:/

[deep mango]

126 pdes

[rose dock]

[deep mango]

Good class but quite hard

Depends on the prof

[fair mural]

this is pretty funny out of context

[deep mango]

I took that before any analysis which was a big mistake

[fair mural]

thinking that you did 126 pdes

[rose dock]

lol

[deep mango]

I have probably done around 126 pdes

Idk

Thats hard to gauge

[primal seal]

Not sure if this is the place for this, but anyone want to start a small analysis or rigorous calculus study track/group?

[modern geyser]

If you’re doing this for a class then you should try to meet up with people from ur school

That’s what most teachers recommend

Work together on the homework but write up ur own

[primal seal]

I’ m independent actually

[modern geyser]

Independent?

[primal seal]

Self studying

[dense belfry]

Nice

[leaden torrent]

wait wtf today has a different sequence of primes

i didnt notice and used my usual strategy

and it didnt work LMAO

huh

i always thought they started with a bunch of 2s though

did i just get lucky every time

ic

i havent played every day so i guess i just missed the days where it didnt

yeah i can imagine if i didnt waste all my good guesses thinking "wtf how did i mess up the math"

oh yeah if i wasnt an idiot that's literally exactly what i wouldve done

idk if theres a "more optimal" strategy but ||just "count up by the denominator until you can classify solutions" seems fairly consistent||

at the very least it makes the math easy lmao

by "math" i mean

"grade school arithmetic"

screw subtraction

nah i mean like

if you make random guesses like 459 and 337 and whatnot

you're gonna have to do some NASTY 3-digit subtraction

at some point

(unless you go for the truly optimal strategy, which is just "guess randomly 10 times")

(it only has a 1% winrate, sure, but it minimizes the amount of time you waste playing Zpordle and lets you do more productive things.)

[dense belfry]

Wait namington

Are you not using CRT?

[leaden torrent]

of course i am

[dense belfry]

Okay good

[leaden torrent]

well i didnt this time because i gave up when i realized i fucked it lmao

[dense belfry]

When I fuck it up I just open it in incognito

[leaden torrent]

i couldve still salvaged it im sure

but idc

[dense belfry]

And do up until I fuck it up

And forget what I guessed

Oh lol

There's only one strategy though

So it's pretty boring

Hmm

Go on

I mean that's not viable

So I'm not even going to consider it

[leaden torrent]

it is if you invest your level-ups into your luck stat.

[dense belfry]

Well unfortunately I invested everything into my neuroticism stat

[leaden torrent]

i wonder what stats would actually be optimal to level up IRL

probably charisma and luck

int isnt bad

[dense belfry]

This is some Isekai tier shit

I once unironically said that I thought int was the only stat that mattered

[leaden torrent]

res would probably be a pretty shite stat

actually wait

does res also protect against like, stress and mental illness

resilience

yeah res/con/whatever you call it

[dense belfry]

I need some res buffs

[leaden torrent]

dnd stats dont have luck tho

so i assumed we're not using those

i was just going with generic jrpg stuff

and res is commonly "magic resistance"

yeah but magic is often conflated with like, mental damage and stuff

so im thinking it wouldnt be a stretch to say it helps you stay focused and level-headed and sane

probably more useful than like

Evasion

how many times have you needed to dodge shit

just seduce the robber with charisma

[bright hill]

[leaden torrent]

it's not quite the same thing as what we're discussing but i do adore disco elysium's stat system

i'd pour everything into inland empire and live in a world of my own delusions.

[flat harbor]

visual calculus you say

[leaden torrent]

in narrative you play a detective, so its your ability to get sketches of events from things like skid marks, footprints, bullet holes

i recall it being very useful at like 2 points

and otherwise kinda dead

[fair mural]

is it fine if i don’t completely get or am not good at everything the first time around doing linear algebra?

[toxic gale]

I don't think you're supposed to get everything the first time right. As long as you grasped the important concepts, you can always come back to revisit the smaller details when you revise.

The first time I did linear algebra, I could not for some reason grasp simple concepts like matrix factorizations and change of basis. I'd say this is pretty normal.

[fair mural]

thanks, that’s kinda what’s stumping me, except it’s diagaonization

i can regularly do at least maybe half of the exercises so i guess that’s good

[toxic gale]

Yeah, diagonalization is a bit hard to understand at first, I think. When I first did it, I was just told to memorise A = PDP^-1 without knowing why it worked.

[fair mural]

the book i’m using for it randomly mentioned the P part of diagonalization without really explaining it unfortunately

i’m referring to this, P = Q here

i don’t even know what theorem 2.23 is referring to lol

[toxic gale]

This is the explanation given in my book. I'm using a more non-math book though, because it doesn't mention general fields F like I'm guessing your book does.

[neat lintel]

Im guessing that Q is the existence of an invertible matrix

and you construct it using basis beta

snd the theorem 2.23 states that maybe

[toxic gale]

What book is that, by the way?

[fair mural]

friedberg linear algebra

[toxic gale]

Ah. I'm using a scrub book probably made for engineers.

[fair mural]

i don’t see a “theorem 2.23” in the book

[primal seal]

I use friedberg

[cold needle]

friedberg is nice

[primal seal]

Let me see what you’re saying

[toxic gale]

I use Lay's Linear Algebra and Its Applications. I only chose it because it looked pretty.

[primal seal]

Oh that was someone else

[toxic gale]

I'm sure I'm gonna need to read Friedberg or another theoretical book in the future.

[primal seal]

Friedberg or Lang’s intro are good

[toxic gale]

Considering the book I'm using doesn't go into stuff like Jordan canonical form and dual spaces.

[primal seal]

Yeah a lot of books either choose theory heavy or application heavy

Depends what your goal is and how much math you’ve seen (or what you intend to do)

[toxic gale]

I'm going with less theory for my first round through and then doing the theory stuff later.

Like I'm trying to mostly self-learn first year undergrad material at the moment, so I'm reading books which are less theory-heavy.

[primal seal]

Oh cool!

[toxic gale]

I learnt a bit of this stuff already, but I quite literally forgot everything.

I remembered doing ODEs, but I can't remember a thing about how to solve them now. So I'm revisiting stuff, and writing notes this time, to try to remember better.

[primal seal]

Meh, no big deal. Always easier to relearn or remember upon seeing

Hard problems help too

Those fuckers imprint the material to your mind

[toxic gale]

Good point. I should try more of them.

Hope to get past this material soon, because some of the more advanced stuff like complex analysis sounds super interesting to me.

[rose dock]

My personal experience with linear algebra was everything started making sense like 2 weeks to a month after I first saw the material

[fair mural]

most of the stuff actually makes sense so far, it’s really just the diagonalization stuff

[rose dock]

So I'd do one topic, go onto the next, and then the previous topic started to make sense

[neat lintel]

Guys, what does this syntax mean?

I've never seen the parentheses with the two bounds of a sum before

[toxic gale]

The sum of binomial coefficients from i = 0 to i = k.

$\binom{k}{i} = \frac{k!}{(k - i)!i!}$

[fathom swallow]

PhenomPlasma

[neat lintel]

ohhh

alright! Thanks a lot!

[neat lintel]

wait though

doesn't the expression get kinda screwed if i = 0?

[karmic zealot]

it's k choose i

[toxic gale]

Nah, 0! = 1, so you're fine.

[neat lintel]

oh

right

LOL

[neat lintel]

is this how we pronounce it?

[karmic zealot]

yea

[toxic gale]

n! is the number of ways to arrange n objects in a line in order. If you think about it that way, there is 1 way to arrange 0 objects (i.e. not put anything at all), hence 0! = 1.

[neat lintel]

I forgot the definition of a factorial, so that's on me

[karmic zealot]

if you have a set of k objects, k choose i is the number of combinations of i objects you can form from that set

[neat lintel]

thanks for Le Remindere

[neat lintel]

I see, so the binomial coefficients according to pascal

or rather, their sum

[neat lintel]

in the case here

just as our friend PhenomPlasma said

anyway, I'll get back to reading! Thanks a lot, you two! :D

[toxic gale]

Yeah, it's the sum, which comes up when you try to do binomial expansion.

[karmic zealot]

phoneme plasma

[neat lintel]

you are now obligated to change your name to PhonemePlasma

also, your pfps are quite adorable

epic taste

[toxic gale]

Haha, thanks. Changed it for April Fool's, but I actually like it, so I'm gonna keep it for a bit.

[karmic zealot]

i wanna be a horse one day

[toxic gale]

Ah, aspiring horse. A mighty ambition indeed.

[karmic zealot]

neigh

sorry i'm still practicing that

[neat lintel]

I think you're getting pretty good at it :o

[sonic ether]

Is there even a channel that would be well fit for relational algebra or is that too unbased to be covered in this server?

[limber thunder]

I mean #groups-rings-fields is a thing

just don't expect a ton of people to know what relational algebra is

if it's about algorithms or stuff there's #numerical-analysis

[ember fog]

what do you guys think of the math sorcerer youtube channel, is his advice good and useful or is it mostly rehashed self help?

oh lmao looks like my same question was asked this morning

it seems that opinions about him are divisive

[hot cipher]

If Jeremy has 3 apples. Why does he ware blue clothing?

[devout nacelle]

[ripe wasp]

you’re welcome

[cunning quarry]

Hola hola

DM me ASAP

[torn willow]

Ok,I just realised pedagogy could actually be a useful skill outside teaching

If you understand the mindset behind how people in a particular field think,you can learn that field easier compared to not doing that

[bronze pelican]

Yes

They say the best way to learn is by teaching

[stray kite]

is there a general name or anything for this particular type of inner product on function spaces?:

$<f_1, f_2> = \int_a^b f_1(x) f_2(x) \dd{x}$

[fathom swallow]

CoolShot

[neat lintel]

You could report it in modmail

To not create chaos and not accuse others

[leaden torrent]

yeah in the future

please just send it to modmail

rather than doing it publicly

[little dirge]

@odd narwhal I hear you like espresso

[odd narwhal]

Perhaps

[little dirge]

Im thinking of doing a dynamical systems project regarding that

[odd narwhal]

Interesting

[little dirge]

do you know of any particular things i could look in depth at that might exhibit some tasty bifurcations

ive been thinking about it, but nothing really stands out to me id say

[odd narwhal]

Hmmm

You could look at how the initial distribution of grounds in the portafilter affects flow maybe? That might be hard to model

[little dirge]

hmm

[odd narwhal]

This is generally very important for espresso making. Uneven distribution causes channels and destroys.your extraction

[little dirge]

yup. Indeed indeed, I can see why that might be hard to model

maybe some analysis regarding proportions of fines

[odd narwhal]

Oh

That could be good aswell

That sounds more reasonable

[little dirge]

look at results post shot with a refractometer or something to give me more intution on building the model

thing is i would love to find something that exhibits period doubling/chaotic behavior

i guess we will see

[cyan goblet]

driven damped pendulum

[rose wind]

Per the mods, I apologize for any disruption I caused and any inappropriate comments made. It will not happen again.

[cyan goblet]

textbook example of a system that exhibits period doubling and chaotic behavior

[rose wind]

I wasn't, but alright.

[little dirge]

i wanna do something espresso related though ahha

[cyan goblet]

ah

[odd narwhal]

I don't know if you'll find smth like that but I have no intuition for espresso flow

[cyan goblet]

oh i got it

[odd narwhal]

Like maybe under certain circumstances you'll see that with channeling?

[cyan goblet]

affix an espresso puck to the end of a thin wire

[little dirge]

Yeah, thats the thing. I have a lack of intuition for espresso flow on this end as well

[little dirge]

ahahahaha

lol

[cyan goblet]

then turn the expresso puck into a damped driven pendulum

[little dirge]

tru

[cyan goblet]

ok i got a lil dilemma on my hands

i love physics

i love math

and i will most likely need CS sometime in my future if i go down the CS side of quantum computing

but my uni does not offer CS as a minor

so then i have two options: Physics and CS majors + math minor or triple major

the last one sounds batshit insane so i will probably not do that

but god i love math and i dont want to miss out on mathy stuff just because i do a minor

so just how much of math will i miss out on if i do a minor?

from an undergrad perspective

[neat lintel]

Why don't you do what interests you

If you want to learn math, you can do it in your free time

¯\_(ツ)_/¯

[cyan goblet]

i already do that but i wont get to do the fun math classes, right?

[blazing pawn]

I think a CS major is broad enough that if your interest is firmly in the intersection with physics you probably dont need a full major

[cyan goblet]

sure i could still learn it on my own time

[blazing pawn]

Like if you're literally just into quantum computing and nothing else i feel like you could just take a few CS courses focused on that specifically

rather than a full major

[cyan goblet]

true, but I do want to keep the door open for the potential that i’ll do something other than quantum computing

[blazing pawn]

thats fair

[neat lintel]

If there will be fun math classes

[cyan goblet]

because rn im leaning more towards the research side of quantum computing

or maybe even just quantum sensors

but that’s a diff thing

[cyan goblet]

there’s a few that catch my eye

wrote it down somewhere and dont remember what they were but they did catch my eye

maybe i could just walk into the lecture and listen in anyways

[neat lintel]

At the end of the day it's your choice

[cyan goblet]

yeah im just trying to figure out what would be the most sensible for the future

though i can turn math into a major and drop cs if i decide on doing that. i guess i have a decent amount of flexibility for the next four years

[blazing pawn]

That sounds fair

If you're absolutely confident you want to do physics then you can focus on that first and sort of split your attention between math/CS

[neat lintel]

According to statistics, you probably won't stay in uni doing research

[blazing pawn]

and then go with whichever you'd be more interested in

[cyan goblet]

true

[neat lintel]

So for better future you might want to do more physics and CS

Math has a huge appeal but it's a little ... you know

[cyan goblet]

i dont know what you’re referring to tbh

[neat lintel]

It's hard to apply it to anything concrete

[cyan goblet]

oh

i guess that’s true

[neat lintel]

Easier to do that with physics and CS

[cyan goblet]

also true

man i miss when i was in elementary school

no worries in life

just field trips

[neat lintel]

You'll be older you'll have to pay the bills

[cyan goblet]

oh well ty guys for the input

lmfao

[neat lintel]

And you have better way of doing that if you learn physics/CS

[cyan goblet]

lmfao

very true

[neat lintel]

Yeah, it's harsh truth

[neat lintel]

how tf do I get my lines back

Nvm, found it

Great success!

[deep mango]

👏

[still cypress]

@rocky shuttle I found a way!

:D

[rocky shuttle]

Well done! You have actually used two Heaviside step functions in the denominator

[still cypress]

Indeed I have ^-^
Took some time to find out how to make one since I just saw it defined the way you solved my question yesterday, but I made it work

[alpine kindle]

https://www.reddit.com/r/196/comments/tvxcd3/trans_man_realizes_how_affection_starved_men_are/?utm_medium=android_app&utm_source=share
an interestingly depressing post

[stone ferry]

Can confirm

[hushed turret]

[still cypress]

Wait, it isn't really a Heaviside function, is it?
A Heaviside function is defined for x = 0 (H(0) = 1), but this one isn't

[rocky shuttle]

The value at x = 0 does not really matter for the Heaviside function, it can be anything. Usually, it's defined as 0, 1/2, or 1, depending on the application

[still cypress]

Is no value also okay? 🤔

[rocky shuttle]

You can exclude 0 from the domain of definition if you want to

[still cypress]

So I can call $\frac{\frac{x+3}{|x+3|}+1}{2}$ a Heaviside function even though there's no value (for x=0 lol)*?

[fathom swallow]

Asgard

[rocky shuttle]

This expression is defined for all $x\in\mathbb{R}$ except for $-3$, so if $\mathbb{R}\setminus{-3}$ is your domain of definition, it defines a valid function (which I still would call a Heaviside function)

[still cypress]

Alright, thanks! :D

[fathom swallow]

Zanarcane

[neat lintel]

cringe

[fair mural]

i cringe at your message saying cringe

[neat lintel]

i cringe at you and your cringe isnt significant

my cringe >>>

you cringe at my cringe when infact it is based

based cringe

[fair mural]

sir what

[vagrant moss]

So what does the server pfp represent?

Like is a plane of space or is it a graphing function

[hushed turret]

it's a torus

[alpine kindle]

it's a coffis cup

[fair mural]

tokidoki

[bright hill]

...

what's intimacy again?

[deep mango]

Closeness.

[sleek wing]

I'm late but good post

and it is a conspiracy against me specifically

[vagrant moss]

So is a torus like a magnetic field?

[hushed turret]

it's a shape

[vagrant moss]

But like what defines it

[sleek wing]

set of all points some distance from a circle

[median zinc]

Uhhhh.......?

[vagrant moss]

I WAS RIGHT

[sleek wing]

think about it

[median zinc]

A torus is a cartesian product

I'm not sure what you are suggesting

[sleek wing]

it's also formulated by a cartesian product

or is it (yes)

but just because you're right doesn't mean that I'm wrong

[median zinc]

I actually don't know enough to say if you're wrong

[vagrant moss]

So it's the shape of a particular accelator or donut or smth

[alpine kindle]

S¹ × S¹

[vagrant moss]

What is S?

[sleek wing]

the circle

S^1 is anyway

[alpine kindle]

yeah

[vagrant moss]

Huh

So circle times circle?

[median zinc]

Does it always have such a representation?

[sleek wing]

S^2 is the sphere, S^3 is the 3-sphere, and so on

[sleek wing]

yeah, although if the distance is greater than whatever radius the circle has it's self-intersecting (cringe)

[median zinc]

trippy

[vagrant moss]

Well if a torus is S1xS1 wouldnt that make is S2 which is a sphere?

[median zinc]

Anyway I think my definition is better - it's standard

[alpine kindle]

no
the powers don't work like that

[sleek wing]

$S^2 \not \cong S^1 \times S^1$

[alpine kindle]

they just say what dimension it's in

[fathom swallow]

Wew "Dreaming Discs" Tbh 💿

[modern geyser]

This topoloygy?

[sleek wing]

S^2 is the smash product of S^1 and S^1 though I believe

[modern geyser]

Smash ?!

[median zinc]

This is not helping newcomers

[sleek wing]

shame

[vagrant moss]

But if you replace a with a variable like 3, it's 3x3=9

[sleek wing]

it's a set

[vagrant moss]

So like it represents multiple values?

[median zinc]

Honestly I think Wikipedia's starting line is a good starting point
torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.

[sleek wing]

oh look what I said

[median zinc]

@vagrant moss If you can understand that, then you know what's a 2-torus

I'd like all the set people above to stick to Euclidean geometry first

[vagrant moss]

Is 2torus like a chain?

[median zinc]

It's a donut [EDIT] surface - it's specifically hollow

[vagrant moss]

Then what's the difference between a torus and 2torus

[median zinc]

You need to understand how the donut is a cartesian product

The standard torus being discussed is a 2-torus. The 1-torus is a circle.

[vagrant moss]

Oh oki

[alpine kindle]

it's the surface of a doughnut

[median zinc]

Focus on this

[median zinc]

This is right.

[vagrant moss]

So would a 3torus include a 4th dimension?

[alpine kindle]

yes

you can't fit one into 3d euclidean space

[median zinc]

Not sure how it looks if you try to project it down

[vagrant moss]

You can understand it's shape but not its depth in a lower dimension right?

[alpine kindle]

uh

what

[vagrant moss]

Uh idk 😭

I don't even know half the things people are saying in this server

[alpine kindle]

a 3-torus is locally 3-dimensional

wherever you are

it looks like 3d euclidean space at that point

[vagrant moss]

Like idk what Euclidean is or what a set is or what S is used for or anythin

[alpine kindle]

euclidean space is like
normal space

[median zinc]

Makes it hard to talk honestly, hmm.
But you can think of Euclidean as the usual space you work with

[alpine kindle]

1d Euclidean space is an infinite line

[vagrant moss]

Oh so like dimensions?

[alpine kindle]

2d euclidean space is an infinite plane

3d is an infinite 3d space etc

0d euclidean space is a single point

[vagrant moss]

Oh so it's like a theoretical space for math

[alpine kindle]

uh

it's by far not the only space you can do stuff in

like

[vagrant moss]

Hm?

[alpine kindle]

you've done calculus?

[vagrant moss]

I'm in 10th grade

🤷‍♂️

[alpine kindle]

so

uh

[vagrant moss]

Try to explain it normally and I can say what I don't understand

[alpine kindle]

most of the functions you see normally

like sine function and the squared function

[vagrant moss]

So like f(x)^2?

[alpine kindle]

no

like f such that f(x) = x²

this function is (at least at first) defined from real numbers to real numbers

do you know what a real number is

[vagrant moss]

Yes

And imaginary

[alpine kindle]

ok

good

that will make this much easier

so

the real numbers

can be interpreted as 1-d euclidean space

because it's just an infinite line

[vagrant moss]

Makes sense

And 2d Euclidean space is an infinite plane right?

[alpine kindle]

yes

but

that can apso be represented in terms of real numbers

specifically by combining two real lines

R¹ × R¹ ≈ R²

[vagrant moss]

OH

[alpine kindle]

and you can keep going like that

[vagrant moss]

So basically your making two of the lines instead of multiplying the values

[alpine kindle]

yes

but

we don't need to use real numbers

we can use complex numbers instead

[vagrant moss]

And how would that work?

[alpine kindle]

complex numbers are just the real line

and the imaginary line

put together

[vagrant moss]

Huh

And what are Euclidean spaces used for in the real world

Or is it just theoretical

[alpine kindle]

our universe acts like euclidean space

[fair mural]

the complex plane can be thought of as the xy plane where the x axis is the real part of a+ib and the y axis is the imaginary part of a+ib

[alpine kindle]

at least as far as we can see

[alpine kindle]

it's another example of 2d euclidean space

[zenith tinsel]

hey guys, sorry to bother but can somebody give me a hand on #latex-help thanks

[vagrant moss]

So if we had a quantum computer, we can make a Euclidean space and simulate parts or the universe?

[fair mural]

i don’t know what a quantum computer has to do with this

[vagrant moss]

Its a powerful computer that can simulate lots of things at a faster rate 🤷‍♂️

I just used it Bc if we had one, it would work for simulations

[alpine kindle]

we can already simulate euclidean space

[vagrant moss]

We can simulate infinity??

[alpine kindle]

you can simulate part of it

[alpine kindle]

a quantum computer can't do this anyway

[vagrant moss]

And a quantum computer can simulate a bigger part

[alpine kindle]

i mean

[vagrant moss]

🤷‍♂️

[alpine kindle]

if you have a supercomputer
vs a small weak quantum computer

which one is going to work better

[vagrant moss]

Depends how small

Bc I'm pretty sure quantum computers use atoms as the binary for the computer

So positive and negative charges

[alpine kindle]

i mean

[vagrant moss]

Hm?

[alpine kindle]

idk

enough about how quantum computing speeds stuff up

[vagrant moss]

XD

I like quantum stuff

Space and time stuff too

[rocky shuttle]

Euclidean space is a model of our physical space, where you can measure angles and lengths

And where parallel lines don't intersect

Most of classical mechanics take place in Euclidean space

[vagrant moss]

So it's a theoretical world with ideal conditions for math

[rocky shuttle]

Yeah

[vagrant moss]

Well then back to my original question before that, what would a Torus be used for

[bright hill]

drinking coffee

(sry, I had to)

[vagrant moss]

XD

[fair mural]

https://tenor.com/view/topology-cup-mug-donut-gif-17014077

[vagrant moss]

But why-

[fair mural]

topologically equivalent

[vagrant moss]

@fair mural 😏

XD

JK JK

[bright hill]

coz they're homeomorphic

[fair mural]

cringe

[vagrant moss]

Homophobic?

[fair mural]

homeomorphic you mean, not that i know anything about this

[wind abyss]

quantum would never stoop so low as to know something in topology

[vagrant moss]

Idek what topology is 😎

[rocky shuttle]

Tori are also used for computer games where if you go out of screen, you return back from the other side

[bright hill]

homeomorphic is just the technical term to what you said lol

[vagrant moss]

Never even heard of it until today

[fair mural]

i know

[vagrant moss]

That's just a loop

[rocky shuttle]

Exactly

A torus

[fair mural]

i was correcting your misspelling

[vagrant moss]

then why invent a torus when we have a loop 🤔🤔

Or circle✨

[rocky shuttle]

A circle is a 1D torus

[vagrant moss]

Then say loop

[rocky shuttle]

If you loop the screen, it's a 2D torus

You can wrap it into a donut

[vagrant moss]

So then it was invented for its use of its versatility between its dimensions?

[rocky shuttle]

Imagine gluing the top side of the screen with the bottom side

And the left side with the right side

You would get a donut

[vagrant moss]

But why explain it like that?

Your just connecting two points

[alpine kindle]

because it's useful

you can connect the two ideas

wrapping around

and the surface of a doughnut

[vagrant moss]

Too confusing for my algebra 2 brain 😔

You guys just keep repeating the same stuff in different ways

[alpine kindle]

wdym

[vagrant moss]

I get what it is but idk what for in real life

[alpine kindle]

uh

[bright hill]

bragging rights

[vagrant moss]

Like how in the world is a torus a coffee cup

[vagrant moss]

📝📝📝📝📝📝

[alpine kindle]

because they kinda work the same way

in terms of paths

[vagrant moss]

So then this server is represented by a torus which means this server is people bragging??

I'm so smart

[sleek wing]

wym, the server icon is a coffee mug

[alpine kindle]

it's not really useful in real life

[bright hill]

it's not, it's just that mathematicians like to make play games

[vagrant moss]

Mb mb

[tall badge]

wym, its a straw

[rocky shuttle]

The server icon has always been a looping game screen

[bright hill]

they say "what would happen if we played according to these rules?"

[fair mural]

long donut

[vagrant moss]

Soooooo if a torus is a coffee cup then how come you can pour coffee into a coffee cup but not a torus 🤔

[sleek wing]

one is convex the other isn't

[bright hill]

in the case of topology they say "what would happen if we were able to morph any shape however we want but without any tearing or creasing"

[vagrant moss]

Oh so it's a ✨inverted✨coffee cup

[sleek wing]

[sleek wing]

not really

the hole in the handle becomes the hole in the torus

[vagrant moss]

So then anything with a hold can become a torus?

Like a mug

[sleek wing]

anything with one hole, yes

I think

[vagrant moss]

straw 🤔🤔

[sleek wing]

any topologists in chat

[vagrant moss]

Does a straw have one or two 🤔🤔🤔

[sleek wing]

one

[fair mural]

speak to me in a year when i have some mild knowledge of topology wew

[wind abyss]

lmfao who would out themselves as a topologist

jkjk topologists ily

[alpine kindle]

well
if it's hollow inside

[vagrant moss]

Is topology like the study of stupid shapes?

[sleek wing]

absolutely none of this is in a first topology course lol there's barely any geometric intuition

topology is the study of topological spaces

[wind abyss]

look up “3b1b inscribed rectangle”

[vagrant moss]

Smart 📝

[wind abyss]

and watch the yt vid

[fair mural]

wait i can’t tell, is there geometric intuition in an intro topology course or did you mean there isn’t?

[vagrant moss]

Yessir!

[bright hill]

and homeomorphisms between them

[fair mural]

i assume there is

[sleek wing]

there's some but no coffis cup type beat

[wind abyss]

i thought topology was useless for a while until i watched that vid 👍👍

[fair mural]

rip

[sleek wing]

not in mine anyway

[alpine kindle]

no
it's the study of squishy shapes

[rocky shuttle]

And clopen sets

[fair mural]

when will i get to donut coffee cup stuff

[sleek wing]

dislike that definition greately

it's a generalisation of real analysis

[fair mural]

clopen

[sleek wing]

clopen

[bright hill]

clopen

[vagrant moss]

Oh morbis strip is topology?

[alpine kindle]

the ways you can squish them
and paths on them

morbius

[bright hill]

morbis

[sleek wing]

ermmm aqktually paths is homotopy not topology

[vagrant moss]

Close enough?

[wind abyss]

[alpine kindle]

i swear that's the same field

[sleek wing]

it's a subfield of alg top

so yes, but shhh

[bright hill]

what was your question again? @vagrant moss

[sleek wing]

coffis cup

[vagrant moss]

I dunno at this point

[bright hill]

[rocky shuttle]

A mobius strip is a topological space

[bright hill]

don't blame you with all of wew's shitposting

[vagrant moss]

The fact that 👌is a torus, bothers me

[rocky shuttle]

A torus is a topological space

[sleek wing]

I'm rather intoxicated DarQ you must forgive me

[fair mural]

drunk wew

let’s go

this could be interesting

[sleek wing]

tipsy at most

[fair mural]

darn

i’ll have to take it

[alpine kindle]

wew gonna do something crazy

like make representations for nonabelian groups

[rocky shuttle]

Why would you do that

[vagrant moss]

So topology is making squares in closed shapes?

[sleek wing]

reps for abelian groups, or as I like to call them, lifted reps of cyclic groups, are boring (over char 0 fields)

[wind abyss]

tipsy wew reminds me of gus

fsr

[alpine kindle]

no

[alpine kindle]

here

[sleek wing]

you don't really have the required background to really get what topology is about

[vagrant moss]

Oki

[sleek wing]

unfortunately

[vagrant moss]

I'm watchin a video on it rn

[sleek wing]

probs a good idea

[wind abyss]

3b1b 👍👍

[fair mural]

quoted from wikipedia “topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.”

i think that’s an understandable explanation?

at least for me

[alpine kindle]

so
squishy shapes

[wind abyss]

here we have a case of feldspar and quartz

[sleek wing]

nether quartz

[rocky shuttle]

It doesn't have to be geometric objects though (?)

[sleek wing]

everything is geometric

[vagrant moss]

So basically taking a nice perfect sphere and BRUTALLY SLAMMING IT ON THE WALL

[wind abyss]

nethere ite

[sleek wing]

emruld... or

[wind abyss]

wait i can’t spell

[fair mural]

sure as long as it obeys those conditions

[vagrant moss]

Great

[rocky shuttle]

everything is topological

[vagrant moss]

Sounds evil

[alpine kindle]

everything is an elliptic curve if you try hard enough

[sleek wing]

yeah and then you google the definition of a topology and it's nothing like this

[sleek wing]

ok right right listen listen ok ok

what if right

elliptic curves right

but with y = x^5+bx+c

[alpine kindle]

y² you mean

[sleek wing]

yeah

[fair mural]

crazy how topology starts off with just sets and basically turns into weird geometry

[sleek wing]

same thing (for y = 1)

[bright hill]

scientists go to great lengths for the sake of science

[bright hill]

pure evil

[alpine kindle]

look the same but squished more

like

sharper ig

[sleek wing]

woahhh

[bright hill]

[sleek wing]

I wonder if there's any specific theory on these curves

[alpine kindle]

this is a weapon

[sleek wing]

kinda makes sense I think

[fair mural]

weird looking axe

[sleek wing]

a weapon of maths disruption 🤣

[alpine kindle]

elliptic axe

[sleek wing]

deforestation but epic

[alpine kindle]

deforestation⁹⁹

[fair mural]

peak comedy wew

[sleek wing]

thanks quantum

[wind abyss]

abelian grapes is peak conedy

*comedy

you should watch it 👍

[vagrant moss]

Did and done

[fair mural]

holy god there’s 18 pages in this section i’m currently working on, this is gonna take forever

[tender tulip]

Hm, I thought that was only when considering Weierstrass’s elliptic

[vivid halo]

no?

[tender tulip]

Fair enough

[vivid halo]

any Abelian variety of complex dimension g is a complex torus of dimension g

so long as you fix a principal polarization, the converse is true

[tender tulip]

Alright

Is there any good intuition for that besides weierstrass’s elliptic

[vivid halo]

in the case of elliptic curves no