#serious-discussion
1 messages · Page 532 of 1
Do you ever drink with Joe Miller?
And Mariya Soskova
I haven't unfortunately Emma
just git gud dami
I don’t speak American. 4.0 out of 100?
4.0 GPA is max
Wow. Tryhard.
My ug gpa was like a 3.3
My first year gpa was like a 1.8
Or something
It would have been much worse if I hadn't dropped all my classes except one second semester
cute pfp
Allegedly
I skipped 2 year's worth of math and ended up with a like 99 average
In my first abstract algebra class I skipped like a month in the middle of the semester
Went to tutoring with grad students instead though.

Because most students are really bad at abstract algebra
Emma you sound like a model student
Prolly
abstract algebra sounds hard
So proper math
Yeah it wasn't a very good school so the class wasn't very hard
I wonder if that anecdote says something about the quality of the lectures
The lectures were good
Currently studying field extensions before doing some Galois theory. Abstract math is cool
That wasn't the problem
The students were mostly math education students
And didn't care
Or want to be there
Oh I was going to say maybe the lectures were actually not understandable by them
Yeah they weren't
But it wasn't the professors fault
The lectures were actually really clear
After giving 2 semesters of lectures I've come to accept that if my lecture was the most beautiful lecture but no one understood it, it was a bad lecture 
I mean they got through the class mostly
I don't think they didn't understand
They just weren't engaging
Because they just needed the class as a requirement
git gud noob
For some reason
idk why
And they didn't actually care about it for the most part
idk how far the professor should go in accomodating for that
Sometimes it really is just on the students
I'm just naturally hard on myself
You guys lecture?
But yeah I think for example if you're teaching remedial classes you're not going to accomplish much for most students
In the long run
Unless you spend a lot of time
Like a lot a lot
And do lots of personalized attention
Yes we do
Are remedial classes like ones which you take cus you failed th3 standard ones?
Wow let’s make fun of slurp cuz he has social anxiety okay wow DarQ so mature

Like for remedial students the waters are very very muddied
And they are perpetually confused about everything
Cool
My first semester was pretty much a remedial class
My second semester was an honors class
And don't believe that they can understand things
They could not be more different from each other
Yeah
It makes you wonder what the point is
In shifting the onus onto the students
To take classes they're immediately going to forget
And are just doing for a requirement
And make them feel bad about it
I don't really know why we teach math to a lot of people in undergrad
Bad physics student. Can confirm
It just seems like we do because we do
The point I'm making is that access to tutors etc explains only a tiny proportion of the variance in attainment between socioeconomic groups and the relevant literature is abundantly clear on that. I'm not sure about the fluency thing. That's already the major focal point of the UK math curriculum so I suppose that's a statement about the US curriculum on which I am not qualified to comment.
To fuel the machine
Ig but the non math majors end up needing it as prereqs for other classes, no?
I'm back futhermuckers
Flashback to the one time where the math assignment on confluences was relevant to the algorithmic test
If someone is failing the same math class consistently over and over again (which a lot of people do)
I don't see why we keep pushing this on them
And the solution is to make the classes easier
I am surprised by this valence formula
Apparently
When it comes to socioeconomic stuff influence how well people do in education
Which hurts other people
It's beautiful and powerful
Yea tbh making classes easier lowers the standard of the course imo
What you cited actually says that parents teaching their kids explains a tiny proportion, not access to tutors. Although you probably have a bunch of education literature I'm not aware of, so maybe the literature also ends up agreeing with your point regardless. Has it been agreed on what is the explanation?
Tutors would only really explain the distinction between like, doing alright but not so well as to be able to afford tutors, and the level above
But I think big parts are just gonna be like
Having a parent at home
Are there any stats on the effects of math anxiety?
Rather than being raised by TV and baby sitters
I haven't seen any
Funding available to schools
Math anxiety seems like a feedback loop kind of thing
But I do recall studies saying it's measurable
Like without knowing too much research but just imagining
There is no single explanation. The education gap is an extraordinarily complex issue consistent of countless interacting factors, and it isn't remotely clear at this point how to address all said factors simultaneously
You can see why this kinda thing would happen
.......
Math anxiety means that unable to answer simple questions in front of public?
Yeah Dami you can see
But that's not enough
For this sort of thing
Stats are needed
I guess I should dig through the literature sometime
@velvet dagger do u like my name

So why did differentiated instruction become the most popular method of attack for the educational gap? Or does it even claim to solve it at all?
Your eyes are data collectors
Your imagination is running the data processing algorithms

My frontal lobe is a linear regression machine tru
Icy I'd say differentiated instruction is relative to, you have a class in front of you
Not all of your students have the same needs
So if you try to force fit everyone into the same style, it'll be trivial for some of the good students, now you're stifling their growth
Simply because differentiated instruction leads to better outcomes
And it's too fast for the struggling students, now you're amplifying their struggles
So it's called adaptive pedagogy
But socioeconomic factors can also influence, for instance which class you are in
Josh said it's the new focus in the UK
If you're in a school that's underfunded
The quality of education can and often does drop. Maybe the higher quality teachers avoid it
The ones who are there might have to work multiple jobs
My conservative brother in law tried to tell me that inner city schools are over funded
So is this just saying that this is one thing that we know works in non-negligible amount, and we don't currently know of another thing we can do on top of that?
To afford cost of living + buying some spare school supplies that their school can't afford
It's the most easily implementable strategy that has been shown to be of statistically significant benefit
Also some of your students, regardless of how much you differentiate
Don't have parents that are like
Obviously there are many issues with differentiated instruction, mostly relating to workload
Helping them on their homework, effectively a form of having a private tutor (with a cost of parents' time, but time is money here)
I see. So what I'm surprised about is that the main focus isn't on searching for additional methods of attack, but rather focusing on adaptive pedagogy
Yeah helping your kid on homework is really important
Or parents that are generally invested in their students' educational development
But all of this doesn't even consider the fact that the pedagogical literature is still yet to reach a consensus on how best to teach students who are good at math
Before kindergarten they would play games to help you learn the language better
So yeah the structure of things in the US is such that socioeconomic status can fuck you up before the gate
My parents weren't super educated but I got lucky that I had a stay at home mom
Also the focus of education being to train workers
Vs personal development
Is interesting
So e.g. when I was a kid, I had a speech problem
Ah right I see the misunderstanding here. Adaptive pedagogy is what is taught to new teachers. The literature itself is pretty much nothing but people trying to figure out how to fix shit lmao.
Ooooooh
Because my parents tried to teach me 4 languages at once
English, Berber, Arabic, and French
My language education is so weird
And it was a bit chaotic because Moroccans mix languages
So my dad would speak to me in English and Berber
Like I was supposed to learn Hebrew in like 1st grade
Quelle idée saugrenue
If you teach a kid multiple languages apparently you should have one person speaking to them in each language
But yeah issues of pedagogy are complex and very often straight up paradoxical. Just read up on the "Big-Fish-Little-Pond effect" in the context of mathematics lmao
And everything later on assumed I had that
Does language have effect on your math abilities?
Taking exams in a language you don't know
BUt it turns out I got confused by the mixing languages
Is surreal
And just shut down mentally
So at age 2.5-3 I had the speaking level of a 6 month old
Is French best language for math?
Why would it ?
The best language for math is first order logic
It's quite language independent
I think some languages have better way to describe mathematics
In their native language
French would be a bad one if the language does matter that much
I feel like questions regarding particular language speakers being better at mathematics is straying very close to Sapir-Whorf stuff, i.e. the most controversial shit in modern linguistics lmao
Josh they're just language realists
But French language is usually allowed still in journals for publications
I mean that's because a lot of math, esp AG and PDE I think, is done in French
4*20+10+9=99
do you have any evidence or example to support this?
So what? Some journals accept papers written in word?
Matters of research and journals are disjoint from pedagogy
What top journals in math except languages except from French and English?
Accept*
The idea that some languages are better at describing mathematics seems dangerously close to the idea that some languages are more expressive than others, which is some borderline race science bullshit
Technically suiss french doesn't call them that way
the idea that some languages are more expressive than others isn't a priori racist or wrong. But it takes serious evidential support
I've literally had conversations with self described race realists
It is actually the vast available literature in certain languages make advantage for native speakers
So weird
My big-fish-little-pond effect ended in 8th grade when I did well enough in a state math competition to be on a team with top people in other schools in the state for the national competition
Yeah I agree with that
That was quite the eye-opener
This literature is very controversial
Standing out is detrimental until you stand out enough
I was simultaneously a big fish in a small pond and a tiny fish in a normal sized pond
In elementary school
SSK: I am not gonna attempt to make calls on that, but even if you know it's true that there are languages which are more conducive toward learning math than others
Research and journals have influence on pedagogy
Not really
I have that experience to thank for me being here right now, unironically
Research/journals are about proving theorems that interest the mathematical community
Sure, but the plural of anecdote is not data and the BFLP effect is very widely documented and a very difficult problem to mitigate
Like for example, why is German not represented as much nowadays? Gottingen at some point in time was like
THE math place
Indeed, one of the best known methods for mitigating it is differentiated instruction
🙂
Of the world
Hmm I wonder what happened to Germany
I know nothing about language. Why wouldn't one be more "expressive" than another? Or, at least, why isn't it possible that you can express something in one language that you can't easily express in another?
In the 20th century
Wait, my anecdote wasn't toward any pedagogical point
Excellent question Emma
I wonder if we'll ever know
But yeah so that just led to less math being done in German compared to before. It doesn't say anything a priori about the language's ability to say things, and especially not about any kinda Sapir-Whorfness
So if it is the case that there's a mathematical Sapir-Whorf going on
Apparently a lot of people went to NYU and U Chicago
Yeah it's a good question. Expressive isn't really a well-defined term here. I'm more referring to the very colonial idea that some languages are "primitive" in the sense that they are broadly limited in what they are able to convey. This type of thinking isn't very common these days though.
You cannot conclude which languages benefit based on research activity
Since a ton of other factors influence it
I am like asking and explaining together. A person with French or English mother tongue does have certain advantage because of vast literature available in the native language. I believe someone having read French articles and books can be more mathemarically aware than someone from kenya reading English books say. Obviously limitations of number of books play certain role but also the thinking process must be impacted by language of thinking
France is also super insular. One of my profs in undergrad told me that if you go to Germany (which still has some S tier math, arguably best math place in Europe is Bonn rn?)
Yeah. There were a lot of writers back in the golden age of eugenics writing about how primitive the native African languages are, for example, largely because of the simple phonology of some families of languages (or at least apparently phonologically limited to a western European's ears)
If you go to a talk in Germany, they ask the audience if anyone doesn't speak German. If anyone says yes
The talk will be in English
you may have a point but it doesn't mean French in and of itself is a superior language for expressing mathematical ideas over any other language
This isn't German mathematicians giving talks abroad, this is while you are in a city whose street signs are written in German
Or they just default to English
But French used to be the lingua franca and France is super sensitive about losing that spot to English
So they make a thing out of not translating their materials etc
French used to be the lingua franca
However, this is only a problem at top level where if n mathematicians who work in a given area live in one country
Well yeah no shit somebody who isn't a native speaker of English is going to struggle learning math from an English language textbook
That can be a serious percentage of all math research done in that area
thank god its not anymore, i dont want anyone thinking im a frenchman
Like whether the single man that is Pierre Louis Lyons decides to publish in English and French
Is actually important for the relevant subset of the PDE community
Amazing
All languages have their own pros and cons...and probably some topics which Japanese study in their Japanese language makes them pretty naturally inclined to think faster in that topic. In that sense the more variety of native language books may give advantage
It would be trivial to translate them
I've literally put entire PDFs into Google translate
And it works really well
Surprisingly
SSK: that's not a property of the language though, it's a property of the country
Like if America decided to emulate Japan's system for teaching math as a country
The materials could be produced instantly
For math papers I think it's technical enough that Google translate works
What...does it keep the meaning intact
Yes for the most part
I think math books would be hard to translate
So now this is just talking about quality of education systems rather than quality of language. Because if you teach someone Japanese and then English and they live in the USA
It has improved over the last few years
A lot of math words are just used verbatim
google translate still suffers with chinese
"I think"
SSK unfortunately I must break it to you that not everyone has as good intuition about life as I do
In non English languages
When people venture to make guesses about things they have little experience in
It's usually Dunning Kruger or worse, pure speculation
When I do it's insight and the professionals of the field should be taking notes
Yeah you seem to be doing a lot of speculating
With Dami I allow it because he can yeet me off the server
Property of country? Of course Russians germans Japanese Chinese French all translate stuff into their own language most of the time. But there are many others who just rely on English
Also because I'm right

based dami
all hail dami
SSK: yeah that's a country's choice though
That's not embedded in the language
Like
And at the level that it matters they can deal with it
You can't do data analysis on the linguistics of the Lithuanian language and confirm that if they are to use instructional materials developed by another country it must be Japanese and not Chinese
It's a choice made by individuals who are in charge
Lot of available material and some books in certain language might just hit your heart when you get introduced to a topic. For example the way a topic is introduced to you is very important. Native language may have importance to it
To make things seem natural
"might just hit your heart"
What
Like I really don't know why you think you have the ability to separate all of the other shit from the language stuff
Now that's the scientific method we all know and love
To make the claim you're making
Alright I'm gonna compute the homology of the aorta and figure out that Italian just hits different
Physiologically
unlike you i have a rib cage. nothing will ever hit this heart
Like I don't wanna be sarcastic or flippant here because it seems like you're trying to engage but you get what I mean right?
Homology of the adelic aorta?
I think I failed to bring out the point because of lack of evidence here and non precise remarks
don't
SSK unfortunately you did indicate successfully what point you were trying to make
It's just not backed up atm by
Anything
We're taking the default position of "things are complicated and we don't know, it doesn't seem likely that this is a thing that matters given the history of that sort of idea"
Be it evidence, or even pure reason, like if you at least gave an active feature of a language and suggest that this feature makes it more difficult to reason about arithmetic
I still feel that learning math from your mother tongue books would be very helpful like it is for many mathematical countries
Then we could at least contemplate that
And as the one making the strong claim you should have some evidence
I mean learning language in your mother tongue being easier isn't even your original point
learning anything in your mother tongue is useful
Availability of resources in a language at kindergarten level isn't a property of a language
It's a property of the resources
And I'm gonna speculate a bit here myself but I'm pretty good at that so I'll allow it
Yeah resources aren't sufficient except for a few languagea
whoever invented arabic clearly stated that no math textbooks should ever be translated into arabic duh
But I think you are hard overstating the lack of availability of resources in other languages
Yes how do you know SSK
That those resources aren't available
That doesn't seem like a hard thing to do
To translate a book
Like it's a pretty minimal expense
Like we're not talking Hartshorne AG or books of that form
I've never once read a quality math textbook in any language other than English
And you don't need many books for elementary education
Because once you're older you simply learn what you need
Once you're older changes a lot of things
How many different math resources were you exposed to in elementary school?
Many layers of weird assumptions here
That should be backed up
If you want to argue this
So unless you're gonna claim that there are countries which don't have books in their native language about fractions and decimals and just go with Pearson or McGraw Hill untranslated
Then yeah give some sources
Well even if they were going to claim that
I am declaring that the null hypothesis here is that most countries have at least shit like that available in their language
They should still give sources
I feel like this is some weird incompetency of the state assumption?
I have come to the point that I feel comfortable in English math books. But had it been from school time...i am sure I would have tried reading books in native language also...and this phenomenon is much pronounced in higher education of many countries.
Much pronounced in higher education of many countries according to your most recent LSD trip or what?
Also pedagogy for like
Exactly
K-3
Which level of education are you describing
Is not the same as pedagogy in college
Under graduate
In college you're supposed to be a big kid and can just learn what you need
And graduate
The pedagogy is git gud
Okay you should have specified earlier
"Supposed to"
Yes
And then they do just as well as the native speakers in math
The statement here is that not learning in your birth language is a disadvantage
Hell a lot of my eastern European profs were some of the strongest
Yes kinda and the reason is lack of available literature
But is far from the original claim
Because once you're talking about doing high level stuff, work ethic and talent are needed to overcome even the raw mathematical obstacles
Anyway you should get a bit better about stating what you are claiming SSK
Like I doubt there are too many people who would've succeeded in math if only Rudin was in Lithuanian
I apologize...English is my weak point
That's fair
Yes that's true
English is my third language
And a lot of ppl write in a way that gate keeps ppl who don’t know English too well
I think we just got triggered by the language that SSK was using
Because it invoked bad ideas of the past
I think it certainly slows u down at every level
Or I guess I shouldn't say calculus books but
But it seems that was just a miscommunication
I feel blessed about this place because I can type my questions here and that too about higher level
I guess
people who write in english expect their audience to read in english... I don't think that's gatekeeping
And I mean I have tried reading French papers before it was painful
So I can emphasize
Empathize
You can write in a way that’s gatekeeping
Did you try using Google translate on the entire document John?
Hmm
A lot of things I had to figure out how the translations worked
Pretty much there are sorta levels of filtering if that makes sense. So you have classes that are mostly taken by people who are gonna do mathematically-related careers but not necessarily gonna continue in math
Ah okay
eg calc/ODEs
Good to know
I mean I guess if you're using idiomatic english phrases and slang and stuff
Exactly
I always try to make my writings as like, basic as possible
Bc I don’t wanna gatekeep esl ppl
For me category theory scares me Or even the algebra scares me because it is all English words written. I prefer equations everywhere which I can still understand better. That's why I am more happy with analysis
If those classes lack resources in the native language in many countries and it's relatively uncommon that people have n years of school in English or French before starting college, that I buy as a real barrier. But once you're talking someone who wants a research career in math
Why dami
The fact that most math is done at this point in English, and to some degree in French, actually makes language barrier less of a thing rather than more of a thing
Why don’t u read only French papers for a week and then tell me that
Beacuse you only have to learn one, maybe two, languages
You think all this doesn't affect research?
Also John that was the worst example you should've told me to read mathematical German or Russian. Mathematical French is pretty easy overall lol. It sucks but it's not hard
Contrast it to the possibility where each person publishes in their home language
I've seen multiple people who are not native English speakers express preference for this state of affairs
i think its the choice of the author
and other ppl can translate it after if they want
Because then you can just sit down for a while and learn English super well and now you're in perfect shape
i dont like how ppl just think english should be the defualt
not everyone can do this and it sets ppl not from english speaking countries at a very heavy disadvantages
Yeah but that's still less of a barrier than trying to decipher one of who knows how many languages
Not really. By the time you have to rely on english to find teaching material you should be at a level where you have learned english for long enough to fully understand the triviality that is mathematical english
"triviality"
I know some kids from iran who were no less than genius but dropped maths because they only understood their persian math books and after certain level persian books aren't available
They can solve very complex problems much faster than I thought
Compared to the level of English studied on english class in parallel, yes
I think having a default is probably a good thing. I think the fact that it is English is probably due to problematic reasons. But I do agree that having math largely published in a single language is more accessible
and if they don't have an english class.....?
i think forcing ppl to publish in english just gatekeeps a lot of ppl
Like I admit there's a possibility of survivorship bias but it also kinda stands to reason that the convenience of the ability to write math in your native language is far less than the inconvenience of having to decipher 12 languages because your sources are all in different languages
and also prevents ppl from getting into math in the first place
I think it would be a bigger issue if fundamental results were published in many languages
And this holds even for non-English speakers
I would personally rather have more language publishing, with possibility of translations, if it means more ppl get into math
Possibility is different from actuality
I think less people would get into math hahaha
It is incredibly convenient that one only needs to learn a single language to understand basically all of the modern literature
i mean it is convenient but i feel like u guys are just like
It is not ideal that the language of choice is one of the largest colonial forces in existence
If you think it’s such a problem, you’re likely not the only one John. Why not start a business and make some money off it? You’ll find out quickly if you’re into something or not
ignoring how hard english is for many ppl
It's so much harder to find a resource in Japanese, a resource in Swahili, 3 resources in English, and 2 resources in French
when i grow up ill translate a lot of book to bengali
And have to translate them all to Latvian
Let me switch to laptop
but thats not for now lol
One sec
But then thankfully you can publish in Latvian
You know bengali
It's so much easier now to just learn a single language
im bengali
I would 100000% rather be forced to learn a new language than have math published in multiple
Than try to play with 12
translation services are just like not possible
This is coming from non-native speakers as well
there is no incentive mechanism for translation
theres a reason even grothendieck has papers not yet translated to english
let alone some rando's phd thesis
isnt accessibility enough of an incentive?
like personally i think ill write my papers both in english and bangla
People's work would die in obscurity if it was not translated and most of it would not be
Thank god Neukirch book is translated
People would have their results scooped simply because people didnt know they existed
Like who would even translate anything?
Why would they?
You're assuming that because all languages are now things people can publish in
Translators don't know enough math and mathematicians have other things to be doing
Abstracts have to be in one language
That all the materials would be translated
Lol
Machine translation is nowhere near where it needs to be
Like I think its fucked up that english is the language of choice for things that need to be universal
ok maybe this is all fair but u guys have to admit how unfair all of this is for people from say bangladesh or india
but I would 10000% rather have all math written in a single language that I need to learn than multiple
It's unfair to everyone who doesn't speak english!
And that sucks
but unfair solutions aren't necessarily inefficient ones
But literally those same people from India nad Bangladesh would find math less accessible
cause i knew a lot of ppl who were gatekept by like, english basically
I think that it would be a huge barrier to young researchers of any language if results were being published in many languages
like
I reference papers all the time that were uploaded to the arxiv like
this year
If all languages were represented. Because it wouldn't imply that you could mostly stick to your language
that speed would be destroyed if i had to wait for translation
maybe we just need to wait for better AI
Yeah machine translation is probably the best hope
It would imply that you now need to deal with a ton of languages
I think its one of the biggest like
Yeah machine translation would be OP
accessibility issues out there
Luckily companies are taking it pretty seriously
like Google has been trying hard to get really good and fast OCR translations
Lmao spacebar that's clever
I don't get it why something like handwriting to latex has not come up yet
it already exists ssk
Maybe we should adopt Latin in teaching to make maths really upper class and inaccessible again 
its very hard and has a market of like 5 people hahaha
i have an app that does that
detexify is kind of a thing
No that's just symbols
But also that's not as important as other stuff
or well handwriting to latexified math
If someone's barrier to math is that they don't wanna learn tex or even some hypothetical thing like Microsoft equations that's click and drag
But some people use vim etc and claim they fastest
Then unless there's some weird exceptional case I can't think of rn where that's valid
latex is really easy compared to like
I'm just gonna allow that gatekeep
Yeah I am saying how to live tex in class
oh well some ppl just type it up
i have friends that do
i personally just write it on my ipad
Yeah I'm not saying it isn't unfortunate that you can't stick to your native language when doing research math
Just that the proposed alternative actually just makes it even harder
Because rather than learning one you're juggling
i mean as much of a meme as it is like
Live texing is mostly about macros
not your text editor choice
so just pick a text editor with macro functionality that you like
and invest a lot of time into making clever macros
my standard preamble is so long now lol
But still live tex requires you to be able to constantly see the output
And lyx does it well
hmm i mean not necessarily and something like overleaf can compile as u go ig
I once live texed a talk with a lot of commutative diagrams and barely kept up 😔
anyhow i personally dont even like taking detailed notes during lectures
Overleaf takes whole lot of time to compile
cause it distracts u imo
I'm leaning toward not doing that again
i just write down bullet points on my ipad
IPad is the best I agree
its a good investment if u can afford it
I also iPad with Goodnotes
Also tbh English is kind of easier than a lot of languages to pick up according to most people I know that learn 3+ languages and aren't native English speakers (mostly in contrast to Arabic, Berber, French, Spanish, and German). The circumstances that led to it being lingua franca were definitely not such considerations as opposed to less pleasant ones, and there probably are easier languages out there, but maybe it's better than having Latvian as the lingua franca. And I do think having a lingua franca in math research is the strat.
I think that's just handwriting functionality
i honestly think it is more reasonable to take sketchy notes during lecture and if you really want to type them up later
Maybe it's more that Americans are more willing to work with people whose English is eh but understandable compared to Europeans tho lol
the only reason to live-tex is if you already know the material well
and ur doing it for other people
Available with goodnotes as well
the act of re-typing the notes rather than using OCR is going to help you remember them better
I agree
Max that's an interesting point
right
Does it cover equations?
this was a handwritten hw
of mine
(questions are copied but everything else i handwrote)
john
ok john
how is ur handwriting worse than mine
true or false
i thought i was a lower bound
lol
probability density can never be negative
Yikes
they were calling the wavefunction
probability density
in the class
not my fault
why not just tex this
lol
this is so cursed
this was quicker
Do you have carpal tunnel syndrome?
isnt probability density in between 0 and 1 by definition
I have
are you a dog at a keyboard
yo i just wanted to show off the tex smh
re: johns writing
But my handwriting is nice
yea john. we flaming your notes now
bruh im getting bullied
Now you know what it's like to be a premed
wait is probability density the psi norm squared or is it psi
lmao
amateurs
Being lazy in your work and getting bullied for it
ok its a pchem class do u expect me to type up problems for it smh
i always use langle and rangle for my expectation value :(
because mcintyre denoted it as such so i did that
yeah i dont think we were at the brakets at that point lol
But yeah I think officially |psi|^2 is the probability density
Rather than psi itself
Educate
lol
So notability and goodnotes are kinda same
they're pretty similar yeah
But good notes has presentation options with lightning pen for teaching
I see
Yes Max but brand loyalty
same max
i wonder if i could sneak ppl here into the ucsd topology semianr
ok ill use beamer for ur class. should be good cause i havent used beamer b4 and i need to get used to it
i use goodnotes because i already paid the 7 doll hairs for it
also because it has a dotted paper option
and i love dotted paper
notability has dotted paper
god dammit
Both are great
does it have textbook solutions
except for a half decent file organization system
ok fair
luckily i dont need one
i just manually organize things
notability to me is like, an online binder, the type u use in hs ykwim
hahaha yeah
But does it have infinite board
Onenote has in both directions
i used to use onenote
I use one nite
all the time
It’s shit
exactly why i stopped using it
I don’t like the feel of how it writes
ill tell u why
feels so backwards
microsoft.
And it’s slow and it keeps having to load
it'll just snap back to the top of the document randomly
But infinite board is useful sometimes
or sometimes when i write it just doesnt do anything
what i really want is like
Yes! I thought that was an issue with me
a shared infinite whiteboard that works well on tablets
no it is so god damn annoying
Do y’all have any better free alternatives?
Hmm
ikr max
Goodnotes has multiplayer thing
yeah at least they're one time payments
Goodnotes win finally
thats up there with the best $9 ive ever spent lol
Cheaper
dont wanna sound like an oldhead but i am getting real sick of everything being subscription model based
sub models suck
im ok w being an old head
even when you actually save money
sub models suck
which thankfully i did bc my ipad broke and the new one i got from warranty was able to get the notes back
they feel bad
i have gotten cheated out by many auto subs
i have never in my life referred back to my own handwritten notes hahah
oof i write down all the references from talks on those lol
i havent taken lecture notes in a while
considering i just finished my senior year of high school so i really didnt care about anything for the last school year 
oh
used to write in microsoft edge, but I feel like it's gotten worse now
What
like if you have a pdf opened in edge, there's an option to draw
What’s the difference between annuities and compound interest?
Hey this last paragraph got me thinking…what would be the contribution of the speed of an actual bullet that makes it penetrate flesh? Cz the raindrop ofc won’t kill the person it drops on..right?
Well the terminal velocity of a raindrop is like 20-30 mph so there’s that
The first phrase is important: “with no drag…” In reality, the raindrop reaches terminal velocity way before it gets anywhere near that speed.
*edit: I see what you’re asking now. Although a water droplet traveling fast enough could certainly kill you, there are other factors of a bullet which make them more deadly; namely, the property of hardness
kinetic energy depends on velocityt
and that energy would be expended in the process
How we defined integrals is so neat
Thanks
Generating functions, as applied to a hard puzzle used for IMO training.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share the videos.
Artwork by Kurt Burns
Music by Vince Rubinetti
102 Combinatorial problems, by Titu Andreescu and Zuming Feng
https://amzn.to/3wAPoNq
Generat...
Finally, some 3b1b
olympiad level counting 
Oh lovely.
How pleasant
Oh god I see roots of a polynomial being permuted
When I said I wanted another group theory video this isn’t what I meant GRANT
3blue1brown is a hack
could someone give me some guidance on what I should study next based on what I know thus far? I'm an amateur with extremely rudimentary understanding so basically I'm looking for subjects beyond the basic real analysis and linear algebra that would maybe nudge my brain into thinking things more in a more "mathematically mature" way, if that makes any sense
- Pentagon
- Partition
- subsets
Euler’s Pentagonal Theorem
bad title if I'm being honest lel
Slurp when a 6.5/10 man wants to sell his kidneys on the dark web

He's not my thing
Stfu grant is at least an 8
What about Henry Cavill?
You like facial hair?
Henry cavill as superman 👎
Also he’s hot regardless of the amount of facial hair
Wtf
Okay who’s the hottest celebrity in your opinion?
no
Yes
Yes
It's not a coincidence people care so much about homology and homotopy
Henry Cavill as the witcher is a godsend
True
most people are straight, so it’s probably fair to assume that most mathematicians are too
This turned me bisexual
what did you think HoTT stands for? if you thought Hot Twinks you'd be right
only 5% of the population is homosexual iirc
Ryc is not a good sample. He’s barely even mathematician. He’s like a physicist or computer scientist more than a mathematician.
topology
so, probably not
Everyone’s gay for me
So your figure is way off
cringe
hi quantum
Quantum
hi
i can call it cringe if i wanna
quantum calls everything cringe
Obv I can’t demonstrate here any more
render and message me the image dumdum
I'm guessing that's a separate field from algebraic topology
yes
topology there just means like
general topology
point set topology

How am I a computer scientist
you use computers
yeah this was my impression but given that I've sometimes gotten the wrong impression for assuming something I felt was self-evident, I want to make sure. sometimes that involves making dumb questions 😄
good enough for me
...
a is not in topology tho?
bruh what

You literally were talking to me about something stupid with complexity yada yada yada
Oh yeah I forgot
Yes ok
You forgot… about the paper you contributed to?
Yeah
It seemed like a big deal for you when we discussed it
I only did the math part of it

I don't think of it as computer science
complexity theory has non trivial intersection with pure math tho, iirc
“A non trivial intersection” Shuddup
And yes it does
But
The paper was like APPLIED CS
It was like
Yes
He was talking about RAM and caches and shit
Pop quiz
Oh fuck

Ok i tried to think of questions but that would require me to remember what I talked about
lmao
slurp: "do u have nightmares about me 😳"
me: "oh we had a conversation yesterday? i forgot
"
Was it yesterday?
do you think i remember?
Also stfu I’m literally the most important figure in your life
HAHA senile old brain goes BRRRRRRRRR
I mean
I'm not that surprised since you were drunk until 2am and only slept for 4 hours

Ye
Yeah. I'm a no fun frank
Typical franks....
What does this mean
Joking about euler's pentagonal theorem
I'd say so
Ik I’m probably not aloud to say this but if someone is nice enough to go help me in #precalculus I would really appreciate that ❤️
Yes
But I don't know if there's like
Any weirdchamper technical shenanigan happening
Derivatives are fractions 
Sorry sorry
Derivatives are a ratio of differentials

someone talking CS 👀 ?

Why does big analyze even exist, I know my program will take 2*10^544 years for an input size of 100 😦
What are bare minimum prerequisites for measure theory and lesbesgue integration?
what the HECK is your program
real anal probably
rudin chapters 1-8
Are contents of chapter 8 necessary? Ive heard its about fourier transforms
it's not that you don't need them
they're just bad
so don't
(one of those covers lebesgue integration anyways
)
Oh okay
Btw textbook that my school uses is a bit obscure
So it might require a bit different things
Anayways thanks

So what do you recommend regarding contents from this chapters. skip it or do it with other books?
Btw this is the book assigned
you should certainly do something else
whether that's a measure theory or something outside of analysis altogether, that's your choice
ello guys uhh can someone send me some courses that will help me reach calculus faster i am currently doing from khan but its very long
I haven't done measure theory myself yet but #books-old has this: #books-old message
you can also ask in #book-recommendations if you want
are you comfortable with algebra?
trig?
um
i mean i know basic algebra 1
slopes
@bright hill
hello?
tbh, I'm not that familiar with US's math HS curriculum 😅
so I can't give you a difinitive answer
oh ok but my main goal is to be able to reach calc fast
my best advice is to check out MIT OCW single variable calculus course
and see how it goes
yeah
I think you should try OCW and see if you can keep up
if you ever get stuck you can always ask here
k
what are the prerequisites
ye ok
Wait what was that big brick called again
I think Steward Calculus xdddsddd
What
u blocked me?
also ur messages are gone
oh ok
oh ok
😳
Is it alright to ask a chem question here? Or is there anyother off topic chat?
you can try a help channel, but dont expect anything
there is a chemistry server in #old-network
Hello I'm a noobie in math..
and I'm wondering if anyone's interested to be my friend
For my project I was studying the use of logarithmic calculations in the trajectory of stars, which I wil have to conduct an exploration on
Does anyone know about this area
btw is this suitable for a high school student
“Logarithmic calculations” tell me very little about what you’re actually doing
I know some stuff about the relative movements about bodies in the night sky if you wanna ask anything though
Well it was about how Kepler used logarithmic calculations to help calculate the trajectory of bodies
He even published a book on it
So I was thinking of using that method in my exploration
It is only in the initial stages so I cant give anything concrete
Sure, sounds like a good approach for, what I assume is, a high school project
My math teacher says it may be too complex
Would anyone have some knowledge about the use of logarithmic calculations, logarithmic charts, etc.
I am having difficulty finding the method he used online
Does any one have any advice for getting through Number Theory ? I'm hating this lesson so much due to how boring I find it to be. And because that, I'm not being able to focus and study it.
So far, we did Divisibility, and Congruence






