#book-recommendations
1 messages · Page 231 of 1
further evidence 33A is just an exercise in row-reduction for 10 weeks
RREF by hand 🤢
RREF RACE
AlgeBro 
rn I'm doing Matrix Limits and Markov Chains in lin alg
which is wild shit I'm a little lost so I gotta grind today to understand
Bro
Why do you like it?
Oh yeah I've heard that's the correct homological algebra book
the remarks sections towards the end of each chapter are pretty nice
depends on what you're trying to learn
like it isnt a weibel replacement
I thought it just took Weibel and replaced it with correct theorems
jk
I might reference that a bit for intersection homology, I've been missing so many classes but I think this week I might have a shot to recover. Symmetric spaces group isn't meeting, and no class on Friday. So I can prob just go hard on the other stuff and get caught up on everything aside from intersection homology.
And then I know for a while in the middle intersection homology was going through some homological algebra, kinda to bridge the standard formalism with perverse sheaves
What the heck is intersection homology
I know what homology is but maybe not well enough
ye you need some derived cat stuff
So ordinary homology works nicely on manifolds, not as much on singular spaces
Intersection homology is a version that works nicely on singular spaces, pretty much you're excluding chains that intersect the singular locus "too much"
Hmmm I think I'm following what you're saying. Tbh I don't even know why people studied homology in the first place. I only know about it cause of TDA type stuff. It's all hype beast as far as I can tell BUT the theory does sound cool. Maybe if I knew of historical math problem that homology was developed for I would have a better appreciation. I know everyone fell in love with TDA

thank you.
why are there so many books named "a transition to advanced mathematics"
theres one by Chartrand, Polimeni, and Zhang
and theres one by Smith, Eggen, and St. Andre
Two books with the same title is relatively not that many
There are probably a lot of books called like "Introduction to Real Analysis"
Yeah of course
wait i didnt realise advanced mathematics required transitioning
is this why im bad at it
because im cis?
hartshorne
Lmao
hartshorne

Introduction to the study of Hartshorne
Hartshorne is a commutative algebra book
Angetenar some people will kill you for saying that

It is an algebraic geometry book lol. More commalg heavy than many
I don't do algebra
I used Rudin for analysis, people like Kolmogorov-Fomin but it's old and uses funny terminology
there isnt much commalg after chapter 2
"Intro to Mathematical Analysis" by Kriz and Pultr seems like it's the most comprehensive of the intro analysis books
was going to ask about fomin's here , so what do you mean by funny terms ?
take a calculus book and prove all the theorems
Which one? Kriz?
chapter 2 is definitely the most commalg heavy part
I will not comment on Hartshorne in the future
And about old terminology, I forget what it was offhand
But I think it doesn't have the usual definition of a "compact operator"
the most important think you have to know about hartshorne
its that his name is pronounced "hearts + horn" and not "heart + shorne"
thing
You can check it out then. It basically does like, bit of set theory -> topology -> functional analysis -> measure theory
"Elements of The Theory of Functions and Functional Analysis"
What about
I felt it read fairly smoothly
That I don't think is what you'd be reading if you're thinking of Rudin lol
Anything wrong with just Rudin straight up?
This is in a sense the most terse and fast
(Also I should say people like Pugh but I find it somewhat obnoxious)
Because you do not cover intro analysis at all
(In how it treats topology, it's fine after)
(Sloth , any answer ?)
are u telling me the measure theory chapter of pugh is in any way acceptable 
Oh yeah I mean, the thing I remember offhand was that it defined a compact operator differently
I don't know it lol
o ic
I know multivariable calculus is prob better than the Rudin analog
i'm working through it for my analysis class and i hate it
lol
i was reading Garling's Analysis textbook but it turns out ... uh not for me xD
Read Rudin's paper on the behavior of topological spaces made out of ultrafilters under the assumption of the continuum hypothesis
Idk Garling
pugh ch6 has "proof is obvious from the picture" and non-rigorous definitions and what not 
Mirza K&F won't cover multivariable calculus stuff
And idk if it does stuff like Arzela-Ascoli
is zorich's book equally decent for intro ?
it's called "Calculus and Analysis in Euclidean Space"
Oh it does actually
Yeah
Chapter 2 does a decent bit of stuff you'd learn from an intro analysis class it seems
Okay yeah so
Here already you see an annoying piece of terminology
K&F defines a "compact set" to be one whose closure is "compact" in the usual sense

And a "compactum" is a space which is "compact in itself", aka actually compact
But it's not a compactum
I mean it doesn't cause problems but it's annoying. So that's the main thing to remember going into this book
he should've used "post-compact"
Is there a term for compact non-compactum sets?
precompact?
precompactum?
oh, nvm
If you're fine with having to clash terminology and perhaps unlearn later ones then this is a good book. Probably pick up something like Spivak Calc on Manifolds after for the multivariable calculus
@willow pecan compactn'um
Sure thing fam
precompact families of functions are important in complex analysis 
Hi, I know there is some very recommended book which contains all of the math for physics undergrad studies, Arfker/Arfken or something like that? does anyone know what im talking about? 😅
Arfken/Weber/Harris, I guess.
Mathematical Methods for Physicists is the title iirc.
thank you! 😄
Riley is the undergrad one
Arfken and Weber is the Grad one
@brave kayak
Ask the physics server if you don't believe me :V
Nice.
anyone have some good book recommendations to learn pure math from....zero to decent I guess?
Is there a series like the schaum's outlines but for pure math only and with less mistakes?
Books to learn pure math
Its kid of hard to give a recomendation if theres not a specific topic you wanna learn
In the begining I geat you could learn some basic set theory and logic
Proof writing
Maybe look into the book
Journey into Mathematics: An Introduction to Proofs by Joseph Rotman.
Also theres a few of these books listed in #books-old
- INTRODUCTORY BOOKS
A Programmer’s Introduction to Mathematics (Jeremy Kun)
Aimed at programmers
Explains e.g. linguistic conventions and jargon in a very accessible way; well suited to self-study
Mathematical Proofs: A Transition to Advanced Mathematics (4th Edition) (Chartrand, Polimeni, Zhang)
No prerequisites
https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0134746759
Very clearly written, neither too slow nor too fast. Modern notation and low levels of handwaving. Contains worked examples and outlines of proofs, full solutions to many exercises. Later chapters serve as introduction to various topics.
The Art and Craft of Problem Solving (Paul Zeitz)
Assumes some basic calculus and comparable fundamentals. Anyone with an open mind should be able to profit from it.
The book is really well written, and focuses a lot on the process of solving a problem in addition to actual problem solving. It has a lot of problems after theory. It focuses on the basics of problem solving, and have chapters on problem solving strategies, cross-over tactics, combinatorics, number theory, geometry and some analysis and linear algebra.
How to Prove It (Daniel Velleman)
No prerequisites
A great introduction to proof oriented mathematics (higher/pure mathematics), for people who have never done that kind of thing before.
I found a series of books by springer that is called problem books in mathematics but it seems to be more advanced than the schaum's outlines one.
Are you still choosing books, Forsaken? 
anything in old literature that speaks about math applied to gambling?
I need to make a part of a math presentation with gambling as its theme dedicated to gambling in literature
and tbh I have no idea where to look, I found some stuff about gambling but there is nothing mathematical about it
Look at probability
this is a very broad topic
again probability is the place to look
you could discuss stuff like expected value and ways to seemingly "beat the system" (and why they don't work) like the martingale betting strategy
maybe mention how casinos try and make it as hard as possible for you to make mathematical estimates about the value of a given table
through weird rules that skew the expected value, or unclear slot machine outcomes, or whatever
and if you really want to take a deep dive into expected value as a value measurement, maybe try discussing https://en.wikipedia.org/wiki/St._Petersburg_paradox
though that may be a bit tangential to your "gambling in literature" theme
Persi Diaconis is pretty cool
Slim have you met him?
I organized a talk that he gave

I went to one of his talks

Also my advisor is friends with him ig

I found Il fu mattia pascal
by luigi pirandello
(im italian)
and also, to make up for the lack of maths in that book, Ill refer to il de ludo aleae by girolamo cardano
which was the first ever book to be written about probability
by a gambler and physician

oh wrong chat LMAO

good books to learn algebraic topology?
there are none


there is no good book but if you want to learn it read hatcher i guess
@pseudo forge the basic flowchart is, Hatcher if you like pictures, Bredon if you like smooth manifolds, tom Dieck if you want a very algebraic/categorical/homotopic approach, May if you want a grand total of 3 exercises, Rotman if you want something a bit more chill that leans algebraic
Does May really have no exercises?
One of the grad students at my uni recommended it bc I'm more "categorically minded" according to him
theres a tom dieck reading group rn in some AT server if you're interested
finding it pretty slick so far
I recall trying to read hatcher once. It was weird
hatcher has too many damn pictures for me
im like yes i can draw the picture but i dont see how it works
tom dieck is like lays all the groundwork for you and trusts you can draw the picture
sometimes i find tom dieck is overly detailed but it rarely lacks detail
tom dieck has a scary amount of detail
haha yea
i usually end up like seeing the theorem and trying to intuit the proof out first
May is good, but probably not good if it is your first pass at algebraic "blah"
ye may and tom dieck definitely assumes you know how somewhat to categories already
Officially May doesn't require much categorical stuff
this might sound weird, but manifolds + de rham --> AG (hartshorne) --> AT (May) might not be a bad arc
officially it intros categories to you as well
lowkey me rn except replace may with tom dieck
I think with May you can kinda just "read harder" and it's probably fine?
But I think there are fewer examples/exercises than would be good
depends
@ripe granite so one of my undergrad profs is actually of the opinion that schemesy AG should come after a lot of stuff lol
I took an undergrad AG class with him, and he's like yeah there's a certain amount of AG content that makes sense there
You don't even need serious commalg
Affine varieties, translating between the algebra and the geometry, projective varieties, Hilbert polynomial, degree, Bezout's theorem, 27 lines on a cubic surface
Then he thinks you basically shouldn't touch AG for like a year lol
You should do Hatcher, Guillemin-Pollack, and Bott-Tu
schemsy schemey
Then you either do Griffiths-Harris or AM->Hartshorne
I mostly agree
sounds clearer than jumping into these directly tbh
the thing is AT doesnt have a lot of good books
main issue i had with am was like i rarely knew "why" until a bunch of SE answers
so doing some AG will give you some experience with algebraic blah
I used to think that but I feel like...
and then you should be able to deal with shitty htpy theory texts
There's no universally good AT book but it's kinda, for every person there's a suitable option
I think most people would be solid with either Rotman (easier) or Bredon (harder)
And then it's like
If you lean hard toward algebra already there's May and tom Dieck
again, whatever I say shouldnt be taken seriously
And if you like anime there's Hatcher
I should shill harder for Bredon than I do, in my mind it's the closest thing there is to "the correct AT book"
i feel like prob better to start with rotman/bredon to get a rough sense of direction then may/tom dieck
a lot of AT books have some super dry stuff
do AG
learn some AT in an ad hoc manner
and read papers
Lol AG is harder for me to get into somehow
Like I know all the cool places where it's going
But quasicoherent blah over Noetherian your mom is just like
Smh
lmao
One day I'm gonna stop being a wuss and just learn it
you just need to stare at groth or deligne for long enough
But it is not that day
and you will be inspired
time to set groth as my phone backgroumd
That pic of Groth holding Atiyah
Any good books on Fourier series with actual
(lebesgue) integrals.
In my analysis class we are using Folands Real Analysis and currently doing the chapter with Fourier analysis
With actual integrals right?
Idk what that means
Lebesgue.
What about lebesgue integrals
That's illegal lol.
not if u buy the book
start with hatcher to build Intuition :smug:
then take the dieck or maypill
hatcher intuition heh
i tried
and couldnt
id say rotman was the first book to click to me
hatcher exists to make u learn how to draw pretty pictures
HAHAHAHA
AT is so sad for me cause i like it but im also not very good at it
meanwhile me with the tom dieck pill
typing out some notes cuz ch 5 and 6 uses a lot of ch 4 and i dont rlly have too much intuition for the behavior of ch 4 stuff yet
mhm
trying to show some sort of functoriality for the double mapping cylinder he seems to skip over it lol
i did ch3 of tom dieck by skimming it once and then reading it again and proving every proposition myself 
ch3 is more like once you understand the big outline everything seems so nice
quite slick tbh
it very much is
just poke around with categories oops done
haha
he fully develops it in ch4
then only uses it in ch6
ch4 is like mathematical preliminaries lol
first half of ch4 appears in ch5 and second half in ch6
kool
also doing the "dont read any of the proofs do it all yourself" thing
tbh its much more fun this way
def longer tho
:egg_hank:


it's ok you arent the only crackpot here
thank u for blocking it out 🙏
i still think the last few exercises of ch 1 are literally deranged
for sure
its fun though
chmonkey can cope and seethe all he wants but developing spec from the ground up on ur own is so good
what do you mean
I had to do a lot of that
also yeah, chapter 1 is garbage
I never got past it because the exercises are mad
ik u did it but u said its bad
its Fun
the nullstellensatz exercise is evil though.
Aria moment.
Nice
huh seems like i jus need \hspace{bigbig} and it fixes the problem
wtf
i dont understand but i shall not quesion
Until you add another thing and it breaks
HAHAHAA
Any recommended books for those in highschool?
Pre Uni the best source is Khan Academy
College works too since I'm just getting a list for a channel topic lol
But if you are really really insistent on getting a book then there is lang's basic math
yes
Awesome
#books-old also has a bunch of stuff if you didn't see it
books section needs to be updated with intro high school books
Considering 75% of this server is highschoolers, that's probably a good idea
i put in a request ages ago for langs basic maths to be added into #books-old
but i dont think the google form is being monitored any more
Means I'm a part of the remaining 25% since I'm a middle schooler
fascinating
what do you mean by "fascinating"?
Sarcasm
Oke
So what you meant then?
Thats also sarcasm 😂
Oof.
Double sarcasm
I'm sarcasm.
ima add to the AT book pile and mention croom's "basic concepts of algebraic topology"
it's even easier than rotman
coom
Anyone know of any decently understandable books on category theory?
Riehl
Her book is fantastic
one of the few texts I consider the book to read, honestly
Riehl is particularly good at writing about subjects that have had conventional shifts so that everything in her texts is more or less up to date with current nomenclature
I'll check it out, thanks!
I found some easy to follow notes by paolo perrone that were posted last year.
yeah, Riehl's great
for a very, very elementary and gentle one, I always recommend Lawvere, Conceptual Mathematics
avoid Categories for the Working Mathematician like the plague unless you happen to be a working mathematician
how about leinster?
Oh, why is it bad? (Too advanced?)
I like Leinster
MacLane goes into some very nitty gritty details about set theory and foundations and stuff, and is just kind of hard imo
its also outdated in some senses
esp terminology
i think he likes, distinguishes between metacategories and similar issues
I have referred to Maclane for certain results
All of which, so far, were given as “look at pages... of Maclane for a reference” and so I did
yeah i mean it was probably the best reference text for a long time
What textbook would you recommend to study probab. and stat.?
There are so many I am literally screaming
Bourbaki
There is Munkres
Requires no intro except some mathematical maturity
Runde, V. - A Taste of Topology?
It develops all elementary concepts and proves all standard theorems in just ~165p.
Nice, have fun
Janich is like 200 pages, but haven't read it completely yet @gray gazelle
Can someone suggest an intermediate-level textbook on set theory for me? I have a fair amount of background in first-order logic and basic model theory, and am currently an undergraduate student in mathematics (and so also have some familiarity with naive set theory).
Enderton is p easy
I'm looking for something preferably not too basic, because I'll probably find it too slow.
Hello! Anyone that has a book/PDF on basic representation theory to recommend for a high schooler? I feel fairly comfortable with basic algebra and basic linear algebra, however, the PDF's that I have found online are a little too complicated for me. My teacher has recently started to talk about representation theory but I want to dive deeper into this.
Actually, I think that I found a nice PDF: http://www.math.lsa.umich.edu/~kesmith/rep.pdf. From just scrolling around for a bit, I think that this PDF is well suited for dummies like me!
High Schooler
Representation Theory
One of these things is unlike the other.
Anyways - by Algebra do you mean "Jacobson/Artin Algebra" or Elementary Algebra where you solve quadratic equations and the like?
I hail from a similar background on self-taught Lin.Alg. and going over abstract algebra (it's the former) and using this book for Representation Theory -
https://cdn.discordapp.com/attachments/730480887803674688/801462998509420574/IMG_20210120_094741.jpg
Been working out great so far



Oh, my teacher actually gave me similar text on abstract algebra! It is quite complicated for me tho...
well it's a very common format

all the "Graduate Texts in Mathematics" books look the exact same
apart from the name of the book
they are also very complicated, and I would recommend you to stay away from them considering you're a high schooler
Yeah... I have read parts of it, however, the tempo is a little bit too fast for me. I feel like I don't really get the intuition
Yea,You should probably do The ugtm series first
you should probably put representation theory on the shelf for now
try becoming much more familiar with abstract algebra
the one in the undergraduate texts in mathematics series
I think it's by lang
there's also a million other great abstract algebra textbooks
such as d&f
Well I have actually written my final project on abstract algebra. I have gone over groups, rings, fields and bits of Galois theory. I do not know if this is enough to learn representation theory tho
I don't want to learn everything, I just want to learn the basics
you should probably also be familiar with modules
in abstract algebra
also probably need some working category theory knowledge
Wait
no?
for rep theory?
All you need for basic rep theory is a decent linalg background and group theory

its complicated and interesting but the prereqs arent a big deal
Well category is something that I am not that familiar with and I kind of get the "intuition" behind modules. I think that they want to generalise vector spaces over fields, right?
So the inverse requirement gets dropped with modules, right?
Modules are just vector spaces over rings
Axiomatically they don't look very different
Oh okay!
But the underlying additional axioms on fields
cause Vector Spaces to be much nicer
than Modules
in general
But yeah for rep theory at the level of, for example, Fulton Harris
you really don't need anything other than linear algebra and finite group theory
maybe some experience w complex numbers and complex inner products is useful
it goes off the rails pretty quickly because it turns out the next most general class of groups other than finite for which rep theory is very useful
is (compact) Lie Groups
so it ends up getting more advanced
but you can get all the big ideas just using finite groups
Okay, I will give it a try then! And like I said, I do not really want to learn EVERYTHING in rep. theory, just the basics.
Then, if I have time, I could start to dig in to Lie groups
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should
so this one?
yeah
Okay, thank you so much! I will check it out!
np
(Replying so it doesn't get buried)
Shot in the dark, are there any good books or lectures or videos about programming in abstract algebra?
Like, there are apparently algorithms to compute a lot of hard algebraic data
but I have trouble wrapping my mind around combining abstract algebra and programming in, say, python
Ideals, Varities, and Algorithms by Cox, Little, and O'Shea does some computational algebraic geometry
there also is A Course in Computational Algebraic Number Theory by Cohen but it's more towards number theory (and no specific language)
and the standard for computer stuff is Modern Computer Algebra by von zur Gathen
(although probably too 'basic' for your needs)
Where do I learn cat theory in context of programming
Applied category theory twitter
Pls serious replies only
@ mniip
@ mnoop
@ mnoopers
@ mnoopy
@ mnoopie
a mad lad

@fast portal maybe https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/
however if you're not already familiar with cat theory I'm not sure this is a good idea
Fine fine, baby's first intro to cat theory?
It exists -
Good course - https://applied-compositional-thinking.engineering/
Motherfuck
riehl
but learning category theory from riehl might be tricky if you arent somewhat literate in a lot of early undergrad level math
You are telling me there is a way to learn it without prerequisites? 👀
🤔
And soft prerequisites?
category theory is a language that brings together a lot of mathematical ideas and is therefore usually taught that way
but in theory you can learn it in a vacuum
you shouldnt
Wait so was Cat Theory an attempt at Theory of Everything™️ but for math?
i think a lot of constructions will seem somewhat random if you have no examples to draw from
like imagine learning about model categories without knowing any topology
it would just seem erratic lol
i think the standard reason is like
say you want to become a “well-rounded” mathematician in some sense
i think category theory first does little for you
but category theory after learning other stuff
can paint a very important picture
yeah that is my point hahaha
like
its hard to have any intuition about categories
if you dont have a diverse background of examples
like i would find adjoints mystifying (and did when i first read about them) without a bunch if examples i could prove by hand
Suddenly all of those memes about Cat theorists declaring everything in terms of categories makes sense.
uh I guess thinking methodically falls under structural thinking
personally i think its kind of silly to entrench oneself in one point of view
i think all the best mathematicians are very good at switching between them depending on what they want to do
(similar to model categories vs infinity categories stuff)
maybe my point is more one should make an concerted effort to train the other hand
yeah for sure
i do think theres some truth to it
ive seen people who like, just dont want to think about a question if it cant be solved one way or the other
In my experience - an intro to this kinda course doesn't expect from you much if you know some basic Lin.Alg. and proofs (Though knowing some Algebra and/or Topology is a plus)
The applied one I learnt was based on understanding of robotics, control theory and optimization
I saw someone applying lie theory to robotics
Group actions to move robot arms and joints
i think it's quite standard to use quaternions for rotation stuff
i can apply robotics to category theory by making robots draw diagrams
Ye, I'll send you my pdf right now. Do PayPal first though.
joking about piracy probably not a good idea btw
no
Tfw learning about topological fibrations via type theoretical intuition for sum types

It's helps in jumping across different domains ("a co-design approach to robotics ")
One of the challenges of modern engineering, and robotics in particular, is
designing complex systems, composed of many subsystems, rigorously and with
optimality guarantees. This paper introduces...
Quaternions are probably the most common things to apply to computational dynamics (Especially in Autonomous Quadrotor control)
"Co-Design".... Isn't that the dual of "Design" ?
No.wonder engineers are known for such wondrous stuff like Tacoma Narrows Bridge incident

That's actually a thing -
There has been some interests in robotics circles to simulate some results in reasoning found in neuroscience work via a robotic arm drawing/doodling/writing answers corresponding to a question
what does that have to do with category theory
Well, an extension of logical reasoning can actually work towards simulating results for robots to do proofs for us?
probably not
What

“using category theory to capture the essence of human thought” 
I agree that I did not get it at all, but "using" was your word.
I would equally sully "Category theory is the essence of human thought"
I might even sully it sullier
i think that if you think category theory is at all capable of capturing the essence of human thought you have not seen enough human thought lol
it can’t even capture the essence of all mathematics lol
mniip crank confirmed
Always has been
You need to either read the full question, or you need to expand the notion of what thougt is
ok i'll take the bait
why do you think category theory is the essence of human thought
"Generalized"
Doesnt really mean much
Any thing can be a generalization of anything if you try hard enough
i think you'd really have to break your neck to view schemes as generalized triangle inequality lmfao

Speaking of that, Harthshorne wrote a book on classical geo
That convo was like at least half shitpost
which half isn't 
Look do you never hit a blunt and have like a shower thought that makes sense on some spiritual level

Yall giving ephemeral conversation the scrutiny of peer review
thats bc its very funny
This hot take isnt even original
lol this shitpost is amazing https://ncatlab.org/nlab/show/nPOV
This was the og one,ig
does that page claim that nPOV captures human thought
i dont think Urs is that silly
I swear it makes sense guys https://bartoszmilewski.com/2018/01/11/the-earth-is-flat/
Bartosz is definitely a character

What makes you say that lol
Honestly at times I feel like Bartosz is the Wildberger of CS
Ive spoken out against him myself bwfore
Bartosz is generally seen as like
good at what he does
but a crank in his pontificating

His blog/videos are what got me into higher level math
doesn't mean he's above criticism tho
im sure this is true of a good number of people
but he often says like
ridiculous things
about category theory
and how it related to other things
there was some discussion of this the other day
Deja vu I feel like we have been here before
about his claims about General Relativity
god that reminded me that I should've taken general relativity instead of multivariable advanced calc
Uhhhhhhhhhhhhh
you should probably take the latter before the former lol
You do not wanna take general relativity before advanced multivariable calculus
Hmm? Okay
our multivariable advanced calc is a toned down grad analysis course
start here

sorry drunk about ping
its just instead of abstract spaces we only look at rn
I already took our differential geometry course, and gen rel is after diff geo
for undergrads at least
both are senior level and require real analysis
Ah, when you say "advanced multi" that sounds like, practically borderline diffgeo
Like calculus on manifolds
Which you very much want for GR I'd feel
But yeah I mean... analysis is cooler than diffgeo for me
Anyway
Screneshot
I'm more partial to algebra
if you like algebra why are you taking any of these courses lol
just take like alg top
for fun

Hmm, I think "capture the essence of human thought" is a lot stronger than what n-cat pov is capable of
Plus I'm in my first topology course rn, so getting into alg top isn't really an option
My impression is that it's just, let's look at everything it does give us insight into and look at it from that pov
Human thought seems way too complex for that
Yeah lol
Knowing nothing about actual weed I can buy that this is a classical "hints blunt" moment
honestly ive never experienced that kind of high

i more or less am just like a slightly slower version of my normal thought patterns while high
Given that I hear you typically have a lot of crazy insight that's actually just nonsense once you get your cognitive capabilities back
i think that is like
mostly rumor or like
first time you’ve ever hit a blunt
stuff
people who have used it a few times generally get over seeing it as this “deep” experience
at least for THC
So reading the article on the nPOV
It seems like they're not internally consistent about what it is lol
Or how strongly they wanna push it
Part of it is "We write from the pov that category theory/higher category theory is useful"
And like alright why not lmao
i think practically the nPOV boils down to
But occasionally bleeds and at least tries to explore the claim that "category theory is the right language to describe the world, or at least the world of mathematical ideas."
we will write unapologetically assuming that the reader is fluent in higher category theory
and we will frame topics in this language even where this is not necessary
my guess would be that that page was written by different people
I just mean the underlying philosophy
Could be
I sorta feel like I've got a vague idea of where these different levels of strength are coming from though
Like right now Scholze hasn't worked his magic enough
For anyone to be able to look a PDE person in the eye
And with a straight face say "Higher category theory is relevant to you"

But I think deep down some people wanna believe?
(This article doesn't mention Scholze but if anyone's gonna do it it's prob him lol)
With his rigid analytic whatever the fuck
i mean its an incredibly useful POV without a doubt
but the idea that all of human thought is amenable to it
is pretty ridiculous
i would not be shocked if it can say something about all of mathematics
idk i think there are clear examples of things that category theory can’t do
like as much as Freyd-Mitchell is a very powerful theorem
it also is very clearly saying there are things category theory can’t see
whether the collection of all things category theory can’t see is all “trivial” is a different question
but I don’t believe it
Yeah I think human thought is overdone. Mniip cites Curry Howard and... I'm not gonna claim to actually know it but
Okay so I'm gonna preface this by saying
Well even Curry Howard is an incredibly restricted subset of human thought
unless the claim is that either mathematics or programming is capable of expressing all of human thought

I feel like when you're doing a proof there's sorta the "syntax vs semantics" question
Curry-Howard in my impression is a bit of a syntax-y thing
While in a lot of cases where there's "content" it's in the semantics. You can get the x => y but not as much the "idea"
well
Maybe I'm being a Platonist here
the typical human brain is a turing machine
max
proof:
alex turing was, quite literally, a turing machine
and the typical human is dumber than turing
hence less computational power
but can still visualize tape
so we have equality.
qed
But yeah idk for those of you listening am I talking out of my ass here?
I guess let's soften it to just saying, I don't think the theory of proofs can really subsume the proofs themselves. Kinda like how, okay real numbers are a set but analysis isn't a subset of set theory
This is sorta why I don't at a glance buy Curry-Howard even really saying that ncat business can fully subsume math, corollary human thought
Then again who knows Scholze seems to be a magician so...
I feel like this exact discussion was had sometime earlier in this server
if a brain can be accepted as equivalent to a turing machine
or something
Curry-Howard isn’t directly related to nPOV
I think jesse brought up some paper that discussed some results if we assume the brain is a turing machine or something
if my memory servers right
im not sure this is the same at all

which is probably a meme
Scroll up a bit for mnoop crankery
So I'm gonna make some possibly ballsy assumptions here on what mniip was gunning for (up to a hits blunt moment)
@molten wave I should ping you here, if my depiction of anything you say is inaccurate please do let me know
But it seems like Curry-Howard basically says "proofs are programs"
At least up to homotopy it says that
nah it's a more vague and philosophical realization
of the human approach to solving problems
using separation of concerns
I see
curry howard is a theorem
"it" isn't Curry Howard so much as
i guess if you pair it with Church-Turing you get something pseudophilosophical
Sorry I was out
But yeah when mniip was saying
"Curry howard isn't a coincidence, it's how people think"
That I think is the vague realization
that's along the same lines of thought
again the things I'm saying here are precisely vague
profound bs tier

I heard from... a source that Bourbaki’s point set is the literal best point set still
I wouldn’t normally make this recommendation to any living human but you use Lang so idk if you’re still alive at this point
that sounds scary
im confident that id come up with bad intuition if i tried to do it on my own
at least for basic courses like topology
maybe after gaining a solid background w all the basic classes of a degree it'd be a good idea
okay but do you actually want to learn all that point set 
you dont need very much for that then
the first chapter of bredons topology and geometry is enough
i dont think theres any inherent value in reading books that are especially terse
i mean bredon isnt long winded either but do u want to read bourbaki because you think the content and style would be good or because bourbaki is famous for being hard 
idk a lot of people (including me tbh) fall into the trap of "famously difficult but advanced = good" but in the end it just ends up eating a lot of time and often not really giving u very much
i enjoy terse styles too I think. It's just nice being able to (and being forced to) fill in details for proofs so that I understand them better
theres nothing wrong with terseness
rather than just having my eyes glaze over proofs and pretending that I understand them
i also think its better
but like
do u really want to read bourbaki talk about uniform structures or whatever 
Terseness for the sake of being terse is not really good though
Skipping over small details, fine
Skipping over large details, not fine
terseness is fine, but giving no intuition is not
d&f is way too far in the other direction
You can shit on d&f all you want, it is still my treasure
I liked D&F because I have no algebra brain cells
d&f is really good
lmfao, same
I really love d&f because of how easy it is to grasp
(except this section on injective/projective/flat modules)

but that's probably just me being too dumb
I doubt d&f can make it any easier
it's just a weird concept
(for me at least)
you're at the point where things start to get super interesting
i think dfs style is not super conducive to like
sometimes when im reading something i want to have it set up so i can read the statement and then try to prove the thing on my own
and then after i do that check back
and its kind of hard to do that with df
im reading halmos' "logic as algebra" and goddamn it is sassy
it has a very like. dry sense of ironic humor
(That the preceding sentence commits the error of using a thing as a name of that thing is just adding wanton insult to cruel injury)
idk it has a lot more personality than most texts i've read
i only picked it up because i have a student who needs help with it
and i went for an algebraic interpretation anyway
hi, i remember seeing a large book of problems in analysis. by a russian i think? wondering if someone knew its name
demidovich ?
oh it was the one by john erdman, but thanks
whats a good book that a 9th grader would understand? the topic doesnt matter
a 9th grader could possibly understand hartshorne
That is unironically hs level
@golden locust likes me
oh
well i didnt know the author and i am not native english speaker and thought it was some idiom or whatever, so i translated it and it came out "nothing"
so im sorry D:
(don't read hartshorne)
yea that was the mistake
hartshorne
Wait then what do you read for alg geo
Hartshorne
Hartshorne

@flint forge you asked about books that presented a computational perspective for algebra a few days ago
Bernd Sturmfels has a book on his website titled "Invitation to Nonlinear Algebra" which focuses on computational alg geo
He also has some survey articles
"3264 Conics in a Second" comes to mind
👀👀👀👀
What
I'm just budding in cause that sounds cool. I had been looking at that ideals varieties and algorithms book but that sounds like it's in a similar vain
Sturmfels' book is probably written at a higher level
He taught a course based on it a few semesters ago and it seemed to be very fast paced and sort of a disaster
I wonder if I can find those lectures
You can certainly see the lecture notes on his website
Some video recordings as well
From an earlier iteration
stacks 
Your a mad man lol
Would have to be a 9th grader that’s pretty damn good at math
@broken meadow

who sniped
i want to see you get your first blood
i already banned 3 ppl before
nice
Oh
in the same day

namington is very fast
Destroyed by fax and logic
I'm an afk owner of some anime server, and one day I checked back on it and saw some cringery
2/3 of my complex anal lectures this week are cancelled 

sadly i cant ban metalninja
sadge
But,he can
i can't ban metalninja either
,ban namington
This may only be done by a moderator!
,ban @broken meadow
Failed to ban @broken meadow: You don't have permissions to ban this member!
Fail
pog
huh
i dont think id be able to give it back though

do it
i can't remove yours though
Metal,Remove Nami's mod role
you wont
Now
this is very strange
oh never mind
it showed the x when i hovered over it
but it didnt actually delete
unless it just takes time to update

,ban namington
This may only be done by a moderator!
,whohas moderators
Members in Moderators
=====================
1. samanthaCS#6064
2. RokettoJanpu#6002
3. .jun#0008
4. DMAshura#3583
5. Namington#1983
6. Faye#2862
7. mniip#9046
8. Rijinaru#5601
9. Puerøsøla#0494
10. woog#7945
11. MetalNinja27#7212
12. fiona#1729
13. dGhost#0069
14. Daminark#6041```
Imagine if power hieracy order was graded instead of just being lexicographic

Sorry, It's not even lexicographic

lmao Daminark is last

who are the other old men
dGhost presumably
fino presumably
MetalNinja27 presumably
woog presumably
Puerøsøla presumably
Puerøsøla is canonically old

im old ? pain
i thought woog was almost as old as namington
What r these numbers
Coordinates to send hitmen
It has something to do with the date.

jesse has a nice short name
woah 8da got 1
Actually, there was a magic for me, I think the bot knew that I should be number 1


@sudden kindle highly rec Ender's Shadow if liked Ender's Game
about Bean?
What's with these numbers?





