#book-recommendations

1 messages · Page 231 of 1

mossy flume
#

all of these are meant to be the only lin alg class one takes here at UIUC

#

none of them have any lin alg pre reqs

marble solar
#

further evidence 33A is just an exercise in row-reduction for 10 weeks

mossy flume
#

RREF by hand 🤢

hollow drum
#

RREF RACE

ripe granite
#

AlgeBro zoomEyes

mossy flume
#

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

hollow drum
ripe granite
#

also, completely unrelated to the discussion

#

Gelfand and Manin

#

good book

hollow drum
#

Why do you like it?

sage python
#

Oh yeah I've heard that's the correct homological algebra book

ripe granite
#

the remarks sections towards the end of each chapter are pretty nice

ripe granite
#

like it isnt a weibel replacement

sage python
#

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

hollow drum
#

What the heck is intersection homology

#

I know what homology is but maybe not well enough

ripe granite
#

ye you need some derived cat stuff

sage python
#

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"

hollow drum
#

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

willow pecan
raw pawn
#

thank you.

tacit creek
#

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

willow pecan
#

Two books with the same title is relatively not that many

tacit creek
#

uhhh

#

probs true

#

anyways

willow pecan
#

There are probably a lot of books called like "Introduction to Real Analysis"

tacit creek
#

i assume theyre not the same books

#

hmmm

willow pecan
#

Yeah of course

quick hornet
#

wait i didnt realise advanced mathematics required transitioning

#

is this why im bad at it

#

because im cis?

willow pecan
#

Rudin

gray gazelle
ripe granite
#

hartshorne

sage python
#

Lmao

ripe granite
#

hartshorne

willow pecan
sage python
#

Introduction to the study of Hartshorne

willow pecan
#

Hartshorne is a commutative algebra book

sage python
#

Angetenar some people will kill you for saying that

willow pecan
sage python
#

It is an algebraic geometry book lol. More commalg heavy than many

willow pecan
#

I don't do algebra

sage python
#

I used Rudin for analysis, people like Kolmogorov-Fomin but it's old and uses funny terminology

ripe granite
#

there isnt much commalg after chapter 2

sage python
#

"Intro to Mathematical Analysis" by Kriz and Pultr seems like it's the most comprehensive of the intro analysis books

gray gazelle
#

take a calculus book and prove all the theorems

sage python
#

Which one? Kriz?

ripe granite
#

chapter 2 is definitely the most commalg heavy part

sage python
#

Or K&F?

#

Ah I didn't realize that. I just know the coverage seems great

willow pecan
#

I will not comment on Hartshorne in the future

sage python
#

And about old terminology, I forget what it was offhand

#

But I think it doesn't have the usual definition of a "compact operator"

dense pewter
#

the most important think you have to know about hartshorne

#

its that his name is pronounced "hearts + horn" and not "heart + shorne"

gray gazelle
#

thing

sage python
#

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"

willow pecan
#

What about

sage python
#

I felt it read fairly smoothly

willow pecan
#

Stein and Shakarchi

#

No intro analysis

#

Straight to Fourier analysis

sage python
#

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?

willow pecan
#

This is in a sense the most terse and fast

sage python
#

(Also I should say people like Pugh but I find it somewhat obnoxious)

willow pecan
#

Because you do not cover intro analysis at all

sage python
#

(In how it treats topology, it's fine after)

gray gazelle
#

are u telling me the measure theory chapter of pugh is in any way acceptable hmmm

sage python
#

Oh yeah I mean, the thing I remember offhand was that it defined a compact operator differently

#

I don't know it lol

gray gazelle
#

o ic

sage python
#

I know multivariable calculus is prob better than the Rudin analog

gray gazelle
#

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

willow pecan
#

Read Rudin's paper on the behavior of topological spaces made out of ultrafilters under the assumption of the continuum hypothesis

sage python
#

Idk Garling

gray gazelle
#

pugh ch6 has "proof is obvious from the picture" and non-rigorous definitions and what not opencry

sage python
#

Mirza K&F won't cover multivariable calculus stuff

#

And idk if it does stuff like Arzela-Ascoli

ripe granite
#

for multivariable calc

#

there's a book written by Shurman

#

pretty good

gray gazelle
#

is zorich's book equally decent for intro ?

ripe granite
#

it's called "Calculus and Analysis in Euclidean Space"

sage python
#

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

willow pecan
sage python
#

And a "compactum" is a space which is "compact in itself", aka actually compact

gray gazelle
#

that's amusing

#

(0,1) is compact.

sage python
#

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

gray gazelle
#

he should've used "post-compact"

willow pecan
#

Is there a term for compact non-compactum sets?

gray gazelle
#

precompact?

willow pecan
#

precompactum?

gray gazelle
#

oh, nvm

sage python
#

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

willow pecan
#

compact'unt

sage python
#

Sure thing fam

sudden kindle
#

Precompact

#

Means closure is compact

gray gazelle
#

precompact families of functions are important in complex analysis hmmm

brave kayak
#

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? 😅

karmic thorn
#

Arfken/Weber/Harris, I guess.

#

Mathematical Methods for Physicists is the title iirc.

brave kayak
#

thank you! 😄

fast portal
#

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

karmic thorn
#

I just remember Arfken is a bit more comprehensive than Riley.

fast portal
#

Aye

#

It is the grad one after all

karmic thorn
#

Nice.

blissful vine
#

anyone have some good book recommendations to learn pure math from....zero to decent I guess?

cobalt arch
#

Is there a series like the schaum's outlines but for pure math only and with less mistakes?

sudden kindle
#

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.

cobalt arch
#

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.

karmic thorn
#

Are you still choosing books, Forsaken? catThink

gray gazelle
#

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

willow pecan
#

Look at probability

quick hornet
#

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

#

though that may be a bit tangential to your "gambling in literature" theme

willow pecan
#

Persi Diaconis is pretty cool

#

Slim have you met him?

#

I organized a talk that he gave

sudden kindle
#

I went to one of his talks

willow pecan
sudden kindle
#

Also my advisor is friends with him ig

willow pecan
gray gazelle
#

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

willow pecan
#

Why are you playing tf2

#

When you have a project to be doing

gray gazelle
#

ahem

#

for mathematical reasons

#

ok let's get it over with

sudden kindle
#

ahhhhhh

#

i keep getting distracted

#

YAMIN FOCUS

willow pecan
sudden kindle
#

oh wrong chat LMAO

willow pecan
pseudo forge
#

good books to learn algebraic topology?

gray gazelle
#

there are none

willow pecan
pseudo forge
gray gazelle
#

bad TTerra

polar tulip
#

there is no good book but if you want to learn it read hatcher i guess

sage python
#

Should I make an AT book megathread?

#

😛

#

At some point maybe. For now I'll say this

fast portal
#

Yes.

#

More megathreads are good.

sage python
#

@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

storm sleet
#

One of the grad students at my uni recommended it bc I'm more "categorically minded" according to him

sage python
#

Not no exercises but noticeably fewer than in the other books

#

2-3 per chapter

calm crane
#

theres a tom dieck reading group rn in some AT server if you're interested

#

finding it pretty slick so far

gray gazelle
#

I recall trying to read hatcher once. It was weird

calm crane
#

hatcher has too many damn pictures for meopencry

#

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

ripe granite
#

tom dieck has a scary amount of detail

calm crane
#

haha yea

#

i usually end up like seeing the theorem and trying to intuit the proof out first

ripe granite
#

May is good, but probably not good if it is your first pass at algebraic "blah"

calm crane
#

ye may and tom dieck definitely assumes you know how somewhat to categories already

sage python
#

Officially May doesn't require much categorical stuff

ripe granite
#

this might sound weird, but manifolds + de rham --> AG (hartshorne) --> AT (May) might not be a bad arc

calm crane
#

officially it intros categories to you as well

#

lowkey me rn except replace may with tom dieckopencry

sage python
#

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

calm crane
#

probably but youll end up with like

#

ok so how do i exactly compute a colimit even

ripe granite
#

depends

sage python
#

@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

gray gazelle
#

schemsy schemey

sage python
#

Then you either do Griffiths-Harris or AM->Hartshorne

ripe granite
#

I mostly agree

calm crane
ripe granite
#

the thing is AT doesnt have a lot of good books

calm crane
#

main issue i had with am was like i rarely knew "why" until a bunch of SE answers

ripe granite
#

so doing some AG will give you some experience with algebraic blah

sage python
#

I used to think that but I feel like...

ripe granite
#

and then you should be able to deal with shitty htpy theory texts

sage python
#

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

ripe granite
#

again, whatever I say shouldnt be taken seriously

sage python
#

And if you like anime there's Hatcher

ripe granite
#

as I havent actually read an AT book properly

#

yet

sage python
#

I should shill harder for Bredon than I do, in my mind it's the closest thing there is to "the correct AT book"

calm crane
#

i feel like prob better to start with rotman/bredon to get a rough sense of direction then may/tom dieck

ripe granite
#

a lot of AT books have some super dry stuff

#

do AG

#

learn some AT in an ad hoc manner

#

and read papers

sage python
#

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

ripe granite
#

lmao

sage python
#

One day I'm gonna stop being a wuss and just learn it

ripe granite
#

you just need to stare at groth or deligne for long enough

sage python
#

But it is not that day

ripe granite
#

and you will be inspired

calm crane
#

time to set groth as my phone backgroumd

sage python
#

That pic of Groth holding Atiyah

ripe granite
#

but actually tho

#

the amount of shit deligne did is insane

grave egret
#

Any good books on Fourier series with actual pepecough (lebesgue) integrals.

sudden kindle
#

In my analysis class we are using Folands Real Analysis and currently doing the chapter with Fourier analysis

sudden kindle
#

Idk what that means

grave egret
#

Lebesgue.

sudden kindle
#

What about lebesgue integrals

grave egret
#

Nvm, I'll check.

#

Any pdf version?

sudden kindle
#

Library genesis

grave egret
#

That's illegal lol.

flint forge
#

not if u buy the book

steel viper
#

then take the dieck or maypill

calm crane
#

hatcher intuition heh

#

i tried

#

and couldnt

#

id say rotman was the first book to click to me

steel viper
#

hatcher exists to make u learn how to draw pretty pictures

calm crane
#

HAHAHAHA

steel viper
#

AT is so sad for me cause i like it but im also not very good at it

calm crane
#

meanwhile me with the tom dieck pill

steel viper
#

lol

#

yeah

#

are u doing the mapping cylinder stuff

calm crane
#

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

steel viper
#

mhm

calm crane
#

trying to show some sort of functoriality for the double mapping cylinder he seems to skip over it lol

steel viper
#

i did ch3 of tom dieck by skimming it once and then reading it again and proving every proposition myself smugsmug

calm crane
#

ch3 is more like once you understand the big outline everything seems so nice

#

quite slick tbh

steel viper
#

it very much is

calm crane
#

just poke around with categories oops done

steel viper
#

the fiber sequence sneak peak is nice too

#

puppepilled

calm crane
#

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

steel viper
#

im going to read thru ch4 when i get home

#

rn i am doing AM

calm crane
#

kool

steel viper
#

also doing the "dont read any of the proofs do it all yourself" thing

#

tbh its much more fun this way

#

def longer tho

calm crane
#

yea im skipping over a lot of proofs

#

the proofs are kinda too detailed lololol

steel viper
#

:egg_hank:

calm crane
azure stirrup
steel viper
#

proving the nullstellensatz :sadge:

#

going to be so cringe

calm crane
#

it's ok you arent the only crackpot here

steel viper
#

thank u for blocking it out 🙏

#

i still think the last few exercises of ch 1 are literally deranged

calm crane
#

HAHAHAHA

#

ch1 is quite hard yea

#

gets easier from then

steel viper
#

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

dapper root
#

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

steel viper
#

ik u did it but u said its bad

#

its Fun

#

the nullstellensatz exercise is evil though.

calm crane
#

eww the big diagram doesnt want to center itself in latex

#

am disgusted

gray gazelle
#

\centering

calm crane
#

still doesnt work

#

it's like

#

somehow more rightwards than centered

fast portal
#

le hspace has arrived

#

Actually does negative hspace work for a whole figure

calm crane
#

:o

#

lemme try

#

i forgot about that HAHAHAA

fast portal
#

Aria moment.

calm crane
#

it works

#

hypeee

fast portal
#

Nice

calm crane
#

huh seems like i jus need \hspace{bigbig} and it fixes the problem

#

wtf

#

i dont understand but i shall not quesion

fast portal
#

Until you add another thing and it breaks

calm crane
#

HAHAHAA

modern night
#

Any recommended books for those in highschool?

fast portal
#

Pre Uni the best source is Khan Academy

modern night
#

College works too since I'm just getting a list for a channel topic lol

fast portal
#

But if you are really really insistent on getting a book then there is lang's basic math

modern night
fast portal
#

yes

modern night
#

Awesome

fast portal
#

#books-old also has a bunch of stuff if you didn't see it

modern night
#

Oh! I missed that. Thank you!

#

Whoa, a bunch of stuff indeed.

sudden granite
#

books section needs to be updated with intro high school books

sudden kindle
#

Considering 75% of this server is highschoolers, that's probably a good idea

sudden granite
#

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

gray gazelle
quick hornet
#

fascinating

sudden kindle
#

Middle school = highschool = elementary school

#

It's all the same

gray gazelle
#

Wut

#

XD

gray gazelle
sudden kindle
#

Sarcasm

gray gazelle
#

Oke

quick hornet
#

how dare you insinuate such a thing

#

i would never be sarcastic in this server

gray gazelle
#

So what you meant then?

sudden kindle
#

Thats also sarcasm 😂

gray gazelle
#

Oof.

sudden kindle
#

Double sarcasm

gray gazelle
#

I'm sarcasm.

warm glen
#

ima add to the AT book pile and mention croom's "basic concepts of algebraic topology"

#

it's even easier than rotman

gray gazelle
#

coom

reef oar
#

Anyone know of any decently understandable books on category theory?

flint forge
#

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

reef oar
#

I'll check it out, thanks!

pale scarab
reef oar
#

Ooo

#

I'll give those a look as well.

slow roost
#

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

warm glen
#

how about leinster?

gray gazelle
slow roost
#

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

flint forge
#

its also outdated in some senses

#

esp terminology

#

i think he likes, distinguishes between metacategories and similar issues

dapper root
#

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

flint forge
#

yeah i mean it was probably the best reference text for a long time

proven mountain
#

What textbook would you recommend to study probab. and stat.?

#

There are so many I am literally screaming

prisma snow
#

All of them hmmm

#

If you master them all, you will be a stats genius

karmic thorn
#

Bourbaki

fast portal
#

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

prisma snow
#

Janich is like 200 pages, but haven't read it completely yet @gray gazelle

limber mesa
#

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).

prisma snow
#

Enderton is p easy

limber mesa
#

I'm looking for something preferably not too basic, because I'll probably find it too slow.

icy frost
#

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.

silver herald
# icy frost Hello! Anyone that has a book/PDF on basic representation theory to recommend fo...

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

karmic thorn
static crest
gray gazelle
#

Springer sugoi

hasty turret
icy frost
#

Oh, my teacher actually gave me similar text on abstract algebra! It is quite complicated for me tho...

static crest
#

well it's a very common format

hollow current
static crest
#

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

icy frost
#

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

hasty turret
#

Yea,You should probably do The ugtm series first

static crest
#

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

icy frost
#

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

static crest
#

you should probably also be familiar with modules

#

in abstract algebra

#

also probably need some working category theory knowledge

flint forge
#

Wait

static crest
#

no?

flint forge
#

for rep theory?

static crest
#

trust max

#

more than myself

flint forge
#

All you need for basic rep theory is a decent linalg background and group theory

static crest
flint forge
#

its complicated and interesting but the prereqs arent a big deal

icy frost
#

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?

flint forge
#

Modules are just vector spaces over rings

#

Axiomatically they don't look very different

icy frost
#

Oh okay!

flint forge
#

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

icy frost
#

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

flint forge
#

Fulton Harris is the book I learned out of

#

I think its pretty good

icy frost
#

so this one?

flint forge
#

yeah

icy frost
#

Okay, thank you so much! I will check it out!

flint forge
#

np

limber mesa
hollow current
#

Enderton's elements of set theory may be

#

or Jech's intro to set theory

flint forge
#

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

willow pecan
#

Ideals, Varities, and Algorithms by Cox, Little, and O'Shea does some computational algebraic geometry

stray veldt
#

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)

fast portal
#

Where do I learn cat theory in context of programming

willow pecan
#

Applied category theory twitter

fast portal
#

Pls serious replies only

karmic thorn
#

@ mniip

willow pecan
#

@ mnoop

fast portal
#

@ mnoopers

prisma snow
#

@ mnoopy

hollow current
#

@ mnoopie

pure iris
#

if no one wants to do it, ill do it

#

@molten wave

#

xd

violet grail
#

a mad lad

molten wave
#

however if you're not already familiar with cat theory I'm not sure this is a good idea

fast portal
#

Fine fine, baby's first intro to cat theory?

fast portal
#

Motherfuck

flint forge
#

but learning category theory from riehl might be tricky if you arent somewhat literate in a lot of early undergrad level math

fast portal
#

You are telling me there is a way to learn it without prerequisites? 👀

#

🤔

#

And soft prerequisites?

flint forge
#

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

fast portal
#

Wait so was Cat Theory an attempt at Theory of Everything™️ but for math?

flint forge
#

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

fast portal
#

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

flint forge
#

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

silver herald
#

The applied one I learnt was based on understanding of robotics, control theory and optimization

quick hornet
#

wait how does that work

#

how do you apply category theory to robotics

sudden kindle
#

I saw someone applying lie theory to robotics

#

Group actions to move robot arms and joints

quick hornet
#

that makes more sense to me

#

than category theory

stray veldt
#

i think it's quite standard to use quaternions for rotation stuff

#

i can apply robotics to category theory by making robots draw diagrams

quartz verge
#

anyone willing to share spivak

#

sell*

prisma snow
#

Ye, I'll send you my pdf right now. Do PayPal first though.

quick hornet
#

joking about piracy probably not a good idea btw

quartz verge
#

no

quick hornet
#

mods dont mind but discord admins do

#

they've deleted accounts for less

quartz verge
#

i need a physical book

#

a book that i can hold, smell.

molten wave
#

Tfw learning about topological fibrations via type theoretical intuition for sum types

willow pecan
molten wave
#

I swear it makes sense

#

Its all just the grothendieck construction

silver herald
# quick hornet how do you apply category theory to robotics
silver herald
lost wyvern
silver herald
#

No.wonder engineers are known for such wondrous stuff like Tacoma Narrows Bridge incident

willow pecan
silver herald
flint forge
#

what does that have to do with category theory

silver herald
#

Well, an extension of logical reasoning can actually work towards simulating results for robots to do proofs for us?

flint forge
#

probably not

hasty turret
flint forge
#

thats so cursed lol

#

mniip has lost the right to call others a crank smh

molten wave
#

What

willow pecan
flint forge
#

“using category theory to capture the essence of human thought” sully

molten wave
#

You didnt get it at all did you

#

Its not "using", its what it "is"

flint forge
#

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

molten wave
#

Fair

#

Facts tho

flint forge
#

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

willow pecan
#

mniip crank confirmed

hasty turret
#

Always has been

molten wave
#

You need to either read the full question, or you need to expand the notion of what thougt is

gray gazelle
#

ok i'll take the bait

#

why do you think category theory is the essence of human thought

hasty turret
flint forge
#

so, so cursed

#

lol

sudden kindle
#

"Generalized"

#

Doesnt really mean much

#

Any thing can be a generalization of anything if you try hard enough

flint forge
#

i think you'd really have to break your neck to view schemes as generalized triangle inequality lmfao

willow pecan
hasty turret
#

Speaking of that, Harthshorne wrote a book on classical geo

molten wave
#

That convo was like at least half shitpost

flint forge
molten wave
#

Look do you never hit a blunt and have like a shower thought that makes sense on some spiritual level

willow pecan
molten wave
#

Yall giving ephemeral conversation the scrutiny of peer review

flint forge
#

thats bc its very funny

molten wave
#

This hot take isnt even original

hasty turret
#

This was the og one,ig

flint forge
#

does that page claim that nPOV captures human thought

#

i dont think Urs is that silly

molten wave
storm sleet
#

Bartosz is definitely a character

flint forge
#

bartosz is like

#

the worst possible choice

#

to defend you

#

lol

willow pecan
storm sleet
#

What makes you say that lol

#

Honestly at times I feel like Bartosz is the Wildberger of CS

molten wave
#

Ive spoken out against him myself bwfore

flint forge
#

Bartosz is generally seen as like

#

good at what he does

#

but a crank in his pontificating

willow pecan
storm sleet
#

His blog/videos are what got me into higher level math

#

doesn't mean he's above criticism tho

flint forge
#

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

fast portal
#

Deja vu I feel like we have been here before

flint forge
#

about his claims about General Relativity

storm sleet
#

god that reminded me that I should've taken general relativity instead of multivariable advanced calc

sage python
#

Uhhhhhhhhhhhhh

flint forge
#

you should probably take the latter before the former lol

sage python
#

I just jumped in the channel lol

#

And I see that and I'm like

#

Nah

flint forge
#

sloth

#

read the mniip screenshots

#

thats the real discussion here

sage python
#

You do not wanna take general relativity before advanced multivariable calculus

#

Hmm? Okay

storm sleet
#

our multivariable advanced calc is a toned down grad analysis course

flint forge
willow pecan
flint forge
#

sorry drunk about ping

storm sleet
#

its just instead of abstract spaces we only look at rn

storm sleet
#

for undergrads at least

#

both are senior level and require real analysis

sage python
#

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

storm sleet
#

I'm more partial to algebra

flint forge
#

if you like algebra why are you taking any of these courses lol

#

just take like alg top

storm sleet
#

for fun

willow pecan
sage python
#

Hmm, I think "capture the essence of human thought" is a lot stronger than what n-cat pov is capable of

storm sleet
#

Plus I'm in my first topology course rn, so getting into alg top isn't really an option

sage python
#

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

flint forge
#

there is a lot of math that just like

#

is not amenable

sage python
#

Human thought seems way too complex for that

flint forge
#

to the nPov

#

let alone all of human thought

#

lol

sage python
#

Yeah lol

#

Knowing nothing about actual weed I can buy that this is a classical "hints blunt" moment

flint forge
#

honestly ive never experienced that kind of high

willow pecan
flint forge
#

i more or less am just like a slightly slower version of my normal thought patterns while high

sage python
#

Given that I hear you typically have a lot of crazy insight that's actually just nonsense once you get your cognitive capabilities back

flint forge
#

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

sage python
#

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

flint forge
#

i think practically the nPOV boils down to

sage python
#

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."

flint forge
#

we will write unapologetically assuming that the reader is fluent in higher category theory

sage python
#

Which is veeeeeeeeeeeery ballsy

#

Yeah in practice

flint forge
#

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

sage python
#

I just mean the underlying philosophy

flint forge
#

and there is a cold war

#

around changing it

sage python
#

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"

willow pecan
sage python
#

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

flint forge
#

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

sage python
#

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

flint forge
#

Well even Curry Howard is an incredibly restricted subset of human thought

sage python
#

My knowledge of logic anything

#

Is next to 0

#

Buuuuut

#

Let me armchair a bit

flint forge
#

unless the claim is that either mathematics or programming is capable of expressing all of human thought

willow pecan
sage python
#

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"

quick hornet
#

well

sage python
#

Maybe I'm being a Platonist here

quick hornet
#

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.

sage python
#

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...

static crest
#

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

flint forge
#

Curry-Howard isn’t directly related to nPOV

static crest
#

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

flint forge
#

im not sure this is the same at all

static crest
#

I mean I only just came here

#

and saw what dami wrote

willow pecan
static crest
#

which is probably a meme

willow pecan
#

Scroll up a bit for mnoop crankery

sage python
#

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

molten wave
#

nah it's a more vague and philosophical realization

#

of the human approach to solving problems

#

using separation of concerns

sage python
#

I see

flint forge
#

curry howard is a theorem

sage python
#

"it" isn't Curry Howard so much as

flint forge
#

i guess if you pair it with Church-Turing you get something pseudophilosophical

sage python
#

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

molten wave
#

that's along the same lines of thought

#

again the things I'm saying here are precisely vague

#

profound bs tier

willow pecan
dapper root
#

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

willow pecan
#

Bourbaki has a very specific viewpoint

#

Very formal and no intuition

#

Uh ok

warm glen
#

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

steel viper
#

okay but do you actually want to learn all that point set hmmm

willow pecan
#

Point set topology does in fact suck

steel viper
#

you dont need very much for that then

#

the first chapter of bredons topology and geometry is enough

willow pecan
#

????

#

Weird fascination with old white men

steel viper
#

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 hmmm

#

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

tranquil ocean
#

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

steel viper
#

theres nothing wrong with terseness

tranquil ocean
#

rather than just having my eyes glaze over proofs and pretending that I understand them

steel viper
#

i also think its better

#

but like

#

do u really want to read bourbaki talk about uniform structures or whatever hmmm

willow pecan
#

Terseness for the sake of being terse is not really good though

#

Skipping over small details, fine

#

Skipping over large details, not fine

ripe granite
#

terseness is fine, but giving no intuition is not

steel viper
#

d&f is way too far in the other direction

gray gazelle
#

You can shit on d&f all you want, it is still my treasure

willow pecan
#

I liked D&F because I have no algebra brain cells

ripe granite
#

d&f is really good

static crest
#

I really love d&f because of how easy it is to grasp

#

(except this section on injective/projective/flat modules)

gray gazelle
static crest
#

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)

ripe granite
steel viper
#

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

rocky charm
#

im reading halmos' "logic as algebra" and goddamn it is sassy

willow pecan
#

Ok

#

In what way?

rocky charm
#

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

marble grotto
#

hi, i remember seeing a large book of problems in analysis. by a russian i think? wondering if someone knew its name

broken meadow
#

demidovich ?

marble grotto
#

oh it was the one by john erdman, but thanks

broken meadow
#

oh ok

#

np

round zenith
#

whats a good book that a 9th grader would understand? the topic doesnt matter

gray gazelle
#

a 9th grader could possibly understand hartshorne

round zenith
#

how is ur role honorable @gray gazelle

#

thanks @hasty turret

hasty turret
#

That is unironically hs level

gray gazelle
round zenith
#

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:

gray gazelle
#

(don't read hartshorne)

round zenith
#

yea that was the mistake

calm crane
#

hartshorne

hollow drum
#

Wait then what do you read for alg geo

hasty turret
#

Hartshorne

willow pecan
#

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

willow pecan
#

What

hollow drum
#

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

willow pecan
#

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

hollow drum
#

I wonder if I can find those lectures

willow pecan
#

You can certainly see the lecture notes on his website

#

Some video recordings as well

#

From an earlier iteration

steel viper
hearty steppe
#

Would have to be a 9th grader that’s pretty damn good at math

gray gazelle
static crest
#

any mods?

gray gazelle
#

@broken meadow

broken meadow
#

yikes

#

that's a ban

#

fiuck

gray gazelle
broken meadow
#

got sniped

#

right as i was doing it

gray gazelle
#

who sniped

broken meadow
#

idk

#

idc

willow pecan
#

Metal did not get a kill

gray gazelle
#

i want to see you get your first blood

broken meadow
#

i already banned 3 ppl before

static crest
#

nice

willow pecan
#

Oh

broken meadow
#

in the same day

gray gazelle
#

o

#

wow

quick hornet
willow pecan
gray gazelle
broken meadow
#

namington is very fast

hasty turret
static crest
#

I'm an afk owner of some anime server, and one day I checked back on it and saw some cringery

gray gazelle
#

2/3 of my complex anal lectures this week are cancelled sadcat

static crest
#

and banned like 5 people

#

was fun

willow pecan
quick hornet
#

sadly i cant ban metalninja

static crest
#

sadge

broken meadow
#

not anymore

#

😔

hasty turret
#

But,he can

broken meadow
#

i can't ban metalninja either

gray gazelle
#

,ban namington

hasty eagleBOT
#

This may only be done by a moderator!

broken meadow
#

,ban @broken meadow

hasty eagleBOT
#

Failed to ban @broken meadow: You don't have permissions to ban this member!

broken meadow
#

Fail

quick hornet
#

wait i can remove your mod role

#

wtf

static crest
#

pog

broken meadow
#

huh

quick hornet
#

i dont think id be able to give it back though

gray gazelle
static crest
#

do it

broken meadow
#

i can't remove yours though

hasty turret
#

Metal,Remove Nami's mod role

static crest
#

you wont

hasty turret
#

Now

broken meadow
#

this is very strange

quick hornet
#

oh never mind

#

it showed the x when i hovered over it

#

but it didnt actually delete

broken meadow
#

oh

#

visual glitch ig

quick hornet
#

unless it just takes time to update

hasty turret
steel viper
#

,ban namington

hasty eagleBOT
#

This may only be done by a moderator!

gray gazelle
#

,whohas moderators

hasty eagleBOT
#
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```
hasty turret
#

Imagine if power hieracy order was graded instead of just being lexicographic

willow pecan
hasty turret
#

Sorry, It's not even lexicographic

steel viper
#

what is it based on?

#

texit explain yourself

willow pecan
gray gazelle
#

Hey guys

#

anyone here know how to factor stuff

willow pecan
ripe granite
#

lmao Daminark is last

steel viper
#

where he belongs smugsmug

#

with the other old men smugsmug

willow pecan
broken meadow
#

who are the other old men

willow pecan
#

dGhost presumably

#

fino presumably

#

MetalNinja27 presumably

#

woog presumably

#

Puerøsøla presumably

#

Puerøsøla is canonically old

steel viper
#

namington

#

fiona and woog are neither old nor men

willow pecan
broken meadow
#

im old ? pain

gray gazelle
#

i thought woog was almost as old as namington

ionic wren
#

What r these numbers

wooden sparrow
silk quartz
#

It has something to do with the date.

willow pecan
obsidian valley
#

metal has a nice short name flonshed

#

rare

willow pecan
#

jesse has a nice short name

obsidian valley
#

woah 8da got 1

willow pecan
#

rare

#

8da changed their nickname

obsidian valley
#

oh

#

cheater

willow pecan
#

A did bacono

#

And mniip presumably

#

And metal

gray gazelle
#

Actually, there was a magic for me, I think the bot knew that I should be number 1

willow pecan
static crest
gray gazelle
sinful pewter
#

@sudden kindle highly rec Ender's Shadow if liked Ender's Game

sudden kindle
#

I think I read that

#

It was a long time ago

sinful pewter
#

about Bean?

karmic thorn
#

What's with these numbers?