serious-discussion

[echo geode]

thanks

[bright hill]

[echo geode]

Ok i posted my forum hopefully someone will answer

I really need this for extra credit

algebra is so complicated..i cant imagine geomentry

I feel like they over complicate it

[oak oxide]

Hello, does someone know how class mass normalization is used? I think it is the simplest way to treshold when having a multi-label classification problem

I want to understand how equation (9) can be generalized?
https://mlg.eng.cam.ac.uk/zoubin/papers/zgl.pdf

[neat lintel]

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

it's good stuff

[long matrix]

meow

[neat lintel]

in the simplest case it really is just plugging matrices into convergent series

[long matrix]

ic

[neat lintel]

most people's first encounter is the matrix exponential

useful in ODEs

[long matrix]

yh i seen ig

not rlly understood

[reef carbon]

.

[devout nacelle]

The Wiki article doesn't have any useful references to read further, do you have any?

[unborn trellis]

i liked chapters 6-10 of quantum theory for mathematicians by hall

[neat lintel]

pedersen

book hard but good

[unborn trellis]

of course you can also find this on basically any book on functional analysis or operator theory

[devout nacelle]

I found something on the internet: https://www.mathematik.tu-darmstadt.de/media/analysis/lehrmaterial_anapde/hallerd/ISem21complete.pdf

This is probably entirely devoted to the thing and presupposes a background in standard functional analysis

[unborn trellis]

yeah I wouldn't raw dog that

[neat lintel]

yeah put a condom on first

[brittle socket]

[cold needle]

why jerry 1 emojy

for that post

there is lore..

[jovial ember]

So what if we tied a rope to a universe

And the other end to an electric generator

So like energy

[hasty leaf]

You can do something like that in universe with a black hole maybe

[bright hill]

3b1b did a video on the topic

Have you seen?

[neat lintel]

#help-0

[neat lintel]

thats like so much number theory

ok

idk wut dat is

i need help with formulas on google sheet

[tranquil dove]

is the integral of 1/root over u : ln(u^1/2) + c ?

[tight comet]

,w int 1/sqrt(x)dx

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 草w#3875

[tight comet]

is that what you're looking for?

[tranquil dove]

yes

can u explain why that is the integral tho

[hollow cradle]

wow uh hi y'all

[coral plume]

Hello

[hollow cradle]

wassupp

[coral plume]

Nthm u?

[hollow cradle]

music

[coral plume]

Oh that's nice

[hollow cradle]

yess

do people talk other stuff here or just

maths

😭

[coral plume]

A bit of calculations for science profits but not much

[hollow cradle]

ahhh

i totally don't understand

[coral plume]

What is it you don't understand?

[hollow cradle]

what do you mean by calculations for science profits

[coral plume]

Well normally is some cases science and math get integrated into eachother

[hollow cradle]

yes

[coral plume]

To solve a equation u would some science definitions

Like the motion of a constant

Which is science

Then the formula which is algebra

Thats math

See what I mean?

[hollow cradle]

yes i got that much

[coral plume]

Oh okay then

[hollow cradle]

why complicate your sentence

oh well this IS a maths server

[coral plume]

It's professional

Yes

When u talk about knowledge u treat with delicacy

[hollow cradle]

well

agreed

[coral plume]

Yes

[hollow cradle]

would u solve a riddle

[coral plume]

Depends

[hollow cradle]

it's a choice between yes or no

pick

[coral plume]

Hmm

Yes

[hasty leaf]

Could be an intellectual trap lmao

[coral plume]

That's why I said it depends

:/

[hollow cradle]

if yes is no, and once is never, then how many sides does a triangle have?

[coral plume]

Two?

[hollow cradle]

yes

it took me 5 mins to figure it out

[coral plume]

Lol

It was a pretty easy riddle

[hollow cradle]

yes it seems that way now

[coral plume]

Mmh

[hollow cradle]

if you don't mind me asking

what do you do

[coral plume]

Yes

[coral plume]

Wdym

As a job

Daily life

Studies

Plz be specific

[hollow cradle]

studies

[coral plume]

It's in my bio

[hollow cradle]

noted

where are you from?

[coral plume]

Australia

[hollow cradle]

ohh nicee

[coral plume]

Yes

What about u?

[hollow cradle]

India

[coral plume]

Oh nice

[hollow cradle]

u read?

books

fiction i mean

[coral plume]

Yes

Lots of books

Well mostly educational but still read fictional books

[hollow cradle]

ahhh

[coral plume]

Yes

[hollow cradle]

that's good

[coral plume]

Mhmh

[hollow cradle]

have a top 5?

[coral plume]

Ye

[hollow cradle]

tell then

[coral plume]

Books

[gaunt idol]

Where in Australia?

[coral plume]

Perth

[gaunt idol]

Nice, Adelaide here.

[coral plume]

Oo

Interesting

[hollow cradle]

yes, your top 5 fav books

[coral plume]

K

Moby dick

Avantia

Shadow house

Percy Jackson

Roald dahl

[gaunt idol]

Looking for Trouble?

[coral plume]

Wdym

[gaunt idol]

Dahl..

[hollow cradle]

percy jackson is the only one i've read out of them

lol

[coral plume]

Ye

[hollow cradle]

nope

[coral plume]

Elaborate plz

[gaunt idol]

Looking for Trouble is a book by Dahl, I read it in primary school.

[coral plume]

Oh ye

[hollow cradle]

😭 oh

[coral plume]

The context u put it in wasnt easy understand

[gaunt idol]

Yea that's fair

[hollow cradle]

way to make one feel stupid

[coral plume]

Hm

[gaunt idol]

What level maths have you both studied?

[hollow cradle]

i'm a child

pls

[coral plume]

Oh

[gaunt idol]

or Physics..

[coral plume]

Ap physics c

[hollow cradle]

10th grade, however much that is

[coral plume]

But I study under for fun

[gaunt idol]

Is that high school?

or Uni

[coral plume]

Uni

[gaunt idol]

Nice, what degree?

[hollow cradle]

are you old 😭 should i call you bhaiya

[gaunt idol]

36

[coral plume]

Scientist

Physicist

[hollow cradle]

uncle

[gaunt idol]

So Bachelor of Science (Physics)?

[hasty leaf]

What does that term mean

[coral plume]

Ye I study physcis

[hollow cradle]

hindi for older brother

[hasty leaf]

Ah nice

[hollow cradle]

yes

[gaunt idol]

Cool

[coral plume]

But in bio explain everything I study

When I say physics and chemistry

I say virtually decent amount of branches

[gaunt idol]

Sounds good. Well done

[coral plume]

Thx

Kinda stressful

[gaunt idol]

How long since you finished?

[coral plume]

About couple months I move onto my next degree

[gaunt idol]

Which is?

[coral plume]

Chemistry

[hasty leaf]

I'm Chem major nao in IT

[coral plume]

Thats cool

[hasty leaf]

I had a paper published in local physics journal for fun

[coral plume]

Yee

So u practically study same thing I do

[hasty leaf]

Maybe lmao

[hollow cradle]

i am actually a baby compared to y'all

[coral plume]

Oh

[hasty leaf]

But I'm alot more IT nao

[coral plume]

Ye

I do education for fun

[gaunt idol]

Same here, did my degree purely out of interest

[coral plume]

Actually the same

[hollow cradle]

how's it like

[gaunt idol]

Greatest experience of my life

[coral plume]

Yes

[hollow cradle]

glad for you

[coral plume]

But can be frustrating

[hollow cradle]

that's only natural

isn't it?

[coral plume]

Ye

[gaunt idol]

I envy anyone who it comes easy to

[coral plume]

Ye

Btw quick question

In some atoms theory's some people think

Its under physics or chemistry which one do U think it goes under

[gaunt idol]

Did you mean Atomic Theory?

[coral plume]

Even though bot are theoretically correct

Yes

Or just atoms

[gaunt idol]

I dont understand the question

[coral plume]

So the subject atoms

People think it could go over physcis some chemistry

Which one do U think

[gaunt idol]

I'd say Physics. Considering chemistry generally relates to the interaction between atoms and molecules

[coral plume]

I would say chemistry for the atomic number

[gaunt idol]

Physics covers what is in chemistry and then covers all other aspects of the atom and subsequent subatomic particles.

[coral plume]

Ye thats what I mean

[hollow cradle]

that people are obssesed with putting everything in boxes

[coral plume]

Hm

[hollow cradle]

tho it does make life easier

[coral plume]

Yes

[gaunt idol]

There's an old saying, 'All science is either physics or stamp collecting'.

[coral plume]

Yup

[hasty leaf]

The fun things may straddle the boxes ..
Interdisciplinary stuff

[gaunt idol]

When you get through a degree in any discipline, none of it matters. You learn that pretty fast

[coral plume]

Yes

[hollow cradle]

science is the single most fascinating thing to me

[brittle socket]

You mean math

[coral plume]

Same

[hollow cradle]

tho i wanna be a powerful buisness woman

[hollow cradle]

maths is fun

makes you think

in ways you wouldn't normally

[coral plume]

Yup

[hollow cradle]

my best friend says i'm mad

tho she's the one who devots herself to history

[gaunt idol]

Everyone who tells me they hate maths (99%) of people just had a shit teacher, nothing more.

[coral plume]

Science and maths are my strong holds

[gaunt idol]

You just have to unlock something fascinating about it

[hollow cradle]

ahahaahahaa, truee

[gaunt idol]

Have you started learning Matrices?

RREF, Row/Column/Null Space, Rank etc..

[hollow cradle]

no sir i'm in 10th

a baby, like i said before

[gaunt idol]

Ahhhhhh you're lucky. You get to learn all the fun stuff. When Matrices clicked it was an epic moment.

[coral plume]

What about a metric

[hollow cradle]

computer and maths for me

[gaunt idol]

Metric Tensor?

[hollow cradle]

biology i have a hard time with

[hollow cradle]

hehe

[coral plume]

Hn

Ye

[gaunt idol]

Metric Tensors are a 3rd year Uni subject

[coral plume]

Yes

[hollow cradle]

hn?

[coral plume]

But want talking about those

[coral plume]

I was suppose to say ha typo

[hollow cradle]

ohh

[coral plume]

Ye

Mmh

[hasty leaf]

Yes pretty useful

[winter flame]

hi, quick question, if X is normally distributed with mean 0, is P(X>a) = P(x<-a) ?

[deep mango]

Yeah. It's one of many "symmetric distributions" with that property

Coming from the fact that the gaussian density is an even function

[winter flame]

oh thanks

and is P(X<a) = P(X<=a) ?

[deep mango]

Yea

If you have more questions, try #probability-statistics

[winter flame]

thanks

[surreal sapphire]

@agile snow don't post unsolicited advertisements

[bright hill]

I was wandering if I should ping you guys but got disctracted

I was about to message modmail

[surreal sapphire]

🤷

in most cases i would prefer modmail i think

[bright hill]

[agile snow]

sorry, it was just for research!

[shrewd flower]

how do you study smart not hard for math?

[woven whale]

just study instead of spending all of your time on thinking of the best way to study

[wraith whale]

probably do practice problems

[zealous garden]

Practice problems, try to anticipate the text/instructor/video/..., take the time to ask yourself (and answer) questions that aren't in the material

[west jackal]

if you understand the concepts, then it's easier to remember and apply imo. also helps if you're reasonably able to derive the results. that isn't always possible, but i know a guy who just derives all the techniques from differential equations on the fly when he needs them, instead of memorizing a bunch of techniques he doesn't use that often.

[proud olive]

You take a shit load of really hard courses and then you just find that out yourself

Failure isn't an option

[storm sage]

Don't torture yourself

Tbh I would focus less on study techniques and more on actually studying and being engaged in the material, actively trying to understand what's going on, etc

[chilly hull]

maintain good health

[storm sage]

physical health AND mental health

both are important

[chilly hull]

you will be a lot more efficient and be capable of going on for long periods of time if you are healthy

you're less tired, you're motivated, you're more focused

the main limit when it comes to mathematics is time and effort and having being healthy allows you to maximize both of these

[fleet oyster]

@undone wren I am pretty sure you don't need to finish all of velleman before reading something else?

you are totally allowed to go do something else lol

[undone wren]

for me personally, i don't think i could because i'm not enrolled in a math major, lol

[mint canopy]

I think you intended to ping @neat lintel, lems

[undone wren]

i study computer science in college

[fleet oyster]

uhh no you can

[fleet oyster]

nope

[mint canopy]

My mistake

[neat lintel]

Hi

[mint canopy]

I do agree with you, fwiw. I don't think there are any math books that I have read cover-to-cover.

[fleet oyster]

have you done any calc @undone wren

[undone wren]

my motivation for studying velleman's book was so that i could have a good transition to studying other topics more rigurously like analysis, linear algebra and discrete math

[undone wren]

yes, up to multivar

[fleet oyster]

a lot of stuff in velleman is very important you just don't need to learn them all at once

the topics a "discrete math" book covers is also pretty much identical to the coverage velleman gives

transition/proof books aren't so different from discrete math books

at least wrt hammack/velleman

[chilly hull]

hammack

[fleet oyster]

hamkins has a book about proofs for example that is very different from those 2

it's literally all about proofs from different areas of math

p cool

[chilly hull]

stopped reading after chapter 4 once i figured out how the logic behind everything worked

[neat lintel]

me too :>

[chilly hull]

but the part i read was very good

[fleet oyster]

yeah you don't have to finish those kinds of books front to back

you can you just don't have to

[chilly hull]

it was a great introduction to sets

and basic proof techniques/logic

[fleet oyster]

if you've learned basic set and function stuff, basic logic, and know what a proof by contradiction is you are good to go for like a first course in real anal/linalg

[mint canopy]

I would say that finishing velleman or similar books before reading any other mathematics is a lot like learning a language by learning all the grammar before learning any vocabulary or even speaking a single sentence. It is possible, but it is miserable and slow. Learning 'on-the-job' is the way to go.

[chilly hull]

yeah that's why i stopped after ch4

[fleet oyster]

but sections about counting/binomial, general relations (posets, equiv relations) are also pretty important but yeah you can learn those 'on-the-job'

for sure

[chilly hull]

i was like "hey i think im ready to start schroder"

[mint canopy]

This is not to say that these books are unhelpful, not at all. Just that one shouldn't feel that it's a gate that one must pass before doing other math.

[undone wren]

chapter 4 is brutal, i'm almost finishing it

[neat lintel]

Discrete math books tend to be less proof-y and more about topics like graph theory, combinatorics, generating functions, etc while proof books are more about proof strategies, set theory, number theory from what I've seen

[fleet oyster]

yes, but still most of the content is the same

[mint canopy]

Perhaps you should look for a proof-y discrete math book

[chilly hull]

for hammack

i think you would be fine reading just

chapter 1 2

some of 3

and 4

[neat lintel]

What book would that be?

[mint canopy]

I'm not sure frankly, I'm not well-read in that field. Perhaps others have suggestions

[undone wren]

@fleet oyster you think i could tackle linear algebra in a rigurous way with the knowledge i have about proofs? this is all i've studied so far and have done every single exercise

[chilly hull]

definitely

[fleet oyster]

youve done more than enough are you kidding?

what do you think the average student knows before tackling linalg

[undone wren]

i've done like 1000 proofs, not even kidding

[fleet oyster]

yeah you just don't need to do this

[neat lintel]

Discrete math books seem to be more for intro to computer science while proof books are transition into advanced math, I am not sure what book would be inbetween these D:

[chilly hull]

dude you've done WAY more than you need for proof-based linalg

well

idk for proof-based tbh

[neat lintel]

I'm on page 58 :D

[undone wren]

alright, i'll see if i can study linalg and keep studying this book

[chilly hull]

chapter 1 of artin is killing me

[undone wren]

wait till you reach 2.3 and above

[fleet oyster]

so looking at velleman, the rest of the book is still pretty important depending on the linalg book you might want to tackle the functions section

[undone wren]

that's when shit gets real

[neat lintel]

artin is abstract algebra not linear, right?

[fleet oyster]

but that is pretty short

[chilly hull]

artin is a mix of both

[mint canopy]

I have a suggestion. You said before that you're interested in skipping ahead to some more 'advanced' mathematics. Once you've read chapter 3 of velleman (the proofs chapter) I think you'd be equipped to read some abstract algebra.

[fleet oyster]

artin is both

[mint canopy]

Linear algebra is, broadly speaking, a part of abstract algebra

[neat lintel]

Don't I need integrals for this?

[mint canopy]

No.

[undone wren]

alright, i'll do the chapter of function and do linagl then

[mint canopy]

The vast majority of abstract algebra has no relation to calculus.

[neat lintel]

Is this a threat

[chilly hull]

analysis does have a relation but

it is possible to do analysis without calculus (although VERY questionable)

[fleet oyster]

well, algebra is highly important to analysis but much less so the other way around

[neat lintel]

That sentence felt oddly satisfying to hear

[fleet oyster]

at least before a graduate level exposure but even then

[mint canopy]

I think, after you feel comfortable with proofs, you could read chapters 0 and 1 of Fraleigh's "A First Course in Abstract Algebra".

Chapter 2 is also within reach at that point, I think.

[undone wren]

the proofs from there and beyond that part start getting harder and stop being so intuitive

[wintry dragon]

Lol, I'm barely surviving undergrad. Graduate level math sounds like a nightmare.

[fleet oyster]

no it is heaven

[chilly hull]

early or late undergrad

[wintry dragon]

Late. I just took advanced calculus last semester. Idk how I survived that.

[mint canopy]

Graduate mathematics is difficult, but it is fun, because I enjoy math.

[chilly hull]

i cant wait to get to

ch2 of artin

should have gotten there a month ago if it werent for college applications

[neat lintel]

Looking forward to it

[fleet oyster]

oh speaking of artin, I should shill a yt playlist

https://youtube.com/playlist?list=PLA58AC5CABC1321A3

[bronze wedge]

[fleet oyster]

lectures based on artin

low quality vid but very high quality instruction

[mint canopy]

I hope so; difficulty in math is a fun challenge!

[wooden flax]

imo for intro to proofs linalg or analysis is good

i think baby rudin is the best intro

for proofs

[neat lintel]

You guys make math seem possible, I feel I am no longer blocked by this huge titan barricade wall called calculus, I am a free birb

🕊️

[mint canopy]

I firmly disagree with this. There are many other good places to learn proofs. Baby rudin is an unnecessarily obtuse book.

Furthermore it is a book for learning analysis, not proofs.

[bronze wedge]

It's like trying to pick up topology from a geometry book

[chilly hull]

schroder

[mint canopy]

If your goal is to learn analysis, baby rudin is not a bad choice, but you should be clear about this.

I don't think it's the best choice, but I wouldn't call it a bad book per se.

It is a mediocre choice in my opinion

[chilly hull]

munkres is also scary

[fleet oyster]

rudin is a great book imo just a bad way to learn analysis the first time

[chilly hull]

i have 0 idea what a basis for a topology is even after i read it like

3 times

[undone wren]

magic trick?

[wooden flax]

for topology Munkres and Bourbaki are good

[fleet oyster]

munkres is garbage at treating what a basis is honestly

[chilly hull]

like i get what a basis is but when you tell me to do anything of meaning with it

[fleet oyster]

yeah no it shouldn't be like that

[bronze wedge]

Bourbaki

[wooden flax]

Yes

[fleet oyster]

imo willard > dugundji > munkres based on the parts I've read, don't think munkres is bad tho

[mint canopy]

I vow never to read Bourbaki, so I can continue to laugh at the Bourbaki arguments that happen online

[wooden flax]

Bourbaki>everything

[mint canopy]

^ haha

[bronze wedge]

Bourbaki is written as an introduction to topology for people who already know topology

[wooden flax]

alot of the people who flame it are those who have only heard rumors about how scary it is and how it should never be touched

open it up, read some of it

form your own opinions

[wooden flax]

spivak on drugs

[neat lintel]

whats the point

if you are post doctorate and forgot about the basics?

[bronze wedge]

I'm fine with Bourbaki, but I don't think it's a very good book for beginners

[neat lintel]

I tried spivak once, never again

[fleet oyster]

there is not much of a point now over other books, it was a necessary kind of book in its time

[neat lintel]

oh okay

[mint canopy]

It is often helpful to see things in multiple different ways.

[fleet oyster]

back when foundations and first principles of math weren't so organized

[mint canopy]

This is also true ^

[neat lintel]

Spivak made me give up on math, didn't touch it for a year and a half until I found velleman

[neat lintel]

I see

[mint canopy]

My point is that seeing two different authors discuss the same topic can be helpful in understanding said topic

[chilly hull]

i tried reading artin while i was studying calc 1 equivalent

it didn't go well

[mint canopy]

Often a single author can have certain quirks and idiosyncracies that become clear when contrasted with another author

[fleet oyster]

yeah I was saying the same thing recently, ppl get too attached to one book

[neat lintel]

I picked up spivak after lang's basic mathematics

[fleet oyster]

I favor skimming 50 of em at once

[mint canopy]

Math is an activity, not a series of books!

[fleet oyster]

ye

every author has its own perspective, I would have never seen some of them if I just stuck to one book

[wooden flax]

depends on what you call beginner

although Bourbaki theoretically starts with set theory I certainly wouldn't recommend it to someone who dosen't know that already

[mint canopy]

This is also a good reason to read books on the side of a course you're taking, imo

[fleet oyster]

yes

[chilly hull]

i think i can get some benefit out of reading rudin too then

[mint canopy]

I sincerely do not recommend rudin, at least not until you have learned some analysis already.

[fleet oyster]

of course

[chilly hull]

ive read the

1st 4 chapters of schroder

[wooden flax]

My favorite book for analysis is Browder

it has no prerequisites, is well-motivated and has the same content as Rudin

all in 1

🙂

[fleet oyster]

browder does more no?

[wooden flax]

yup

[fleet oyster]

pretty insane

[wooden flax]

its a good book!

german education system>>

[mint canopy]

Sounds excellent

I'll put this in a list somewhere

[wooden flax]

i have a list

[vale viper]

I can confirm that I read Rudin after having already taken 2 semesters of analysis and while it was very great, it is not for your first forray into analysis.

[wooden flax]

of what i want to learn by end of may 2025

[bronze wedge]

imo Rudin PMA then Malliavin "Probability and Integration"

[wooden flax]

if i send it here im gonna get flamed though

[mint canopy]

Oh and while we're talking about topology books too, while it's not the ideal introduction to topology, I think Lee's Introduction to Topological (not differential) Manifolds is a book of rare quality.

[fleet oyster]

you mean not smooth I believe

[mint canopy]

Ah yes, that's the other book's title

[fleet oyster]

he has topological, smooth then riemannian iirc

[wooden flax]

I don't like Lee.

Too slow

makes me want to 💤

would take munkres over that any day

[mint canopy]

OK

[bronze wedge]

I like James's book for ugrad topology

[fleet oyster]

is lee slow compared to munkres? I haven't read too much of either but they didn't feel too different in speed

like lee is a larger book but I think it covers more stuff too

[mint canopy]

Lee is not focused on an introduction to topology. I don't think the comparison of Lee to Munkres is a good one to make.

[neat lintel]

@undone wren what book did you pick up for linalg btw?

[granite hound]

I'm a big fan of "Linear Algebra Done Right" by Sheldon Axler

[wintry dragon]

Is advanced calculus an early subset of real analysis?

[neat lintel]

Don't think so

[undone wren]

i was going to do https://codingthematrix.com/ and depending on how much i liked that one, go for axler which i heard was good

[neat lintel]

I hear bad things about this book because of determinants

[mint canopy]

Can you clarify what you mean by advanced calculus? Also, while the field of analysis does certainly contain calclulus, do you mean simply an introduction to analysis?

[granite hound]

idk, I liked it, but then again I only recently figured out what determinants actually are via 3b1b

[wintry dragon]

Something like that. I took a class on "advanced calculus" that was basically just proving calc 1.

[neat lintel]

This website is very good lol

[granite hound]

Though whether that was a result of the book/class or my own forgetfulness idk

[neat lintel]

"Example Applications" fantastic set of points @undone wren

[mint canopy]

Then I would say that, essentially, yes: it is a subset of analysis. However it does turn out eventually that tools from calculus become useful in proving things that don't immediately seem related to calculus.

[fleet oyster]

axler needs calculus, and the book in general is a bit analysis focused

imo it gets too much hate but I think it should only be used alongside a more "algebraic" book, and would be good to have some past linalg exposure

[undone wren]

you gotta know how to code though and i don't think it's that rigorous when it comes to proofs but my main motivation for doing it is that i will do an equivalent course eventually in uni

[mint canopy]

I must say that I have only skimmed Axler, but my understanding is that it can be very confusing if you are not already somewhat familiar with the fundamental concepts of linear algebra.

[undone wren]

so, may as well study its applications and latter study it rigorously or maybe do both

[granite hound]

Someone give me motivation to continue studying topology

I know it'll help a lot in my various areas of interest

[lyric nimbus]

topology is a really broad term. What are you struggling with?

[granite hound]

But I keep getting bored just past the starting line

I get the concepts well enough when I put in the effort. It's just putting in that effort that's killing me

[lyric nimbus]

what are you reading?

[granite hound]

I was going through these notes because there's tons of problems attached, but I found it too detached to start off with
http://www.math.toronto.edu/ivan/mat327/?resources

Currently going through these notes
https://pi.math.cornell.edu/~hatcher/Top/Topdownloads.html

[lyric nimbus]

if you find it boring, read anything other than point-set topology. It is just an incredibly dry subject

[granite hound]

I see. Is there another sub-field you'd recommend for getting my feet wet?

[lyric nimbus]

Depends what you're into. The classification of surfaces is some good, honest geometry to give you a taste of low dimensional topology

[granite hound]

I don't mind dry math, but I need to get an intuition for the surrounding subject to thrive there

[lyric nimbus]

intuition for point set topology is mainly going to come from things like functional analysis

[fleet oyster]

what kind of math are you interested in?

[neat lintel]

How do you guys name your PDF books, for example "Stewart, Calculus" or "Calculus, Stewart" or some other way?

[granite hound]

I do well in maths that I can approach from a more discrete perspective, logic, number theory, group theory, lambda calculus and similar systems, etc

[fleet oyster]

do you know about compactness theorem in first order logic?

[fleet oyster]

author first 100%

[lyric nimbus]

tbh the first chapter (the fundamental group chapter, not chapter 0) of Hatcher's algebraic topology book would be approachable for you and is probably going to be more fun to mess around with

[granite hound]

I do not, looks neat tho

[neat lintel]

Do you also write year?

[fleet oyster]

you are assuming I'm organized lol

[granite hound]

I've also got an interest in type theory, but I think I'd enjoy it more if I developed a stronger foundation in other maths first

[fleet oyster]

but if I were I'd just do author then book title

[granite hound]

I'll check that out, thanks!

[fleet oyster]

compactness in logic refers to a certain type of topological space being compact

and is one of the fundamental theorems in FOL

[granite hound]

Oh he's got it available for free online? What a bro

[storm sage]

I agree, his intro to point set is so much more well written than the equivalent in Munkres

although obv Munkres has a lot more content afterwards

[lyric nimbus]

yeah but like, who gives a fuck about Urysohn's lemma

[bronze wedge]

Urysohns lemma is one of the most useful results in topology

[storm sage]

urysohn's lemma is cool af

[lyric nimbus]

You're probably right, it's just never come up again for me in the decade since I read Munkres. Maybe I should have gone with T_{whatever} spaces

almost literally nothing about point set topology has ever been of real importance to me in arithmetic geometry, to be fair.

[storm sage]

haha

[flat harbor]

@burnt ledge @nocturne tusk hiiii

[nocturne tusk]

hiiiiiii

hiiiii

hii

[flat harbor]

brave new world

[burnt ledge]

hiiii

infiltrating into disc2

like a #boss

[flat harbor]

i need to brush my teeth n shower

[nocturne tusk]

evacuating

[flat harbor]

brb

[nocturne tusk]

imagine doing things....

[quiet coral]

How do you draw what you wright? I cant draw very good but rlly wanna draw a charecter i made.

[burnt ledge]

you could try to use one of the several text-to-image models that are around

and if one of them is close to something you were imagining then you can either draw using that as a reference or just edit that

or maybe combine aspects from several

[quiet coral]

Tysm

[burnt ledge]

happy to help 👍

[nocturne tusk]

I'd love to get into art but I just cannot be bothered with all the technical stuff

I seem to have this issue with everything I want to get into...

[quiet coral]

i can wright super good but my art is...

[brittle socket]

Hmm but would you distribute the time you spend between the two?

[void tundra]

I keep pma around as a reference

Altho not the physical copy

So far i havent needed to look at it yet while doing abbott

[barren anchor]

You just bounce when you hit a wall

I second the general idea

Another strat is to just peruse both shallowly for any given concept and go with your gut for which to go in depth with

I usually end up bouncing at walls to surveying 2-3 resources and shallowly peruse both beyond the immediate content to try and predict a decent stretch

[vale plover]

is hoffman kunze out of print or something? i can't find any place that prints new hardcovers

it's a popular book, but i guess its situation could be similar to niven, zuckerman, and montgomery's number theory book

i had a hard time finding nzm

i have a used copy

[quiet coral]

im boared why is yellow existent cant it be something else like idk blurgin

[livid flint]

good blurgin

[quiet coral]

blurgin is the new yellow i now declare!!!

[bright hill]

I found this exerpt while leafing through hubbard and thought it might help someone

thoughts or comments are also welcome

[ripe wasp]

what's it about

isnt it something about product spaces

i remember reading about it once

something something the product topology is too fine

idk

[bronze wedge]

No

[ripe wasp]

oh wait is that tychonoff i got confused lmao

[neat lintel]

https://tenor.com/view/وشهاظا-reading-focus-huh-what-gif-17524883

what does it say

so small

[small dust]

lmaoo

you can open the image and zoom in

[neat lintel]

I did its so blurry my phone broken maybe

[long matrix]

thats what this guy is doing and failing

[neat lintel]

[small dust]

[fair mural]

blowo

[flat harbor]

helohelo

i suspect its the coffe i had earlier

but i dont get it

i had it at 3pm..... what the hell

[flat harbor]

omg hi babe

after lurking in discussion for half an hr seeing the downfall of civilisation firsthand

im thinking of making discussion 2 my homeground

[arctic grove]

[violet wraith]

[fleet oyster]

this is great

[eager reef]

skipping ahead to examples if I don't understand something is something that has helped me a lot

[versed nimbus]

Learning gravitational equations got me floating

[valid steeple]

what kind of higher math do people who are good at combinatorial stuff do (other than CS)?

[woven whale]

algebraic combinatorics?

[sand wadi]

Tropical geometry

[odd brook]

i mean

they can just. Do combinatorics

[neat lintel]

can you elaborate on this? like i know some standard undergrad combinatorics books, but how would one proceed once you're done with the basics

[neat lintel]

the wikipedia seems to that it's a subfield of ag, and i'm not willing to learn that, at least for now

[odd brook]

are you looking for a more advanced book?

[neat lintel]

sure, that helps

[odd brook]

stanley - enumerative combinatorics is maybe my favorite book ever written

incredibly vast and fun

ranges in difficulty and touches a frankly incredible amount of material + coolest problems I've come across in a book

[neat lintel]

thanks! i'll take a look at it

i know that there is algebraic combi, but is there any important analytic branch of combi?

[odd brook]

There is analytic combinatorics but I'm less familiar with it

Like the closest I'm acquainted with is looking at asymptotics for either partition-related functions or growth rates of certain combinatorial sequences maybe

[neat lintel]

hmm i see, i have more analytic intuition than algebraic (rn) and it's my major interest

so i also wanted to know about the analytic techniues

thanks for helping! the book seems very interesting

[odd brook]

of course! it should have some analytic perspectives in there as well, although never too heavily

[sand wadi]

Additive number theory 🤓

[quiet coral]

999 is best number

[cloud willow]

Why?

[quiet coral]

turn over your phone

[cloud willow]

666 you like the devil number?

[quiet coral]

no im kidding its just cuz 9 is my fav numder

[bronze wedge]

mathematics of statistical mechanics

probability

[jovial ember]

What’s your opinion on JEE? Cool test yeah?

[void tundra]

ah yes, pure memorization

[deep mango]

I thought jee was a meme but then shyshu made me do some of the problems and they were hard :(

[deep mango]

No that would be hollow knight watcher knights

[cinder zephyr]

Shafarevich can die in a hole

my handwriting cannot handle using both of these letters

in the same context

[jovial ember]

Get better

Draw a tornado mess

And then a tame zeta

[cinder zephyr]

that's basically what happened

[neat lintel]

oh God

your zeta looks like ebola

[quiet coral]

Whats the point in life

[hollow sundial]

that's a zeta and not a varphi?

$(\xi - a \varphi)^2$

[fathom swallow]

riemann

[brittle socket]

I handwrite them like this

[void tundra]

thats actually quite nice (the left one)

[brittle socket]

Thanks lol

[neat lintel]

hm

[ripe wasp]

dang that's clean af

[brittle socket]

Thanks :D

[bright hill]

Grass artiste™️

[brittle socket]

[void tundra]

write a whole textbook where you force people to do exercises using pen and paper and \xi

[void tundra]

petition to peer pressure grass into writing a textbook

[brittle socket]

Since you made a guess about me, I'll also make one about you . Did you take H2 Further Math? I would guess yes

[void tundra]

hmm

no actually

[brittle socket]

Oh really

[void tundra]

which is why i dont know much linalg

[brittle socket]

Guess we are both wrong

[void tundra]

I thought it was too grindy tbh

but then again so is regular H2 mathematics

[brittle socket]

Hmm why

[void tundra]

like arithmetic grindy

[brittle socket]

If I take Chemistry I probably will die

[void tundra]

oh....

i can relate

[brittle socket]

Ah

[void tundra]

you probably should pick further math over chemistry tbh

[brittle socket]

If not that, then what did you take?

[void tundra]

no i just took regular h2 math lmao

[brittle socket]

No but you need at least 3 H2s?

[void tundra]

our school requires 4 yeah

[brittle socket]

For everyone?

[void tundra]

err

ur only allowed to do 3 if u do too poorly

[brittle socket]

Smells of IP huh.

[void tundra]

I mean yes

[brittle socket]

haha ok so what did you take then?

Just curious

[void tundra]

physics chemistry and economics

very normie

[brittle socket]

Chemistry

[void tundra]

chemistry is really bad

[brittle socket]

Ah yeah classic PCME

[void tundra]

the amount of memorization is just

anki was such a lifesaver tho

[brittle socket]

Oh boi yeah my bro once told me he failed H2 Chemistry, even though he normally does quite well academically (I think)

[void tundra]

although it was fun manufacturing toxic gases in my school's lab

[brittle socket]

I use that as well, when I have stuff to rmb

[brittle socket]

[void tundra]

chemistry is a failure farm ngl

the only chemistry I know now is that the group of symmetries on ammonia is D_4

[brittle socket]

Tbh if I could go straight into a uni math programme I would right now, even though I might get shit on

[void tundra]

ehhh you probably wont

[brittle socket]

[void tundra]

some schools offer "H3 mathematics"

[brittle socket]

Yeah I know that, did you take it?

[void tundra]

nope

[brittle socket]

Ah I see

Imagine if you didn't want to take a CCA in JC and when your teacher asked you why you just told them you want to do more math

[tight comet]

hello only imo golds allowed in this server

[void tundra]

so like

[brittle socket]

In my opinion golds yes?

[bright hill]

Truee!!

[void tundra]

u can

i doubt u get questioned

[tight comet]

Are you the next Ana Caraiani

[brittle socket]

Yeah I know

[void tundra]

yes

[brittle socket]

Who's that

[void tundra]

you'll definitely sound like an insufferable nerd tho

[tight comet]

bruh

[void tundra]

not that you are :)

[brittle socket]

That might be the truth though

[void tundra]

but it definitely is a meme

as in

[brittle socket]

What are you referring to as a meme?

[tight comet]

https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=Caraiani

[void tundra]

not doing a cca to study more math

either you sound like a nerd or a mugger

[tight comet]

no real muggers study math

proven

mugger only tell you how to solve a DE

they can even do the integration mentally

[void tundra]

,w integrate x^2

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by DerpZ#9141

[void tundra]

ah okay

[brittle socket]

Lol what

[tight comet]

yes, imagine WA, but human

[void tundra]

havent done an integral in a year oops

[brittle socket]

Its alright

[void tundra]

thats kind of sad

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by wintersavory#2490

[void tundra]

like wolframalpha has a lower error rate than

[tight comet]

everything this can do, forget it
https://docs.sympy.org/latest/modules/integrals/integrals.html

[void tundra]

a human

cos integral

im guessing

[tight comet]

By this I mean forget about at least 80% of all integration. You really only need remember specific integration tricks

[void tundra]

ask the memorizers to integrate 1/x^2+1 without immediately vomiting the answer

someone who memorizes

instead of trying to go for true understanding

[tight comet]

,w int from 0 to pi ln(1 - 2 a cos x + a*a) dx

[brittle socket]

Goes for true understanding
Learns real analysis in JC

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 草w#3875

[void tundra]

i saw a 30min video on bprp doing this lmao

[void tundra]

real analysis is kind of good understanding tho

like imagine submitting your work

[brittle socket]

Yeah it is

[void tundra]

and then you use 4 pages to prove that it's differentiable first

[brittle socket]

lmao

Your teacher:

[void tundra]

leave all the lemmas as exercises for the reader (your teacher)

[brittle socket]

[tight comet]

lul no answer

[void tundra]

also when doing """vectors""" make sure to invoke lots of theorems from algebra

is that even integrable

yeah most probably

[tight comet]

https://www.cantorsparadise.com/richard-feynmans-integral-trick-e7afae85e25c?gi=f83e9bb83fa2
I am missing a>=1
But I don't think supplying that will help the computer

[brittle socket]

Cantor

[tight comet]

WA can solve the substituted one onwards

I think

[void tundra]

occasionally use it to find limits

when checking the help channels

[brittle socket]

Why did you hide your color lol

[void tundra]

why not

[brittle socket]

[void tundra]

bot

use @quasi jetty

[tight comet]

,w int from 0 to infty 1/(1+x^2((1+a)/(1-a))^2) dx

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 草w#3875

[void tundra]

what a painful integral

[brittle socket]

If I ever become an honorable, I will still hide my role colour just to be funnei

[void tundra]

they should make you honorable now

for being grass

idts actually

not very ppl overrides everything else

[brittle socket]

Hm?

[void tundra]

grass is important

therefore grass is honorable

potato is also undergrad apparently

idk

get a grad degree in math just to better have a chance to get honorable in this discord

[brittle socket]

Moth also

Ari too

Yeah they are an undergrad I think

[bright hill]

A lot of undergrads are honorable lel

[brittle socket]

Just that they have grad level knowledge

[void tundra]

time to get a phd

[brittle socket]

To be fair she doesn't come online often nowdays I think

[bright hill]

Chmonkey, John, ereh, timo

Etc

[void tundra]

isnt chmonkey a grad student lmao

[brittle socket]

Wait what? Chmonkey is an undergrad?

[bright hill]

I think so?

I'm not sure

[brittle socket]

[bright hill]

(he certainly sounds like one )

[brittle socket]

Lmao why

[void tundra]

see abstract algebra channel

[bright hill]

It's not actually that hard to have grad level knowledge

Like

[void tundra]

i feel like someone is about to sully you

[brittle socket]

Hmm

[bright hill]

AT is technically grad level

But you only need pointset and some group theory to get started

And those have only proof writing as a prereq

[void tundra]

i mean that takes time to learn so

[bright hill]

You can get there in a year

[void tundra]

and you lose out on all the other interesting bits of math

[bright hill]

If you're focused enough, way less

[brittle socket]

If lets say I want to read Lee, I need to read finish most of Schroder, a lin alg book, and an intro alg book first

[bright hill]

I mean

[brittle socket]

I have no such strength, I am weak

[bright hill]

If you're gonna do pure math you're gonna do these at some point anyways

[void tundra]

if u do get there u can get G+ lmao

[bright hill]

I think the standard for G+ is way higher

[void tundra]

wait is it

[bright hill]

Yea

[void tundra]

AG level?

[bright hill]

Hmm

Dunno

[long matrix]

the role?

not rlly

[bright hill]

You prolly need to at least do a fair bit of that

[void tundra]

how so

[brittle socket]

Lmao why do you have Graduate+ together with pending G+

[long matrix]

u just need to have graduated righ

idk

[void tundra]

i mean no u dont even have to have graduated

u just need to be studying grad math

[bright hill]

Coz he got it

[long matrix]

oh ok

[bright hill]

That means everyone can

[long matrix]

darqs doing cat theory

he can get it

[void tundra]

ah yes, let me the 5th grader obtain G+

[bright hill]

I don't lel

[brittle socket]

Really?

[bright hill]

I technically am doing graduate algebra

[brittle socket]

Oh lol

[brittle socket]

Mice

[bright hill]

But i won't count myself as graduate level at all lmfao

[void tundra]

in the future

does rudin func analysis
nah im just undergrad level

[bright hill]

It's just that aluffi sprinkles a lot of category theory here and there

Mostly just terminology

[brittle socket]

Ah I see

So much stuff to self-study, so little time

[bright hill]

Like

[void tundra]

technically you can never run out of math to study

if you do just invent more math

[bright hill]

I haven't even finished baby rudin

[brittle socket]

I haven't even finished Enderton's Set Theory book which is only like 280 pages long

[void tundra]

string theory be like:

[bright hill]

Don't worry grass, you're doing far better than most

[brittle socket]

Thanks for the encouragement lol

[bright hill]

It's just that this server's standards are waaaaaay too overblown lmfao

[void tundra]

I mean it is a discord server about math so

you do have to be fairly interested

[bright hill]

Cringe.

[brittle socket]

You need group theory in Chemistry?

[bright hill]

me who does all of math as a hobby

[void tundra]

probably just gotta know what a dihedral group is

no way ur gonna be asked to prove anything lmao

proof: mathematicians alr did it qed

[brittle socket]

I just used a good old prove method. Its called "I'll come back to it later since I can't think of any ideas now. I surely will return to it in the future... soon... eventually...."

[void tundra]

thats what we call

exercise for the reader

where the reader is future you

[bright hill]

Nah

That's called copium

[brittle socket]

[void tundra]

"This proof is too trivial now so I will leave it for once I forget"

[brittle socket]

I could solve that exercise easily but Enderton added an extra condition that makes me go

[brittle socket]

"I bookmarked it so I will surely come back to it in the future" Copes harder

[void tundra]

me proving fermat's little theorem:

nah that just falls out as a corollary of lagrange anw so

[bright hill]

@long matrix what does the graduate role give you?

[long matrix]

nothing

a chay

chat vc

nothing else

[void tundra]

u get to feel superior

[brittle socket]

The right to assert dominance

[brittle socket]

[bright hill]

[long matrix]

no one respects me cus of it, wasta time

[bright hill]

Cringe.

[long matrix]

i was expecting slurp to kowtow to me

[bright hill]

It would be hilarious to give slurp the G+ role lmfao

@neat frost weren't you doing measure theory?

[brittle socket]

What about giving Slurp honorable?

[bright hill]

That's grad stuff, right?

[vast surge]

Slurp for honorable

[bright hill]

Omg, that's even funnier

[vast surge]

@ Moderators Slurp should get honorable

[long matrix]

if slurp got honorable wed never hear the end of it

[void tundra]

this actually needs to happen just because it'll be funny

[brittle socket]

DerpZ help me get out of the deep dark

[void tundra]

oh my god

you are stuck there?

log off now

ill finish this anal proof and i'll come help

[brittle socket]

Im not on lmao

[void tundra]

oh

like u logged off in there?

[bright hill]

Great minds think alike, derpz

[brittle socket]

Yeah but Im just close to it. Are you gonna come on later? We could raid it together

[void tundra]

if ur not on I'll treat myself to one more anal proof

lol sure

[bright hill]

Oh, they responded

[void tundra]

and one subchapter

who responded

[brittle socket]

There's a machine by illmango that switches off the wardens

[bright hill]

LOLLLL

[brittle socket]

LMAO

[void tundra]

LOL

[brittle socket]

I have to save that

[void tundra]

"which of the requirements has slurp not met?"

[void tundra]

oh yeah the mobswitch

[brittle socket]

Hm?

[void tundra]

warden mobswitch?

[brittle socket]

Ah yeah

Lol loch comin in

[surreal sapphire]

please read up on the #rules about sharing personal information of others

[vast surge]

"these are people who have consistently demonstrated courtesy, reasonability, and helpfulness around the server; and whom we consider to be exemplary members of our community."

I'd say all of them

[void tundra]

proof?

[bright hill]

I mean

[vast surge]

Obvious, left as an exercise for the reader

[bright hill]

I thought public information was ok

[void tundra]

hint plz :(

[bright hill]

[void tundra]

too hard

[vast surge]

hint: consider the proof of lemma 69.420

[odd narwhal]

please do not spam modmail

[void tundra]

lmao I literally just typed in from:Slurp in the search bar

[bright hill]

Sry haha

[surreal sapphire]

hm, being serious i thought about it and sharing modmails you sent should morally be allowed

though not necessarily on this server

[void tundra]

curious as to why not on this server

[surreal sapphire]

you can feel free to shit on moderators or wtv but doing it publicly here is not a useful discussion to have

[void tundra]

I don't really think he was shitting on mods tho

[bright hill]

I think he means sharing modmail messages in general

[surreal sapphire]

i mean yeah, in this case i appreciate sharing the fact that i am very funny

[leaden torrent]

how about you stop using modmail, which pings all moderators, in order to generate funny screenshots you can share to your friends in #serious-discussion

unless you want me to ping everyone to make a joke

[vast surge]

I just looked in my modmail messages to see if there's anything juicy

There isn't

[bright hill]

I didn't know it pings all mods

I thought it just relays the messages to a channel that mods can see

[void tundra]

is modmail open source

[bright hill]

I don't think so

Actually, i don't really know

[void tundra]

its not on github.com/discord-math tho

oh wait

[bright hill]

Yea

[void tundra]

its a module in @quasi jetty

[bright hill]

Huh

[bright hill]

I see

[brittle socket]

There's a github for this server?

[bright hill]

Yea

[leaden torrent]

.

[void tundra]

https://github.com/discord-math/bot/blob/main/plugins/modmail.py

[bright hill]

mb