book-recommendations

[marble solar]

I actually like Susskind's Intro to QM

I think it's much more casual than Griffiths

[gray gazelle]

sus

I've already worked with permutation tests, I want to improve my ability in probability and statistics, I just want to have a source with a lot of exercises of different difficulties, I know I could do all the exercises in Casella & Berger but I haven't studied any pure maths, so this is not gonna work for me

You are assuming wrong

btw, thanks for the help @hearty steppe

Yes, and I want to solve that by doing a lot of exercises

[smoky surge]

idk if this kinda stuff exists but are there any short pdfs/lectures for getting your head around the fourier analysis

i dont really want to read a whole book and idk what to look for given that this feels kinda specific

non-rigorous is fine

[willow pecan]

Lol

You can never have enough intuition for Fourier transforms

[smoky surge]

😦

is it really that hard to form intuition

I just need to do it like right lmao

[sage python]

The point of that comment was more, more intuition is always better

[smoky surge]

oh yay

[sage python]

/The Fourier transform is a deep object

[smoky surge]

if I wanted a light intro where do I get started

[sage python]

Rather than like "your understanding will be deficient to do the things you want"

Uh, people like Stein's Fourier Analysis, I haven't used it myself

[smoky surge]

ill give it a look

gracias

[willow pecan]

S&S is of course a lengthy book

[smoky surge]

~~so basically just watch 3B1B and pretend I know it? ~~

[willow pecan]

3B1B is far from enough intuition

[smoky surge]

i know im memeing

[narrow talon]

@gray gazelle you mentioned your probability base is not where you want it to be, maybe check out the book by Ross on probability? It may be a little easy but if it isn’t then it should provide a wealth of problems

As for stats I must disagree with cat man. I am of the mind that intuition for stats is largely gained by getting data and doing stats, in this way I think applied books are great for getting more intuition about statistics (think any book that mentions “with R”)

As for math stats (if that’s what you’re interested in) Wasserman is a good alternative to Casella Berger that’s imo more entertaining and more modern, though also less thorough.

[gray gazelle]

Wow, thanks a lot

[gray gazelle]

Yeah, my thinking is also like your thinking and I'll search any book that has that

[primal summit]

Bump

[tranquil ocean]

Maybe finite group theory by Isaac? Idk there are a lot of directions you could go and it depends what you want to learn

It depends if you want to stay in pure group theory or not I guess. You could learn something like geometric group theory which has a lot of cool groups

Representation theory is a common next step too I guess, but maybe you want to learn some ring/field theory first before that

@primal summit

[primal summit]

I mostly meant pure group theory

Since that's a subject that doesn't really have a dedicated course beyond a first course in my uni

[tranquil ocean]

Then yeah, I think finite group theory by Isaac is a nice book

[primal summit]

Alright i'll check it out, thanks

[tranquil ocean]

also his character theory book might be interesting

[elfin ingot]

Hi does any have any book recommendations that would be understandable to someone planning to do maths at uni and might look good on an application

[sudden kindle]

No

[cursive orbit]

do you usually list the books you read on your application?

[elfin ingot]

Lol

[willow pecan]

No you don't

Unless you're in the UK then you mention one you read in an essay for some weird reason

[crystal lion]

sometimes we have to do that in the US too

[gray gazelle]

Calculus by Larsson

[elfin ingot]

Ah thanks will have a read

Yeah if you talk about books you've read it supposedly shows you're interested in the subject

[gray gazelle]

I didn't read it

[marble solar]

You can get the highlights of S&S Fourier

Just by the chapters 1,2,3,4 and the fourier transform sections

[cursive orbit]

you might be able to impress the admissions dude if you read baby rudin

[timber mesa]

I've heard of schools asking for this for grad admissions, sounds a bit pointless for undergrad tbh

[sudden kindle]

you might be able to impress the admissions dude if you read Number Fields by Daniel A Marcus and the admissions dude was me

[timber mesa]

this depends a ton on your actual interests (don't study just to impress people, it gets stressing real quick) and what you already know. AMS's Student Mathematical Library has books on various topics that aren't usually seen in undergrad and are meant for math undergrads, they're pretty nice I think. Maybe you can find something interesting: https://bookstore.ams.org/STML

I've read S. Katok's p-adic Analysis Compared with Real from that collection and thought it was a nice read, complementing with Gouvea's p-adics book

Matrix Groups for Undergraduates seems real nice too from what I've skimmed through

and I've been meaning to read Y. Pesin's Lectures on Fractal Geometry and Dynamical Systems from that collection as well

[sudden kindle]

Anyone have any book reccs for computational number theory?

[tranquil ocean]

Cohen's computational algebraic number theory is nice

[sudden kindle]

Have you used it

Wow this is an enormous book

[willow pecan]

Do floating point issues come up a lot in computational alg geo?

[tranquil ocean]

Nah, I've used it more as a reference when I needed something, but it has pretty nice exposition too

[sudden kindle]

[tranquil ocean]

yea

I guess its written more to be a reference and collect everything but

also the author Henri Cohen is the creator of pari/gp

[sudden kindle]

I cant imagine actually going thru this book systematically

[tranquil ocean]

I mean its not rlly longer than like, a normal textbook, and big chunks of code take up a lot of room too

[sudden kindle]

Oh fair

[split pond]

@desert copper also maybe try spivak's calc on advanced manifolds

[gray gazelle]

advanced manifolds

[glossy grove]

manifolds

[split pond]

you were the one who recommended me lol

[desert copper]

lmao

[desert copper]

Are there any major prerequisites

[split pond]

linear algebra?

[gray gazelle]

PDEs

what are y'all smoking

[gray gazelle]

I was joking

no one makes jokes, ever

[gray gazelle]

Chicken are eggcellent

[bronze raven]

Anyone have any articles about importance of foundational math? I see it as way of concretely justifying bigger constructions in math, but I really dont know what it is outside of that. Any resources would be appreciated.

[crystal lion]

"man i fold"

a common phrase said during a game of poker

[novel iris]

@sweet lotus do you by any chance know a good resource on the theory of lattices and whatnot with the application of quantum logic in mind?

also ig a resource on quantum logic if you like one. My first foray into the subject was with Omnes

thanks!

[little jay]

Hey. I'm trying to find away to prove Fourier series and this has proven to be a difficult task. I've tried to find a decent proof from Stein Shakarchi's Fourier analysis an introduction and several other books, but the most I've been able to understand or find has been a "let's assume that f(x) = a_0 + sum of... is true and here are methods for solving the values a_+, a_n, b_n"

[willow pecan]

You are trying to prove the existence of Fourier series and want to find a reference?

[little jay]

Most sources, or the bits which I've been able to understand begin from assuming that this expression true. And then the terms a_0, a_n and b_n are solved from there. This however does not feel like a valid proof, the assumption that this statement is true to begin with is my issue.

So any books containing proofs of the existence fourier series would be helpful

[willow pecan]

Ok

The only bit of work that you need to do to show that this expression is true is to show that cos(nx) and sin(nx) form a basis for L^2([0,1])

You can probably find this on MSE

[glad prairie]

this is a hard thing to prove by the way

first of all, you need to figure out what you care about. uniform convergence? pointwise convergence? convergence in L^2?

also, are we allowing functions to be continuous / differentiable / smooth?

"why do fourier series converge" is a very complicated question

[little jay]

Yeah that's kinda what I've assumed from all the source I've found skipping at least parts of the proof

[glad prairie]

let me see if i can find a nice proof for the L^2 case (which is the easy one i think)

[little jay]

that L^2 basis seems like an useful thing to understand

thank you

[glad prairie]

Here's a nice proof using the Poisson kernel (section 1.2): https://www.math.arizona.edu/~faris/methodsweb/fseries.pdf

there are lots of proofs, i'll try to find a less nasty one

[lapis sundial]

I find it interesting the Poisson kernel is used cause I'd expect Dirichlet to be useful for that lol

I am a newbie at fourier analysis tho ofc rip

[shadow tusk]

https://youtu.be/pTnEG_WGd2Q are the books he recommends good enough?

[gray gazelle]

Hello, I just wanted to know if Evan Chen's book on Geometry is any better than the free one mentioned on his website

https://www.olympiadgeometry.com/

Guess I will just study the free chapter and compare it if I should

[crystal lion]

the trick is to not learn euclidean geometry

[gray gazelle]

Why

@crystal lion

[analog pollen]

I can’t say about the books before calc but they are fine

His calc, diff eq, linear algebra are pretty decent

The rest I wouldn’t know about

[eager stump]

I think just having a working mathematician rec means someone found some value in it. Mileage may vary for certain things and depending on your interests you don't need to have multiple texts on one topic. There's always library browsing if you're in doubt. A lot of books can be requested through interlibrary systems

[flint forge]

the correct answer to this question is that there is no need to pick out more than one book at a time

and if you'd like to learn a subject

[gray gazelle]

I've tried following this path once (this was what jumpstarted my journey into math tbh), but honestly learn what you are interested in and dw about your book not being the best or not (ofc it helps to look up reviews and compare it with other books) but don't overthink it. Like don't waste ur time thinking about how to learn when you can just start learning! Although learning how to learn is also pretty important too, and while I don't have a solid answer for math, from what I know many people like to say practice makes perfect especially for smth like math.

[flint forge]

you can always ask for a recommendation here

pre-set paths are not good ways to learn mathematics outside of strict prerequisities

its a slow process and you don't need to plan this much ahead, honestly

[marble solar]

But if I have the optimal learning platform, surely I'll learn 200% more

[polar tulip]

"learning math start to finish" is clickbait, of course

but also I do take an issue with the approach here actually

I don't like "intro to proofs" style books as being the place you start learning math

[marble solar]

I think intro to proof books should be banned

Nobody should read them

[polar tulip]

these books often fall into the trap of not having any interesting content, and just being a grab bag of language and techniques without context

my go to rec for new mathematicians is analysis 1 by tao, but there are lots of good options depending on what you're interested in learning

[broken meadow]

every other problem is like "oh 3 is an odd number and 2 is an even number so we got a contradiction woohoo"

[polar tulip]

plenty of people on this server started there, so it's very easy to get help too

[shadow tusk]

Noted

Thanks guys

[shadow tusk]

What are the prerequisites?

[polar tulip]

none, but if youve done computational calculus before, it will be more motivated

[tranquil ocean]

Pretty hard disagree. I really enjoyed learning some naive set theory and logical ideas before going into higher math

[flint forge]

im with doubledual i hate intro to proofs stuff

well okay

maybe like

spending 1 or 2 weeks on it

could be beneficial

[polar tulip]

there are good ways to do this, i learned set theory first too. but if the book is "intro proofs" it usually doesn't get to anything interesting

[flint forge]

honestly the IBL method

is perfect

best math intro course

[broken meadow]

my teacher was based enough to at least give us Raymond Smullyan content in my intro proofs class

[flint forge]

unless you need to learn multivar in which case you're fucked

[shadow tusk]

The IBL method?

[flint forge]

IBL method refers to a specific course

[shadow tusk]

The DN method??

[flint forge]

actually

[tranquil ocean]

It was interesting for me just because it was the beginning of formalism, and it was interesting how you can formalize a lot of things

I don't think it really needs to be interesting by itself

[flint forge]

i wonder if anyone here has access to the UChi ibl scripts

[broken meadow]

nah just like

selected examples

[flint forge]

because they are really nice intros

[polar tulip]

you can google it they're out there

[broken meadow]

he gave us puzzles to try to cast in the notation we learned

to help solve them

[flint forge]

nice

[broken meadow]

not any of the hard ones but the knights knaves stuff

[polar tulip]

but i think it's only really good if you have access to a knowledgeable mentor

[shadow tusk]

:pepecry:

[polar tulip]

but like, chatting with people on discord is good enough, so it's viable

[broken meadow]

there were some others too but i forgot 😔

[shadow tusk]

Smh no emoji

[shadow tusk]

Seen this one on brilliant

[formal bane]

what classifies as higher level math?

You guys were talking about getting started with it through [x] book, but can higher level math be anything as long as it's of sufficient difficulty?

[flint forge]

Higher level math in this server normally refers to proof based mathematics

At the very least something you would not be able to see in high school

[sudden kindle]

D-modules

[valid moth]

D── modules

[past ice]

My favorite "intro to higher math" kind of books is this set of notes by Aluffi http://www.math.hawaii.edu/~pavel/Aluffi_notes.pdf

don't go through a 400-page "intro to proofs" book, please

[formal bane]

I'm guessing there's no set guidelines then

higher level math seems boring

vastly different from competition math

is there a higher level math based off of synthetic geometry? I would like that

[eager stump]

wut

[formal bane]

To be fair, this is all based off of glancing at a couple of pictures

differential equations might be fun

[eager stump]

i mean the way i see it, it's where fun is at

it might take a lot of work for it to be accessible though

[steel viper]

[misty wyvern]

the bad news is you can't solve competition math problems and publish papers about your solutions

[gray gazelle]

any good number theory books?

[gusty smelt]

What type of number theory? I recommend Ireland Rosen for elementary if you are familiar with algebra

[gray gazelle]

Yeah elementary

holy

graduate level

any undergrad ones?

actually that topic might be graduate level

[gusty smelt]

Oh dw a lot of textbooks are under the name graduate texts in mathematics

It’s undergrad IMO

[gray gazelle]

okok

[gusty smelt]

I know some others that are recommended is wiel basic number theory

And hatchers topology of numbers

[gray gazelle]

what about Algebra?

dummit and foote?

[gusty smelt]

No it’s a bad book

[gray gazelle]

oh really"?

[gusty smelt]

Try Artin

Yeah df is like the driest book tbh

Artin explores a lot of application of the,topics and does a lot of linear algebra too(that you can skip if you are familiar with the stuff)

[gray gazelle]

Yeah yeah

Covers the same material?

[gusty smelt]

Df has a lot of stuff in it, but for a first year equivalent both have enough

[gray gazelle]

Hmmm

Okay

[past ice]

That's a meme not a recommendation lolol

[gusty smelt]

Oof I see

Well I got trolled lmao

[past ice]

reading the preface and then the table of contents is just hilarious

[gusty smelt]

Ok it’s a cft book lmaooo

[past ice]

i think what weil considers "basic" and "elementary" is different from what humans consider to be such

[gusty smelt]

How tf does he expect no number theory thonkzoom

For him elementary facts about rationals must be like

Kronecker webber lmao

[past ice]

imagine learning how to add fractions then diving into this book

[gusty smelt]

4th grade book

[misty wyvern]

Y'all know that story about a high school ordering a batch of textbooks called Basic Algebra or something, only to realize Basic Algebra referred to abstract algebra

[quick hornet]

the higher you go in mathematics, the more textbook names try to make you feel stupid

in high school you get shit like

"honors AP calculus" and stuff

trying to make it sound super duper elite

even in early undergrad you see "advanced linear algebra" and whatnot

and then suddenly everything is introductory until you've been a grad student for 4 years

obligatory

[sage python]

Which book is that?

Oh

[sage python]

Basic Number Theory

I think he'll say you need algebra but not number theory tbh

[quick hornet]

you really ought to go in with number theory though

like at LEAST ireland-rosen tier

[sonic vessel]

Can someone give example of some good books on functional equations for beginners?
I literally have zero information about functional equations

[karmic thorn]

I doubt if there are lots of books on the topic, but maybe you can find some notes on Evan Chen's website?

[sonic vessel]

There was a "introduction to funtions" lecture note but I didn't understand anything from it

[gray gazelle]

Can someone direct me to a good book on Olympiad Geometry? Whenever I search it up I find Evan Chen EGMO only nothing else :(

And the Beautiful Journey through Olympiad Geometry doesn't cover a lot of stuff I think I am weak at

• EGMO is too expensive for me, it costs like 4000 Currency

[sonic vessel]

where are you living in

[gray gazelle]

India

[sonic vessel]

hmm

in India it is not illegal to pirate books

isnt it

[gray gazelle]

It isn't

[storm harness]

[sonic vessel]

heyhey wait

I can explain

go to libgen or zlibrary

search your book

[gray gazelle]

I haven't encountered any books which are more than 400 Currency here

• the books by Indian authors aren't good because they teach JEE level and JEE doesn't have Geometry at all

[sonic vessel]

thats ok

EGMO is really good

[gray gazelle]

Albeit texts in geometry don't exist here for high school level

[gray gazelle]

Libgen?

Lemme see

[sonic vessel]

z library is easier

and its web looks better

pirating for knowledge is not sin

fax

[storm harness]

Wow convenient 😌

[gray gazelle]

[timid vector]

yeah egmo is the gold standard for oly books

[tribal bridge]

yeah

[coral narwhal]

Use libgen to get to zlib

[gray gazelle]

[manic fox]

[shadow tusk]

yummy free knowledge

[gray gazelle]

Ping?

[willow pecan]

Pingala

[shadow tusk]

https://openstax.org/subjects/math what do you think about openstax's math books?

[gray gazelle]

So friends, I never got a book recommendation for self-learning Calculus.

spivak's

try reading that

Bro, bro. . . Bro.

I am inquisitive and open to learning. . . But shouldn't I. . .Yknow, go through one book first THEN do Spivaks?

No?

Spivak is a introduction

Seriously?

Yes

Hmmm

Read the preface of it

If you don't know something from it's pre requisites then learn that and start with Spivak

That makes sense.

https://www.amazon.com/dp/0914098918/ref=olp_aod_redir_impl1?_encoding=UTF8&aod=1 This one, right?

Yes

I'd get a PDF but my eyes are really hurting lately so. . .ja lol.

Have a look at it on Google books

Thanks Shivansh, you're a gem.

A HOMEWORLD GEM!! AHAHAHAHAHAH

Heh

I am so relieved you got that. . .

[manic fox]

sussy dhaka

[gray gazelle]

wat?

based and mirzapilled , sussy dhaka

Tell me more about this mirzapill.

math

I see.

[misty wyvern]

any neato books published in the last year?

[analog pollen]

For what purpose are you learning calc?

[willow pecan]

Omniscient Reader's Viewpoint

[broken meadow]

Urbanism.

[willow pecan]

Imaginary Cities

A Field Guide to the Hidden World of Everyday Design

[misty wyvern]

books with math in them

[willow pecan]

You did not specify

[misty wyvern]

true, hence why i specified now

[gray gazelle]

Well, there are several reasons.

The first is the holistic goal : Understanding calculus will make me smarter and increase my IQ as if I mastered calc, I will understand the patterns of moving particles from the ground up.

The second is : I plan to start my own business and have several business goals, but the thing I want to make is something on par with google. Thing is, to MAKE google the founders had to have advanced mathematical and programming understanding.

The third : I plan to make games, and have a metric fuckton of ideas for games, but math is HUGE.

[misty wyvern]

you don't really need calculus to be a bidness man

[gray gazelle]

I understand that, but I'm not learning calc first THEN business.

[misty wyvern]

if you're making game engines then maybe some calculus wouldnt be a bad idea

[flint forge]

no game company will ever rival google

just like

on principle

[misty wyvern]

this too

[analog pollen]

What do you want to learn in the future?

[gray gazelle]

Right now I'm taking the Wharton class track of business.

[analog pollen]

Physics!

?

[misty wyvern]

nobody wants to learn physics, dont be silly

[gray gazelle]

Well, physics, linear algebra and possibly beyond.

Also, its very possible for a game company to rival google.

[flint forge]

lol

[gray gazelle]

Is it possible today? Nah, not with the economies of scale and how games tend to be fast moving.

With a metaverse, however? Definitely.

[flint forge]

lol

[misty wyvern]

you underestimate what google does

[analog pollen]

If your goal is to learn physics I don’t think spivak is necessary

[gray gazelle]

I underestimate nothing, my G.

[flint forge]

except possibly your ego

[gray gazelle]

Now, do I know EVERYTHING google does? HEEELL no.

[hollow current]

how google can know anything

google is not a person

[gray gazelle]

Well MaxJ, that may be true. . .But, I'll worry about that in my 40s when I start having kids.

[hollow current]

so you know nothing

qed

[karmic thorn]

Why is this in #book-recommendations

[hollow current]

manan make me yellow

[misty wyvern]

why not

[gray gazelle]

ITS THE MODS, RUN!

[hollow current]

and you shall get the answer

[gray gazelle]

smoke bomb

[karmic thorn]

Beyond my abilities

[hollow current]

anyway i suggest profilactic mute

[gray gazelle]

What about linear algebra? Surely spivak can help with that?

[hollow current]

spivak is not linear algebra tho

[analog pollen]

Linear algebra isn’t that important in physics

[gray gazelle]

Well no, but when I took linear algebra there were trig-invested questions that I couldn't solve to save my life.

[analog pollen]

To learn as a course

[hasty turret]

See chapter 1 of spivak com

[misty wyvern]

you should start with rudin, google researchers can read it, so you should be able to too

[gusty smelt]

What kind of physics do u do lol

[marble solar]

Just gotta learn it from Calculus on Manifolds

[hollow current]

you should write rudin as google researches

[gray gazelle]

Rudin? Wat's Rudin? Is that the Analysis book or something?

[analog pollen]

I mean you won’t need a course on it

[hasty turret]

wdym

[broken meadow]

all of the physics majors i know are taking linear algebra or are learning it via their physics courses

[misty wyvern]

linear algebra isnt important in physics

sounds like a Physics 101 opinion

[analog pollen]

I said it wrong lmao

[hasty turret]

Next what? Statistics is not important for physics?

[gray gazelle]

I feel like reporting a murder now. . . .

[hollow current]

physics is not important in physics

[flint forge]

lmao that's like saying that infinity lie algebroids are not important in physics

[misty wyvern]

tbh if you see how physicists do statistics you'd be tempted to say they cant do statistics either

[flint forge]

you guys need to read more schrieber

[marble solar]

have you seen how statisticians do stats

[misty wyvern]

yes, its very sad

[gray gazelle]

So is this Rudin : https://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/007054235X ?

[marble solar]

You'll be tempted to say they don't know what they're talking about OR they don't know how to communicate what they're talking about

||But that's true of every technical field||

[hollow current]

there was a joke

[misty wyvern]

you can tell if a statistician knows what theyre doing by asking them what grade they got in real analysis

[hollow current]

so student comes to prof saying that he thrown coin 1k times and got 470 times heads

and asks why

[marble solar]

If they got an A, they aren't a statistician

[hollow current]

like probabilty is 0.5 so why

prof says that student forgot about deviation

[misty wyvern]

they're a reverse probabilist

[marble solar]

It was a joke, because why would you be talented and still choose to go into stats

[hollow current]

and studens is like "gotcha so amount of heads will be in 470-530"

[marble solar]

It's an option for people who couldn't make it in math

[hollow current]

and prof answers not exactly

[marble solar]

||Like me||

[hollow current]

student asks so wtf is going on, are these laws a lie

and prof says well

if they would be violated

i would be surprised

[misty wyvern]

short answer: they made a mistake
long answer: they thought AI was cool but wanted to do it rigorously unlike the CS freaks, so they did stats instead

[gray gazelle]

BOOOOOOOOOOOOO

[hollow current]

stfu

[gray gazelle]

GET OFF THE STAGE!

The telling of that joke took longer than the actual Snyder Cut.

[hollow current]

your mom took something longer than this telling

so

\abhi

[gray gazelle]

. . .Mom jokes??? Really???

You know I should feel sad for you, but. . . .

NOBODY. . .

and I mean NOBODY

talks about my mother like that.

[shadow tusk]

can't find Fearon's pre-algebra on libgen

[gray gazelle]

Except the entirety of Xbox Live. . . .

[hollow current]

spam isbn

spam name/surname etc

wtf #chill

[misty wyvern]

can we ban everyone in this channel. i'm willing to make the sacrifice for the greater good

[hollow current]

#chill is a lie

[broken meadow]

let's not talk about l*bgen in here

we do not condone piracy

[gray gazelle]

What are you? Stupid? You ban half of the entire channel dude. . . .

Be Thanos, not Adolf. DUH.

[broken meadow]

...

what

[hollow current]

are you condoning being horny?

[gray gazelle]

😬

[hollow current]

metal talk when

[broken meadow]

lets also not compare people to adolf fucking hitler

[gray gazelle]

Bro, have you BEEN to the internet? Everybody is compared to adolf ducking hitler.

[hollow current]

(c) Stalin

[broken meadow]

@gray gazelle knock it off

that is patently false

lmao

[gray gazelle]

I don't know melia, I mean I tweeted about how I enjoyed a steak once and a Vegan had. . .opinions.

[broken meadow]

this is frivolous

[gray gazelle]

Tru tru, but on the internet arguments start over something frivilous.

And when people start arguing, you know what happens. . .

[karmic thorn]

Nevertheless this conversation has lost its merit, and continues to fill up #book-recommendations . It's a good time to call it off.

[broken meadow]

im done here

[gray gazelle]

Fair.

[shadow tusk]

eating meat isn't really frivolous

[gray gazelle]

Here we go. . .

[karmic thorn]

....

[broken meadow]

...

[shadow tusk]

...

[gray gazelle]

dot dot dot

[broken meadow]

this is not the channel for this

#chill

[karmic thorn]

I literally insisted not to fill up this channel with more off-topic stuff a few messages back.

Can we stop here?

[misty wyvern]

reposting Q:

Skorokhod embedding from graphs to manifolds, anyone got a reference?

i'm just looking for a babby writeup because Brownian motion on manifolds is defined by the laplacian which makes it not immediately a transposition of what happens on R^d.

[gray gazelle]

I'm thinking of learning about differential equations

[broken meadow]

oh no

[gray gazelle]

is knowing calculus and linear algebra good enough?

[broken meadow]

yes

for basic stuffs

[gray gazelle]

ah

[broken meadow]

stuff you would see in books like Nagle saff snider or boyce diprima

only require calc and linear algebra

[gray gazelle]

hmm any advice in learning it?

[gray gazelle]

thanks will look into them

the uh no is scary

[broken meadow]

the only advice i have is to be persistent because they are bad books

there are no good books in ode at this level

[gray gazelle]

well what should I also learn before diving in

[broken meadow]

🤷‍♀️ for these books nothing else is necessary

[gray gazelle]

well for the more complicated stuff

[broken meadow]

later on when you learn analysis there ought to be better tomes on the material that are more theoretical

which i am not familiar with

given that i have not learned any analysis yet

[gray gazelle]

lol

so would you say analysis, calculus and linear algebra would be the best prerequisites before completely diving in DE?

[analog pollen]

No analysis

[marble solar]

Not really, it depends on what your end goal is

If you want to learn differential equations

Then just go learn differential equations

[broken meadow]

you already have what you need to learn diffeq

the theory is just more work

[marble solar]

There's no reason to beat around the bush. You can pick up other things along the way

Treat that as interesting side things, you can't learn everything at once

[gray gazelle]

true

[misty wyvern]

for harder DEs analysis is unavoidable even to approach practical solutions.

but you can do a lot before that

most of engineering in fact

[gray gazelle]

would pauls notebook be a nice more summarized resources?

[broken meadow]

pauls notes are fine

[marble solar]

I love paul's online notes for just about any subject

So it's a great way to get your feet wet

[misty wyvern]

doesnt khan acdemy have an odes course

[gray gazelle]

I think so yea

[analog pollen]

Don’t think so

[misty wyvern]

[gray gazelle]

they do

[analog pollen]

Oh damn

[gray gazelle]

https://www.khanacademy.org/math/differential-equations

perfect

well I'mma go dive in, thank you all for your help

🥗

[analog pollen]

Good luck with your studies

[misty wyvern]

when you mentioned modular inclusions it became clear to me the standard takes like rudin functional are probably beneath your level

you're excused

[analog pollen]

Lmao

[misty wyvern]

modular inclusions, which ive never heard of, are clearly some research level operator algebra stuff, is it likely that it pops up in a standard reference

[sage python]

@sweet lotus I like Borthwick but its angle on the material is probably less your style

I think "A Short Course on Spectral Theory" by Arveson is a more C* algebra angle

Not sure if this contains what you're looking for or not lol. Borthwick is more, does a bit of abstract spectral theory and then zooms in on Laplacian/Schrodinger operators on manifolds, and graphs

Ah okay

Yeah these are the two I know, sorry if they're not what you're looking for

[misty wyvern]

Maybe check out the Fell and Doran "Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles" 2-volume set, see if it has anything to offer you.

no worries, its my kink

[gray gazelle]

holup

[pure shell]

Hmmm guys, any book recommendations on differential geometry?

[misty wyvern]

At what level

do you know any topology

[gray gazelle]

and what kind

[pure shell]

Yes, just finished self studying topology

Trying to get into differential geometry

[gray gazelle]

tu (introduction to manifolds), lee (introduction to smooth manifolds) (admittedly these are more "introduction to basic constructions on manifolds" than differential geometry books)

[sage python]

If you hate yourself want to learn about curves and surfaces

Do Carmo

If you still hate yourself but want something more interesting are looking for more general diffgeo, there's the other Do Carmo

[misty wyvern]

I really like Tu

[pure shell]

K, I hate myself so I'm definitely gonna look it up

[misty wyvern]

Don't do do Carmo

[gray gazelle]

do carmo is a bitch to read

jesus christ it's so painful

[marble solar]

was the pay off worth it?

[pure shell]

Hmmmmm

[sage python]

"The other Do Carmo" = Riemannian geometry

[misty wyvern]

Tu and Lee are all you need

[sage python]

Well that's not diffgeo exactly

[gray gazelle]

^see my edit

[misty wyvern]

Actually don't learn differential geometry, do finance and make money instead

[sage python]

Honestly fair

[marble gulch]

lol

[sage python]

But yeah I mean I kinda appreciate hyperbolic geometry

[pure shell]

Hhhh lol but I hate myself. . So.

[sage python]

And probably characteristic classes

@pure shell wait are you Moroccan?

[gray gazelle]

you need at least some of the manifolds stuff lee and tu offer to do what people mean by differential geometry anyways

[pure shell]

Nah

[sage python]

Oh lol

Saying hhhh for laughter is a bit of a Moroccan thing

[obsidian valley]

[pure shell]

Oh ok didn't know that

[crystal lion]

the only proper definition of diff geo is the appendix of a GR book

[lapis sundial]

lol was gonna make a GR joke

[sage python]

Serious suggestions only

Nah but yeah like basically there's a weird trio

[pure shell]

Yes, but thx guys, gonna look it up...

[sage python]

There are "Intro to smooth manifolds" books

And they're gonna cover like, def of a manifold, tangent space/bundle, smooth functions, etc

Lee and Tu are in that category

Then there's differential topology, which studies the topology of smooth manifolds

[misty wyvern]

Lee's "Introduction to XYZ Manifold" books are great, Tu is probably more difftoppy

[pure shell]

Oooo sound nice..

[gray gazelle]

tu's intro to manifolds is just watered down lee ISM

[misty wyvern]

Don't worry about it, just pick one of Tu and Lee to read and you'll know what to do next

[pure shell]

Ok

[sage python]

So you'll learn stuff like transversal intersection theory on manifolds etc

Guillemin-Pollack and Minor are the accessible books in this category

There's also Hirsch

Which is tough

[gray gazelle]

(it's still a good book; also, lee ISM is like seven hundred fucking pages)

[sage python]

And Bott-Tu if you know algebraic topology

Finally there's diffgeo

Here you're putting some structure on top of just being a smooth manifold

Often a Riemannian metric

[lapis sundial]

would you say it's necessary to have studied analysis in R^n (e.g. spivak/munkres) before embarking on one of these books?

[sage python]

This subject is incredibly painful, and Do Carmo is the relevant name here

Yeah it is

[gray gazelle]

do u know the implicit function theorem and its equivalent statements

[lapis sundial]

those books seem a bit of an awkward middle ground between diff geo and real analysis but i guess it's useful lol

Oh I mean I know I'm not yet prepared for differential geometry anyway (it was more out of interest) but I have looked at the implicit function thm briefly in munkres and stuff

or like, inverse function theorem too etc

[lapis sundial]

(what equivalent statements are there?)

[sage python]

Inverse function theorem, constant rank theorem

[lapis sundial]

ah, sure

[valid moth]

@broken meadow

[sage python]

W... What

[valid moth]

metal has 1 result for hhhhhh, 8 for hhhhh, 22 for hhhh, 39 for hhh, 73 for hh

[sage python]

Is metal actually just my son or something?

[misty wyvern]

lots of h's in this chat rn, are we talkin h-cobordisms

[sage python]

Yes

[valid moth]

no we are talking about hoo asked

😎

[sage python]

eyyyyyyyyyyy

[broken meadow]

i use hhhh a lot

lmao

[crystal lion]

pick a different letter

like p

[broken meadow]

jajajaja

[crystal lion]

pppppppppp

[prisma snow]

55555 (this is how thai people laugh)

[obsidian valley]

hhhh & qqqqq are pretty common among the chinese students i know

[crystal lion]

ikr im so funny

[crystal lion]

k is pretty common among the...

[valid moth]

brazilians

[crystal lion]

really

i was thinking a different group

[prisma snow]

the colonizers

[crystal lion]

bingo

[steel viper]

virgin hhhhh vs chad wwwww

[broken meadow]

j

[valid moth]

wwww

TRUE

www >n<

[formal bane]

Why would you want to publish papers about your solutions?

I mean you can publish solutions, but I still don't get the point

I'm genuinely curious; I'm not trying to say one is better than the other

[prisma snow]

I guess their point was that you are not doing new math if you are doing competition math. You are just applying methods you have learned. That's not something you can do professionally (ie publish papers on or get paid )

[misty wyvern]

Don't you want to be tenured and spend your years doing nothing while collecting paychecks

[sage python]

Lmfao

[polar tulip]

competitive math problems involve knowing a bag of tricks, and are only “hard” because you need to know the tricks + time limits

it’s not a very deep thing lol

[viral scroll]

For me the true beauty in math is to construct theory

"construct theory" is weirdly phrased because some people might say to theorise

[willow pecan]

Wow do you do algebraic geometry

[viral scroll]

Why that face hahah?

[viral scroll]

No

[willow pecan]

Algebraic geometry seems like your cup of tea

Category theory as well

Constructing theory

Obviously solving problems is not important

[flat lantern]

lol

[viral scroll]

I too young to tell for know, I understand that solving problems involve building theory obviusly but I would like to focus on the building process principally

Obviusly you cant separate both activities completely as they are interelated

[quick hornet]

if you wanna focus on the building process, may i recommend Minecraft

[sudden kindle]

The problems are only an excuse to build theory

[primal summit]

Solutions to problems can have real world applications and I don't need that kind of negativity in my life

[valid moth]

basically builders vs pvpers in minecraft

[misty wyvern]

If mathematicians weren't so OCD about making sure their work stays pure, they'd pick up thousands of free citations in interdisciplinary journals.

[willow pecan]

Would they?

[misty wyvern]

Except category theorists, who will never do anything useful.

Haskell doesn't count.

[willow pecan]

Who is going to start citing arithmetic geometry?

[misty wyvern]

Mochizuki, a known applied mathematician who applies mathematics to black magic.

[viral scroll]

men I love black magic

[crystal lion]

women I love black magic

[primal summit]

Non-Binary folks I love black magic

[glossy grove]

without a comma, your sentence's weird.

[sudden kindle]

Im gonna ask this again: I wanna learn a proof of the Uniformization Theorem from complex analysis. Any Book / resource recommendations ?

[sudden kindle]

Thank you!

[marble solar]

I'm interested in some of Riemann's earlier work

Does anyone have a link to an English Translation of his work

There's one on amazon that's out of stock

[gray gazelle]

calc 3 book?

[misty wyvern]

If Wikipedia isn't enough for you then try Hubbard and Hubbard.

[forest sleet]

Any specific paper? I can only find his prime number paper translation on claymath, but I'd be up for trying to translate a page or two if it's something specific. (Not saying my translation will be any good though but it'd be fun to practice)

[marble solar]

I'm primarily interested in his PhD Thesis

[forest sleet]

There seems to be an English translation on vixra of all places... 😅

I'll take a look when I'm on computer tomorrow

https://vixra.org/pdf/1408.0132v1.pdf 😅

Never thought I'd link a vixra paper that wasn't the two page proof of collatz in Microsoft paint

[astral laurel]

Hello. Can anyone recommend me some good books on probability?

I major computer science in uni, but I am on math double major and wanting to learn some mathematical optimization algorithms. While reading some stuff, martingales are regularly comming up and I have no idea what this is.

I have bit of analysis background. To be specific, I took both Introduction to mathematical analysis and Real Analysis. The latter is grad freshman/undergrad senior course which covers first half of Rudin's RCA. Since I was quite fine with it, I understand some basics of measure thoery and L2 spaces and so on

Someone I know (grad student) recommeneded me durrett's probability textbook, but it seemed bit too much for me. He also said that he haven't read the whole thing but he heard that it was good. Will this book be helpful for me? If anyone who actually went through the book can give me some info it would be very helpful

I have 6 weeks of to seriously study full time and then a whole semester to invest partialy. Thanks in advance for reading such a long question!

[sage python]

So I've taken a class out of Durrett. Tbh I wasn't very focused on that class; I just kinda barely figured out enough to do psets and crammed for tests. That said, I was able to do so successfully, which I think suggests the part of the book we covered wasn't too hard. It basically reviews the needed measure theory

I barely hit chapter 4 which is on martingales and where stochastic stuff starts

So I'd say it's probably successful to you but maybe it's not the most efficient way to get to that material

[astral laurel]

It seemed like I have to read hundreds of pages if I choose to study Durrett

[sage python]

Yeah it's inefficient

Maybe Lalley's notes

http://galton.uchicago.edu/~lalley/Courses/381/index.html

http://galton.uchicago.edu/~lalley/Courses/383/index.html

[astral laurel]

Maybe I can skip some measure theory since I studied RCA, but still it was quite overwhelming. Still the reason I am considering to read it is because Markov chains and Brownian motion might be helpful for my study (I am not sure here) and if it is the case it might be worth investing my time. Still I am finding something more narrow and then if I need other topics I can then read other chapters of Durrett

Thanks Daminark. I will check those notes!

[sage python]

Yeah the strat is gonna be to skim the measure theory part just to get the notation

It's mostly like, okay a probability space is a space of measure 1

Measurable function to R is a random variable

[astral laurel]

Only probability - related stuff I have done was like distributing n balls with different colors to m people and calculating some weird stuff

[sage python]

And remember the Borel-Cantelli Lemma

[astral laurel]

Never thought it requires so much analysis lol

[sage python]

Hahaha, yeah it gets nuts as time goes on

The definition of a martingale is very messy for what I think it describes

I'm pretty sure it's got an interpretation as n step gambling

[astral laurel]

When I was taking analysis course I thought it was purely for fun to me and has merely nothing to do with what I want to study

Since I am CS student

After taking optimization course there were like martingales everywhere...

• Stochastic Differential Equations

[sage python]

Yeah that stuff gets scary

I mean I get why martingales would show up maybe? Tbh I don't have the greatest intuition for them

The definition is fucked you have some like

Sequence of sigma algebras

And you sorta define some very general notion of conditional expectation

[astral laurel]

Hmmm

Interesting and scary

lol

[sage python]

And then you give me a sequence of random variables such that the conditional expectation of each with one of the sigma algebras is the next one

It's big but the origin is from gambling

[astral laurel]

There were some weird people studying graph algorithms
like understanding graph operations as events with some probability distribution, and they were throwing some weird theories which I had no idea.

What you said now like kind of make sense, it can be useful for what I want to study

Thanks. I will first read some lecture notes you recommended

[sage python]

Markov chains?

[astral laurel]

In their proofs it was like 'theorem x.y is obvious from properties of martingales'

and like "wth is that I was suffering for hours"

so I wanted to study them 🙂

[sage python]

Makes sense lol

[astral laurel]

Thanks for recommendation 🙂

[sage python]

I think I can kinda give you the general idea quickly tbh

So

Expectation

Again a probability space is a measure space Omega with measure 1

(Omega,F,P)

A random variable is a measurable function X:Omega->R

The expectation is just \int_Omega X dP

Well consider the case where Omega is finite. Then I can specify probabilities of points

In particular, if the distribution is uniform, so p(x) = 1/|Omega|, then expectation is literally just the average

So that gives you an idea why expectation is expectation

Alright so now

Let's say X is in L^2

Then the expectation minimizes the distance in L^2 between X and any constant function on Omega

So now the trick is you define conditional expectation of a random variable X given a random variable Y with the same idea

Actually pulling up Durrett to remember details

Okay he just defines it with respect to a sigma algebra

Basically E(X|F) is gonna be defined as, the random variable that's your best guess for X if your data is F

So it'll be a random variable Y that's first of all in F, and second its expectation restricted to any set in F agrees with that of X

I'm pretty sure there's an L^2 projection interpretation floating around somewhere here

But basically yeah E(X|F) is your best guess of what X is if the only data you have is F (since X might not be measurable wrt F)

So if X is measurable E(X|F) = X

If F is just the stupid sigma algebra then E(X|F) is just constant, the expectation

Okay great so

[gusty smelt]

Oh neat prob theory

[sage python]

Right right so basically you're basically considering the random variable Y that's F-measurable and which minimizes E((X-Y)^2)

Okay now time for the big reveal

Let's say F_n is an increasing sequence of sigma-algebras

And then you have a sequence of L^1 random variables X_n

X_n is measurable wrt F_n

And E(X_{n+1}|F_n) = X_n

That's a martingale

Okay cool what the actual fuck is this bullshit

Basically I think it's like, a betting strategy

[gusty smelt]

I think ppl usually say that E[X_(n+1) | X_n] =X_n and the sigma algebra is implicit

[sage python]

Wellllllllll

[gusty smelt]

The way to think of it is “zero drift”

[sage python]

That's in a certain case

Where F_n is the smallest sigma algebra st X_1,...,X_n are all measurable

[gusty smelt]

Yeah and that’s what is usually used as far as I have seen

[sage python]

That I could see denoting as E(X_{n+1}|X_n,...,X_1) or something

But in principle you could be more general

[gusty smelt]

Yeah that’s fair ig, but when we talk about Martingles the applications in mind is zero drift stochastic processes

[sage python]

I mean I'm not talking with those applications in mind in particular

[gusty smelt]

Fair enough ig

[sage python]

Like idk if there are others for which the more general situation matters

[gusty smelt]

Sorry for interrupting ig

[astral laurel]

Oh I am on something right now, so I will read what you wrote for me later! Thanks Daminark and John :)

[sage python]

If you ask a harmonic analyst they'll say Haar measure is all that matters and probabilists will seethe

Well a certain type of harmonic analyst, and also I meant to say Borel measures rather than Haar measure

It's morning. But yeah anyway point being I never want to be ignorant of who I might piss off.

Maybe logicians (jk love you Ultra)

Anyway yeah martingales have some nice theorems like optional stopping and shit. So I imagine the idea is you give me something irl and whoooaaaaa it's a martingale

[gusty smelt]

In my experience though like, martingles have very nice properties (things like Brownian motion or simple random walks) and what you usually do is for sufficiently nice stochastic processes you decompose it into martingale and something else and then do stuff to that.

Yeah exactly

Doobs optional stopping gives nice solutions to things like gamblers ruins

[sage python]

That said it's 6:35AM for me so I'm gonna say this is my optimal stopping time and go back to sleep

[gusty smelt]

See ya

[misty wyvern]

If you ask a harmonic analyst they'll say Haar measure is all that matters and probabilists will seethe

I'm a probabilist and the Haar measure is all that matters.

anything important is a topological group action

more importantly, acting on tempered distributions

[lost grail]

What books do you recommend for starting complex analysis?

Like, an introduction book

[karmic thorn]

Here's a review of some of the most popular ones.

[misty wyvern]

how does rudin do for complex in rca

ive never learned complex actually, i just drilled quals problems

and picked up random bits

[forest sleet]

@marble solar it looks like an actual translation, you can compare at least equations and sections with the original German at https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Papers.html The missing few paragraphs mentioned in the translation before section 6 can be roughly translated with Google translate/dictionary as

If the position and the meaning of the limitation of T and the position of its winding points are given, then T is either completely determined or at least restricted to a finite number of different shapes; The latter, insofar as these determined points can relate to different parts of the surface lying on top of one another.

A variable quantity which for every point O on the surface T, to speak in general, that means without excluding an exception in individual lines and points[footnote], assumes a determined value that changes continuously with its position, can obviously be viewed as a function of x,y, and anywhere in the sequence of functions of x,y that we will discuss, we will define the concept of it in this way.

Before we turn to the consideration of such functions, however, let us turn to a few more discussions about the connectedness of a surface. We restrict ourselves to such surfaces that do not split along a line.

[Footnote]
Although this restriction is not required by the concept of a function per se, it is necessary in order to be able to apply calculus to it: a function that is discontinuous at all points on a surface, such as For example, a function that has the value 1 for a commensurable x and a commensurable y, but otherwise the value 2, cannot be subjected to differentiation or integration, that is to say (directly) to infinitesimal calculus. The arbitrary limitation for the surface T will be justified later (Section 15).

[marble solar]

Yeah, I found a publisher that'll do it

@forest sleet there's an obscure US publisher that'll print me a hard copy of all of Riemann's works

[forest sleet]

oh nice!

[marble solar]

It's a bit pricey, $90 for softcover

$140 for hardcover

but fuck it

[foggy relic]

whats a good book for an introduction to analytic number theory

[foggy relic]

i dont know complex analysis so i cant do apostol

[tranquil ocean]

I uh

don't think you should learn analytic number theory without complex analysis

Technically you can do without of course, especially at the start but

I guess it depends on what you're looking to learn and why

[foggy relic]

i see

where would you recommend to learn complex analysis then

[tranquil ocean]

Stein and Shakarchi maybe, that book is somewhat number theory oriented too

[foggy relic]

i know some number theory

how much does that book need?

[tranquil ocean]

None? It's a complex analysis book

I'm just saying that they touch on some number theory applications, moreso than other complex analysis books

[foggy relic]

ohh

ok

thanks

do you know if this is good by any chance?

https://www.edx.org/course/complex-analysis?source=aw&awc=6798_1627082152_b32348a1333bfe4b1fbc93dd0bc81f40&utm_source=aw&utm_medium=affiliate_partner&utm_content=text-link&utm_term=301045_https%3A%2F%2Fwww.class-central.com%2F

[marble solar]

Actually, you can!

Look at Stein & Shakarchi Fourier analysis

The last two chapters are analytic number theory

From a real point of view for the most part

Also a lot of apostol isn't complex analytic at the beginning

[foggy relic]

so i should do stein and then apostol?

[marble solar]

Yeah, do stein and shakarchi volume 1

If you want to learn complex analysis the best book is ahlfors

[foggy relic]

oh the other dude recommended stein for complex anal

[marble solar]

They're wrong

Don't fucking listen to them

[foggy relic]

also is this fine if i all i want is enough anal to understand apostol

[foggy relic]

oh ok

[marble solar]

The problem with stein and shakarchi's complex analysis

Is the way they do contour integration

It doesn't make any sense

and it just avoids things that makes it easier

[foggy relic]

i see

[foggy relic]

.

[broken meadow]

when zoph is a number theorist

[tranquil ocean]

?

[broken meadow]

.

i would listen to zoph

[marble solar]

S&S for complex analysis?

THat's a yucks from me

[sudden kindle]

Stein shakarchi is good

Just as a reference too

[marble solar]

Go look at the toy contours

And tell me

It's good

[sudden kindle]

If you have a question about single var complex analysis

Just look it up in S&S and read the proof

[marble solar]

And then you see toy contours

And you're like what the fuck is that

https://math.stackexchange.com/questions/283365/what-does-toy-contour-mean

[tranquil ocean]

Eh, I learned complex out of S&S my first year, and MIT uses it for their complex analysis class too

[broken meadow]

dam

that sounds nice

[crystal lion]

mit uses it, it has to be good

[broken meadow]

i had brown and churchill and that doesnt even count imo

[crystal lion]

oh my god my blue color

[tranquil ocean]

i wouldnt put that much weight into my opinions lmao

[sudden kindle]

We used ahlfors in our grad level course and I just dont like that book

[foggy relic]

zoph 2 op

[foggy relic]

i dont think a good way of determining whether or not a resource is useful is whether it is used at mit

[crystal lion]

i was being sarcastic

[foggy relic]

oh sorry

i thought it was fr lol

because a lot of people are like "MIT??? this has to be the best thing to learn from ever"

[eager stump]

poor mit faculty doesn't know where to get their books from if they're the reference

[foggy relic]

dies S&S include most of the proofs or just leave most incomplete @tranquil ocean ?

[shadow surge]

Does anyone have a good linear algebra textbook that has good details on quadric surfaces? I'm trying to understand how to transform an ellipsoid but am having a fair bit of trouble on the in between steps.

[sudden kindle]

It includes proofs

[foggy relic]

oh lol thats what mathstack said

[gray gazelle]

excuse me could anyone recommend me any novel with rusty nails

i'm so bored

[willow pecan]

Omniscient Reader's Viewpoint

[gray gazelle]

ayy tyty

[crystal lion]

are stein and shakarchi’s books more comparable to baby or papa rudin

wait actually

[marble solar]

Not really comparable to either

They're just different

[crystal lion]

the RA book starts with measure theory and lebesgue

hmm

[misty wyvern]

If you read either the Stein Shakarchi or Rudin series you probably won't need to read the other, but their coverage styles differ. The former is more pedagogical, the latter is more concise.

And there is some difference in the material as well. Rudin does more operator algebra, does differential forms briefly, etc.

[sage python]

S&S is more like big Rudin

In terms of coverage

[misty wyvern]

And the first half of rudin functional

[sage python]

If you include 4 maybe but I think S&S4 has a very non standard topic selection

So I have no idea how much intersection there is with grandpa Rudin

But yeah baby Rudin... Isn't a prereq for S&S but is mostly lower on the scale I'd think

[misty wyvern]

SS feels like they're building towards harmonic analysis or ergodic theory in terms of coverage, loosely.

As in if there was an SS5 it would've been one of those two topics probably.

[gray gazelle]

Book for discrete mathematics

Especially for Relations

For UnderGrad

[solemn rover]

i have no personal recommendation but Susanna Epp's book on discrete mathematics is popular in computer science classes

[delicate lotus]

are there any ELI5 books for on-the-go

[hasty turret]

wdym

[radiant bay]

Are the Strang MIT Lectures a good companion to more proof-based linear algebra books (Axler)?

[hasty turret]

No

[radiant bay]

Is it more of a geometric (intuition) approach on the objects in Linear Algebra?

[analog pollen]

I saw some of the lectures and they’re not proof based

It’s more on how to DO linear algebra

[narrow talon]

Not necessarily

More numerical actually imo

[remote ginkgo]

anyone got book recs on clifford algebra?

[crystal lion]

linear and geometric algebra by macdonald

[remote ginkgo]

thanks

[crystal lion]

the author has a lecture playlist on youtube too

[vagrant sedge]

Hi. Just curious. Does anyone here know a book that would be like "problem book on mathematical modeling"?

[willow pecan]

Reality

[vocal hatch]

I'm looking for good books on parallel programming, using MPI for example. Does anyone know something they would recommend?

[willow pecan]

Like

How to multithread in general?

Or how to actually do code that executes in parallel

[vocal hatch]

I know my way around multithreading in general, so anything that covers advanced concepts would be interesting

I've been learning about specifications like openMP, MPI, and GPU accelerator specs, so I'm fine with anything that focuses on any of those as well

[willow pecan]

https://developer.nvidia.com/gpugems/gpugems/foreword

This is more GPU focused

[vocal hatch]

I don't work in computer graphics, but there might be some interesting techniques in there, thanks

do you maybe know about any resource that is more generally applicable?

[willow pecan]

Lots of these techniques are generally applicable

If you look through the list of topics a lot of them are not about computer graphics

But doing GPU acceleration requires at least some baseline knowledge about computer graphics because of the hardware and stuff

You could also look through https://sites.google.com/lbl.gov/cs267-spr2020/ but it might be a bit too basic for you

[vocal hatch]

Alright I might take a closer look at the CG techniques, might be worth it

CS267 looks perfect to me at first glance, thanks for pointing it out! Seems like they're going through lots of different techniques by applying it to different problems, and it's probably about more than just writing the code

I mean I would like a formal treatment, so this looks nice

[glad prairie]

CS267, not even once.

[willow pecan]

What

Demmel and Yelick teaching together is v wholesome

[past ice]

anyone have a good measure-theoretic intro to fourier analysis?

[misty wyvern]

@past ice Duoandikoetxa

https://bookstore.ams.org/gsm-29

[vocal hatch]

Is that good or bad? 😂

[oak pecan]

any HPC computing book will cover all of these, but for more than a hello world, you should probably pick your programming language and exact approach. there's not too much to say about openmp, the entire point being that it's supposed to make parallel compute easy. mpi is very specific and mostly used in the HPC space with supercomputers, and GPGPU (like CUDA) was made hot over the last decade especially with ML, and before was (and still is) being used for HPC purposes

[vocal hatch]

Yeah HPC would be a good way to go. I learned all I know about this from the yearly HPC courses from Argonne National Laboratory. The recorded sessions are pretty good but some of the instructors make it difficult to understand them, so I wanted to look for some other source

[vocal hatch]

do you maybe have access to the recorded lectures?

[glad prairie]

it's a good course, i'm just joking

[vocal hatch]

that's good to hear 😛

[vocal hatch]

did you take the class in person?

[glad prairie]

no, i just know demmel quite well and a bunch of the course material

[radiant bay]

Is QM Griffith doable for someone with only some background in LA and MVC? Been trying to dip myself into physics but QM and Elemag are the only ones that sparks my interest

[lapis sundial]

I'd say yes from what I've seen

It should give explanations on some maths anyway ig

[foggy relic]

Has anyone read this book called god created the integers

Is it worth reading

[analog pollen]

Yea

But I wouldn’t start with qm

Start with classical mech

As analytical mechanics is very important in qm

[radiant bay]

I have under my belt some Mechanics (Kleppner), however mechanics is really not sparking interest to me.

[analog pollen]

You need to have some analytical mechanics experience

Especially when learning more in depth

Cuz griffiths doesn’t

[willow pecan]

No I do not

[analog pollen]

But if I recall you still need to know analytical mechanics for griffiths

[radiant bay]

Alright, thanks for the tips!

[analog pollen]

Btw no graduate level analytical mechanics is needed, Taylor’s is fine

I still recommend just doing all the physics first then qm

E&M is also important

For qm

[sharp latch]

Apologies if this is a bad question, but I don’t have a complex analysis course at my school, just real analysis and complex variables. Can anyone recommend a good book for complex analysis that naturally follows from those two courses?

[analog pollen]

Complex variables = complex analysis

[sharp latch]

That’s what I thought originally, but the course doesn’t look like it goes super deep

Hence confusion

[analog pollen]

Yeah I haven’t had that course tho, but all I know is complex variables is the same as complex analysis

[willow pecan]

Consider Stein and Shakarchi's complex analysis

[sharp latch]

That looks like what I was looking for. Thank you!

[halcyon garden]

Easily

I disagree with the idea of analytical mechanics being important for qm(in Griffiths), like you , I did kleppner in sem 1 and griffiths qm in sem 2

[analog pollen]

Yeah nvm

Was confused with shankar

[analog pollen]

Btw if you want a good introduction, use griffiths with shankar. They’re pretty compatible

[foggy relic]

.

[zealous jetty]

what is MVC

multivariable calc?

[broken meadow]

yes

[sudden kindle]

Model view controller

[zealous jetty]

monoid valued category

[prisma snow]

mean value corollary

[willow pecan]

Mixed variable control

[uncut zealot]

My Vhemical Comance

[zealous jetty]

I guess it depends on what ur interested in, but if you don't like atoms and 'spatial' stuff blah blah, griffiths could get rather boring

i have no idea if this is a good idea or not, but Ive always wondered what life would be like if you learnt the "finite dimensional stuff" first, like from a quantum information standpoint or something

[willow pecan]

Givental has a QM book

[zealous jetty]

nielsen+chuang does have an intro to QM in their textbook

oh wait I think I looked at that once, Ill check it out

yeahh.... i rememebr this cat

[willow pecan]

Don't cats have 5 fingers

[zealous jetty]

I guess it really depends on what ur interested in; my main point being that if you like thinking about qubits/information/finite dimensional stuff, you don't really need to know all the spherical harmonics, L^2 space, blah blah stuff

[uncut zealot]

Out of context

[zealous jetty]

u like atoms?

[subtle siren]

Yes

[frosty girder]

who doesnt

[zealous jetty]

u like spherical harmonics?

yeah but... they r annoying? lol

all the calculations are just random integrals, exponential factors, trig factors, yuky

[lapis sundial]

Lol ye

Does anyone know any qm books for mathematicians that are good lol

Or at least ones that don't make me have to turn a blind eye to certain manipulations every now and then lol

[willow pecan]

Givental's book perhaps?

[lapis sundial]

might check that out thanks haven't heard of it actually

[analog pollen]

Idk if this is what you are looking for but the sakurai book is a good graduate level book