book-recommendations

[lime sapphire]

Khan academy

[hollow peak]

Not at all

Some experience with pdes will be helpful though

[subtle mango]

dope thanks

i was planning on doing fa then pde lol

i think the pde book i want to use needs fa? can’t remember

[lime sapphire]

Going into fa that early sounds p brave 😐

[hollow peak]

It's not so relevant until the end of the book

The first half is typical functional analysis of Banach/Hilbert spaces

Probably brush up on Zorn's lemma and baire category before you get to the chapter on uniform boundedness

[sage python]

Wait isn't Brezis the intro to PDE?

[hollow peak]

It's a functional analysis book with an eye toward linear pde

[sage python]

I know that, I just mean like

You don't really need background in the PDE, it feels like it introduces what it does, no?

[hollow peak]

Yes, I'm just saying it's useful to have been exposed to sobolev spaces previously

He goes through all the necessary Lp stuff though

[sage python]

I guess the reason this throws me off is, if someone's looking through Evans I thought the advice would be "Learn Sobolev spaces through smth easier like Brezis" lol

[hollow peak]

I did the reverse 🤓

[sage python]

Lmfao

Yeah my impression is you really just need real analysis for Brezis

[subtle mango]

yep i was planning on doing evans after brezis lol

[gusty pollen]

What year level are yall?

[pliant stream]

Third year undergrad

[subtle mango]

freshman undergrad

[gentle arrow]

high school senior

[grave thorn]

Neither of the above

[vital bane]

same

[hollow shore]

I thought you were a freshman in math

[cinder cave]

So there seems to be this tendency to avoid recommending Rudin to unworthy souls. I posted a few days ago about a recommendation for a good extracurricular introduction to analysis for a CS undergrad. I got some great suggestions that I really appreciate, but I keep returning to Rudin's approach. It's just the most concise, direct approach to the subject that I can find. Is the tendency to place the text on a pedestal just based on gatekepping and narcissism, or is there actually some practical reason I should avoid the text as a relative layman? So far it just seems like a better-articulated version of everything else

[vital bane]

if you like the book, use it, if you don't, switch it out for another one

it's as simple as that

[halcyon garden]

Another thing to consider is that brevity does not necessarily mean better-articulated

[cinder cave]

My problem is that most texts seem to linger on how to read logic and write proofs for too long. It isn't necessarily the brevity that I like. It's the fact that he seems to cut to the chase and actually inteoduce new concepts almost immediately.

[halcyon garden]

What books were you comparing it with?

[vital bane]

again, if you like rudin, use rudin

[halcyon garden]

While Pugh does have a section on basic logic, you can speed read it in 10 mins and attain one new insight even if you are not a complete noob . But if you feel like other books are too slow, you should probably use Rudin... but for most people learning intro analysis, they probably aren't used to writing proofs and hence may need good exposition as opposed to elegance/brevity. Plus I've felt that Rudin doesn't convey the context of theorems/definitions as good as something like Pugh.

[loud cradle]

I don't think it's about gatekeeping or narcissism, it's just recognition that rudin requires more mathematical maturity than most other introductory analysis books (particularly if used for self-study), so may not be suitable as a default recommendation unless the reader has that maturity level. Sounds like you do, and sounds like you enjoy the book (so do I) so by all means keep using it

[forest sleet]

there's carothers real analysis if you want to skip all the tedious stuff about R and go straight to metric spaces

[umbral swift]

hi

[peak anchor]

can someone recomend a book to me plz

[fervent perch]

homotopy type theory

[delicate hemlock]

goodnight moon

[tulip saffron]

hello, I'm applying for a data scientist job and it requires a lot of knowledge in A/B testing/experimental design. But Im not very familiar with it.
For A/B testing I was recommended a great book called Trustworthy Online Controlled Experiments.
but I still want to know what's your textbooks for A/B testing/Experimental design? and what's your final exams like?
And is there a A/B testing case study problem set I can look into?

[remote ginkgo]

rudin is good

i used it to learn how to write proofs

however i should suggest that i do think it can be omitted

i think you can probably just read munkres topology and chapter 8 of shifrin's book for integration of diff forms on manifolds

then chapter 1 of big rudin

[cinder cave]

More than learning how to write proofs, so far I've just enjoyed that he presents the material using very concise, eloquently written proofs. I also really like the order of the chapters. At first glance, it's very spazzy and all over the place, but he combines seemingly unrelated, interdisciplinary concepts into new ideas. I really appreciate that. It's actually a fun textbook

[remote ginkgo]

yeah his second book is even more fun

[cinder cave]

Which one?

[pliant stream]

Real and complex anal

I think rudin is great, albeit highly unmotivated, so not great outside of a course context

[cinder cave]

Real and complex anal is an interesting abbreviation choice lol. I don't necessarily need motivation. I kinda just...like the stuff

My goal is to understand complex analysis though. I'm a CS undergrad and every time I try to approach quantum computation I run into complex analysis stuff I just don't get

Plus the entire calculus series felt very hand wavy and based on leaps of faith. I'd like to remedy that feeling

Honestly I wish I could afford to just go to school for the rest of my life and take all these courses. I'm already 32 though so that ain't happening

[pliant stream]

I mean it's not really about liking the stuff

Like you just need exposition which rudin doesnt give

[cinder cave]

True. I'm supplementing with video lectures based on the book though. Winston Ou has a decent YouTube series

[forest sleet]

you can do Stein Shakarchi complex analysis without much real analysis

[cinder cave]

That actually looks like a solid text. Thanks! I still intend to learn real analysis but your suggestion looks pretty heavily focused on Hilbert spaces, which is obviously my goal

[surreal phoenix]

I recommend you try the Francis Su lectures as well, despite their subpar video quality. They're awesome, I love the way he explains things, and the quality isn't that bad, you'll be able to make the writing out

[cinder cave]

Thank you so much! Ou is a great lecturer but some of his board work is straight illegible

[surreal phoenix]

Any time! Su's lectures worked great for me 👑

[pliant stream]

Tbh I think Professor Ou’s lectures are poor

It kind of feels like an undergrad who took analysis trying to teach it

[sage python]

Baby Rudin is quite good overall, though I do have a list of reservations

[loud cradle]

are those reservations called chapter 9, chapter 10 and chapter 11?

[shell geyser]

Out of sheer curiosity, what do peeps here think about Bartle's Introduction to Real Analysis? I've been using it and like it so far. Seems well explained, reasonable exercises. Only thing I disliked was the treatment of limsup and liminf so far.

[pliant stream]

Never heard of it

[loud cradle]

i've read parts of three other books by bartle, and he's a good author in general. i haven't read that one but would assume it's good. what was the issue with how he dealt with limsup and liminf?

[sage python]

1. Chapter 2 left me a bit confused about the idea of a subspace. So I thought compactness was a property of a subset of a metric space. Also I didn't internalize that boundedness wasn't a property of a space super well. I think it should make these points more clear

Chapter 9 feels rushed
Chapter 10 is moronic
Chapter 11 is pointless

[pliant stream]

Yeah the topology chapter in Rudin could be better

[loud cradle]

iirc in chapter 2 his treatment of connectedness was also slightly weird, but i don't have my copy at hand to check

there were a couple of theorems whose proofs could have used elaboration, notably the equivalence of the series and limit definitions of e

and l'hopital's rule was a bit of a mess because he tried to handle all cases simultaneously (again going by memory here)

[shell geyser]

I think that it's just unintuitive, because limsup is not defined as the limit of the supremum of the tail. Now that I have a bit more experience with analysis I can wrap my head around this better, but when I first got to it I was confused.

[surreal phoenix]

compactness isn't a property of a subset of a metric space...?

i love rudin..

it's fine, munkres will save me

[loud cradle]

his definitions are probably the most useful characterizations though

limsup/liminf are a bit confusing the first time you see them, probably regardless of what definition is used

[shell geyser]

Mm, fair. Guess it's just not an intuitive concept.

Doesn't help that it's introduced in chapter 3 but not used for a few chapters.

[loud cradle]

my intuitive description is "the tail of the sequence stays within these two bounds", but there's another equivalent description that is also very useful: the limit of any convergent subsequence lies between those two bounds, and moreover, there exists a subsequence that converges to the limsup, and another one that converges to the liminf

and of course, "the sequence converges if and only if liminf = limsup = some finite number"

[pliant stream]

The easiest definition is probably like the suprema of the subsequential limits

[loud cradle]

agree, and it's nice that in this case, it turns out that "supremum" is actually "maximum" since that value is achieved.. however, the "infinitely often" and "all except finitely many" characterizations translate more nicely to the definitions of liminf and limsup of a sequence of sets

so it's good to know the equivalent characterizations as well

[pliant stream]

Ah that’s true

I guess that’s always a problem for later though when you have more maturity

[cinder cave]

The concept of mathematical maturity is strange to me. I posted and later deleted a stoned musing last night about the idea. Basically, it feels like there will always be some concept that my "maturity" isn't sufficient for. For those of you who have significant "maturity,": Does it ever actually feel like you are at some "frontier" of mathematics, or is it actually just always the case that you can keep connecting higher levels of abstraction to previous seemingly unrelated concepts? For me, the prospect of reaching a level of maturity in which I can no longer gain enlightenment seems lonely and scary to me.

I mean, obviously you can never know everything. But one of the greatest things about math is, at least for me, the fact that it never feels like you run out of material at a higher level of maturity. Is that accurate, or do you really hit a wall at some point?

[loud cradle]

yeah for sure, "maturity" is a subjective concept and its meaning depends on context: you may be sufficiently mathematically mature for stewart's calculus but not necessarily for hartshorne's algebraic geometry

there's always more to learn and I suspect (but have no way to prove) that any "hitting a wall" is only subjective and that if you can get yourself to point X, you can always get yourself to point X + epsilon, for some definition of epsilon

[halcyon garden]

https://youtu.be/zHU1xH6Ogs4

For some reason I confused the speaker with Curtis McMullen

[cinder cave]

This is a great video

[sage python]

See now you know why I'm eh on Rudin 😛

Really compactness is a property that should be thought of as applying to a metric (or topological) space itself

When you say oh a subset of a metric space is compact if open covers have finite subcovers, you might wonder, well hmm, if I think of A as a subset of Y instead of X, and Y has different open sets

Then does that change whether A is compact or not?

[gentle arrow]

wait sloth what should i watch out for in schroder

[sage python]

And it turns out not really as long as you haven't changed the structure on A itself

I don't know it super well to address pitfalls, honestly even Rudin you don't necessarily need to "watch out" for much in the sense of, if it does mislead you that can be corrected

Point being don't let my lack of knowledge be a deterrent here

[gentle arrow]

no like how is the book overall

[sage python]

It seems good at a glance to me

[vital bane]

damn strad what kinda linear algebra are you studying

[surreal phoenix]

that (apparently incorrect) statement was something I learned from rudin, not LA, but right now I'm doing sorta theory sorta computation kinda LA

like, incorporates the theory of vector spaces and such in developing computational methods, that's what I'm seeing so far

[vital bane]

nope, I'm convinced you're studying functional analysis right now "says he's studying LA, talks about compactness"

[surreal phoenix]

Lmfao

[vital bane]

Nice

[surreal phoenix]

I wish I were badass enough to pretend to be a beginner....

[vital bane]

I am a beginner

[surreal phoenix]

Ma man 😎 🤝 😎

[vital bane]

[surreal phoenix]

noobs till the end (hopefully not very long)

[vital bane]

Lmao

soon we wont be

[foggy hemlock]

What book should I read for P-adics

I just finished this handout https://www.math.brown.edu/reschwar/INF/handout8.pdf

Which gave me a basic intro to them

How should I continue after this

[gray gazelle]

I've heard very good opinions about Gouvea's book, haven't read much of it though. My prof recommended me 2 books: p-Adic analysis by Koblitz (apparently quite hard and goes in depth, but probably not as algebraically as you might want to) and first chapter of Borevich-Shafarevich Number Theory.

[foggy hemlock]

Thanks I will try Gouvea and Koblitz

[gray gazelle]

Is there some good resource to learn index notation in tensor algebra really quick

Like everything with kronecker delta and the € permutation

[azure yarrow]

Does anyone know where I can find solution manual for "calculus and analytic geometry" 4th edition?

I'm not sure if this is the right place to ask this, but if anyone knows please share.

[pure solstice]

Author?

[azure yarrow]

George B. Thomas

[pure solstice]

https://www.academia.edu/44901175/Calculus_Solutions_by_Thomas_9th_edition_Calculo_Thomas_Finney_9na_ed_Manual_de_Soluciones

[livid ermine]

Have anyone read the book "Galois' Dream" before and have anything to say about it? It seems to cover really interesting topics very succinctly without being too dense.

[fallow cypress]

wait I thought rudin emphasized this, he said the whole point we care about compactness is it doesn't matter what space we embed it in

[sage python]

I didn't remember this hmm

Maybe our prof didn't mention it?

[fallow cypress]

Maybe difference in edition, I dunno lol

But yeah he gave a whole example where a subset was closed in one space and not in another and then it was compact no matter what so he said the embedding doesn't matter and the space itself can be called compact

Something like that

[gray gazelle]

Wdym by embedding? Choosing a topology?

[fallow cypress]

I mean treating it as a subset of a different metric space

e.g. treating R as a subset of R vs one of R^2

[gray gazelle]

So in a metric space every compact set is closed

[gray gazelle]

so if he was giving the same example here, that's just not true

[fallow cypress]

oh yeah I misstated, I meant he then proved a thm that compact doesn't depend on what it's with respect to

[gray gazelle]

that would be only true for topologies over finite sets, or finite topologies

[fallow cypress]

? wdym

hmmm did I misremember something

It's for metric spaces btw

[sage python]

He's thinking that you're saying it doesn't depend on the topology of A even

[fallow cypress]

Oh

Okay lemme be more precise

Actually nvm I'm lazy I'll just copy rudin's when I have it on hand

[sage python]

Hahahaha

[fallow cypress]

Suppose K \subset Y \subset X. Then K is compact rel. to X iff K is compact rel. to Y

"By virtue of this theorem we are able, in many situations, to regard compact sets as metric spaces in their own right, without paying any attention to any embedding space." goes on to talk about how this isn't true of open vs closed

[glacial tartan]

Discrete Mathematics books recommendations?

[fickle whale]

I think R as a subspace is still relatively closed in R^2

[fallow cypress]

yeah it is closed

that was just an example of what I meant

[fickle whale]

I c

[zealous light]

Rosen's book is good

[gray gazelle]

Book for Data science???

[analog horizon]

any good book for probability theory

[heady ember]

What level

[analog horizon]

intro

[heady ember]

What is "intro"

[analog horizon]

starting with combinatorics, discreate and continous random variable, and the other stuff

[heady ember]

Was about to say you could check out the measure theory book dami listed lmao

[analog horizon]

i also want some computational exercises

not only theoretical

[heady ember]

Highschool level or?

[analog horizon]

universtiy

[analog horizon]

what book is that

[heady ember]

Pinned

But in order to read that you at least need to have done a course in real analysis

Like a full course with baby rudin, schroder, etc

[analog horizon]

ok

[analog horizon]

can you link

[heady ember]

The first pinned msg

This one

[analog horizon]

thats a measure theory book ?

[heady ember]

Yeah but it has some probability inside i believe

martingales

[analog horizon]

ok .. ill check it

[heady ember]

I mean I meant that as like just a comment that you could check it out and see if you like it but others will probably be able to help you find the book you want better

I was originally just trying to help to make your qns more specific so others can answer you easily

[analog horizon]

oh thnx

[sage python]

@analog horizon based on your description of what you want it's possible measure theoretic probability is overkill for you

Ross I think is the "standard undergrad probability book"

[gray jungle]

i love blitzstien and hwangs book too for pre measure theory probability

[vale granite]

Book recommendation for Lie Algebra ? (basics)

[analog horizon]

cheers

[sage python]

Humphreys is good

[hearty steppe]

Hey Dami, I’m gona start Strogatz soon. I’m enjoying Brin and Stuck. Officially started it last night

Dynamical systems theory*

[vale granite]

Ok thnx

[foggy relic]

Hall is also good

[stray veldt]

use khan academy

[sage python]

I don't think I know Strogatz super well offhand, link?

[vital bane]

khan academy has everything from 1st grade math to 1st year university math

(it's a website, with video lectures and articles and problem sets)

[gray gazelle]

What books would you recommend for Combinatorics, Probability and Statistics?
From introductory/beginner level to advanced

[stoic zealot]

maybe this will do
A First Course in Probability by Ross
https://amzn.to/3m6SwJA

[gray gazelle]

Anyone know a good place to deeply learn the foundations/basics of geometry? :P

[stoic zealot]

Geometry by Jurgensen
https://amzn.to/3qCFkzL

look into this if you want

[rigid barn]

Can I get a book recommendation on algebras (over the real/complex numbers would suffice, I don't need full generality)? I need to learn the structural basics, like central simple algebras and the radical/Wedderburn-Artin and whatnot. Bonus if there's material on Clifford algebras.

[hearty sluice]

thoughts on these books? Being used in some of my courses next semester

(modulo the monograph, idk how that got there)

[sage python]

Bott Tu is great, idk what the second one is, and Rotman's a good writer so people def simp over him (though I heard homological algebra is a bit slow?)

The others I'm unfamiliar with

[hearty sluice]

the second is the mysterious monograph that somehow got in my library reqyests

[sage python]

Ah hah

[hearty steppe]

https://g.co/kgs/4dZnWu

Didn’t start it yet. Im completing each of my dynamics books chapter by chapter. Well I’m not even going thru all the content, just half the book in most of them I think

Or maybe it’s half of the first book. The other books are just a few hundred pages. But the content can be pretty compact so we will see

[sage python]

Dope

[hearty steppe]

Yea it’s gona be a real butt kicker but im surviving

[sage python]

Stayin alive, stayin alive

[vital bane]

woah niceee

[vital bane]

damn you sloth king now that song is stuck in my head

i hate you

[sage python]

🙂

[candid garden]

Ah, ah, ah, ah,
stayin alive,
stayin alive,
Ah, ah, ah, ah,
stayin aliveeeeeeee

[vital bane]

@fickle whale

it's from "fiber bundles" by husemoller

[fickle whale]

The people who call them clifford algebras use them very differently from the people who call them geometric algebras, the fundamentals of the math are the same though.

I gotta check that out

[fickle whale]

Like in the appendix of Classical Mechanics by Goldstein he starts talking about the clifford algebra formed by the dot and cross product with the pauli matrices

[vital bane]

oh that's pretty cool

but yes it's not the same geometric algebra

[remote ginkgo]

rotman's advanced modern algebra is too wordy and not wonderfully organized. he has a fine intro to algtop text but i do prefer lang's algebra to his

@fickle whale

[dusty lava]

Any approachable book to ODEs and PDEs geared more towards physics and specifically QM?

[remote ginkgo]

yep

[vital bane]

isnt there only like 1 diff eq in QM?

2 if you count relativistic QM

[remote ginkgo]

@dusty lava http://sheafification.com/index.php/2022/08/14/the-fast-track/

[vital bane]

[remote ginkgo]

you may also wish to read Arnol'd

https://link.springer.com/book/10.1007/978-3-662-05441-3#toc

he also has a fine ODEs text

[hearty sluice]

Class also has listed Dummit and Foote and Lang

[remote ginkgo]

really, extremely, supremely not a fan of dummit and foote

[hearty sluice]

Why's that?

It's very well loved, much more so than lang lol

At least locally

[remote ginkgo]

i am aware

if everyone else likes something that you find absolutely rotten to its core, what is there really to say

[hearty sluice]

Perhaps what makes you think it's rotten to its core

[remote ginkgo]

i have had to both learn and teach from it

particularly sylow's theorems,group cohomology, and some later parts on intro algebraic geometry

and found it extremely difficult to follow when learning (compared to lang which i find effectively light reading)

[hearty sluice]

This is the course after the first year algebra course so it won't cover sylow among other things

[remote ginkgo]

and not terribly nicely structured when teaching from it

[hearty sluice]

Lemme find the course description, see of you have any thoughts on the relevant parts from the book

[remote ginkgo]

this was for a second semester of algebra

kk

i do not know of any parts of the book i find better in exposition than lang

[hearty sluice]

Ok course description is really short and I expect incomplete, but it is

We will study categories and functors, composition series, the Jacobson radical, and
semisimple rings and modules.

[remote ginkgo]

d&f's exposition on composition series is ok

there is very little in the way of functorial talk

the module theory section is far & away outclassed by lang

[hearty sluice]

Neither really seem to do much of category theory tbh so I suspect we'll use one of the other listed texts for that

Lang does have that one chapter or section, but it's brief and not very in depth

And the course is called Categories and Modules

[remote ginkgo]

lang does

a lot

[hearty sluice]

I read chapter 10 or what have you but I wouldn't really call that a lot

[remote ginkgo]

lang literally begins its first sentence with a category

[hearty sluice]

Unless there's more elsewhere

[remote ginkgo]

the whole book is categorical in flavor

df mentions categories like 4 times in the whole text it feels like

[hearty sluice]

Maybe I just glossed over the cat theory references since I don't know it well

Or just comparing it to like Aluffi

[remote ginkgo]

aluffi good 👍

it's about like aluffi

but yeah the part of df on the holder program is fine

[pliant stream]

springer

but any book on calculus will have that material

https://link.springer.com/search?query=uniform+convergence&facet-discipline="Mathematics"&facet-content-type="Chapter"

i think mit 18.02 is excellent

i think early on, learning from videos is much easier than reading books

hmm try looking at books covering analytic geometry

these might even be in calculus books, but you don't need calculus to understand what's going on

for example, chapter 12 and onwards in Calculus Vol 1 Apostol

there's nothing perfect to do, just try and see what works for you

if you can already do all the problems on khan academy, then why do you need something harder?

but if so, perhaps try precalc by axler? or what I suggested above

yes, but you'll encounter harder problems once you need to

so just moving on to a different topic may be better for you in the long run

like you will 100% encounter this again when you see vector calculus

[wheat cargo]

i would like to recommend fitzpatrick's "advanced calculus" for a first course in analysis. its easier than rudin and a bit less rigorous. it is arguably more difficult than abbott and ross and more comprehensive than both of those books too. the book itself is extremely clear and has interesting and insightful exercises, and the order in which topics are presented is very nice too

i really like the book, so i thought id recommend it is all to anyone looking for a book like this

[worthy terrace]

best books to self learn group theory and representation theory.

With enough example and abstract enough but not too much

I saw representation theory by Benjamin Steinberg but that only touches representation theory and not group theory

[brittle breach]

for finite groups there is Serre

[worthy terrace]

this one?

right

Thanks, will take a look

[dapper root]

This doesn’t teach group theory

[worthy terrace]

yeah exactly, it is all about representation theory. Just looked at the table of contents

[brittle breach]

yeah

[worthy terrace]

most seem to recommend "an introduction to the theory of groups" by J Rotman

so I think I'll give it a go

[grand thistle]

any recommendations for a second look at group theory and algebra in general?

i’ve tried dummit and foote and found it very very boring and felt like it was very dry

i’m trying to find something that also has some stuff about categories in it

rn i’m looking at lang and aluffi

[dapper root]

If it’s for group theory specifically there’s a book by Isaacs

Which is p good

[grand thistle]

but i’ve heard lang is very difficult

[grand thistle]

alright i’ll check it out

[foggy relic]

aluffi is very nice, but some of its problems are not very good

he has great exposition and is gentle

[grand thistle]

yeah i loved his exposition, i’ve read chapter 1 before

[grand thistle]

though, im a bit split between the two since i'm more so just looking to get a solid foundation for algebra and the overly emphasized category stuff might be unnecessary

[foggy relic]

well aluffi does a pretty good job at both imo

[grand thistle]

yeah, i guess the best way to find out is to try both

[foggy relic]

[grand thistle]

i wanna do more like probability and analysis stuff though, so im just tryna make sure i dont forget all the stuff i learned in group theory and field theory this summer and to learn about rings and modules

[foggy relic]

(asking for myself) How is this book for intro probability? https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxnYXJyb2NpZW5jaWFzfGd4OjZlYjJmMTBkNzIxN2M5Njc idk if this or Ross or maybe bertsekas is better

[grave thorn]

This is not an intro probability book

[foggy relic]

it isnt?

[grave thorn]

Intro probability means "no measure theory"

[foggy relic]

well it defines the measure theory needed right

[grave thorn]

As in the book does not use any measure theory whatsoever

This book does

[foggy relic]

oh i see

so is it bad for a first take then?

[grave thorn]

Unless you have a background in analysis

[foggy relic]

well ive done pugh

but 0 probability

[grave thorn]

That should be enough

imo Jacod and Protter is better though

[foggy relic]

would this vs ross vs bertsekas be best?

[grave thorn]

Ross is not at the same level

[foggy relic]

does it use analysis?

[grave thorn]

Yes

[foggy relic]

right but would it be better for my first time learning probability

[grave thorn]

The main question is: what do you want to learn? Measure theoretic probability, or probability

Since you have a background in analysis

[dapper root]

Aluffi is not category heavy

It just introduces it at the start

[foggy relic]

he does barebones of cat theory

[dapper root]

But it doesn’t get heavy until the last two chapters

[foggy relic]

yeah he uses it a bit in homo alg chapter

[dapper root]

then he’s doing homological algebra and it makes sense

[grave thorn]

Measure theoretic probability is probably better

[dapper root]

[foggy relic]

more interesting?

[grave thorn]

Ross exercises: calculate this integral

[foggy relic]

[grave thorn]

Whereas measure theoretic probability exercises ask for proofs

[foggy relic]

gotcha

is jacod mt probability or probability

and does it assume mt or not

cuz i dont know any

[grave thorn]

Jacod and Protter is measure theoretic probability (but it doesn't assume any measure theory)

[foggy relic]

great 😄

you think its better than dudly right?

[grave thorn]

Alternatively, you could use any of the highlighted books here:

[foggy relic]

oh i think ive seen Shiyarev

its much more difficult i believe?

[grave thorn]

Its more of a reference book tbh

[foggy relic]

ooh ok

hows the middle one then? compared to maybe jacod

[dapper root]

Are you studying to be a quant?

It looks like you’re tryna make some $$$$ with those book choices

Hahaha

[grave thorn]

That's not even the finance bookshelf lmao

[foggy relic]

is this a personal library 😮

[foggy relic]

this

[foggy relic]

a lot of donations to springer!

[grave thorn]

Lots of typos

But still good

[foggy relic]

i see! well thanks i will use jacod then 😄

[brittle breach]

Richard BORCHERDS, group theory playlist
https://youtube.com/playlist?list=PL8yHsr3EFj51pjBvvCPipgAT3SYpIiIsJ

he has one on ring theory as well which uses category theory

both are based of Langs book

[grand thistle]

hmm looks great

i might use it to supplement an actual text

like lang as you said

[grave thorn]

imo Richard BORCHERDS is a pretty good resource

iirc he got the fields medal

for something

prob in algebra

[sage python]

Oh shit time to judge you for your books

Dayum wow you got a lot of stuff in the vein of stochastics

I know fuckall about that lol

[remote slate]

a good source to learn telescoping series?

[vital bane]

why do you have so many stochastic and probability books

[shy compass]

my supervisor has an entire bookshelf full of the last 20 years of the annals of probability

[grave thorn]

lmao. I wish (though I'd prefer that it'd be "annals of applied probability")

[grave thorn]

Finance.

[vital bane]

so that's how you make a lot of money

[remote slate]

where can i find some practice questions?

[heady ember]

Most calculus books probably have them

Like Pauls Online Math Notes (Well yeah this isn't a book but you get my point)

[remote slate]

not asking for calculus, i am asking for classical algebra

[heady ember]

Oh oops

[remote slate]

do you know any such resource?

[vital bane]

I would start with youtube, there's a lot of videos about competition math things like telescoping series and certain famous identities and stuff like that

[heady ember]

Wait is "classical algebra" hs algebra or AA

[vital bane]

I think they meant elementary algebra (hs algebra) since they were talking about telescoping series

[coarse frost]

hs algebra

(here at least)

[heady ember]

Ohh

[safe lintel]

Why are standards for algebra different everywhere

Like the stuff that was part of my algebra 2 course seems to be pre-algebra in other places

[sage python]

I imagine it's because nobody coordinates

Different states in America have a fair bit of autonomy over their school curricula and they just kinda vibe

[bright epoch]

Also "algebra" isn't really a well defined subject anyway, at least not the way it's used in highschool

[last crest]

looking for books/lecture notes on symplectic geometry to supplement da silva

[molten wave]

@stray veldt I found a cool book https://www.jjj.de/fxt/fxtbook.pdf

[tribal fjord]

hey i graduated from high school and my major is dentistry so my major has nothing to do with math but i still want to improve my math what do you guys recommend?

[hearty sluice]

what are you looking to improve?

calc?

[honest river]

An Infinitely Large Napkin - Evan Chen

[solemn rover]

❗ ❗ ❗
WARNING
THIS USER HAS RECOMMENDED A BAD BOOK
COMPETITION MATH NERDS, PLEASE SAFELY PROCEED TO THE NEAREST EXIT
BREEZY HANDWAVING IS NOT A SUBSTITUTE FOR COMPREHENSION

[heady ember]

[fickle whale]

Is that why you're honorable?

[tardy walrus]

Why would love be a group?

[gusty hearth]

is there any good (short) reading on crystallographic groups

[hearty steppe]

Hey anything that is combinatorics + differential geometry?

[grave thorn]

algebraic topology is pretty combinatorial (and ig is pretty related to diff geo?) idk for sure, ask ttera or some other diff geo person

[hearty steppe]

Uhhh I mean I’m looking for stuff very specific to work with that deals with combinatorial structures and manifolds at least

Algebraic topology is like a whole arena of stuff

[hollow peak]

geometric group theory

when I think of combinatorics of smooth manifolds i think of algebraic topology of smooth manifolds but that's not really combinatorics in the way you're thinking

a good starting point for those ideas are learning about simplicial homology and cech cohomology

cech cohomology is the limit of cohomology of chain groups of locally constant functions on n-fold intersections of open covers

in practice this looks like computing the combinatorics of refinements of open covers of spaces

[gusty smelt]

ggt can be very combinatorial yeah

[tulip blade]

Topological graph theory maybe.

Maybe something like this: https://www.sciencedirect.com/science/article/pii/S0001870807001454

Id look stuff up on google.

[halcyon garden]

Today's my first day as a math major

[hearty steppe]

What you recommend I check out in terms of books or sources

[hollow peak]

I personally am not familiar with ggt beyond it matching your description so idk

[gusty smelt]

cat for ur level use the book ``office hours with geometric group theorist''

[primal mica]

Many solid state books have something on this, but if you mean specifically in regards to group theory there is an introductory textbook in chemistry by Cotton, called Application of Group Theory to Chemistry or something like that.

[gusty hearth]

yeah, specifically wrt group theory

thanks 🙂

[hearty steppe]

Definitely gona check it out mate

Contents look nice

What are your thoughts on Miklos Bona? Might work through it a little more if I need the insight

But I think I’m ok right now. I just know it’s there

Yea seems like that is more foundational reference if I need it for the combinatorial stuff and I feel like when I got a taste of it, sure it was rigorous in its approach but, maybe a bit too much of a focus on the refinement of the combinatorial foundations rather than exploring a bit more

[vital bane]

khan academy

[stray veldt]

oh nice, i couldve used the GP intro a few weeks ago
chapter 4 and 5 especially seems useful to me

[prime oak]

Opinions on introduction to topology and modern analysis - Simmons?

[formal tinsel]

what are the prerequisites for studying modern mathematical finance?

[molten wave]

yea I came across this when I ran into a problem in applied arithmetic

[honest river]

how is this a bad book?

[solemn rover]

I find the preface insulting and it sets the tone for the rest of the book.

This is a book written by a guy who thinks that he and his friends are able to digest complicated mathematical content 6x as fast as the average math student. First of all this is just stupid, unrealistic and wrong. Second of all, beyond being obviously false, this is pretty rank elitism and mathematics already has a serious problem with the prodigy fetish and the worship of the divine minority who are able to go at a much faster speed than anyone else. The fact that the Fields medal has an age cap of 40 is another example than this.

I think that there is a place for books which exposit material at a high level without worrying about presenting full proofs but rather concentrating on the main ideas, as long as they clearly reference where to find the full proofs. These books could be useful in collecting and surveying areas of mathematics with a long historical development which have changed their themes and focus over time.
These books are probably becoming more important as the subject matter of mathematics grows more vast.
I'm not fundamentally opposed to high level surveys.

However this book is addressed to high schoolers who are doing olympiad competitions and don't yet have the same mathematical maturity of someone who has completed an undergraduate math degree. For these people mastering technical definitions and rigorous proofs is a priority. The attitude here strikes me as something like "We're smarter than everyone else so we shouldn't have to do the hard work of reading and writing proofs."

There is a difference between doing mathematics and spectating on mathematics. If you read a serious book on set theory and learn how to use forcing to solve problems, you are doing mathematics. If you watch a numberphile video on Cantor, you are spectating on mathematics. It is about how superficial the engagement is. I consider the Napkin to be a form of spectating on mathematics, i.e., mathematics as entertainment. It is simply too concise to say anything substantial. You cannot walk away from this book really understanding what a differential form is.

At a certain level of superficiality you can't actually say anything substantial about the subjects you're talking about and you're functioning like a machine learning language model, just stringing together grammatically correct sentences involving these jargon words

[honest river]

Alright i take that. True. This book is not a replacement for the whole semester of (for example) calculus. Still it's a good book to at least get interested in the topics of higher math one would like to pursue more.

[solemn rover]

Yep, I'm just giving you my answer. Read what you want to read, I won't be offended if you choose to read a book I find annoying.

[vital bane]

"natural explanations supersede proofs"

Lmaoo what?

that preface

[tulip spoke]

I am studying 11th and i want to get better at solving problems. Is there any books like the art and craft of solving problems, or corvering the same topic i want to read that book but i don't know calculus just the really basic stuff to do some physics .

[tough zealot]

you chose to focus on the only part thats not even a problem

[analog lava]

i like this guy this guy knows shit

[honest yarrow]

Anyone know this book?

[sudden kindle]

woah what;s this about??

[vital bane]

Lol I didn't read the whole thing

but how is that not a problem

natural explanations don't supersede proofs, they both complement each other

[tough zealot]

I think that was only a bullet sentence based on what they said

[gray gazelle]

@drowsy thicket linear algebra

no

[tulip blade]

I never read it :/. I just know it exists bc it was kind of a big deal.

[pseudo forge]

not true

[gray gazelle]

linear algebra are taking at the same time as calculus

[vital bane]

yea some linear algebra is used in multivariable calculus

[indigo mesa]

You need linalg for proper multivar calc

[gray gazelle]

I can recommend tao's notes on linear algebra

[pseudo forge]

Even for engineers, linear algebra is taken concurrently with Calc 1 or 2

[vital bane]

like the total derivative is a linear transformation

(i.e the derivative w.r.t all the variables)

[pseudo forge]

And calc 3 is much readily understood with an understanding of LA

[vital bane]

like vector addition, scalar multiplication, dot product, cross product stuff like that?

I think you can find a linear algebra book that starts off with basic stuff like that and then slowly moves onto more actual linear algebra

[gray gazelle]

that's what tao kinda does

[vital bane]

https://terrytao.files.wordpress.com/2016/12/linear-algebra-notes.pdf

this?

then you can watch this

https://www.youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B

it's very good!

[pseudo forge]

does he have smthng similar for calculus (not analysis)

[gray gazelle]

@vital bane yup

[gray gazelle]

I do not think so

[vital bane]

@drowsy thicket start with this

[vital bane]

and then go to this

I guess

yes, well it's more like starting off with basic high school stuff and then transitioning to basic university stuff

[gray gazelle]

btw tao used friedberg Insel and Spence as a supplement for exercises

in his notes

otherwise they are free the notes that is

[subtle mango]

fis is good

[pseudo forge]

u could also use Khan Academy if reading isn't you're forte

[vital bane]

also ofc use #linear-algebra if you don't understand something to ask questions

[pseudo forge]

depends where but yea

[vital bane]

I guess?

but I personally would use a book

yeah

you could solve them after watching the videos

[manic cairn]

Munkres is very representative of undergraduate math.

Judging from your interests, I’d read Munkres, then follow it up with Lee.

Once you start needing to deal with Lie group representations and algebraic topology, I’d also pick up a book on algebra, for which I recommend Lang’s Undergraduate Algebra.

(Munkres and Lang I found much easier than Lee and Hatcher, although that might be my weak analysis background.)

[inner token]

What's the algebra book people on this server like? Not dummit and Foote, but guy who's name starts with A, I think

[coral narwhal]

Artin

[inner token]

Thanks!

[coarse frost]

lil late but congrats op!

[dapper root]

Nah it’s Aluffi

[night prism]

Axler

🤪

[pseudo forge]

linear algebra done right lol

what a title

[inner token]

Love the heck out of this book

[vital bane]

yes it's awesome

[pseudo forge]

our prof for LA 1 for math majors worships Axler

[vital bane]

[coarse frost]

Nooooooooooooooooooooooooooooo

[vital bane]

it's artin

[regal wasp]

Is there a book for calculus of variations

I just sort of picked it up from physics/functional analysis but I want to know more

Or is it all just dual variational problems

[vital bane]

gelfand and formin's "calculus of variations"

seems like a good book

i personally havent read it yet, but it seems nice

[foggy relic]

Chmonkey knows where it’s at

Aluffi is the single best algebra book

[split basin]

if you have the necessary background there is Struwe's "Variational Methods"

[solid fog]

any recommendations for books on differential geometry

[hollow peak]

For smooth manifolds, intro to manifolds by Tu or intro to smooth manifolds by Lee, then you can read Do Carmo, Tu, or Lee for Riemannian geometry

If your looking for classical DG, do Carmo also has a good book for that

[solid fog]

alr thanks

[foggy relic]

Pressley's book is good for minimal prerequisites (DG of curves/surfaces assuming only calc3+LA w/o analysis)

[lusty elk]

I have an old, originally Russian, textbook called Differential Equations and the Calculus of Variations by Elsgolts. The first part covers the theory of differential equations whilst the second part covers the calculus of variations.
The front pages say that it is based on a course of lectures the author developed at the Physics Department of the Lomonosov State University - so it is aimed at physicists I think.
I haven't reached the second part yet, but from what I have read so far Elsgolts really likes to motivate the theory with examples taken from physics and the natural sciences. I can't comment on the rigour, but it does have theorems and proofs. Most of the exercises (the earlier ones at least) seem pretty computational.

[grave thorn]

Is it terse? To me the original Russian ones seem less terse than the translated copy

[lusty elk]

Hmm, doesn't seem too terse to me. Then again the only other book I have read so far is Rudin's PMA.

[crisp river]

https://www.asurascans.com/manga/my-school-life-pretending-to-be-a-worthless-person/

the people on this server

[vital bane]

it's a good book for beginners

[lime sapphire]

Stumbled upon this funny book in my university library

[grave thorn]

This was in the agriculture section, right?

[lime sapphire]

How did you know??

[coarse frost]

invictus....

[vital bane]

[formal tinsel]

why agriculture?

[vital bane]

because algebraic geometry is extensively used in agriculture, so most farmers need to learn and master complex algebraic geometry

[dapper root]

Real

[loud cradle]

"farmer john is gathering sheaves from his field (or more generally, his ring) which is bounded by the following polynomials..."

[gusty smelt]

someone called?

[fallow blade]

has any one seen that website humblebundle ??

where they give really cheep book

is there a math equivalent

[main void]

Is there any nice resource to learn about profinite groups and their cohomology?

Im reading about group cohomology in d&f and they mention that the cohomology of finite groups can be extended to profinite groups but don’t really go into details, i was hoping there would be some more specialized resource

[mystic orbit]

get rekt

[coarse frost]

shaddap

backstabbers dont get to talk.

[mystic orbit]

how much of allufi have you done?

[mystic orbit]

I might be a backstabber

actually

no

[coarse frost]

what no

u literally are

[mystic orbit]

I might be a turncloak

but you my friend

is the backstabber

[coarse frost]

how am i a backstabber

coz i stopped the book coz of exams??

how does that make me a backstabber

[mystic orbit]

[coarse frost]

i literally told u i wont be able to continue

dont pensivebread me!

stop!

[lean latch]

anyone have a rec for a highschool algebra book? im looking to use one in tutoring so it doesnt have to be have to be good for self study just maybe have some good diagrams and exercises

specifically algebra 2

[grand thistle]

what are the prerequisites to spivak's physics for mathematicians?

it says
"No specific mathematical knowledge is expected, but for the purposes of this book on mechanics the material in A Comprehensive Introduction to Differential Geometry Volumes 1 and 2, will generally be regarded as a prerequisite"

but i feel like that's only for the later chapters

the first mention of a manifold is like halfway through chapter 4

[grand thistle]

this is in reference to his own diff geo books btw

[pseudo forge]

Are you interested in mechanics?

you could of course just start reading and read into diff geo when it starts being used

[grand thistle]

im just looking for a physics textbook that isn't the average like cookbook engineering textbook

spivak's seemed pretty cool

[pseudo forge]

hmm

there are nicer ones out there

that focus on mathematical physics

[lime sapphire]

Spivak has a mech book?

[pseudo forge]

physics book

[pseudo forge]

Mathematics
• Boas - Mathematical Methods in the Physical Sciences
[Early-Late UG | Rigor: Moderate | Explanations: Moderate | Figures: Few | Problems: Plenty]
Covers many topics seen in an undergraduate physics major. Has a decent chapter on Tensor Analysis for a first exposure.
• Riley & Hobson - Mathematical Methods for Physics and Engineering
[Early UG | Rigor: TBD | Explanations: TBD | Figures: TBD | Problems: TBD]
{Description TBD}
• Zill - Advanced Engineering Mathematics
[Early UG | Rigor: TBD | Explanations: TBD | Figures: TBD | Problems: TBD]
{Description TBD}
• Schey - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
[Early UG | Rigor: TBD | Explanations: TBD | Figures: TBD | Problems: TBD]
{Description TBD}
• Friedberg, Insel & Spence - Linear Algebra
[Early UG | Rigor: TBD | Explanations: TBD | Figures: TBD | Problems: TBD]
{Description TBD}

• Stone and Goldbart - Mathematics for Physicists: A Guided Tour for Graduate Students
[Late UG/Graduate | Rigor: TBD | Explanations: TBD | Figures: TBD | Problems: TBD]
{Description TBD}
• Arfken and Weber - Mathematical Methods for Physicists
[Graduate | Rigor: Moderate | Explanations: Short | Figures: Few | Problems: Plenty]
Better as a reference text or supplement to a main text.
• Byron and Fuller - Mathematics of Classical and Quantum Physics
[Graduate | Rigor: Moderate | Explanations: Moderate | Figures: Plenty | Problems: Plenty]

Zills is a little more handwavey than the rest though

This is taken from the physics servers reccs on math methods/physics exposure

[grave thorn]

Hall is goated

[grand thistle]

tbh i'm not really trying to get into physics seriously, i just wanna know the basics and be exposed to like the lagrangian and hamiltonian stuff which i'm pretty sure is useful in math as well

[grave thorn]

Try Hall's quantum theory for mathematicians

[grand thistle]

alright ill look into it

what are the prerequisites for it?

i'm only at the level of some group theory and some anlysis

[grave thorn]

The first section isn't very heavy

And it teaches Hamiltonian mechanics etc

The second part gets pretty technical though

[grand thistle]

does it require any classical mechanics though?

i have like a very limited knowledge of physics

[grave thorn]

Nope

Its designed for someone with a math background

But no physics

At all

[pseudo forge]

yea chaps 6-10 are intense with spectral theory

But the rest is pretty great for what ur looking for

[grave thorn]

Unfortunately they give the weird physoid version of Feynman-Kac

[pseudo forge]

yea I'm not sure why he does that

[grand thistle]

hmm

this actually looks amazing thank you

i think i need just a bit more knowledge of linalg and analysis

[gray gazelle]

LADR v LADW?

Good book suggestions for stats or for linear algebra?

[pseudo forge]

Depends on the objective

[gray gazelle]

Well I put it in detail in #probability-statistics

But

This is what I have to do
Poisson, approximations using Poisson, linear combinations of random variables, linear combinations of poisson and normal variables, continuous random variables, sampling, estimation, hypothesis testing for discrete distributions
Continuous random variables, inteference using normal and t-distributions, chi squared tests, non parametric tests and probability generating functions

Linear algebra tho? I just need a whole new book

I don't like writers who call every result trivial

[subtle mango]

khan academy

see recalculate

precalculus*

[subtle mango]

good books for premeasure-theoretic probability theory?

my class uses Knowing the Odds by Walsh, is that any good?

[grave thorn]

Jacod and Protter

Or use any of the highlighted books here

imo Jacod and Protter>all of them though

Shiryaev is meh, athreya and Lahiri is filled with typos, Sinai focuses too much on asymptotics

[gray gazelle]

Best books?

To be more specific, I've been studying math for about a year, and I'd like to develop a more wholisitic understanding of the field as a whole

Is there any other option besides studying as much math as possible?

And if not, what are some book recs

[foggy relic]

All of it actually

[mystic orbit]

[foggy relic]

Did it all mod homo alg a year ago and did homo alg more recently

[mystic orbit]

bruh moment

[foggy relic]

In my dreams

[mystic orbit]

algebrained

[cursive orbit]

@gray gazelle yo nice to see you here

[gray gazelle]

[placid pollen]

I trust you because of your pfp. This man randoms

[formal tinsel]

what are the usual prerequisites for studying measure theory, and what books do you recommend?

[grave thorn]

real analysis

[placid pollen]

Did someone here once mention Willard had an incorrect proof or theorem? I ask because we started a topology class and seems complicated for the sake of being complicated. Introducing neighborhoods, interior, and adherent points or limit points smooth things out to understand what closed or open means

[formal tinsel]

so far I'm studying measure theory after having done real analysis and some topology and finding it a little difficult

[loud cradle]

what book are you using for measure theory?

[formal tinsel]

introduction to measure theory by terrence tao

[placid pollen]

Try reading Kolmogorov & Fomin's Theory of Functions. The metric spaces chapter is really good, better than Baby Rudin

[grave thorn]

kolmogorov and fomin is goated

[mystic orbit]

a book for a economics-smooth brained individual please

[zealous light]

This is probably not the best place to ask for that fwiw

If I think of anything I'll dm you

[mystic orbit]

sure lol

[formal tinsel]

what part of economics?

[mystic orbit]

actually, I don't give a shit about politics

[mystic orbit]

economics has parts?

[placid pollen]

I think he thought you asked for an economics book. In which case I would recommend Nicholson & Snyder's Microeconomic Theory. Macro I've heard is sometimes bs mixed with ideology. But I don't think you asked for an economics book. Seems like you just asked for a book

[mystic orbit]

yeah

uh

just something so that I'm just a little more informed on the subject

[grave thorn]

mankiw and taylor

[mystic orbit]

rather than literally smooth brained

[formal tinsel]

varian is usually used for undergrad micro

[placid pollen]

"Economics" or "Macro"?

[grave thorn]

economics

[brisk ice]

what book would some one use for a more "general" approach to multivariable calculus (ie something that doesn't just stick to R^2 and R^3) and what would such prereqs be?

[mystic orbit]

tbh I'm yet to see multivar calc that restricts itself to treating R^2 and R^3

[brisk ice]

I mean it dwells on basically only those dimensions

[mystic orbit]

the ones I know about are hubbard which was pretty good and not overly terse

tterra also swears by spivak's calculus on manifolds but it's way more terse

[brisk ice]

regards to pre-reqs. A strong background in linear algebra?

[mystic orbit]

for hubbard, just calc 2 lmao

[brisk ice]

okay

[mystic orbit]

for spivak's yeah

lin alg is gonna be pretty handy

[swift raptor]

hey im starting multivariable soon, and looking for a good textbook, any recommendations?

[brisk ice]

[mystic orbit]

see above lol

[swift raptor]

oh

ok lol

[high linden]

Any good explain like I'm five textbooks for Linear Algebra, Mathematical Proofs, and Statistics?

[swift raptor]

my program requires multivar in order to do linear algebra tho

I feel like if you click on someones profile here and check mutual friends Batman will show up lol

[brisk ice]

weird. I can really see where linear algebra might show up in calc but not so much a direct application of calculus being required for linear algebra.

[swift raptor]

Huh. weird

[brisk ice]

I have seen the course set up as "corequisites"

[swift raptor]

Idk I wanted to do linear, but I needed multivar so i applied for that first

¯_(ツ)_/¯

[brisk ice]

https://tenor.com/view/why-not-both-por-que-no-los-dos-yey-gif-15089379

(memes go in #chill I know )

[swift raptor]

[brisk ice]

Hmm I wonder what the prof would say as a reason you can't take both at once. Especially for linear algebra. You can always see if the prof will approve you to take it

[swift raptor]

I definitely dont have time to do both at once tho thats the problem

Im quite happy to just do it one at a time

[fickle whale]

What do you guys recommend for Algebraic and/or Differential Topology

I'M BLUE

[swift raptor]

pog active

[brisk ice]

well I guess if you want to take Lin Alg first you could just ask for approval

[swift raptor]

meh multivar starts in 3 days and im too lazy to anyway. plus its a little late

[brisk ice]

Oh well then

[swift raptor]

also I have done math through this program for a while, and the prereqs are very strict so

[brisk ice]

I mean when I was following an online course they will mention all the vector type stuff you will need

[swift raptor]

[brisk ice]

Now some of the reason for doing X and Y might stem from concepts in Lin alg

or even a direct application of it

[swift raptor]

ohh okay

welp one of my friends is doing lin alg so ill get help from him

[fallow blade]

did someone one say MARCO economics who is marco

[pseudo forge]

Is ahlfors the best for complex

as a first

[fallow blade]

where can i get free books

[forest sleet]

the library

[fallow blade]

but i mean textbooks on math

[forest sleet]

oh I mean university library

many have free ebook access as well

especially to springer

[fallow blade]

ohyeahh.. except .. i am in highscool and dont have permission to check out books

-_-

[grave thorn]

If not, many books can be found online

[fallow blade]

but where!!

https://tenor.com/view/shades-bitch-where-meme-gif-7409952

what websites

[forest sleet]

can't post on discord since they can shut down the server for it

[fallow blade]

oh no dont want that

[forest sleet]

reddit doesn't seem to have the same issue though

[grave thorn]

While I would not recommend doing this a lot, most books can be found by searching up "x book filetype:pdf"

[fallow blade]

yeah i just got this stewart early trancendentals callculus book as a freee download and it was like 60 dollars on amazon kindle

buy the typographyis way better on kindle

you can highlt zoom in take notes

but im not paying money screw that

[grave thorn]

You should

Its worth it

[marble solar]

Stewarts Calculus is an expensive door stop

Although the series estimation bounds are nice

[fallow blade]

its not even that good its like whatever i am 1/3 of the way through and have been reading for couple days

[marble solar]

Thomas' University Calculus

is a lot better

[fallow blade]

ty ima check it out

[shell geyser]

I think Thomas and Stewart are pretty similar and cover basically the same stuff. Though I too preferred Thomas.

[marble solar]

They are similar in a lot of ways

Except the examples tend to be less computationally heavy, and more interesting theoretically

The section on revolutions of solids & what not are completely different

[shell geyser]

Not gonna lie it's been a while since I read either. I do remember liking Thomas' writing style more.

Nowadays if I revise calc I just use lecture notes. More compact.

[marble solar]

I work at a college

and I frequently refer to both

So I can pick out the differences between them

Another egregious thing is that stewart doesn't have the inverse function theorem

(Not to mention a terrible proof of the chain rule)

[shadow tusk]

🏴‍☠️y websites

[weak violet]

how is pinter as an intro to abstract algebra?

[smoky inlet]

Things to make and do in the 4th dimension is an absolutely epic book

[pseudo forge]

I see, thanks

[gray gazelle]

you

yo

I have been looking for a physics book that can explain why in the is the state of solitude gets soo amazing when you can build the electronic components with normal OHM'S law but all of the sudden you realise ohh we need Math too in order to get it done, Think Spidy Think but then you again stuck at the illuminating part of the component and get frustrated and asking everyone to recommend a physics book. :}

[kindred wing]

The Geometry of Kerr Black Holes is an amazing read! It is pretty advanced, but its introduction should make most of the concepts understandable in it.

[gray gazelle]

damn thanks.

[kindred wing]

Oh, I am so sorry, that was just a general book recommendation. I don’t know if it will be exactly what you were asking for.

[sudden kayak]

Please recommend a good history book on Statistics

[spring cedar]

Somebody gimme a quality website where i can do math courses

[gray jungle]

https://ocw.mit.edu/

[spring cedar]

Thank you very much

[hearty steppe]

This geometric group theory book looks like a nice reference if I need it for my study of dynamical systems but I feel like it’s not quite what I was looking for. Just seems a bit too general in terms of approaching differential geometry and combinatorial structures (it’s not actually specifically tackling these areas in an obvious manner)

Actually there are some definitions of things in my dynamical systems texts that I might be able to conveniently cross check in this office hours geometric group theory book, that’s at least something to work with

Books

Do you want to learn or cram things into your head? Learn = book

Need a quick reference = handout

20 pages is a quick reference to me

Pretty quick if you ask

Not always

Maybe the important bits to some extent

[fickle arrow]

Which book is recommended for probability ? I am reading Probability the logic of science but I feel like I am not getting most of it. Is there anyone who have read it and have any suggestions? PS:I am not a beginner in probability. I want to explore probability deeply.

[marble solar]

DURETT

[grave thorn]

I will continue to shill Jacod and Protter

[dull vault]

I was watching 3b1b videos on Linear Algebra, and was enthralled during the dot product and duality episode, where he showed that dot products are actually matrix multiplications.

Do you know which articles/books he might have referenced to learn such a method?

[marble solar]

Uhhhh

the def of matrix multiplication

[weak lake]

what's a good book for someone who has never studied linear algebra before

[hollow peak]

Linear algebra done wrong

[coarse frost]

Artin has a lil bit of LA with no assumptions, but it can be kinda boring at times ig

i like it still

[viscid citrus]

is there any Real Analysis book with exercises and solutions? Looking for suggestions as I am having a hard time looking for proofs online.

[proud tusk]

rudin is quite popular so i assume you would find solutions?

[brittle breach]

why you say that

[orchid mortar]

If anyone has an alternative to van der Vaart's Asymptotic Statistics ( https://doi.org/10.1017/CBO9780511802256 ), please recommend them to me. Please ping me if you are recommending anything.

I'm trying to find a more modern equivalent of the same material, organised in generally the same way

[hearty steppe]

Im glad im giving this book a peek https://www.jstor.org/stable/j.ctt1vwmg8g

thanks guys. Actually does fit things into a combinatorial perspective kinda

also i think this gives some of the best illustrations I have ever seen in a math book

[hearty steppe]

second thoughts about the book; its great, but its not relevant for what I'm doing ultimately. Great reference on some more intuition on groups though!

[hollow peak]

Does anyone know of a good reference for global analysis? Or perhaps an introduction to geometry and pdes? The last book I looked at went crazy immediately by working on frechet manifolds but I'm looking for something a little slower paced

I guess I'm more looking for geometric analysis, preferably not jost

[smoky inlet]

because it is epic

[fallow blade]

wtf are you talking about

[weak violet]

how is pinter as an introduction to abstract algebra?

[elder sierra]

what are some good books for a first course in differential geometry?

[night prism]

Pinter’s [anything] is a good intro to [anything] in my opinion

[weak violet]

? what other subjects does pinter have books on?

[night prism]

Set theory I know

I’ve seen another too but can’t recall

[hollow peak]

An Introduction to Manifolds, Tu

[proud gazelle]

any thoughts on Hubbard & Hubbard - Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach ?

[heady ember]

I have also heard another popular rec here before; Lee's series of books on diff geo

[main void]

Im towards page 200 in Tu’s “introduction to manifolds” and am using lee to complement certain subjects

While the book definitively has it’s shortcomings (mainly the exercises) I think it’s a better first read than lee, lee goes into a lot of detail which, on a first read at least, doesnt seem too relevant (imo at least, im sure its interesting, i jyst dont want to work through 400 pages to be able to understand differential forms)

That being said im not sure how linear lee’s book is

[remote ginkgo]

olver - applications of lie groups to differential eqns

[remote ginkgo]

i don't like lee at all

[main void]

Ill bump this again, in case anyone knows, most references i found were quite a bit too advanced

[remote ginkgo]

sternberg is better

so is kobayashi & nomizu

though less formal

[remote ginkgo]

lang has an intro to profinite structures via projective limits etc

maybe profinite groups are in it

[main void]

Lang

Ill look into it once im back from my bike trip, thanks

[remote ginkgo]

np

[elder sierra]

thank you very much kind sir

[elder sierra]

thank you very much kind sir

[remote ginkgo]

also i have a bunch of recs at the list

http://sheafification.com/index.php/2022/08/14/the-fast-track/

[elder sierra]

wdym "recs"?

[remote ginkgo]

recommendations

[elder sierra]

wow amazing than you very much, this is very helpful

[fickle whale]

It's pretty good, reading through it right now, it was my first interaction with Abstract Algebra

[safe lintel]

@vital bane

[vital bane]

go study

dont come back until you finish

[safe lintel]

okie

[vital bane]

[grand thistle]

anyone know of a concise pdf or book that reviews basic linalg in about like 75 pages or less?

basically one that has all the main theorems and concepts necessary for multivariable analysis after baby rudin

[gray jungle]

halmos or artin probably , altho halmos is pretty technical

[grand thistle]

finite dim vector spaces?

[gray jungle]

yes

[grand thistle]

right

[gray jungle]

dont expect to learn much from it , but its a strong reference

[grand thistle]

why the latex so goofy tho 🤨

bruh

[gray jungle]

there should be a better pdf version of size 205 pages sean its one of the first that show up when you look for the book , not sure if thats a legal version or not so i wont link anything

nor ask you to look for it

[grand thistle]

oh yeah found it

[grand thistle]

hey this actually looks amazing

very concise

exactly what i'm looking for

learning some group theory actually enlightened me a lot about some linalg facts

like how rank nullity is just first iso for vector spaces

[sturdy shore]

yeah halmos is great

[mystic walrus]

did you find?

[tacit abyss]

does anyone know any good introductions to C* algebras?

looking for one that goes fairly far

[karmic thorn]

@gusty smelt maybe

[gusty smelt]

Murphys book on the topic is p good

[pseudo forge]

@glad prairie

[glad prairie]

Pedersens analysis now has a good introductory exposition, then from there I like C* algebras by example.

[gusty smelt]

I second that, pederson ch4 is a good but brief introduction

[mild yoke]

Any good A level math books?

[sage python]

@dapper root so what's the shtick with old vs new Matsumura anyway? Now that old has been tex'd

[dapper root]

Difference in presentation

Order is different

Some proofs are expanded and stuff

[solar anvil]

any good books for learning logic?

[sudden kindle]

This is worthy of being a copypasta

Oh

I misread

It as "any good book for learning topic?"

[solar anvil]

:(

[sudden kindle]

My bad I'm sorry

[polar mango]

Guys I am in desperate need for a calc 1 book

My teacher is absolute trash and I think imma have to teach it myself

Any recommendations?

[pseudo forge]

single variable + multi

[pseudo forge]

stewart is good for the most superficial understanding

[polar mango]

Do you know if there exists a pdf for it

[pseudo forge]

yes

[polar mango]

Ok

Do you know where I can find it?

Free preferably

[safe lintel]

How do I remove the studying self role

,iam notstu

[hasty eagle]

No selfroles matching notstu.
See ,selfroles --list for the list of valid selfroles.

Aug 26, 2022, 5:33 AM

[stray veldt]

this is the wrong channel

[safe lintel]

Oh

[stray veldt]

but try /roles

[safe lintel]

Ty loch

[heady ember]

Paul's Online Math Notes, free from the author. Just google it

Well technically its not a book but idt it really matters

Oh yeah and Khan Academy too

Or if you really want a challenge, you could try Spivak's Calculus, though it has more of proof-based exercises instead of computational ones so it might not suit your needs

[karmic thorn]

@solar anvil here

[hybrid chasm]

I remember you

heh

[hearty steppe]

In terms of dynamical systems theory outside of complex dynamics I think I am gona stick to Brin and Stuck and Strogatz. The other books I looked at are a bit too mathematically terse to be relevant for what I’m doing

[subtle mango]

i'm using strogatz rn for my nonlinear DS course

i like his writing

[blazing violet]

Can anybody suggest me a good book for calculus

[blazing violet]

Thanks for that

[heady ember]

np

For most ppl Pauls' Online Math Notes and Khan Academy would probably be the choice

[hearty steppe]

Well I’m not taking a course I’m just trying to see what I can understand and apply it to my research

That being said. Ergodic Theory book recs? Hopefully something that is applied math approachable but still has good theoretic content

I might just stick to these current reads. Maybe they’ll be enough

[blazing violet]

Okayy

[quasi abyss]

Hello, I am using the book Calculus: A Complete Course by Robert A. Adams and Christopher Essex for my Single-variable Calculus (Calc 1 & 2 combined) course. Anyone have experience using this book? Also would be more than grateful if someone could provide a study guide based on this book, I have been Googling everywhere to find a University other than the one I am currently enrolled in who uses this book and provides a study guide based on this book.

[heavy thorn]

books relating set theory?

[gray gazelle]

but that doesn't make much sense

[gray gazelle]

Jech's Set theory

It's a graduate book but he also made some undergrad books iirc

[oblique hatch]

What would be reasonable next steps for someone interested in representation theory after a book like Representations and Characters of Groups by James and Liebeck?

[split basin]

was there some chapter that you particularly liked? there are multiple routes one can go with representation theory

[oblique hatch]

There were two parts, one in the book on permutation representations and one in some lecture notes I was also reading on compact groups

[split basin]

hmm ok if you like mathematical physics (where both of the concepts you mentioned are used) you could have a look at Sternberg's "Group Theory and Physics"

at least from the TOC the book you mentioned seems to not have treated any lie groups

[inland dawn]

hey all, does anyone have any recommendations for learning formal language theory?

[crisp river]

Any opinions on An introduction to algebraic geometry by Kenji Ueno?

Personally there are so many typos

[hearty sluice]

thats not an opinion

[dapper root]

[sage python]

Ueno seems good, I was gonna use it to learn AG except I didn't get super far before life and burnout put that on pause

[grave thorn]

I have this book on (deterministic) control theory, but it doesn't seem that good of a reference

Does anyone know a fairly in depth coverage of control theory from the same perspective as ^^^

[tulip saffron]

Statistical Inference by George Casella vs Mathematical Statistics with Applications by Wackerly, which one do you prefer?

[gray gazelle]

why don't they just called it rough?

Rough Analysis and Control Theory

[grave thorn]

Non smooth analysis is the actual technical term

Used to refer to the subject

[gray gazelle]

Is there also a more modern book? Actually I have Kirk at home but I don’t like the typesetting, printing and equation setups lol. You can just tell it was written in the 70s and I hate that.
The book by Daniel liberzon seems nice but sadly it only covers the continuous case afaik

@timber copper you might know too

I even thought about rewriting Kirks book in pretty latex, this way I’d learn it and have a prettier reference for later

[timber copper]

Lewis has a recent edition on his optimal control book (named: Optimal Control) that looks good (also the second chapter is entirely focused on the discrete-case) that you may be interested in

also the recent version of Bertsekas's dynamic programming and optimal control doesn't seem too bad either; I've only really read the 1995 edition which was not a good time

[silver herald]

👀👀

Has the math server -> control theory pipeline been established now???

Also, @grave thorn Etherality's suggestions are banger. I have been reading on Viability theory by Aubin as of late. Extremely interesting but has strong assumptions about certian things when developing methods.

https://www.springer.com/gp/book/9780817649104

Also, hello Yohan! How are things up for you now?

[silver herald]

Also, if you are looking for standard text on mathematical control theory, the standard reference is usually Sontag's text.

https://link.springer.com/book/10.1007/978-1-4612-0577-7

[gray gazelle]

For linear systems this looks also quite nice: https://federico-ramponi.unibs.it/docs/linsys2014.pdf
There are more recent versions somewhere in the web with added material

Personally not a fan I‘d read Linear System Theory from Hespanha or feedback systems from Astrom/Murray

I didn’t read Ogata though I just see that is has 900 pages and immediately dislike it. Also for its name being modern control he covers many frequency methods

These make a great combination too

Red one can only be ordered from Switzerland tho if I remember correctly

[zealous light]

Talk of control theory

[heady ember]

Just get the pdf somewhere online

[gray gazelle]

Couldn’t find any since so I bought it haha, I think it was only 30€ though

[heady ember]

zlib?

[gray gazelle]

It’s not an officially published book. It’s a 4th edition lecture notes

But better quality, detail and readability than most books

[heady ember]

Ah I see

[zealous light]

I’ve also been wanting to look at Isidori Nonlinear Control Systems as was recommended by my internship advisor last spring if anyone has skimmed/read it before

[silver herald]

Ogata is kinda an intro controls text. Not really for "modern control policies"

I do concur with the fact that linear systems theory is usually a good starting point for most people. I do think Sontag is an easy read for someone who' formally from a pure math/optimization theory background looking to learn (linear and nonlinear) control from scratch (and is usually the recommended textbook for applied math students doing a control theory course)

[gray gazelle]

I skimmed it without any knowledge of differential geometry and as expected I could not understand anything from the book

[silver herald]

I recall there are some Kyrlov subspace based frequency domain methods for nonlinear control theory

[zealous light]

Yeah that sounds about right, it seems like a very diffgeo heavy book which I kinda like

[timber copper]

Ooh yes isidori based

[grave thorn]

👍

[timber copper]

Also brockett's paper on the early days of geometric control is good expository material for the subject

[zealous light]

Noted, I’ll take a look!

[gray gazelle]

has anyone read Hardy's An introduction to the theory of numbers

or The Higher Arithmetic? by Davenport

[livid ermine]

Aluffi subsection tier-list

S:
6.4, 3.7, 8.1, 8.2, 7.2, 7.3, 7.6, 9.3
A:
5.6, 5.4, 4.1, 4.2, 4.4 , 6.5, 6.6, 6.7, 8.3, 8.5, 8.6, 9.2, 9.1.
B:
1.4, 1.2, 4.3, 4.6, 6.1, 3.2, 3.3, 2.6, 2.8, 2.9 (the rest of ch7), 8.4
C:
6.1, 6.3, the rest of ch V, 3.4, 1.5, 2.5, 2.6, 3.1, 3.4, 3.5
D:
Ch 3.6 (its actually not too bad, I just had a really hard time understanding this chapter, fuck algebras, and fuck finite type algebras in particular), 2.4, 1.3, 1.1, 2.2
F:
2.7
???:
2.10, rest of ch9 (I haven't read those)

[dapper root]

Lmfao

This mf ranked the subsections 😅

[gray jungle]

actually based af

[sage python]

This is kinda next gen

[foggy relic]

absolutely based

[sudden kindle]

Can someone pin this

[foggy relic]

^

wait im gonna double check this

i have my book in my bookshelf

[foggy relic]

you should also rank the subsections in the categories

7.6 is probbaly the best subsection overall