book-recommendations

[fading python]

yeah

simmons is pretty good
thank you val

[quick hornet]

i havent heard of an exam that required that

i doubt itd be the worst source though

[fading python]

I used Apostol and Spivak
I'll check that out, thanks

[quick hornet]

i dont think apostol or spivak cover it

[fading python]

what do you recommend then

[quick hornet]

i dont have recommendations, i honestly have never had to worry about tricky integrals

[fading python]

oh

i even checked out the YouTube videos on the topic, didn't grasp it much😔

guess I'd have to ask a teacher

[gray gazelle]

i mean it isn’t even that important

[slender sphinx]

tbh I don't really remember it in either of those books either

[dapper root]

Justifying it requires some notion of uniform convergence right??

I don't actually remember when it's valid to do so

[fading python]

id like to learn it, even though it won't be in syllabi or questions

[gray gazelle]

just learn complex analysis

lol

[fading python]

Justifying it requires some notion of uniform convergence right??
😮

[quick hornet]

it applies in all cases where this makes sense

[fading python]

just learn complex analysis
okay😢

[quick hornet]

now this formula probably looks ugly as sin

thats because it is

hence why instead we think of it as "differentiating under the integral"

[fading python]

it's very ugly

[quick hornet]

i mean the proof is easy

its just that figuring out how to actually apply this in a

human-usable way

that actually simplifies things

[fading python]

yea I saw flammable maths video on it and he made a mistake and I couldn't follow

its just that figuring out how to actually apply this in a
human-usable way
guess I'll have to practice more

[quick hornet]

though @dapper root theres an aternative (and imo more clean) way to think about it

but it requires measure theory

this might be related to what you were thinking of

[dapper root]

Nah, my thinking of it

[fading python]

what level of math is this

[quick hornet]

measure theory, as i said

[dapper root]

removed some of the like clutter in the terms I think

[quick hornet]

usually taken as a second or third course in analysis

[fading python]

Grad or undergrad

ohh

[dapper root]

wut?

[quick hornet]

oh yeah

i mean as i said

no one actually thinks of leibniz's rule

using this formula

like thats its formal statement but everyone thinks of it as "differentiating under the integral"

[dapper root]

Yeah I'm looking at that like wtf

[quick hornet]

such as in wikipedia's example here

that said i dont think many people care about the rule in the first place

except for, like, people coding CASes

[fading python]

okay

that's a good perspective

[quick hornet]

but yeah you need your function to be "suitably well behaved" for this to work

[fading python]

the divine knowledge of knowing how suitable it is, how easily does it come to one

[white cradle]

https://cdn.discordapp.com/attachments/716264872018706443/725569097974415390/unknown.png

is there a way to restate this in probabilistic terms

lemme try

[main flax]

@white cradle #❓how-to-get-help

Got em.

[valid moth]

@main flax #❓how-to-get-help

[zealous elbow]

Anyone else here used: How to read and do proofs by Daniel Solow? I used it and thought it was a great intro to proofs and mathematical thought. It was recommended to me by my algebra prof.

[gray gazelle]

Is anyone familiar with Vector Analysis by Janich? Does it cover similar content to Analysis on Manifolds/Calculus on Manifolds by Munkres/Spivak resp?

[edgy silo]

Can anyone give some references on studying of ideal of a non-commutative ring...

[outer carbon]

This is the problem with book channel

[quick hornet]

be part of the solution

[hollow current]

again

any good books treating DE?

[civic carbon]

I am not familiar with the DE literature, but you should probably be a bit more specific about the level of treatment you're looking for.

[night knot]

You could try Krantz, I liked it from a library read (though, I haven't gone over it completely thus you may need a second opinion)

We used Zill's book for the most part, that seemed fine

[zealous elbow]

I liked steven strogatz nonlinear dynamics and chaos. We use that book for ODE 2.

[hollow current]

but for ODE 1?

[velvet briar]

I do have Zill's advanced engineering Math, which was an easy book going through ODEs

As well as other higher calc

If you're looking to solve odes then this book is great. If you're looking for rigour then this ain't it

[north spire]

@hollow current I really like George Simmons's Differential Equations with Applications and Historical Notes

My university uses arnold's text for our first ODEs course so maybe you wanna check that out.

[foggy fiber]

My university used Shepley Ross' Differential Equations third edition text. Not sure a fourth edition was ever produced.

[hearty steppe]

Hey I found this book stumbling on the interwebs https://www.amazon.com/Problem-Solving-Strategies-Problem-Books-Mathematics/dp/0387982191

Any comments on it?

oh looks like comp math

competition*

[atomic sorrel]

Hey, anybody can review this elementary algebra by hall and knight?

Has anyone tried that?

[main flax]

can you post table of content here, so we can look at it

[atomic sorrel]

Has many of them lol

[main flax]

doesn't look like elementary algebra

can you take a pic of the first few chapters

[strange osprey]

@atomic sorrel Umm...brother? Why can I see your real name in this server?

[silver herald]

[strange osprey]

Yes, I have no idea why I can see my brother's real name Atharva on this server.

Didn't know he was good at math

Because he is quite the opposite actually

[main flax]

you know different people can have the same name right?

[slender sphinx]

No publius

[strange osprey]

thinking noises

[slender sphinx]

My name is copyrighted

[strange osprey]

super thinking noises

mega thinking noises

[slender sphinx]

Zoph lurking

[strange osprey]

Oh sht

Run

Actually don't run.

I want to see what happens.

[tranquil ocean]

please stick on topic for this channel

[strange osprey]

Whew

Sure

I thought the channel was chill for a sec.

[warped wave]

hi guys. I own thomas calculus but it's so thick and exercises are not challenging enough + so many of them. It's hard to keep track of what to read or do in thomas it seems so disorganized. Do you have any recommendation for calculus but not so rigorous like spivak's?

[marble rock]

stewarts

[gray gazelle]

Apostol

[marble rock]

apostol is rigorous

[gray gazelle]

Easier than spivak and not as rigorous as spivak

It's the natural step down from spivak

Imo

[restive raptor]

is there a particular reason you don't want to do spivak? do you want to avoid rigor entirely, do you find it daunting, or is there another reason? if you want to avoid rigor entirely, yeah, go with stewart; if you want a little rigor but toned down, apostol is a step down from spivak as well imo

your other option is to find problems through like MIT open courseware or something, and then just use the book for learning

[warped wave]

I'm planning to study physical chemistry on my own this summer but it has quite a lot of calculus

it just seems interesting field

[gray gazelle]

Oh lol

So do you want to absolutely know your stuff or just enough to understand physical chem?

[warped wave]

just enough probably, I don't need to know rigorous delta epsilon proofs and such

[gray gazelle]

Dude even apostol covers that

[marble rock]

do stewarts

[restive raptor]

https://tutorial.math.lamar.edu/
https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/
use stewart in that case. These two things are also going to be very helpful. Paul's online math notes cover calculus in a non-rigorous way, and MIT OCW always has great stuff. I've heard great things about this course in particular

both of them also have problems that you can solve, which may be able to supplement stewart

[warped wave]

thanks alot guys

[restive raptor]

however, if you find yourself getting bored by all of these resources

then trying calculus in a rigorous way might not be a bad idea

even if you don't strictly need to know it, it will be more challenging + interesting

[warped wave]

I sure will try reading Spivak/apostol sometime in the future

[radiant crown]

if you're in need of exercises, you could look for a book that just has exercises instead of a whole textbook 🤔

[marble solar]

Schaum's outlines have lots of problems with full solutions

[hearty steppe]

My personal experience with Schaum so far, is the depth of material covered per subject seems a bit lacking.

[limpid gazelle]

In my opinion, Schaum's outline are not that great for learning but for problems with solution

[marble solar]

I mean, students can learn a lot from problems with full solutions

[limpid gazelle]

Yes

To be more specific I meant the explanation of concepts in Schaum's outline isn't great

But I've only read the calculus and statistics books from Schaum's outline

So maybe this doesn't apply to all their books

Also it's just my personal opinion

[lyric cloud]

Does anybody have books on computer algebra systems

[limpid gazelle]

I have a fantastic book about several algorithms but it's in chinese

[main flax]

name?

[limpid gazelle]

计算机代数系统数学原理

[main flax]

where can i download it

didn't find it on libgen

[limpid gazelle]

Lol

Of course it's not on libgen

I don't think it's available anymore

You might find it on some chinese websites

Or

I can share it

[main flax]

dm pls

[limpid gazelle]

Why can I talk here

@sage python

[sage python]

What

[main flax]

@limpid gazelle just learn how to shut it smh

[main flax]

@white cradle no you're not allowed to do that

[limpid gazelle]

@main flax

[long anchor]

[sage python]

Let's keep this closer to on topic please

[pure iris]

Any recommendations on a differential geometry book for independent study? Currently our uni has barret o neils book but imo it is not suitable for independent study

Any recommendations on a differential geometry book for independent study? Currently our uni has barret o neils book but imo it is not suitable for independent study

[steel viper]

have you done like intro smooth manifold stuff

if not then lee is the standard rec

[smoky surge]

Has anyone here read LADR? Would you say set theory would be required to go through?

[wet badger]

Yeah

I think Set Theory is like prereqs for LA

[smoky surge]

really everything ive seen says you really dont need anything more than like Calc 2

Ive gone through book of proof so ive had some proof intro someone else was talking about this and i just wanted to know if anyone had gone through that specific book

Also isnt your avatar mukrow holding LADR LOL

thats awesome

[quick hornet]

im pretty sure axler introduces the set theory definitions you need

you dont need a particularly deep look

like you probably dont even need to know what countable means

as long as you know "what's a set, what's the empty set, what's a union, what's an intersection, what's a complement, is {{}} = {}?" youre probably good

and maybe familiarity with what injective/surjective/bijective means but

pretty sure axler covers those

[flint forge]

lmao in litt's talk today he was like 'its okay if you don't know (small intro level topic)

and then later assumed everyone was familiar with cohomology rings

[smoky surge]

he introduces injective/surjective

when he talks about isomorphisms

[lyric cloud]

sorry for asking again but does anybody have good books on intro to computer algebra systems

[cold lagoon]

the maple or mathematica documentation depening on which one you want to use?

🤔

[lyric cloud]

documentation?

i meant, books on solvers and stuff

and the algos used in them

and how they were optimized

Stuff like that

[hollow current]

i havent read this still

ut i have this

[gray gazelle]

piracy moment

[hollow current]

*distribution of knowledge

[ruby isle]

Hey all

What typically comes after calc 3 if you're on an engineering path?

[flint forge]

Diffeq

I think

[ruby isle]

Linear algebra or diff

ah

[flint forge]

Both

[ruby isle]

any cheap texts you can recommend?

[flint forge]

Honestly you shouldnt really do calc 3 w/o linear

All texts are free

[ruby isle]

too late lol

[flint forge]

Google libgen

[ruby isle]

hmm

thanks

[flint forge]

Anyway idk any diffeq so cant rec a textbook

Nor comptational linalg honestly

[hearty steppe]

I feel like Calc 3 and linear sort of compliment each other but I mean the book I was using gave you a whole chapter intro to vectors so I think it’s doable to do Calc 3 first. I used Stewart Calculus

Then again I did know some linear beforehand

[ruby isle]

Not really understanding this lib gen website

I see nothing about textbooks

\just articles and such

[hollow current]

LA would help in calc 3

but it is not necessary

[hearty steppe]

I feel like they compliment each other

Depends on how far in linear you get

[hollow current]

Not really understanding this lib gen website
@ruby isle putting ISBN of book in search and u are done

[hearty steppe]

Where multivar can be useful

Probly with tensors n shit

[ruby isle]

okay, I see

I just need a specific book recommendation, then

[hollow current]

ok what do u want from linalg?

more theory or more practice?

[ruby isle]

I'm not taking any classes this summer, so I just want to get started with whatever I can by going through a textbook

[hollow current]

well, i am doing lin alg through https://libgen.is/book/index.php?md5=7FDCFFF8CC68893EEC16116EC5DA74A2 this one

it provides a lot of theory

a lot

but is not proving anything and does not provide much examples

so for practice u can take Strang's linear algebra or sheldon axler linear algebra done right

[ruby isle]

thanks. any recommendations in regards to linear?

I'm sorry

differentials

[hollow current]

well

people recommended Zill's advanced engineering mathematics

also, Krantz partial differentials

Birkhoff Ordinary differentials

Simmons differential equations with applications

[marble solar]

Gilbert Strang has good lectures on Linear Algebra at MIT OCW and a text accompanying it. The go to gold standard for lower division differential equations is Boyce and DiPrima

But depending on if you want something specific out of it there could be better texts

[ruby isle]

any suggestions on what programs to open these books with?

Kindle isn't working and I can't find anything native to my windows PC that works

[hollow current]

wdym

windows should have pdf reader

[ruby isle]

hmm...

apparently IE should work but I haven't been able to get it open

[hearty steppe]

So I am not sure if it is ok to share download links to books in here? Not to put anyone on the spot but sharing this info out in the open can potentially shut down these sources. So please don’t share this kind of info out in the open?

[hollow current]

apparently IE should work but I haven't been able to get it open
@ruby isle Chrome?

i mean chrome should be able to read pdf

[ruby isle]

Don't have it on my pc atm

[hearty steppe]

If nobody can use these sources cause they get shared out in the open too much then everyone loses

[ruby isle]

Gonna have to try on my mac and see if this is easier

[hollow current]

[ruby isle]

lol

[hollow current]

linux > macOS > windows

anyway, foxit reader is nice

[ruby isle]

yeah, at least with the link provided above, nothing on my iPad supports the file type and I assume it would be the same for anything on my laptop

[flint forge]

All OS rankings are usage dependent

Ranking them is kinda silly imo

[brazen yarrow]

Hello . i have just noticed this channel about books

who reads stephen king?

[marble solar]

I am re-reading The Brothers Karamazov

Does that count bomber man?

[pulsar aurora]

I don't think I ever read a singler Stephen King novel. Well, no, I did read his semi-autobiography On Writing which is fantastic

[gray gazelle]

Idk man rudin seems to be really really good imo

[quick hornet]

not familiar with kolmogorov, but im curious what errors you found in rudin

maybe i've only worked with later editions where those are fixed

[gray gazelle]

Highly possible

[quick hornet]

well that follows from explosion

[gray gazelle]

Smh

[quick hornet]

but thats interesting, that error isnt in the copy i have so

i guess earlier editions were a lot sketchier

with this stuff

i didnt realize that

[gray gazelle]

1976

Oof

Let me actually see if mine has this error

[quick hornet]

ah yeah that should have a "positive"

[gray gazelle]

The first ineqality you posted has been corrected

[quick hornet]

before "real y"

and yeah its corrected in 3ed

[gray gazelle]

Yeah it's all good in the later editions

[quick hornet]

anyway yeah its understandable why thats offputting

unfortunatley im not familiar with kolmogorov

[gray gazelle]

It's the standard

[marble solar]

If I had to go based on name, I'd imagine Kolmogrov does a fine job. But it's hard to say without being too familiar

You don't necessarily have to choose one or the other. You can see how they both approach same theorems

Compare and contrast the methods, level of detail, etc.

What do they leave in? Leave out? Why? etc.

[sage python]

Kolmogorov Fomin is weird

It reads nicely but on the whole idk if it's good to read

[gray gazelle]

sounds Russian

[sage python]

It is yeah

It uses terminology that's either out of fashion or otherwise non-standard

[gray gazelle]

hMrmrmrmrmmrm

welp that’s interesting

[sage python]

And it like, kinda covers Lebesgue measure/integration but I don't think it does so particularly well tbh

[gray gazelle]

hmm

[sage python]

Most of the functional analysis treatment iirc is done with l_p spaces instead of L_p

What else is there to note

It kinda is at the level of Rudin? Maybe somewhat higher. Like it doesn't really talk about calculus and I've heard someone say the book sorta assumes you know Heine-Borel even though it defines like, sets and metric spaces and topology?

So I'm guessing it assumes you've seen like, "advanced calculus" I guess, a class which talked about topological notions on R^n but not metric spaces

And you've seen differentiation and integration but not Lebesgue

(The more recent Russian editions of the book apparently do differentiation on Banach spaces which seems coo)

But yeah overall it's awkwardly situated

[gray gazelle]

I wish I could understand that, but the lot of it goes Over my head completely.
it is truly amazing how advanced you, and some other brilliant people on this server are... truly, I admire y’all.

Anyways speaking of books— I am getting some books on calculus in the mail :D. (Calc vol 1 and 2 by apostol.) heard that and spivak were good beginner books

Ignore the linear algebra part in apostol lol

Also why spivak AND apostol?

[quick hornet]

it is truly amazing how advanced you, and some other brilliant people on this server are... truly, I admire y’all.

people are "brilliant" for knowing undergraduate level math?

honestly stop thinking people who know more than you are so smart or w/e

they've just done more

viewing people as some monolithic unachievable idea of "smartness" is only harmful in the long-term, not to mention inaccurate

[sage python]

A lot of us are just older lmao

Well I guess there are a bunch of high schoolers which makes a bit like damn I wish I had gotten started in math in high school

But that aside, I happen to just be brilliant but Namington, for instance, just has more experience really

[gray gazelle]

Nami got spanked

[gray gazelle]

Is it so wrong to set goals and compliment people for pursuing mathematics?

[dim forge]

Rosenlicht's analysis is my choice for a first book. Really easy to read. I wouldn't use Rudin as a primary source. There's some good stuff, but the exposition can be truly awful, the topology chapter and last two chapters are bad. Rudin's problems are great though. I don't understand why Spivak's book is recommended at all, it seems like a drawn out analysis book. I would and did just learn some calculus then learned analysis. Apostol has the same issue except I couldn't even read Apostol. I found Bartle's introductory book really tiring. Terence Tao's Analysis I is available free online, I found it too slow though. Kolmogorov is not suitable for a beginner. For an advanced book I like Lieb and Loss more than Kolmogorov, Rudin's real and complex analysis, Folland, or Royden (the worst out of these). There's a book called "elements of integration" by Bartle which can be a nice intro to measure theory. I think Rosenlicht's book and Lieb and Loss are the best choices overall.

Don't take it as an insult. This stuff is not so difficult to learn despite how it seems right now. You will learn it eventually, others are just farther than you right now. But yes this stuff is nothing special compared to the grand scope of math currently.

[gray gazelle]

I don’t, it’s not an insult, and I understand that they’re not gods.

[hollow current]

but rudin's topology chapter is nice in terms of anal

[gray gazelle]

time to remove myself from this channel.

[sage python]

I liked Rudin's topology chapter lmao

[hollow current]

i mean you do not expect that rudin give u complete view on topology

[sage python]

I don't know Rosenlicht so I can't comment. Spivak is the book that's recommended for like, absolute beginners

Rudin 1-7 for me is absolutely fantastic but

I don't think it's feasible for most people to do it if they don't know calculus or proofs you know?

(I think it is feasible for someone who's had one of the two but tbh both is optimal)

[hollow current]

when reading rudin's integral riemann-stieltjes

you are like

[sage python]

I don't remember it being too bad? Though it's been years and I had seen integration from Spivak first so tbh I probably just looked at it and was like

[hollow current]

i mean it is sometimes quite hard to understand the proofs

[sage python]

Oh yeah lol this is familiar

[hollow current]

but the exposition is nice

[sage python]

Stieltjes changes things a bit though

[dim forge]

Back when I was learning it, I did not think Rudin's topology chapter made any sense. Maybe it's not so bad and it was just me. I still think the last two chapters are strange, to say the least. It doesn't really matter much though since they're designed just to give a taste of future analysis. My experience was struggling with Rudin for nearly the whole semester, then picking up Rosenlicht and catching up within two days. So despite the praise I do not usually recommend Rudin to others.

[gray gazelle]

if u think chp 6 of rudin is difficult then u gonna have hard time with later chps

so like

^

[restive raptor]

sometimes people just find certain parts hard

[hearty steppe]

I don’t think Rudin is very optimal alone for self study. Gotta use other books too.

Speaking from experience

[pulsar aurora]

For self-studying though, you shouldn't rely on one source anyhow.

[gray gazelle]

I don’t think Rudin is very optimal alone for self study. Gotta use other books too.
i agree ,
but the only book in my mind (the only one i knew lmao) to start with analysis was rudin, so i sticked to it and it went well!!

tho my classes teacher recommended trench to start with 😛

[velvet briar]

I'm open to the idea that Rudin isn't ideal if you don't already know analysis

But the proof style is really good

If really terse

[gray gazelle]

i would rather recommend tao over trench if you think rudin is tough

But the proof style is really good
yesh

it improved my proof writing skills alot

[civic carbon]

I really like Royden fro a second analysis course

the problem with a first analysis course is that it is hard to make it feel interesting. I do think Abbott does a good job at that

[hearty steppe]

Abbott has been great so far. I’m also going to be using Schroder along with Abbott.

[limpid gazelle]

I love Abbott

Better than Rudin in my opinion

But of course Rudin covers much more

[valid moth]

haveyoureadPugh@limpid gazelle

okay-this-class-is-starting-to-pick-up

well-not-really-yet-but-there's-some-hope

[limpid gazelle]

Bruh

Google “how to change push to talk key” please

[sage python]

I don't like Royden all too much, in general I don't really agree with the whole, do it in R or R^n and then do everything again for general measure spaces

[civic carbon]

I think that approach is very nice for self-teaching. Not what I'd use as a reference.

[flint forge]

yeah dami i have no idea what you are proposing here?

Start with general measure spaces?

[sage python]

Because I don't think things are especially simpler for Lebesgue measure, like it'd be just the same arguments again. So I'd rather just present general measures with Lebesgue as the prototypical example and then delineate to students, hey this property sorta uses the fact that we just have a measure on a sigma-algebra, this property relies on Borel-ness, this is actually specific to R^n, etc

[flint forge]

Oh I see

but I assume this is like

after developing riemannian

[civic carbon]

yeah, Royden picks up the story after Riemann Integration

[sage python]

Most people will have seen calc so they know Riemann on R anyway

[flint forge]

mmm

Not rigorously

[sage python]

And tbh I think introducing Riemann on R^n is pointless

[civic carbon]

"so they will have seen Riemann on R" is incredibly otpimstic.

[flint forge]

Maybe I agree w that

but i dont actually

I think 99% of the intuition comes from riemannian

[quick hornet]

i have never seen a calculus class (that wasnt actually an analysis class) introduce riemann sums properly

[flint forge]

I still think in riemannian term half the timme

uchicago does a good job in the honors sequence

but not otherwise

[quick hornet]

hence the

(that wasnt actually an analysis class)

[flint forge]

i mean

honors calc

is 100% not analysis

[quick hornet]

is it not

[flint forge]

no

its still very handwavy

[quick hornet]

how do you introduce riemann sums while still being handwavy

does it just like

skip all the theorems about sequence convergence?

[flint forge]

Not that hard?

Yeah more or less ig

you can make most oof the args

[quick hornet]

alright fair

[flint forge]

handwavy

like it just follows spivak

and i wouldnt call spivak analysis

[quick hornet]

¯_(ツ)_/¯

whats the minimum to call something "analysis" then

proving heine-borel?

[flint forge]

I would say that its about what is done in class and what is done outside of it

there are not that many proofs outside of class

and the proofs in class are often omitted or replaced with simpler ones

[civic carbon]

I do not typically talk about Riemann sums at all when I introduce integration.

I do talk about them in Calc II when I talk about integral approximation, and make a passing note about this being a way to rigorously define integration.

but "it's the area" is a perfectly cromulent definition.

[quick hornet]

ah hm

[flint forge]

idk about that

[quick hornet]

so it doesnt expect students to do many proofs

[sage python]

Sorry I'm back

[quick hornet]

but does expect them to do riemann sums?

[sage python]

But yeah so honors/Spivak calculus is a fairly rigorous presentation of Riemann integration as I see it

[flint forge]

I think at least the visual of riemannian

[quick hornet]

like formally?

like formally?

rather than the terrible AP calculus approach of just plug and chugging

[civic carbon]

If you're going to be nitpicky about defining what it means to do a definite integral, you need to be nitpicky about what it means to say the area of a circle is pi*r^2.

[flint forge]

is super important

[quick hornet]

ugh sorry

[flint forge]

I don't see whats weird about that nami

i cant send messages

I think at least the visual of riemannian

[quick hornet]

my internet is being fucky

yeah its discord apparently

[flint forge]

😦

i am postponing this convo until discord gets its shit together

[quick hornet]

test?

nope

[flint forge]

i am postponing this convo until discord gets its shit together

[quick hornet]

👀

i think its

alive

now

[broken meadow]

test

hmm

yes

[quick hornet]

ok anyway

im not sure im a purist about like

idk

im curious what you mean by "not many proofs"

how do you go through spivak without doing proofs?

like what other material is there to cover

theres computational stuff sure, but most analysis classes cover a little bit of computation just cause you kinda need to know the vague details of it

[flint forge]

oh man this category video m watching

is so slow

that at 2x speed

im bored

[quick hornet]

is it just differences in the "focus" of the course?

like for context my intro analysis course had like ~30% of the psets/exams being "compute this integral" or "determine whether this series converges"

but the focus was still proofs; proving heine-borel was a homework problem for example

which is why i mentioned it

[flint forge]

yeah i would not consider computations

to be analysis

like that 30% is calculus to me

[quick hornet]

i guess thats fair

and is the honors calc sequence at uchic then like

majority computational stuff

even if it covers the proofs?

[civic carbon]

I think the most analysis-y thing I do in calculus courses is talking about bounding error in integral approximations.

[sage python]

It's more proof-y but I think the distinction between a calculus class and an analysis class is less the rigor and more the scope

[flint forge]

oh man zeta

that was by far my least favorite thing

in calculus

lol

i hated bounding error sm

[civic carbon]

I have jokingly said it should be called Complex Calculus instead of Complex Analysis because all the ugly stuff that makes it Analysis is absent.

[quick hornet]

I think the distinction between a calculus class and an analysis class is less the rigor and more the scope

[flint forge]

i disagree w this

strongly

[quick hornet]

where do you draw the "scope line"

[limpid gazelle]

I hate the error bound for taylor series, so difficult to remember

[quick hornet]

since this seems contrary to max's point

[flint forge]

to me if the difference was scope

[civic carbon]

Pro Tip: Never make students remember anything

[sage python]

Like calculus is a subset of analysis, and a class that zooms entirely on the subset is what I'd call a calculus class, even if it's perfectly rigorous

[flint forge]

calculus just should not exist

i dont think this comparison makes sense dami

unless by subset you mean 'the subset without the rigor'

calc like like a baby pool

[civic carbon]

its' funny that the definition of analytic is as far from what I would consiser analysis as possible.

[flint forge]

ur still in the water

but you dont have to swim

[civic carbon]

LIke, I would say "Calculus is the study of analytic functions" and "Analysis si the study of not necessarily analytic functions"

[sage python]

Nah I think like, the process of learning how to compute derivatives and integrals can be done either just "Here are the rules" or "Let's prove everything"

[quick hornet]

so when do you leave that realm and enter the realm of analysis

[flint forge]

yeah i dont think this is well defined or accurate

calc isnt treated like a subset of anaysis

if it were

the material would be presented similarly

which it isnt

[quick hornet]

like id consider most statements about formal power series to fall more in the "analysis" class

like proving that derivatives actually coincide with how we wnat them to work and whatnot

but these statements are necessary to talk about integration

[flint forge]

if the focus of student work is computations

then i would say you lean calc

if the focus on student work is proofs

then that leans analysis

[quick hornet]

hold on let me give a pset from my intro analysis class

it was actually called "honors calculus"

so im curious how yall would classify it

[civic carbon]

I would say there are plenty of computationally focused analysis courses as well. Like "Fourier Analysis" or "Analytic Number THeory" certainly focus much more on computation than on proofs, but are definitely analysis to me

[civic carbon]

I mean, problem 3 is straight up standard Calc II.

I'd have that on an exam.

[quick hornet]

yeah

like these are "structured" as analysis problems but

they're asking calculus material

[civic carbon]

I would not consider anything involving the definition of continuity to be calculus.

[quick hornet]

well problem 1 isnt really definition of continuity

tbh

its just saying "recall sums and compositions of continuous functions is continuous" and then writing min{f, g} as such

but we of course proved that "recall" statement prior

via the definition

[sage python]

The reason I don't buy that distinction in terms of proofs vs computations is that the latter can have various levels of rigor as well

[civic carbon]

yeah, I'd still never touch anything close to that in my calc courses, but there is a lot of pedagocical philosophy behind these choices.

but I think if you just pretend all real functions are analytic, and occasionally point out that isn't true, you're doing calculus.

[quick hornet]

i suppose thats fair, my answer to problem 3 above took up an entire page

whereas im pretty sure a less rigorous course could do that in

2 lines and an integral calc

[civic carbon]

but I do make them do "proofs" of convergence of improper integrals/series and such. Although they're very structured proofs.

[sage python]

You can focus in class on building up precisely the theory necessary to learn how to properly do the computations, so limits were done with delta-epsilon, FTC was fully proven, etc

And possibly offload some of those proofs to students

[civic carbon]

I very badly want not to talk about the mean value theorem in calculus courses, for example 😛

[quick hornet]

also holy shit my proofs back the day were wordy as hell

[insert limit computation here]

[sage python]

But the idea is still how to compute limits/derivatives/integrals, the question is whether there's rigor or not. But to me each subject cares about its computations somehow, and so a subset of the computations analysis cares about falls under the realm of calculus

[valid moth]

looks like @limpid gazelle's proofs

[civic carbon]

but I suppose I structure my real analysis class a lot like a calculus course. Just wholly focused on why these complicated messes are the right definitions of these things, and not focusing on like, doing the chain rule.

[limpid gazelle]

Bruh

Don’t ping me

[civic carbon]

but that is also sort of the problem with intro analysis, historically. Mathematicians spend 150 years doing calculus before someone was like "hey wait a minute, none of this is rigorous" and then suddenly people were like "we should fix that" and then it turned out all the weird stuff Euler did was right.

[quick hornet]

alright heres another example

would you consider this a "calculus" or "analysis" question?

[civic carbon]

but the things they then went on to do, e.g. especially Fourier Analysis, just cnanot be done with the touchy feely let's just pretend every function is nice kind of thing.

[quick hornet]

its certainly a question on calculus material

[civic carbon]

But those things that you genuinely need this approach for, generally are not in an undergrad analysis course.

[quick hornet]

but i dont think its suitable for a calculus course

[civic carbon]

(Indeed, much to my chagrin, they weren't in my grad analysis course either)

[quick hornet]

even thoiugh its just a very simple integral

[sage python]

Well, I think it's good for a rigorous calculus class, not an engineering one

[quick hornet]

i guess thats fair

[sage python]

It would also belong in an analysis class

[valid moth]

I think the solution is to not teach students analysis at all

nor calculus

[sage python]

Make them all read Rudin themselves and get good

[civic carbon]

Ultimately, I think I buy Stein-Shakarchi's argument that you should teach Fourier Analysis then Complex Analysis and then Real Analysis

[valid moth]

1st year math major curriculum: algebraic [insert various fields].

[civic carbon]

(although it is damn weird)

[flint forge]

what

i disagree w that

so hard

i would literally have left math

lol

[sage python]

He means Real = measure not Rudin

[flint forge]

thats still bad imo

people already have to spend too much time doing analysis

or analysis-adjacent things

[quick hornet]

im curious what you'd think about this question also

its obviously a computation question

but uh

i dont know of a good argument without just

using the rigorous definition of the riemann integral

[civic carbon]

I'm a big believer that before you teach someone ridiculous technology, you have to teach them to understand questions that only that technology can answer.

[I'm looking at you Algebraic Geometry!]

[flint forge]

I think that is like

[sage python]

I think that's a mindset you want to have later on

[flint forge]

a somewhat biased perspective

[sage python]

Like once you're getting into research math it's like

[flint forge]

based on your learning style

[tight crag]

I believe that too actually

[flint forge]

also more importantly

[sage python]

Alright you need to approach math with a certain skepticism as to its usefulness

[flint forge]

no one wants to spend this much time in undergrad on analysis

well some people do

but the majority want to like

have time to learn something else lol

im okay with swapping complex and real but i think its unnecessary

at the end of the day

real analysis sint that bad

and i dont know if i buy the argument that it needs even more prereqs

[sage python]

But when you're learning the basics of math I think efficiency is more of a priority

[civic carbon]

I'm a very big believer in Conway's quote to the effect of "You teach people by asking them interesting questions they want to know the answer to"

[flint forge]

That only works with classes that are optional

[civic carbon]

I think the only subject where this is genuinely difficult to do is linear algebra.

[flint forge]

You can't be sure that they will be interested in questions you are interested in

like i have yet to hear a single analysis question

that i care about at all

but i survived it

and its whatever

[sage python]

What I kinda think should be done in analysis is that you do calculus and analysis in 2 years with linear algebra interspersed, and that the division of content should be way more streamlined

[flint forge]

like ideally you would teach all courses in 3 passes

like that

but its just not time efficient

linear algebra should just be calc2 concurrent

easy

again any suggestion that requires even more time be dedicated to analysis

seems inherently silly to me

[sage python]

Basically I think they should compress the 160s\multi into 2 quarters and have third quarter be linear algebra

[pulsar aurora]

@civic carbon Personally, where linear algebra shines for me is the practical problems it can solve. That is what I find interest about it... not necessarily the theory, unless the theory teaches me more ways to solve problems. 😛 It's like learning a power tool. You don't want to sit there learning how to use it, but to actually use it and build shit.

[flint forge]

Just do calc 2 and linear at the same time

[civic carbon]

I don't necessarily think more time needs to be put to analysis. I think people need to deglorify the idea that math students need to sit through a proof of everything. They don't.

[flint forge]

Oh sure

I agree with that

[sage python]

Or maybe replace the multi part with some linear algebra, and then some more advanced LA topics like multilinear stuff can be done along with differential forms

[flint forge]

I disagree that your early classes should have materal you can't prove however

Like

maybe sometimes

but in general I think you should only omit proofs if a student could read them on their own

[civic carbon]

I'm very pro-linear algebra to be clear. I just don't think you can put the interesting stuff about it [Maps induced by Frobenius on Etale Cohomology] before the boring part [This is a matrix. This is an eigen value..]

[flint forge]

i mean linalg is just boring imo

like its an amazing toolkit

but most toolkits aren't inherently exciting

[civic carbon]

(I may have a very biased definition of what part of linear algebra is interesting)

[flint forge]

I mean the interesting parts

are applications to other fields

[sage python]

Eh stuff like Cayley-Hamilton, spectral theorem especially, SVD and low rank approximations to matrices are all pretty cool to me

[flint forge]

and arguably numerical stuff

but the later is an elective

and you need other fields for the former

i dont see how Cayley hamilton is cool

[civic carbon]

this is why a first linear algebra cours should assum the base field is F_2, so there are no rounding errors to worry about

[flint forge]

without algebraic context

and even then i think its whatever

lmao zeta

im unironically here w that

F_2 is a great pedagogical tool

I want to give a completely visual talk on F_2 simplicial homology

[civic carbon]

I think once has a strong understanding of abstract algebra, the minimal poly/Cayley Hamilton stuff gets interesting.

[quick hornet]

F_2 is too rigid though

[civic carbon]

I mean, everyone loves the Fano plane

[flint forge]

i dont

[civic carbon]

the definition of an eigenvector over F_2 is very nice.

[quick hornet]

too nice

it doesnt give any linear algebraic insight, it gives insight into how F_2 works

[flint forge]

F_2 is the perfect field

[quick hornet]

i wouldnt mind working over F_p though

[sage python]

Max your interests are bad anyway lol

[flint forge]

i just don't get excited by basic linalg lmao

[sage python]

They're not the same as mine

[quick hornet]

when i TA'd lin alg i avoided R and C like the plague

Q is fine though

[sage python]

Which is extremely questionable

[quick hornet]

as are F_p

[civic carbon]

oh yeah, I like in grad courses you can do linear algebra over Q or Z and then I'm happy

[sage python]

The typical char 0 field is Q_p don't @ me

[quick hornet]

over Z

if only

[valid moth]

lol

[flint forge]

linalg over Z >>>>

[civic carbon]

linear algebra over Z is my life sadly

[sage python]

Lol apparently Laci's wombo combo class did a bunch of LA over Z

[flint forge]

i mean

anyone who does homology

does a lot of linalg over Z

[sage python]

No I mean, he taught the basics of it to people lmao

Proved structure theorem I'm p sure

Which he didn't do my year

[quick hornet]

working over fields is for CHUMPS

[civic carbon]

yeah, exactly Max. Or, secretly the same thing, anything with Elliptic Curves

[sage python]

Each time he teaches the class it's very different lol

[quick hornet]

i work exclusively over Z, Z/6Z, and F_1

[civic carbon]

you immediately work with the tensor with Q, but you're always keeping track of how this free Z module sits inside it, and getting confused

[flint forge]

my favorite game n learning math

"is this analogous to something i know or just notationally similar"

currently todays episode is about a tensor hom adjunction

[quick hornet]

imagine having pattern recognition abilities

[flint forge]

where tensor isnt actually tensor

[quick hornet]

couldnt be me

[flint forge]

and hom isnt actually hom

[quick hornet]

also i feel like this convo has strayed a bit from #book-recommendations

[flint forge]

i love rudin

anyway back to what i was saying

[quick hornet]

ok thanks

[sage python]

Lol yeah I think it got to this point because of Royden?

[flint forge]

we should train an ML algo to recognize book discussion

so it can auto-mod

[smoky surge]

not sure if this belongs here but does any one have a good economics text book for someone who knows noting aobut economics and doesnt like math lol my friend wants to learn a bit and she a self proclaimed 'not a math person' so idk if anyone has one they like

[pulsar aurora]

A lot of economics relies on understand math though. 😛 Just in my intro Macro, we did a lot of graph and equation manipulations.

That said, there are a lot of non-math stuff that relates more to local/national law and government functions.

So, maybe any economic books will do, but she'll have to miss key-concepts by skipping the math.

[flint forge]

Freakonomics is fun

I wouldn't suggest reading 'serious' economics without some understanding of math

But Adam Smith -> Friedman -> Keynes isn't a terrible short-summary

and then you'd want to read some more recent stuff

Non-mathematical economics writing has a bad habit of applying mathematical-reasoning to situations without discussing whether those models are being applied appropriately which is why math understanding helps

[smoky surge]

yea i know thats where i was struggling to find something that isnt too math heavy

[flint forge]

Are they interesting in something specific?

[smoky surge]

just in learning a bit

when i say they know nothing i mean nothing Im looking for like a basic intro to supply demand/freemarkets that kind of thing

[pulsar aurora]

You cannot understand or do any of that without math.

I mean, at the most basic, you're gonna be looking at a graph

[civic carbon]

cold take: knowing a bunch of math really doesn't much help with economics. At the higher levels, you'll want to have an understanding of partial derivatives.

[pulsar aurora]

I'm not saying they need to know math, but that math is involved

[civic carbon]

But you definitely need to be able to look at graphs.

[pulsar aurora]

The economics book my class used taught us the sheer-basic math to understand it

[civic carbon]

oh yeah, I wasn't intending to contradict you, I was mostly just saying, the non-zero amount of math you need to get on board is also enough to get really far.

[pulsar aurora]

Sure, there are some concepts in the macroecon text that had 0-math. It was almost Law-ish in the sense that it was discussing the role of the Fed and who has power and such

Or maybe civics

[civic carbon]

yeah, and of course if you go into deep stuff you get into all kinds of super hard math, e.g. if you want to understand DeBreu (which is one of my favorites).

[pulsar aurora]

Economics strengthened in my interest in mathematics. 😛

[civic carbon]

I was a math/econ double major in undergrad and took a lto of grad econ classes for fun. It's sweet stuff.

it was pretty ahrd for me to pick which to go to grad school for.

[flint forge]

uh i disagree pretty strongly?

Unless you're counting legrange optimization

and like stochastic models

etc

Like my real point is that you need to understand why the models are bad

[civic carbon]

I think I'd have made a better econ researcher than math researcher, but I think teaching econ would be much less fun.

[flint forge]

which you need a deep understanding for

[civic carbon]

well, if you're a researcher yeah you get into all those things. But you can do multiple semesters of econ without any of that.

[flint forge]

Yeah but if you want to read books to understand econ it might be legitimatley counterproductive to read without being able to criticize

[smoky surge]

I mean like reading heavy math theories

[flint forge]

like the literature is very persuasive to non-experts despite being often flawed

[smoky surge]

Graphs are fine

[flint forge]

i mean friedman sounded reasonable to me on a first read

[civic carbon]

though I know plenty of PhD economists who cannot take derivatives to save their lives.

I think econ writ large has a big problem with too readily accepting math-y journal articles because they're afraid it will make them look dumb if they don't.

[flint forge]

i agree

i also think they really abuse a lot of the math they use in trynig to take it too far

like if your foundational assumptions are shaky, taking the math farther makes you less and less accurate

and if you use that to guide polcy

you get things like the IMF screwups

although this might be more ideological than mathematical

yeah my real issue w economics is that people are too ready to take models with many assumptions

and just not verify those assumptions before using results

[civic carbon]

yeah I'm not at all interested in economic modeling, and economists I know do not take that very seriously. The result of a good economic model should be that the effect of a policy has two counterveiling forces, and it is impossible to determine in general which is stronger, and hence you can't even determine the sign of the thing you're modeling.

[flint forge]

Yeah i agree w that

[civic carbon]

and for policy, that's incredibly useful. You just have to make sure you don't trust it too much.

[smoky surge]

Though I do think as we get more and more data I’d bet our economic models get better

[civic carbon]

Though I've never met an economist who thought they could confidently say anything about anything, so I have not observed the overconfidence in economics you perceive

[smoky surge]

Way less assumptions

[civic carbon]

I don't think that is really the point of economics.

I mean, there is the whole empirical/statistical side of econ, but I can't run away from that fast enough 😛

[smoky surge]

What do you think the point is

[flint forge]

I'm not entirely sure what the point of economics is tbh

[smoky surge]

It’s just a really broad field

[flint forge]

the empirical side at least seems useful to me

but pure-math-econ just sounds like math without freedom lmao

[smoky surge]

I think it’s good for influencing public policy

[flint forge]

no

see

thats what im saying lol

its terrible for that

[civic carbon]

For me, the cycle of economics is taht you observe some behavior that contradicts the very basic model. So you build a model that gives you that behavior, and go "aha, now it makes sense"

[flint forge]

yeah but like

that seems

deeply unsatisfying since your predictions aren't reliable

[smoky surge]

I don’t necessarily mean for like monetary policy

[flint forge]

Like research-based econ is far more fruitful for policy

[smoky surge]

I’m talking about things like housing and welfare as well

[flint forge]

than bad models

housing models dont work

nor do welfare models lol

[civic carbon]

my degree is actually in economics of public policy haha

but I'd say that understanding the forces let's you understand why your policy idea is terrible.

[flint forge]

but you can't justify that one is good

[civic carbon]

and leads to a more nuanced understanding of policy.

[flint forge]

like maybe you can say the math suggests something is good

but i am inherently skeptical with math is the main argument in favor of a policy

[smoky surge]

What do you prefer

[civic carbon]

well, it's not an economists job to write policy. It's an economists job to say "You have decided you want to do X. If you do Y, then we think it will have effect X, but it will also have effect Z"

but if an economist is using math in an explanation of public policy, they're doomed, because public policy goes trhough politicians

[flint forge]

Yeah you can use the math as a rule of thumb

but I think anything hard to do with math

or anything where the math is kind of a close call

is where you have instant issues

But even those rules of thumb exist bc they've worked historically

like one of the fundamental econ 101 results

[civic carbon]

e.g. "would a $25 minumum wage be good" is not a well formed question, but an economist could talk a lot about how it would impact a lot of different groups, what it would do the macroeconomy, to trade, etc etc. And maybe, as is often the case, the net effect of a bunch of contradictory forces would be unclear.

[flint forge]

is that profits = 0 in the long run

I agree w that zeta

i just think people often try to do that last step

maybe not the real economists

but their readers

[smoky surge]

Yea when I think what economics do is just to inform what we believe will happen it’s not an exact science it’s not even close

But it still helps to inform

[civic carbon]

oh yeah, my understanding is that two ifferent groups, one liberal and one conservative, each bribed people to do a study to get opposite conclusions about the impact of the $15 minimum wage in Seattle 😛

[smoky surge]

Yea but that’s an issue in nearly all fields

[civic carbon]

Economics is wrought with implicit bias. E.g. if you devote your life to studying environmental economics, it is unlikely you are neutral on the environment.

[smoky surge]

Part of the issue too is it’s so easy to make the data say whatever you want

But I’d still say it’s our best guess

[flint forge]

That seems

contradictory lol

[civic carbon]

yeah, I think Max and I are basically saying that the empirical side is a mess, but the theoretical sidei s helpful

[smoky surge]

I thought max said the opposite

Like research-based econ is far more fruitful for policy
@flint forge

Did I misinterpret that

[flint forge]

I think that if you actually dig into it the research is generally more conclusive than not

[smoky surge]

I read that as research on the current environment

[flint forge]

Like we know a lot of things from historical data

its a mess

but we have a few guiding principles well understood

I don't really trust predictions of models

they can be helpful if and only if you understand the caveats

often times people here 'the math says .... ' without understanding the limitations of the approach

and thats where you get issues

[smoky surge]

Ok so models can be helpful we have to be careful

And most people don’t understand the math well enough to get those limitations

Is what you are saying

[civic carbon]

I think it is also slightly misleading that there are two kinds of modeling... like the simple toy models vs economic forecasting

[smoky surge]

So you don’t think economics is helpful for trying to help with affordable housing

Either to identity issues or suggest solutions?

[civic carbon]

I think the toy models are incredibly useful for understanding how complex systems work and I think by and large that is the skill most economists possess. Most of that does not require much math.

For me, as soon as an economist brings data into something and does any analysis on it to try and calcuate something from a toy model, e.g. "I calculated the deadweight loss due to microsoft's monopoly on web browswers 1997-2003" I don't buy it.

[hearty steppe]

I think it’s partial. Cuz economics doesn’t understand other disciplines? It just tries to assign value?

Like an economist is not a chemist

[flint forge]

Oh I don't mean that side of empirical

I mean the side of like

comparing economic policies in different places

and trying to figure out broad strokes effects

[hearty steppe]

Way off topic tho I think lol

[civic carbon]

yeah, that can sometimes be useful, although it can be incredibly difficult. You really need randomized experiments like they do a lot in development economics.

[flint forge]

Yeah its hard

but the results are in my opinion more valuable than models

when we do get them

[civic carbon]

I think the two are often well synthesized eventually, .e.g "the subsitution effect is usually stronger than the income effect, all else being equal"

[smoky surge]

Ok yea then I think we are in agreement where I see the big value of Econ is for like affordable housing wage growth etc

But broad stroke economics is super complex

There is just so much noise in the data

[flint forge]

Depends I think

Often times economics models don't capture enough

I don't think I agree on housing

[civic carbon]

and some things are just hard to measure. Like really really important questions like "what is the optimal drug patent length" are just unmeasurable.

[flint forge]

The real world is too pathological for clean models to predict it

Like models say that rent control is a terrible idea

but there are plenty of historical reasons to think it might have a purpose

same for protectionism (in developing nations)

[civic carbon]

the problems with rent control are more sociological than economical imo

[flint forge]

Yes

But economists are in my opinion too ready to ignore sociological factors

[smoky surge]

Wait I agree there

[flint forge]

Like lots of neoliberals only take economic analysis into their opinions

[civic carbon]

I've just never known an economist like you are describing

[smoky surge]

Economic models have to take in sociological factors

[flint forge]

I think I might be using a larger definition of economist than you

but I mean milton friedman is a key example

[smoky surge]

That sounds like you are describing a pure libertarian

[flint forge]

No

not at all lol

anyway I have to read before a meeting

[smoky surge]

Good luck on your meeting

[civic carbon]

I'm going to go and get my run for the day in

[gray gazelle]

does anyone know of a textbook that might cover the following material?

This course will develop advanced methods in linear algebra and introduce the theory of optimization. On the linear algebra side, we will study important matrix factorizations (e.g. LU, QR, SVD), matrix approximations (both deterministic and randomized), convergence of iterative methods, and spectral theorems. On the optimization side, we will introduce the finite element method, linear programming, gradient methods, and basic convex optimization. The course will be focused on fundamental theory, but appropriate illustrative applications may be chosen by the instructor.

my uni is introducing this (grad-level) course next semester and im interested, but i probably won't be able to take it / fit it into my timetable

so i'd like to have something to read if i can't get into it

it's a new course so i haven't been able to find anything on it

there's nothing on the prof's page either

[peak trout]

How can i get

textbook

I need ICE-EM Mathematics 8 3ed

anyone know how to find a pdf file

[gray gazelle]

i googled "ICE-EM Mathematics 8 pdf" and found some sketchy links

if you wanna risk having russian hackers on your computer you can go click those

[peak trout]

rip

[peak trout]

holyt shit

Just found it

actual

[gray gazelle]

[kind thistle]

@peak trout I found ICE-EM Mathematics 10, it is good?

[peak trout]

Nah its fine

I found it and i needed 8

cause 10 is for different grtade

sorrty

[kind thistle]

ok

[gray gazelle]

I am assuming i can ask about intro level books here ?
If so , Any intro level book recommendation to learn real analysis ? Which have decent quantity of problems (not over too many like Bartle- Shelbert)

[gray gazelle]

@gray gazelle there was a prolonged discussion about this earlier which might be helpful

Just search real analysis in this channel

alright

I am guessing this one https://discordapp.com/channels/268882317391429632/716264872018706443/728133996684509225

@gray gazelle

[gray gazelle]

Ye

[prime oak]

Intro to game theory textbooks?

[kind thistle]

Intro to convex optimization textbooks?

[gray gazelle]

❓

[white cradle]

???

[molten wave]

@urban scaffold this is not your advertisement outlet

[urban scaffold]

It’s a call for papers....I figured some people here might want to publish essays

No?

[prime oak]

spam Intro to <X> textbook? here

[buoyant spire]

are there any free open access math journals?

and are there any that authors don't need to pay in order to submit to them?

[gray gazelle]

Arxiv?

[gray gazelle]

that's not a journal

[urban scaffold]

Yeah, my call for papers doesn’t require you to pay

SUNY is publishing it

You’re all more than welcome to submit

[marble solar]

There are open access journals, some big publishers have an option to submit papers through an open access channel

[vague pelican]

Do open access journals even get any attention

[marble solar]

Ehhh not the ones that I've looked at

Elsevier has some open access options

When my advisor and I submitted to the arxiv I got flooded by open access options in my email

[gray gazelle]

is there a mathematics practice book that covers all of this:
Lesson 1 - Logic
Lesson 2 - Set Theory
Lesson 3 - Abstract Algebra
Lesson 4 - Number Theory
Lesson 5 - Real Analysis
Lesson 6 - Topology
Lesson 7 - Complex Analysis
Lesson 8 - Linear Algebra

[main flax]

are you looking for a 3 thousand pages + book?

[gray gazelle]

uhm

yes and no?

It doesn't really matter for me, how many pages there are

[main flax]

i'm trying to say that such a book probably doesn't exist, unless all topics are covered with little to no detail at all

[radiant crown]

What kind of book is a "practice book"?

[gray gazelle]

maybe, I should look into one detailed practice book, that covers one topic

What kind of book is a "practice book"?
w8

sorry, idk ):

maybe a book consisting mostly of exercises?

yes

with practice I mean exercises

i dont know of any such books covering such a breadth of topics, but you can probably compile exercise books from each topic

I found one http://disi.unitn.it/~ldkr/ml2014/ExercisesBooklet.pdf

for "logic"

I over thought this about

I can just search on google, just for exercises for a specific topic 🤦‍♂️

nice, now I know how to work,
thank you guys for giving me ideas on how to "practice" or "exercise" per topic.

[dim forge]

There's a book "Abels Theorem in Problems and Solutions" which is based on some lectures by V.I. Arnold. It's aim is to take a student from nothing at all to proving the impossibility of the quintic formula. Probably the closest thing I know of.

[civic carbon]

there's that All the Math you Need for Graduate school book

[although you do not need logic or set theory haha]

[hearty steppe]

More like all the math you need for non-math students

[raw herald]

gre math prep books maybe lol

[jade anvil]

Are there recommended books on math history? I'd like to know how different math concept were developed.

Would be great if the book dived in deep with the mathematics too, not just an overview.

[quick hornet]

pretty sure Stillwell is the standard broad-overview text

Stillwell's Mathematics and its History that is

but it depends on what you mean by "dived in deep with the mathematics"; there will be no replacement for an actual textbook on the subject in question on that end

[jade anvil]

well, for most part, i felt like math textbook introduced a topic generally from modern people pov, but i'd like to understand how the pioneers developed certain concept in math

let's say linear algebra... why determinant?

i want to know who came up the idea of determinant and why does it work

what's their thought process

same could be said about imaginary number, especially euler formula

for most part when I read math books, "it just works" is the only thing i got

[gray gazelle]

I hate it when they either don’t describe it enough to derive a proof or neglect to prove it... whatever theorem that may be

[slender sphinx]

Unironically look at the history section of these concepts on Wikipedia and check the sources they reference

[gray gazelle]

anyways

I found some good books by Apostol on calculus, and I want to know whether they are a good place to start for a beginner.

[quick hornet]

i dont think stillwell spends much time on the specific history of the determinant

but he certainly spends a great deal of time on the imaginary/complex numbers

as in, multiple chapters

[jade anvil]

maybe is there like specific history book for each topic?

[gray gazelle]

That’s a lot of math history... could do some digging and see but idk

[quick hornet]

there are, but such sources generally assume you already know the theory of the field in question

[gray gazelle]

hMmm

anyone mind answering my question? Is apostol’s calculus vol. 1 a good place to start for beginners?

[quick hornet]

anyway this article might be of note if youre interested in the determinant specifically https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/

[slender sphinx]

@gray gazelle it's fine I used it

[quick hornet]

there's probably more specific textbook recommendations you could find if you trawl stackexchange and whatnot

[gray gazelle]

k thanks

Perhaps

[quick hornet]

its worth noting that the concept of a determinant predates the notion of a matrix

though the term "determinant" wasnt used till later

rather, statements that today would be phrased in terms of the determinant were given as results on sums and products of the coefficients of a system of linear equations

this is, naturally, a much more clunky way to communicate these ideas

the fact that this idea - we can determine solvability of systems via computing some number based on sums of combinatorial products of their determinants - behaves so "nicely" with respect to matrix multiplication [in that det(AB) = det(A)det(B)] is a property that was only realized later

specifically by cauchy in 1812

again though, this actually predates the concept of matrices as we know them

cauchy would not have written this as AB or whatever - matrix multiplication wasn't a thing - he actually again talked about it in terms of sums and products of coefficients, in what was no doubt a very tedious and painful proof relative to modern ones (which are like the trivial case of noninvertibility + like 5 lines to cover the case where A, B are both invertible)

[indeed from a certain perspective, we define matrix multiplication as we do because it makes the above statement work, as well as being congruent with how we want to present systems Ax = b]

[smoky surge]

how bad would it be to skip the exercises regarding products of vector spaces? It seems kinda boring in LADR?
i also havent seen products of vector spaces that i can remember in a more computational setting

[flint forge]

You should do them

[valid moth]

can you give an example

[smoky surge]

😦 ok

[marble solar]

@jade anvil Boyer's history of calculus and it's ideas is an excellent read

[gray gazelle]

eavesdropping on book convos

[marble solar]

It's not eavesdropping if it's freely available in the chat

[gray gazelle]

that’s true

[marble solar]

@gray gazelle Do you like Stein's Functional?

I've never learned functional properly

Yeah

I've read the first 3 extensively

Doing almost all the exercises in 1, 2, and 3

I've been more or less indoctrinated by S&S

So I don't know if I"m just brainwashed or it's quality stuff

Yeah I've been reading S&S since 2017, and they were assigned at UCLA, and my MS at CSULB

my MS qual in analysis was on volume 3, mainly chapters 1 & 2

Yeah

MS qual was only first semester. Topics in Real covered 3, 4, 6, and 7

We skipped chapter 5 since that's sobolev spaces

Yeah, their treament of L^p is strange

In fourier and real they only do L^1 and L^2

Yeah the L^p is for the last one

That was probably extra material, supplemented rudin or folland

Mainly towards PDEs

and Sobolev Type things

Not interested in weird topology stuff

I can DM you the arxiv thing that's up. I don't wanna post it here since I don't wanna dox myself

msg'd

So any kind of FA geared toward that kind of harmonic analysis/PDE type stuff

Both the prof. and I have never learned PDEs