book-recommendations

[gray gazelle]

looks correct

[mossy flume]

@earnest gazelle I don't do every single problem out of textbooks

But also I'm not self studying so idk if you're self studying maybe you should be doing every problem

But also breaks are underrated

Come back to that section the next day

[gray gazelle]

do exercises

[willow adder]

b-ok.cc

[near hare]

Did anybody study Understanding Analysis 2nd edition?

i cannot find any solution manual of the exercises in this book

[calm crane]

have faith in your solutions

[silver herald]

Until they are wrong

[hollow current]

just define your solution to be correct

[hasty turret]

My solutions are never wrong

[karmic thorn]

don't write solutions and they'll be vacuously correct

[hollow current]

don't define incorrectness

[prisma snow]

All my solutions are always correct

How can it be a solution if it's wrong?

[karmic thorn]

Solutions can be temporary, or work in some circumstances and fail in others.

[silver herald]

Unironically the correct opinion

[prisma snow]

Don't force your morality on us.

[silk quartz]

Forcing a morality on someone is morally wrong.

[carmine geyser]

Godel's incompleteness theorem in a presentation everyone can understand

(I don't seriously claim this is actually a form of Godel's incompleteness theorem)

[silver herald]

LOL

[sudden granite]

Ohhh, I wrote that days ago though

“Days ago”

[cobalt arch]

Any books that show the interconnectedness of mathematical branches?

[graceful bridge]

I don't think there is any book that is dedicated to showing interconnectedness of many different branches. But there certainly are many subjects that applies one branch of mathematics to a completely different one. You can usually see it in the subjects name, for instance: algebraic topology = applies algebra to topology

[cobalt arch]

Hm that is unlucky

Maybe a historical book would fit the description?

[graceful bridge]

But if there is such a book, I would be very interested myself

[cobalt arch]

Maybe category theory could come close to that

[graceful bridge]

Yes, this is probably true

I guess it is a way of formalizing connections between different fields of math, but I don't know if it always works, I don't know a lot of cat theory

[obsidian valley]

This question is probably too vague and general to be answered effectively

[hollow current]

hi jesse

[obsidian valley]

You can find books that apply [field a] to [field b], for sure.

hi vimes

[cobalt arch]

I guess this is inherent to the subject in question itself and not a fault on my part

Thank you for the input though

[obsidian valley]

Yes

[karmic thorn]

I did suggest Mathematics and its History by Stillwell the last time you asked. Did you check it out?

[cobalt arch]

No haha:). I will check it out now though.

[graceful bridge]

There seems to be a lot of subjects that can be applied to combinatorics: https://en.wikipedia.org/wiki/Combinatorics Look at the subfields

There is even smth called topological combinatorics

[cobalt arch]

That is interesting

[obsidian valley]

everything can be applied to something else

just take a few math fields

[cobalt arch]

I found some books about the history of math so I will use those.

[obsidian valley]

mash them together and google them

[graceful bridge]

In light of that, it's too big of a task to cover all connections in a single book. And it's also a bit unclear what would be the target audience

Terence Tao actually said: "I make my living by understanding one field X and apply it to a field Y". https://www.youtube.com/watch?v=MXJ-zpJeY3E

[undone badger]

are there books that introduce how to approach math? (how to think about math) More of a casual read than something heavy into theory 😓

actually found some in the books section ^_^

[sudden granite]

Fantastic.

[karmic thorn]

Is Topology of Numbers by Hatcher a good starting point for learning elementary number theory?

[stray veldt]

seems very nonstandard

and it only does quadratic forms?

which is cool, but there is a lot more stuff to NT

[karmic thorn]

Yeah, it covers only quadratic forms.

I'll probably stick to Burton, then. Would look into it when I have to cover quadratic forms.

[stray veldt]

it's not like you ever have to do quadratic forms

they have historically been studied a lot and serve as motivation for a lot of modern stuff

i guess my take is just study quadratic fields

[karmic thorn]

The elementary number theory class this sem would be covering all this, so apparently quadratic forms are not needed.

[karmic thorn]

I see.

[stray veldt]

this is more standard elementary nt

unit III at least

kinda basic

unit iv then has some analysis stuff

[karmic thorn]

Yeah, I think Burton's book should be more than enough.

[stray veldt]

i think its more interesting (and worthwhile) to study quadratic forms from a higher point of view

[karmic thorn]

I'm guessing they'll be skipping proofs at least.

[stray veldt]

by using http://www.math.toronto.edu/~ila/Cox-Primes_of_the_form_x2+ny2.pdf

[karmic thorn]

This seems to have abstract algebra as a pre-req.

[stray veldt]

yeah, at some point you will need that anyway

quadratic forms are related to quadratic number fields, which are finite field extensions of Q

[karmic thorn]

Hmmm, so add a finite number of elements to Q to give it some kind of closure?

[stray veldt]

by related i mean

there is a literal isomorphism

yeah

like Q[i]

thats the prototype i guess

[karmic thorn]

Q[i] is Q+sqrt(-1)?

[stray veldt]

Q union sqrt(-1)

and then add enough elements so its still a field

[karmic thorn]

I meant that lol

Hnmmmmm

[gray gazelle]

Which book should i use for introducty differential eq.?

[stray veldt]

historically a lot of this NT stuff was the motivation to develop algebra

but i guess this shouldnt be in books channel

[karmic thorn]

Lol

[gray gazelle]

any1

[sudden granite]

👉👈

[sturdy relic]

Apparently G.F. Simmons Differential Equations with Applications and Historical Notes is good. If you google it you can download a pdf

Don't trust me though, I haven't read it

[gray gazelle]

Thank you moontiger95!

[timber mesa]

I've sort-of read it (when I was a TA for diffeq actually ) and it's pretty good even if a bit dated.

another (and the most typically used one I think) is Dennis Zill's but honestly at intro level they're all pretty similar

[livid ermine]

are you using burton?

david m burton was the book we used, and we covered almost exactly this

[timber mesa]

seems like the first 9 chapters of Burton

[karmic thorn]

Yes, I'll be using Burton.

[karmic thorn]

Aah, seems to cover way more than my curriculum. Neat.

[gritty egret]

AOPS

[gray gazelle]

AoPS

[hollow current]

aoPS

[hasty turret]

aops

[sudden granite]

aoPs

[karmic thorn]

Aops

[gray gazelle]

[crystal kraken]

[hollow current]

AopS

[hybrid dawn]

Aops?

[gray gazelle]

Aops indeed

[crystal kraken]

aOpS

[sudden granite]

aopS

_ _

[river birch]

AoPs

[past yew]

aopS?

[sudden granite]

I said that already.

AOPs

[gray gazelle]

??

is aops what nerds spam instead of f?

[sudden granite]

[ripe granite]

are you the real Jim Simons?

[tight crag]

If he was he would know the answer to his question

[gray gazelle]

damn : (

that hurt

[gusty socket]

guys

I NEED help with math

someone help

[quick hornet]

#❓how-to-get-help .

[gray gazelle]

[cobalt arch]

any books on financial mathematics?

also do you know what prerequisites such a book has?

[dawn maple]

That’s an AoPs moment right there

[graceful bridge]

Maybe you could give this one a try: https://www.springer.com/gp/book/9781461435815 I have not read any of it myself, but the author is a mathematician and decent textbook writer from what I know

[cobalt arch]

thank you laffen I will check it out

[graceful bridge]

Cool, let me know what you think of it

[gray gazelle]

a few years ago I was googling for random things connected with glibc math implementation, various gnu projects such as mpfr, mpc etc., so I was trying to find a search query for google to give me a list of books on this topic, and I remember that I found a book which had something like "algorithms for arbitrary precision (or multiple-precision) implementation", which I scrolled through with horror and didn't save it somewhere. now I want to find it again, but for the last 30 minutes I'm really struggling to do so. I think it had like actual pseudocode implementations of a lot of algorithms and concepts. I'm not sure whether it was inria or springer, but it wasn't a free book. but that was definitely the best one on the topic. perhaps somebody knows what I'm talking about or is excellent at google-fu? I really browsed all these projects and looked up the literature they are referring to, it's not there as far as I'm aware. it was rather new back then, a few years ago

Handbook of floating-point arithmetic looks very close to what I'm looking for, maybe it was that book, or maybe not. I feel like the one I meant has only one author, but not sure

[unkempt grove]

i have a pdf of apostol and its chock full of formatting errors, should i still read it?

[gray gazelle]

ew

[unkempt grove]

libgen gave me this unfortunately

if you know of a better pdf, i'd really appreciate it

[storm sleet]

my favorite one is poor formatting in Dover ePubs

Where any non-standard math font is terrible

[obsidian valley]

[novel iris]

what's a book that has a nice, pedagogical discussion of the construction of R via cauchy sequences?

[gray gazelle]

pugh does that in chapter 2

and pugh is nice, so maybe that's nice

[novel iris]

sounds good, ty!

[unkempt grove]

nvm archive.org has actual book scans up to borrow

[willow adder]

epic

[sudden granite]

@limber hollow

[limber hollow]

Thanks!

[gray gazelle]

Abyone here used "A First Course in Calculus" by Lang?

[gray gazelle]

I tried and it was pretty difficult. Didn't really feel like a first course. The way my ap calc teacher taught it was way easier and simpler

@gray gazelle

[sudden granite]

Stewart's Calculus ftw

[gray gazelle]

Thomas', not Stewart's

[sudden granite]

😕

[gray gazelle]

Lang's books seem to be harder, yeah.

Maybe less suited for applications compared to Thomas, more suited as a stepping stone to advanced calc.

I'm working slowly through the exercises in Basic Mathematics and they're not easy.

[vapid scroll]

Is it a bad idea to try and read and do exercises from the spanish version of a book because you can't find the pdf for the english version of a book you need for class?

im not really fluent but lots of the words look similar

they have the correct number of exercises, but i am not sure if they are the right ones.

[prisma snow]

@vapid scroll what book?

[vapid scroll]

Elementary Classical Analysis

[vapid scroll]

So I can't find the 98 reprint and it looks like im going to use the spanish version for now 🙂

It is very close to googlebooks' 98 scan.

and the spanish doesnt look hard

[gray gazelle]

by marsden? it is in on libgen

ah, 98 reprint, i missed that

[halcyon hornet]

Hi.

I am in class 7 and I need some recommendations.
I really want to be great at math and can give as much efforts as needed, and also really win the IMO and such.
So I mainly need help with AoPs Books Recommendation for now(I am studying AoPs Prealgebra now, in like chapter 10).

Do I really need to get and study all the books(all 12), or will it be really great only with the 2 volumes(3 with that extra 1, so all 3) of the competition math series(provided that I have studied prerequisites already).

And I live in India.

Your responses are really appreciated, Thank You very much.

[karmic thorn]

I'd suggest you to tackle one book at a time at the beginning, so maybe start with their prealgebra/algebra book.

[halcyon hornet]

Doing the prealgebra one.

[karmic thorn]

Alright, follow it up with their algebra book. Then you could digress to geometry and number theory.

[halcyon hornet]

So I need to study all of them?

The price is the real problem.

Or else I would love to study them all.

[gray gazelle]

libgen

[karmic thorn]

You can grab some PDFs online, but AoPS books are signficantly harder to find.

[halcyon hornet]

I will buy the 2 Volumes of the Competition Math anyway though.

[halcyon hornet]

It's not good enough.
Most don't have answers, and many have many parts omitted.

[karmic thorn]

Complement the AoPS books with their website, which is brimming with lots of relevant problems. Questions asked in previous olympiads should be useful as well.

[halcyon hornet]

Exactly, I have hunted a lot for them.

[gray gazelle]

if you can't find them, make them

[halcyon hornet]

?

What do you mean.

[gray gazelle]

I meant what I wrote.

[halcyon hornet]

How do I make them?

[karmic thorn]

Write a Diff Geo book to ace the olympiads

[halcyon hornet]

Wow.

[karmic thorn]

Regardless, AoPS is not the only place to practice for olympiads.

[halcyon hornet]

Can you please mention others.

[karmic thorn]

If I remember correctly, World Scientific has its own olympiad math series which is priced more reasonably.

I suppose you could get more help on the math olympiad server.

[halcyon hornet]

How?

[halcyon hornet]

What is that?

[karmic thorn]

#old-network has the invite to a math olympiad server.

[karmic thorn]

World Scientific is a publisher. 😅

[halcyon hornet]

Oh yeah I am already there.

[karmic thorn]

I guess you should be able to find some resources there, or maybe a list of book recommendations relevant for IMO.

[cobalt arch]

is lang's book a first course in calculus harder than spivak?

[gray gazelle]

Yea, I'd only recommend it if you're really committed

[cobalt arch]

so which book is more rigorous, lang or spivak?

anyone?

[warped cedar]

spivak

[cobalt arch]

Has anyone read Arthur Engel's Problem-solving Strategies if so is it recommended for learning how to prove?

[waxen elbow]

hey, what would you recommand for a first exposure to linear algebra ? my brother want a complete course, i only got Roman's at home but i think this is a bit too advanced. I've heard about LA done right by Axler or LA by friedberg/insel/spence

[gray gazelle]

friedberg's book is great

roman is too much for a first exposure

and axler has the problem of avoiding determinants

[waxen elbow]

yes, they are on the last chapter which is weird

[ripe granite]

We used Hoffman and Kunze

it was pretty good

[waxen elbow]

but it covers a lot of things

[gray gazelle]

axler's proofs are elegant but the determinant is such a fundamental tool

it's too useful to ignore

imo

[waxen elbow]

someone told be friedberg's is like H&K but in a modern way

[ripe granite]

I haven't read friedberg so idk

[waxen elbow]

well friedberg's seems to be a good option, i'll see h&k

[karmic thorn]

Friedberg g o o d

[gray gazelle]

f r i e d c h i c k e n g o o d

[sage python]

Yeah Hoffman-Kunze is a bit old school so I wouldn't be surprised if Friedberg is good, I'll check it out

People also seem to like "Linear Algebra Done Wrong" by Treil

[broken meadow]

my class is using friedberg and i like it so far but ill see at the conclusion of course how i like it

seems to presume understanding of basic matrix operations and stuff ? not sure

thats fine tho

i like that it starts with vector spaces generically

[sage python]

Seems like it's got a fairly light hand?

[broken meadow]

ya seems to be for new ppl 😌

which is good because im new 😌

[valid moth]

the based combo is axler primary + hk secondary (for det and some other sections as needed)

[hollow peak]

I will always shill for LADW

it's a proof based second pass that moves at a sane pace and has simple exercises

so easy to move at light speed through

only problem is that it's not very dense so you end up only skimming through a lot of more interesting theory on vector spaces

so then read knapp

[marble solar]

The one that I shill for that is Schaum's outline to Linear Algebra

Saved me on rational canonical and jordan canonical form problems

[frosty wyvern]

Hi. Where can I find a pdf of Fremlin Measure Theory Vol 4 and 5? I tried downloading the files on his website but they're separated TeX files per section.

[graceful bridge]

@frosty wyvern All volumes seems to be on libgen

[frosty wyvern]

Ohhh okay that did not cross my mind. Thank you so much!

[gray gazelle]

What's the verdict on Schaums? Worth it for calc and LA? Outlines or worked problems?

[marble solar]

Some of them are fantastic, some of them are horrible. The Linear Algebra one is very good

[gray gazelle]

Will look at that thanks.

[muted hearth]

anyone encountered these before?

they're from the 50s/60s

the one I have is such a cute book now I want them all

[obsidian valley]

I've personally only heard of the Halmos Set Theory text and mendelson logic

[marble solar]

Projective geometry is something people should learn more about

Rather than a tack on topic

[sage python]

@hollow peak honestly it feels more like a first pass than a second lol

[weak fossil]

Hey guys, can you recommend a calculus book thats not too rigorous and dry, with pictures, glossed over proofs, and 1000+ pages? I'm self studying in high school and I just started, I prefer easy texts with a ton of colours and graphics and stuff like that. I tried Thomas's calculus but it was too dry.

[hollow current]

prolly silvermann

[marble solar]

That's a tough one to hit, cuz the thousand plus pages books are all dry

There's the Humungous books of calculus problems

I used that and they were pretty decent

[broken meadow]

thomas... too dry... oof

[weak fossil]

Yeah Ive been studying for just over a year, calc is my third book I'm reading, English isn't my first language, and I need it easy else I'm not succeeding

[weak fossil]

How does analytic geometry work with calculus? Silvermanns book seems to be calculus with analytic geometry?

[weak fossil]

Really? I thought the shorter ones would be more concise and rigorous?

[pulsar geode]

yo just got coxeters book

[sage python]

@weak fossil more concise yes, but concise is often correlated with dry

[weak fossil]

Yeah, but Moon said that thousand plus pages books are all dry

which is counter intuitive?

[sage python]

Sorry sorry

I meant being too drawn out is what's correlated with being dry

If it's concise it's tougher to read but more interesting

If there's too much chit chat it's just dull

[cobalt arch]

Greub or shilov for linear algebra?

[weak fossil]

Oh

I thought dry meant just raw information without the chit chat bit

[sage python]

Unless that chit chat is funny or something

@cobalt arch idk those, what impressions do you have of them?

[weak fossil]

Well... when I was starting out to self-learn I was recommended langs basic mathematics

That is the definition of dry to me lol

Im a fan of the opposite, lots of colors, pictures, diagrams, etc

[sage python]

Oh yeah Lang's writing is dry. Colors/pictures/diagrams definitely spice it up, all I was saying is that sometimes too much exposition makes a book start to drag. Like yeah let's get to the point please

[cobalt arch]

Well greub is a bit dated but it has a rigorous exposition and it is a graduate textbook while shilov is a mix of theory and applications and it is for undergraduate. I really can't decide.. What is considered the bible of la?

[sage python]

Looking at Shilov it starts with determinants which is... interesting

[cobalt arch]

Hm is roman too advanced?

[sage python]

Jesus fuck Greub talks about homology lol

Shilov seems a bit strange, good but strange

[quick hornet]

i certainly wouldnt consider greub a suitable text for learning out of lmao

its a fine reference

dunno anything about shilov

[sage python]

I think Shilov is trying to hit this weird balance of theory and computations

Just glancing at the contents

[cobalt arch]

I like pure theory

[sudden kindle]

I like compute

[sage python]

This book confuses me so much

I think it's good but it confuses me

[quick hornet]

like here's how greub introduces v.s. isomorphisms

[sage python]

Greub seems advanced but solid

[quick hornet]

its obviously written as a reference

[sage python]

If you're good it might be worthwhile

[cobalt arch]

Isn't roman just better at that then? Being a reference I mean.

[sage python]

Let me see Roman too then lol

[quick hornet]

arguably, sure

roman does cover more stuff

but i dont think it goes as deep into the algebra

[sage python]

Roman is the most advanced of the three it seems

[cobalt arch]

I don't know I want a text that does not shy away from theory

[quick hornet]

the second half of roman is like

"almost functional analysis"

its a bit... off

but thats basically what it is

[sage python]

Roman's probably the least afraid of technology here?

Though I guess there's that homology chapter in Greub

[quick hornet]

greub literally introduces isomorphisms by talking about factor spaces so

idk

[cobalt arch]

I can try greub if he goes the deepest of the three into theory.

[sage python]

Greub strikes me as technically self-contained but sophisticated

If you're smart you can handle it

Roman feels like it's not really trying to pretend like it's self-contained and def has more stuff

[cobalt arch]

I see I will check them out myself and decide

[quick hornet]

just fyi greub has like

literally 0 examples

[sage python]

What's your current background in linear algebra?

[quick hornet]

as mentioned its written as a reference

so its assumed youll be able to come up with the eaxmples youreslf

[sage python]

And how clever do you think you are?

[quick hornet]

it does have some exercises

but its not the bulk of the content

[cobalt arch]

I don't have any background in linear algebra but I do need a self contained and rigorous exposition that goes deep into theory.

As for being smart I don't know how that can be measured holistically. Sure iq tests have a correlation with g but that is it.

[quick hornet]

again i would not recommend using greub for a first course.

[sage python]

Yeah I'm not asking for some strict formal rating here

I'm saying do you think you're a clever person? If I rant without being careful do you think you could follow?

[quick hornet]

you dont actually see a concrete example of a vector space in the "vector space" chapter like

at all

[sage python]

Honestly Shilov seems like it covers most of the important parts of Greub?

[quick hornet]

you see it in exercises

but not in the exposition

[sage python]

Like idk it's hard to compare, I feel like Greub does a bit more by some metric

But it's not totally clear

I'd need to do a more detailed comparison than I'm really willing to

Roman is probably a bad idea if you haven't seen linear algebra before

[quick hornet]

okay thats not totally true, you do see a polynomial vector space in one example!

hurrah!

[sage python]

A lot of its fancier stuff is either gimmicky or will come up later anyway

If you take algebra later, or functional analysis

Then you'll learn what's here anyway

[quick hornet]

and like if you look at the exercises

it assumes you already know how to prove things

and how "proof language" works

like

this is from the first chapter

if you dont know what "replace an axiom" means

(ie show equivalence between the two statements)

youll have no clue what to do

[sage python]

I'm guessing that this guy knows how to prove stuff if he's trying to optimize for sophisticatedness

Idk I don't have a great read on Greub, it feels like one of those books that's not designed to be learned from but if you're slick you can do it

Shilov looks pretty good

Tbh I could also see a case at that point for just reading Artin's algebra

[quick hornet]

¯_(ツ)_/¯

you miss a lot of linear algebra theory from just artin, dont you?

like

you learn the essentials

but you miss stuff like orthonormalization

[sage python]

Does he not do that? I haven't worked much with Artin myself lol

[quick hornet]

or SVD or whatever

[sage python]

SVD I haven't seen come up too much really, just in finding low rank approximations to matrices

Which you apparently like for ML purposes or smth

[quick hornet]

perhaps not from a pure perspective but its very important for applications

[sage python]

Shilov's pretty geometric if that appeals to you

https://cosmathclub.files.wordpress.com/2014/10/georgi-shilov-linear-algebra4.pdf

For reference Namington

[quick hornet]

like MIT has begun cutting a lot of the content on gaussian elimination from their course in order to focus on more SVD stuff

[gray gazelle]

i still don't understand SVD

[sage python]

I mostly learned linear algebra from lectures in a summer thing, and then later my analysis class had us read and do problems from Hoffman-Kunze

[quick hornet]

ew imagine doing geometry

[sage python]

Earlier people said that Friedberg et al is a more modern Hoffman-Kunze, honestly at a glance seems like it's mildly nerfed by comparison

[cobalt arch]

Is hoffman-kunze the standard text?

[sage python]

Idk if there is a standard text lol, I liked HK

[quick hornet]

i just wikipedia'd the SVD and it has this fantastic line:

Mathematical applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix.

[sage python]

Thing about these books is that I don't feel they're very linear

[quick hornet]

"dude i want to compute the rank of this matrix"

"okay hold on let me spend 2 motnsh on the theory of complex unitary matrices"

[sage python]

Lmaooooo I just realized how that sounds

I meant like

You can't linearly order them

[quick hornet]

"at the end you'll be able to find the rank by computing 500 determinants/eigenvalues"

[sage python]

Like each book does some stuff that another book doesn't, they sorta alternate in focus

Corollary is that it probably doesn't matter a whole lot which one you use

Eventually you'll learn what you need to know so just choose one that isn't Axler and go with it

[cobalt arch]

Hm I see thank you I will probably try HK and shilov.

[hasty turret]

Strang

[quick hornet]

honestly i have no intuition for SVDs either

re 8da

like i was told the geometric intuition

[sage python]

Strang isn't quite suitable for Forsaken lol

[quick hornet]

"its a rotation then a scaling then a rotation"

"and we can describe all (complex) linear functions like this"

but idk

[sage python]

Forsaken wants something serious

[cobalt arch]

Is strang too advanced?

[quick hornet]

its like the geometric intuition of the determinant for me

[sage python]

Nah it's for children lol

[quick hornet]

like yeah you CAN think of determinant as an area

[cobalt arch]

Haha

[quick hornet]

or rather as describing how the transformation affects area

but

[hasty turret]

But it isn't useful?

[quick hornet]

is that actually useful for anything

it feels like something they say just so the determinant seems like less of a random construction

but "random construction that gives powerful invariants" ends up being a theme in mathematics

see cohomology (or, hell, K-theory)

so... meh

why bother

[sage python]

The main flowchart I can give you is:
Shilov seems non-standard but gets to good material
HK is good but a bit old-school
Greub seems rough but it's got content
Roman is a bit excessive

Namington: I mean change of variables in integration

[gray gazelle]

i thought LADR is a fairly standard text

[quick hornet]

what about it?

[sage python]

It's a setting where determinant as area actually does something for you

[cobalt arch]

I will try greub wish me good luck

[gray gazelle]

although i haven't read these other books so i can't comment how it compares to them

[sage python]

LADR is bad

[gray gazelle]

LADR is bad? no! you're bad!

[sage python]

Axler thinks about determinants like a fucking moron

[quick hornet]

i mean

i can honestly say i never used that intuition

when doing change of variables stuff

[sage python]

And it makes his treatment of stuff like characteristic polynomials stupid

[quick hornet]

i just saw determinants of jacobians as magic fancy numbers

where if your determinant is 0 or if its nonzero you can use certain theorems

cut-and-paste

maybe this is why i never got analysis 🤔

[sage python]

Yes but you can black box anything like that lol

[gray gazelle]

yeah, this is my understanding of determinant

it's just some number, either 0 or not

[sage python]

I think multilinear alternating stuff is the way to think about it

[quick hornet]

honestly i dont really get how to think of jacobian determinatns

like

[sage python]

And that linear algebra students need to just stop being sissies

[quick hornet]

at all

i have 0 intuition for them

"either the linear approximation of your function is invertible or it isnt"

"and depending on whether it is or isnt, you can sometimes make conclusions about its extrema or whatever"

[sage python]

In my mind it's just like

[quick hornet]

"kinda like the fact that an invertible cts function on R is monotone except worse"

[sage python]

Locally how much does your function scale volume?

[quick hornet]

so what would a 0 determinant mean

it compresses the volume into a singularity?

[sage python]

Well no, think dimensions

If you collapse somebody to a hyperplane

Its measure in ambient space is 0

[quick hornet]

yeah chief im sorry im not sure how this visualization is supposed to help

[sage python]

Wait just think of a linear map right

What happens to the unit square?

If your map is singular then the image lives in a proper subspace so its Lebesgue measure is 0

Also the determinant is 0

Jacobian determinant is that but locally for a smooth function

[quick hornet]

oh so youre doing like

dimensionality arguments on the rank of the jacobian

or what

[sage python]

Yeah pretty much

That's at least how I think about this

[quick hornet]

meh i feel like if i tried to actually think about that i'd get my brain all twisted up

[sage python]

And it kinda indicates why it pops up in change of variables

Like I think if you work through the proof geometrically or something that's basically what's up

[quick hornet]

i honestly majorly blackboxed the proof of change of variables

[sage python]

I mean same

[quick hornet]

im sure it wouldnt be hard to rederive

just annoying

[sage python]

I think it's less garbage if you have Lebesgue differentiation theorem

[quick hornet]

well "rederive" is the wrong term

since like

i still dont know the exact statement of change of variables

its a fucking mess

with like 40 hypotheses

which come up only when the planets align every 40 exercises

[sage python]

Lmao, I'm pretty sure there are even sharper versions than the standard

Pretty sure the statement is not too bad

As given in normal multivariable calculus

But there's probably some super super minimal one in Federer

[quick hornet]

well i remember it took literally an entire page to state in my intro multivar analysis course

and we werent doing diff geo or calc on manifolds or anything

just multivar on R^n

[sage python]

Wait I thought the usual statement is just like

If phi is some C^1 diffeo

[quick hornet]

yeah but you can sharpen it by like

let phi be defined on some compact subset of your open-set domain with jordan content

and then if there is a measure 0 set such that phi restricted to its domain minus that measure 0 set is injective

or whatever

[sage python]

Yeah I think most of the time people don't go that deep lol

[quick hornet]

and the jacobian determinant of phi is either nonzero

or is subject to certain niceness conditions with its rank and the local behaviour of phi

for all values in the aforementioned set difference except potentially points on teh boundary or something

or something like that

it was a nightmare

[sage python]

Yeah this is the statement in Spivak

[quick hornet]

and then you get the famous int_phi(S) f = int_S (f circ phi)|jacobian determinant of phi|

[quick hornet]

for all cts phi(U) -> R^n

[sage python]

Again sharper things are out there but I think a typical multivariable calculus class doesn't bother too much with that

[quick hornet]

¯_(ツ)_/¯

[sage python]

Lol yeah wikipedia has a pretty oof statement

[quick hornet]

i was trying to find it on wikipedia but i couldnt

just the diff geo version

which is somehow nicer

[marble solar]

hey look it's spivak

[quick hornet]

actually thats unsurprising

diff geo makes every statement from multivar nicer

see stokes

[quick hornet]

okay we didnt build up quite that much theory

and i think our resulting statement was longer lmao

[sage python]

Yeah so I'd wager that was a very particular feature of what you guys did lol

[quick hornet]

¯_(ツ)_/¯

i remember in practice we just used like

the main 3 or so transforms

without bothering to check that they worekd

ie cylindrical, polar, the other one

[sage python]

I don't know that stuff well lol

[quick hornet]

i dont either

👀

[sage python]

That's the thing I know a good number of the theorem statements in calculus through differential forms or measure theory but

[quick hornet]

i remember there was a final exam question that expected we use it

but instead i just cited

the proof of a random theorem from our notes

(it was an open note final)

which did the hard work for me

[sage python]

I've never really worked with these sorts of fancy coordinates

[quick hornet]

and as ar esult i never invoked change of variables whatsoever on that final exam

😎

[sage python]

Nice nice

[quick hornet]

i forget what the exact question is but it was some weird set

like

a 4-cylinder with a hole through the middle or something?

and we had to compute a certain integral over it

[sage python]

Nerd

[quick hornet]

and we were expected to use cylindrical coordinates because

duh

its a cylinder

but i omegabrained it

and realize we could apply uh

italian name that starts with c

cavareli or something

cavalieri

that's it

which was not whatsoever the intended solution

but it technically worked 😎

[sage python]

Lol for a sec I thought you were thinking of that one guy

Luis Caffarelli?

[quick hornet]

so yeah i just applied this

[sage python]

But your calc class prob isn't using his theorems lol

[quick hornet]

with a weird ass construction

which again, wasnt the intended solution at all

but it did work

[sage python]

Lol what'd your TA/prof say?

[quick hornet]

well it was on a final so i never got feedback

just the marks

[sage python]

"Okay fine but fuck you"

Amazing

Oh Caffarelli is Argentinian

I guess I feel like most vaguely southern European sounding names involving analysis are Italian lol

Prob because of Luigi Ambrosio

[marble solar]

Caffarelli looks like a fucking boss

Kinda just wanna move to Texas just to meet him

[sudden granite]

@valid moth I would like to say thank you for recommending Lang’s Basic Mathematics. This book is fantastic 👌

[valid moth]

np

[timber mesa]

there was tons of Italian immigration in Argentina so probs. not too far off

[valid moth]

the argentines are wannabe europeans

[wooden sparrow]

I wanna be a European

[timber mesa]

aren't we all

[gray gazelle]

FUCK YOUR WHITE SUPREMACY

[tacit shadow]

does anyone have a pdf of Disquisitiones Arithmeticae in english? I assume there's no copyrights on it but I can find no pdf through google

[sudden granite]

@tacit shadow

I am uploading it right now.

I converted it to PDF for you

[sudden granite]

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks.
Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics—and they are mostly clever fools—seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.

This book seems like it’s going to be very good (:

(calculus made easy)

[winged palm]

@wheat salmon

[gray gazelle]

My friend never said that

@sudden granite chess?

or y'busy

I mean I got business. I'm a busy man

[sudden granite]

It's 12:19 am

@gray gazelle

I still have math hw

[gray gazelle]

12:39 pm

Business

[sudden granite]

No

[gray gazelle]

No?

[sudden granite]

How can you be 12 hr 20 min ahead

[gray gazelle]

I'm in the future

[sudden granite]

Impossible

[gray gazelle]

,time

[hasty eagle]

The current time for Skqwiggl is 12:20 PM (+04) on Mon, 01/02/2021.

[sudden granite]

See

smh

[gray gazelle]

,time 429744723117342732

[hasty eagle]

The current time for arjun is 12:20 AM (PST) on Mon, 01/02/2021.
Skqwiggl is 12 hours ahead, at 12:20 PM (+04) on Mon, 01/02/2021.

[gray gazelle]

Idot 🙄

[sudden granite]

I have like 20 word problems left

[gray gazelle]

lmao

what's the maths on?

[sudden granite]

i can play tmrw

[gray gazelle]

what topic

[sudden granite]

oh it's just trig functions

but dumb word problems 🤮

sinusoids

all that jazz

[gray gazelle]

ah right

I haven't gotten to that yet

my math class

is so far behind everyone

[sudden granite]

yep

[gray gazelle]

It's so boring

cause i covered everything

and teacher speaks for all the class, I mean i barely talk so he thinks I'm just averaging like the class

[sudden granite]

Read Spivak's Calculus

[gray gazelle]

yessir

[marble solar]

You ok?

[gray gazelle]

yes yes, of course. just that i saw some weird things being said in chat

[marble solar]

Just checking in, seemed out of context for me

[hasty eagle]

You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.

[gray gazelle]

can anyone tell me a good book for game theory beginners?

[gray gazelle]

Osborne Martin's book is usually recommended

[gray gazelle]

Thank you

book recommendation for olympiad functional equations?

[hollow current]

olympiad functional equation

was ist das

[gray gazelle]

stuff like this

[hollow current]

just define f to be zero function

[karmic thorn]

This might be useful: https://web.evanchen.cc/handouts/FuncEq-Intro/FuncEq-Intro.pdf

[gray gazelle]

ok ill check it out thanks !

[tacit shadow]

Amazing! Thank you so much!

[sudden granite]

No problem

[cobalt arch]

Rigorous precalculus books? (Geometry, trigonometry, algebra)

[obsidian valley]

rigorous precalculus

[cobalt arch]

Haha I just don't like computation 😩

I have found some books on each of these topics but I would like some more recommendations:)

[sudden granite]

Lang's Basic Mathematics

@cobalt arch

[cobalt arch]

Does it cover all of the above?

[karmic thorn]

But- precalculus is largely about computations.

[cobalt arch]

Yeah I know:/

I just wished there were some books that were more theoretical

[karmic thorn]

And appeal to rigour doesn't mean you can discard computations. Computations are a part of learning.

Lang is pretty good at what it does, from what I've heard.

[static crest]

ya, lang is pretty well regarded from what I've seen

[sudden granite]

Lang has a lot of proofs and covers a wide range of topics

I can send a PDF if you would like

[cobalt arch]

I can find the PDF but ty:)

[static crest]

[sudden granite]

kk

[cobalt arch]

Interesting

[sudden granite]

The only thing this book lacks is the basic probability stuff I think

[cobalt arch]

It does cover a lot of ground

[sudden granite]

Definitely

[cobalt arch]

I just hope that he doesn't spread himself too thin by having such a wide ranging exposition of material.

[sudden granite]

He is very good about the way he covers the topics

[cobalt arch]

Are you going through the book yourself?

[sudden granite]

Yes sir

I am around 100 pages into it

[cobalt arch]

Oh okay:)

[sudden granite]

I am in Honors Precal

Thought this would be a good book to read to strengthen fundamentals before I do Calc

[cobalt arch]

Okay I see

I will send recommendations if I find something of interest

[sudden granite]

Sounds good

This book is from the 1970's and lacks color

I don't feel that it diminishes the quality of the book though

[cobalt arch]

All the better

[gray gazelle]

Which book should I read if I want to know mathematics used in physics but not in depth as I am reading physics on my spare time.

Need to cover quantum mechanics and Electromagnetism

[sudden granite]

I would ask Physics server

in #old-network

They have a section with book recommendations

[karmic thorn]

Probably get a mathematical methods for physics book? I'm not sure if they're great for exposition since they tend to focus more on being comprehensive, but you could Libgen and try something like Arfken or Riley.

[hearty steppe]

They actually don’t have a book discussion channel there tho. Someone should bring that up to their mod team

They have a reading group mini server but I mean... that’s a bit different

[sudden granite]

Yeah

#book-recommendations is very useful

Chem server also needs it

[hearty steppe]

They have like a pinned channel for like recommended intro reads

[sudden granite]

Yeah

but I asked for which book was better for hs chem in the hs chem discussion channel and they said to put it in off-topic

🤮

[karmic thorn]

It's currently in its 14th edition, afaik.

[sudden granite]

Do the versions make a drastic difference though?

@karmic thorn

[karmic thorn]

I don't think so, not 12th to 14th at least.

[sudden granite]

Ok

Yes

Stonks

[gray gazelle]

@sudden granite : hs chem is author?

[sudden granite]

No

There was a book by pauling and some other guy

I didnt know which one was better

[cobalt arch]

is advanced trigonometry by durell a good book to self-study trigonometry?

[marble solar]

There's this book called trigonometric series

It's a tad difficult, but it's good

[cobalt arch]

Is this good for self-study and learning trigonometry?

[marble solar]

||It was a joke||

[cobalt arch]

:(

[marble solar]

Trigonometric series is an advanced math text

That most people would have a heart attack reading

Simple - most people don't read it

[quick hornet]

damn i need this book

i googled "how to have a heart attack" but nothing useful came up

just some webMD articles about risk factors or whatever

i need short-term solutions

[gray gazelle]

Wow, ultra making some bold accusations

[quick hornet]

i googled it before

i was hoping there was

a wikihow article

sadly not

i was planning on making an even less funny joke

[gray gazelle]

Maybe "how to induce heart attack", although I do agree there is probably no wikihow article

[calm crane]

shankar and griffiths

both have math chapter 1s

which covers majority of the necessary math

[silk quartz]

@quick hornet https://jamesjmurray.com/2016/06/29/conspiracy-theory-heart-attacks/

It's about finding the fiction writers. They research this sort of thing endlessly.

[gray gazelle]

Can u share its pdf?

[gray gazelle]

What are some interesting mathematics books to read to non mathematicians. I have these many with me.

1. The Music of the Primes: Why an Unsolved Problem in Mathematics Matters Why an Unsolved Problem in Mathematics Matters

2. Prime Obsession: Berhhard Riemann and the Greatest Unsolved Problem in Mathematics

3. Infinite Powers: How Calculus Reveals the Secrets of the Universe How Calculus Reveals the Secrets of the Universe

4. The Calculus Story: A Mathematical Adventure A Mathematical Adventure

5. How to Solve it - A New Aspect of Mathematical Method: 34 (Princeton Science Library) A New Aspect of Mathematical Method Princeton Science Library

6. Journey through Genius: The Great Theorems of Mathematics

[ripe granite]

fearless symmetry looks pretty good

[gray gazelle]

Any book for number series ?

[marble solar]

Apostol's introduction to number theory

[cobalt arch]

Most rigorous real analysis text?

Is baby Rudin the way?

[marble solar]

Rudin Principles isn't that rigorous

If you want to understand, start at Spivak's Calculus

If you want rigor + understanding you go to Pugh's Real Analysis

If you want a painful little book, you go to Spivak's Calculus on Manifolds

If you want to be confused, you read Rudin

[cobalt arch]

Is pugh really better than Rudin?

[marble solar]

Yuh

[cobalt arch]

Why is that so?

Can I do away with spivak and move on to pugh immediately?

[sage python]

Lmao, what Moonbears is saying is controversial

I hold Rudin > Pugh

Also wait aren't you supposed to be learning linear algebra? Do that for now lol

[cobalt arch]

Haha I am all over the place:)

I see so is Rudin better than zorich too?

[sage python]

I mean you can't really linearly order books like I mentioned with LA books

Idk Zorich at all tbh

[cobalt arch]

Yeah I understand that

[karmic thorn]

I hold Tao>>any other analysis text for intro.

[cobalt arch]

But I just want some recommendations

I more so seek a book with complete coverage of the literature if that is feasible

for intro

:)

[karmic thorn]

Both volumes of Tao's Analysis.

[hasty turret]

Starting with set theory axioms seems weird for a analysis book

[cobalt arch]

Are you referring to tao?

[hasty turret]

Yes

I don't know why you would ever need axiomatic set theory,if you are not doing logic

[cobalt arch]

Hm that is an interesting approach nonetheless

What would you recommend?

[hasty turret]

idk, Haven't done analysis

[sage python]

Forsaken actually there's an analysis book you might like which is super broad

[cobalt arch]

And rigorous?

[hasty turret]

Aman Escher?

[sage python]

It covers a decent ish amount of linear algebra

I mean most of these books are fully rigorous anyway

[cobalt arch]

Okay

[sage python]

Kriz and Pultr

Intro to Mathematical Analysis

[cobalt arch]

Is Amann escher good actually?

I have heard some things about it

[hasty turret]

It starts slow

[sage python]

Idk it

Kriz covers a decent amount of linear algebra, and it does a lot of stuff that's not usually covered in an analysis class. It mostly does Lebesgue, rather than Riemann, integration

Does some complex analysis, calc of variations, functional analysis, Riemannian geo

So it's got a nice survey of things. I think its chapter 1 is a decently self-contained gloss through single variable calc

So yeah idk I think it's fair to just pick that one up and then read it for, tbh probably well over a year lol

And not worry about books for a while

[cobalt arch]

Yeah I tend to overdo it when it comes to books

Functional analysis in a real analysis book haha

[sage python]

I mean I def get the sentiment of wanting "the optimal" book

[cobalt arch]

I mean that is interesting

[karmic thorn]

If you're talking about comprehensive, Amann-Escher's 3 volume Analysis series covers pretty much all of undergrad analysis+some introductory differential geometry.

[sage python]

I actually think Kriz is basically that is the thing

[cobalt arch]

Hm

This is such a dilemma

[karmic thorn]

The approach is a bit non-standard, in the sense that Amann-Escher starts off with broad generalities first, which might be hard to digest but if you can stick to it, it's pretty solid imo.

If you haven't done a lot of proof-writing before, I'll continue to push for Tao's Analysis.

[hasty turret]

I will never understand why intro analysis books start with basic logic and set theory

[karmic thorn]

I mean

It's a good way to see how things come into beinh

*being

And you can actually skip that part without losing much

Because construction of number systems rarely comes up anywhere, I guess

And it's a good way to write proofs about ideas which seem too obvious, and see how they emerge from bottom up.

[cobalt arch]

How can I get acquainted with proof writing? Do I need another book entirely or an analysis text that is intro proof based?

[past yew]

any books which “start from scratch”? I want to learn math without any assumptions whatsoever, like even if it has a bunch of trivial things I want to have a solid foundation

[karmic thorn]

I'm not a fan of using books for proof-writing; learning it in context is much more natural.

[cobalt arch]

I see

[karmic thorn]

Tao's Analysis. 😌

[past yew]

Wait even algebra and things like this?

like elementary algebra

[karmic thorn]

Kinda. You start by building the natural numbers using the Peano Axioms.

[past yew]

Sounds cool already

Peano Axioms are nice

[tight crag]

second order or first order peano axioms?

[cobalt arch]

If you want elementary algebra you can read shafarevich's discourses on Algebra.

[karmic thorn]

Then you cover some axiomatic set theory, followed by construction of integers, rationals, and finally reals. By the time you construct reals through Cauchy sequences of rationals, you already become familiar with a lot of notions underlying completeness, Cauchyness, etc.

[past yew]

Oh that sounds really cool

also noted @cobalt arch

[cobalt arch]

Cauchyness

[past yew]

Liquid I was meaning 2nd order

[cobalt arch]

Hm tao sounds interesting

[karmic thorn]

No idea lmao, Tao lists 5 peano axioms(existence of 0, existence of successors, 0 not being a successor of any natural, equal successors implying equal numbers, and PMI)

[past yew]

Yeah then it’s 2nd order

I think, because it quantified over a predicate?

[cobalt arch]

Ted is Amann escher comparable to tao and if so which one is better?

I want complete, rigorous and systematic coverage of real analysis

[past yew]

multiple books is probably a good idea, looking for a perfect book doesn’t really make total sense imo

[karmic thorn]

Amann Escher is extremely terse. ¯\_(ツ)_/¯

I prefer readability over rigour for intro.

Especially if you haven't done proofs before.

[cobalt arch]

I mean in one way it does N-C

[karmic thorn]

And Tao is fairly comprehensive; you could probably follow up with something terse or advanced.

I keep switching between different sources for learning as well.

[cobalt arch]

Because reading from multiple sources can be a bit tedious at times and cumbersome.

[past yew]

Do any of y’all know of a book which derives everything starting from ZFC?

[cobalt arch]

And you might get more confused

If you want zfc then analysis isn't for you haha I don't think that such a text exists

[past yew]

I would love such a book, ah darn

[tight crag]

N-C you are just going from one extreme to another

[past yew]

Who are you?

Anyway

[tight crag]

[past yew]

I don’t know people after they block me

lel

[tight crag]

lol fair enough

[cobalt arch]

I mean I am sympathetic to N-C because I want it covered all myself but yeah if you want complete coverage of analysis amann escher is the way and for zfc you have the legendary jech text (the graduate one although the other one is good too).

[past yew]

Jech sounds cool

[cobalt arch]

I mean jech might be too much and he might skip a lot of things

[tight crag]

Jech is far too much

[cobalt arch]

But his other book is good

[past yew]

axiomatic set theory would probably be a good book

I just don’t know a good book on this topic

[cobalt arch]

Karel hrbacek and jech introduction to set theory.

They have written a book together check it out

It is rigorous I think and it is the predecessor to jech's graduate text.

[past yew]

Huh, will look at it, it starts off with ZFC I’m guessing?

[hollow peak]

kolmogorov

[cobalt arch]

It starts with them yeah the first chapter is about the axioms

[hollow peak]

it's terse and somewhat old but very, very thorough

[past yew]

Oh cool

I’m going to try this out along with Tao analysis sometime

Thanks y’all

[cobalt arch]

It goes over relations, functions, orderings, natural numbers, finite, countable, uncountable sets, Cardinal numbers, ordinal numbers, alephs, then it goes on to talk about the axiom of choice then the arithmetic of cardinals, the set of reals, filters and ultrafilters, large cardinals and it closes with ZFC.

It has the axioms in the first chapter though

[cobalt arch]

Hm is that the case?

What does it cover?

[past yew]

Ah I see

[hollow peak]

I would say it's a very a good second or third pass for real analysis

So it goes through the first semester of real analysis (in rigorous depth, maybe too much for a first pass) in about 70 pages

then it moves into linear spaces and some advanced linear algebra

[cobalt arch]

70 pages 😩

[hollow peak]

function spaces, linear operators

measure, integration

[past yew]

Is ZFC 2nd order?

[hollow peak]

and then advanced measure theory

[cobalt arch]

Oh what would you expect from kolmogorov

[hollow peak]

http://tomlr.free.fr/Math�matiques/Fichiers Claude/Auteurs/Kolmogorov/Introductory Real Analysis - Kolmogorov Fomin(1).pdf

this is the best pdf I can find

it's a dover book so you can find a physical copy cheap

[cobalt arch]

Hm

Libgen

If you want full rigorous coverage of precalc I have some recommendations NC

One is the text on algebra I told you about

[hollow peak]

honestly the approach of "everything from scratch and super rigorous" is kind of a meme nowadays

everyone tries it until they inevitably can't handle it

[past yew]

oh

[hollow peak]

take it slow and steady and build upwards

like, that's why rudin is kind of a meme among young people while it's considered the gold standard among academics

[past yew]

What about just the everything from scratch part?

[hollow peak]

my personal opinion is that getting bogged down in foundations early is boring

if you're into that, then it's great

[past yew]

I like foundations tbh

[hollow peak]

but I personally don't find everything from scratch

[cobalt arch]

For trig you have sl loney and then durrell and for geometry you have geometry: euclid and above which covers some non-euclidean geometry later on too.

[hollow peak]

you read some basic stuff once or twice, understand the constructions of the reals, assume ZFC intricacies whatever

then go fast and loose with AoC

[cobalt arch]

AoC stands for?

[past yew]

Axiom of choice

[hollow peak]

^

[cobalt arch]

Oh xd

[past yew]

well, I guess this is my OCD talking but is it possible to have also the logical rules included along with ZFC?

[cobalt arch]

You don't need to know at all Axiomatic set theory to start from scratch most books require only naive set theory and they build up from there.

[past yew]

like ZFC + 1st order logic axioms

[hollow peak]

N-C, have you heard of the principia mathematica?

[past yew]

Nope

Wait

[hollow peak]

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

[cobalt arch]

Principia mathematica is the bible

[past yew]

is that the one with the 1+1=2 meme, I’ve heard it in that context

[hollow peak]

yeah

that's why you don't get bogged in foundations

[tight crag]

principia was very important at the time

[past yew]

Yeah I personally like foundations so I’d be fine with it

like

I have a lot of free time right now as well

[hollow peak]

when people cared significantly more about the basic structure of set theory

[tight crag]

well it was very important as a target for early computability theorists

[hollow peak]

I think it's interesting don't get me wrong

I just think for someone learning math

getting into uber rigorous logic and set theory is not the way to go

[cobalt arch]

Well if you want full coverage of the foundations of math go back to the vienna circle, logical positivism, analytic philosophy and then kant haha.

[tight crag]

yeah there is a standard pretty good intro to math path

which I would recommend

[hollow peak]

meme textbook chart

start with jech

then book of proof :^)

[cobalt arch]

Yeah hrbacek and jech is good

[tight crag]

the more concrete the better early on

[cobalt arch]

I don't agree

[tight crag]

so yeah book of proof is good, discrete mathematics and basic number theory and combo are good

[hollow peak]

in an alternate universe they are teaching school children category theory

[tight crag]

obviously the best first book is Soare

[cobalt arch]

Cat theory without preexisting knowledge of math is

[hollow peak]

how do you teach category theory in a vacuum

it only really makes sense with motivation

[cobalt arch]

Well that is it if you want to learn the foundations of math learn philosophy

Yeah

It is like the scaffolding without the building

I wanted to learn cat theory but then I realized exactly that which was that it is a tool for tools. If you don't have em you can't need it.

Or shall I say cat

[hearty steppe]

Soare?

[obsidian valley]

Probably Robert Soare Turing Computability

[cobalt arch]

Any books on analytical geometry?

[karmic thorn]

[cobalt arch]

Do you want my syllabus?

Maybe it can be of help determining which book to read although I have exams in 4 days but I am burnt out:)))

Yeah I know jesse xd

[obsidian valley]

Forsaken how do you simultaneously know that Hrbacek & Jech is a good set theory text and also need a reference for analytic geometry

LMAO

Just get Langs Basic Math or something

[cobalt arch]

A good text is good and that is hrbacek and jech..

[obsidian valley]

but...

how are you able to judge it's quality?

lmao

[cobalt arch]

I mean knowing one but not the other doesn't make them mutually exclusive

I have read parts of it and parts of other books and that was the most well structured. I don't understand where you are coming from.

[obsidian valley]

I'm just confused about your level of mathematical maturity lol

[cobalt arch]

Can you judge when a book is good if you don't have expertise in the field?

Where do you draw the line between someone that can recommend books and someone that can't?

[karmic thorn]

Expertise would be a stretch, but having some understanding of the contents, and having consulted other literature on the same contents can help.

[obsidian valley]

This contradicts with your ability to read the book (and judge it's quality) as far as I'm concerned

[karmic thorn]

Forsaken, I think I can relate to your present situation-you want to study maths bottom up, thinking you should start studying in utter generality and rigour, starting from foundations and building up from there. Am I right?

[cobalt arch]

Well you are

Also

This doesn't mean that I can't understand what I read mate

[karmic thorn]

I'm not contesting that.

But this approach is not ideal imo.

[cobalt arch]

I am referring to jesse.

[karmic thorn]

Oh

[obsidian valley]

You should not attempt to learn math from axioms up because that is not the way math has been actually created/discovered

[karmic thorn]

Regardless, I suggest you stick to one topic which isn't very far removed from the maths you already know. This could be linear algebra or real analysis.

Also, you don't have to pick up the "most rigorous" books on either of these subjects.

[cobalt arch]

That doesn't mean that you can't have such an approach

[hasty turret]

That approach sucks

[karmic thorn]

Stick to introductory texts which help you understand the ideas and intuition, while acquaint you with writing proofs.

[cobalt arch]

Well isn't that subjective?

[obsidian valley]

It means that the approach will be difficult

The "foundations" of math are not easy to understand

[karmic thorn]

I agree with MoonBears here. That approach doesn't align with how we learn to pursue abstract subjects like maths. To drive a car, you don't learn its mechanics bottom up.

[obsidian valley]

You won't even have context for why stuff is done in a certain way

[cobalt arch]

Well if you think about it every mathematician should read philosophy too to understand fully the underpinnings of foundations.

[hasty turret]

No

[cobalt arch]

Yes

[obsidian valley]

The axiom of union literally makes no sense unless you've worked with sets before, for example