book-recommendations

[tender cobalt]

its like spivak of multivariable

[vital bane]

what

what book did you use?

[fresh skiff]

Well i am in 4th year and like studying real Analysis and lin alg

[vital bane]

Afzal is a math major TIL

[tender cobalt]

i am in a differential geometry study group, the teacher taught basic pointset topology at the beginning

thats where i first learnt about it

[tropic nacelle]

nice

[tender cobalt]

though i suck at it because i didnt do much exercises

[tropic nacelle]

remember guys that ~99% of all students who study maths probably won't get to this level

[vital bane]

tends to happen when one tries to learn DG without real anal and Lin alg

basics are very important

[tender cobalt]

yes 💀

but all others here are physics majors

they got 0 idea as well

😂

[vital bane]

ah so it's for physics majors? then it should be fine

[tropic nacelle]

time to find more maths majors lmao

[tender cobalt]

so last 2 months ive been stumbling back and forth

[vital bane]

if you get insanely cracked at basics, then you will not have too much trouble with more advanced subjects like D G and FA

[tender cobalt]

and i cant sit my ass down to study consistently

[vital bane]

this was my mistake as well

consistency is insanely important

[tender cobalt]

i am wasting too much time exploring new subjects and books

😭

[vital bane]

I went through huge stretches of time where I did aboslutely nothing and just sat on my ass instead of doing analysis or lin alg

[fresh skiff]

But it's equivalent not being math major.
I mean there is no point to be a math major in a college, that has no teacher for math subjects like (top, RA, CA, FA, AA...)

[vital bane]

now my lack of discipline has come back to haunt me

[vital bane]

yea same here

[vital bane]

you should just laser focus on real analysis and Linear algebra

[tropic nacelle]

yes there are unis that only offer applied maths or stats and not pure maths

[tender cobalt]

so i should go finish shifrin

i like how he is applying linear algebra to all calculus concepts

[vital bane]

have you also checked out Shiffrin's lectures on youtube?

[tender cobalt]

yeah

i am following them

[vital bane]

noice

[tender cobalt]

gigachad

sigma

[fresh skiff]

Mine was offering pure. But unfortunately all teachers have qualifications applied.

[vital bane]

true sigma male algebra

[tender cobalt]

after this i will probably study his diff geo notes

[vital bane]

yea he emphasizes how it all starts off with linear algebra and how calculus, epecially differential calculus is about local linearity

[tender cobalt]

120 page diff geo notes

that also has stuff like chrisitofel symbols or something

[tropic nacelle]

okay that's just a scam...

[tender cobalt]

and geodesics

on curves and surfaces

[tender cobalt]

Yeahhh

[vital bane]

it's the case in a lot of colleges in India and Pakistan

[tender cobalt]

Bangladesh too XD

[fresh skiff]

It is. Even tho we don't have a separate department. We use to study in some lab of mining engineering lol

Just a year. I have passed 3 years

[tender cobalt]

Bro these countries are shit unless you become engineer or doctor

For mathematics it is just bad af

[tropic nacelle]

really? no wonder, their focus on engineering is becoming a cancer

yeah so when people talk about IISER or something I now realise that good quality institutions like those are the exception

if that's the case then China has a better pure maths environment 100%

[tender cobalt]

china is just too good bro

but if you wanna go study there you gotta learn chinese

[tropic nacelle]

I guess, depends on how qualified you are also

a lot of Chinese unis will do anything to attract foreign professors

[fresh skiff]

So true. My friends in Hong Kong told me about it.

[tropic nacelle]

ah nice (Hong Kong has a completely different education system btw)

[fresh skiff]

Oh

Yeah it's like separate state, not included in china

[tender cobalt]

it's a whole country

[tropic nacelle]

special administrative region

[tender cobalt]

but somehow china controls them idk why lol

[tropic nacelle]

it's like Greenland and Denmark

[tender cobalt]

even the police are chinese police

[fresh skiff]

Oh i see

[tender cobalt]

America Greenland and Denmark... hmm

[vital bane]

yea top institutions offer world class education in pure math, pure sciences, because they have the funding to do so

[tropic nacelle]

if Ramanujan were born again he'd probably leave India too

[vital bane]

he did

[tropic nacelle]

I know

[tender cobalt]

i covered shifrin until chapter 3 gradient

how long do you think it is going to take to finish the rest

[tropic nacelle]

oh that's a nice mix of analysis in R^n, LA, and point-set topology

[vital bane]

how quickly can you finish it?

[tender cobalt]

really wanna learn chapter 7 and 8 soon 😩

[tender cobalt]

yea

i will jump into functional analysis after this 😈

[vital bane]

no you need measure theory first

and more LA

[tropic nacelle]

like I really like the fact our uni just does computational multivar first

get stuff out of the way, covers basic basic complex analysis too

[tender cobalt]

erwin kreysig book dont assume measure theory

idk if its good tho

[vital bane]

Erwin????

https://tenor.com/view/erwin-shinzou-wo-sasageyo-horse-gif-8914717

[tropic nacelle]

IDK like computational courses then proof-based repetition/generalisation seems like the most natural structure to me

[vital bane]

Shinzo Sasageyo!!

[tender cobalt]

SHINZO SASAGEYO

[tender cobalt]

bro like

i studied calculus from thomas calculus

its a better version of stewart with some theory and proofs

single variable calculus that is

[vital bane]

yea computations are important

[tender cobalt]

then i decided to learn multivariable calculus RIGOROUSLY

[tropic nacelle]

yeah like the advantage is that you're not stuck learning both at the same time

[tender cobalt]

but i didnt want analysis cuz i still wanted computations

but with proofs

so i picked shifrin

[vital bane]

still, there's no point in rushing to FA, having a solid basis before you jump to advanced topics will be far more beneficial in the long run

[tropic nacelle]

it's like we do not teach high schoolers analysis from no background

so why would we expect students who may be a few years older to do that

[vital bane]

Just keep grinding everyday, don't think about how long it will take

and before you know it, you will have finished the entire book

[tender cobalt]

do i need FA for diff geo 🤔 cuz thats what i wanna study

[vital bane]

no, for diff geo all you need is RA, general top, LA

only minimal amount of general top

[tender cobalt]

i mean the advanced one with manifolds

[vital bane]

yes that's also what I mean

[tender cobalt]

oh wow

[tropic nacelle]

yeah that's still correct, a manifold is just a generalisation of Euclidean space

[vital bane]

locally euclidean spaces moment

[tropic nacelle]

it's a topological space also

[tender cobalt]

idk why these bozos need look locally euclidean

why not globally

😭

[vital bane]

that's just R^n lol

[tender cobalt]

they shy fr

[tropic nacelle]

I mean that's the generalisation bit

[tender cobalt]

I need multilinear algebra right

[vital bane]

yea exterior product and tensor product show up a lot in Diff geo, like curvature tensors are often rank 3 or rank 4 tensors, and you need the extrior algebra for differential forms

though this is often covered in your differential geometry course/book

so I don't think you need to study a separate multilinear algebra book for that

just get really good at pure LA

[vital bane]

because usually those books are from a more algebraic POV than is necessary for diff geo

[daring lake]

its nice and simple

i only did 2 chapters tho

it was too easy for my taste so i switched back to rudin

[tender cobalt]

so axler or fis level LA is enough ?

[tender cobalt]

I see

[daring lake]

builds up from metric spaces so if you got some decent LA and RA background you can easily follow

[vital bane]

Yea FIS and Axler

though I would suggest using FIS as your main text and using Axler as a reference

or maybe even

H&K as a reference

[daring lake]

Roman

[tender cobalt]

I was actually thinking to study roman

and go through the struggle

[tender cobalt]

Roman as main text, FIS and Axler as reference

💀 will i die

[daring lake]

ye

[tender cobalt]

Roman covers some tensors and exterior algebra though

[daring lake]

roman does like a lot of module theory

[tender cobalt]

Metric Vector spaces, Hilbert Spaces too 💀

yea

[vital bane]

research papers on Linear Algebra from 1800s as main text, with Roman as reference

[tender cobalt]

module theory begins on chapter 4

[vital bane]

the real ones do this

[tender cobalt]

okay i will go study emmy noethers paper

well the teacher from differential geometry study group suggested roman :/

that's from where I know roman from

[vital bane]

"Linear Algebra level 3"

not level 1

level 1 is inventing linear algebra yourself

only plebs use books to learn from

[tender cobalt]

[tender cobalt]

remember, Everoiste Galois ditched mainstream books and went straight for research papers

[vital bane]

I don't think he did

[tender cobalt]

i read that in a galois theory book idk

[vital bane]

I think he failed his university entrance exam once

[tender cobalt]

think it was by harold edwards or something

[vital bane]

I see

[tender cobalt]

oh

crazy

[vital bane]

this is how I will make myself feel better after I fail my entrance exams

[tender cobalt]

yup...

There you go @vital bane he ditched books 😭

okay bro enough chattery i gotta lock in and finish shifrin

bye

[vital bane]

interesting, I didn't know multilinear algebra was used in rep theory

[tender cobalt]

Oh i see and also rep theory = representation theory?

Also guys any differential geometry book recommendations? Or do I start with a manifolds book like lee or tu

[molten gulch]

multi linear is so much fun

[tender cobalt]

just like how multivariable calculus > single variable calculus , multilinear algebra > linear algebra 😈

[molten gulch]

😭 lmao

linear > multilinear

[tender cobalt]

why :c

[molten gulch]

because you should know the linear case first

[rigid trail]

but... generalization 💅

[molten gulch]

generalize once you know what tf you're doing

[tender cobalt]

[rigid trail]

yeah and then it gets better fr

otherwise why bother generalizing

[tender cobalt]

any book recommendation

[molten gulch]

I mean, lee and tu ARE diff geo books

[tender cobalt]

but its named manifolds lol 😭

i dont see any "geodesic" or "curvature" anything

oh wait tu differential geometry and lee riemannian geometry

[molten gulch]

Lee, Riemannian

[tender cobalt]

This book is designed as a textbook for a graduate course on Riemannian
geometry for students who are familiar with the basic theory of smooth manifolds.
😭

[marble solar]

You should know smooth manifolds before doing Differential Geometry. Are you looking for undergraduate differential geometry like Andrew Pressley?

[tender cobalt]

Is smooth manifolds THAT broad of a topic

and i cant get away with just a definition?

[marble solar]

Yeah

[tender cobalt]

I am looking for the modern ones

is there any modern diff geo book that is self contained

that has the manifold theory within itself

[marble solar]

There's the Comprehensive Introduction to differential geometry by Spivak

That is 5 volumes

The first 2 are probably what you're looking for

[tender cobalt]

2200+ pages 😩

[marble solar]

Eh, the first two are what you're probably looking for

I've read the first one in detail, it's actually quite good

[tender cobalt]

what do they cover

basically i am looking for a self contained book that will cover geodesics and curvature in manifolds (and riemannian geometry?)

(of course before reading modern differential geometry i will learn the undergraduate diff geo of curves and surfaces)

[full cairn]

I don't quite understand the difference between differential topology and differential geometry. Is Lee's smooth manifold book about differential topology, and his Riemannian manifolds about differential geometry?

[molten gulch]

You need to still do some manifold theory

[marble solar]

Obligatory not a geometer nor a topologist: but the topology will be concerned with classification, how can you use derivatives on manifolds, and what kind of results do you have as maps between manifolds. Riemannian geometry will put a metric on things so you can measure distance

I'm sure there's a lot more to it than that, but as I see it that's the tl;dr

[tender cobalt]

neat

[full cairn]

I see, the metric kind of turns diff top into diff geom 👍 that makes sense, because that's pretty much the difference between normal geometry and topology

[fresh skiff]

what app is this?
doesnt seems like adobe

[tender cobalt]

so in geometry you make measurements like ancient times

"metry"

[marble solar]

Ok, a really cool book that probably won't be suggested: Susskind's Lectures on General Relativity give a good lay person's introduction to the issues with some entertaining physics ideas

It's under the theoretical minimum series

The nice thing is that physicists usually don't care about the logical formalism and the setting for where the math will work. They just need to make an intuitive sense for how to calculate with the tools

[tender cobalt]

i actually started reading sean caroll general relativity which is "manifolds with applications" XD

[marble solar]

Do you have the background to understand that?

[vital bane]

5 morbillion pages

[vital bane]

no it's GR

lol really?

[tender cobalt]

i dont have the physics background

but in terms of math it assumes nothing other than linear algebra

the linear algebra it assumes i have it but

the tensor stuff and manifolds are so condensed

[marble solar]

Mathematicians tend to take things more slowly & develop more thoughtfully. Physicists really care about making sure they can consistently get the right calculations rather than being certain that they are absolutely correct ~ check out the theoretical minimum if you don't have the physics background for Sean Carrol's book, because as I understand it Carrol's book is for grad students

Susskind takes his time to explain the tensor stuff

It's kind of nice, actually

[tender cobalt]

i thought the theoretical minimum book was popsci

[marble solar]

Nope

[vital bane]

I should check out the theoretical minimum series

[marble solar]

It's decently serious, just not at the level of a university textbook

[tender cobalt]

GR actually seems a great way to quickly jump into diff geo

[marble solar]

It's more informal, supposed to give you an entertaining story + some interesting physics problems, and introduces the math you need to begin to understand the ideas

It's the theoretical minimum amount of math & physics you need

This isn't really the place for that, so let me ping you in a different channel wheat

[tender cobalt]

Alright sounds good ill check it out

[molten gulch]

okular, it's a KDE app

https://okular.kde.org/

[fresh skiff]

thank you so much Ryan

[molten gulch]

yw

idk how well it works on windows

but I assume it should work

[vital bane]

KDE, Kalher Differential Equations

[molten gulch]

neam how's abbott going

[fresh skiff]

maybe he will complete abbott soon but he cannot done with his thread

[molten gulch]

check adv lounge

[fresh skiff]

neither me, i was searching that. I dont wanna fall in some issues (am already weak when it comes to windows )

[tender cobalt]

its good i just tried it, you can download from microsoft store

[fresh skiff]

ok thank you

[old elk]

Speaking of topology and geometry
Is anyone following Stefan's topology book ?

[molten gulch]

full name, ISBN preferred

[old elk]

I have 3 pdf in the topology subject and I would like to know which one is the best, I am with algebraic topology but one is different from the other in some things haha.

[deft wave]

What's a good calculus book(s) I am looking for calculus 1-3 books

I'm desperate

[normal crystal]

Thomas or Stewart Calculus is pretty standard

[deft wave]

Thanks

[plain barn]

welll some stuff related appeared for me while studying topology and differential geometry

[gray gazelle]

2919 pages

DANG

Never seen an algebraic topology book introduce diff top before $\pi_1$

[hasty eagle]

Larue’s #1 Lawyer

[earnest wolf]

any good book / lecture notes that teach the 'standard' undergrad ODE trics?

[remote sparrow]

https://tutorial.math.lamar.edu/classes/de/de.aspx

https://www.amazon.com/Elementary-Differential-Equations-Boundary-Problems/dp/0470458313

[earnest wolf]

google search gave me Khan Academy also

this is too cursed for my eyes
|| dy/dx is not a freakin' fraction ||

[vital bane]

I find it quite nice

[vital bane]

non-standard analysis moment

[tender cobalt]

i wonder how separable equations are covered rigorously

[delicate sandal]

Anyone know good textbooks for number theory

[proven lantern]

https://math.stackexchange.com/a/3565677/1322489

[thorn jay]

Hey guys i am 10th grader and looking for improving my basic algebra factorisation all those stuff and geometry can anyone suggest me any books ?

[slow roost]

to be honest, you don't need a different textbook from whatever your school uses for that. You just need to do lots of practice

read and do the exercises, and if you need more exercises you can get them online

[tropic nacelle]

Khan Academy is nice

what you really need is practice, and Khan Academy gives you almost-instant feedback through doing those quizzes

if you really want a book go on Art of Problem Solving

you can buy it from there

[indigo mesa]

Are there any (proof based) linear algebra books known specifically for good exercises? I'm trying to compile an exam preparation sheet for my students and would like to add some more

[unique depot]

big math tome 2 (2bac sm)

[fresh skiff]

Linear algebra by Fridberg (FIS),
Advanced linear algebra by Roman,
Linear algebra done right by axler,
Iirc the 4th books name is linear algebra by Werner

[vital bane]

Werner Greub

[fresh skiff]

Oh yes this

I always forget his name

Ugh

[vital bane]

they are kind of trivial, I mean they are perfectly fine if you're learning it for the first time but if you're looking for a challenge, AoPS and similar books are the way

[vital bane]

I used to say "Gerub" instead of "Greub"

bro apparently has a geometry book as well

[fresh skiff]

Still quite near, all i remember it's "Werner G..."

[tropic nacelle]

they said they were looking for help on basic algebra and factorisation

[vital bane]

yea they said "improving", so I'm sure they've learnt it before, they want harder problems

regardless, both of those will help (Khan Academy stuff and AoPS)

[vital bane]

and they are also perfectly fine when you're brushing up on a topic that you haven't seen in a while (as I am finding out rn )

[swift sierra]

Hello! I am looking for recs on books in functional analysis. I have read Kreyszig, Conway and skimmed through Rudin. In particular, I'm looking for books that would expand more on the different topics presented in Conway. So any books that extensively look at topological vector spaces/locally convex spaces, Banach algebras are appreciated.

[tender cobalt]

wow

[marsh ingot]

Marián Fabian . Petr Habala . Petr Hájek
Vicente Montesinos . Václav Zizler, Banach space theory

The contents are good

No Banach algebras sadly

[swift sierra]

I will check it out, thank you! :)

[warped wave]

I don't find the problems in Churchill & Brown's Complex Variables and Applications to be very challenging. Any book with more challenging problems (but still cover the topics in Brown & Churchill)? I'm not looking for books like Stein & Shakarchi, because the contents of this book and Churchill's are somewhat different.

[vital bane]

so you want an application oriented complex analysis book with more challenging problems?

[warped wave]

yes

I want to get my foundations solid first before jumping into books like Lang's complex analysis or Stein & Shakarchi.

[vital bane]

I think the foundations for Stein and Shakarchi and other pure math oriented complex analysis books is just real analysis and multivariable calculus tbh

[proper iron]

Can somebody suggest a book on quant finance for beginners?

<@&286206848099549185>

[remote sparrow]

https://www.amazon.com/Problems-Linear-Algebra-Matrix-Theory/dp/9811239088

https://link.springer.com/book/10.1007/978-1-4020-5495-2

[remote sparrow]

https://www.amazon.com/Complex-Variables-Introduction-Applications-Mathematics/dp/0521534291

[old elk]

hahaha the guy has a lot of modern stuff in those notes

[old elk]

i have the pdfs haha

[tacit jay]

best books for self study for olympiad maths (number theory, geometry, combi, functional equations)?

[barren vigil]

Check #math-discussion

[stuck zephyr]

I have to check something in No Access

[fresh skiff]

Wdym

[sudden kindle]

? This is the right channel for #book-recommendations

[earnest wolf]

@proper iron
see discussion here

especially this

[naive lava]

so, i'm kinda in a dilemma here, i will start reading up on measure theory and you know "advanced" analysis, but i'm having a difficult time choosing between big rudin and folland, fwiw i read undergrad analysis from rudin and i quite liked it, and i'm a physics person, soo... end goal is kinda spectral theory but i'm also very much interested in some math here too

[proper iron]

Thanks mate

[barren vigil]

No image perms

[old elk]

[still herald]

Probability and Statistics by Hogg recommend for beginners/someone dumb? 👀

[vital bane]

try out both

[naive lava]

I feel like I will enjoy rudin but as you said before, it might lack exposition, and since I don't know exact contents, maybe I should've asked, including stuff in excersizes, which covers more stuff?

[tender cobalt]

people like folland a lot for his writing style and i think he also has lots of applications

[pliant wadi]

Is there some resource that you can remember that talks about both Dehn Surgery and Khovanov Homology?

[hasty sluice]

Any discrete math book recommendation?

[vital bane]

"Concrete Mathematics" by Knuth and Graham

[molten gulch]

discrete maths by epp or discrete maths by rosen

[earnest wolf]

#book-recommendations message

[zenith iris]

sup guys, I wanna create my 3d objects from the scratch using programming languages such as python or perhaps C , I’ve learned about matrixes recently and I think I’m ready for this. Where to start?

[dusk hemlock]

do you know enough programming?

[zenith iris]

yea Ig

but not sure

[dusk hemlock]

why are you in book recs

[zenith iris]

perhaps smb knows a great book for this

[dusk hemlock]

ah

[normal crystal]

if you want a Computer Graphics textbook
a standard is Fundamentals of Computer Graphics by Shirley et al

[orchid echo]

it doesn't have dehn surgery but this summary paper by Dror is really good

https://www.math.toronto.edu/~drorbn/papers/Categorification/Categorification.pdf

the author actually has a lot of papers on the khovanov homology

might be worth skimming through to see if anything is helpful

[obsidian blade]

hi, I have some set theory background, got as far as working with ZFC, cardinals, ordinals etc. My goal is to eventually get proficient in logic and set theory (say as far as model theory, continuum hypothesis and similar topics). I think a good place to start is logic and getting to Gödels theorems. Any recommendations?

[remote sparrow]

#book-recommendations message

[obsidian blade]

thanks! do you have a recommended one?

[remote sparrow]

westerstahl and leary/kristiansen are good

[obsidian blade]

thanks!

[rotund eagle]

any sources for me to get better at number theory and cryptography

[heady ember]

That's a concrete recommendation

[pliant wadi]

OH HEY

Thanks a ton!

[nimble tendon]

Thanks a kilo

[neon aspen]

what books you guys would recommend for going from basics algebra to IMO level stuff? or any other resources because i'm just getting into olympiads

[normal crystal]

the Art of Problem Solving series fits that

[neon aspen]

any other book? they seem too expsensive for me...

[stoic beacon]

does anyone have a book/books on ODE transition to chaos theory?

[austere knoll]

The Communist Manifesto

[tender cobalt]

What's the difference between presley and de carmo on diff geo of curves and surfaces?

[austere knoll]

elvis presley died yesterday and carmen sandiego was chinese

[tender cobalt]

Idk who elvis presley is but rip

[austere knoll]

well he was a famous pyschomathematican with theories about the geometric dialysis corvergence theory

[austere knoll]

IMO mrpg well i think you should runescape as they have a great economic model

[ruby rock]

whats your opinon on the geometric dialysis convergence theory compared to carmen sandiegos evolution of fractionating surds

[austere knoll]

well i think we need to intergrate under the curve and the transform the dialectic asymptopes to find the equation for the sumation for carmen

[ruby rock]

yeah but actually vicktoria whamsley opposed that theory with the natural geometric equation of fractionating indentation so i actually believe against that

[ornate pagoda]

is this only math books or can I ask for fiction?

[austere knoll]

you can ask for both.

[ornate pagoda]

like numerology or something?

[ruby rock]

yep

[austere knoll]

i would recommend great expectations for non fiction and fiction id recommend carbon fullerene theory

[ornate pagoda]

I can't find that second one(

[ruby rock]

its on amazon

i got it its a really interesting read actually

[coarse dust]

i could talk abt the carbon fullerene theory for days actually

[ornate pagoda]

give link pls

[austere knoll]

wait sorry

i think we have language barrier

i sorry

im from north macedonia

i will send link

[stoic beacon]

never asked for fairy tale fiction

[austere knoll]

nah edith prailasky literally talks about eliptic curves in that book tho

in the preforward synthesis

[stoic beacon]

wish i cared but like

do you have chaos theory books

[ruby rock]

edith prailasky has one

her 3rd book i think

[austere knoll]

literally edith prailasky

like buddy can u literally read

come on man

[stoic beacon]

must be banned in my country or something cause im not getting any useful results on that person

[austere knoll]

aww thats sad sorry

[worthy viper]

edith prailisky has great books actually

have u guys read the trignometric bipolarism?

[ruby rock]

literally

[worthy viper]

its actually a fire book

[coarse dust]

i havee

[stoic beacon]

can you send me that one

im gonna find that authur

[coarse dust]

ill try find it for you

[austere knoll]

nah the issue is

[normal crystal]

they're trolling

[coarse dust]

shes only got 1 book on amazon i think as the rest of hers are difficult to find

[austere knoll]

edith is actually quite suppressed

in mainstream media

cuz shes quite contriversal

[ruby rock]

?

[austere knoll]

great books tho

[worthy viper]

bro what

no way you actually havent heard of her LOL

[stoic beacon]

thank you

[ornate pagoda]

literally tried two search engines, can't find that second one

you lie

[austere knoll]

what coutnry are you based out of

im sorry cuz im from north macedonia

i think its a different translation

[tender cobalt]

Wild

[worthy viper]

do you know the english name of the book?

[ornate pagoda]

send the name in north macedonian then?

[austere knoll]

i would flippin send it if i knew

i borrow it from my library

[coarse dust]

i havent heard of that one either

r u sure its actually a book?

[worthy viper]

nah is pint trolling bro

no fucking way

[stoic beacon]

LMAO

[ruby rock]

i saw it once

maybe

like years ago

i think its out of print by now it must be really old

[tender cobalt]

@stoic beacon if i recall correctly then 3blue1brown's website has some chaos theory book recommendations

[austere knoll]

nah cuz i borrowed it from my local library

[coarse dust]

u gotta be lying

[stoic beacon]

checking right now

uhh its more like a video tutorial

[limpid bear]

so your background is like an ODE class I suppose ?

[austere knoll]

nah cuz slender is trolling

i think

[coarse dust]

yeah😭

[stoic beacon]

yeah im doing PDEs a few weeks from now

[worthy viper]

yeah ignore slender

he's a regular spammer

[limpid bear]

well you could try hirsch smale and devaney, it's kinda built up for this exact transition

or you could pick up a dynamical systems book directly if you feel like it

[stoic beacon]

ill check that out but look at this one i just found

can i send links here

or should i dm you

[limpid bear]

I think so

[stoic beacon]

this is a bit too much

[limpid bear]

I haven't read it, but it's quite a well-known book, it's certainly good

[normal crystal]

Strogatz has lectures on YouTube

[remote sparrow]

holy metadata

[limpid bear]

never a bad idea to try out a few books and pick the one that sounds better for you

[remote sparrow]

you can remove everything after the "?" and the link will still send fine

[stoic beacon]

oh my god

[remote sparrow]

@stoic beacon btw that strogatz book is in its third edition

[normal crystal]

he removed everything after someone's ?

just not in the link

[remote sparrow]

the student solutions manual you sent is for the second edition

[remote sparrow]

deleted the message instead of editing 🤷

no he sent an amazon link

with a shit load of metadata

[normal crystal]

I'm aware

[remote sparrow]

https://www.amazon.com/Nonlinear-Dynamics-Chaos-Steven-Strogatz-dp-0367026503/dp/0367026503

third edition ^

if u can find copies of the second edition for cheap that's fine too

[stoic beacon]

how did you meta data not leak

[remote sparrow]

well i googled and clicked the amazon link

but you can just delete everything after the question mark

[stoic beacon]

https://www.amazon.com/Nonlinear-Dynamics-Student-Solutions-Manual/dp/0813349109?

got it

[umbral olive]

hi! sorry im new but im a pyschology undergrad student who wants to get back into maths. Can anyone recommend some books to me to get back to all of the crazy stuff in did in high school? thank you

[ruby rock]

edith prialasky 'a prolegomena to the voices of hope'

[worthy viper]

as a edith glazer i think you're actually wrong tho

[ruby rock]

??

[worthy viper]

becuz i think thats more of her epistimalogical work

[ruby rock]

so what do u recommend then

[worthy viper]

and even though there is lots of maths

well id say you should instead look towards edith's ambitious on the basis of all mathematical tooling

which explains the axioms of understanding

of the basis of mathematics

[ruby rock]

well frantikaK said that hes new

so i wouldnt suggest any of that

because the axioms of understanding on the basis of mathematics are complicated for a novice

you really delve deep into the topic you see

[worthy viper]

well yeah i would agree but i think it shows more understanding towards the reader

[ruby rock]

a prolegomena to the voices of hope expresses ediths first theory of the computational laws of alrogithmic colombian dynamical systems

which would be more suited towards a novice

[worthy viper]

yeah ig but in context to the question tho to thicken @umbral olive's understanding of mathematics

i think my recoomendation is bette

however i think both those books are good reads

[umbral olive]

wow interesting

but can you guys send the link to her books

because i can't find her on google

[tame tree]

theyre trolling

for a serious answer, try the art of problem solving series

[ruby rock]

???

someone here hasnt read edith prialaskys work

[worthy viper]

lmao real

edith's work is actually so good

[ruby rock]

yeah ok name 5 books

[worthy viper]

uh

so we have her short story anthology marmite makes good tea

and also

horses who fall dont stand

[ruby rock]

yeah thats only 2 of her newest

newgen

name 3 more

[fallow cypress]

two trolls <@&268886789983436800>

[normal crystal]

it's 4 if you scan back

[primal summit]

Got em

Cheers

[grim ore]

This just reads like someone talking to themselves on alts

like weirdly enough

[tropic nacelle]

hi ShiN

[lilac ginkgo]

hello

HAHAHAHA

[tender cobalt]

What's the difference between presley and de carmo on diff geo of curves and surfaces? whats the best book for diff geo of curves and surfaces

[slow roost]

Do Carmo is more challenging

it's been a while since I've tried to read that one. Pressley is the most accessible intro to diff geo I've seen

I recommend both though

also Needham's Visual Differential Geometry is super nice

he has a very unusual style of exposition which is rather flowery and not always the most rigorous, but I love it as a supplement to other reading

[obtuse lagoon]

Where do I start to learn Number Theory? Can someone help me?

[slow roost]

what's your background like?

[marble solar]

Go with Pressley. There are solutions at the back

[fresh skiff]

I am thinking to do Number theory too. Not now but soon, like i will be having background of Real analysis and lin alg (proof based one)

So what book will be suitable

[obtuse lagoon]

I am a 9th grader

[tender cobalt]

Thanks

[slow roost]

number theory is one of my weakest subjects so I'm on the lookout for recs too

[proud atlas]

guys book recs please

[normal crystal]

book 1
book 2
book 3
yw

maybe be more specific what you want

[marsh ingot]

What topic?

[proud atlas]

math

I'm indecisive pls pick for me

[marsh ingot]

What branch?

[proud atlas]

Thank you. This is lovely

[hasty sluice]

Has any one read How to prove it?

I found many errors in problems and solution

[fresh skiff]

yes

i read 2.5 chapters

it was really a nice book, i think i saw a few typo but cannot recall properly
I have not read the latest edition btw

[supple ferry]

In the linear algebra book by FIS (4th edition), do they ever have an exercise or theorem/proposition to prove the uniqueness of the square root? Also, in LADR by Axler, he doesn't talk about elementary matrices, right?

[fresh skiff]

uniqueness of square root?

isn't is something related with Real analysis?

[molten gulch]

The sqrt(2) thing is a basic number theory proof, idk about uniqueness of roots overall tho

[supple ferry]

I meant square root of a positive operator (as Axler calls it) 🙂

[fresh skiff]

oh

[supple ferry]

I know there's an exercise in FIS about existence, but I couldn't find anything about uniqueness.

The uniqueness of a positive square root of a positive operator is one way to prove the uniqueness of the polar decomposition (I'm sure there are other ways, maybe easier, as well).

[vital bane]

non-linear dynamics and chaos?

[steep haven]

I want to learn calculus. I know a little about derivatives, integrals and limits + some applications but not more. Can someone recommend some books?

[grim ore]

Idk how many people would critisize me for this, but honestly the open source and free textbook openstax isnt that bad

It has problems to select from and test yourself on as well

It has content Calculus I-III which is differentiation of one variable until multivariable differentiation and integration along with applications and series

[steep haven]

do you have a link?

[grim ore]

https://openstax.org/books/calculus-volume-1/pages/1-introduction

https://openstax.org/subjects/math

[steep haven]

this book specifically or any from that site?

also is there any way to download it?

[grim ore]

Yeah i think you can also download it if you go to the second link I sent

Just scroll or click on calculus on the side bar and instead of viewing online you can download it

[steep haven]

found it

[grim ore]

All of it is free and open source, idk too much about the other texts tho. My calculus classes only used the openstax religiously

[steep haven]

do you think it makes sense to read precalculus

[grim ore]

Idk about any other text tbf so thats up to you

[rigid trail]

no

[pliant wadi]

What's a good place to self-study about PDEs from? (I have taken Functional Analysis and ODEs before)

I want to learn it for mostly other things that interest me such as Dynamical Systems, Stochastic Processes, etc. I don't wanna get into it hardcore at the moment per se, just trying to pick up some useful, versatile ideas.

[ripe moat]

I recommend watching some Steve Brunton on YouTube. His focus is more on the engineering side so should be good for your use case

[pliant wadi]

Oh I see. And if I were to encroach on the other side, what would you recommend?

[remote sparrow]

yes

[remote sparrow]

https://www.amazon.com/Partial-Differential-Equations-Applied-Undergraduate/dp/1470464918

it's lower level than evans, but working through evans doesn't appear to be your goal

[normal crystal]

it really annoys me that AMS switched to PB at higher cost

[pliant wadi]

Oh hey dudeee, you have helped out yet again. Thanks!

[remote sparrow]

yeah, and i own a few AMS hardcovers now, and they're quite nice

none were new but they open easily

unlike springers

[pliant wadi]

Eventually I'll get to it, but there's something I want to try rn but I can't quite get into Evans immediately.

Not this semester

But maybe the next one, I'll get to Evans eventually for sure. Like, that's the next to next goal. Sort of.

Oh also, I wanted an opinion.

We were working through Brezis for our Functional Analysis course, is it considered a good book for PDEs too?

[remote sparrow]

axler talks about matrices. he just doesn't go over things like gaussian elimination

[gray gazelle]

Munkres Topology, then T&G by Ronald Brown

[proud atlas]

Okay thanks for the recc

[supple ferry]

it seems to me Axler does not talk about elementary matrices though, whereas FIS have a chapter on this. On the other hand, I can't find that FIS prove the uniqueness of a positive square root of a positive linear operator in their book, which Axler seems devote a section to.

[remote sparrow]

kristopher tapp's book is great

lots of pretty pictures and explicitly assumes a real analysis and linear algebra background

[remote sparrow]

what's an "elementary matrix?"

[tribal crow]

matrices you get by applying a single row operation to the identity

[supple ferry]

yes, what ourfallenstars said

[remote sparrow]

yes, row operations and stuff like gaussian elimination are not covered

LADR can be used as a first course but he assumes most students in courses using his book have already had exposure to those concepts

[snow saffron]

Can anybody recommend me a book for Real and Complex Analysis? I am interested in these topics especially after taking Calculus 2 and Multivariate Calculus and would like to do some independent study. I am looking to take classes for this at my university but I would like to know if anybody can recommend me something that can give me a good introduction into analysis.

[remote sparrow]

#book-recommendations message

[vast leaf]

I like Explorations in Complex Functions so far

[slow roost]

https://link.springer.com/book/10.1007/978-3-031-68934-5

this is a really really cool new book. The price tho

[livid lintel]

Any books regarding programming language theory?

[remote sparrow]

https://books.friesenpress.com/store/title/119734000096993421/T.-Hillen,-I.E.-Leonard-and-H.-van-Roessel-Partial-Differential-Equations

https://www.pearson.com/en-us/subject-catalog/p/applied-partial-differential-equations-with-fourier-series-and-boundary-value-problems-classic-version/P200000006203/9780137549702

https://www.amazon.com/Partial-Differential-Equations-Walter-Strauss/dp/0470054565

[normal crystal]

https://softwarefoundations.cis.upenn.edu/

https://www.cs.cmu.edu/~rwh/pfpl.html

https://www.amazon.com/Programming-Language-Pragmatics-Michael-Scott/dp/0124104096

[random mortar]

@remote sparrow You're a hero. Thanks.

[snow saffron]

Can I start it from just a calc 2 and multi variable calc base?

[vast leaf]

Might be slightly tough

[remote sparrow]

gamelin is accessible with your background, but typically complex analysis is taken after real analysis

[lilac raven]

any suggestions for analysis of navier stokes equations?

not looking for an engineering book but like using modern pde approaches

[remote sparrow]

what math do you already know

[lilac raven]

basic functional analysis and pdes on the level of evans

sobolev spaces

what else is relevant

[remote sparrow]

maybe taylor's books might have more relevant information

don't really know any other references

[lilac raven]

taylor's books?

[vast leaf]

I feel like real and complex analysis are different enough that they can be studied in either order

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-33859-5

https://link.springer.com/book/10.1007/978-3-031-33700-0

https://link.springer.com/book/10.1007/978-3-031-33928-8

[lilac raven]

i found two springer books that are what i was thinking of

but ill check these out thanks

https://link.springer.com/book/10.1007/978-0-387-09620-9

[remote sparrow]

volume iii has a chapter on navier-stokes for incompressible fluids

[lilac raven]

https://link.springer.com/book/10.1007/978-3-319-27760-8

[heady ember]

Taylor's PDE books...

_I fear no man... But this... thing.... whispers it scares me.

[lament sphinx]

any good book recommendation on linear algebra? High school oriented or something?

[molten gulch]

Friedberg Insel and Spence

[lament sphinx]

Ty

[lilac raven]

looking through it and this is terrifying

2100 pages of pdes…

[remote sparrow]

he is a very prolific author

he has written a variety of other textbooks

[little vault]

Can anyone recommend some textbooks about differential manifolds? It is best to be relatively basic, and will introduce some corresponding algebraic structure, thanks!

[ionic zephyr]

https://tenor.com/view/anime-gif-23610619

[remote sparrow]

wtf is that a john milnor reference

[lilac raven]

loring tu intro to manifolds is algebraic

and not too advanced

[little vault]

hahaha, interesting anime

thank you!

[little vault]

thank you, i will look at it !

[hexed dagger]

book recs for machine learning fundamentals and tools

[vital bane]

wtf LMAO I'm stealing this gif

[manic coral]

Hello, I want to start math from the basics(prealgebra to calculus) and i do have an inclination towards competition math, here is a book list ive prepared(any suggestions/alternatives appreciated)

1. Hall and stevens Geometry
2. Hall and knight algebra
3. David burton Number Theory

My main question is that are these good for the theory base and any more suggestions/ alternatives. For example hall and stevens doesnt cover trig which isnt ideal.

[ionic zephyr]

lmao i searched up differential manifolds annd it popped up. ><

[ionic zephyr]

idk the anime. what is it

[ionic zephyr]

ofc:)

[vital bane]

maybe you can add a trig book

(I don't know any at the prealgebra/comp math level though)

[manic coral]

All others are good?

Can u have a look the pdfs are easily available online

[vital bane]

I don't know about others, I've never looked through them, but I do know Hall and Knight's algebra is pretty good, but i was mostly responding to "For example hall and stevens doesnt cover trig which isnt ideal."

there is also "Higher Algebra" by Hall and Knight if you want to check that out

[manic coral]

Alr so david burton seems good but i cant seem to understand it

[vital bane]

did you read the preface to see what the prerequisties are?

[manic coral]

How much of algebra do you need to understand NT

[vital bane]

@brisk ice I think you were doing Burton right?

[manic coral]

Do you still have any normal suggestions for a trig book

I just want it to cover the theory

[brisk ice]

Yes it is fine

Finished the course

No real complaints and you can find solutions from all the problems up to like chapter 9 or 10 from a previous edition

[manic coral]

For me the first page on induction doesnt even seem comprehensible

[brisk ice]

Took "modern " algebra at the same time. I would say for Burton the cross over wasn't all that much until one chapter (primitive roots).. a lot of the chapters it is more than knowing stuff about number theory helps with modern algebra

Like knowing algebra didn't help in NT for really anything but that small section but I just learned it in NT. But the stuff in NT was useful and helped for algebra

[vital bane]

modern algebra = abstract algebra

[vital bane]

yea knowing NT is actually super helpful in abstract algebra

[manic coral]

The first page talks abt elemnts and uses mod signs

I an aware briefly abt the modulus

But no idea what elements are

[brisk ice]

Like learning modular arithmetic, phi function, divisibility rules, euclidean algorithm, solving linear integer equations (diophantine)

[manic coral]

Will sets, and the topics u just mentioned be covered in higher algebra hall and knight

[brisk ice]

Maybe you just need some background in basic set theory. Too be honest I think you just need to know an element is an item in a set

[brisk ice]

I'm not sure what that is

[manic coral]

I think neamesis knows abt the book

[brisk ice]

I would just say Burton is very elementary

Like in the sense it can't get more basic and minimal as far as prior knowledge

I think the first chapter even starts with induction but maybe basic ideas about sets and proof techniques might be of use. For sure want to do the exercises and some of the proofs you read once just to say you did. But tbh they are somewhat hard and I don't think I could come up with them or prove certain things from scratch

[manic coral]

I was told the same, so i was confused why i couldnt comprehend the book’s First page

[hollow shore]

what's your background in Math?

[brisk ice]

Like I got to stuff on sum of 2 squares and sum of 4 squares. The proofs in that section where not obvious. Pretty much just learned the formula or what condition must be true to compute sum of squares and if it is possible for a prime

[manic coral]

Basic high school marh

*math

In 10th grade rn

[brisk ice]

What is the page

[hollow shore]

Oh I see where the trouble is rn

[vital bane]

first

[manic coral]

Binomial theorem and mathematical induction

[hollow shore]

You need some Mathematical orientation before reading a proof based book

[manic coral]

Uh pls elaborate

[hollow shore]

much of it can be attained by osmosis but I'd suggest you go through some book which talks about it and make mental notes of the things which the author talks about

[hollow shore]

I'd assume you haven't gone through the Definition-Theorem-Proof format Math material. It starts out with you familiarizing yourself with basic Set Theory, Logic (so that you know the distinction between a convincing argument and a valid one), etc and then you try to engage with the material. In order to make yourself familiar with this lingo I'd suggest some resources in no particular order...

https://jdh.hamkins.org/proof-and-the-art-of-mathematics/

https://richardhammack.github.io/BookOfProof/

#proofs-and-logic message

also you can ask questions about where you get stuck or if smth is not clear in the relevant channels

[manic coral]

Alr

I also had a query

Ginme one sec

Are u familiar with the Aops series?

[hollow shore]

vaguely

[manic coral]

Well their intro book on NT was very much comprehensible for me

Now i dont want to use this specific text as id have to pirate it

But are there any related ones?

[hollow shore]

lemme look

https://math.gordon.edu/ntic/

this seems to be pitched at the audience with a modest background

[manic coral]

This seems nice

Ty ill have a more in depth look later

Thx to everyone rly appreciate it

[south scarab]

I wanna learn stochastic calculus / stochastic differential equations.

Don't know anything about em. I'm in calc 2

Ping me plis ty

[rigid trail]

Why not ordinary diffeqs first

[south scarab]

i can do very very basic differential equations

i think im a quick learner so i try to juggle topics

[rigid trail]

Learn more cmon

[south scarab]

ok

[rigid trail]

I had the same issue

Trust me u gotta lock in

[south scarab]

do i do PDEs after? or stochastic differential equations

[rigid trail]

Hmmm

Idk I'll let someone else answer because I haven't studied beyond ODEs much yet

[south scarab]

ok

[loud cradle]

did you already study probability? if not then do that first

[lilac raven]

https://www.cmor-faculty.rice.edu/~cox/stoch/SDE.course.pdf

read through this

if you find yourself struggling with any one specific part (such as probability, ode/pde, proofs, etc) than you can always drop it for now and go learn that topic and come back

but yeah ideally you should do a course in odes and probability as well as have some background in analysis/pdes to truly absorb it

[vast jackal]

Hello guys how do i really prepare for the IMO?
when I look out on Google I see this that they require to solve alot of problems but currently I'm in 8th I'm just wondering how do they study for it because when I tried 1983 AIME p1 it was not on my level at all I didn't even know the math, my highest level I can say of right now is quadratic equations

[hexed dagger]

cool peeps pls hit me up with some recs, i am sure you know cool stuff

[remote sparrow]

you may have more luck asking in the statistics server

https://discord.gg/52xdj6jf

[hexed dagger]

cool, ty 🤟

[stark turret]

Is there anything to suppliment the probability class I am taking? I am kind of struggling.

Like the basic discrete and finite stuff

[remote sparrow]

https://stat110.net

[upper hull]

I want to dive more on chemistry for industrial production . Any books recomend ?

[mortal ore]

i would ask the chemistry server

[upper hull]

Okay

[signal cedar]

Any recs for getting into diff eqs? (Fluent in calc 1-3 btw)

trying to learn them conceptually but also tricks and stuff to solve them

[heady ember]

Hyped because of the relatively low price
No purchase option :kekwait:

[timber mesa]

I lowk want this book too lol

[mortal ore]

shits always sold out this time of year

damn students

[timber mesa]

damn students studying

[mortal ore]

(i am damn students)

fr tho its crazy how even textbooks i aint ever heard of

just gone

like

[heady ember]

There was a 75% off sale on Princeton University Press (the official publisher). But guess what? The shipping fee was 3.86 times the on-sale price 🗿

https://tenor.com/view/daeth-funi-periflight-dies-from-gif-22212023

[remote sparrow]

should be a sale in february

[oblique girder]

Hi, I've graduated with my degree in mathematics but I'm looking to teach myself a bit about financial mathematics. Any recommendations for books about that? I don't exactly know what there is to learn about it yet, but if there happens to be a foundational book that covers the basics and gives me a taste of what the more specific sub-branches of that are like, I'd love to know

[sudden kindle]

5.0 rating

[stiff cave]

I recommend the Harry potter and chamber of secrets for studying higher level mathematics

[limber fern]

What's a good book for self studying an introduction for complex analysis? I've been reading Lang's but i think it woulf be nice to read another as well

[remote sparrow]

gamelin

[limber fern]

Oh okay thankies

[vital bane]

<@&268886789983436800> squid game guy is scamming people again

thumbs up reacted to the wrong message Ghost

[remote sparrow]

oh also there's a complete solutions manual written for lang

https://www.amazon.com/Problems-Solutions-Complex-Analysis-Shakarchi/dp/0387988319/

[limber fern]

Oh wow thanks

Thank you hyouka pfp

[remote sparrow]

a couple of other references you may want to consider are conway and greene-krantz. i wouldn't say these are absolutely ideal for self-study (could depend on your experience with analysis more generally), but they're more detailed than gamelin. greene-krantz especially starts off with pretty elementary notions and early exercises are pretty simple for being a graduate text. there are some people who complain about its inelegant treatment (i do have to say i'm not impressed with how often differential operators are used in the early chapters, as greene-krantz deliberately wants to treat complex analysis as an extension of multivariable calculus on R^2 while relying as little on geometric/topological notions as possible) and the number of typos in later chapters.

mathews and howell has very straightforward explanations

it's nice for learning the computational aspects of complex analysis, but there are proofs too

brown and churchill is about the same level as mathews-howell and is more concise

[limber fern]

All of those sound very near! Thanks. Mathews howell one sounds pretty interesting in particular

[cobalt arch]

Do you know of a book on general topology that is about 2000 pages? I have been looking for it but to no avail.

It is 4 volumes I think

[cyan valve]

Are there any texts that discuss more advanced algebraic structures like basic algebras, differential graded algebras, etc that you wouldn't find in an intro grad algebra text?

[sly verge]

Türk varsa Mustafa Özdemir Olimpiyatlara hazırlık 2-3-4 iyi kitaplar

Geometri için de My geometri

[leaden valley]

Yes you do PDEs after ODEs

[tender river]

thanks

[merry canyon]

Can anyone share the solutions pdf for Stewart's Calculus?

[earnest wolf]

https://quant.stackexchange.com/a/38872

hmmm

maybe we should create a thread in General Interests for quant / Mathematical finance

[formal parcel]

Is Howard Anton’s elementary linear algebra a good book?

[oblique girder]

Hey, really appreciate the link! I'd love to be added to the thread if it does end up getting made.

[livid lintel]

Any good book on Website UI/UX designs?

[pliant wadi]

where should I start reading about vector bundles?

any interesting resource?

[graceful moon]

Lees Introduction to smooth manifolds is the common recommendation for diffgeo/difftop

[molten gulch]

<@&268886789983436800>

[pliant wadi]

I'll check that out, thanks 👍

[slow roost]

note that Lee doesn't really get to diff geo "proper" until the 3rd book, Intro to Riemannian Manifolds. The first 2 books are mostly topology / diff top

but it's a fantastic trilogy

actually it's a quadrilogy now with Intro to Complex Manifolds. I haven't read much of that one

Smooth Manifolds has a good chapter on vector bundles

[mighty tartan]

wait Lee made a fourth book in the manifold series?

didnt hear about that

my measure theory prof actually went on a 2 week long diff top/geo tangent so i looked into his first book. I like the style, if i will need more of it for future lectures i will definitely buy them

[remote sparrow]

it's published with AMS rather than springer

[marsh ingot]

Its the complex manifolds one?

[dim sierra]

Yes

[merry sphinx]

i found this once and it took far too long to download

like, tf is 224,000 kb?

[dim sierra]

224 MB isn’t too unusual

It’s weird tho because the book isn’t even that long

[merry sphinx]

most of the stuff i have is like, 5-15 kb i feel like, big ones are maybe 25-40

[remote sparrow]

that's weird

i have a pdf that's 29 mb

you can find it on you-know-where too

[ivory shore]

It happened to me, i downloaded a book about Fourier Analysis. Idk why it happens

But 224.000 kb it is a lo

lot*

[heady ember]

Mine is just 30 000 kb

[vital bane]

tangent haha

[heady ember]

Book cover

[tribal crow]

[remote sparrow]

https://math.stackexchange.com/questions/1852384/linear-algebra-textbook

does the jordan form chapter still leave something to be desired in the fifth edition? (note the top reply is from 2016; the copyright date for the fifth edition of FIS is 2019)

[ivory sable]

Does anyone know a very mathematically rigorous chaos theory/ dyanmical systems book?

Like a book that presupposes knowledge of top/ basic analysis

Comprehensive too

Strogatz doesn't really go into top and stuff much

[loud cradle]

The existence and uniqueness proofs for the jordan form are fine, but the examples of how to compute a jordan basis leave a lot to be desired. They more or less admit this and leave it to the reader to work out how to do it in general:

(i am referring to the 5th edition)

[sleek python]

Never really tried it but this is a book that was rec in my diffeq notes for an intro to chaos, back when I was in uni: Differential Equations, Dynamical Systems and An Introduction to Chaos from Hirsch, Smale and Devaney

Don't know if it fits your purposes but may be worth a look

[remote sparrow]

feel free to check the bibliography in the back of strogatz's book as well

he cites many more rigorous texts

[remote sparrow]

https://link.springer.com/book/10.1007/978-3-031-02398-9

i googled "jcf algorithm" and happened to stumble on this little booklet length article

[tribal crow]

my course that followed FIS' 5th ed. didn't teach the JCF out of the book

I never read the chapter, but a few of my peers said that they found it super confusing and not very helpful

we learned the material and general algorithm out of my prof's notes instead

[remote sparrow]

https://bookstore.ams.org/dol-44/

that material is also repeated here

[vital bane]

I guess it's not difficult to make solving separable equations rigorous, it's just a change of variables

which makes a lot of sense

I was wondering about this myself

[tender cobalt]

ohh

[vital bane]

making change of variables rigorous in R is just an exercise in intro real analysis

the physicist way of solving separable equations🗿🗿🗿

🗿

so low res

[balmy crown]

Is there any good book for real analysis?

I know this gets asked a lot here but ive bought my 4th book and it is so unsatisfying to read. Ive gotten so far Understanding Analysis by Abott, Analysis 1 by Tao, The Way of analysis by Strichartz, and intro to real analysis by Lebl

[marsh ingot]

So not a intro to real analysis?

Try Folland

[balmy crown]

Havent heard of that one. Ill give it a try

I just want something with some soul in it

The books arent hard to understand but as im looking at proof after proof it just feels so unsatisfying

Like give me some motivation, why should we care about this. I felt Book of Proofs was a gold standard for this and I havent read a math book that matched its magic even though there are plenty written in the same format

And I read that cover for cover twice. I still reference it and never get tired of it

[marsh ingot]

If you feel brave enough then

Baby Rudin

Since I understand that you have seen analysis already from some sources

[balmy crown]

Lol ive been tempted to give that one a read. I've heard a lot of people talk about it.

[marsh ingot]

If its good in case you have seen real anal before

[quick hornet]

rudin is still the gold standard book for exercises in analysis

the exposition, on the other hand, is very polarizing

i think he has a habit of being too "cute" with his proofs

rather than being demonstrative

like if you have a theorem that can be proven in a "standard"/"prototypical" way via method x, but theres a special consideration that allows you to cut out a few steps from method x and reach the conclusion in a somewhat different way

rudin will often go for the faster route rather than the more representative one

which is actually probably a good thing for a reference text, stuff like that can help form a more holistic understanding and theres value in boiling down results only to what is strictly "necessary"

but probably not the best for a first timer

[vital bane]

Why specifically are you unsatisfied by these texts?

[balmy crown]

There's no conversation with the reader, its just proofs. I know its important but its so dry and I learn very little from them. After undertsanding a proof im sitting here like "who cares" and they just continue on to another proof.

[vital bane]

???

have you actually read Understanding Analysis?

there's so much motivation for everything, in fact before he starts any chapter there's an entire section (the first section) about motivating what's to come

[balmy crown]

Not too much of a fan on how he writes the discussion and I skip the epilogues after reading a paragraph of it every chapter

[signal mountain]

skips all the writing
"There's no motivation"

[balmy crown]

Its too wordy and sophisticated. I think theyre great parts to have but talk in a more simple language during those moments, leave the sophistication for the proof writting.

[vital bane]

I hope you find a good analysis book that suits you

[heady ember]

Are you trying to read a math book, or a novel?

The former requires active reading at each turn

You can't expect to easily piece everything together

[signal mountain]

Perhaps a video / lecture series (on yt / MIT OCW e.g. respectively) would suit you better

[chrome wasp]

Have you tried Pugh or Schroder?

[balmy crown]

I get that, but give me some humanity, some life in these books. As I mentioned, I think Book of Proofs is a perfect example of this.

[chrome wasp]

Or Apostol, Wade, Browder, Nikolsky? (4 different books)
Tho I didnt end up reading any of those except one paragraph I was seeking.

[signal mountain]

Is it possible you are just not that into real analysis

(totally fine btw)

Obviously you need to do it but you don't have to love it, many don't

[dense grotto]

any books for learning manipulations or out of the box/creative ideas to improve approach in problem solving? anything that's a good source for learning mathematical thinking

[heady ember]

Any serious math book would probably do the trick

[ivory shore]

I'm studying that book and i like it. Also i have a spanish book similarly to abbot's proofs, maybe i can share it to see what do you think

[heady ember]

If you can't sit down to watch a lecture/read a text, then I don't think you're set up for success for analysis (or much of math).

[ivory shore]

do you suppose to learn real analysis from tik tok?

[dense grotto]

can you recommend any that fulfill my requirement

[heady ember]

Rudin

[heady ember]

Your question is too broad. What field are you interested in?

The only way to get better at problem solving/critical thinking is, probably, to actively problem solve/think.

[balmy crown]

Havent heard of them but I'll definitely look into it, thank you

[dense grotto]

well just competitive math in general and... often times you solve a difficult problem that involves "some out of the box idea" (which you can't think yourself)...

you are taught that method and you apply it in similar situations. HOWEVER we aren't taught to learn to "think" that way i.e the thought process behind that idea. How did it strike the solver? That's what I'd like to learn

And also some manipulation ideas, like those that get applied while solving integrals

[heady ember]

I have never really been interested in comp math, so I have no recs for that.

[heady ember]

you are taught that method and you apply it in similar situations.
Yeah that sounds like what my highschool math experience was like.

[dense grotto]

oh, in most books they just show the solution without teaching the thought process. And I'm not finding conceptual difficulty at all, Its the out of the box manipulations and ideas that are somehow never directly taught.

[dense grotto]

I've read some books like The Art and Craft of problem solving they are good

Especially the algebraic part (adding 0 creatively) and (multiplying by 1) were really relevant to me

[balmy crown]

I do personally like calculus.

Part of my problem is with math as a whole. I think they make the language a lot more sophisticated than it should be, making it not as accessible to most people and leading them to hate it.

My other problem personally is that I neither like exclusively pure math or completely applied math. I can't just learn through end less proofs but I also dont like it when they throw equations out of thin air, tell us what it does and when to use and expect us to completely understand it. I like something in the middle that uses a mixture of both.

[heady ember]

I think they make the language a lot more sophisticated than it should be
I highly disagree with that claim. I don't really see how that is true.

making it not as accessible to most people and leading them to hate it.

• Many languages are sophisticated because of the history of their development, more so than they need to be, from what I know?
• I think keeping an open mind and having persistence is a necessity to get anywhere in math. If one can't have enough of both to learn the language of how modern math is done, I can't see how they'll get far anyways. But, that's just my opinion.

[elfin lance]

I'm currently working through Essential Calculus by James Stewart. As I'm on chapter 8.6 (on series), I'm wondering if there's a good book I could work through with lot's of problems in it for refining my ability to work with series after I finish this chapter. Secondly, since I'm very involved with using FFT's and complex numbers in my computer programming, I'm curious if getting through the rest of this calculus book would give me the tools to work with complex numbers, or if theres a book I should study on calculus with complex numbers. Thank you :)

side note; this is just self study, so I'm not sure which direction to take from here to continue my study, but I'm also studying a physics book alongside this as I'm interested in the subject of computer simulation and modeling, like fluid sims or path tracing (I've written a few path tracers before but I'm feeling happy I'm getting into the math correctly lately :D)

[molten gulch]

For complex numbers at that level I guess you could take a look at Brown and Churchill's Complex Variables book after you finish Stewart, AFAIK a little bit of multivariable calculus is helpful to understand how line integrals work

for FFT I'm not too sure, I learned all I know of those in code by reading blog posts, watching youtube, etc....

[elfin lance]

I've got a signal processing book I picked up for my partner last year that will teach me using fourier transforms; Signals, Systems, and Transforms :)
I feel a strong interest though in calculus with complex numbers in general though, but I'll add that book to my list! :D

[molten gulch]

Ooh yeah signals systems is fun

[elfin lance]

That book seemed to do well for him, he sat down and showed me the fourier transform of some simple functions on paper haha it was cute

[molten gulch]

I also assume most texts on differential equation theory will contain some information about laplace and fourier transforms

and if you ever want to go further and brush up on formal real and complex analysis, you can study harmonic analysis

[elfin lance]

ahhh we have the book "Differential equations a modelling approach" by Giordano Weir

oh! harmonic analysis, that sounds like what I might be interested in. I hear about spherical harmonics a lot, is that a special branch of harmonic analysis or something?

[molten gulch]

I'm more familiar with spherical harmonics related to representation theory of groups but I believe they do have some connection with diffeq's

but I'm not at all very familiar with that stuff

[elfin lance]

ahh, interesting. this has helped me organize at least some direction beyond this book though. I appreciate the recommendations :)

[balmy crown]

I dont mean like language like the greek notation, I think thats wonderful but should be taught earlier since it better helps understand how to think mathematically.

I meant more on the language level that people use to talk about things first introduced. Its a bit difficult to explain. Its like I mentioned with Abbotts discussion and epilogue pages. I know what the chapter was about and I know what he's trying to say but its so wordy and sophisticated that it gets lost in translation.

[molten gulch]

do you mind if I PM you

[elfin lance]

I'm so happy I finally had the opportunity to start studying calculus. haha I've used it so much in programming but I've never had a chance to work with it properly on paper. Getting addicted to integration :3c

[elfin lance]

absolutely, go for it

[molten gulch]

Integration is definitely fun, we personally fell in love with maths when we started learning about infinite series a year or 2 ago

[heady ember]

My point about language was this: even if the language of math is more sophisticated than it needs to be (which I disagree with), I don't get why it would lead people to hate on it more. My lack of understanding comes from how people seem to lack the same 'hate' towards learning new languages, which can often be complicated due to their history.

[loud cradle]

Ha, i just checked and apparently had already downloaded this at some point, but i don't think i've ever looked at it. Will check it out now!

[ivory shore]

For series i usually use a spanish book "Cálculo Diferencial e Integral de Funciones de una variable" by Francisco Javier Pérez Gonázalez, i highly recommend it. FFT's and complex numbers maybe "Advanced engineering mathematics" by Peter V. O'Neil, one of my favorite books. Reciently i'm reading "analysis fourier and its applications" by Gerald B. Folland, maybe you can find interesting things

[elfin lance]

awesome, I'll have to look into these, thank you.
I don't know Spanish but maybe I could still work through that one?

[ivory shore]

Definetily

[static widget]

hey guys, is there any advanced linear algebra PDF that i can use ?

[molten gulch]

how "advanced"

Have you just completed your first class in matrix algebra or-

[static widget]

yes hahaha, by advanced i wanted to learn more than matrix

idk how can i give you my level

like i stopped with equations system and all

vectors

and i want to learn further

[ivory shore]

for example eigenvalues, vector spaces??

[static widget]

yes exactly

[strange tree]

did you see eigen-things? inner products?

[static widget]

nope

[strange tree]

Linear Algebra Done Right

[ivory shore]

that one

[static widget]

thank you ! imma try to find a free PDF of that

[ivory shore]

sheldon axler, you can also find it on youtube

[strange tree]

https://www.axler.net/ in fact, it is free

[static widget]

thanks a lot rly

[heady ember]

Based Axler again

[static widget]

thanks thanks thanks guys rly

[heady ember]

LADR has an unusual treatment of certain topics (determinants and characteristic polynomials) though

So, you might also want to check out Linear Algebra by Friedberg, Insel, Spence

Or some other text like LADW

[static widget]

if i watch axler videos, do you think i could get enough level to teach myself physics ?

and ofc exercicings myself ofc

[loud cradle]

LADW is free so no harm checking it out, but i dislike it quite a bit

feels very much like unpolished notes as opposed to a proper book

[heady ember]

Axler and its equivalents (proof-based linear algebra texts) are probably way more than you need for Physics. Such texts are targeted more towards math majors

[static widget]

okay okay good rly

thank you guys

[heady ember]

np

[static widget]

i hope y'all did pass your exams

[ivory shore]

are you having classes??

[static widget]

yes

[ivory shore]

thanks btw

[static widget]

but im not rly an engineer or mathematician ahahahha

im an economic student so my math is waaaaay less harder as yours
but i want to learn math by myself

[ivory shore]

the better thing you can do

[static widget]

yes.

[ivory shore]

if you have doubt about the spanish book let me know

[ivory shore]

in my case I took aerodynamics, fluid mechanics, etc classes and the maths behind them is a bit complicated so for that reason i'm studying math more deep

[static widget]

i wish luck for that man, sounds rly intersting tho

[ivory shore]

thanks man!! yes, it's really interesting and blow up your mind how many things are in a fu***** aircraft

[static widget]

honnestly, do you think that you 'll still use calculus and all when you 'll work ?

[gentle jasper]

Does anyone know if there exists a book that teaches manifolds (somewhat similar to Spivak’s Calculus on Manifolds) using Lebesgue Integration?

I’m not sure if it’s pedagogical useful to spend time learning manifolds with Riemann Integration, but I’m also not sure if there’s an equally decent introductory book

[ivory shore]

It depends on which area you will work. Someone can work with maintenance aircrafts (it not include math tools) as well as to desing an aircraft from zero and you must know how to work with mathematical tools like FEM (Finite Element Method), Aerodynamics, Aircraft Structure, capability, Thrust, Avionics, etc

[vital bane]

certainly not "Way more" if you're planning on learning Quantum Mechanics and GR, in fact you need even more linear algebra!

[floral oxide]

yeah, you are right. qm has like second order partial derivatives, and gr has tensor equations and stuff with partial derivatives too

[outer turtle]

any book rec for learning lin alg?

[tribal crow]

how rigorous?

[outer turtle]

doesnt matter as long as i understand fundemental ideas and have a good intuition from it

[tribal crow]

I suppose if you’re okay with rigour then I would suggest something like Axler or Friedberg, Insel, Spence

my personal preference is the latter book

Treil also has a nice linear algebra book

I’m not as well acquainted with the less rigorous linear algebra books, but I’ve heard Strang and Anton be cited as good sources