book-recommendations

[topaz rune]

He has one on elasticity theory and one on fluids, which are both in the realm of continuum mechanics / media

And in volume one he must also consider rigid bodies and rotations etc I guess

[lusty ermine]

guys can someone reccomend me some good discrete maths book

im bad at it, and i dont want to spam but, im in help15 btw, and stuck with a introductory question, so if the book is related to this topic (Eulerian circuits and something else), I would be very grateful :3

[sage python]

People like Rosen

[lusty ermine]

ty

[subtle fractal]

any good books with polynomial manipulation

[tulip blade]

Im not sure if encyclopedia type books are the best for learning. For 1. Ive heard convex opt by boyd and combinatorial opt by korte and vygen, for 3. complexity theory ofc arora and barak maybe the book by oded goldreich.

[gusty coral]

can someone help me with quadratic functions?

[finite gale]

!help

[hybrid sparrow]

Please read #❓how-to-get-help

[topaz rune]

Is there a nice short reference for measure and integration theory which does not exceed 30 pages or so?

[sharp hull]

solve cencage

[hushed lynx]

what are thoughts on how to solve it? i'm thinking of getting the book to develop my problem solving skills are there other texts that would be recommended?

[scarlet pumice]

Is there a book I should use to get myself up from year 11 math to uni algebra & calculus of one variable?

[remote sparrow]

well there are no references which meet your criterion that are textbooks, at least there's that much

probably someone has notes out there

[steep badger]

well if you are interested in smooth dynamics, you can try Climenhaga and Katok's measure theory from a dynamics point of view. Otherwise Silva has a pretty short and hands on book on measure theory and ergodic theory.

[topaz rune]

Ironically I need it for Nonsmooth dynamics

[topaz rune]

Yeah was looking for nice and short reference notes about most important stuff

[steep badger]

Invitation to Ergodic Theory

ohhh well

Anything ergodic theory holds measure theoretically, so it works well beyond smooth dynamics.

[ocean spindle]

Rosen

[lusty ermine]

ty

[gray gazelle]

I would like to learn olimpic mathematic. Someone knows some books for this?

[tawny copper]

Mathews "problem solving tactics"

but be around aops and the math olympiad discord server

[earnest atlas]

still need help with it?

[gusty coral]

yes 😭, i have a test on monday and my teachers ppt doesnt give an explanation on how to get in that specific part, ect

[earnest atlas]

i dmed

[gusty coral]

checked 😅

[gray gazelle]

Any recommendations for books on differential geometry? I'm currently taking a course on it, but I don't particularly like the lecturer or how he's teaching the material. It seems to hand wavy, and so I'd like another perspective on the subject.
Any recommendations are appreciated 😄

[lime vessel]

Jeffrey Lee

[gray gazelle]

Thanks! I'll definitely take a look! ❤️

[remote sparrow]

is this a curves and surfaces class

or is this more general

[gray gazelle]

It's a curves and surfaces class, but I would like to learn more general subjects as well. I don't want to read a book just to only go over what we've done in class already.

[remote sparrow]

loring tu and john lee have textbooks on manifolds, which i often see get recommended when someone wants a more general approach to differential geometry

https://www.amazon.com/Introduction-Manifolds-Second-Universitext/dp/1441973990

https://www.amazon.com/Introduction-Smooth-Manifolds-Graduate-Mathematics/dp/1441999817/

according to amazon's "frequently bought together" tu has a book on differential geometry as well, but it might depend on either of the previous two books

https://www.amazon.com/Differential-Geometry-Connections-Characteristic-Mathematics/dp/3319550829/

a curves and surfaces book you might enjoy is the one by tapp

https://www.amazon.com/Differential-Geometry-Surfaces-Undergraduate-Mathematics/dp/3319397982/

do carmo is a standard text for curves and surfaces

https://www.amazon.com/Differential-Geometry-Curves-Surfaces-Mathematics/dp/0486806995/

[gray gazelle]

Thank you! Do you have a preference between these two?

[remote sparrow]

tu is generally regarded as a bit easier, so i would go with that

[gray gazelle]

I see, thank you very much!

[remote sparrow]

https://www.reddit.com/r/bookbinding/comments/1661drk/advice_for_rebinding_printondemand_academic/

for those thinking about buying more recently published textbooks, there may be hope for rebinding it

[sturdy shore]

tu's diffgeo has at least half of his manifolds book as a prereq

[remote sparrow]

thanks for clarifying

[gray gazelle]

amen

[zinc lantern]

Anyone know any books on modular arithmetic

[finite gale]

You could either go towards a discrete math text or an elementary number theory text

[gray gazelle]

any online algebra 1/2 books?

[clever orchid]

AoPS intermediate algebra

or introduction to algebra depending on the level of your course

[remote sparrow]

https://www.amazon.com/Calculus-Applications-Undergraduate-Texts-Mathematics/dp/1461479452

https://www.amazon.com/Multivariable-Calculus-Applications-Undergraduate-Mathematics/dp/3319740725/

https://www.amazon.com/First-Course-Calculus-Undergraduate-Mathematics/dp/0387962018

https://www.amazon.com/Calculus-Several-Variables-Undergraduate-Mathematics/dp/0387964053

https://www.amazon.com/Calculus-Rigorous-Course-Aurora-Originals/dp/0486809366

there are a few choices that do not take "hundreds of pages" to get to differentiation

[gray gazelle]

thankss

[topaz rune]

a 5 min youtube video

username checks out btw lol

then read spivak etc

idk maybe some calc 1 book that is commonly used

what is that?

ah lol

yeah i mean then your ony resource is short articles like wikipedia or youtube videos, pretty much

put 1.5-2x speed

yeah

btw i think this is only common belief among some people or self learners because they do it wrong. A textbook is meant to be studied for at least 6 months (semester) or even a year or more, depending how fat it is

its not like you read it for 2 days and understand everything

its months of 10++ hours a week

[topaz rune]

at least that is the equivalent of taking a textbook as a uni class

yeah i mean if youre in high school or something and want a little head start watch some khanAcademy, thats pretty good

[past finch]

Is anyone familiar with the "for dummies" series of books? I'm trying to restart by getting a better understanding of the basics of calc/trig. Do you think these are a good place to start or are textbooks going to be a lot clearer?

[topaz rune]

they are quite popular tbh and often rated very good on amazon. Maybe pirate one and check if you like it. I havent read one though and cant recommend based on experience

[gray gazelle]

they’re good

[subtle fractal]

any good books with polynomial manipulation

[icy knot]

Who here has read any literature on “Mathematical Modeling?” I purchased a book from Amazon to learn about it.

[topaz rune]

Mathematical Modeling can mean very much.

Literally every STEM field that is not math does ‚mathematical Modeling‘ as it’s primary purpose, basically

[dawn rose]

Hey guys can you recommend a linear algebra book. It's my first time taking the course, and I heard that it would be proof based (few computational stuff) which is different from the Calculus courses I've taken. I am looking for one that would be good for self-study and for someone who hasn't taken proof courses (idk what they're called but I'm referring to those proving by induction things idk)

[lime vessel]

Friedberg Insel Spence / Axler are nice

[obtuse sapphire]

Any good books for calculus? I'm currently going through the richard courant and john fritz introduction to calculus and analysis, but would like to know some other good ones to check out. Also please tell if the one I'm reading rn is bad or not

[dawn rose]

would you recommend that to someone who has no background on proofs?

[lime vessel]

I think it would be a good idea to separately learn (the basics of) #proofs-and-logic

Which is much simpler compared to any calculus or algebra

Before diving into proof-based linear algebra

[dawn rose]

I don't have much time to learn it separately 😦

[gaunt current]

Hi, what are the requirements to learn number theory? it just sounds cool and im quite interested

[wide plover]

numbers

you need numbers to do number theory

[gaunt current]

any books? to learn, numbers?

[wide plover]

do you know a little combinatorics?

like basic counting stuff using the fundamental principle of counting?

[gaunt current]

no, ive just started 11th grade.. how/where do i learn that? any book reccommendations?

[lime vessel]

This is probably more than all you will ever need https://math.berkeley.edu/~hutching/teach/proofs.pdf
Even the gist of it will suffice

[wide plover]

okay umm.... there's this book by george andrews

very elementary and will handhold you a lot

lemme fetch it

here

[gaunt current]

wow, thank you veryy much

[heady ember]

I second FIS

I don't think its necessary to learn proofs separately, if you at least know/heard of basic proof techniques and know some mathematical reasoning. i.e. stuff like direct proof (nothing much to be said for this), proof by contradiction, induction, contrapositive, converse, inverse, biconditionals.

I think its pretty much unavoidable that you get slapped around a bit when first being introduced to proof-based math so take it easy, don't expect to ace everything immediately. Try to have fun in the challenge

Uh but im just a rando highschooler on the internet so what do I know

[remote sparrow]

#book-recommendations message

[remote sparrow]

an ability to read and write proofs. you can either learn it as you do the material or you can read a separate book that teaches you how to read and write proofs

[novel obsidian]

For this whole proofy thing/ introduction to higher maths I strongly recommend a set of notes by Paulo Aluffi called 'an introduction to advanced mathematics'

They Start off with very simple ubiquitous concepts like sets, functions and equivalence relations and finish with selections of more advanced topics such as the Cantor-Bernstein-Schroder theorem and the zariski topology

But are honestly super accessible and cool

Personally I only got up to the section on dedekind cuts but I found them super helpful for the stuff I'm doing now

[lime vessel]

That's the math major route

[dark tulip]

Could anyone recommend a book on combinatorics theory that is suitable for olympiads preparation?

[wide plover]

#competition-math

they can help you better

[dark tulip]

Alright thanks

[lime vessel]

Siriam is nice

Also tangentially related generating functionology

[wide plover]

such a good book, not combinatorics sadly

does have some nice ideas to count things though

[lime vessel]

I've found its main use to be combi in oly

[wide plover]

well, i just skimmed through the book because it seemed fun, never really used it beyond a few probability poblems

since i never solved a single olympiad problem

[buoyant pilot]

I like proof by 0=1

[wide plover]

the book A=B also comes to mind

[dark tulip]

Geenerating functions is a combi thing ?

[lime vessel]

Cuz nonlinear recurrences for one

[wide plover]

definitely, it really helps to count things

[dark tulip]

Ahh alright thanks for the suggestions

[tawny copper]

Generatingfunctiology is a very slow book and the exercises very computational, not very suitable for oly imo

[fresh iron]

the Hardy's book of course : https://blngcc.files.wordpress.com/2008/11/hardy-wright-theory_of_numbers.pdf

[topaz rune]

Why sully, it’s true. ‚Mathematical Modeling‘ doesn’t even exist as a proper math discipline

It’s physics or engineering, basically

[tawny copper]

There is a better pdf

[fresh iron]

surely! find it on the first link (i have it at home the paper version)

[tawny copper]

Do you have the one with Andrew Wiles preface + extra section on elliptic curves?

Its from china I think

[fresh iron]

oh nope, not this version

ahaha all the online books/articles are from russian or chinese servor 😂

[tawny copper]

Honestly Hardy and Wright is a very good book

But beginners shouldnt focus on the details I think, just read some of the interesting parts and not worry if some points are missed

[fresh iron]

yes !!

[fresh iron]

an advice which is available also for all scientific papers 🙂

[tawny copper]

But they should also use another book/text, an easier one with problems. And most of the effort should be put there probably

[tawny copper]

Yeah. It actually took me some time to realize this 😭

[fresh iron]

me too😭

after that the main issue with the book, most of them are quiet linear, so you have to take them as a complementary of the prof's lectures

[remote sparrow]

this book has no exercises. i don't know if this book is intended as a textbook, though.

but it does prove its theorems

[crude yacht]

The following books have been recommended to me. They are really expensive. Online reviews seem really good and makes me want to buy them. I had purchased the e-books of 4 & 5 back in 2018, but then life got in the way. Before I purchase 1, 2 & 3, I would like to know if any of them overlap, are unnecessary, or are overrated. My interests lie in maths, philosophy and logic. Thank you in anticipation:

1. Introduction to Logic by Irving Copi, Carl Cohen, Kenneth McMahon
2. Mathematical Logic by Roman Kossak
3. Philosophical and Mathematical Logic by Harrie de Swart
4. What Is Mathematics?: An Elementary Approach to Ideas and Methods by Richard Courant, Herbert Robbins, Ian Stewart
5. How to Solve It: A New Aspect of Mathematical Method by G. Pólya

[heady ember]

if you're interested in mathematical logic, check out clerk's reading list pinned here

[dawn sandal]

What am i supposed to do then?

[coral prawn]

download them from totally legal websites

[crude yacht]

Other information would be helpful, like: do they cover the same topics? is one book better than the other for a particular topic? personal reviews?

[remote sparrow]

i know copi's book is not really aimed at mathematics undergraduates

more so for philosophy students

[tawny copper]

use a vpn

there are free ones

dm

but edit the message or delete it lol

[swift dome]

thank you

[dawn sandal]

I guess it's still relevant. I'm a physics major

[empty harbor]

Falconer is good book

About fractals

I love

[crude yacht]

Would you say Copi's book is Logic in the form of literature (English sentences) while the books by Kossak and Swart woudl be Logic in the form of Math symbols? Of course Swart's would be deeper than just Math, but have Philosophical reasoning behind it as well? And would all three books go well together?

[deep field]

has anyone taken look at robert ash's book Real Variables with Basic Metric Space Topology?

like i know robert ash is a very good writer but this book doesn't seem to be as popular as other books by him

[fierce hedge]

I didn't knew he had a book on analysis, I'll check it

[remote sparrow]

@mellow wren any reasons why you're not a big fan of hubbard and hubbard?

[novel obsidian]

Anyone who has studied from spivak's calculus on manifolds, are a first course in real anaylsis and linear algebra (on the level of axler) good enough pre-req wise?

[remote sparrow]

a book like copi's is a broad introduction to what counts as correct and incorrect reasoning. it is mainly a book to build critical thinking skills. a textbook on introductory mathematical logic (such as enderton, goldrei, mendelson, or mileti) has a much narrower scope. the main concern is analyzing models of deductive thought. a lot of time is spent on first-order logic, a model strong enough to capture everyday mathematical reasoning. limitations of these models (like godel's incompleteness theorems) are also discussed.

[remote sparrow]

yes

it states as such in the preface

[novel obsidian]

authors lie

[remote sparrow]

that is sometimes true, but a quick skim shows it is telling the truth

[remote sparrow]

are image perms disabled for me in this channel

[finite gale]

Try and find out I guess

I think it's disabled in here or adv lounge but idr which one (or both)

[lime vessel]

Here

Unless active

[remote sparrow]

how does one get active or very active

i post a fumo meme in #chill every day and i normally hang out here

[lime vessel]

#discussion message

[remote sparrow]

i used to be able to send pics in here though

probably because i got banned for my april fools' joke

[finite gale]

You either shitpost a lot in discussion or you type a lot in normal channels

[tender river]

what was the april fool's joke?

[remote sparrow]

#book-recommendations message @finite gale

[remote sparrow]

it was "click here for free fumo:" with a shortened url

the link was harmless

i think it was a fumo video

[finite gale]

i dont get it

[crimson hearth]

Is Arnold's dynamical systems book good for someone who has a bit of experience in dynsys and analytical mechanics?

[remote sparrow]

oh i was just mentioning a time i was able to send pics in this channel

[finite gale]

oh

[remote sparrow]

do you also know real analysis

if you have all of those, then you should be good

[crimson hearth]

Ah I see, no I do not ;-;
Is it like serious analysis or just basic epsilon delta stuff

[fallow cypress]

we turned it off at some point

because of spammers

[empty junco]

grief

[remote sparrow]

solid one-semester introductory course covering differentiation and riemann integration

[crimson hearth]

Ok not...awful

[crimson hearth]

I guess now is the time to ask for analysis book recs?

[remote sparrow]

there are many accessible books

abbott is a good choice

[mellow wren]

I find it a very shittly written book for the audience they're targeting and notably I find that a lot of the material in the book isn't useful
i.e. I don't find that knowing about differential forms in R^n at that point in your education is something that you need or will really care about in any way
I'd much rather a student grab some UG differential geo book to learn half of the stuff that H&H cover

[jagged panther]

what books should i read for olympiad algebra?

and want to start number theory but dont know where to start(i forgot everything number theory related) if you have any recommendations kindly suggest some

[remote sparrow]

@mystic orbit any reasons why you like hubbard and hubbard? perhaps why you favor it over some of its competitors?

[empty harbor]

Good book on porosity of fractals, please.

[remote sparrow]

ah linear algebra is also necessary

[crimson hearth]

Oh yeah of course

[mystic orbit]

I confess I don't know what its competitors are

maybe spivak?

but the two aren't even comparable

they serve completely different purposes

anywho, I just like it a lot coz it briges the gap between hs and uni math very well, the only prereq being calc bc

it's very chatty and the margins are huge specifically for spouting cute facts around the text body or just commenting on it

which I find super cute

there are a few caveats, like introducing the eigenvalues in a cryptic algorithm that's supposedly "more computation friendly"

I hear you but

at least introduce the characteristic polynomial

I'm also straight up just biased since it was my first math book

and I only did the first 200-250 pages so mostly just LA

[lusty ermine]

Hi guys, do you guys recommend any books on solving systems of linear congruences?, like the one from this problem, Let ( a ), ( b ), and ( c ) be integers such that the following equations hold:

\[
7a + 3b = 4
\]
\[
2b + 11c = 5
\]

Find the remainder when ( b ) is divided by 77.

[hasty eagle]

renato (ping if reply)

[mystic orbit]

uh, I would just do linear algebra if I were you

why such a specific request?

[tender river]

this is number theory??

[mystic orbit]

you can do linear algebra on rings

:)))

[remote sparrow]

shifrin or colley

[remote sparrow]

see burton or dudley's book

generally pops up in the context of the chinese remainder theorem

[fierce hedge]

never heard of colley is this a recent book?

[remote sparrow]

no

first edition was released in 2002

apparently a fifth edition exists, which was released in 2022 and has a new author, but no pdf for it is online yet

the fourth edition was printed in 2012

https://www.amazon.com/Vector-Calculus-4th-Susan-Colley/dp/0321780655

apparently the 5th edition is only available through pearson's website

it's probably print-on-demand garbage anyway

[lusty ermine]

really?, I thought this was more introductory

and just now someone told me CRT is not even needed 💀

[tender river]

critical race theory?

[wide plover]

Chinese remainder theorem lmao

btw if you are joking, I definitely missed that

[lusty ermine]

[remote sparrow]

sorry for necro, but was this a paperback or a new hardcover

[fierce hedge]

This was a paperback, probably an Indian edition one

[remote sparrow]

ehhh i guess that's to be expected

but the hardcover is so overpriced

[fierce hedge]

The worst part is the pdf is also not good enough that I could print it

[remote sparrow]

yeah

[fierce hedge]

Dude why do you have a 3d spinning Malboro packet as your pfp

[lusty ermine]

I only read pdfs, cant afford to buy :(, maybe in the furure

malboro red :'v

[remote sparrow]

buying used is generally better if you want an old book anyway, and it's cheaper to boot

buying new copies of textbooks is generally a bad idea because their construction quality is awful

i still buy books that are more recently published because i still want a copy to read from away from my pc but i really wish i could lay them flat for example. lot of new books are essentially paperbacks with cardboard covers

without breaking the damn book

[fierce hedge]

I wish I had this option in India, here old books are usually more expensive than new copies

[tawny copper]

Buying books for reading is a waste of money

Unless you want to collect books, which is totally different

[remote sparrow]

i mean, the closest analogue to a physical book is a dedicated e-reader (not an ipad)

those are pretty expensive for how limited their functionality is though

however, you could have a very large library on there of less than legally obtained ebooks

so i guess it's kinda worth it?

[tawny copper]

Also

Libraries exist

[remote sparrow]

yeah but i don't want to borrow books

[tawny copper]

Why

I can borrow books for months lol

In fact, I have

[fierce hedge]

Not everyone has access to decent libraries

[remote sparrow]

also that

[tawny copper]

but the solution is not to buy books anyway

[fierce hedge]

[wide plover]

you can never get the smell of books from any tech

it's just not the same

[remote sparrow]

look, i can agree that if you have very limited funds, you shouldn't prioritize buying physical books

[wide plover]

the feeling of turning pages is so good

[remote sparrow]

but i love books

what if my hard drive gets corrupted

[tawny copper]

I said, this is totally different

[fierce hedge]

So people who get eye strain from reading PDFs and do not have access to decent libraries should do what?

[chrome yacht]

i like to steal books sometimes

[remote sparrow]

or all the shadow libraries get taken down

😭

[lusty ermine]

honestly, whats important is the pdf material :v

maybe when I get big money ill buy dem books

[remote sparrow]

i effectively did once lol. basically i just took a book, library declared it lost, so i paid the replacement fee. basically like buying the book from them lmfao

[tawny copper]

Yeah all the arguments you can give is "smell, turning pages, etc"

[tawny copper]

If this really happens, print the pdf

Lmao

[chrome yacht]

lol people at my college used to do that

[tawny copper]

Pretty sure is less expensive, and you can just print a single chapter

[remote sparrow]

i love printing loose pages!!!!1

[fierce hedge]

For me printing is more more expensive than buying books

[lusty ermine]

[tawny copper]

How

[fierce hedge]

Wdym how I don't decide the print rates or the book rates

[remote sparrow]

if you know your book uses a thin magnetic tape as an anti-theft device, hypothetically you could run a very strong magnet over it

don't steal books though

[tawny copper]

Honestly

[remote sparrow]

it's for the public good

[lusty ermine]

[wide plover]

i straight up took books from the uni library, covid happened, they never asked them back

[tawny copper]

Im skeptical that paper is much of an improvement over screen for eye strain

[wide plover]

[tawny copper]

But I could be wrong

[wide plover]

try paper once

[tawny copper]

Also, Im pretty sure 99% of you here defending paper do not suffer that

[tawny copper]

Lol ofc I did

[fierce hedge]

You either have some premium screen or low quality eyes

Possibly both?

[remote sparrow]

idk, textbooks used to be dirt cheap according to some older profs and had a very high construction quality to boot

[wide plover]

yeah, capitalism moment

i can't buy a springer book without getting straight up broke that month

[remote sparrow]

and the book falls apart within a few years

[wide plover]

i bought harthshorne, it was like half of what my college payed me during masters

[remote sparrow]

never buy old textbooks new

only used

cheaper and ironically the copy will last you longer

since the books are just made better

[wide plover]

i just print books now if there's a good enough e-copy

[remote sparrow]

where do you print them

i tried lulu but their printing process is surprisingly finicky

couldn't just upload a pdf as is and just have them print it

[wide plover]

in my country, there exists this company called printster

[remote sparrow]

yeah numbily uses that

he also lives in india

[tawny copper]

Its not I think, regular people do not buy stuff from Springer. Its universities, which get state funded

[wide plover]

still capitalism

the regular people do not buy papers from journals, yet academia is fucked

somehow people realised that this economic policy is very... lucrative...

[tawny copper]

Because its universities who mantain journals alive spending the money from state funding lmao

[hazy elk]

Why don't mathematicians band up together and eliminate the middle man then

[tawny copper]

Super responsible

[hazy elk]

Editors and referees would still exist

[wide plover]

too much political power is in the hand of the companies

[wide plover]

yep

[hazy elk]

I mean nothing is stopping some big names in math coming up together and forming a journal right?

[tawny copper]

Yeah right

[wide plover]

nope, but I really don't know why

do math unions exist?

[tawny copper]

Isnt arxiv trying to do that a bit? Maybe Im wrong tho

[wide plover]

arxiv is a preprint site

not a journal, that's the issue

[deep field]

wow

robert ash's book is surprisingly good

[fierce hedge]

The real analysis one?

[deep field]

yep

i've only taken look at the first chapter

[fierce hedge]

I have the pdf but it's hard to render for whatever reason

Oh there's an epub version also

[deep field]

don't use epub

the images are broken there

[lusty ermine]

Anyways, pdf >>>>>

[deep field]

my first impression with the book: the table of contents is quite similar to rudin but the explanations are much friendlier

also i think the book's topics is less sophisticated than rudin but goes in more deeper than , say, abbott and ross

[old elk]

Hi guys, I would like to learn group theory on my own, I would like to know which books you recommend.

[wide plover]

Gallian is a very good book.

I personally like the book very much. Very cute exercises, and holds your hands where needed

[gentle arrow]

artin

[old elk]

Please send me the pdf file

[deep field]

search it yourself if you want it

[old elk]

i found it

[old elk]

Thanks for your feedback :D

[turbid fulcrum]

how long does it take 4 u guys 2 finish 1k pages of math textbook

[old elk]

In reading it or understanding it?

[tawny copper]

obviously understanding

and getting the skillz

[old elk]

wow

[tawny copper]

2 days

this is obviously not a smart question to ask, hopefully you realize

[turbid fulcrum]

well i wanted to know how long it takes 4 u guys

cuz ive been reading a 1k page math textbook for 6 months and not halfway there yet

im asking so i know if my pacing is normal or not

[tawny copper]

think of what you are saying please

[turbid fulcrum]

wdym

[subtle fractal]

any good short books that cover everything about calculus i need it for my cousin and i cant find my old book

[fierce hedge]

It's called my pacing for the reason that it's yours will highly depend on you. If you think you're going slow, try increasing your speed a bit.
If you're unsure and the book you're reading is common enough, try searching for some course based on the book and see the pacing in that course.

[pliant stream]

Maybe u r slow reader😦

[crude yacht]

I am reading an out of print book "Calculus" by Lev Tarasov. I got the PDF url from this server in the #books-old or #resources channel somewhere. Couldn't find it on Amazon, or any online book shop... so I took a print of the PDF! A very well-written book, which is written as a dialogue between Teacher and Student. Very few typos here and there. And honestly, I have read a few textbooks decades ago, and none of them are in the same league as this book. I am also using YT/ProfessorLeonard's Calculus playlist as a video companion with this book.

[remote sparrow]

#book-recommendations message

[mystic orbit]

[narrow relic]

I spent about 4 months reading 45 pages or so of an analysis book for about 90 minutes a day

[stoic sleet]

Hey, i have a course that starts with ODEs. PDEs , cauchy problem, then has some complex analysis, and finishes up with fourier and laplace transform

any book you guys suggest for these?

[old elk]

Does anyone know where I can get the topology book by munkres ?

I can't find it and on amazon the prices are quite exaggerated.

[remote sparrow]

https://www.amazon.com/Topology-Classic-Classics-Advanced-Mathematics/dp/0134689518/

[remote sparrow]

https://www.amazon.com/First-Course-Partial-Differential-Equations/dp/048668640X

[stoic sleet]

this one has them all right

i'll check that out

[pliant stream]

i can sell u mine lmao

but u can get the intl pearson edition for pretty cheap

alternatively just print out the book

[remote sparrow]

a standard ODE textbook is boyce and diprima. tenenbaum and pollard is also good. boyce has coverage of boundary value problems and a tiny bit of PDEs, which tenenbaum and pollard does not cover. however, tenenbaum and pollard fully prove existence and uniqueness by picard's method. the course description sounds like an intro to PDE, though. i'm going to guess that ODE coverage won't be super extensive, maybe just a review of some basic techniques, especially separation of variables.

[stoic sleet]

you want to see an average exam of the course?

maybe it will help

[remote sparrow]

sure

[stoic sleet]

#real-complex-analysis message

some other exams ask you to solve an integral with starting point |z| = 3

this course feels like it has so much of different matters but none is quite in depth

like touching a lot but not too deep

[remote sparrow]

oh, i don't know how to read the language of your exam

but the course description fits pretty closely with the book i recommended you

maybe you could show the book to your professor and ask if this text could be used as a reference for your course

[stoic sleet]

i can help on what they are asking for

[remote sparrow]

ok

[stoic sleet]

i think the ode textbook by boyce and diprima might be better @remote sparrow

the other one seems quite advanced for me

[remote sparrow]

tenenbaum is actually very elementary and accessible

[fickle whale]

What's a good ODE book

[foggy relic]

https://www.google.com/books/edition/Ordinary_Differential_Equations/JUoyqlW7PZgC?hl=en&gbpv=1&printsec=frontcover

[remote sparrow]

there are many ode books aimed at different audiences

[fickle whale]

My concerns are geometry, physics, and getting through ODEs as quickly as possible so that I can get to PDEs

[remote sparrow]

boyce and diprima or any other similar book will work

after that, consider reading strogatz or hirsch, smale, and devaney for dynamical systems

hirsch is a bit more sophisticated and while it can be read without knowledge of linear algebra and real analysis, it is best appreciated knowing them both

strogatz has a much lower bar for entry, only really requiring a thorough knowledge of single variable calculus and an ability to work with separable ODEs. some multivariable calculus and linear algebra is interspersed through the book. fourier series is developed on an as-needed basis.

there is also blanchard, devaney, and hall, which is designed as an alternative to books which focus almost exclusively on closed-form solutions like boyce and diprima

[old elk]

EDO sotomayor

Edo dennis zill

EDO Carlota Lopez

[gray gazelle]

I started to learn mathematics, someone have some hints?

[hollow shore]

https://www.math.clemson.edu/~macaule/classes/m17_math2080/

this is a good course I found on ODEs which follows a different variant of boyce diprima

[remote sparrow]

paul's online math notes on ODEs seems like it follows boyce and diprima as well

don't stress out too much over knowing all these techniques for producing closed form solutions though

[fervent magnet]

What are some places to buy cheap ebooks?

[heady ember]

piracy

[fervent magnet]

Buy

[remote sparrow]

there is zero reason to buy ebooks unless nobody has uploaded the book yet

if you want to spend money on a book, buy physical

[fervent magnet]

It’s not cheaper?

[remote sparrow]

why pay for them though

when you can obtain them illegally without any consequences

[heady ember]

[fervent magnet]

You pirate books?

[remote sparrow]

yes

[fervent magnet]

Ethics

[remote sparrow]

lol, if you really want to abide by that idc

[heady ember]

Uh well book publishers charging hundreds of dollars for one book just because they can isn't particularly ethical either

[remote sparrow]

umm excuse me, two wrongs don't make a right here 🤓

[heady ember]

Well, I didn't say piracy is right

[remote sparrow]

#book-recommendations message

meanwhile the print quality

[heady ember]

That's a big rip

My copy came nicely

[remote sparrow]

don't worry, i got a much better copy after i returned that one

[heady ember]

ah nice

[fierce hedge]

Even quality wise I find its much much better for me to print it than buy it. Like Indian editions are cheap paper BUT for the slightly higher price I can get the book printed on high quality 85 gsm paper with hardcover.

The only reason I think my purchased copy of Rotman Algebra is decent because it's old book that was printed on good quality paper.

Like the Indian editions of FIS and DnF is much much worse

[hollow shore]

Indian editions are available everywhere but India, I found

rudin, d&f, herstein, etc

[coral prawn]

well they need to make a living

[fierce hedge]

You're not looking at proper places then. I found Indian editions of all of them

[heady ember]

Yeah, well, I don't think the cop of producing one book is hundreds, nor does the author receive much of the revenue?

[coral prawn]

but not many peeps buy math books- there's already a wide variety and a niche audience of sorts.
And yeah perhaps it'll be fairer if the money was used to fund the author and not the publishing/print company

but yes they all can cope if we can get it for free anw

[hollow shore]

they are all out of stock rn

[tulip saffron]

if I want to learn tensor manipulations, which book should I read?
I dont think la books cover this do they?

[lyric gate]

Is there any book (or any forms of resource would be fine) that teach you how to write proof? Not about logics, or proof methods, but how to articulate your ideas. My proofs are just messy and unreadable by anyone but me.

[stray veldt]

i dunno, you learn this by just reading proofs

in general a proof is just a english (or whatever) language text

[stray veldt]

a book on commutative algebra might work; gathmann's notes on commutative algebra are freely available and have a chapter specifically on the tensor product of R-modules

[mystic orbit]

I do

Sometimes

[teal vale]

(sorry being being very late lol) Probably history, science or maths

why not

looks hard but fun to read

thanks

[fierce hedge]

NO, have you ever done axiomatic set theory?

If no then stay away from that book

[teal vale]

no

[fierce hedge]

It's a hardcore grad level set theory book

[teal vale]

Just for learning that i'm gonna read it

[fierce hedge]

I don't think you'll be able to read it, you need some background in set theory to be able to read it

[teal vale]

yeah i don't think i should be reading graduate level stuff as an 11th grader

[heady ember]

Or your course mandates the purchase of a certain book

[fierce hedge]

Or forcing people into using newer editions of the book which doesn't vary much from the previous editions

[dawn shoal]

Does anyone recommend some problem set book with solutions for multivariate calculus?

[tender river]

#calculus message

[fierce hedge]

A problem based course in advanced calculus by Erdman. I hope it's not too advanced for your purposes

[dawn shoal]

I might actually be looking for something even more advanced

And thank you!

[fierce hedge]

Oh then you should try looking at the one Pika recommended

[ocean shore]

Does anyone know a good book for game theory?

[dawn shoal]

Correct me if I'm mistaken, but isn't that book for the introductory calculus? But that's probably my mistake because I know calculus is a pretty ambiguous term across countries. I'm looking for problems for real analysis when everything starts resembling linear algebra, so stuff like Stokes' theorem, the Hessian matrix, etc.

I'm at work now, but I can provide a broader set of topics we're going to cover in a few hours

[fierce hedge]

Well I assumed it to be more advanced, I didn't actually knew. That said if you're looking at advanced stuff then there's a lack of problem books. You'd have a better luck at finding problem sets of courses on that particular topic.

[dawn shoal]

I see. :( Thank you both for the help, really appreciated 🙏❤️

And sorry if my message came off as rude. I read it now and I guess it might have... That wasn't my intention

[heady ember]

Our book indeed, comrade

[tawny copper]

#book-recommendations message

[remote sparrow]

#book-recommendations message

[fierce hedge]

nah, it was pretty normal. Chill

[gray gazelle]

What do y'all recommend for pre calculus 🥲

[hollow shore]

Basic Mathematics by Serge Lang

Gelfand's texts are good too

[sterile pelican]

Those two authors are a gem for precalc especially Gelfand’s Algebra and his Functions & Graphs

Basic Mathematics by Lang encapsulates all you need for precalc and is not boring like the other precalc books, since others tend to involve mindless computations

[tulip saffron]

what's the generally recommended books for machine learning here?

[empty mortar]

high dimensional statistics by wainwright

[small perch]

Can someone suggest graph theory textbook or maybe other source?
I know nothing about graphs. Not going to read it rn, Just have some linkage with books I read rn and I think need some familiarity with definitions and notations, especially in set-theoretic manner

[sterile pelican]

Out of curiosity what would be a good book to learn statistics-related topics after Blitzstein's probability? I was initially thinking Hocking's Linear Models

[spring pendant]

https://en.m.wikipedia.org/wiki/The_Simpsons_and_Their_Mathematical_Secrets

Very fun book for anyone interested in studying math as a disciple but does not have a math background

Math needs new energy and books like this intro can help you get your students who may not know how interesting math and the universe is … 2b interested in math

I’d like to thank my pod mates … lol jk screw pod mates … but yeah thanks to the fella or lady who recommended this book …

Awkward we use the same discords

.
🙂
From the Wikipedia :

Rather than just explaining the mathematical concepts in the context of how they relate to the relevant episodes of The Simpsons, Singh "uses them as a starting point for lively discussions of mathematical topics, anecdotes and history".[2] Topics covered include Fermat's Last Theorem, which Singh has written a popular book about, and Euler's identity.

[pliant stream]

depends what kind of statistics

[sterile pelican]

Hmm I am not entirely sure

[pliant stream]

wassermans book is an okay introduction

[sterile pelican]

All of Stats by Wasserman?

[pliant stream]

then u could decide what to read from there

yes

[sterile pelican]

I do have that book I did some snippets of his probability proofs

Hmm I could continue it it is a cute book

very concise too

I was initially hoping to have a deeper book like Hocking's linear models but honestly I am not sure what a statistician tends to poke around the most, or need to be a working statistician

[pliant stream]

try the book stat foundations of ds

[sterile pelican]

By Jianqing, Runze, Zhang, and Zhou?

[pliant stream]

yes

[sterile pelican]

Oh this is nice

even has machine learning

[pliant stream]

i havent really read it much but it should be good

[remote sparrow]

wackerly, mendenhall, and scheaffer

[sterile pelican]

One thing that frustrates me with most ML books is that they don't explore the maths deeply

[pliant stream]

there's some abuse of notation in the book that could be confusing, but it should be oka

okay

[remote sparrow]

A Walk Through Combinatorics by bona covers some graph theory, but is a more general combinatorics textbook

[sterile pelican]

Ah this is a stats inference book?

[remote sparrow]

it's a mathematical statistics text

it does cover some statistical inference

[sterile pelican]

Hm I will have a look at these two books thanks

[subtle fractal]

any good books i can use to practise factorising equations i need to learn to do this really fast

[mystic orbit]

why.

[subtle fractal]

for complex numbers in geometry

[mystic orbit]

that doesn't explain anything lmao

you can prolly find something in khan academy tho

there's a complex numbers module iirc it had a lot of factorization stuff

[shy meadow]

Khan academy is too good for basics

[subtle fractal]

i just need practice problems i know how to factorise equations

if that makes sense

[frigid plinth]

is RD sharma and agarwal gud to refer in grade 10?

[shy meadow]

oh

[shy meadow]

yeah ive used agrawal it was good

[frigid plinth]

alrightt

thnx

:))

[shy meadow]

🙂

[pliant stream]

How to learn algebra for statisticians?

[frigid plinth]

algebra ez

dw

watch tutorials or sum

[tawny copper]

many diophantine equations can be solved by factoring

so look for some nt problems, idk if you have already

[frigid plinth]

how do u solvve it?

[tawny copper]

by factoring

[subtle fractal]

add 1 to both sides and you get (x-1)(y-1)=4 at least that's how i solved it and it's pretty trivial from there

[shell osprey]

What books are good for undergraduate statistics and also numerical analysis

[pliant stream]

?

i don't know algebra now I'm lost >.<

[formal bronze]

Since when have statisticians needed algebra?

[sturdy shore]

group of symmetries of data samples

[pliant stream]

To learn free probability and rmt

[formal bronze]

Interesting

[remote sparrow]

wackerly mendenhall scheaffer for stats and my school uses burden and faires for numerical analysis

[shell osprey]

Thanks

[hollow nymph]

Are springer books usually pretty good?

Looking for DE, PDE, measure theory, and diff geometry recs

[sturdy shore]

they publish an absurd amount of books, so this is hard to answer

but I'd lean yes?

[sturdy shore]

measure theory: axler, folland
diff geo: tu - intro to manifolds -> diff geo
pde: evans

[remote sparrow]

content wise they are generally fine

a few full color books seem to be well-made, like axler's books and tapp's diff geo of curves and surfaces

but expect your book to be crappily made if it's a primarily black-and-white book and you choose to buy new

[hollow nymph]

What do you m ean?

"color books"

[remote sparrow]

books that have full color

that's quite rare tbh

[hollow nymph]

OH I completely read over the "full color" in your first message

Yeah I haven't had a colored math book in a while

[frigid plinth]

dont worry

[frigid plinth]

what concept u learning rn?

like about what in algebra?

[sterile pelican]

Cox has beautiful colours

[hazy sandal]

how to learn coordinates?? Whenever I practice coordinates, I become lost. This is making me very tensed, pls someone give tips

[sterile pelican]

Basic Mathematics by Lang

If you are willing to try then Functions & Graphs by Gelfand

[hazy sandal]

well I want tip on how to read coordinates from my school book to be able to solve any type of questions

what should I do for that?

[sterile pelican]

The only way is to understand how to do it, you can use Khan academy for that or use the books I mentioned (good books tell you how). There is no real tip nor secret to maths let alone read coordinates, maybe you can make personal analogies but I cannot help you there

You can ask for help here but not on the book-recommendation channel

[mystic orbit]

measure theory: folland or royden

diff geo I'd say intro to smooth manifolds but I haven't read that book, I just like lee's writing style a lot

[mystic orbit]

<@&268886789983436800>

unsolicited ad

[meager jackal]

thoughts on introduction to topological manifolds by lee?

curious what others' experiences with the book are

[glass adder]

sounds cool

[gray gazelle]

.
.
i dont make money from Singh , y censor ?

<@&268886789983436800>

blackcube hate symbol to many

and the book you took down ... i dont make money from that book and its an excellent book ... and i explained it was excellent for getting new people without math backgrounds interested in math ...

does mr dark cube have some unusual sway around here ?

[mystic orbit]

what

black cube hate symbol?

bro I didn't even read your message

what..

are you proposing we fight?

this is rather amusing but i gtg

[gray gazelle]

.
.
are you racist against Singh mathemeticians ?

[mystic orbit]

the reason I pinged mods is that unsolicited ads are against the rules

as I said, I barely even read your message

[gray gazelle]

<@&268886789983436800>

people who act like blackcube here are not safe

[mystic orbit]

[night gorge]

🤨

[gray gazelle]

<@&268886789983436800>

i didnt make any ad ... this is a math book recommendation threat right ?

i posted the wikipedia link to a math book by Singh

[mystic orbit]

who tf is singh?

it means lion?

[tender river]

black cube is hate symbol against jesus?

[mystic orbit]

nah I think jesus is chill

[sturdy shore]

I always knew DarQ was a terrorist

[mystic orbit]

for his time at least

[gray gazelle]

if you recommend a book ... in a book rec thread ... how is it not an ad ?

i didnt post amazon link ... i dont make money from that publisher or book

arent all posts in the book rec thread ads ?

[mystic orbit]

1. it is an ad, yea

2. and no, typically they're in answer to some book rec request

[gray gazelle]

you must not spend much time here black cube

[mystic orbit]

[tender river]

no don't

[sturdy shore]

this guy is unhinged wtf is this

[mystic orbit]

can you stop threatening me

lmao

[sturdy shore]

<@&268886789983436800>

[gray gazelle]

i called you dangerous

you snitched to have singh censored

.
.
trust me old timer ... you are dangerous

[mystic orbit]

https://tenor.com/view/explaining-talking-speed-i-am-the-danger-skyler-gif-19043411

[gray gazelle]

<@&268886789983436800>

we should ban hate symbols in avatars

MODS

delete all of my posts and all of the posts by this dangerous snitch ...

this is a waste of oxygen ...

thats what old timer trolls do ... steal life via snitching

[night gorge]

What are you actually saying

Are you running this through some post processing AI and spitting out the results

[mystic orbit]

they're saying I'm dangerous

[night gorge]

[tender river]

this is a waste of oxygen

[night gorge]

Terry Davis reincarnated in the mathosphere be like

[empty junco]

https://tenor.com/view/senator-armstrong-armstrong-metal-gear-rising-mgr-speech-bubble-gif-25397532

[vocal trellis]

dex dux

[dusty grail]

Does anyone have a physical copy of Axler’s “Measure, Integration and Real Analysis”? If so, is it printed in color or just black and white? I’m considering buying a copy but i saw a review that said they received a black and white copy which would be a bummer cause I like the colors in Axler’s books

[remote sparrow]

last semester my university bookstore had this book stocked. the pages were in full color and were made of nice glossy paper. the binding, to my eyes, looked good too.

[dusty grail]

sweet thx for the info👍🏼

[uncut star]

Can anyone recommend a book on fiber bundles with physics applications?

[median saffron]

I don’t like your name or PFP

it’s very not good

[fierce hedge]

The fuck, is that shit allowed here

Dude which part of this is intended for #book-recommendations

[quick hornet]

pls ping mods if youre unsure

in this case, the answer was "no"

[fierce hedge]

thanks, will do

[oak forge]

can someone recommend me a very simple introductory book for PDE? Every book i've found here tends to be too hard.

[uncut star]

Has someone recommended Haberman's PDE book yet?

[oak forge]

Not yet, I'm gonna take a look, thanks!

I've been struggling with PDE's for quite some time

all DE's

[oak forge]

Excellent book! Thank you so much!

[fallow cypress]

I don't think that DarQ's avatar is intended as a hate symbol.

Also if anything, DarQ has negative sway around here, we do the opposite of what he tells us to do

[upbeat vine]

Can you tell what aspect of PDEs you're struggling with? Say why aren't you going for Evans, for example

[fallow cypress]

If they're looking for "simple, introductory" then I imagine they don't have much of an analysis background

[mystic orbit]

wtf!

D:<

[gusty smelt]

lol

[finite gale]

It might not be introductory but is it simple and intuitive

[oak forge]

I don't think i struggle with anything specifically, I generally tend to take much longer to understand on ODE and PDE. I prefer more algebra, topology, etc.

Probably I'm not sure how to study them. From my experience, ODE was all about memorizing tricks and techniques to apply to equations

[oak forge]

Evans is way beyond what I need

[oak forge]

Yes exactly

[upbeat vine]

Walter Strauss is the usual recommendations then

[finite gale]

I was memeing

[oak forge]

Well I don't

That's why I'm avoiding these hard books

[oak forge]

Thank you for the recommendation!

[finite gale]

i don't think there is much point in "studying" pdes without analysis background

[remote sparrow]

https://www.youtube.com/watch?v=-yksoVsb47s

two other books not in the video are those by zachmanoglou and weinberger

i think hillen and weinberger have full solutions

[fallow cypress]

it depends what your purpose is

if you're an engineer or physicist it makes complete sense

if you're aiming to be an analyst then yeah it doesn't make sense

[finite gale]

ngl i forgot engineers exist

[sturdy shore]

understandable

[remote sparrow]

DAE pi = e = 3???/

haha engineer approximations go brrr

[fallow cypress]

this is wrong

pi = 3 + O(1)
:)

[remote sparrow]

ummm but that term is negligible, so it's basically the same thing as 0

[dreamy horizon]

is griffith's intro to electrodynamics good for a first course in EM? i am not vibing with serway and jewett even though i liked it for mechanics

[finite gale]

it's common knowledge that 0*1 = 0

[dim sierra]

I think it's normally used for a second course

[dreamy horizon]

yeah i think you're probably right

just going off the table of contents

[tardy oasis]

what the hell was this entire conversation

[trim elm]

We used it for our first EM course

But our first EM course jumped straight into vector calc

There were good reviews of the book within the class

[remote sparrow]

it's not the intended audience

if you really know your vector calculus, i suppose you could use it over serway and jewett. but the point of the intro E&M class is to build your physical intuition.

these introductory courses also come with a lab component that serve as a common baseline of examples that your more theoretical classes will draw from

these introductory courses also teach you to exploit symmetry. yes, there are more general mathematical formulations which also produce the right answer for the special cases you learn in introductory E&M, but understanding the situation physically is just quicker than grinding through the calculation in those cases.

[remote sparrow]

https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107

second edition of horn and garcia's matrix-theoretic second course on linear algebra is now available

[charred lagoon]

Challenges and thrillcs of pre college mathematics

https://www.amazon.com/Challenge-Thrill-Pre-College-Mathematics-Krishnamurthy/dp/9393159149

[worn cipher]

Perhaps have a look at Khan Academy 🤔

[gray gazelle]

hey

[deep field]

dunno if this question is appropriate for here, but has anyone read python crash course(the book name)?
I've heard that the book is good but i am a bit concerned about the title 'crash course' as this might indicate that the book has less contents/much easier than another books on python

[gray gazelle]

bro this is a mathematics discord server

but I do have some recommendations

[deep field]

mind telling me? thanks in advance

[swift dome]

Number theory, algebra, and probability/combinotrics are the topics I'm looking to practice. There is an olmpiad exam that I've been preparing for, so I need some good references that I can look into that will cover everything from the basics to most of the advanced topics in it. plus discrete mathematics (graph theory), which will cover most of the undergraduate math too

[tawny copper]

Mathews "problem solving tactics" maybe

[grizzled drum]

*This is a second year mathematics course for engineering students which introduces fundamental mathematical concepts that are used in many areas of physics and engineering.

This course includes two streams, vector calculus and complex analysis. The vector calculus stream studies calculus for functions involving multiple variables. Topics covered in this stream include curves in space; optimization methods for functions of two and three variables; double and triple integration; line and surface integrals, and the theorems of Green, Gauss, and Stokes. The complex analysis stream studies differentiation and integration for functions of a complex variable. Topics in this stream include mapping problems; the Cauchy-Riemann equations; the Cauchy-Goursat Theorem and Cauchy’s Integral formula; Taylor and Laurent series; and applications of complex function theory to real integration.*

im looking for book suggestions

the most i know of complex analysis is e^{i theta} = cos theta + i * sin(theta)

vector calc im not too confident

[uncut star]

is this a math methods class? also what level?

[grizzled drum]

Somewhere around second year

[uncut star]

undegrad right? Have you tried Boas?

If you want slightly more advanced, Riley Hobson Bence or Arfken could work

But they're also the kind of book you don't wan to carry around 😅

so get a digital copy if you can

[grizzled drum]

I see that Riley Hobson Bence and Arfken both have digital versions (kindle)

They seem to have good rating

[uncut star]

yeah they're standard references

[grizzled drum]

Does Boas have a digital version

[uncut star]

I think so

[grizzled drum]

I cant seem to find a digital version of it on amazon

[uncut star]

well if you want a physical copy, Boas is easier to carry around

Just get a used one

or go to your school's library

[grizzled drum]

I think I found the digital pdf online

❤️

[crimson leaf]

Maybe look into Kreyzig engineering math

[grizzled drum]

👀

[sterile pelican]

Kreyzig's Functional Analysis? :^)

[remote sparrow]

brown and churchill is a standard reference for complex variables for an audience of scientists and engineers

there is also gamelin, which is directed at math students (and includes some advanced, graduate topics, but the undergraduate topics are covered gently)

vector calculus is covered in any mainstream multivariable calculus textbook assigned for "calculus 3," for example stewart

i.e. third semester calculus, after covering limits, differentiation, integration, sequences, and series in a single variable

[broken shoal]

I did a course on Ordinary Differential Equations in 2022, but then I haven't had any math courses this year. Now I've got Partial Differential Equations and I wanted to go over ODE again before this semester starts. Does anyone have a book that's good for like being reminded about how ODE works?

I saw a recommended book in the #books channel but the description said that it's not good for self study.

(Please @ me if you've got a recommendation!)

[ocean spindle]

Fundamentals of Differential Equations (9th Edition), by Nagle, Saff, and Snider

unless u want to use a diff book

[broken shoal]

I think that's the one that the channel was talking about

[prisma inlet]

Anyone have book recs for integration practice? Not like calc-learning books, but integral-specific, with good practice problems/some of the less commonly used methods etc. that might be good for integration bees etc.

[latent cosmos]

there's a mathematical treatise written in the form of a conversation between three characters that I can't remember the name of

one of the character's names translates directly to 'ignorant' or something similar

I'm trying to remember the name of it

It's several hundred years old

[latent cosmos]

Anybody know the name of this book?

[latent cosmos]

Nevermind. Was finally able to find something while I was looking for it online

Discourses and Mathematical Demonstrations Relating to Two New Sciences

[proud gazelle]

in what order should I read Princeton Lectures in Analysis?

and what are they prerequisites

[remote sparrow]

instead of looking through a book, consider looking at notes, such as paul's online math notes on differential equations

[remote sparrow]

in chronological order of release

you need only a firm background in real analysis

kiselev's two volumes on geometry

[tawny copper]

Gordon "complex integration", Nahin "inside interesting integrals", Moll "irresistible integrals", Valean "Almost impossible sums and integrals" I and II (this last one is considerably more hardcore), https://www.youtube.com/@maths_505

[tawny copper]

Im pretty sure I, II and III are mostly independent lol, so just read what you want

[lusty ermine]

hi guys

can someone recommend me a good book for solving pdes

[hollow peak]

For basic undergrad plug and chug, maybe check out strauss

If you want theory, read Evans

@lusty ermine

[lusty ermine]

#help-4

specifically its regarding the method of characteristics

what do you think it will suffice?

[sage python]

Pfft nowadays we use Taylor

[old elk]

I have one

Abdul-Majid Wazwaz , Partial Differential
Equations and
Solitary Waves Theory

Here's what you're looking for 10/10 my teacher passed that book on to me a week before the midterm, I hope it helps you too.

[empty harbor]

Good book for Potential Theory, please?

Specially aimed to fractals

[crystal cedar]

The Cat and the Hat is a good book to learn trigonometry

Peppa's Magical Unicorn is a good book for calculus

[coral prawn]

https://nusmods.com/courses/MA2202/algebra-i

For a course like this would an abstract algebra book like Rotman suffice? (Heck rotman feels overkill)

[oblique hatch]

Looks like first 3 chapters of rotman iirc
Maybe a subsection or two from later

[coral prawn]

Right. Looked similar in terms of content pages too.

Just to be sure we're talking abt modern algebra rotman and not intro to theory of books rotman... right?

[fierce hedge]

Both have very similar content, to the point that a lot of stuff in his advance modern algebra is just copy pasted from the ug book while making it a bit more terse. I see no reason why you'd use his grad book

[coral prawn]

Ic (BTW no I'm not reading this yet before u ask I'm asking for a friend)

[fierce hedge]

I see, in any case. FCAA should be enough, it's proofs are better written and more suitable for ug course

[rustic quail]

Does anyone know if there is a Swedish version of the book 'Calculus: A Complete Course 10th ed'? I would be very grateful if you have one to share

[remote sparrow]

https://www.amazon.com/Introductory-Course-Differentiable-Manifolds-Aurora/dp/0486807061/

just found this on amazon

don't know if it's good

not interested in this material but hopefully someone wants to check it out

[maiden halo]

you could check out Casella & Berger if you want deeper math

[sterile pelican]

I had considered either Berger or Wasserman, ended up getting the latter before

[fallow cypress]

my class uses haberman

it doesn't cover the method of characteristics until like ch 11 tho

but it's a book geared towards engineers so it's more about solving pdes and less about theory

[languid kettle]

I need to refresh multi variable calculus to read intro to manifolds by tu

Any recommendations?

Preferably something small

[gusty smelt]

the answer is you dont need to refres multi variable

as long as you know what a partial derivative is you will be good

infact I'd say learning diff geo will give you a much better intuition for all the random stuff from calc3

[sage python]

Eh I mean for the sake of intro to manifolds

You need to know stuff like inverse/implicit function theorem

[gusty smelt]

oh yes true

[sage python]

Also change of variables in integration is what makes differential forms click

[gusty smelt]

To me its the other wayaround

lol

I understood all of these change of variable bs after seeing dif forms kek

[sage python]

That feels a bit flipped somehow. Like it recasts it in the forms language but, if you were to ask yourself why we integrate forms on manifolds rather than just functions on a measure space

The point is that there is no canonical measure on an arbitrary manifold. We can pull back Lebesgue measure through different charts and get incompatible answers, the defect being... Jacobian of the transition map

[gusty smelt]

well id say even more than that, even if you got a nice measure on your manifold, you would still fail to integrate over "lower dimensional" subspaces since they have measure 0

[sage python]

So if you wanna choose a single consistent measure on the manifold which is (smooth function) (pullback of Lebesgue) in any chart

[gentle arrow]

speakig of dg dami look what i found

am i ready

[sage python]

That forces you to look at differential forms

[gusty smelt]

Oh i see what ur trying to say, i meant something different dami kek

so you are trying to say, integral of diff forms invariant under change of coordinates from different charts ig?

[sage python]

Yeah, in fact if you were to try to define a "smooth measure" on a manifold to be just smooth function * Lebesgue in any local coordinates

You'd get a differential form if the manifold is orientable

[gusty smelt]

ig like, what I meant to say was that these things (like change of variables) made sense to me when recast in the language of diff geo, with tangent cotangent vectors etc

more than they made sense to me in calc3, where someone drew an annoying picture

[sage python]

Lol fair, I guess calc 3 is an awkward intermediate

[gusty smelt]

Ig diff forms themselves probs dont give the intuition for change of variables

[sage python]

Yeah differential forms makes it look nicer for sure, like oh this change of variables statement is just pullback of forms

[gusty smelt]

I was thinking more like "oh yeah just combine the wedge rules and use the fact that a cotangent vector is dual to a tangent vector" etc

[sage python]

But the "reason" for it is, any object we're gonna integrate on a manifold has to pull back in this way

Look up "densities" on manifolds

[gusty smelt]

even the language of derivatives being linear maps immediately cleared so much up for me

[sage python]

This is kinda the link between forms, measure theory, and the integration that happens on Riemannian manifolds

[gusty smelt]

but in any event like, calc 3 is v unnessacary for diff geo imo

right

[sage python]

Depends on the diffgeo. If week 1 they prove equivalence of definitions of submanifolds of R^n using implicit function theorem...

[sage python]

So where are you at in the things you've done?

[gusty smelt]

well implicit/inverse function theorem is like, almost never proved in calc3 so you arent losing much

and anyhow just read the proof of these before learning diff geo ig

[sage python]

I guess when the person says "multivariable calculus" it's ambiguous whether that means Stewart Calc 3 or Spivak Calc on Manifolds, and I'm assuming that since they're reading Tu...

[gusty smelt]

I mean id also say the same fort calc on manifold, seems like a waste of time to me to do that instead of jump right into diff geo

like, i concede the implicit/inverse func theorem are important to know

and also like what partial derivatives are

[gentle arrow]

uhh

[gusty smelt]

but those arent worth wasting time on spivak imo

[gentle arrow]

we covered some ring theory
i think my topology is fine
and then schroder 1-8

[sage python]

I mean inverse/implicit function thoerem means most of chapter 2 already, since obv you need to relearn chain rule. Changes of variables are probably still gonna be in the background. Probably not gonna be many computations involving Fubini's theorem or Lagrange multipliers I suppose

Or wait no you need Fubini for Stokes' theorem

[gusty smelt]

no you dont?

ok you might actually

[languid kettle]

I’m at tao analysis ii, fouirer series chapter… i guess i should finish differentiation chapter and go to dg

[gusty smelt]

change of variables is taught in diff geo in a better language already

chain rule also

like its better to see the rules in the diff geo language and thats how u rerembmer it

than anything

[sage python]

The rules in the diffgeo language follow from the statements in R^n is my point

[gusty smelt]

sure, but its not worth learning it in the old language is mine

[sage python]

Like how do you know that compatibility of charts is an equivalence relation?

How do you prove chain rule for maps between manifolds? You just say take local coordinates then cite R^n

[gusty smelt]

yes but supposedly you have either already seen the proofs or have used these before, as they are asking for a refresher. Its not worth relearning these proofs, just learn the diff geo language

actually ill go further

it wasnt worth learning the proofs in the first place

[sage python]

I don't like black boxing the foundations that hard lol

[gusty smelt]

I dont think anything is to be gained from knowing the proofs of these tho lol

like if you have done analysis already you can just say to yourself "just extend"

[sage python]

Well that's a case for not relearning proofs more than it is now knowing in the first place as you went further lol. Chain rule is a quick and easy proof and it's practice thinking of derivative as a linear map. At least remember the statement of it so that you know what you're citing

[gusty smelt]

yes i agree with remember the statements!

[sage python]

Change of variables and Fubini, depends on the examples they have you compute. I could see a case for just saying I proved it once

[gusty smelt]

and you will have the statements in diff geo

[languid kettle]

I’ve done pinter algebra, tao analysis 1, half of analysis ii, topology notes hatcher

am i ready to read tu?

[gusty smelt]

idk what tao analysis covers but probably

[sage python]

Did you see inverse and implicit function theorem?

[gusty smelt]

and i mean like, you should just jump in and see if its enough

[languid kettle]

I see one variable one of inverse func theorm… mutlivar version are covered in next chapter

[sage python]

Maybe do that then. Chain rule and inverse function theorem are the blood of manifold theory

[languid kettle]

Okay

[gentle arrow]

damn i havent seen implicit function theorem

[gusty smelt]

yes you should learn the inverse func theorem atleast, but then jump in

[sage python]

Yeah if you did computational calc 3 that's deficient. Doing it in Schroder or CoM you'll learn derivative as a linear map, inverse function theorem

Related to the latter is existence/uniqueness for ODEs, also smooth dependence on initial condition

[gentle arrow]

i have never seen computational calc 3

and i never will

[gusty smelt]

thats a complete waste of time to do CoM after computational calc 3

just jump into diff geo

[sage python]

The problem is you don't know the right language to even do diffgeo. Calc 3 teaches you chain rule in 3d as a weird sum of partials

Where do you learn that no, this is a statement about linear maps

[gusty smelt]

yes and thats good enough? i dont understand what you are saying cause like, diff geo will introduce this framework

for example lee does

[tough zealot]

I see no problem with going into classical diffgeo directly
as in surfaces embedded in 3-space

[sage python]

When I took it, it was assumed that you knew it

[gusty smelt]

well he is talking about tu and supposedly it introduces the framework

like the linear map is a one line deal right

and also you went to uchicago they assume stupid shit

[sage python]

Like I took a GP course which is lighter than Lee

[tough zealot]

not sure I agree with that
in retrospect it may be

Lee super based btw

[gusty smelt]

like most schools will not assume like, calc on manifolds level of backgrounds at all

and Lee certainly didnt, again dont know about tu

[tough zealot]

tu doesnt either

[sage python]

Doesn't Lee assume you know even covering spaces before you start?

[gusty smelt]

well thats for later chapters when he gets into the depths of like, orientation etc. Lee does have a bigger topology prereq for sure, but not like until much later

[tough zealot]

it has them in the addendum
the point is LRM references LSM in terms of smooth covering spaces, which references LTM when talking about general covering spaces

[sage python]

Ah it has appendices which reviews the stuff. I was looking at the first chapter which did assume you understood derivatives cold

Also I gotta teach but we can talk later

[rigid barn]

All you really need* is a good handle on n-variable derivatives, i.e. total/partial derivatives, Schwarz's lemma, etc. For this, see the chapter on differentiation in Munkres' Analysis on Manifolds (don't be put off by the title, the derivatives are for general functions in R^n), it'll take you only a day or two to get through it. Inverse/implicit function theorem comes up at one point, but that's covered in Tu itself. One last thing you will need at one point briefly is the change-of-variables theorem. It takes some time to develop the R^n integral and the proof of the theorem itself is pretty tricky, so you're better off taking it on faith and just googling the statement unless you feel like going down that particular rabbithole.

* That is, assuming you've met functions R^n->R^m before and know the basics like their limits/continuity and so on. If you've never met multivariable functions, read the first couple of chapters of Munkres.

[rigid barn]

Or if you're reading Tao, that works too, he covers differentiation and other topics very well, you can have that as your primary reference (personally I prefer Munkres for the typesetting). With your cited background you should be adequately technically prepared for Tu (in terms of parsing the text itself), the question is how much the subject will make sense to you as a whole.

[tardy fjord]

is the book "game theory 101 the complete textbook" by spaniel a good game theory book? bc i just finished it and i feel like i haven't learned anything of importance

[hearty steppe]

Hey any other books a bit more approachable from an interdisciplinary complex systems point of view for learning Fourier Analysis? Maybe I should give S&S more time but a lot of the exposition is quite dense and feels a lot like the exposition in Brian C Hall’s books, not really a fan

Looking for something a bit more explanatory and touching on the abstraction of the details rather than just straight digging into equations

[remote sparrow]

are you asking for complex analysis books

oh wait, s&s also wrote fourier analysis

lel

umm there's a book called Fourier Series by tolstov

[hearty steppe]

I think I archived that one but I haven’t read it yet. Lots of people online seem to recommend that among some others

Not many people outside this server recommend S&S it seems. That’s straight up the hard read for someone with a mathematical physicist or analyst background

Some nice points made but too much time spent on deriving equations and not really explaining the steps, but I guess the steps are assumed based on a more heavy analyst background

[rigid barn]

Why don't you like Hall, I think he's pretty great (from what little I've read). Also, I think SS are a meme, even if I haven't used it that much.

[remote sparrow]

for fourier analysis or complex analysis

re: s&s

hopefully not schutzstaffel!

[remote sparrow]

well s&s and tolstov are the most popular ones that use only riemann integration

for fourier analysis

[rigid barn]

I've read bits of their complex analysis and that's exactly what led me to conclude they're a meme. Can't speak to Fourier or functional, but real was meme-y too.

[remote sparrow]

fwiw daminark wasn't a big fan of s&s complex analysis either

which is noted in the pins

[rigid barn]

Freitag and other german authors are much superior. Those guys know how to do Funktionentheorie justice.

[hearty steppe]

I couldn’t vibe with his quantum theory or lie representations books.

Just didn’t like his exposition

[remote sparrow]

is remmert someone you recommend

there don't seem to be very many exercises in the text though

[hearty steppe]

Fourier has to do with harmonics

Not just complex analysis

So I’m interested in learning more about adaptive resonance theory

Which is a big motivator for diving into Fourier analysis/series

[rigid barn]

I've read only a couple of bits of Remmert, but it was fine, and I think it's a valid rule-of-thumb that German CA books are good. IIRC his book was a little too long and had some unnecessary deviations, so I think Freitag is better for being concise (although the proofs are swept under the rug sometimes), but you surely can't go wrong with it.

[hearty steppe]

So I gotta learn more about stuff like the Laplacian

And the abstraction of Fourier transforms

Ok I moved on to chapter 2 in S&S and it’s starting to explain stuff. I guess it’s one of those books that opens with a hard chapter introducing the potential of where the content goes.

[remote sparrow]

the intro chapter isn't trying to be rigorous

it's giving you a sense of where you're going to go

which is stated directly in the text

[gray gazelle]

read russian literature guys

trust

its the best out there

[rigid barn]

Oh yeah, tough gal? Name one you've read (in Russian).

[gray gazelle]

Преступление и наказание

most basic one tbh

it was still good though !!

[rigid barn]

я думал, ты о мат-литературе

[gray gazelle]

oh nah you have any recommendations for good math ones though??

[rigid barn]

полно, зайди на сайт МЦНМО, там бесконечные списки книг (доступные онлайн)

[gray gazelle]

ох, ок, спасибо !!

[hearty steppe]

🙃

[hearty steppe]

Based on the exposition of the second chapter so far, I think I may have a change of mind haha

[sterile pelican]

Oh fancy seeing you here again @hearty steppe (yes I have returned here for now)

[heady ember]

Speaking of Complex Analysis, it reminds me of how Yamin always likes to shill their prof's complex anal book

[remote sparrow]

which one

[heady ember]

https://press.princeton.edu/books/hardcover/9780691207582/a-course-in-complex-analysis#preview

[sterile pelican]

One complex analysis book I wish to do personally one day would be the two volumes of Freitag

[silver stirrup]

Hey does anyone know any good Number Theory books for AMC 12-AIME?

I tried aops intro but it doesn't cover a lot of stuff like euler's phi, euler's formula, fermats little theorem, etc

I like the pace of the books though

[remote sparrow]

these topics are covered in both burton and dudley's books

[pallid yew]

does anyone have any book reccomendations

[sterile pelican]

that depends

[lusty ermine]

hi guys