book-recommendations

[halcyon hornet]

Does not Stewart cover Differential Equations too? So will I have to do Differential Equations after Completing Stewart or does Stewart contain all of it?

Stewart's Calculus.

[frosty girder]

Stewart

[gray gazelle]

Thx bro

Is steward very hard?

[humble acorn]

not completely

its very basic

[frosty girder]

not sure
its not hard ig, but its not very loved

[halcyon hornet]

Aolroight.

I will need to learn Differential Equations after Calculus for Physics and to learn Chaos Theory.

[sage python]

I doubt Stewart does enough ODE stuff for a class

I think the computational standard is Boyce DiPrima?

[gray gazelle]

you might also wanna supplement going through a calculus book with khan academy

[humble acorn]

yeah

khan academy for the concepts and stewarts for the problems

[halcyon hornet]

There are 2 different views here-

1. Do Spivak, Do Spivak and Do Spivak.
2. Do Stewart's or Thomas's and then do real analysis.

[sage python]

Senku not exactly

[halcyon hornet]

3B1B for the concepts, no?

[humble acorn]

bro first do either one then think wht to do next

[sage python]

Tbh you kinda just misrepresented everything

[halcyon hornet]

Oh.

[sage python]

Feels like it's borderline intentional

[humble acorn]

its not like if u do spivaks over stewarts u wont know calculus

[sage python]

With how you phrased the first view

[humble acorn]

both books are fine

just pick either one finish it and then think what to do next

[sage python]

So here's the business when it comes to calculus books

[gray gazelle]

OKSIR

[maiden slate]

I wouldn't overthink what textbook to get too much. just like get a pdf and try it for a bit and if doesn't seem that good don't use it

[sage python]

If someone doesn't care much about proof-based calculus (eg most science/engineering/business books) then Spivak is too much of a diversion from the material you're looking for

Now I also think there are books that are probably nearly as good as (if not as good as or better than) Stewart, and which are a fraction of the cost

[manic cape]

Are they learning on their own or along with some course?

[halcyon hornet]

Own.

[halcyon hornet]

Stewart is like 12$ here.

[sage python]

So I wouldn't likely recommend Stewart itself anyway. But Stewart is the only book at that level I'm aware of so I just refer to that general type of calculus book as Stewart

[frosty girder]

[manic cape]

I never really used any books for calculus

[sage python]

For people learning proofs, you have two paths from 0 to "I know analysis"

[manic cape]

Since calculus resources are quite extensive and a lot are free online

[sage python]

First path is you start with a non-proof based calculus level, a la Stewart

[frosty girder]

I just used ncert books for calculus firstly, those are the books used in HS, and then did random shit and questions, and now im here

[gray gazelle]

Is this book good?

[sage python]

Then you do real analysis, at the level of Baby Rudin. Does the theory of derivatives and integrals pretty fast since you saw them from a computational pov already

[halcyon hornet]

This is Stewart's, the same version I have.

[manic cape]

Lol that is a ridiculous price

[gray gazelle]

Yea

[maiden slate]

honestly yeah you might wanna just try ncert+internet, the textbooks are actually quite good

[gray gazelle]

NCERT?

Okie first lemme built a strong base

[sage python]

And most of the time is understanding how ideas like continuity and power series apply in settings like metric spaces

[maiden slate]

Indian central syllabus highscool textbooks

[sage python]

Then you can do measure theory, functional analysis, etc like in Big Rudin

[gray gazelle]

Oh is it good?

[frosty girder]

yeah

[maiden slate]

as a HS textbook

[frosty girder]

they are decent on an intro level

[maiden slate]

if you're in HS it's good

or younger

[frosty girder]

They have tons of questions, sometimes the ones that will make u think

they wont make u a "master of calc"

[gray gazelle]

I am in class 9

So I guess it should be useful

[sage python]

The other option is you do Spivak Calculus and then Royden Real Analysis

[frosty girder]

since indian system doesnt use hyperbolic trigs at all

[frosty girder]

Roydens book? never heard that one before

[gray gazelle]

I have done limits, deriviatives

I will perhaps use ncert to build up my base on integration

[maiden slate]

tbh it's better than introducing them as random functions

[gray gazelle]

And then do the stewarts.

[sage python]

I know of it because someone I know took analysis at my school and apparently they use Royden now

The thing about Royden is that it's got both measure theory and basic metric spaces

So it's kinda like, some weird Rudin \cap big Rudin business

[frosty girder]

yeah

[maiden slate]

there's a baby Rudin and a big Rudin?

[frosty girder]

[halcyon hornet]

That is what I always though.

[frosty girder]

im just using Apsotol, it has a chapter on measure theory as well, yeah

[maiden slate]

also hey what do you think of abbot?

[gray gazelle]

Is stewarts good for a beginner who.knows abt basic deriviatives and limits

And not much advanced stuff

[coral narwhal]

it goes baby papa grandaddy

[halcyon hornet]

Yes.

[sage python]

So yeah this is why I think you can go Spivak -> Royden and you've done most of the material in Stewart \cup Baby Rudin \cup first part of big Rudin

[gray gazelle]

Time to order it

[halcyon hornet]

Ask the others too.

[frosty girder]

what is papa rudin and grandpa rudin?

[gray gazelle]

Okk

[frosty girder]

measure theory and more advanced analysis?

[gray gazelle]

Uhh pls help anyone

[coral narwhal]

RCA and funanal book I think

[frosty girder]

sure

[gray gazelle]

Thanku gentleman

[frosty girder]

RCA? Real and complex analysis?

i see

[sage python]

Baby Rudin - Principles of Mathematical Analysis
Big/Papa Rudin - Real and Complex Analysis
Grandpa Rudin - Functional Analysis
Great Grandpa Rudin - Fourier Analysis on Groups
Great Great Grandpa Rudin - Function Theory on the Unit Ball of C^n

[maiden slate]

foruier analysis on groups?

[sage python]

Yup that's a thing

[manic cape]

cool subject

[maiden slate]

is function theory on unit ball a real thing?

[sage python]

Also yup

[maiden slate]

that feels a bit too specific tbh

[manic cape]

it only sounds that way because you're calling it a theory of something

[frosty girder]

Ooo interesting

[sage python]

It's a research monograph more than a textbook

Fourier Analysis on Groups is incredibly wide and important

My shtick is suuuuuuuuper connected with that math

[frosty girder]

Ooo

it sounds interesting as well

why is everything interestingggg

[sage python]

If it wasn't either interesting (to someone at least) or applicable, nobody would study it

[frosty girder]

True

[wise umbra]

Adelic Fourier analysis

[sage python]

And Lie theory in general 🙂

[gray gazelle]

I know this is a maths discord but, can anyone recommend a book on how to properly write code? I mean I know the syntax very well and can write functions and classes... But when I code I don't have a clear plan, I just throw everything at the wall and see if it sticks. I hope you understand what I mean.

[coral narwhal]

https://openbookproject.net/thinkcs/python/english3e/

[gray gazelle]

Is this generalizable to c?

[obsidian valley]

Just read the OG C book if you want to learn C

If you want to learn to write software you need to read a software book

[gray gazelle]

I am doing that

[obsidian valley]

It sounds like you need help architecting stuff

[gray gazelle]

Yeah that's the word

It's like knowing the words but not how to structure it

[obsidian valley]

I mean look at like Clean Code/any book about design patterns

those are good starting points probably

idk where you really get a start in this stuff

i doubt anyone reads books first

just like. mkaing projects, and reading through other peoples projects

and seeing how stuff works

is the best place

you wont really have the context to appreciate proper software books rn IMO?

[gray gazelle]

I see

Ill check out clean code

Thanks

[subtle siren]

Other than books I'll recommend just choosing a language and sticking to that language's norms and/or use formatters that stick to that. e.g. Python uses 4 spaces, not tabs. This is PEP 8.

Each language's "clean code" IMO differs.

I also would recommend learning modern C++ rather than C.

[fervent lava]

c++ primer. It a good book on modern c++, it mostly c++ 11 but that a good starting point. I have read 90 percent of it.

I also recommend learncpp.com

[gray gazelle]

I'll look into both

[fervent lava]

Also you need to find a project to do while you learn.

[gray gazelle]

Im gonna try to make some math animations using manim

[ornate bough]

Has anyone got some standard graduate level mathematical physics textbook in mind? Something to get a taste of what one might expect in the courses, specifically like the amount of rigour in the math involved.

[gray gazelle]

https://www.qcaa.qld.edu.au/senior/senior-subjects/mathematics/specialist-mathematics/syllabus

Any book reccomendations based on my syllabus? particularly units 3 and 4.

[analog pollen]

Nakahara is pretty standard

Or something like mathematical methods of classical mechanics, ive seen ppl recommend it. (Havent read myself)

[ornate bough]

I will look into it, thanks.

[analog pollen]

Its a great book

You dont rlly need topology or anything

[ornate bough]

I've read Arfken, but some people said you need more rigour so it kinda made me worry. Thanks

[analog pollen]

Just need to be familiar with like lin alg at a high level kinda

[analog pollen]

Yea arfken is afaik undergraduate

Nakahara covers stuff like topology, manifolds, abstract algebra

Even string theory at the end

[ornate bough]

I see, thanks.

[analog pollen]

Np

I see you are a mathematical physicist so this book should be no problem for you haha

[ornate bough]

Aspiring 😔 I know very little

[manic cape]

Simon and Reed,

[ornate bough]

Thanks, I'll look into that as well.

[frosty ermine]

Stewart talks about diff eq for about a chapter, and it is a very simple introduction to it.

[solemn rover]

What dackid says is true.

there's much more to differential equations than is in stewart but you should really just focus on spending a year with stewart before worrying too much about what comes next

there would be no point to opening a differential equations book without a solid foundation in single variable calculus

[junior merlin]

https://www.youtube.com/playlist?list=PLmmYSbUCWJ4x1GO839azG_BBw8rkh-zOj this series is great. helped me a lot

[brittle latch]

not gonna advertise other servers but if you were to sit a couple million monkeys in front of shitty macs and one of them were to type out "the programmer's hangout discord" and press enter that monkey might pog

@junior merlin just read your profile you tryna coach me thru my analysis final in two days

[junior merlin]

id be happy to help can you vc?

[brittle latch]

oh i was memeing lmao but i might actually botherr you

i spent my entire day trying to shove heine borel into my brain so im taking a small break

[junior merlin]

if you bother me I'll just leave

ooh heine borel

based

i always think hiney borel in my head because i'm mature

[brittle latch]

yes

[brittle latch]

no quite cringe in fact

[junior merlin]

whats confusing you the statement or the proof

bc the proof still half confuses me

[brittle latch]

both lol

i asked a bunch of stuff in #real-complex-analysis so maybe that's more apt

anyways im still technically on my break, only saying that cuz it'll be my last one for a few hours, so i'll be back in a bit

[junior merlin]

noice

lol

[karmic thorn]

@severe adder While I believe a large subset of users here agree with the contents of your (now deleted) post about big publishers, Discord usually dislikes promoting piracy in any form due to legal obligations. In the past this has even lead to server deletions, so we are forced to tread with caution. Consequently, we cannot encourage piracy or sharing of pirated material here.

[gray gazelle]

Lol I've seen dozens of "pirate servers" over the years

like literal servers dedicated for that

but yeah I agree with don manan

[smoky zephyr]

can someone recommend me a linear algebra book that isn’t insanely difficult

[gray gazelle]

abstract linear algebra or matrix-y row reduction stuff

[gray gazelle]

"linear algebra done right" by sheldon axler

it's an intro to linear algebra book

plus it has a video series by the author on youtube

[halcyon hornet]

I recommend asking Edd because he used to be the Linear Algebra king here I think.

[crude sable]

what is your focus?

beginner/intermediate/adv

[smoky zephyr]

beginner

[crude sable]

Linear Algebra by Sheldon Axler is a good starting point

[smoky zephyr]

ok, thanks

[crude sable]

I prefer it over Fredberg

[gray jungle]

i dont think hoffman/kunze is "insanely difficult" its quite nice actually in how it builds up
depends on what style you enjoy

[smoky zephyr]

@gray gazelle no

thanks, i’ll check them out soon

[analog pollen]

i liked schaum's, maybe you want to check that out?

[fluid bay]

"linear algebra done wrong" by Sergei Treil has a good balance of theory and computation. Def try all the reccs at first and see what u like best

[smoky zephyr]

i tried it but got lost in the first few pages unfortunately @fluid bay

maybe i wasn’t paying enough attention the whole time

i’ll try it again i guess

[fluid bay]

hm. My advice would be to try to ask questions in #linear-algebra as you go. It's probably an initial hurdle kind of thing.
Another option would be to try a book that's not vector spaces-first, like Gilbert Strang's linear algebra. It'll be more concrete in the beginning than any of these books people have recommended to you

[smoky zephyr]

well looks like i have a lot of stuff to look into lol

thanks

[fluid bay]

yea np. linear algebra is one of those things where everyone has an opinion about what's the best book, or the best way to learn/teach it. Just pick a few reccs and roll with whatever is speaking to u the most

[broken meadow]

Friedberg worked well for me

[abstract walrus]

Polynomials

[gray gazelle]

if possible could someone recommend me a game theory book(intermediate's fine)

[gray gazelle]

wohnst du in friedberg?

[thorn canyon]

Can anybody recommend me any book for mathematical analysis, not too long, cuz I am not good at these proof and real analysis things

Understandable for high school passed student

And if not a whole book, then some site where this is explained properly

[analog pollen]

abbott understanding analysis

[gray gazelle]

That only has real analysis

[inner mantle]

Suggest me manga like aot pls

[karmic thorn]

Manga Guide to Linear Algebra

[frosty girder]

[crude sable]

i tried that manga ngl

[inner mantle]

WeW

[south salmon]

It’s so funny, whenever I look up calculus of variations + some mention of book, it suggests those manga guides

the two seminal works in calculus of variations and optimal control, clearly

wait i’ve never seen the cover for Liberzon before

I’ve only just used it online

[robust relic]

So I've found that I really struggle with proofs, even though I've tried solving after seeing answer proofs over and over. Is there any book that could train me in the "logic of proving" so to say?

[gray gazelle]

How to Prove it by Velleman

[robust relic]

I'll look it up, thanks!

[gray gazelle]

or Book of proof, but I like the first one more

[robust relic]

I'll take a look at both, thanks

[robust relic]

Author name?

[gray gazelle]

Hammack, both are free pdf online I think

[robust relic]

Cool

[gray gazelle]

So... today I learned I'm going to fail one of my calculus classes ;-; and I didn't learn sh** about Green's Theorem, Gauss Theorem and Stokes Theorem (well I learned that are insanely annoying ;-;)... soooo does anyone know a good to study that??? I'm totally lost

[smoky zephyr]

pauls online notes

[gray gazelle]

do you a link?

or a way to me to find?

[novel obsidian]

https://tutorial.math.lamar.edu/

[gray gazelle]

thanks dude

[novel obsidian]

np

[gray gazelle]

I don't like Gauss😂

[odd spade]

Hello fellow math nerds. Does anyone have a good functional analysis book recommendation? I have taken complex/real analysis with stein & shakarchi/folland so if you have any recommendations at that level

I wanna mainly learn some over break for a topics course I am taking next sem

We got up to the elements of functional analysis with Lp spaces in Folland this semester

[slim peak]

Functional Analysis by Rudin, is quite good, Functional Analysis, Sobolev Spaces and PDEs by Brezis also is.

[odd spade]

Okay cool thanks I like Rudin

I'll check them both out

[slim peak]

Functional Analysis oriented to Operator and Spectral Theory,
A guide to Spectral Theory, by C.Cheverry and N.Raymond.

[odd spade]

Oh that's cool I do like operators

[slim peak]

In my opinion, you will need the three to get a good overview of each of them. Especially read first Part 1 (Chapters 1-4) of Rudin, and Functional Analysis Part of Brezis' (Chapters 1-3), then check what you want

[odd spade]

Okay cool thanks

[sage python]

Ooooo

[nocturne sky]

Any recommendations for an optimization book?

[tender egret]

Can anyone recommend a comprehensive introductory book about Tensors that isn’t too heavy on any formalisms and just a bit lighter on rigour with a metric crap ton of exercises and examples? Preferably with good exposition as well but I feel like I’m already asking too much. Alternatively, please just recommend all your favourite tensor books, regardless of if it fulfills the criteria. Thanks :DDD

[gray gazelle]

Maybe check out Dummit&Foote

[severe adder]

I didn't know, thank you for letting me know. Wouldn't want to do anything to jeopardize this server. Just wanted to share with potential like minded people.

[slim peak]

"On tensor" "not too heavy with formalism"

Bro

are you kidding us ?

[tender egret]

I probably should've said abstraction instead. either way, if not possible doesn't matter

I can deal with formalism

Basically disregard everything I just said. Can anyone recommend any books on Tensors with a ton of exercises or just Tensor books in general?

[obsidian valley]

why do u want to learn specifically tesnors

arent tensors like. used for stuff

lol

[slim peak]

otherwise I could recommend Serge Lang, Algebra, Chapter 16

lol

[tender egret]

well, I was going through the whole forms stuff and found tensors so I thought it was interesting and wanted to learn more 🙂

[tender egret]

thanks

[slim peak]

That's a joke

Still about Tensor algebras

[tender egret]

oh lol I really can't tell about this stuff

[slim peak]

but probably not what you are looking for

[tender egret]

not exactly, but close enough. I'll take a look anyways

[slim peak]

You should check books on Riemannian Geometry isntead

[tender egret]

do you have any particular recommendations?

[slim peak]

First a differential geometry book Lee's one "Smooth Manifolds"

[thorn canyon]

Yo thanks :-P

[slim peak]

Then Riemannian Geometry and Geometric Analysis by J.Jost

[tender egret]

great, thanks. I'll go check them out

[karmic thorn]

I'm keeping a close eye on these developments on a personal level as well, Wiley/Elsevier/American Chemical Society have joined hands here to get the two academic pirating giants banned, but the courts here may not give blind copyright judgements in favour of the former. There is some hope.

[manic fox]

😔

[livid garnet]

where was this last 3 years oh my god

[novel obsidian]

paul is a king

[gray gazelle]

Hi, I've got one question

Where do I find the solutions for the Open Logic Project book?

[scarlet elbow]

Is there any fun to read books which you can read while laying on your bed and not caring about solving problems or understand difficult concepts?

[novel obsidian]

like math books?

I have plenty of novels to recommend

[slim peak]

Histoires Hédonistes de Groupes et de Géometries

Funky co authors, with fun remarks in it

but still some deep maths in it

Like Quaternions, Group Representation, Exponential maps on explicit Lie Groups of Matrices

[scarlet elbow]

Is it available in English?

[slim peak]

I do not know

I think probably not

[scarlet elbow]

Oh

Well thanks for the suggestion

[scarlet elbow]

Yess, but if there are some novels which are too good then pls recommend

[tender egret]

Idk if this is helpful or not but there’s always Chaos: Making a New Science by gleick

There’s no real math talk or math in it, it just talks about the discovery of Chaos Theory

I find it fun and nice to read though

[gleaming sandal]

I am quite interested in studying quantum computing
is it possible to dive in to that area without knowing much of the physics?
i would like to read some textbook that operates only with math/linear algebra
I studied quantum mechanics at uni but i dont remember much
I only remember that it was basically the analysis of spectrum in terms of eigenvalues

[finite saffron]

this is actually a really helpful link (one of my main sources for the last year or so)

[strange osprey]

quantum mechanics is no joke, it does require first of all an understanding of high school physics and classical mech, plus linear algebra

also differential equations

[whole rain]

Did you read their message ?

[smoky zephyr]

they didn’t say anything about studying qm

they just wanted some books for quantum computing

nami already answered their first question

[night knot]

Try "Classical and Quantum Computing" by Shen, Kitaev, and Vyali

[halcyon scaffold]

Steven Roman's lattice and ordered set seems pretty good too

It even went in depth to talk about ordinals

[gleaming sandal]

Great! Ty

[quick crypt]

Does anyone know of a book that gives a comprehensive treatment of summations, along the lines of what calc textbooks give for integrals? Or a book with lots of summation exercises, including exercises involving multiple sums?

[solemn rover]

have you checked out "Concrete mathematics" by Knuth

[quick crypt]

fuck u

(i know him from elsewhere, im not just randomly being a jerk)

[sage python]

You should specify him = Kanga Gang Made Man

For a sec it reads like Knuth

[solemn rover]

haha just messing with you man

[quick crypt]

ik ❤️

[gusty smelt]

only to u :)

[sage python]

no u

[finite saffron]

,av ann

[hasty eagle]

427 members found matching ann!

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[finite saffron]

wait sorry wrong channel

[hasty eagle]

Member selection timed out.

Dec 12, 2021, 4:02 AM

[smoky zephyr]

oof

[warm bramble]

[empty mortar]

cat book

[inner token]

Cats or cat theory

[lapis sundial]

Both please

[orchid musk]

would coxeters projective geometry help understand silverman's rational points on elliptic curves? there's some people saying it's a synthetic construction of geometry so it wouldn't help but im unsure what that even means

[stray veldt]

what makes you think that it would help?

synthetic geometry means it starts with axioms directly related to geometric objects and then derives further stuff from those

kinda like euclid, but for projective geometry in this case

silverman defines projective space as some quotient of a vector space more or less, so it's a lot more hands on

it feels like it's just an extension of linear algebra in some sense

i don't know too much about the synthetic approach but afaik the techniques don't translate really well although the projective spaces defined are "the same" (except in dimension 2 or something)

@orchid musk

[orchid musk]

hmm alright, thanks ill keep that in mind

[teal orchid]

Anyone have recommendations for a second linear algebra course? (Vector spaces over general fields, jordan forms, something something decompositions, generalized eigenspaces etc.)

preferably one thats terse and theoretical

[analog pollen]

I think friedberg is the way to go

[karmic thorn]

Roman's Advanced Linear Algebra, maybe?

[teal orchid]

thanks guys ill check em out

[brittle breach]

Paul Halmos "Finite dim vector spaces"
Or
Axler "lin alg done wright"

[brittle breach]

These might be more what u looking for

[analog pollen]

not axlers book lmfao

[brittle breach]

I never read it

[teal orchid]

axler's exactly the book im unsatisfied with hahaha

[tender egret]

I’d recommend Linear Algebra Done Wrong by Sergei Treil

[brittle breach]

fundamentals of linear algebra carrel (available on line)
Was what I used

Halmos is clean and to the point

[teal orchid]

oh alright

[tender egret]

In any case, linear algebra done wrong is decently thorough and is open source(is that the term?) so you can easily get it online so it might be a nice companion book

[teal orchid]

yeah i see thanks

[tender egret]

GL

[whole rain]

n

[gray gazelle]

jordan forms, something something decompositions, generalized eigenspaces etc.
friedberg's good. or you can just learn some basic module theory :^)

[hearty steppe]

Ehh I was totally not ready for that book. Idk. Might revisit it. But that one didn’t quite click with me

The Halmos text*

[sage python]

Would module theory likely cover that? Jordan form maybe as an application of stfgmpid but

I feel like they tend not to go into as much detail into the linear algebraic stuff like char/min poly

[dapper root]

They do…

[broken meadow]

lol

[gusty smelt]

stfgmdd

smh

[sage python]

Oh tru

[sage python]

I see, yeah I haven't really seen much of the char/min poly done over modules tbh. Maybe slight review for the sake of establishing notation for JNF but in my class it was assumed you saw it before

[solemn rover]

Dami, the Cayley-Hamilton theorem states that an operator on a finitely generated R-module M is integral in End(M) as an extension of R

it's necessary to get the basic results from field theory to extend to modules

like

It's obvious that a finite field extension is algebraic

but in the case of modules, it's not immediately obvious that a module-finite ring extension should be integral

you need Cayley-Hamilton or something like it to prove this

[sudden kindle]

Whats an operator? An R mod homo from M to itself?

[brisk ice]

did book recommendtions move?

[smoky zephyr]

yeah

[teal orchid]

module theory looks really good actually. do you know of any book that covers what i want using modules?

[sage kelp]

What's a good book for a second course in real analysis? (I finished Bartle's introductory book)

[brittle breach]

baby rudin

@sage kelp

[halcyon hornet]

Any YouTubers(like 3B1B or something) for Combinatorics or Number Theory?

[tender egret]

Michael Penn isn't really like 3B1B but he does cover pretty much anything that so much as breathes

Sorry, can't be of much help here

[halcyon hornet]

👍

[sudden kindle]

Any books to learn about Weil conjectures?

Preferably with minimal background required

[sage python]

Seems I've convinced you by saying that huh. Jokes aside depends on whether you want just statements or proofs

[sudden kindle]

Statements

[sage python]

Proofs are gonna take a lot of background. Scheme theory itself was basically invented for that purpose lol (mildly but not entirely facetious), and I think the last one involves l-adic cohomology

[sudden kindle]

Yeah I heard something like that before

Thats pretty interesting

Its always cool to see the historical motivation for new tools

I'm most interested in the analogy between geometry and number theory, yknow curves are analagous to number fields

[loud rampart]

What books should I refer for prmo and stuff?

[frosty girder]

what have you done till now?

[halcyon hornet]

My time has come.

[loud rampart]

Done some school modules stuff

[halcyon hornet]

-1st - Challenges and Thrills of Pre-College Mathematics.
-3rd - An excursion in Mathematics.
-2nd - Mathematical Circles.

[loud rampart]

Thank you 👍

[frosty girder]

[frosty girder]

These books will be more than enough for prmo and rmo

or whatever its called now

lol

[loud rampart]

My friend bought ctpcm so I'll borrow from him

[halcyon hornet]

IOQM.

[frosty girder]

yeah that

[loud rampart]

Yeah lol

This will be my second attempt

[halcyon hornet]

Grade 10?

[loud rampart]

Yep

[halcyon hornet]

Are you serious about cracking these exams?

[loud rampart]

Ye lol

[halcyon hornet]

Me too!!!!

[loud rampart]

I wanna achieve something

Grade 10 too?

[halcyon hornet]

Okay if that is the purpose it will be harder.

[halcyon hornet]

Grade 8.

[loud rampart]

Ohh

Good luck mate

[halcyon hornet]

CBSE or ICSE?

[loud rampart]

I scored 32 in my first attempt

[frosty girder]

[halcyon hornet]

Out of?

[sudden kindle]

@sage python I guess instead if Weil conjectures explicitly, I'm more interested in learning about zeta functions in algebriac/arithmetic geometry and seeing the paralels to zeta functions in number theory (i.e. Dedekind zeta functions)

[frosty girder]

why do u need to worry then?

[loud rampart]

Whaaaa

Cut off for boys was 38

[frosty girder]

ah i see

[loud rampart]

And 32 for girls

[frosty girder]

sadge

[loud rampart]

Wish I was a girl lol

[frosty girder]

[loud rampart]

102

Aaand wbu?

Which grade are you in?

[gray gazelle]

Help me

[frosty girder]

im in 12th

[loud rampart]

Nicee

[frosty girder]

[gray gazelle]

Pls solve it.

[sudden kindle]

I want to learn about Artin L-functions too

[frosty girder]

#❓how-to-get-help

[loud rampart]

Preparing for jee?

[sudden kindle]

This is not the right channel stop

[gray gazelle]

Help bro

Pls

😭

[sudden kindle]

Can JEE people move to #discussion

[loud rampart]

Jus rationalize it

[gray gazelle]

I can't I'm doing other

[loud rampart]

Whaat

[gray gazelle]

Questions

[loud rampart]

It doesn't even take 1 min

[sudden kindle]

@odd spade where can I learn about Artin L functions?

[frosty girder]

sadly

also lets not talk about jee

thanks

[crude sable]

Any good book similar to "Berkeley problem book"?

@loud rampart please go to #discussion

[halcyon hornet]

WOAHHH.

[halcyon hornet]

8th.

[gray crystal]

didn't know there were so many indians here

[frosty girder]

u would be surprised

[clear merlin]

I am CBSE but idl about him/her

okkk

about jee ahh?

[hearty steppe]

I’m not surprised. I’m never surprised

[frosty girder]

[frosty girder]

But im sure noob666 was surprised

[odd spade]

Luckily there are lots of docs

Via googling

[sudden kindle]

CIA googling

[odd spade]

I did it again I literally just woke up

But yeah I learned everything I know about them from docs but ofc books for the actual NT

There are several nice docs on google that basically cover the whole thing

[nocturne sky]

Any suggestions on how many problems I should actually spend the time to solve for Spivak's Calc? Should I just go through all of them?

[storm sleet]

Any good resources for constructive real analysis?

[still jay]

You could try Errett bishop’s foundations of constructive analysis. I don’t know if there’s much more literature on the subject

[crude sable]

what's constructive real analysis?

[odd spade]

there is computable analysis too i believe

[gray gazelle]

Hello, i want to learn calculus, i'm completely new in the subject, what a good introductory book can i use?

[crude sable]

I really don't have any recommendation on introductory calc,

[smoky zephyr]

i have a recommendation but it’s a website lol

pauls online notes

it’s what i used, the site owner is a college professor

[fervent lava]

https://www.whitman.edu/mathematics/multivariable/multivariable.pdf

It single and multivariable calculus.

[gray gazelle]

Thanks

[prime oak]

with most texts, does it really make that big of a difference which edition you get?

[dapper root]

Kinda depends

If it’s like an early undergrad textbook, the type that gets like 20 editions (Stewart) probably for terms of hw

For other textbooks, the material is usually pretty similar, but they kind of come in two flavors I feel

1: new editions is basically correcting minor mistakes, misspellings, etc
2: they add some amount of content, usually not enough to make the old one useless but maybe that’s the stuff you want most?

[terse mason]

so just wondering, do the problem solving books around maths

actually help you get better at solving math problems and if so, could someone recommend me a good one to start with ?

[modern stone]

I’ve heard Polya’s “How to Solve it” is a good book for this

[halcyon hornet]

Yeah.

[random spear]

What would someone recommend for learning #category-theory with an UG group theory background at most?

[terse mason]

Thanks !

[quaint scroll]

Is there any good book on topology for compsci?

[orchid musk]

Try something in topological data perhaps

[tawny jetty]

just curious on why you have been unsatisfied. I'm on CH6 rn of LADR, but I went over to "linear algebra done wrong" because I couldn't wait to see determinant stuff. I also wanted to see the matrix computations.

[royal cargo]

right so ive learnt the basics of calc (differentiation and integration) i think you guys call this calc 1 so what textbook can i get that will provide me with something that builds from this so im assuming you guys would call it calc 2 and calc 3

id prefer for the texbook to be black and white (no color)

[hearty steppe]

It’s called not taking shortcuts and reading an actual mathematics book on topology if you have the maturity to understand it.

No offense

I know I’m the one to talk at times but I am humble enough to say that my undergrad degree in computer science is ultimately a waste of time in the grand scheme of things because I decided I wanted to actually understand math

Although I do recommend mechanical puzzles. Perhaps some like these that involve topological thinking https://www.tavernpuzzle.com

[gray gazelle]

@hearty steppe in what way do you think your CS degree is a waste of time?

I too want to understand the math

[marble solar]

If you want to learn math, then you do math

If you want to be employed with a good job and learn math, then you learn math & CS

I got my BS & MS in Pure math, and from a financial point of view this was largely a waste of time

[orchid musk]

i think it's still fine if they wants the relevant topology concepts to their field rather than learn rigorous topology if their end goal is comp-sci, i don't think it's a shortcut rather than a way to introduce a subject through a lens someone is familiar with and if they want to learn more than is required for what they're doing they can tackle a mathematical topology textbook

[fervent lava]

I am currently CS major and my interest in math first came from doing computer graphics. Now I am studying math for math reasons.

I still love computer science.

[gray gazelle]

@fervent lava that's kinda how I feel too

I love both CS AND Maths at the same time, some could argue that CS is a part of math

[fervent lava]

It definitely is.

[brittle breach]

I want a rudin style number theory book,

[radiant night]

I was ahead in math two grades since 2nd grade and finished 1st year calculus before graduating high school. But I didn't know math until much later because I stopped before it got good. I discovered math from programming, specifically Haskell. Monads, Monoids, Fields, Groups, Rings, etc. were not things that I had learned in many years of programming. Everyone was also talking about the HoTT book and TAPL ("Homotopy Type Theory" and "Types and Programming Languages") that were above my head. So I had to build a foundation in math from that.

[marble solar]

Apostol intro to analytic number theory

[hearty steppe]

In what sense was it a waste of time

[marble solar]

Financially

[hearty steppe]

Oh

Sorry

[marble solar]

yUh

[hearty steppe]

How you been mate

[marble solar]

gonna move discussion over to discussion-2

so we don't take over books

[marble solar]

#serious-discussion

[marble prawn]

i think govorov problems in mathematics is amazing book for practise!

[gray relic]

I want to learn geometry for Olympiads can anyone suggest me a good resource for that

[halcyon hornet]

Depends on country too.

In general, AoPs Volume 1 and 2 and AoPs website.

[crimson pagoda]

hey

[regal wasp]

Is there a supplement to Humphries Lie algebras?

Seems very light without one

[teal orchid]

The first 6 chapters are perfect imo. I would have liked more material on vector spaces over general fields, determinants, trace and characteristic polynomials. His theorems on matrices also dont stick to my brain, idk might just be me or might be because Axler doesnt dwell on matrices.

[karmic thorn]

Any introductory reference for EF games? I was watching a very old talk about it by Hodges, that piqued my curiosity about the topic.

[gray gazelle]

Evan Chen's "Euclidean Geometry in Mathematical Olympiads" fits the bill.

Coxeter's "Geometry Revisited" can also serve as a good reference along side the book stated above.

[atomic stag]

Im looking for an Book for python
to clear my basics like file handling, Libraries etc

[gray gazelle]

have you checked the python docs

they are good

https://docs.python.org/3/tutorial/index.html

[little jay]

Hey, I'm not exactly sure where this goes but I've been thinking about doing a thesis on a subject which is related to soft body deformations, nonlinear algebra, color science and photography. The main subject would be figuring out a way to approximate a non linear transformation in R3 space when the original and transformed locations of let's say 40 somehow evenly distributed points are known. Some image processing applications refer to these color transformatons as LUT(look up table) transforms. In case anyone knows good sources or keywords for this topic, I'd be grateful.

[pale scarab]

Evan chens book is the best I have seen on Olympiad geometry. I would go through AOPS geometry first though. Its not necessary but the problems are much harder.

[late plinth]

anyone have p good book on quantum computing?

[gray gazelle]

could anyone please suggest me a good book on how to get started with problem solving for a high school student who is tryin' to learn the beauty of Mathematics?

[karmic thorn]

Proof and the Art of Mathematics by J.D. Hamkins might be worth looking into

[odd spade]

Hatcher's Algebraic Topology

Jk I actually suggest looking into some logic books

Like the Goedelian puzzle book

Tho it is more of a tricky logic book, and should be used with a problem solving book

[earnest jay]

Aye cuties

I'm looking for a good analysis book

Beginner friendly and designed for self learning

If that's a thing

[orchid musk]

i really enjoyed analysis, a long form mathematics book by jay cummings, while there aren't exercise solutions the exposition and clarity is really nice, especially for beginners

[earnest jay]

Thank you

[gray crystal]

Paul Zeitz's Art and craft of problem solving
Or Lorsen's problem solving through problems

[sage kelp]

You can try Real Analysis for the Undergraduate by Pons, and Bartle & Sherbet Real Analysis

[earnest jay]

Thank you, I'll check those

[surreal phoenix]

Understanding Analysis by Abbott is a certified classic

[frosty girder]

true

and its a nice book

[icy knot]

Abstract Algebra and Complex Analysis? Probably with the Pinter book for the former.

[sage python]

Artin is likely the correct answer for algebra

For complex, depends on your level

[turbid tiger]

Hello everyone,

I am a recent Computer Science graduate. I want to learn advanced mathematics and grow as a mathematician in general. Preferably, the things that I will start learning should be at least remotely related to machine learning and deep learning. They don't have to be directly or closely related to ML. I am not sure if that is relevant thought.

The topics that I want to independently study in the next year:
1- Abstract Algebra
2- Statistics
3- Optimization
4- Real Analysis
5- Category Theory

I appreciate any textbook recommendations or even lectures in these topics suitable for someone with my background.

[hollow peak]

How familiar are you with proof based mathematics?

[uncut zealot]

I feel like the book by Pinter might be a good bet for you for algebra, if you want something somewhat light as an introduction to self-studying math. Lots of it comes out in the exercises, and it has a nice conversational tone. For real analysis, the openstax calc I textbook is pretty good (kidding! - but it's a solid free calc textbook). Baby Rudin is a standard; I've heard good things about Tao, and I'll be reading his Analysis II next semester; Understanding Analysis is another one I've heard good things about. I won't comment on stats or optimization. Do category theory last; if you don't know abstract algebra yet, you're a far way away from being able to properly motivate it.

[turbid tiger]

I think I am fairly familiar with proof-based math

Basically my formal background:
Calculus 1
Calculus 2
Linear Algebra
Intro to Statistic and Probability
Discrete Math
Discrete Math for Computer Science
Machine Learning (included more statistics and linear algebra)
Design & Analysis Of Algorithms (a substantial portion of the class was proof-based)

[turbid tiger]

Thank you very much, I will look into the books you mentioned!

[fickle wadi]

Hello! I'm interested in doing a reading course on big mapping class groups, and I'm looking for an appropriate book (google only yields one result)

[misty wyvern]

Do people here have a favorite complex geometry book?

Isn't this like your thing @sage python

[radiant night]

"What is the Name of this Book?"

It depends on exactly what you mean by problem-solving.

That is a recreational logic book. So like you know the puzzle of the two guards? There are two doors with two guards. One guard always tells the truth. The other guard always lies. But you have no idea which is which. How do you know which door to take?

[gray gazelle]

Ask him if a=a ?

[radiant night]

I suppose that could work, although it might depend on how you define identity.

But you don't have to know which guard is telling the truth and which is not.

you only have to ask one guard one question.

[gray gazelle]

The one who says yes is telling the truth the lying one will say no

?

[radiant night]

But that would still not tell you which door to go through, you can only ask one question to find out what door to enter.

[foggy gorge]

Someone can suggest me books to learn Algebra and Arithmetic?

[icy knot]

For both Abstract Algebra and Complex Analysis it would be beginner level. I’m a senior undergrad.

[karmic thorn]

You can check the pinned messages, Dami has compiled book reviews for both subjects.

[grizzled cloak]

hey im in 6th grade and im wondering if there is any good books for algebra, currently I am borrowing the complete idiot's guide to algebra at my library but I wana be open to new books

[halcyon hornet]

AoPs PreAlgebra for now.

[rapid merlin]

Does anyone have any recommendations for a baby undergrad? I'd like a book that's a bit more specific than the usual textbooks and which explores a topic to a greater depth. I have some familiarity with abstract algebra (took a course on groups rings fields + linalg out of artin), pointset+algtop out of munkres and real and complex analysis out of rudin and ahlfors respectively

Honestly the book could even be from a math adjacent field, I'm just interested in seeing how these tools I've learnt are applied at a more advanced level

[radiant night]

This is the free book that I used to practice algebra and trigonometry before I went back to college: https://www.stitz-zeager.com/ It's "college algebra" but there is no material that is different between middle school algebra and college algebra (it is what is known in math as "elementary algebra" -- algebra is actually a far bigger field). Books for middle school students just try to be more "engaging" and "kid-friendly."

You'd want to start with "Precalculus Prerequisites a.k.a. ‘Chapter 0’", which is a whole textbook in itself. https://www.stitz-zeager.com/ch_0_links.pdf

I used an Amazon Kindle (the black-and-white kind) and later I bought a big e-reader but you could also use a laptop (phone is probably too small). I just sat down with my pencil and paper and did math before work, on breaks at work, after work, on my days off. My coworkers thought it was ridiculous to do math that wasn't assigned as homework but that's how you get good at something. If you want to play an instrument, you have to practice scales all the time, even if there's no teacher telling you that you need to do so many. It just takes practice.

Try to avoid putting your calculator even on the table. I always question my arithmetic if there is a calculator nearby. So do it all by hand unless you got the wrong answer and are trying to find your mistake.

[radiant night]

The book has plenty of humor and is casual. It is explicitly a review book rather than one aimed at people learning the material for the first time but I don't think it would be bad to supplement your school textbook.

"Chapter 0" starts with Set Theory and then Number Theory. This is method of teaching young people was sometimes called "New Math." The US tried hard to push this method in the 1950s-1970s to try to get American students up to speed with other countries and advance in science but it confused a lot of teachers trying to teach it and parents trying to help their kids. But it isn't difficult unless you get stuck on math being reciting your times tables.

These are the real foundations of mathematics and it might help you understand why people still research mathematics to this day and why this Discord server exists. It also has plenty of applications in computer programming if you are interested in that.

[radiant night]

I also highly recommend Professor Leonard on YouTube. You probably know Kahn Academy. But there are some other good resources. Professor Leonard has recorded whole classes from Prealgebra to Differential Equations (advanced Calculus). I think this course on how to approach math problems is very useful: https://www.youtube.com/watch?v=cqk4vcuKoBQ&list=PLDesaqWTN6ETc1ZwHWijCBcZ2gOvS2tTN

[civic orbit]

What is a cool book on useless math? Someone recommended a book like that too me, but I forgot what it was. Kinda old, kinda famous. It had overly elaborate proofs for simple math. Any suggestion to which book this is or any similar book?

[lapis sundial]

Topology by munkres

[quick hornet]

http://i7-dungeon.sourceforge.net/math_hard.pdf

Mathematics made difficult

[civic orbit]

Yes, thank you. That is exactly the one I was looking for 🙂

[broken meadow]

fuck u namington i was just about to suggest it and then i forgot

[broken meadow]

this one is probably the best one

[hybrid flicker]

most elementary number theory book?

like basics?

[surreal phoenix]

that gave me a lethal amount of laughter for no reason, thank you

[smoky zephyr]

@remote ginkgo do you agree with this?

[lapis sundial]

Lmao

I'm glad

[hybrid flicker]

pls

[remote ginkgo]

Yes

[rapid merlin]

But pointset is fun! 😭

[gray gazelle]

Stitz and Zeager +1. Best coverage of trig I've seen (it's not an individual class here, yet you will hit university math and be assumed to know it well). I purchased a printed copy of their college algebra as a reference and it's good.

Furthermore, unlike most books at that level, it reads like a math textbook.

[hearty steppe]

People really gona throw shade at studying topology. Come on now lol

I will begin to throw shade at studying mathematical philosophy though because I was arguing with people on another server about Kantian views on mathematics and I’m like ugh…

We should probably care more about Riemann’s views on mathematics a lot more than Kant’s. That’s just how it is. Kant just came around about 100 years too early to be much of an influence anymore.

[quick hornet]

[sick wigeon]

Hello! I read some elementary real analysis (the contents of a first course i believe) and i am liking it very much. I would like to buy for myself a encyclopaedic text for mathematical analysis which covers a lot of topics and some advanced ones too which i can leisurely keep reading on my own and will be useful for the math courses i will be taking. Any recommendations?

I heard zorich is pretty good in this regard (of being encyclopedic)
Any other suggestions/comments? 😅

[radiant night]

As an engineering student, I knew I needed to know Trig well. I was going back to school at 33 and the last time I took a Trig class was 8th grade and the only thing I remembered was "SOHCAHTOA". The book definitely helped.

It reads like a math book that has humor and isn't totally dry. 😀

[gray gazelle]

rudin

or analysis 1,2,3 by Armann?

https://link.springer.com/book/10.1007/b137107

[sick wigeon]

Rudin feels insufficient to me in terms of being comprehensive. It's too concise i felt although i don't dislike it.

[sick wigeon]

Wow didn't know about this three volume series

Thanks
I will look at it and let you know 👍

[gray gazelle]

its mid imo

but there is a lot of things

i havent gone over each of them

[sick wigeon]

They do cover a lot of ground right?

[sick wigeon]

Oh i see

[gray gazelle]

i think

[sick wigeon]

I wish zorich would have been buyable

Costly

🥲

[analog pollen]

just use libgen

[sick wigeon]

Hmm
But i wanted to have a hard copy of one such analysis text atleast

[chilly mango]

Next year I intend on studying computer science. I started reading PCM with the intention of reading it cover-to-cover for the purpose of reinforcing my mathematical foundation. I want to have any holes I might have filled up. However, it was brought to my attention that this won't pay off enough and the book is mostly useful just as a reference (or, clearly, a companion). Is this true? If so, what is an alternative?

[quick hornet]

The requisite mathematics will typically be introduced over the course of a CS curriculum

I'm assuming, if you're studying mathematics beforehand, that you're interested in theoretical CS specifically, or at least doing something academia-ey in graduate school and beyond?

[If not, practicing programming on the usual sites (hackerrank, etc) or working on projects (githubs, etc) that you're interested in is probably a way better use of your time than literally anything else]

If so, the important thing is less knowing the mathematics that exists (which is what the princeton companion is meant to exposit) and more knowing how to do that mathematics

which you can't really learn except by taking a course in it

but because the mathematics you need for CS research is very dependent on what, exactly, you're doing, it's hard to give recommendations there without more specifics

(and to be clear, no one expects an incoming undergraduate to have any idea about what field they want to do, or indeed, to even know of the fields that exist)

@chilly mango

[chilly mango]

Thank you very much

I don't imagine computer science as manual labour, coding work. I thought that a theoretical base is implied

[quick hornet]

typically but not always

the term is used inconsistently, especially at an undergrad level

partially because there's crossover but mostly because universities find it easier to market "science" degrees than "technical" degrees

[chilly mango]

For now I've found a collection of exercises from another college, which does seem to provide something I need, it has quick explanations for what I'm supposed to know

[quick hornet]

anyway, back on track, the reality is that different parts of theoretical CS require vastly different mathematical prerequisites

a computability theorist will need to be intimately familiar with formal logic/model theory/formal language stuff

whereas someone doing algorithms might not even know how to define a model

[chilly mango]

That is daunting

[quick hornet]

but in turn they'll probably be familiar with a lot of analysis

that said, the "baseline expected knowledge" is at least somewhat similar to a pure mathematician's

linear algebra and calculus, enough abstract algebra to be comfortable with things defined in terms of groups/rings/etc, enough analysis to understand common inequality bounding techniques, and undergraduate level statistics

as well as, of course, the ability to prove things, but that's typically picked up in the context of the aforementioned

PCM, as I said, is good for getting a baseline understanding of what's out there but less so for learning how to actually do it

which makes sense as it's a companion/review text

people use it to prep for the GRE and stuff

(though princeton has a separate GRE prep guide that's better at that job)

[chilly mango]

I see

[quick hornet]

on one hand, there's no real fast track for learning all this

on the other, you're not expected to learn it quickly

your school might require these courses as part of your CS degree, but even if it doesn't (again, requirements are inconsistent), you'll typically not have too much trouble fitting them into your schedule alongside the CS courses

i would recommend focusing more on the CS coursework early on so you have a better idea of what interests you and what directions you want to specialize in

that isn't to say you should neglect the mathematics - certainly take as much math as you can do and put forth effort in the math courses you're taking - it just becomes more of a priority once you have more direction

maybe you despise the turing machines section of your course so you rule out computability stuff

but on the other hand, you find error correction codes and RSA encryption interesting

so you start looking into informatics, cryptography, etc

which will require you to learn algebraic number theory (and therefore abstract algebra and a bit of modern geometry)

[chilly mango]

You gave me enough insight for now, thank you. I think I'll return if I can't find what I need once I do actually know what it is that I need. For now I'll keep myself busy with exercises, though I must ask, what's a good resource for exercises? I'm mostly just preparing for the entrance exam

[quick hornet]

The university might have resources for prepping for the entrance exam

entrance exams aren't universal and are sometimes meant for a placement thing (so you're not really meant to study for them)

so it's hard to give recommendations over the internet there

[chilly mango]

Understandable. Though I don't get what you mean by not being meant to study for them

[quick hornet]

Like the university might use the exam to determine what classes or programs you're placed in

so if you study it and get a high score on the exam when you're not actually comfortable with all the material in the courses, there's a potential you get placed "too high" and fall behind since you're not actually familiar with the prerequisites besides the narrow band you prepared for the exam

again though, this isn't universal

but I've seen it with students who tested out of calculus with an AP test before

they got 5 on the AP since they memorized techniques for AP calculus questions specifically, but didnt have the basic comfort with stuff like function composition that were necessary to not get lost in future courses

to be clear, most of these students were comfortable enough to be able to get caught up without much hassle

but still

[chilly mango]

Ah, I'm not familiar with that system. I'm from Serbia — the placement dictates whether or not you're taken in and whether your education is funded from state budget or not

[quick hornet]

ah, I see

then it is probably a good idea (and expected) to study for them

but I'm not at all familiar with Serbian education so I won't comment further

[chilly mango]

Once again, I appreciate your time

[quick hornet]

yeah, I realize that I didn't really give you any practical things to do

but honestly I'd focus on that entrance exam for now and "calibrate" your goals once you have a semester or so under your belt

[chilly mango]

You're right, that's what hovered in my mind

[misty wyvern]

You'd be surprised at how many computer science papers are just coding work, implementing someone else's results.

It's a valid way to succeed in some parts of academia.

[gray gazelle]

<@&268886789983436800>

[wispy pebble]

b&

[regal wasp]

Stein and Sakarchi is good for grad complex analysis and real analysis

Right?

[quick crypt]

Does anyone k ow a book of calc exercises that make you think somewhat pedantically about the definitions and formalism?

[brittle breach]

Abbot

Rudin

[sage python]

Stein complex is completely introductory

Stein real is after a Rudin-level analysis class, whether that's undergrad or grad depends on you

[quick crypt]

Sir, I am a calc 1 student

[sage python]

Edgar I was talking to chernberries lol

[quick crypt]

doubt

[smoky zephyr]

can i get some sullies too

[smoky zephyr]

no one gave me a sully i’m sad

[fossil arch]

what's a more conversational book for a second course on real analysis? covering measure theory and whatever else there is, maybe some intro to other analysis topics like fourier, harmonic, functional, probability (or whatever it is), etc

I like slow and conversational, not super efficient books

self contained if possible

[fossil arch]

Just read this sorry Dami LMAO I'll take a look maybe

[sage python]

I'm not specifically endorsing those fwiw

Stein Real, people like, I find it's a bit odd since it's kinda redundant, first presents everything as Lebesgue measure and then repeats itself for abstract measures

Royden does that too but it's pitched at a lower level I feel? (Pretty much can be read after Spivak, Stein maybe needs Rudin tbh)

I like Bass Real Analysis, Folland also seems good

[south salmon]

Yeah, my real analysis class was taught using folland, and I felt it was good

by the end I referred to Stein and Royden for studying for my final

I’d say all three are relatively good options (so basically I’m not saying anything productive to this convo)

[fossil arch]

Alright I'll look into all 3 and compare

Not going to be there for a while though :P

reviewing undergrad real using abbott's book and I really like the way he talks, I liked that about Tao's too when I went through it for a bit

[astral laurel]

Hi! I am looking for some textbooks on mathematical statistics (I am not so sure if this is the correct term)

The thing is, like last summer I tried studying some prob theory to understand concept of martingales. Studying tons of inequalities were interesting and kind of a good exercise to refine my skills on analysis. (I studied several selected chapters of some lecture notes)

This semester I took a deep learning course in our school, I found that while prob theory is helpful, I lack some basic statistics (inference etc) background. I had to understand Bayesian inference and monte carlo methods to understand VAEs. I am able to run through integral calculations, I do not fully understand the statistical approach behind those computations.

So I would like to grab a mathematical statistics book to study for next winter or so. I think I have enough analysis background (I studied measure theory with first half of papa Rudin) and probability theory. Things that I think I want now:

• Short probability recap? (which is not really necessary but might be helpful)
• More focused on statistical inference and bayesian statistics.
• Mathematical rigor might be helpful

Last time people here was very helpful, suggesting lecture notes which I never new they existed. Any help is very much appreciated! Thanks in advance (Sorry for my poor english, its not my first language 😦 )

[smoky zephyr]

i only see a few spelling and grammar mistakes and i can perfectly understand what you’re saying so i think you’re pretty good at english

[astral laurel]

Thanks 🙂

[subtle siren]

Hi, I've never read the books myself but.

1. All of Statistics might be good. (but I don't think there will be much on variational inference)
2. Bayesian Data Analysis Gelman et al might be good.

[subtle siren]

There's also Wainwright (Graphical models, exponential families, and variational inference.) who I've seen cited in statistics for all sorts of reasons

[subtle siren]

Anyway finally I'll add that optimal transport is like huge, and again I've not read enough but I think people cite Villani because he got a Fields

Opt Transport is pretty hard and also brings in modeling questions of Distances (properly metrics) vs KL-divergence (not a metric unless symmetrized, and probability-theory speaking, has issues)

[astral laurel]

Thanks for recommendations! I am currently sending similar requests to other communities and people I know (or people just from other community) seem to mention "All of statistics" quite a lot. It seems very concise, so I think I will take this as a primary source accompanied with more specific textbooks! I will look more through your suggestions later. Thanks again for help 🙂

[modern stone]

Not necessarily a book, but could someone recommend some good analysis lectures on yt?

Also, any thoughts on Needham’s diff geo book?

[brittle latch]

has anyone used the algebra book in #books-old

or have any recommendations besides that

[frosty girder]

i am/was using Artins algebra, it was nice

check out this message @brittle latch

[brittle latch]

merci

also where do yall get textbooks from when not at some institution

like i doubt my public library has any textbooks along those lines

but i go to school far from home and im home over break

[gray gazelle]

||libgen or z library||

[brittle latch]

i mean yeah

but physical books based

[gray gazelle]

I guess you could get a pdf printed and bounded for not so much money

You just have to find someone who does it for a reasonable price and offers good quality prints

[brittle latch]

shiet i'll print it myself at the library ig

[frosty girder]

[brittle latch]

oh also i have a copy of "abstract algebra - a geometric approach" by theodore shifrin

stole it from an old building at uni

anyone used it/know anything about it?

[analog pollen]

Pretty good, i dont even thing you need topology for it, it didnt look very rigourous.

[south salmon]

Villani is good, but Santambrogio Optimal Transport is also a good one bc it’s a newer and more “modern” take on optimal transport

[subtle siren]

Some textbooks are also literally free, or have a free copy (like some book-level stuff on Foundations of ML/arxiv)

[subtle siren]

8+ years and there's a difference? Interesting...

Would you know of anything about Cuturi and Peyre to comment as well?

[brittle latch]

yeahhhh i just cant find myself as engaged by a screen as much as an actual page

ik it's still but idk

just something ive noticed in myself

i’ll prolly try this for a bit

[brittle latch]

i saw that OCW uses this so im probably gonna snag a pdf somewhere

[grizzled cloak]

hey guys which book is better, the complete idiot's guide to algebra 1st edition, or the second edition

and same question for the geomentry book

[nimble ledge]

you can just use whatever edition is easier to find

second edition usually just fixes spelling errors and stuff

||but i recommend http://www.wallace.ccfaculty.org/book/Beginning_and_Intermediate_Algebra.pdf for algebra||

[frosty girder]

[fiery bay]

i discussed this a few months ago, and im starting today - i'm learning math from start to finish ||i'm aware there's no finish, but still, to a high level||. i've essentially finished the ib math aa hl syllabus and im looking to read my first book on pure math. what do you guys recommend? is there a progression?

[sage python]

Spivak Calculus is good for doing some stuff you've done more rigorously

Linear algebra is a generically good followup topic

For that... Friedberg-Insel-Spence maybe is a good rec?

Or "Linear Algebra Done Wrong" by Treil

What was your option topic? @fiery bay

[fiery bay]

umm not sure what you mean by option topic

the maths syllabus has changed from earlier years

[sage python]

Oh

[fiery bay]

there's AA which is calculus heavy and AI which is stats heavy

i took AA

[sage python]

When I took it you had the standard topics and then your instructor chose one of 4 "optional topics"

[fiery bay]

hmm what were the 4 topics

[sage python]

Either discrete math, basics of set/group theory, extra stats, or extra calc

[fiery bay]

https://www.revisionvillage.com/new-ib-maths-curriculum-information/ perhaps this could help?

i'm not sure exactly

im pretty sure mine was extra calc though

[sage python]

If you've seen a bit of series and differential equations, integration by parts

Then probably

[fiery bay]

yeah

[sage python]

So it's like they took HL, took off the options, do they still have IA?

And knocked off a topic or two

Feels like a net nerf tbh

Oh okay so they nuked vectors/3d geometry (honestly a dumb topic for that level), volumes of revolution, added some stuff from the calc and stats options, added some weird topics, slows down some early material... I could see it

[fiery bay]

hmm?

we still have volumes of revolution

that's weird

and we still have vectors

and 3d coordinates lol

[sage python]

Oh maybe SL is the only one that excludes it. The website is weird

Honestly they should replace it with more important topics, 3D geometry can wait a little bit lol

(Of course eventually it's super important but let that happen in multi/linear algebra and include some discrete/CS-y math)

[fiery bay]

yeah 3d is kind of... mind bending lol

anyhow

first book?

[south salmon]

I forgot IB math was just overhauled

I graduated right before then

[fiery bay]

here's a better overview

https://www.inertialearning.com/ib-mathematics-aa-hl/analysis-and-approaches-hl-syllabus/

[fiery bay]

someone recommended loomis' advanced calculus to me

any thoughts?

[marble solar]

Spivak's calculus is amazing

[fervent lava]

I think the book they are talking is a multivariable analysis book.

[hearty steppe]

I am now curious about this book

Anything that has the word “geometric”, “dimensional”, or certain words relaying metric spaces in the title usually has my attention

As long as it’s not Halmos giving me too concise definitions haha

I need to skim thru Spivak more soon as an aid for getting through analysis more intuitively

[sage python]

Not reasonable for you rn

[brittle latch]

lmk if you do go through it

im kinda going through that an artin atm

tryna prepare for my algebra class in the spring

[marble solar]

Books

[brittle latch]

libros

ive asked this before but might as well - how do yall self study from books

like do you just read the chapter and do the problem or what

cuz i like using textbooks in the context of a class

but trying to learn on my own over break w one has been harder

[fervent lava]

pretty much, tho my books are usually read section, do problems.

reread again when I need to.

[brittle latch]

fair enough

guess i'll stop bitching

[hybrid flicker]

most elementary number theory book? please

[prime aspen]

check #books-old

Elementary Number Theory (David Burton)

or
Topology of Numbers (Allen Hatcher)

[quick hornet]

not sure id call those the "most elementary"

i mean obviously thats an arbitrary label

you could argue kindergarten arithmetic is the "most elementary number theory"

but i think its clear what is meant

[prime aspen]

🤔

so next time someone asks for an elemental number theory book it's technically correct to link a 1st grade math book

you evil genius

[smoky zephyr]

elementary

[prime aspen]

fine

i'll give a fair book recommendation

by the greatest mathematician ever

http://gidropraktikum.narod.ru/Euler-Algebra-Eng.pdf

you can skip the first 45 pages it's mostly a wall of text talking about how awesome euler was

[valid moth]

Vro

Touch grass

[gray gazelle]

I'm better than math , that is why I don't use Math

[fiery bay]

So is that an approval on the spivak book

[misty imp]

any differential equation books recommendation?

[broken meadow]

nagle saff snider

or boyce diprima

[misty imp]

ok your claim is noted

[late plinth]

anyone got a good book for linear programming?

have an ok background in linear algebra and basic understanding of simplex

[late plinth]

i liked diff eq and their applications

[fast turtle]

Zill and Cullen

[frozen mist]

i need a good book for stochastic processes

anyone got suggestions?

I'm a beginner tho

[misty wyvern]

Grimmet and Stirzakere

[pale scarab]

I am looking for a good book aimed at early middle school/ elementary school problem solving books. My daughter is 10 but not quite ready for aops books but I want more good problems for her to work on that require problem solving skill but at the elementary level.

[compact swift]

spectrum math?

[foggy relic]

i third spivak

[willow pecan]

Not necessarily problem solving exactly but have you looked through the mathical book list

[gray gazelle]

@pale scarab lang's basic mathematics

And gelfand's books

Altho gelfand's problems are sometimes crazy hard

[torn aspen]

How are the linear algebra recommendations in #books-old

[south salmon]

They are recommendations in #books-old so they are good 😉

[torn aspen]

Has anyone ever used them and can give a good review?

[south salmon]

The strang book and lectures are good

[willow pecan]

You might also look at Friedburg's Linear Algebra

And Linear Algebra Done Wrong

[torn aspen]

hello fellow chinese guy

[torn aspen]

What's good about it

[torn aspen]

I've heard this one is very unorthodox in its methods

[willow pecan]

It's better than Linear Algebra Done Right, at any rate

[gray gazelle]

aluffi

[south salmon]

It's a down to earth and relatively easy to understand, and the inclusion of video lectures on MITs website makes it better if you're more of a learner for video lectures

At least that was what helped me when I took linear algebra a few years ago

[torn aspen]

How advanced does it go?

[south salmon]

It goes through the usual mechanics of linear algebra, but it includes applications like the singular value decompositions and numerical methods for linear algebra
It doesn't go like super advanced, but it makes a good first look into linear algebra that I'd expect in a linalg course

[torn aspen]

I never knew that there are numerical methods for linear algebra so that is good enough for me

is there any reason that one would be put off it?

[willow pecan]

Put off what

Linear algebra?

No

[pale scarab]

Yeah I am not looking to accelerate her learning so much as offering better problems using math she already knows. I have her work through beast academy from aops which is good but was looking for elementary level problem solving books. Lang and gelfand assume high school knowledge.

My philosophy is early on she should go slow and have deep understanding of the basics and can apply them to harder problems. I think an issue some advanced kids get is speeding through the basics to reach higher levels quicker and not spending enough time on fundamentals with more challenging problems.

I will check out the mathical lists I never heard of that but it looks interesting.

[willow pecan]

[compact swift]

“I think an issue some advanced kids get is speeding through the basics to reach higher levels quicker and not spending enough time on fundamentals with more challenging problems” that is so so so so so extremely true

[fervent lava]

I am currently going through it and it works fine for me. I like how quickly it goes straight into linear maps.

[foggy relic]

axler hater

unbased

[willow pecan]

Ok

[tawny copper]

Does anybody know a good text that treats with rigour basic stuff about big o and little o notations, some asymptotic stuff? Some authors make many assumptions which are clear, but I'd like a rigorous treatment from the very basics

[gray gazelle]

crack open a popular analytic number theory textbook

only a half-joke recommendation

[torn aspen]

the book

[tulip blade]

Asymptotia or concrete mathematics maybe

[subtle siren]

Older alternative to Grimmet is probably Cinlar

[brittle latch]

send updates on how this goes, i tutor some of my nieghbor's kids and im very curious about how this goes 👉 👈

pop math stuff probably

matt parker books

or just stuff you find in the science section at barnes and noble

[slim peak]

Here is an advice about a nice Christmas present :
Markus Haase, Functional Calculus for Sectorial operators.

This can please any 7+ years old kid.

[willow pecan]

[compact swift]

love

[deft kite]

I recommend yall listening to podcasts

[willow pecan]

[smoky zephyr]

[willow pecan]

While I agree that podcasts are good, this is not the channel for them

[old jasper]

any books that give pracctise on a variety of elementary integrals?

[analog pollen]

Stewart has alot

@old jasper

[old jasper]

ok

whats the book called @analog pollen

[smoky zephyr]

stewart calculus

[old jasper]

ok

[finite saffron]

7+??

[south salmon]

I mean, if you're understanding functional calculus you're probably 7+

[finite saffron]

but the any part

[gray gazelle]

wtf sectorial opperator

[random rock]

Refugee

[still umbra]

Hi, I'm a math undergrad and I'm coming to the end of my degree. I really like the applied side of math and I've noticed so much of the "high tech" math gets applied in physics (I'm thinking CoV for lagrangian, hamiltionian, hamilton-jacobi etc). One skill I think I'm lacking is the ability to identify "real world problems" and then converting/representing them as math. I.e. I know how to solve different PDEs, what stochastic processes, difficult optimisation problems. etc etc etc but I find it hard to find examples in the real world.

Anyone got advice on how to get better at this? maybe there are textbooks out there with a big focus on this sort of thing. idk.

[willow pecan]

I really liked LeVeque's Numerical Methods for Conservation Laws as a textbook that treated mathematics in context

You'll also want to take courses in other departments like computational fluid dynamics and stuff

Another book is Vallis' Atmospheric and Oceanic Fluid Dynamics

Obviously I am biased because I do geophysical fluids

But generally you'll want to find textbooks from other fields that lean mathematical in nature

You might also like Lin and Segel's Methods of Applied Math I think is the title

But in general mathematicians are really bad at explaining how their work is useful

[pure garnet]

Is there a good biography on isaac newton

[sudden kindle]

I dont think u need to do elementary number theory before moving on to algebraic number theory

All you need is some abstract algebra back ground, but even that can be learned along the way

I wish there were an introductory algebraic number theory text that also introduces abstract algebra along the way, so that its a suitable alg number theory text for complete beginners in mathematics

Ireland and Rosen is not what I am looking for because a large chunk of it is devoted to elementary number theory

Does anyone know is such a book exists?

If course I love the book Number Fields but even that assumes the reader is comfortable with ring theory, field theory and Galois theory

When I was reading the book as an undergrad, I had some exposure to those topics but also had to relearn them more deeply because now I actually needed to use them in a number theoretic context

That's why I think its very good to introduce abstract algebra alongside algebraic number theory. A lot of the abstract algebraic notions can be put into context with algebraic nu.ber theory, and I would argue algebraic number theory provides some of the most natural context for these abstract algebraic notions

So really what I want is an undergrad textbook that introduces both abstract algebra and algebraic number theory, having the number theory provide motivation and context for the abstract algebra

[willow pecan]

Write it

[sudden kindle]

😎 i will

[remote ginkgo]

James Gleick

[gray gazelle]

I may know something similar to this

[willow pecan]

[gray gazelle]

https://www.dropbox.com/sh/lribbpkfooq96gs/AABJsHF8MuGZCkP8J0FxslD7a?dl=0

[spare oyster]

Have you read this one?

[sudden kindle]

I'll take a look

In general I'm skeptical of Olympiad problems providing motivation for anything

[sage python]

@sudden kindle I don't know of any such book that covers a lot of either

Number Theory for Beginners by Weil is kiiiinda in that direction? I think?

But it's like, a 70 page book that starts with the definition of N and ends with quadratic reciprocity and sum of 4 squares stuff, effectively from the algebra pov

(e.g. checking it now, it doesn't seem to use the word ideal, but it does talk about subsets of Z[i] closed under etc and shows that Z[i] is a PID)

I only mention it as a proof of concept of a special case of what you have in mind tbh

Knapp Basic + Advanced Algebra prob includes a fair bit of algebraic number theory though

[crystal lion]

It makes sense why what you are looking for would be of the form of an olympiad-esque reference

Generally people preparing for those contests don't care about the underlying algebraic theory in NT

so learning just enough algebra to get by caters to them

[sudden kindle]

I see

[thin hollow]

What are some good probability and combinatorics books to read at night

[pine trellis]

What is a good advanced linear algebra book

Or rather, a book that develops linear algebra from the ground up, starting with basic definition and theorems, but does so with a more advanced eye. Like the kind of book they'd use at a school that put off linear until after into alg.

Basically I want to relearn linear algebra because the course I took was a while ago and was never that rigorous to begin with.

Ideally I'd also want one I could get a paper copy of fairly cheaply. Or at least that I could find a pdf of online but I prefer having a physical copy.

[forest sleet]

I haven't used it but Linear Algebra Done Right by Axler is for a 2nd course in linear algebra

aimed at math majors

[quick hornet]

Like the kind of book they'd use at a school that put off linear until after into alg.
the chapters in atiyah-macdonald on modules

only partially shitposting

[marble grotto]

What about Roman's Advanced Linear Algebra

[crude sable]

Roman's knew Linear Algebra

[gray jungle]

i like hoffman/kunze

[gray gazelle]

I like cohn's algebra