book-recommendations

[hearty steppe]

how is Baker's lie theory book as opposed to Chevalley?

this may seem like the way to go https://arxiv.org/pdf/2404.11472

[molten gulch]

FTC is a limited case of stokes' theorem

[rigid trail]

Stokes theorem 💜

[tender cobalt]

I call stokes theorem the FTC

[rich sun]

Stokes' theorem is an extension of FTC

[molten gulch]

yes but it's not the same thing

[rich sun]

It's still based on FTC

[molten gulch]

this is wrong, it has a name for a reason

[molten gulch]

this is true

[tender cobalt]

nu >:c

[sterile pelican]

I am curious what people think of Duistermaat’s multivariable analysis

[remote sparrow]

why not advanced modern algebra?

[wet sentinel]

are there real analysis books in portuguese (brasil) ??

[timber mesa]

Lima's Análise Real or Curso de Análise (the latter is more "advanced", has more topics etc)

[wet sentinel]

by more advanced do you mean that it is graduate level or that it is rudin's undergraduate textbook level ?

[timber mesa]

it's maybe the same contents as Rudin's PMA but more in-depth

if you wanted things like e.g. measure theory or functional analysis then I'm not familiar with books in Portuguese

but I'd look through SBM or IMPA stuff

[wet sentinel]

ah no i just wanted a textbook to start real analysis

[wet sentinel]

and what about the first one here

[timber mesa]

it's the standard book for rudin-ish real analysis in many places in Latin America

I've read it myself, only the exercises leave some to desire imo

other than that it's an excellent reference

[wet sentinel]

ohh ok tysm

so it treats theorems etc in metric spaces in general and not just in R and C ?

[timber mesa]

I don't think it does, nor that it's really important to see everything in full generality the first time

the pointset topology stuff in these books is for R or R^n

[wet sentinel]

yes you are right thats not necessary rn

[timber mesa]

oh now that I remember Lima has a separate book, Espaços métricos

https://impa.br/page-livros/espacos-metricos-2/

which might be a good follow-up to his análise books

I suggest looking through IMPA's list of published books https://impa.br/publicacoes/livros/ some of which are sold at SBM's website https://loja.sbm.org.br

[wet sentinel]

alright

and is there a solution manual or something like that to the book

[timber mesa]

I don't think so, aside from maybe students uploading some of their own

but these are incomplete

[wet sentinel]

ohhh ok

tysm again for your recommendations

[trail hemlock]

ive never learned that

[remote sparrow]

it's by rotman too

the first edition is self-contained

the second edition doesn't go over the number theory (it assumes you've already learned it elsewhere, say ug rotman)

[trail hemlock]

does it go over LA as well or no

[remote sparrow]

it assumes linear algebra background

[trail hemlock]

ok i’ll take a look

[mystic orbit]

well stokes theorem is just the ftc too so like

¯_(ツ)_/¯

[molten gulch]

is the number theory you speak of equivalent to what the first 2 chapters of his 3rd edition cover or more?

oh okay yeah he defo covers more in his UG book

[digital scarab]

anyone watches the math sorcerer

[molten gulch]

!da2a

[hybrid sparrow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[digital scarab]

what

[molten gulch]

You're asking about a youtuber and whether people watch them, if you want to know opinions, ask for opinions, don't just ask if people watch them

[trail hemlock]

yeah i do sometimes

[normal crystal]

sometimes I wanna see what old textbooks the local burnout picked up at a garage sale, same

[molten gulch]

Same

[muted talon]

Sorry for necroposting (I think that's the term), but why is that?

[trail hemlock]

4 years ago 😭🙏

[trail hemlock]

why hating on the goat

[sterile pelican]

What's your background in abstract algebra? if you only know LA with proofs, at the level of FIS, Axler, or Berberian, then the book by Cox's "Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra" could work

[cosmic steppe]

Any book advices to start with the derivatives?

[sterile pelican]

As in ODEs or PDEs? Or just the ones you need for say calculus?

I know nothing of those topics btw :^)

[bitter sun]

any reccomendations for linear algebra

[timber mesa]

depends on your major/reason why you want to study LA, either way there's a very thorough answer in pins: #book-recommendations message

personally I did Hoffman-Kunze in math undergrad, good book but a bit terse

Axler's book is honestly good and so is Linear Algebra Done Wrong

out of that list

[sterile pelican]

Berberian is a great book LA too! If you know abstract algera

[tender cobalt]

I do

[sterile pelican]

I do before just to see what he is promoting. However, I cannot say he does book reviews they are more like an "unboxing" of those books

For reviews MAA is a good place to see reviews by other mathematicians really, also Amazon is not a great place for reviews as most are just like "this book is excellent" or "life changing" without explaining why

[digital scarab]

i mean he does dedicate videos to indvidual books atleast i guess

hey guyz how do u feel about cengage's james stuart early transcendentals

am a complete begginer who does know higher algebra and basic trig

is it the right choice

i jus wanna learn calc on the side as a hobby

[tender cobalt]

yea

but I would suggest you check out Thomas' Calculus , it's nicer in my opinion

[sterile pelican]

Or Serge Lang’s Short Calculus I think it helps get through what you essentially need

[topaz berry]

Please suggest me a book that takes a natural approach to combinatorics. I mean a book which starts from almost nothing to advanced combinatorics problems (please ping on reply)

[shrewd tangle]

Is there any linear algebra book that teaches the dual vector space without using matrices (or builds the intuition before introducing them)?

[fresh skiff]

wdym before matrices? but yeah FIS i guess will work

dual spaces comes before the matrix chapter

[tender cobalt]

adobe acrobat detected

[blazing rune]

Dover has a combinatorics book called Foundations of Combinatorics with Applications that's a good introduction for undergraduate students (https://store.doverpublications.com/products/9780486446035?_pos=1&_sid=e20352217&_ss=r).

[torn blade]

whats MAA?

[sterile pelican]

Mathematical Association of America, an organisation for maths and all they have a review section if you google say "Linear Algebra by Axler review MAA"

Like this for instace https://old.maa.org/press/maa-reviews/linear-algebra-done-right

[vital bane]

Axler's book is not "honestly good", it's more like "ehh...it's alright" it's more like a fun book to read after you learn LA

seeing LA from a different perspective (without determinants )

[timber mesa]

[tender cobalt]

certified axler hater (you hate axler just like how much he hates determinants)

[vital bane]

Lol I'm using Axler right now

[torn blade]

i dont think Axler's treatment of determinants is that bad really

[vital bane]

I just mean it's not fit for a first course in abstract linear algebra

at least imo

[torn blade]

its still prob my fave intro lin alg book but if that really turns you off id recommend FIS

[vital bane]

yea I like FIS, but now I like HK more

besides I'm already about to finish chapter 6 of Axler

[fresh skiff]

FIS is so nice, i like it

[topaz berry]

thank you man

[flat marten]

Greub

[vital bane]

ooh Werner Greub?

how is it?

[flat marten]

It's my fav definitely

Takes a less matrix orientated approach

[timber mesa]

Hoffman-Kunze also defines duals as spaces of functionals

bit dated but good book

[flat marten]

And whenever he introduces a new object he covers how it interacts with quotients, duals, etc which i very much like

Also the way he handles dual spaces I love and views them as two spaces with a non-degenerate bilinear map

Which is more general and kinda old fashioned but helped me understand some stuff with lie algebras

However the last chapter called the Jordan normal form the wrong thing and it really confused me

[rain hound]

Love it or hate it, it’s the only game in town if you want a LA book which is an excellent precursor to FA. Which is perfect for anyone who wishes to do quantum computing/mechanics for instance.

[quartz dragon]

Hi... Does anybody know if Sheldon Axler's Precalculus book is as good as Jame Stewart's?

[rain hound]

Linear Algebra Done Right

Generally any abstract algebra book that doesn’t suck will also do this

[earnest wolf]

if the course is proof-based then it's an amazing book

computation-based ones are kinda useless imo

[tender cobalt]

He's good at writing math books and he is a good mathematician known for more advanced books as well. Just took a look at his Precalculus book, it's definitely better than James Stewart's one, also shorter (about 500ish pages where james stewart ones is 1000ish)

[sturdy shore]

axler has a precalc book? interesting

pretty old too

[vital bane]

I do not disagree with what you're saying, it is a good book if you are planning to do FA right after LA, like look at the exercises I'm doing right now in my Axler thread I'm just saying it's not a good first exposure to abstract LA

[vital bane]

first time I'm hearing of it

[rain hound]

tbf it does say it’s intended for a second course

[vital bane]

no i said first exposure to abstract LA

[rain hound]

~~ I do think it’s fine for a motivated/advanced student though ~~

[vital bane]

meaning, I don't like Axler's approach of teaching LA

[sturdy shore]

I'd say axler is a pretty good first exposure to abstract LA

[vital bane]

HK is better 🗿

FIS is better

[sturdy shore]

that is assuming you've taken a more engineering LA course before

[rain hound]

Linear Algebra Done Wrong

[vital bane]

I heard LADW works exclusively over R

[rain hound]

it does

[rich sun]

not even C

whoa

[vital bane]

which is a bit strange because C offers a lot in terms of eigenvalues and stuff

[sturdy shore]

just trying to live up to its name

[earnest wolf]

like, offers??

there isn't even a built-in hashmap, what are we talking about?

non-embedded C is almost dead nowadays..

or like, new software is not likely to use C for anything other than embedded

but regarding the legacy code that was written before my birth... well, yeah. no one is rewriting a huge code base just for the fun of it

[molten gulch]

Kernel, lots of coreutils, etc...

C is a VERY standard language

[dusk hemlock]

[earnest wolf]

heck, rust is inside the goddamn linux kernel

linus wasn't persuasive ||(aggressive)|| enough

[earnest wolf]

but again, this is legacy

I highly doubt anyone who starts writing a new kernel today, without any legacy code, will pick C over say rust

[dusk hemlock]

they will

pick C

they might use rust

but they will probably use c

[earnest wolf]

||well...
they don't like sexy neofetch screens + high pink socks and furry costumes then.....||

[rain hound]

for something intended to be run on say a PC, yeah I’d say that’s true, for myself at least.

But for smaller stuff like embedded systems or anything you absolutely must formally verify everything, C has a use.

Rust has some nice correctness properties if you only care about basic functionality and memory safety.

But if you ever look to formally verify every possible property of a program down to the state of the computer such as memory allocations. You won’t get simpler than a DSL based off a small restricted subset of C.

and C really does have a compiler everywhere

Heck even if we aren’t that strict. I don’t think Rust has a formal verification toolchain at all. C does.

[molten gulch]

AFAIK there is progress being made on this but it'll be a few years, they're supposed to be incorporating the ferrocene spec into core rust's spec some time this year and AFAIK once they get a formal spec and we get the GCC rust compiler there'll actually be incentive for proper verification of toolchains

[full cairn]

It's honestly mindblowing to me that people still choose C for new projects today (atleast on platforms where other languages are an option). It's not just about how cumbersome it is to write in a language lacking modern features like a proper type system, classes, ADTs, support for functional programming, etc.. It's the fact that even a tiny mistake that would be harmless in any other language can turn into a huge security vulnerability

[molten gulch]

I actually can't find the ferrocene spec merger thing even though I read it yesterday

aaaaaaa memory (amnesia) issues are fun

[molten gulch]

The amount of memory leaks we wrote last semester is hilarious

lost tons of points over it, but only goes to show how once you have a few thousand+ lines of C it becomes painful to handle

also let's move this to the technology thread

[full cairn]

can you link the technology thread?

[molten gulch]

#1213610885277421588 message

[orchid otter]

Is fundamentals of astrophysics by Stan Owocki a good book for beginners on astrophysics?

[earnest wolf]

sure. but formal verification is still unfortunately niche

I meant more down-to-earth things

If u have unlimited budget and need to code a moonlander — sure, why not

and don't think I'm biased — I love theoretical compsci and absolutely hate coding. But I try to be realistic — formal verification is still niche in industry, and hence niche requirements require niche methods

[earnest wolf]

||btw, what the heck does a hermitian involution have to do with ?

upd: it's :mathbanachalghermitianinvolution:
||

[molten gulch]

[shrewd tangle]

FIS?

[remote sparrow]

friedberg insel spence

[shrewd tangle]

I'll look up the three suggestions I got

Thanks everybody :)

[quartz dragon]

Thanks!

[rustic cobalt]

Do you have any good recommendations for an analytic geometry book, in Spanish or English?

[full cairn]

My copy of Fraleigh is missing chapter 8 (Groups in Topology)

and "Ectension Fields" is pretty funny. I guess they cheaped out on the international version

[formal parcel]

anyone reccomend a good book for intro to mathematical reasoning?

[molten gulch]

the international editions are generally kinda cheaped out on

[sonic bluff]

Hi guys, for any of yous doing GCSE next year, can anyone recommend me some best books to get Grade A** or 9. And any like Question bank books or PDFs where there is like all sorts of questions on that one topics or chapters. Appreciate it!!!

[loud cradle]

good thing they tell you who wrote each chapter, in case you forgot

[full cairn]

Mathematical reasoning is pretty general. If you want to learn proof techniques, you could look at How to Prove it or Book of Proof for example. Personally I felt like I learned enough about proofs from other subjects like discrete maths and linear algebra, just picking up proof techniques as I go

[gentle jasper]

Does anyone have a recommendation for a resource (book or videos) for analytical proof techniques? I am talking about concrete examples, not big idea stuff (for example, I do not want "so, we can do a proof by contrapositive here since..."

I'm talking about concrete examples like: "a general tool which we use can be seen here: ε/2^k." Maybe we're talking about measure theory and define an interval as (a_k - ε/2^k, a_k + ε/2^k).

But the author or lecturer would explain why we actually define it like this for the purposes of a proof. What is often irritating, is that they'll explain the proof, but they don't explain specifically why one can logically think "okay, I need to prove this, so I will define my variables like this, such that I can use this proof technique, which will require convergence, so I use ε/2^k).

These things are not trivial for beginners. I'm hoping there exists something out there that goes through some real analysis proofs, or analytical proofs in general, and goes into enormous depth on each part of the proof itself. Rather than just depth of the result.

Obviously sometimes explaining why you defined something that way isn't trivial and unhelpful, but I think there is plenty of room for full-blown proof explanations in analysis.

Sorry for the longer message, I just want to make it clear that a general proof book isn't really what I'm looking for, unless it has a very detailed analysis section that uses these sorts of tools.

[slender wasp]

Pearson does weird things like this. For example they have a cheap edition of Artin but without the Galois Theory chapter. anyway, you might wanna check the preface for the changes. I think they may have moved the groups in topology chapter online and put a link for it in the preface. Although in my 8th edition, the online link led to an empty page 😅 maybe they've fixed it by now.

[molten gulch]

Yeah peason international editions are generally missing either the last or second to last chapter of the book and AFAIK also have a crummier index

[slender wasp]

Crummy is putting it mildly. My Artin index is auto-generated and practically useless from what I remmeber.

Sometimes they do fix things though. For example they dropped the Jordan form chapter of FIS from their 5th edition but added it back in a reprint of the same edition. And they are quite cheap...

[molten gulch]

sigh I really don't see why it's so hard for them to just retain the original indices and chapters, what are they gaining by mucking them up so badly

[slender wasp]

yeah don't know, but I shouldn't complain too much. I just got a new copy of Pearson FIS for $5.5 that I'm pretty happy about!

[molten gulch]

damn that's good

[old elk]

I bought the abstract algebra book by Dummit and Foote

It arrives next week, I'm scared, I know the book is quite dense 😢

[fresh skiff]

but its worthy, I have a copy as well

[old elk]

I know the PDF exists, but this damn book will accompany me wherever I go to do my master's degree

[fresh skiff]

Can I use Romans algebra book along with FIS?

or maybe roman requires some AA

[molten gulch]

advanced modern? I mean...it has a lot of algebra in it but I believe it assumes that you already know some abstract (idk how much compared to say, lang, jacobson, etc..., if someone has an answer to that pls do tell us)

[fresh skiff]

no, i am talking about
Advanced linear algebra

[old elk]

I have Thomas' algebra, Gallian's and soon Dummit's, I like each one of them, I have more algebra books than analysis books hehe

[fresh skiff]

thomas hungerford (if i spell correct)?
his UG book or graduate book?

[old elk]

Sometimes it's hard to find every detail in the examples, I had read the homomorphism section of Dummit's and then I realized some things when I went back to Thomas's.

[alpine tundra]

Just finished reading Lessons in Enumerative Combinatorics and I would highly recommend. Probably my favorite math book that I have read so far.

It's a GTM book, but it's on the easier side

[old elk]

No, the one by Thomas Judson, I like how he explains symmetry groups, although today I took a look at the book by the author you mention.

[alpine tundra]

I'd imagine most undergrads and some bright High Schoolers could get something out of it

[fresh skiff]

oh ok got it

[cursive orbit]

https://terrytao.wordpress.com/2010/10/21/245a-problem-solving-strategies/

[gentle jasper]

About as perfect of a response as I could have received. Thanks!

[tender cobalt]

there is a first chapter reviewing some groups rings and fields

and it wont require AA

the usage of algebra in the book is self contained

[fresh skiff]

Review of AA seems like AA is required, and having atleast first course will be helpful

[tender cobalt]

What's it about?

[tender cobalt]

Nope

Ive some parts of the book

[fresh skiff]

Oh i see

[slender cargo]

Probably better to just go through AA after FIS

imo

not sure why you wouldn't

[fresh skiff]

I was thinking to study both together lol

[tender cobalt]

The book is just hard to read because 1. its very terse 2. the examples are insane and random 3. the proofs given are hard 4. abstraction

[fresh skiff]

[tender cobalt]

one thing you can do is read 1 chapter from FIS lets say vector spaces

then read the same chapter in roman for mad rigor

[slender cargo]

Oh. Maybe try Artin's Algebra and use Dummit Foote as another reference?

[tender cobalt]

Hes talking about reading roman's advanced linear algebra

[fresh skiff]

I am talking about linear algebra
Does D&F have LA?

[slender cargo]

D&F does module theory after group and rings

so yes, although it's good to have seen linear algebra first with something like FIS

[fresh skiff]

I will check. I have almost done 2 chapters of FIS now will revise things for 2 days

[tender cobalt]

artin has a lot of la

[fresh skiff]

Make sense. Also i will pick D and F after lin alg

The goated ||Dry af|| book

[tender cobalt]

Roman does module theory after covering basic linear algebra as well

After that he moves on to hilbert spaces

[fresh skiff]

Yeah i checked it

[tender cobalt]

the final chapter is Umbral Calculus 💀

[slender cargo]

I'd just do FIS then and go to D&F afterwards, but that's just me

I'm going to learn module theory next semester so I'm not any authority on the matter, but that makes sense to me

[fresh skiff]

Wow
And I am on the same track

[tender cobalt]

i am on basic analysis + topology + manifolds rn

will get to linear algebra and algebra later

[fresh skiff]

Thank you guys for suggestions :D

[fallow cypress]

Wow this is a very nice article, thanks for sharing

[daring lake]

I studied linear algebra after group theory

[fallow cypress]

Found another neat one linked from that one https://terrytao.wordpress.com/2010/11/02/the-no-self-defeating-object-argument-and-the-vagueness-paradox/

Terry Tao is such an excellent writer

[tender cobalt]

the other day i saw some universities require you to take abstract algebra before abstract linear algebra 😭

[daring lake]

i am EE major so all math is like addon lol

[tender cobalt]

reall

[fresh skiff]

[sterile pelican]

Speaking of Roman I always wanted to read his field theory book after finishing AA

Since I am half way done with AA I cannot wait!

[fresh skiff]

i forgot what book were you using

[sterile pelican]

Ah Anderson and Feil's A First Course in Algebra

Roman's preface did say a familiarity of abstract algebra in his field theory book

[vital bane]

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

[earnest wolf]

so ur claim is C = ℂ?

[vital bane]

twitter be like

[drowsy pond]

Anyone know any really good standout math blogs that are interactive and stuff? (You know how sometimes you stumble across really high quality gems that are well produced, interactive, visually appealling etc?)

[fresh skiff]

oh yeah cool

[remote tiger]

I am in second year of undergraduate, I covered analysis I, II and group theory[not fully yeah have a little bit knowledge]. Now I want to learn analysis rigorously and also topology, what should I do?

Which books will be good for me?

[wet sphinx]

Found this list of books for self learners: https://www.neilwithdata.com/mathematics-self-learner hope its usefull

[earnest wolf]

I mean, didn't u learn analysis rigorously in ur analysis i, ii courses?

[remote tiger]

No..I hvnt read thoroughly

[earnest wolf]

try Abbott — amazing for building intuition in rigorous analysis (because he has good exposition doesn't meant it's elementary)

if u find it easy with the knowledge u have, try something else

[remote tiger]

Okyy

[fresh skiff]

Abbott + Rudin

[tired glen]

@tender cobaltyoo

[tender cobalt]

yooo

[vital bane]

the exercise are good too!

not just good but great!

[quartz dragon]

I'd like to ask for books recommendations for Computer Science... Is there any problem if I ask here?

[earnest wolf]

here or in #theoretical-cs if ur topic in question is theoretical CS

[quartz dragon]

Ok, thanks

I found about Cryptography Engineering (by Niels Ferguson, Bruce Schneier and Tadayoshi Kohno), but I don't know what would be the prerequisites to study it... (I've been studying basic programming)

I'm personally interested in Cryptography

[sterile pelican]

SICP? Not sure if a CS person needs that but I really like that book

The ideas there are wonderful

[fresh skiff]

i saw contents and it seems a good book

this book even contains Universal property of direct sum/product

[sudden kindle]

Interesting

[quartz dragon]

SICP is indeed wonderful

[alpine tundra]

It's about counting certain objects. There is a chapter on counting integer partitions and some chapters on finding the number of trees with certain properties. The book approaches a lot of the problems using formal sums and formal languages

Really interesting read

[mossy flume]

You might be better recommendations in the Cryptohack discord. Cryptohack is a fantastic online resource for learning cryptography by doing actual puzzles and stuff which help you learn the ideas behind cryptography. Google it and feel free to DM me with more questions about it.

As far as texts, Hoffstein's An introduction to mathematical cryptography is standard

[sterile pelican]

I see Silverman and will definitely vouch for it

[quartz dragon]

Thanks!

[tender cobalt]

Nice i was thinking to learn some combinatorics, seems like I'll give it a shot. Thanks

[coarse talon]

Just started calc 3 today, course recommends Calc Volume 3 by Strang, is that good enough or do you guys recommend other books?

[tough vigil]

Hi there

Can anyone recommend me a book on mathematical logic?

I took a course a couple of years ago that covered formal languages, syntactical and semantic implications, and proofs

I want to remember the things i learned

But i’m frustrated because i cannot seem to find materials that cover the topics in the same familiar way

The course i took was entirely composed of the prof’s notes and i don’t know where he got them from

Obviously i cannot get them anymore because i do not go to university any longer

[stuck kiln]

any suggestions for introductory probability texts?

[blazing rune]

Sheldon Ross's text. It touches a bit on stochastic processes, as well.

[loud cradle]

yea ross would be my standard recommendation as well

he has several books, "a first course in probability" is the one i mean

[blazing rune]

Would also recommend the stochastic process one and simultion one if you're looking to go past the first course textbook.

[stuck kiln]

thanks!

[stuck kiln]

I'm mostly looking for a basic introduction

mostly just a major blind-spot i want to touch up on

haven't touched probability in years

[blazing rune]

Definitely the first course, then.

[sterile pelican]

I like Blitzstein's Introduction to Probability

[remote sparrow]

#book-recommendations message

[glad dragon]

"Elon Lages Lima - Análise Real volume 1" is a good start

[acoustic island]

does anyone have recommendations for ib aa hl math textbooks?

[dawn shoal]

You got a link to that discord? nvm, I found it:)

[pulsar quail]

Hey,hey. Does anyone have recommendations for complex analysis textbook with a lot of solved examples?

[full cairn]

I like Asmar and Grafakos - Complex Analysis with applications. It has a decent amount of examples, but I think if you want loads of examples for a particular concept you should find a set of exercises with solutions. I don't think any book will have more than a couple examples for each concept

[tender cobalt]

Any nice analysis books that'll compliment Pugh's analysis? I'm new to analysis. I'm sure Abbot is a good text but is there any other nice texts on analysis?

[ionic zephyr]

https://www.youtube.com/shorts/Nn6bSmcv8RY

[tender cobalt]

This server we're all mathematical intellectuals

[ionic zephyr]

u havent watched it??

[tender cobalt]

Yes

[ionic zephyr]

yes u havent watched it

[tender cobalt]

In this server we're all mathematically intelligent

[ionic zephyr]

uh

what happens if u give ur wife a house

[tender cobalt]

Idk I don't have a wife

[ionic zephyr]

fair

[tender cobalt]

do you know the answer

[ionic zephyr]

huh

answer to what

i didnt ask a question

[tender cobalt]

^

Do yk what happens

[ionic zephyr]

oh

that was my answer

u become mathematically intelligent

would u like to see a screenshot of my book,arks bar

wait dont ask

u dont wanna know

[tender cobalt]

oh

[hollow scroll]

I need some books that can help my students during algebra.
Is there any good one?

[hoary prawn]

guysss

i know that Richard Hammack's Book of Proof is working on a spanish translation

do you know if I can contribute to the project?

[ionic zephyr]

hmm

idk do u have an email or something

or an adress

@hoary prawn

[hearty steppe]

Other texts besides gelfrand for variational methods?

[remote sparrow]

van brunt

[hearty steppe]

Have you worked through cassel? I’m enjoying his lecture series

[formal parcel]

looking for best books on abstract algebra

[mossy flume]

I assume you haven't studied abstract algebra before?

[formal parcel]

mhm

[mossy flume]

Do you know how to write proofs and have you studied abstract linear algebra?

[formal parcel]

yes and no

im a bit new with proofs but i understand them and hope to use abstract algebra to practice proofs further. But i have studied two books on proofs.

[mossy flume]

Ok I would recommend instead working through a text on abstract linear algebra

You're going to learn a lot of concepts from that that'll be generalized when you study abstract algebra

[formal parcel]

Im going to be taking a class on that in the end of january, I was hoping to do abstract along side if possible. If not that I need to figure out another subject to self study along side

[mossy flume]

And thus learning abstract linear algebra will will make learning abstract algebra much easier

And that'll also give you practice proof writing

[formal parcel]

Could you reccomend a good abstract linear algebra book ?

[mossy flume]

Linear Algebra by Friedberg, Insel, and Spence

[mossy flume]

A cool subject to study alongside would be number theory

[formal parcel]

That was on the mind

[mossy flume]

It'd give more motivation for abstract algebra + introduce you to a nice variety of examples

And number theory is pretty

[formal parcel]

are there good proof based number theory books?

[mossy flume]

That's always a plus

[rain hound]

abstract linear algebra is just good to know period. And it’s a really good setting where abstract algebra can be viewed as a potential application to, or generalization of. I leaned really hard on linear algebra when learning abstract algebra.

[mossy flume]

Uh yes but idk any off the top of my head but surely someone in this chat will give you a good rec later

I've taken introductory number theory but I didn't like my book

[full cairn]

Burton's Elementary Number Theory is pretty good

[formal parcel]

Alright. I think ill use the linear algebra reccomended when I start the class and check out number theory a bit while preparing.

I think number theory will also be nifty for small proofs just involving numbers like the division algorithm I saw in my proof textbook.

[versed nimbus]

Hi, does anyone have a book recommendation for an introduction to optimization? (Preferably free or open source).

[formal parcel]

Hey do I need to know any linear algebra definitions or theorems prior to using this book or does this go over everything?

[mossy flume]

goes over everything

[formal parcel]

Thanks. I only ask because I remember the other textbook I used for regular linear algebra started with systems instead of vectors and I was just making sure.

[mossy flume]

I mean systems of polynomial equations are things you should have seen before linear algebra

They're part of the motivation for why people study linear algebra

[formal parcel]

Yeah I’m pretty informed about systems. Pre calculus helped with that

[fading surge]

what a good book for a middle school student for math competitions?

[trail hemlock]

aops publishes a book called Competition Math for Middle School

its pretty good for like amc8 or smth like that

[fading surge]

thx

[remote sparrow]

no

[remote sparrow]

#book-recommendations message

[light fern]

what’s a good book to self study analysis from?

[remote sparrow]

#book-recommendations message

[storm tusk]

Any recommendations for books on topics beyond chapters 1 - 6 (group theory) of Dummit and Foote? Ideally, a book that is fairly readable lol, as I don't have much experience reading textbooks

Context is that I'm trying to find a book / topic for a directed reading program

[sudden comet]

idk

[dapper root]

There’s a book on finite groups by isaacs I like

[fresh skiff]

isaacs martin?

i think he has a book mn general abstract algebra as well

[dapper root]

Yeah

It’s kinda weird tho

I don’t remember how, I just recall it being wirrd

[loud cradle]

this is a great book

[fresh skiff]

oh

[heady ivy]

Hi everyone! I am new here. I need a simplified book with exercises on linear algebra for a complete beginner. Thank you.

[remote sparrow]

https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/0199654441

[meager warren]

Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik.
discussion link :- https://discord.gg/3pNM3H7Z
Anyone who has read the book, currently reading or will start can post some interesting problems, doubts or ideas from and somewhat outside of the book here.

[cloud fossil]

what are you doubting about ?

[meager warren]

not really doubting
just some place to discuss this stuff and what interesting things others can derive from text.

plus some problem discussion

or similar problems

[cloud fossil]

are you starting out fresh or to which chapters are you in already ?

[meager warren]

I have read till special numbers

skipped some number theory portion

[cloud fossil]

i'v done some exercises in wxmaxima with code from the book like here: stern_brocot(list):=block([ans:[], h:list],
L:[0, 1], R:[1, 0],
show(L)::=block(simp:false, buildq([L], first([L[1]/L[2]]))),
for i:1 thru (length(h)-1) do (ans:append(ans, [h[i], h[i]+h[i+1]])),
stern_result:append(ans, [last(h)]),
return(map(show, stern_result)))$ stern_brocot([L, R]), simp:true; stern_brocot(stern_result), simp:true; stern_brocot(stern_result), simp:true; etc....

or like: farey(n):=block([asc:true, ans:[], a, b, c, d, k],
declare(k, integer),
show(L)::=block(simp:false, buildq([L], first([L[1]/L[2]]))),
if(is(asc)) then [a,b,c,d]:[0,1,1,n] else [a,b,c,d]:[1,1,n-1,n],
while((is(asc) and is(c<=n)) or (is(not(asc)) and is(a>0))) do
(k:floor((n+b)/d), ([a,b,c,d]:[c,d,kc-a,kd-b]), ans:append(ans, [a/b])),
ans:delete(1, ans),
ans:append(map(show, [[0, 1]]), ans),
ans:append(ans, map(show, [[1, 1]])),
return(ans))$ farey(6), simp:true;

[native cradle]

Any anthropology book recommendations ?

[meager warren]

problems are quite nice and challenging

I am reading this to build some good math background before startig knuth's the art of computer programming series

[humble spire]

I don't know much anthropology, but have seen this reccomended a few times "Righteous Dopefiend"

[native cradle]

Thanks!

[earnest wolf]

I mean
it's just easier to ask in #discrete-math

[spice bramble]

Books for metric space

[wind trail]

I loved the metric space portion of napkin. Not incredibly rigorous, but a nice introduction to the topic in my opinion.

[nova rain]

guys what book

I am teenager

I learn algebra

[tender river]

Gamelin greene topology

[summer lagoon]

There was this guy called levis strauss (quite criticized nowadays) that wrote a book called “origins of civ” that’s a very short interesting essay

But do you have like a domain you are interested in? Like some subjects its linked to

I guess there’s like a sociolinguistic approch even to that (or the contrary, anthropological approach to sociolinguistic), like it might be more interesting if you take a route to it you already have knowledge of

[native cradle]

I'm taking an introductory course

[summer lagoon]

Oh. Then I’m not knowledgeable enough, but do you know what’s more or less in the course?

[native cradle]

not really

[ember slate]

Should i use a proof book to learn proofs or should i use a discrete math book that also teaches proofs like scheinerman's discrete math?

[remote sparrow]

The Origins of the Family, Private Property, and the State by engels. there are some parts where it is dated, but it remains a foundational text for marxist analyses of patriarchy.

[old elk]

What would be the order of topics to study topology?

[random pebble]

Within topology or requisite for topology?

I think it only directly depends on sets and a bit of real analysis, which itself doesn't depend on much but people tend to study it after linear/basic abstract algebra

[deft python]

I NEED BOOK FOR IMC

[red fog]

Anyone have any recommendations for an abstract algebra textbook. I really don’t like a First Course in Abstract Algebra by Fraleigh

[remote sparrow]

#book-recommendations message

[valid coral]

dummit & foote + herstein

[valid coral]

real analysis

and set theory

and abstract algebra i think?

[native cradle]

I see, thanks!

[normal crystal]

is it a typical four fields survey
if you're interested in cultural anthro, I would suggest reading a good ethnography rather than the classic theory suggested
at first

[normal crystal]

oops, the reply was lost, it was to this

[native cradle]

Judson is nice too IMO

[native cradle]

nah, literally my first non-maths course

it's official title is anthroplogical theory

if I remember right

[native cradle]

thanks

[muted talon]

Hello! I would like some book (or resources in general) to learn about analytic geometry (I think that's the subject). It's been a while since I've been in high school, although I've been able to do calc 1 through 3 pretty ok, although my school is not really rigorous about theory, which is why I would like to revisit it

[sand current]

Can i ask for a math book/workbook for ms and hs math?

[quick hornet]

you can but i dont think anyone has particularly strong opinions; at a middle school/high school level, everything is roughly equally good. i see khan academy and openstax recommended a lot just by merit of being free

[quick hornet]

there isnt really a substantial theory of analytic geometry specifically; analytic geometry just means "geometry with coordinates" (as opposed to geometry without coordinates, i.e. compass-and-straightedge constructions), which is very broad

you can read a linear algebra book and focus on the sections of the geometry of ℝ^n (like the dot/inner product)

or you can brush up on your trigonometry

but typically analytic geometry is seen as a tool used by other fields; its like a mechanical engineer asking for a "book on screwdrivers"

in your calc 2/3 course you migthve broached alternate coordinate systems which is the closest we can really get to saying theres a "theory" of analytic geometry

if you want more of a discussion on that you can check out any multivariable analysis text that has a section on "change of variables"/"coordinate transforms"/"jacobians"/"the fundamental theorem of multivariate calculus"/whatever term they use

[sand current]

what is meritsatx

[quick hornet]

i dont know, never heard of it

[sand current]

mb openstax?

[quick hornet]

free online textbooks

[sand current]

o

ok'

thx

[quick hornet]

https://openstax.org/subjects/math

you probably want the "developmental math" section

[sand current]

yea

tysm :p

[muted talon]

I see, noted. I didn't pay attention to the geometry part of linear algebra books. I will keep them in mind.

Now, would revisiting geometry specifically be useful? Not analytic geometry, just geometry

[quick hornet]

in the abstract, my recommendation is to not worry about revisiting things unless it came up in work youre currently doing and you actually need to go back and revisit it

in practice, a lot of mathematical concepts come back fairly quickly once students see examples of it being used

so unless you feel like it would directly help you with the mathematics youre doing right now, im not sure itd be super helpful per se

[muted talon]

Ohhh. Noted. Thanks for the help :3

Well, this does change my approach. The reason I ask is because I'm trying to self-learn math. I couldn't change majors because of economic reasons, so I'm trying to learn them myself. I think I'll start in calculus (or maybe trig) and work from there

[swift dome]

What's the beginner friendly book for number theory

[vital bane]

I wonder why "analytic geometry" is called "analytic" when we do not use analysis to study geometry, and it simply means "doing geometry using a coordinate system"

surely "coordinate geometry" is a more apt description?

(and I know that's another name for analytic geometry)

[full cairn]

Try Burton's Elementary Number Theory

Bought these for $5 each

[stuck pollen]

Five bucks!?

[trail hemlock]

that’s awesome

[full cairn]

Yeah, I thought it was a scam or something when I found it with shipping it's maybe 7-8 USD each, but still a great price

[stuck pollen]

A godly price lmfaoo

[fresh skiff]

Seems like a good deal.

[fresh skiff]

1 buck = 100 dollar?

[fresh skiff]

I will busy some algebra and commutative algebra or AG books soon

[full cairn]

Nice 👍 Here's my very short recommendations for algebra books:

• Fraleigh is great for beginners, easy to read, covers a lot of intro material except modules
• Artin is a good choice for something a little more comprehensive; covers modules and some of the classical Lie groups. Well written exposition
• Aluffi's Notes from the Underground is a very fun read, very conversational style, introduces categories very gently. Introduces groups after rings and modules, so probably not the best choice if your course does groups first
• Aluffi's Chapter 0 was too difficult for me as a beginner. Still haven't read much of it, so can't really give an opinion

[fresh skiff]

I will do self study. Have already taken 1 year of AA
Long story, but in short the TA who taught us wasn't familiar with the subject. He found some notes or videos online and then he wrote those on the board.

Btw i am studying linear algebra from FIS along with this book there were some other linear algebra books that i am using (like axler and two more)
My plan is to continue (after LA),

• D&F with Artin as reference
• Surely i will take a look at aluffi's notes cuz categories stuff is cool

Thank you so much for your recommendation
When i will start studying AA i will consider them as well

[full cairn]

Cool, good luck with your studies!

[fresh skiff]

Thank you sheddow

[muted talon]

Are all "good books" in English? It just seems that most recommendations are from English speaking authors or have been translated in English. A lot of those books can get a bit expensive compared to more "local" books

However, it could also be a symptom of "I'm in an English speaking community" which is most communities on the internet

[old elk]

Where, I need and I want

[hollow peak]

Recs for com alg other than AM, Eisenbud, or Reid?

AM is too succinct to reference, Eisenbud too long, Reid too simple

[old elk]

I have on amazon the miles to buy uuuh, I have to study hard to get to commutative algebra a teacher is waiting for me to research with him.

[full cairn]

I bought them on a website for used books in Norway. There's not a lot of math books there, but sometimes you can get lucky

[old elk]

That is very far from where I live, could you send me the link by private, maybe it was a teacher retiring.

[full cairn]

I doubt they ship outside Norway, and those particular books are of course gone now. I can't find any books on commutative algebra there now actually

It's https://bookis.com/ btw

[old elk]

you have to try it jeej

[marble solar]

https://web.mit.edu/18.705/www/13Ed.pdf

[mossy flume]

https://dspace.mit.edu/bitstream/handle/1721.1/116075.2/WWCM.pdf

here is a more updated version (2021 vs 2013, so presumably typos have been fixed)

but yes I second the rec

I haven't done a deep dive into it yet

so far just "oh god I need this comm alg fact for AG homework" but for that i've liked it better than AM

[marble solar]

I gave a cursory look at it during my MS program when I was doing Algebraic Curves/Geometry stuff, and it seemed good enough

[molten gulch]

We know an irl friend who used that alongside atiyah during their comm alg class last semester, they said it was alright but that they used atiyah more

[marble solar]

yeah there's no perfect text, the only perfect one for you is the one that you'll write after doing research for 10+ years, from teaching elective classes

[molten gulch]

Yeah, and before that I guess it also ends up being the texts that you like the most or resonate with you and contain all the material you need

[unborn jackal]

how

[civic python]

Has anyone covered “Algebra - From the perspective of Galois theory” by Bosch? If so what is your take?

[golden topaz]

https://mathoverflow.net/a/436855

[prime smelt]

I would appreciate a recommendation for Lie Theory.
I have some knowledge in analysis, measure theory, functional analysis, group theory, algebra, and limited character theory.
I also have some knowledge in Physics (I am a physics major) and some intuition for groups like SU(2), SO(3), U(1),...

[sleek python]

It's an english speaking server so people rec englsih books, even if they themselves may not be native english speakers.

There are tons of good french books for instance

Idk much about other languages since I do not speak them nor have searched for maths books in other languages

Although the more "recent" the maths and the more likely it is that most references are gonna be in english in my experience

(It still depends on the topic though, and it's usually only for highly specialized topics)

[muted talon]

Yeah, that's fair. I'll see if I can find some in Spanish

[versed nimbus]

[muted talon]

Where can one buy used math books on the internet? Other than eBay, of course. What is your preferred site?

[stable dagger]

you can buy on Amazon kindle version, it's cheap

packtpub has some math book

[sleek python]

If there is an academic/scientific/maths library in your town, you may also want to go take a look (and maybe they have a website too)

[stable dagger]

why do you need it? you can just download books from Google

[sleek python]

Some people prefer physical books

[stable dagger]

print out e-books

[sleek python]

Might be more expensive in paper/ink than buying a second hand book

[stable dagger]

no, not expensive

you pay for sewing and hard cover too

[vital bane]

thanks

[stable dagger]

also you can buy PocketBook X to read e-books

[trail hemlock]

https://www.bookfinder.com/
u can put in an isbn and it searches a ton of sites for used and new books

[mossy flume]

abebooks

[muted talon]

Noted. Thanks you two :3

[normal crystal]

that is definitely not one book

[molten gulch]

The books WILL get more abstract as you go along

[hollow drum]

Can someone recommend a text or paper on matroids? In particular, something that might go into the geometric aspects of them like june huh's work. Should I just reach oxley?

[spice bramble]

Is it okay to read proove of all the time online?

I am reading metric space book

[remote sparrow]

i've used alibris a couple of times

[limpid plank]

What book is the best for explaining the basics of the basic branches of Mathematics?

It should be in English.

[valid edge]

Thanks this is great

[trim tapir]

can I find a book that has every mathematical and scientific formulas

[marsh ingot]

I dont think there is

Math is not just formulas

[rigid trail]

if you are a formalist, it could be

[vale drift]

Hi, i want to do graphics programming at professional level. Any recommendation? I want to cover everything i can that helps. A book with code examples better

[limpid plank]

Is there a book that covers ALL of known Mathematics?

[livid lintel]

No

[rare haven]

Combine every textbook ever made

[vital bane]

yes

take book that does not have any mathematics

and take its complement

[marsh ingot]

[formal parcel]

does anyone have a pdf for linear algebra step by step by kuldeep singh

i legit see people here that have been in the server and even some moderators link pdfs for textbooks constantly.

also if anyone has any other reccomendation for beginner linear algebra books i could add to my collection, pls let me know

[timber mesa]

some books are freely available in the author's website, that's about the only instance I can think of in which mods have provided direct links to the files

in any case we can't directly link nor host pirated media here due to discord ToS and us being a partnered server

[formal parcel]

that makes more sense

[molten gulch]

there's linear algebra done right and linear algebra done wrong, those are both free; LADR is a bit (a lot) more abstract, I think LADW is less abstract

[formal parcel]

thats kinda what i was asking for, instead of specifically "pirating"

i heard about those but like what is the importance/difference with determinanats?

[timber mesa]

Axler's motivation to not introduce determinants until the end of the book has to do with certain proofs becoming more clear which I think is a fair point, you can read his main points in https://www.axler.net/DwD.pdf

LADW focuses more on computations while LADR focuses more on "theory" as TCC said

[formal parcel]

Hmm.. I have another question, any reccomended courses I could follow as well for linear algebra? What im most concerned about is taking the best notes for the course

[muted talon]

I have a question. What do you all think about... I'm not sure what to call them. These math books where they teach you about a bunch of math from different topics, like Advanced Engineering Mathematics by Kreyszig

Would it be better to get books about each individual subject, or is that like a good place to start and then move from there?

[formal parcel]

is gilbert strang's linear algebra book great for beginners?

[versed nimbus]

[muted talon]

There's also one of linear algebra and differential equations, which sounds like an uncommon combo of subjects from a newbie's viewpoint

[bright epoch]

is the HoTT book any good

[tough gorge]

u think I can find them for free?

[daring tangle]

diary of a wimpy kid

[gray gazelle]

Hello members, I was hoping to receive assistance in my endeavor to learn about Mathematics. Is someone able to assist? I can explain more in detail once assistance can be offered.

[daring tangle]

#discussion

[split portal]

Margaret Lial has some decent books on basic algebra and trig

[split portal]

Please stop

[gray gazelle]

Thank you. Sadly, my endeavor is a bit more refined.

I wish to start at the basics.

[split portal]

Can you add?

[gray gazelle]

If I am not mistaken it starts with Logic, so I think I will inquire about Arithmatic.

I do not know why one adds or the concept behind numbers - so for simplicity sake, no I cannot add.

[split portal]

The margaret lial book basically requires you knowing how to add and your multiplication tables

[gray gazelle]

I cannnot entertain that book.

[split portal]

Which is roughly what I knew starting college

[gray gazelle]

I would like to start at the basics. Forgive me, basics means for the initiate, Greek.

[split portal]

I mean, addition is just an extension of counting. You can count. By proxy you understand why people would want to add.

[daring tangle]

i thought we talk about math in discussion channels and this channel was for books

but i guess im wrong

mb

[gray gazelle]

I believe Thales.

[split portal]

Giving people bad recommendations on purpose is my issue with you

[gray gazelle]

Euclid

Pythagoras

[daring tangle]

oh u mean the diary of a wimpy kid recommendation?

mb

[split portal]

Yeah

No worries

[split portal]

Euclidean geometry is probably not the greatest place to start

Most books on elementary geometry assume some algebra

[gray gazelle]

I first need Arithmetic

I don't care about contemporary mathematics.

I only care about the foundational classic liberal arts.

[split portal]

Why?

[gray gazelle]

It doesn't serve a purpose for me.

[split portal]

Just want it?

[gray gazelle]

So for mathematics - I believe I am looking for Arithmetic, Geometry, and something else...

Logic, I have no need for.

[remote vortex]

No one does in 2025

[split portal]

Arithmetic in the "classic liberal arts" sense could go so far as meaning actual number theory

If you want to do that you really will need algebra in the sense I am describing to you

Arguably to learn euclidean geometry well you really probably should also learn some algebra.

[gray gazelle]

Sorry for explaining poorly. What is the earliest explanation for Arithmetic?

[split portal]

Much of the rules of arithmetic in a more basic sense themselves are better understood via algebra as well.

[split portal]

The issue here is I don't know what you mean by arithmetic. There are historical usages of that word that literally just mean number theory.

If all you need is like counting, addition, multiplication etc, well that's prealgebra I suppose.

[gray gazelle]

My apologies again. I want resources that detail mathematics as was in the time of Thales.

I do not want anything modern.

[split portal]

Okay, well are you trying to learn math or the history of math? These are not the same thing.

You can purchase copies of the elements for ex

[gray gazelle]

I am trying to learn math from sources that they themselves would have used. Pythagoras, Thales, Euclid.

Elements is Euclidean Geometry?

[split portal]

Yep

[gray gazelle]

Okay, before one understands shapes I need to understand their composition.

I need to know what I am measuring. So what precludes Geometry.

[split portal]

I am personally not a historian but euclid's elements were the standard intro math textbook for a very long time.

Arguably it's a garbage choice to start from tho

[split portal]

This is a silly attitude.

[gray gazelle]

I see. Please explain like I am a child.

[split portal]

Literally any modern math textbook will discuss applications

[gray gazelle]

Applications meaning?

[split portal]

Open a modern math textbook and see for yourself.

[gray gazelle]

I have asked you, who used a word in context, to explain its meaning. Not to be rude, but because I seek clarification for what you mean.

I do not want to see what I see, but ask for what you mean.

[split portal]

My response is not meant to be rude either. I am suggesting it because I think it is something you really should do.

I think genuinely starting from historic sources is a poor way to learn math

[gray gazelle]

I do not understand numbers. So a contemporary book would not mean much. Unless you want me to start at pre-grade school.

[split portal]

On one hand those books are not written for modern readers and are unnecessarily hard to parse because of it

[split portal]

People from earlier times understood numbers less than we do now.

[gray gazelle]

But even pre-grade school is instructional in the same way as one learns the alphabet....it is merely rote. With no understanding.

[split portal]

The greeks thought all numbers were ratios of integers at one point.

[gray gazelle]

Okay, you seem to know your stuff.

So what are numbers?

And what are integers?

And what are ratios?

[split portal]

I would argue that there isn't a single general definition of "number"

We have several formal structures we work with mathematically that work like how we expect quantities to work.

Sometimes what we want differs in various contexts

So often we deal with different structures.

I think saying you don't need logic but trying to start from what seems like a purely philosophical pov is also a mistake.

[gray gazelle]

And the purpose of logic is?

[rigid trail]

math

[gray gazelle]

and the purpose of math is?

[rigid trail]

math

[split portal]

I suppose to assist reasoning usually. But you can study logic for the sake of itself.

None of these things have to have a purpose?

[outer turtle]

math

[rigid trail]

yes

[outer turtle]

awesome

[gray gazelle]

The purpose of math...is math?

[rigid trail]

correct

[split portal]

A lot of math does not have super practical applications

[gray gazelle]

That is....quite a logical reasoning.

[split portal]

Does it need a purpose?

[rigid trail]

practical applications are a side effect

because math is just that great

[gray gazelle]

I understand.

[outer turtle]

circular reasoning isnt too logical imo

[split portal]

What if people just find it interesting?

I don't personally buy the idea that the purpose of math is math

I just don't think it has or requires an explicit purpose.

[rigid trail]

it isn't circular reasoning

[outer turtle]

hm

[rigid trail]

it's circular purpose

[gray gazelle]

It seems there are more people here hurray.

[outer turtle]

fair

[gray gazelle]

Maybe one of you can assist me.

Please give me the earliest foundation of Mathematika.

The root foundation from which one cannot proceed if they don't know it.

[rigid trail]

well humans can ascribe whatever purpose they want onto it ig

[split portal]

No not euclid lmao

[rigid trail]

earliest in a chronological sense?

[gray gazelle]

Is Wikipedia reliable for chronology?

[split portal]

There isn't one single foundation that nobody can proceed without in this kind of thing

[gray gazelle]

Okay.

[split portal]

Many different people from all sorts of backgrounds and abilities do math

[gray gazelle]

So Euclid's elements.

Johann what will I learn from that?

there are 12 or 13 books?

[split portal]

Euclid is just not a good starting point pedagogically

[gray gazelle]

Thank the Gods.

basic (as in foundational) number theory?

Like the concept of numbers?

THANK YOU

[split portal]

The greeks had misconceptions about numbers that you will also learn

Like, this is just bad advice to take seriously

[gray gazelle]

The Greeks also lived life way better and more meaningful in most regards than your most studious and cultured professionals.

[split portal]

Seems like you're pulling that out of your ass.

[gray gazelle]

I don't care about what they got wrong. I only care about what they got right in giving instructions.

[split portal]

You should care about both

[prime smelt]

^

[split portal]

History is full of people grappling with stupid bs the greeks believed

History of math books exist

It would be wiser to at least read those rather than straight euclid

I actually made this distinction to them earlier

[rigid trail]

greeks finding the length of the diagonal of 1x1 square (impossible)

[split portal]

I still think it's not so great to point people in this direction without a good amount of warning

The greeks were full of shit about a lot of things

[gray gazelle]

Thank you Johann for your suggestion. After Euclidean Elements, what comes next?

[rigid trail]

bro is not listening

[split portal]

What are you even talking about?

[gray gazelle]

So give me what I had suggested above. My interests are the classical liberal arts.

[split portal]

Literally nobody uses euclid anymore because it's not good.

Have you ever actually read euclid?

I've read enough to know it's not great lmao

[gray gazelle]

Arithmetic, Geometry, disregard Logic. And there is one more thing, let me look at it quickly.

[split portal]

"Disregard logic"

My guy, part of the purpose of reading euclid classically was to learn proofs and logic

I think you missed the part where I literally asked them if they were trying to study math vs history of math?

[gray gazelle]

Oh, I guess I need (Numbers), and then Geometry.

[rigid trail]

wtf

[crude sage]

Next should be Al-Khwarizmi, The Compendious Book on Calculation by Completion and Balancing. (this is a joke)

[gray gazelle]

So if I start with Euclid, I don't think I can start there.

[split portal]

Like, is the goal history? Or is the goal to learn math?

[rigid trail]

i think the goal is the right to say "i started math using euclid"

[split portal]

Okay, but then modern sources exist for both things and pointing them solely to primary historic sources is probably still bad advice.

[grim ore]

I think they just want to map a chronology of math but i just started reading so no clue

[remote vortex]

Why not Babylonians, who predate Euclid?

[rigid trail]

no idea

[remote vortex]

Not to mention whatever was happening in China, India, or MezoAmerica, which sadly I'm not familiar with

[grim ore]

learning math with euclid is interesting tho

[split portal]

This is also a totally different third option that I think they need to clarify if they want a not stupid answer.

Fwiw euler has a whole book on elementary algebra

If we're playing the historic game this would be as good as any

[remote vortex]

There was a dude?

[split portal]

Gauss has the arithmetica or whatever the heck he called it

Currently forgetting

Pretty sure I have this name slightly wrong

[gray gazelle]

Okay, so here I will explain my goal. So there is no contention into my acts for wanting to learn mathematics at its foundation. I will not engage in bickering for my asking for assistance. You can either offer it, or you can ridicule it, but I have merely asked for instructions.

I want to learn the concept of numbers. What constitutes a number - basic things. The building blocks. Then from there I want to learn Geometry. I want the sources as one would have had to use at the earliest of times in a language that I understand and is readily available - English.

[rigid trail]

peanos axioms

[split portal]

The problem with this approach is that the foundations people had historically were shit for various reasons.

If the goal is foundational then a historical approach is just dog shit

[rigid trail]

yeah newtons fluxions seemed like voodoo to me

maybe im just dumb though

idk

[split portal]

If the goal is historical, then sure. Knock yourself out.

These are very different goals.

[gray gazelle]

Oh boy.

[grim ore]

I am a little lost at why you want to look at "building blocks" of math, but i guess if you want to have a book that summarizes major math discoveries in history: W. W. Rouse Ball. A Short Account of the History of Mathematics

[rigid trail]

start with peanos axioms and set theory if you REALLY want to start from foundations 🗿

[grim ore]

It talks about most of the stuff i think you are asking about

Its for a class in my uni called History of math

[gray gazelle]

Thank you everyone.

[normal crystal]

#book-recommendations had a yap attack

[remote vortex]

Nah, it's just that fluxions and infinitesimals were fundamentally flawed in ways that Newton and Leibniz didn't entirely realize, and it's not until Cauchy and Weierstrass that we developed a sound way of talking about these concepts

[rigid trail]

Good to know that my suspicions were well founded

[gray gazelle]

Most likely due to the way nature is structured.

[split portal]

People sucked so hard at reasoning about sets that the reaction to cantorian set theory got cantor bullied into the hospital

[grim ore]

This book is also on Gutenberg @gray gazelle

[gray gazelle]

I don't know what Gutenberg is.

[grim ore]

Its an open source library

Called Project Gutenberg

[gray gazelle]

Gutenberg press lol

I understand now.

Funny name.

[remote vortex]

I yield to no one in my admiration for Kronecker's contributions to algebra, but where it comes to set theory he was a crank

[gray gazelle]

For Biblical purposes lol

I believe.

[rigid trail]

printers predated him in China 🗿

[split portal]

The ams had a nice series of math history papers but they're a little advanced

[gray gazelle]

Printing blocks vs. press?

[split portal]

Who gave you the epsilon and sherlock holmes in babylon

[outer turtle]

what's happening here

[gray gazelle]

It is called.

[remote vortex]

The entire concept of "dude who invented x" is a gross oversimplification of the way things work (including the fact that for some reason it's always a dude)

[split portal]

Together these books do range historically from the plimpton tablets to modern math

But they aren't exactly a textbook

Oh mactutor also has some awesome history of math resources

https://mathshistory.st-andrews.ac.uk/

[gray gazelle]

Too modern for my taste. But thank you.

I am too simple minded to understand those concepts.

[split portal]

The modern concepts are often a lot simpler than historical ones

[gray gazelle]

Thank you kindly everyone for your inputs.

[split portal]

Half of euler's biography is euler sending letters back and forth to some random historic figure about a bunch of old crackpot theories that were wrong.

I mean tbf

[normal crystal]

dw, that's too modern for him🤡

[split portal]

That's kinda just what science was in general

[rigid trail]

what

quit the old scrolls fetish cmon

focus on correct maths

[split portal]

Let a mf ponder his scrolls and tablets

I will never tire

[normal crystal]

but only in translation to modern english🤡

[split portal]

Do I look like the wheels on this mf 🚗?

[grim ore]

nahhh all my homies get a dictionary and read it in the original language

[split portal]

Ya know toomanyfours these things don't have to be mutually exclusive either

[normal crystal]

the wheels on the dooter go round and round
round and round
round and round

[gray gazelle]

What things?

[split portal]

Nobody is gonna come beat you up if you learn modern geometry and read euclid

You won't be arrested I promise

[gray gazelle]

I am not interested in other people's opinions.

[grim ore]

Also yeah, im curious to know why you want to read something old and kinda outdated?

[split portal]

Yet here you are asking

[grim ore]

Like just wanting to know

[rigid trail]

aww dont be a tsun tsun

[gray gazelle]

I don't want to learn modern branches of mathematics because I am not smart enough to learn their discourse. Nor do they have a use for me.

[grim ore]

What about introductory or elementary books to build up to the higher material?

[split portal]

I think you are overestimating how smart you have to be to learn basic geometry and algebra in a modern sense and overvaluing how people did it previously.

[gray gazelle]

Listen, I am stupid.

[split portal]

Also, a lot of old math was convoluted as hell

[gray gazelle]

Extremely stupid.

[split portal]

Me too dawg

[gray gazelle]

I just want to understand what a number is.

[rigid trail]

euclid isnt going to be any easier my guy

[gray gazelle]

Then I want to understand what a shape is.

That is it.

[split portal]

People put a lot of work historically into finding approaches to mathematical topics to make them easier to understand.

[rigid trail]

okay honestly idk what a shape is, nor do i know what a number is

[split portal]

Fair

[grim ore]

im only a third year uni, and i have only tried to read euclid elements because it was really, idk the right word, but messy to read

[modern ruin]

one can get away with not having to go all the way to modern discourse about geometry to just get an understanding for what a shape is

[normal crystal]

just read one of the pop math-ish books on numbers and shapes

[gray gazelle]

I think I need to.

[split portal]

The joke is about pop math books being shit

[rigid trail]

pls dont banish yourself to the pop math world

[gray gazelle]

I don't even know what pop math is...

but if they can teach me about numbers and shapes then maybe that is where I should go.

[grim ore]

also learning euclids elements, now that im scrolling through it, doesnt look like anything past a hs geometry course

[split portal]

It's okay it was a silly joke

[rigid trail]

"math" books with more pages without equations than with them

[normal crystal]

well, some of the books on numbers are straddling pop math and historical scholarly
but anyway, it would be better than reading ancient texts in translation to learn basic math

[remote vortex]

If you aren't starting your mathematical education with Plimpton, what are you even doing

[split portal]

Euclid is basically the opposite of this

I mean like, in terms of applications, relations to real life, stuff like that.

[gray gazelle]

Sorry, I have one quick question. Is anyone aware when one started their studies in Mathematics around the time of Thales?

[split portal]

It's very dry and unmotivated if your motivation is not doing geo for the sake of itself.

I do not know when the greeks started their mathematical education

Kinda wish we had a math history channel now

[gray gazelle]

I see. I think in their 20's sometimes even early 30's.

[remote vortex]

Most of them never did because they were women or slaves

[gray gazelle]

Kind of curious why that was.

It was something you had to earn the right to learn anyways. Thank again.

[split portal]

Earn by being wealthy and male?

[remote vortex]

I always love it when people imagine themselves in Ancient Greece and expect they'd be discussing high concepts in olive groves rather than toiling to death in the fields or galleys, or dying in childbirth

[split portal]

Even for much of post greek history this feels true

[grim ore]

iirc they also didnt have a public sewage system until the romans

plato himself was roman

No?

[rigid trail]

what the sus

[grim ore]

Am i wrong

[rigid trail]

yes

[grim ore]

damn my bad

I read plato in my ancient lit class during a roman unit so i thought

[remote vortex]

Was he? Plato lived in the 4th century BCE, that was well before the Roman conquest of Greece

[grim ore]

Ah gotcha

[split portal]

A whole man made of playdoh? I refuse to believe it.

[remote vortex]

It's the wonders of philosophy

[grim ore]

you know... that class makes a lot more sense now that im thinking about the plato unit, we read Platos republic and i think it was trying to be used to set up a system for roman politics and a philosophical understanding of "utopian government", rather than (what i believed prior) to critque roman poltics

Its a nice dialogue tbf

[vast jackal]

I love the Renaissance period

[rigid trail]

freaky
in some parts

[grim ore]

True, its realistically not possible and we are far detracted from the course he mentioned, it was kinda cool being able to associate with some novels like The Giver by Lois Lowry

[outer turtle]

guys

[outer turtle]

i think we should make children read archimedes, modern books are too complicated

[grim ore]

I didnt realize The Giver was an almost replica of the "world" he created

[outer turtle]

zyphen

who's your fav greek god

[grim ore]

hmmm probs Haephestus

[outer turtle]

ouh i see

[grim ore]

He brought fire, right?

[outer turtle]

nope that was um

[remote vortex]

That was Prometheus and he wasn't a god

[outer turtle]

yea

exactly

[grim ore]

Oh yeah that was a titan

But still haephestus is a pretty good one to choose

He made stuff

[outer turtle]

in some retellings he's a god but the most popular one is titan

iirc

[outer turtle]

yess

cyclopses

[remote vortex]

Mine's definitely Dionysus 🍻

[outer turtle]

omggg real

Dionysus is a vibe

[grim ore]

Reading like old mythos of greeks made me not like dionysus highkey

he was a psycho

[outer turtle]

oof

[remote vortex]

I mean, they all were

[outer turtle]

hades was chill from what i hear... for the most part

more than most

[normal crystal]

what's the difference between the gods and the titans anyway
just a generation and nomenclature

[remote vortex]

Arachne was not disheartened and boasted that if Athena wished to make her stop, she should appear in person and do it herself. Immediately, Athena removed her disguise and appeared in shimmering glory, clad in a sparkling white chiton. The two began weaving straight away. Athena's weaving represented four separate contests between mortals and the gods in which the gods punished mortals for setting themselves as equals of the gods. Arachne's weaving depicted ways that the gods, particularly Zeus, had misled and abused mortals, tricking, and seducing many women. When Athena saw that Arachne had not only insulted the gods but done so with a work far more beautiful than Athena's own, she was enraged. She ripped Arachne's work to shreds and hit her on the head three times with her shuttle. Shaken and embarrassed, Arachne took her life by hanging

[grim ore]

If you didnt join the party of dionysus, he would literally have his cult-like followers skin you alive and tear you limb from limb

[remote vortex]

But it's alright because Athena turned her into a spider afterwards

[outer turtle]

kidnapping persephone a bit of a bitch move but still

[rigid trail]

bc he was a shut in

[outer turtle]

yea probably

[grim ore]

isnt titans more like elements of the natural world moreso?

[outer turtle]

nooo that is so depressing

[outer turtle]

like me fr

[grim ore]

like gaia earth, uranus sky, chaos space, kronos time, helios sun, nyx moon and etc etc

[remote vortex]

Hades had the right idea, seclude yourself far away from all those assholes and just do your own thing

[rigid trail]

mood

[outer turtle]

nyx is such a pretty name

like

it looks ugly but it sounds so beautiful

[rigid trail]

nick's

[outer turtle]

ewww

[rigid trail]

there i ruined it for you

[outer turtle]

dont do that ri me

[rigid trail]

so it is how it looks

[outer turtle]

its not nuce

[outer turtle]

ughhh

fine

x makes any name pretty

ngl

[grim ore]

Did trap persephone tho

[rigid trail]

ha

[outer turtle]

zeus kindaaa peer pressured

ig

[remote vortex]

I did say they were all psychos

[rigid trail]

zeus is peak "beta male"

[outer turtle]

mhm

[grim ore]

📠

[rigid trail]

idk why the greeks would come up with such a sissy as their king deity

[outer turtle]

dunno either tbh

[remote vortex]

It's because he wouldn't shut up about how great he was

The Trump of his day

[outer turtle]

omg

so true

[rigid trail]

real

[outer turtle]

there was some myth

im recalling where he like

nvm idfr

lol

[grim ore]

i searched it up and found some interesting named titles between zeus and ganymede

[outer turtle]

interesting

might be it

theres also a story about why kreta is the like

border of europe ig

like the edge of europe?

edge of europe sounds like am action adventure movie

prob with dwayne

[grim ore]

lmaooo

[molten gulch]

<@&268886789983436800>

jesus that was fast

I didn't even get my autocomplete to finish

[orchid bridge]

im looking for anywhere that might have some good exercises for an introductory course on ODE. The textbook we are using is Elementary Differential Equations and Boundary Value Problems but alot of the problems are either word problems or abit straightforward.

[vital bane]

maybe try "Differential Equations with Applications and Historical Notes" by George Simmons

what's wrong with word problems

[orchid bridge]

oh nothing wrong but the course does not have any word problems. just trying to compile some additional problems for me and a group of friends that might be closer to course content

[orchid bridge]

thank you i will take a look

[ionic zephyr]

https://tenor.com/view/sat-collegeboard-college-crying-anime-gif-4460727827174692531

[gray gazelle]

anyone know a good source that covers fourier transform in L1 and L2?

[marsh ingot]

Katznelson, intro to harmonic analysis

[hearty steppe]

Thoughts on Nassim Taleb’s books?

[devout hearth]

can someone recommend me books to master circle beginner to advance level

[grim ore]

Idk if I dont have the context, but what are you looking for?

[devout hearth]

i want to understand about circle more deeply and i am a beginner

for that i want an well organize book to master circle concept ,

[grim ore]

Like circles, the conic?

[devout hearth]

yes

[grim ore]

Okok just making sure

I would say from a beginner perspective, a Calculus III/Multivariable calculus book should help, and then proceed into algebra;
A really short but (personally) facinating read is this paper `What Is the Difference between a Parabola and a Hyperbola" by Shreeram S. Abhyankar made me think about conics in a way I never thought of before and its for someone whos fresh out of calculus. It is also by a prof at purdue who I think might have also been the head of dept or even dean

[devout hearth]

thanks for the help

[cursive orbit]

where does one go to learn fractional sobolev spaces?

[timber mesa]

Robert Adams' book Sobolev Spaces has this

I think it's the usual rec for this kinda stuff? I'm not too familiar with fractional sobolev specifically

[cursive orbit]

thanks for the rec, I'll checck it out

[cursive orbit]

also, are fractional sobolev spaces not as important as I perceive them to be? I feel like every time I go to a talk somebody's talking about trying to get like fractional regularity improvements or something like that

[timber mesa]

surely they're important for them then again I'm not sure which contexts they come up in

[tiny spear]

What do you think of Henle's "Combinatorial Introduction to Topology"?

[tender cobalt]

How is Pugh + Rudin combination guys

[red fog]

Thank you!

[floral lantern]

Judson’s exposition is very good

But in my opinion there aren’t enough concrete examples/exercises in the text that aren’t essentially trivial

It does a very good job with the theory and its more abstract exercises