book-recommendations

[valid narwhal]

I see. It’s just that 1) it defines i=sqrt-1 but i think the most you can say is i^2=-1(?) and that 2)addition of a real and imaginary number isn’t made sense of, or that the usual addition symbol is abused here

[slow roost]

they may be skipping some details

[valid narwhal]

I would much prefer that yes

[gray gazelle]

Topology and Groupoids by Ronald Brown, but that's kind of a boring answer haha. Just made me think more "categorically" I suppose?

[gray gazelle]

https://groupoids.org.uk/pdffiles/topgrpds-e.pdf

[gray gazelle]

nice, found the pdf

[fluid violet]

The Bible 🙏

No. I'm king. Duh.

[hardy sail]

What pre calculus book would you guys recommend, I’m looking for a book that throughly explains why?

[molten gulch]

serge lang's basic mathematics is good

[hardy sail]

Thank you

[median scaffold]

Hi, guys, I have a friend who wants to learn math. Can you recommend a good self-study book (or books) that covers everything from variables to integral? Please.

[cunning elk]

why is calculus the stopping point

what's their background

are they starting completely from scratch

[hybrid sigil]

No, I haven't actually read them, only glimpsed some and just know that they exist 🙂

[gray gazelle]

hello everyone, what are your favourite books in developping intuition on Linear Algebra?

[vital chasm]

3b1b has a nice video series

But you can always read different texts and see how they do things differently

I first learnt linear algebra by Sergei Treil's linear algebra done wrong

[tiny gulch]

LADW is great

[clever hare]

Serge Lang is a bit rigorous for people not aiming at pure mathematics.

Are you asking for recommendations regarding Olympiad level mathematics?

[wraith mica]

Yea

[crisp yoke]

hello

i need help with math lecons

[molten gulch]

They asked for a book on the why, a rigorous book would be the only possible option

[normal niche]

Hi
can anyone recommend a book for olympiad maths ( I'm not used to olympiads and yeah, I don't think I know all the theorems too ... ) thanks in advance ( no geometry please xD )

[molten gulch]

Aren't you expected to know geometry if you are participating in an olympiad?

[normal niche]

I'm not really participating, it's just that I'm interested in it 😅

and geometry isn't my thing to be honest

[stuck zephyr]

everyone doesn’t like geometry anyway

[high fjord]

Real

But its also the most interesting when it comes to theory

Out of olympiad topics i mean

[stuck zephyr]

yea i definitely agree with this

im not

[high fjord]

There are two wolfs inside you

Both skip geometry

[junior citrus]

Yo do ppl give math book recommendations here?

I have one that's so goated

[molten gulch]

Geometry only became interesting to us once we started looking at MVC, diff geo, and alg geo

Euclidean geo was our most hated school subject

<@&268886789983436800> username + possibly pirated resource?

[remote knoll]

I deleted the message, but give me a moment to adjust the username

[stuck zephyr]

yep i truly get this

[molten gulch]

Ty omni

[remote knoll]

Hey, sorry, we can't allow pirated materials on this server. It's against Discord TOS.

[vital chasm]

Back when I did national olympiad I only did inequalities lol
https://artofproblemsolving.com/articles/files/MildorfInequalities.pdf
This was the reference i used

Its slightly hard to read for beginners, you should be googling things you dk or asking for help

[junior citrus]

Try this

[junior citrus]

It's alr

[vestal osprey]

Roingus Ryan!

How u doin?

[vestal osprey]

LADAig Linear Algebra Done Alright i guess

[normal niche]

Sorry I just came back
Alright, thanks mate I'll give it a try 👍

[gray gazelle]

proofs are fun! it's school proofs that're bad

[median scaffold]

In my country, the "beginning of calculus" is the end of the school curriculum. If he finish before the start of the calculus, I think it will also be great. If he wants to, he can continue.

He knows some basics, he can solve the conditional 2x=1, but practically yes, it would be worth starting from scratch with algebra.

[remote vortex]

I've always been partial to the compromise title of "Linear Algebra Done"

And for the haters there's "Linear Algebra: Don't"

[vestal osprey]

Better than the titular "Linear Algebra Don't"

Oh

Great minds think alike

[remote vortex]

And lazy minds reach for the same low-hanging fruit

[vestal osprey]

Or jinx I guess

Fr fr

[gray gazelle]

Does anyone know of something like a question bank for all the main topics in undergrad pure math? Some compilation of questions on different topics in analysis, algebra and topology? Preferably organised by topic.

[willow pawn]

What is the general consensus on the book Calculus Made Easy, by Silvanus P. Thompson?

Do people think this is a good book to learn calculus from?

[willow pawn]

Also what are good resources to learn physics, outside of textbooks?

[echo elm]

I can suggest you a channel but this channel is hs level

Not sure what level you want

But here
https://youtube.com/@flippingphysics?si=J_zcVdWBtuTHC9Ku
love this guy

[willow pawn]

HS and above is fine (always good to brush up on the basics), but college level might be more my speed (even if my education in the topic is fractured)

Thank you for the link regardless

[echo elm]

Can’t help you with college level ,but someone might

[willow pawn]

Sounds good

[normal crystal]

MIT has physics courses on OCW/MITX/OL

[cunning elk]

in all honesty i found flipping quite mediocre when i was taking AP phys

i got way more out of watching AK lectures

[echo elm]

Oh,I understood flipping very well ,since I like humor with studying😅 , I used to only watch AK regarding chemistry or so

[vital bane]

Peak:Zero fan detected

[rigid trail]

peakzero 🗣️

[frank sky]

who is AK and what is the guy's full name so i can look him up later after i write it down

i am new here if you cant tell

nvm googled it

ty for the mention anyway i appreciate it

[celest stump]

I really like the way Terrence leaves a lot of exercises for the reader to prove while giving hints and showing the proving methods beforehand. It really motivates one to do the exercises.

Could someone please recommend me such a book for an introduction to abstract algebra?

Note that it doesnt have to be beginner friendly; just self contained about the algebra stuff.
Its also better if it doesnt have solutions in it (even though Ill be using it for self teaching)

[celest stump]

thank you

[willow pawn]

Not for learning calculus
Bummer. Why not? I've heard there are updated versions of it.

[gray gazelle]

yeah, I am a freshman but I have done a lot of pure math in high school, including LA and RA as you mentioned. I'm not really interested in pursuing a career in math or specialising/research, for me it's just a means to develop abstract thinking and a fun pastime. I just want to keep solving problems, tbh

[willow pawn]

Oh. I think I misunderstood what you said about the book not being good for learning calculus.

[gray gazelle]

i don't think it's much more different than what i have done. i just followed standard textbooks for the courses at my and other unis

i do philosophy in my free time yeah, will see if i do math&phil or just math after fist year

[vital bane]

Do physics and math

🗣️ 🔥

you listen to Joji as well? Based

[gray gazelle]

problem is math&phil is not as rigorous as math by itself at my uni, the courses are separate and the philosophy department is my "home department" were i to study there

[gray gazelle]

i suck at physics 😭

i poured all my stat points into math

[gray gazelle]

yes 🫡

[vital bane]

every great physicist once sucked at it, they all had to learn step by step 🗿

[tiny gulch]

yeah!

[gray gazelle]

yeah i guess, i want to see my knowledge or experience help someone directly though, which is why i probably won't go into research

nor will i become a finance bro and sell my soul for money

in the UK we don't really have that distinction for a generic maths major, you pick and choose your "specialization" in your third year

as for why, I guess it's because I did a lot of it and I'd rather use my existing knowledge than have to acquire more in an area that I might not be good at or which will prove it can't sustainably interest me

[gray gazelle]

im checking in again today to see if anyone has any books that significantly changed the way they think

this is the book that is blowing my mind https://en.wikipedia.org/wiki/Computer_Power_and_Human_Reason

[fair fiber]

I wanted to do this actually

I just dont think its feasible now tho

Because there is so much math to learn

[gray gazelle]

ah I am already in uni

[fair fiber]

Bro is at oxford

[wicked fractal]

Wait till you realize a knowledge of physics could help you in math

[fair fiber]

If a knowledge will help me i bet many knowledges will help more

Poli sci majors on their way to triple my salary by going into finance

[wicked fractal]

Agreed. I'm on my way to resolve BSD by knowing political science

[fair fiber]

Delteto vs manifold for no 1 self reacter

[wicked fractal]

Oh

My expertise

Is this your first time doing analytic NT?

Have you looked at Apostol?

If it's too easy you can look at Montgomery or Davenport

[torn blade]

mutual servers would suggest otherwise

but yeah im also taking mostly pure courses at uni even though i might not (probably will not) go into academia

[fair fiber]

fr same

some dude asked me why i'm doing it

and i'm like no fucking clue

[torn blade]

well i know why im taking it

[fair fiber]

I mean chatgpt 8.0 will probably be better than whatever i can do so no need to worry about future just take courses i find interesting and then i can work in mcdonalds when i graduate

[torn blade]

its cause im good at pure and those good scores will reflect well on my cv. id do worse if i focus on applied

[fair fiber]

bro's adding a casual flex

i mean tbh if i cared about my gpa i'd just do social science courses and humanities and get easy As

[tacit torrent]

I honestly don't get the prejudice with the humanities. Doing good work in anything will require considerable labor, and if the humanities people have more free time to pursue greatness outside of the academic impositions made by their degrees then what's the problem?

[mortal ore]

youd be cooked harder in humanities classes than u think

i do philosophy with math and its hard for different reasons but still hard

the lack of ability to formalize many concepts bc of the need to keep them tied to what they mean to average people leaves so much room for misinterpretation

[fading mango]

What do you plan to do after uni?

I don't know a lot but I imagined that doing mostly Pure might be not very useful in the job world

[tacit torrent]

Who cares? Everybody will be unemployed anyways as the global economy is about to crash

[lean badge]

[indigo blade]

howdy
what is a good book that rigorously prove and treat matrix theorems and algorithms ?

[tiny crane]

I’m making a book rn

Not a math book

But a book

[clever hare]

Absolutely Wrong ❌ I absolutely second the channel you recommended, Professor Leonard is a great instructor. But Thomas Calculas (9th Edition) is a lot better than Stewart's and If one wants a bit more rigorous text then Calculus 1 and 2 by Peter D Lax would be even better. @willow pawn

[cunning elk]

thomas and stewart are both decidedly meh

[clever hare]

It's great whether you like it or not. He focuses on basics and that's all that matters. Don't down him, until you've some other guy who can teach better.

[cunning elk]

non rigorous computation spam

[clever hare]

Thomas is better, 9th edition is way better for students aiming at engineering or applied mathematics.

[cunning elk]

why that edition specifically 🤔 all these newer editions are essentially isomorphic

[clever hare]

Like how? How do you expect an absolute beginner to grasp the basics of calculus? Feel free to suggest if there are better instructors out there.

[cunning elk]

also im not at all convinced that any of them are good "applied" books when all they do is slap contrived flavortext onto their "applied" problems

bro must think paul's online math notes are the peak of pedagogy or smth

[clever hare]

Hmm till 9th edition, all the necessary proofs are included, after 9th edition onwards Thomas Calculus like other Calculus books were being used entirely for monetary 💰 benefits by publishers. Toning down the rigour of content and with more multicolour pictures.

[cunning elk]

^they're more "ape this computation so you appear to know what you're doing"

[clever hare]

I knew You would quote these books. That's why I suggested a better book than these in my answer above. Peter D Lax Calculus Vol 1 & 2. They are way better than books on that Caltech website.

[clever hare]

Which are good applied books in your opinion then??

Those books you listed would be hard to grasp for absolute beginners, especially if they're doing self study and no instructor.

But the problems in the book, especially star marked ones aren't that easy for a beginner.

😂

What was his reaction?

[gray gazelle]

well well well

[gray gazelle]

It's question is based on real life

buy ganita prakash

is it really necessary to do computational calculus

or if i just do analysis

i won't be losing anything

im thinking just start reading zorich

this normal calculus book is so ass

[clever hare]

Try to sync both together. Real analysis can be done later but don't do mere computations, include all the necessary proofs and proof based problems. This is the middle path.

[gray gazelle]

that can be interesting

i can read some text of analysis and while doing the computational problems along

[vital bane]

Real 🗣️ 🔥

[fair fiber]

Who said there was a problem? I just said if my goal was perfect grades id study them lol

[fair fiber]

Ive sat in some humanities classes and then looked at exams, id be fine lol, ez A like in highchool, now of course not for all humanity classes, but for atleast 100+? Yea i be fine

[fair fiber]

Philosophy is probably one of the harder ones but ive looked at geo etc and they easy, its just facts lol

[vital bane]

You said there was a problem

I remember you saying humanities are not worth studying or something like that

(jk)

[fair fiber]

i didn't say humanities is theoretical physics

[sage python]

This is less BS than you may think

[wicked fractal]

Yeah lmao

[wet sentinel]

what is spectral theory? what are its prerequisites and where to study it ?

[fair fiber]

Bro is getting ready to learn everything

[molten gulch]

Spectral theory starts with the theory of diaonalization of linear operators and the spectral theorem

So I'd suggest starting with the chapter on spectral theory in most linear algebra textbooks

[wet sentinel]

well i just heard it mentioned more than once so i got curious

[fair fiber]

Spectral theorem🔥 🔥 🔥 (cant remember what it says or the proof)

[wet sentinel]

i see, and then where to go from there?

[molten gulch]

I forgot it too 😭 I think it's something about if you have a hermitian matrix on V, then there's a orthonormal basis of V consisting of eigenvectors of A

[wet sentinel]

also i take it that spectral theory only assumes LA?

[molten gulch]

Uhhhhh the only places I know of are QM and FA

[fair fiber]

Bro study la first please

[wet sentinel]

i will pick that up from lang's algebra

[fair fiber]

Ull speed through la tbh with ur mathematical maturity

[fair fiber]

I have proven some cool facts about vector spaces in algebra but i still recommend doing a la course

[wet sentinel]

the thing is that i was intentionally avoiding LA for now

[molten gulch]

Just sitting through a finite dim LA book like hoffman or friedberg sems like a good use of your time tbh

[wet sentinel]

also i am not planning to study spectral theory (at least not soon), but i got curious to what it is about and where i could see stuff about it if i want to study

its also mainly because someone asked me about it too

[fair fiber]

Noice

Do topology with me🔥

Me and you we are going to wreck munkres

[wet sentinel]

yea i will sit through a LA book for sure, but i was studying many things so i couldnt add LA to them

[wet sentinel]

yea i am waiting for that

[wet sentinel]

i will probably resume LA soon

[fair fiber]

Tbh u can delay it u dont really need it

Immediately at least

[wet sentinel]

so there is nothing as a book on spectral theory? is it only studied in things like a FA book?

[wet sentinel]

yea but well i would need it to do things going forward, thats why i should go through it soon

[molten gulch]

Oh yeah read D&S with no FA experience, that's gonna go SUPER great (no please don't do this)

Wikipedia makes me think the theory of C* algebras might be related too?

I could be wrong

[wet sentinel]

ok so i can conclude that to study spectral theory one should be familiar with FA and in fact one encounters it at the end of FA books?

[molten gulch]

Open up an FA textbook and take a look is all I can say, but the finite dim spectral stuff is covered at-least somewhat in LA books

[wet sentinel]

do you know if FIS cover them?

[molten gulch]

Chapters 5 and 6, though exactly what you're looking for is a bit scattered around

Mainly sections 5.1, 5.2, and basically all of chapter 6

[wet sentinel]

i see, tysm for your help

[wicked fractal]

is this lmfdb

oh wait nvm

that's wiki

[molten gulch]

God how modular form brainrotted are you 😭

[wicked fractal]

the type of brainrot im addicted to nowadays

[fluid violet]

Damn someone put the effort into writing the breve over the i

[sage python]

So, depends on what you're looking for within spectral theory

Finite-dim spectral theorem only needs a little bit of analysis and mostly is linear algebra

And the analysis needed isn't even functional analysis, either you use the fundamental theorem of algebra or (imo better) some optimization

[wet sentinel]

the thing is that i dont even know what spectral theory is so i wouldnt know the answer for this too. But someone asked me about it and i have heard about it a bunch of times so i got interested

[wet sentinel]

ohhh i see nice

[sage python]

So, spectral theory kind of starts from studying eigenvalues and eigenvectors of matrices

[wet sentinel]

ohh this explains why you can see it in linear algebra books

[fair fiber]

bro isn't lang's algebra grad level

how you doing grad level algebra without lin alg 😭

[wet sentinel]

so thats the main goal of spectral theory?

[wet sentinel]

i mean i didnt study a first course on algebra before lang either

[fair fiber]

bro is cracked...

[wet sentinel]

lang covers from the ground up, although the pacing is fast and its hard to follow at the beginning

[wet sentinel]

nah

i tried it before and stopped after he started with isomorphism theorems because i couldnt follow him properly

then i switched to his undergrad book, but recently i came back to it

[fair fiber]

i was considering doing grad algebra next year but got too scared

but you're destroying it already

nice

[wet sentinel]

you meant to say "you are being destroyed by it" right?

its neither destroying nor being destroyed

sometimes i understand quickly and other times i take quite a bit of time to get the point

[daring wolf]

pro

[fair fiber]

grad algebra at posttech

[daring wolf]

taking grad classes

🔥

[fair fiber]

you can tutor me once i'm in korea

[daring wolf]

lmao postech is too far from seoul

sadly

256 killometers

[fair fiber]

bro goes to a uni in seoul? Definitely lying about not being at a top uni

[sage python]

It's the starting point. Things go much deeper though, and if you don't have linear algebra background I probably won't be able to explain

[fair fiber]

i heard it is very applicable in physics

[daring wolf]

i mean my uni is definitely not in top ones like postech lol
but id say its pretty decent

[molten gulch]

Actually we were wondering of where spectral theory goes, we've completed one course in LA at uni and self studied the first 6 chapters of FIS (mostly) so Dami could you tell us how deep the rabbit hole goes or do we need module theory or stuff

[fair fiber]

what are the rankings in korea for math ?

1. Kaist then sky then postech ig ? idk

[sage python]

The quick quick version is, okay if you have the space R^n (R is the real numbers), and you give me n vectors v_1,...,v_n

Then you can create the matrix where v_i is the ith column. If that matrix is invertible, then we say the v_i form a basis

What does being a basis mean? Well let's set n=3, then you can write any vector (x,y,z) = x(1,0,0) + y(0,1,0) + z(0,0,1)

So if you give me v_1, v_2, v_3 and can invert the matrix with those three vectors as columns, then you are able to combine them and get (1,0,0), (0,1,0), and (0,0,1). And then combining those further get you any vector at all

So in a sense, you can imagine R^3 but with coordinates given in terms of the v_i instead of the usual (1,0,0) etc vectors

Now if you give me a matrix A, you say a non-zero vector v is an eigenvector if Av = tv for some real number t

[wet sentinel]

to make things easier for you, i know what a vector space and basis are. Also a bunch of things about linear maps like iso theorems and matrix representations of them

[sage python]

Okay nice

So if T:V->V is a linear map and you can find a basis v_1,...,v_n of V which are all eigenvectors of T, then the matrix of T in that basis will be a diagonal matrix

[wet sentinel]

ohhh nice, so thats diagonalization?

[molten gulch]

Yep

[wet sentinel]

i see

[molten gulch]

If a matrix A is diagonalizable we can write it as A = PDP^1 where D is a diagonal matrix and P is a matrix of eigenvectors of A

[wet sentinel]

earlier you said that spectral theorem starts by studying eigenvalues and eigenvectors, so it starts more or less from here?

[molten gulch]

And by properties of diagonal matrices, A^n quite nicely becomes PD^nP^-1

where D^n would end up just being elementwise exponentiation on each element of D

so no nasty matrix multiplication spam

[sage python]

Now, for a general linear operator T on a vector space (over some field k), you would just compute the characteristic polynomial, find its roots, solve, etc. Maybe it'll have an eigenbasis, maybe not

[wet sentinel]

ohhhh nice

[sage python]

But if k = R and your vector space V is an "inner product space" ie you have some symmetric bilinear form B(v,w) for which B(v,v) ≥ 0 (equality iff v=0)

Then there's a special class of operators called "symmetric" operators, whereby B(Tv,w) = B(v,Tw)

Using a tiny bit of analysis you can show that if T is symmetric, then there's a basis of T-eigenvectors which are orthonornal, so B(v_i,v_j) = 1 if i=j and 0 otherwise

In matrix language, a symmetric matrix is "orthogonally diagonalizable"

Now general spectral theory tries to do this for operators on certain infinite-dimensional vector spaces

[wet sentinel]

and things maybe get trickier because there are no longer matrix representations?

[sage python]

Yeah, and while first isomorphism is still there, you can't do basis counting

[wet sentinel]

i see

so here you start using tools from functional analysis?

everything is start to connect

tysm for your great explanation

have a great day/night

tysm TCC too

[molten gulch]

:3

Ryan would probably know a bit more about this stuff, I'm sadly our resident TCS nerd who incidentally knows some linear algebra

[wet sentinel]

well you were more than helpful!

oh one more thing, @sage python do you have any recommendations for spectral theory? or is finite dim covered in linear algebra textbooks and the infinite dim covered in functional analysis?

[sage python]

Eg on a finite-dim space, a linear endomorphism is injective iff it's surjective

Because rank-nullity

But once you hit infinite dimensions, you can't say infinity - infinity = 0, so you can find operators which are injective but not surjective and vice versa

Functional analysis is a general study of infinite-dimensional vector spaces. You want to restrict to R and C as fields, and you want to equip those spaces with a topology. But then yeah you can recover some of the finite-dimensional theory, including spectral theory

A big subject is studying the spectral theory of operators on function spaces. For instance, you can have an operator which takes a smooth function and spits out its derivative, or the sum of the second partial derivatives, etc. Spectral theory for those guys is basically an analysis of certain differential equations

[wet sentinel]

it seems like there was a problem in the internet for either you or me since a bunch of messages suddenly appeared at the same time

[torn blade]

i don’t knowwww

is it normal to kind of hate all the careers you can go into with a maths degree

i can see myself doing tech or engineering but im nowhere near competitive for those. academia is a whole new can of worms

[sage python]

My internet was fucked for a hot minute that took so long to send

[hidden fractal]

After I finish reading Topics in Algebra by Herstein, which is better to read between Dummit and Foote and Aluffi?

[wet sentinel]

ohh i see np, tysm for your time

[mellow wren]

I really like dummit and Foote because it covers so much more but it's absolutely gigantic

Like realistically you don't really need anything after the chapter on fields

So I think it's manageable

Lots of problems tho which is good!

[hidden fractal]

Also, how does Stein and Shakarchi's complex analysis book compare to Ahlfors?

[mellow wren]

My understanding is that stein is less dry than ahlfors

Physicists use stein very commonly

[mellow rune]

hi i am new here

i am actually a physics undergrad who is trying to study general relativity as of now i will say

but i love mathematics

the reason for being here haha

anyways can i get some recommendations on where to start differential geometry from maybe even some advanced tensor calculus stuff i am kind of familiar with the basics and all

[cursive rivet]

I'm biased towards learning it from the ground up as a differential geometer, but for physics students who don't need to know it rigorously, Frankel's "The Geometry of Physics" is quite good

[mellow wren]

Tbh I remember starting to learn diff geo and GR from Carrol's book
However his treatment of the math is questionable at best and I referred a lot to Loring Tu's book for a more detailed treatment

[ripe lance]

Any books useful for mechanics/classical physics?

Also if possible some resources regarding a very specific topic of questions regarding calculating Center of Mass of objects using integration

[ripe lance]

This one is a bit of stretch though so im gonna look it up myself

[molten gulch]

Taylor

[west comet]

Algebra & Trig by axler

[icy temple]

Thanks

[gray gazelle]

darn i thought every pre calculus books are the same

axler's makes me think twice

worked out solutions at the end of each exercise??!??!

• No bs questions but straight useful ones?!?!

bro

his books are so good tf im just surprised

[spare osprey]

Best books for differential equations by self study

[spare osprey]

Yeah
I have LA and ODE &PDE

Thank you 👍

Where can I find it

Okay 👍

[west ice]

integration in the sense like using the formula, or by intuive steps?

[ripe lance]

Intuition

You know, calculating center of mass of non standard objects

Its has come up in a few of my tests

[west ice]

yes

[west ice]

Intuition is cool but its not test efficient

and in my case, it works mostly for solids

I mean I tried intuition first for normal symmetrical objects

but then i never got thr exact answer

i always got an approximation

[ripe lance]

Well formulaic is fine too

I think my definition of intuition is vague

[west ice]

oh

[ripe lance]

Im just looking for problems like that

For practice

[west ice]

i do have one

ill send wait a sec

this one

the good thing is that if you go by intuition method, the approximation is extermly close

so yeah

[ripe lance]

Seems interesting

Ill try ot rn

@west ice what is the answer?

[west ice]

the answer is 4

[ripe lance]

Hmm

I must have got something wrong

[west ice]

what did you get as center of mass

[ripe lance]

(Sqrt(18),0)

Yep something went wrong

Ill reread and try again

[west ice]

naaaah\

you can dm me for the soln

[orchid otter]

What abstract algebra book would you recommend? I’m reading linear algebra done right now to get a better mathematical maturity.

[molten gulch]

Artin is good

[fair fiber]

is that the guy who made artinian rings

?

[orchid otter]

Is it fairly easy for a first course? Meaning easier than others

[fair fiber]

i think it's reasonable

it's not designed for someone whos seen material before

[orchid otter]

Cool, I’ll check it out

[muted acorn]

masters , and PDE

[neon shoal]

any book recommendations for theory related to precalculus?

i wanna know more about the history and how it works rather than just what to do if anyone understand what i mean

[foggy quest]

"Introduction to the Theory of Distributions" by Friedlander and Joshi is great for learning distribution theory for applications to PDE

It's all you need unless you are really advanced

[slow roost]

for history there are lots of good general history of mathematics books. They tend to cover some things that are shown in a precalculus class, along with many things that are not.

Most precalculus books don't just state results and show you how to use them, but offer derivations and explanations as well. For example, they'll show how to obtain the quadratic formula by completing the square (which, incidentally, is pretty much how it was first done, even before symbolic algebra was invented). So if you really pay attention and study the proofs, you'll understand how and why it works

[small ether]

can somebody recommend me a precalculus book please?

[gray gazelle]

I’m sure there will be more recommendations

The one I used and found absolutely useful

Was pre calculus by James Stewart

Had be soooo prepared for calculus

[small ether]

ok

thank you

[gray gazelle]

If u plan on reading calculus after it you can also always come back to it if

Stuck on some basic thing

For reference

Also there is pre calculus by Axler I recently found and that one is goated as well

Really good examples worked out and every exercise ends with detailed solutions to

Odd number problems

which could have been sooooo good if I had used it

[small ether]

which one do you think is better?

[gray gazelle]

Tbh I think Axler one can def be much better and it’s concise the other one is kinda of you all over the place which can be a good thing but hm

may be use Axler as main text

And use other one as a reference

It has some ad hoc problems which are fun to do

Also good diagrams and all that if u like

[small ether]

ok

[gray gazelle]

What u decided

[small ether]

i searched and there is no place in my country where i could buy pre calculus by Axler

[gray gazelle]

yeah that could be a problem

Perhaps u can look for digital version

If u like

[small ether]

i think this is a good idea

thank you

[radiant marlin]

his father is

i think

[fair fiber]

legend

or ig not legend because i don't like artinian rings

noetherian > > >

did he also do wedderburn artin

=

?

[molten gulch]

Emil is michael's father

[fair fiber]

damn michael artin got the pressure on him to do algebra

[gray gazelle]

i found this book called 'a basic training in mathematics' and it is far from basic hah

[dire stone]

can you jump into bredon geometry & topology with a minimal background of topology or should i read a more introductory text first

i'm familiar with the topology you pick up in a first real analysis course and that's mostly it

[cursive rivet]

should be fine, bredon is "intended" for beginners with that amount of background, but is quite terse

[dire stone]

i'm ok with terse

does it have sufficient exercises

[cursive rivet]

it does

having another book around to explain things you don't understand in a different way isn't a bad idea in general btw, for the first part of Bredon I'd recommend either Lee's topological manifolds book or Munkres

unrelated side note, Bredon was once complained to me by a friend as 'globally great but locally unreadable', which I think is quite hilarious given its content

[full cairn]

Interesting, I've heard the exact opposite about Tu, so maybe if you combine them you get something locally and globally great. Or maybe you get something that sucks both locally and globally 🤔

[graceful moon]

Boy do Hopkins and Levitzki have a theorem for you

[molten gulch]

LOL

[fair fiber]

Didnt know they had a theorem named after john Hopkins university

[shy pine]

Are there any books that just have like a ton of integrals to practice

Like regular ones

[molten gulch]

thomas or stewart calculus have hundreds each

[shy pine]

Whats the book name sry

[molten gulch]

thomas calculus

stewart calculus

two books

any edition is fine

[shy pine]

Oh okay

Tyy 🩵

[tulip hearth]

Any 1 book recommendation for these topics—

[iron beacon]

anyone who has a book recommendation that focuses more on solid mensuration? specifically for architecture students, tyia.

[remote sparrow]

https://www.rxddit.com/r/math/comments/1oegir3/how_many_math_books_can_or_should_a_person/

[tulip hearth]

The only math book I've completed is "A Mathematician's Lament by Paul Lockhart"

[gray gazelle]

are you self studying or taking courses?

i havent yet completed any front to back - im taking courses but also self studying

[peak bluff]

oops

[flat rover]

A book for abstract alegbra pls

I am very confused on which one to choose

I willl be self studying but I have a proof bg

[mortal ore]

dummit and foote

if thats too much gallian is a good first read

then dummit and foote after

[flat rover]

I have decided gallian then

[flat rover]

Which is the best for undergrads actually(though I am in 9th)

[mortal ore]

wdym

[flat rover]

Leave it leave it

[ripe lance]

Which ones

[remote sparrow]

#book-recommendations message

[flat rover]

Thanks

For analysis why don't ppl prefer tarenace two though his book is best and has a lot of intuition

[flat rover]

I am finalizing with gallian as I am beginner with second book foote

[gray gazelle]

Lmao????

This was a thing?

This whole time

Broooo

I never checked

[cunning elk]

not too sure how up to date it is

but it exists

[marble bane]

Hello. I already have a simplistic i.e, mechanical understanding of calculus.
However, I wish to truly understand the inner steps of calculus.
I have decided on two of the following three:

Wade, An introduction to Analysis
Apostol Volume 1 and Volume 2
Terrence Tao Analysis 1 and Analysis 2

I have been told to pick Apostol 1 and Wade, as a start. I cannot study both Tao and Apostol. Please help me understand why either is better for someone in my situation.

I am looking to get to the heart of calculus, without any handwaving. This is because, I have decided to dedicate atleast two years to calculus.

[mortal ore]

I like tao

Haven't read apostol tho so possible even better

[shut dove]

hiii i'd love to know recommendations about books of analysis
like the real elements of analysis, by bartle
(sequences and basic topology in |Rn )
and if possible in portuguese

[marble bane]

Thank you

Thank you. What are your opinions on the followup to Wade?

Thank you for summarising the book's results and prerequisites, and adding your experience with it.

Will it give me clarity into the understanding of multivariable calculus'? I do not desire to rely on a mechanical understanding of calculus alone.

(I wrote " I have an analytical understanding" but I only have a mechanical understanding of calculus. I am sorry for the imprecision, I have edited it.)

Thank you

I am sorry for imposing on you, but I have struggled with this for a considerable number of years now. I never realised that I lacked the true understanding of calculus, when I was feeling frustrated for my academic performance all along.

Will Wade suffice for clarity in single variable calculus, as well?

Spivak is unfortunately not an option, for cost reasons

I buy paperbacks, but only an imported hardback is available for Spivak, on amazon in my nation

Thank you for the confirmation

I feel like I will be missing out by not studying Apostol 1... although calculus beggars can't be choosers

It feels like christmas for some reason, knowing that Wade will cover all of my preliminary flaws. 😆

[sage python]

Eh it's nothing special really

[shadow vector]

I'm also looking for an intro to real analysis but like... for actual idiots please. I tried some of the common big names and just struggled (always as soon as we get to limits and continuity). I have all the prereqs (physics undergrad) and done some proof based lin alg, but when it comes to real analysis I'm just really slow. So yeah, any recs for cases like me?

[lofty mountain]

I mean, Cumming's Real Analysis is a classic.

It's a solid rec.

[shadow vector]

thank you! Haven't checked those so maybe they will go a bit smoother. Ill try 🥹

[lofty mountain]

Didn't getcha?

wHAT? I don't get ya.

Why?

Oh no, I get the joke.

But Cumming saved my life.

(no joke)

[fallen moss]

Any recommendations for algebraic geometry??

I'm finding Hartshorne's book to be a little harsh for me 🥲

I guess I should say my background!

I have read most of Dummit and Foote (not chapters 15 and 16, but everything else), but I haven't had much background in commutative algebra

However, I plan to read commutative algebra on the side! (Any recommendations for that?)

[lofty mountain]

Wait, do you want recs for algebraic geometry or commutative algebra or both?

[fallen moss]

Both! I am mostly keen for algebraic geometry

[lofty mountain]

Sure. Thinking...........................

[fallen moss]

Do you have any course notes, perhaps from your uni??

My uni doesn't offer a course in AG

[lofty mountain]

I'll see what I can do, because privacy..........

I'll try.

[fallen moss]

Thank you so much!

[lofty mountain]

Introduction to Commutative Algebra. Atiyah and Macdonald.

(if you're just starting out)

[fallen moss]

Would that book be sufficient do you think?? It seems quite small!

[lofty mountain]

It is small. @gray gazelle has better recs.

You should check those out too.

[daring wolf]

for commutative algebra, atiyah is a good choice

[fallen moss]

Gathmann's notes seem nice!! After reading it, would it be enough to start a research project in AG?

[daring wolf]

also there's a book by altman, and iirc its free + contains solutions

[fallen moss]

I'm trying to get a project in etale cohomology

[daring wolf]

for algebraic geometry, vakil's one is very good but I abandoned it because it is way too long compared to hartshorne

[lofty mountain]

I'd also suggest Eisenbud - commutative algebra.

[fallen moss]

I've done a little homological algebra from weibel!

[lofty mountain]

It's simpler, though. (Hartshorne gave me hallucinations)

[fallen moss]

I guess Gathmann's notes are not long at all! Vakil's notes seem a lot longer

My main objective is to be exposed to as many ideas as I can

[fair fiber]

here we have to do a bahcelor thesis

[lofty mountain]

Fair enough.

[fair fiber]

[fallen moss]

At my school, we also need to do a thesis in undergrad 🥲

[fair fiber]

good

[lofty mountain]

Don't mind me asking, which continent?

Ah well.

[fallen moss]

Australia

[lofty mountain]

What?!

[fallen moss]

Yeahhhh!

[lofty mountain]

Dammit. I had no idea

[fair fiber]

melbourne uni student

[fallen moss]

My school doesn't even cover module theory for its collection of algebra courses....

[fair fiber]

doing module theory rn fr

[fallen moss]

I guess, self study is the best choice when you have a lack of courses!! 😂

[marble bane]

Hello, I have another question.

Is there a conceptual calculus/analysis video course that I can watch while reading Wade's an introduction to analysis?

A youtube playlist or part of a free online-course.

I was reminded that the average friendly math graduate of the server learns analysis with real courses in colleges, which I can't afford... if there is an inferior video version of it that covers single variable and multivariable calculus as an analysis course, please tell me.

Even 10% of the uni analysis course will work. I will use it alongside Wade.

(Is there a better channel to ask for video courses?)

[gray gazelle]

hey, I am sorry about that. I think knowledge should be available to everyone. That being said, here’s what I found useful:

https://youtu.be/byNaO_zn2fI?si=9jjnRQqJcaoL6WyN
is a video which mentions where you might learn different areas of undergrad math, both including lecture series and books. Everything here can be found online if you know where to look. He mentions Francis Su’s real analysis course video lectures which seems to be sufficient. I’m not sure what the book you’re talking about covers, but I would imagine the material is standard. As for multivariable analysis, you may want to ask here for a book rec and then try to obtain that. I don’t think I’ve seen videos on that but I would imagine there have to be fragments on YouTube, etc.

https://youtube.com/playlist?list=PL04BA7A9EB907EDAF&si=LRgu_th_H-CuQxpy

Also, so you have options - there’s also MIT OCW courses in real analysis

https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/

[marble bane]

Thank you, dear Aude, for pointing me in the right direction. It is alright, I can live with university course knowledge being exclusively buy-only... after all, it represents the hard work of the teachers. However, I am also very elated with what I have just gotten, for they are a great help.

[gray gazelle]

my pleasure, and contrary to what my pfp suggests I am a man. No need to be formal either, feel free to message me if you want further guidance for analysis resources or self study materials. Have fun studying!

[deep dirge]

do we not have a reading group channel anymore? wanted to setup a reading group for measure theory by terence tao in a month or two

[fair fiber]

Im starting MT reading group in jan

[deep dirge]

that would work for me, is it the one by terence tao or another reference material?

[fair fiber]

I hvent decided yet whichever one my course uses probably

[deep dirge]

i see, the terence tao one is very very good, in any case i would gladly join

you have a group yet i can join?

so we can keep in contact

[fair fiber]

No but ill add you

[indigo blade]

is there any good book on matrix algebra?

[marble bane]

How to access reading groups?

[fair fiber]

If you want to read up on groups i recommend any algebra text

[marble bane]

I wish I had the time to sync up, but I am focussing on real analysis right now

I have major fomo wrt your reading group

[graceful fiber]

I got a great book for proof

Proof by jay cummins

[vital bane]

Clearly you are Ram 🗿

[fair fiber]

Bro cannot hold himself back when he sees re zero

[vital bane]

https://tenor.com/view/rezero-wednesday-smol-elilia-re-zero-gif-frederica-re-zero-rezero-frederica-gif-20586070

[fair fiber]

Bro is more excited for rezero than physics or math

Make this man study math

[vital bane]

I'm more excited for physics and math than Re:Zero tbh

dw I'm procrastinating reading the Re:Zero light novel as well

not just math and physics

[fair fiber]

https://tenor.com/view/side-eye-dog-suspicious-look-suspicious-doubt-dog-doubt-gif-23680990

[pallid steeple]

heck yeah

[deep dirge]

[pallid steeple]

this is gonna be so hype

[deep dirge]

I really want to follow Terence Tao's book so have a look if thats alright for u

[pallid steeple]

I plan on reading it as well, I'm partway through his first real analysis one at the moment

will go through baby rudin and probably will join the reading group while going through Folland

[deep dirge]

I havent read an Epsilon of room yet

[pallid steeple]

(not a student atm)

[deep dirge]

Im guessing that's the one?

Im not a student either tbh

Working full time

[pallid steeple]

It's just titled Analysis (and is the first volume) haha

[pallid steeple]

I haven't read it either

[deep dirge]

I see

We can do it after MT, its supposed to be a prequel

[pallid steeple]

sounds good :3

He is a pretty awesome dude

Did you want to read through Baby Rudin at any point?

[deep dirge]

Not right now, got a couple books on my list

Probability and measure by billingsey too

[deep dirge]

U working or?

[fair fiber]

U done top?

[pallid steeple]

Yeah but just food service, I'm taking a leave of absence for health issues and returning next year

[pallid steeple]

me too!

[deep dirge]

Man we gonna have a great time

[pallid steeple]

wym by top?

[fair fiber]

Topology

[pallid steeple]

I was going to take a class for it this semester but had to take the leave of absence haha

I got through a bit of Munkres

[fair fiber]

Im going through munkres with a friend in jan

Lmk if u want to join

[pallid steeple]

That would be awesome haha

it will make taking the class much easier

were you gonna go through Hatcher?

[fair fiber]

For alg top ?

Nah

If i do alg top defo not using hatcher

[pallid steeple]

I see 🫡

[deep dirge]

@fair fiber will you be doing Terence tao book as well in the end? Cos I really like his writing style

Or will you follow your course textbook

[fair fiber]

I will read 1 chapters in both and then see

[deep dirge]

Ic

[fair fiber]

But prolly this since its what the course follows, sorry

[deep dirge]

MT of Terence tao is two chapters total xd

But they are quite long

[fair fiber]

Oh haha

[fair fiber]

Maybe try kuhn as well, just 5-10 pages to see the vibe

[fair fiber]

Im doing advanced measure theory as well after

[deep dirge]

Im prob gonna do probability and measure

And after that an Epsilon of room

[fair fiber]

Ohhh you want mt for mt theoretic probability

Yeah i want to take the course as well unfortunately not offered in places i want to do exchange in

[deep dirge]

Yeah I do ML so

The advantage of not being a student is that i can do whatever I want

[pallid steeple]

That's so cool

Are you planning on returning to school?

[fair fiber]

Cool for theoretical ml you need mt probability, what else ?

[deep dirge]

Doing ML engineering, prob going back for a phd in two years

[deep dirge]

A lot of statistics and linear algebra

[fair fiber]

My uni offers mt probability in the fall if u want to get creditation

[deep dirge]

That gets you covered for the most part

Eh I dont really need credits, do they record lectures tho?

[fair fiber]

Some courses do, im not sure, but u dont have to be in person, u can just do problem sheets at home and exam

[deep dirge]

Maybe i can check as long as the cost is not prohibitive

[fair fiber]

Its free to apply and do the course for eu, you just have to fly in for the exam

[deep dirge]

Oh really

[brazen grove]

recommendations for proof based DE book

[deep dirge]

Thats a nice initiative

[fair fiber]

Yes since all education in sweden is free for eu

[deep dirge]

We'll see how fast my learning is and when I finish MT

[remote sparrow]

altman and kleiman

[fair fiber]

Didnt know ceo of open ai wrote algebra book

[remote sparrow]

not sam altman

no immediate relation with allen altman

[fair fiber]

Ik im joking

[fair fiber]

on a math server bro is asking for engineering books 😠

bro will go from sweetandsourpotato to baked potato

[storm abyss]

I'm in my second year of high school. I wanted books to study until the end of third grade. Any recommendations

[near jewel]

That depends on you high school math curriculum. Usually the book you use in your school is enough to use.

[fair fiber]

Rudin

[storm abyss]

I want to be an eletrical enginner

Some recommendation?

[fair fiber]

I recommend calculus

damn 2nd year of hs, ur gon be competing with chatgpt 8.0 for jobs😭

good luck bro

[storm abyss]

😭 🙏

[storm abyss]

It`s the full name?

[fair fiber]

I recommend khan academy

Calculus is subject name

[storm abyss]

Bro

I completed

[fair fiber]

You completed khan academy calc 1, calc 2?

[storm abyss]

IDK

My school makes us do it every day

[fair fiber]

Lucky mf

[fair fiber]

Start calc 1, calc 2

In khan academy

Ik u havent done it because u would be sure if u did

[storm abyss]

Thanks 😭 🙏

[fair fiber]

Khan academy will cover up to first 2 sems of uni math once ur done with khan ur looking into 2nd year uni math textbooks

[storm abyss]

Wow

I will do

[gray gazelle]

there is an anki deck of all khan academy i can tgy to find it

https://ankiweb.net/shared/info/1596689213 this is what ive been using only doing three every day cause i dont want to be bombarded with them

would have been nice if the person that made it shared how they did it

[normal crystal]

https://tenor.com/view/why-persian-room-cat-guardian-but-why-trendizisst-anyaboz-gif-2156104475561014590

[gray gazelle]

idk arent people paying for this but named something else

[normal crystal]

no, I mean
why would you do Anki of KA

[gray gazelle]

oh cause im insane i guess idk

for some reason always wanted to 100% khan academy math

[fair fiber]

entirety of is is a bit extreme but it makes sense for specific stuff no ?

[normal crystal]

ok, why

[gray gazelle]

you can set it to only calculus

[fair fiber]

i mean to help remember concepts in say calc or trig identities

[normal crystal]

that would be a small fraction of all of KA math
the way you're suggesting it

[gray gazelle]

oh that deck is high school and college only - its 1500 cards each to a module

its not every individual problem

its whatever maybe we can keep in touch i expect to have finished it all in less than 2 years

[fair fiber]

1500 is extrême

[gray gazelle]

ya ...

i take transit so ive got time for it ...

[normal crystal]

and how many modules

[gray gazelle]

its hard to explain i dont know what khan calls them

[fair fiber]

finitely generated modules

[gray gazelle]

but each card is a link to a khan quiz / test

[fair fiber]

aka noetherian modules❤️

[normal crystal]

ok, so why not you know
just do KA
since most of that content has a linear order
and Anki does not

[gray gazelle]

cause that is not effective. a batter who practices to fast ball each time will miss a curve ball in the game

[fair fiber]

ye but 1500 is too much

then ur learning inefficiently

[mortal ore]

what is a "card" in this case

like flash cards?

[normal crystal]

this is a terrible analogy

[gray gazelle]

just look at the link it explains it lol

[fair fiber]

yugi oh card

[mortal ore]

right the ever so famous khan academy yugioh cards

[gray gazelle]

it is not a terrible analogy its a thing cognitive scientists have studied

[mortal ore]

i cant imagine how there would be 1500 flash cards for a calculus class

thats so unnecessary

[normal crystal]

it's terrible because it does not actually apply to what I said

[mortal ore]

especially since calculus is made to rot in the back of the minds of anyone who learns it after so many years

[normal crystal]

anyway, do you

[gray gazelle]

alright, like i said ill let u know how its going im not going anywhere

[fair fiber]

memorize + making connections < brute force memorizing

[mortal ore]

no point in learning math if improving your connection-making skills isnt the number one goal

[gray gazelle]

did you even look at the deck im confused lol

[normal crystal]

Chipper...
"can I get an epub of the Anki deck?"

[gray gazelle]

ok whatevs

[normal crystal]

Chipper is S&SPotato
it was about him

[mortal ore]

i mean there would be some utility in knowing all possible sums of natural numbers up to arrangement of summands

[fair fiber]

i mean people can learn math for other reasons like applications in smth else idt there is need to gatekeep

[mortal ore]

yeah but even then you would want connection making to be the thing youre good at

bc then what do you do when you come across an unfamiliar problem

[normal crystal]

surprisingly, since that's a phone friendly thing

[mortal ore]

its unrealistic to expect a set of memorized facts to back you up very well

[gray gazelle]

havent we memorized the alphabet to the point we dont think about it

[mortal ore]

not because you just memorized the letters

[normal crystal]

it's not
but for your major it could maybe help with some exams
it's meant more for review than first learning

[mortal ore]

its because you put them together and apply them constantly

[gray gazelle]

i literally did tho...

[mortal ore]

it also helps that the purpose of the alphabet is very simple

[gray gazelle]

generally second language learners memorize the alphabets. not just me right?

[mortal ore]

i dont care for biology but pretty sure thats unfair

[mortal ore]

i mean yes but thats far from all they do

[gray gazelle]

well ok then

[mortal ore]

honestly memorization comes easily as a secondary effect of applying knowledge and building connections

ive had this experience recently with topology

i was worried about being able to remember the crazy amount of definitions in pointset topology, but just by doing so many problems i naturally started to remember them bc my mind got more adjusted to it

[gray gazelle]

Extremally disconnected, totally disconnected, basically disconnected, zero dimensional, Totally separated…

hmm im still curious about that anki deck. id like to ask an actual cognitive scientist, im not sure why it got such a rise other than it being such a large number of cards

[mortal ore]

looked at a prelim question at my uni today that started with a "semilocally simply connected topological space" and felt a part of me die

[normal crystal]

this reminds me of another server when this guy was cutting up the Openstax textbooks and making Anki cards for all the books before learning anything

[mortal ore]

turns out i couldnt do it tho bc i havent learned about the fundamental group yet

[fair fiber]

I think people get positive results from anki so they try and exploit and abuse it

[gray gazelle]

did they run out of steam or are they still going

[slow roost]

yeah that's an unwieldy looking but actually very common set of hypotheses to ensure covering space theory stuff works out well

which fundamental groups are related to

[mortal ore]

i assumed it only seemed unwieldy as i have not done covering spaces yet

[normal crystal]

tbf, idk how their math progress ended but it seems like they are still doing the larger goal it contributed to, so I guess they're alright

[molten gulch]

What the fuck???

[fair fiber]

A guy here who had a ms in biology took the easiest math class in math program and told me it was the hardest thing he ever did

Oh wrong reply

[normal crystal]

it was bananas
he also wanted to use the Anki cards to memorize before doing any problems
good times

[mortal ore]

i dont have the courage to call any discipline easy bc i worry that the subject would make me feel just as dumb as math does and id look like an idiot

except for engineering, fuck engineering

[fair fiber]

Nuclear engineers got my respect ngl id be cooked if i tried nuclear eng

[mortal ore]

i got rejected from taking a quantum class bc i didnt have enough physics background so now im salty against nuclear

im kidding

[gray gazelle]

boo

[mortal ore]

at least architects are doing smth creative

[fair fiber]

Engineers try not to hate on architects and industrial engineers
Challenge impossible

[mortal ore]

idc how hard or deep the mathematics part of a discipline goes

i just hate when engineers act like their math is tough shit and its at worst diffeqs or discrete

like be deadass

[fair fiber]

Fr they be talking about how hard their math is but hv never seen a proof

[gray gazelle]

i got a b+ in calc 2 that is the farthest i got

[mortal ore]

the most advanced course mechEs have to do at my uni is linear algebra w/ applications to diffeqs

so its just combining linalg and diffeqs to make both of them easier

no theory

genuinely cant make ts up

[gray gazelle]

i took a discrete math course too that was interesting

[fair fiber]

Difficulty in eng comes from balancing all the stuff like labs, physics, math or even chem etc. the math in of itself is not hard in eng

[mortal ore]

thermo could be tough but i mean isnt it pretty much just multivar applied

fluids too maybe

[gray gazelle]

physics is wild . id like to undrstand how semiconductors work

[fair fiber]

Bro was destined to be math and cs

Tbh if i was murican id do applied math + cs

[mortal ore]

why not pure

[fair fiber]

Dont want to do phd

[mortal ore]

real

[fair fiber]

https://tenor.com/view/side-eye-dog-suspicious-look-suspicious-doubt-dog-doubt-gif-23680990

Nah u mathematician

Dont want the stress, inconvenience, all for low wage and immense opportunity cost

[slow roost]

valid

[mortal ore]

i mean i do pure math but i get why people wouldnt

[fair fiber]

I do pure math too fr

[mortal ore]

stable job, thats a new one

[fair fiber]

Idk if long term it stable but it is true a lot of engineers amd cs students are applying to phds since they cant find private sector jobs

[mortal ore]

i mean i suppose once you get a prof gig

but the postdoc experience can be pretty terrible

[fair fiber]

I mean in some unis if you develop relationship with profs and talk to them u can get stable path to phd

💔

Good luck bro

But if u get phd wont it he funded?

Ig u might not make enough to pay off student loans

[foggy quest]

My department pays PhD students 31k yearly. Yeah the opportunity cost is huge, but the stipend is decent considering the flexibility and freedom of taking classes and doing independent research.

[fair fiber]

Its enough to survive for sure

[foggy quest]

yeah but current applicants are cooked. Departments are severely reducing the number of fully funded offers due to NIH budget cuts

My year were lucky ...

[ancient ivy]

any good resources on non-linear optimization?

[hybrid sigil]

I liked that video from Aleph0 too, and liked his choices (also found a couple of new books from that video like Herstein's "Topics in Algebra" - using it now for my abstract algebra adventure!). I also enjoyed Francis Su lectures when I watched them many years ago, they are great!

[frozen ledge]

For anyone whos studied with the apostol calculus books and spivaks calculus books, which do you prefer? I've taken calc bc but a conversation with my uncle who is a mathematics professor revealed to me a lot of large gaps in my understanding left by rushed or inadequate instruction from my ap class, and he suggested these two books highly. I've done a little bit of research, and see they're both highly praised for a theoretical understanding of calculus

[remote sparrow]

spivak has trickier problems, but at least he has some answers in the back plus a separate answer book for problems not answered in the back. also, spivak doesn't do multivariable calculus or linear algebra, but that's not really an issue.

i think spivak is more interesting

[vital bane]

He does do multivariable stuff in his other book

CoM

[frozen ledge]

As I understood it, spivaks book "Calculus on manifolds" served as his multivariable calculus book. In any case, what differentiates them most is the problems in them? Thats also the pervasive narrative in what I've read online

[slow roost]

Spivak is somewhat infamous for being the toughest single variable calc book around

[frozen ledge]

Well, as long as its difficult in rigor and structure and not just hard to be hard, which I'm sure it's not

then that's fine

[slow roost]

although, it's a somewhat blurry boundary between single variable calc and real analysis

some say Spivak's Calculus is pretty much a real analysis book

[frozen ledge]

Well then I guess a good question then would be

Is it appropriate to read as a reintroduction to calculus?

To be a foundation basically

My school used the supposedly dreadful stewart calculus book, and I'm somewhat worried my foundation in mathematics isn't as strong as I thought, and might not be sufficient to prepare me for spivaks book, basically

[slow roost]

you may want to look at a sample preview of it online to see if it seems manageable or too tough

[frozen ledge]

Thats a good idea

[slow roost]

Apostol is also rigorous and probably somewhat easier

it's a bit unusual in that it does integration before differentiation

[frozen ledge]

I heard that

[slow roost]

but there are probably some good reasons to do that

[frozen ledge]

If it looks too difficult, what should my recourse be? I don't want to just pick one over the other because one is easier, I want a deeper understanding

[remote sparrow]

yes

[slow roost]

you could try some other real analysis books

it sounds like you more want the analysis-theory kind of foundations than computing derivatives and integrals a bunch

there are some quite approachable analysis books at the undergrad level

[frozen ledge]

My uncle said something about how defining the integral first makes the future theorems and proofs more intuitive

[slow roost]

I like Pugh

[frozen ledge]

yes

ive already done enough boring, mindless computations to make me sick

[frozen ledge]

Any that you recommend?

[slow roost]

Pugh, also Tao

[frozen ledge]

Thank you

[slow roost]

I wouldn't recommend Rudin for self-studying the subject for the first time, but it is good. Best to have a group of study partners to work on it

[frozen ledge]

I have a few mathy friends at school

I'll ask

Thank you for your help

[slow roost]

sure, happy studies

[vital bane]

Abbott

it's peak

[frozen ledge]

[frozen ledge]

Thank you, I'll check that out also

[slow roost]

I should have a look at that too, only heard good things

Tao takes about 250 pages to get to calculus proper with differentiation

but it starts with a really nice rigorous construction of the naturals (via Peano axioms), integers, rationals, and reals

he even has a rigorous treatment of decimals in the appendix, which I haven't seen in any other book. Pretty cool

[hidden crest]

spivak expects you to be familiar with writing proofs beforehand, so pick up something like hammack's book of proofs if you aren't

see if you find the first 2 chapters of spivak's exercises manageable

[zinc thicket]

Hello

I am new to the server

I am a non calculus math olympiad guy

[ember maple]

hi

[zinc thicket]

Can you guys please recommend me books for learning Calculus

[fair fiber]

calculus isn't very useful for olympiads

[zinc thicket]

I mean I want to learn it to study University Mathematics

[fair fiber]

i recommend aops calculus

[zinc thicket]

I am not restricted to Olympiads

[ember maple]

shaums outlines

[zinc thicket]

Mathematics is my supreme endavour, I am an explorer exploring the infinitude of eternal mathematics

[zinc thicket]

What that?

[molten gulch]

thomas calculus is fine

[zinc thicket]

Can you send pdf file or link for the book?

[zinc thicket]

I think its not for beginners or is it?

[molten gulch]

Sending PDF's is prohibited on this server

[fair fiber]

https://artofproblemsolving.com/store/book/calculus?srsltid=AfmBOoppo4RLpaCU-8O0t0eFLYkh22dNeOp3nqnkEq51jDFEcJYLwf3S

[ember maple]

be ready for long journey. calculus is just eh surface

[molten gulch]

It's absolutely for beginners, hell I'd even go as far as saying "just learn real analysis"

[ember maple]

that is not a pdf is a cover

[fair fiber]

Well sending pirated PDFs are illegal, aren't open source pdfs fine?

[ember maple]

I am aware of the copy right policy of not pass

[molten gulch]

I know that

[zinc thicket]

But its prerequisite is Calculus right?

Its just rigorous study of calculus

[molten gulch]

yes

[gray gazelle]

khan calc is good enough for the basics

[ember maple]

true be ready to practice alot until you get it.

[zinc thicket]

I dont know about it, please elaborate

[fair fiber]

real analysis is very difficult without much mathematical maturity especially if you haven't done calculus, i wouldn't recommend it

[ember maple]

khan is good enough for highschool but not for university

[gray gazelle]

khan academy is a popular math prep site

[zinc thicket]

I mean I can solve IMO Number Theory and Combinatorics and also can solve Algebra National Olympiad level problems

[gray gazelle]

hmm, isnt it prep for the ap exam which if you score high enough you get uni credit?

[ember maple]

Calculus: Early Transcendentals James Stewart . For what I heard on you tube of people wiht mathematics channels is the pentacle of use in learning calculus

[ember maple]

for the highschool credit yes. but if your goal is learn calclus and pure mathematics not useuful

[molten gulch]

It's an exceedingly dull text

-Ryan

[stuck zephyr]

nice book choice

[zinc thicket]

People in the server are so helpful and responsive to helps, thank you folks

[stuck zephyr]

i have similar book but its for digital systems

[ember maple]

digital or physical same thing. The only difference is which you feel more confortable using.

thanks for the recomendation

[gray gazelle]

has anyone gone through this https://link.springer.com/book/10.1007/978-1-4899-6798-5

[deft lava]

you can copy my work but dont make it obvious ahh

[gray gazelle]

it is far from basic 😥

[zinc thicket]

Thomas ig

[ember maple]

you can start a war with that question. Both are good

[ember maple]

Is this a university student or is this for high school?

[gray gazelle]

Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. its for university students

[ember maple]

ok

[gray gazelle]

it basically assumes you are profficient at calc

[ember maple]

I was going to be childish of ask for this book since you guys are talking about universiuty level books

[molten gulch]

No, there's a chapter on differential and one on integral calculus

It also seems to do some matrix algebra and even differential equations, though I'd just recommend separate books for each

[gray gazelle]

ok it starts with a review of calc that assumes you practiced a lot. better?

[ember maple]

well practice is the key in math. from calculus to libear algebra. Any topic require practice. In my opinion would be wiser to review the basics before you start with calculus

This series is good for practicing.

[gray gazelle]

it says in the introduction However, to keep the interest level up, the review will be brief and only subtleties related to differential and integral calculus will be discussed at any length. idk i feel it is fair to say it assumes proficiency in calc

it says also The main purpose of the review is to go through results you probably know and ask where they come from

[molten gulch]

<@&268886789983436800> pirated materials

[ember maple]

we were told no pdf sharing

[midnight quail]

Ok

[remote knoll]

@midnight quail sorry, I gotta remove it

Discord TOS, I don't really get a say

[ember maple]

Question is image allow or that is not either?

[remote knoll]

A single screenshot of a book is fine

[molten gulch]

Images are fine, but you cannot post the actual book itself, to my understanding

[ember maple]

was niche talking here but got busy. connect later

[molten gulch]

Like in the advanced channels sometimes people have to post a few screenshots from textbooks to provide context for problems

[keen pagoda]

Did someone encounter subject known as Euclidean space, subdivision of linear algebra
Having any recommendations which book to read?

[fluid violet]

Another day another narc

Remember guys, AMAB

[frail fjord]

have u learned being able to do that from like websites or books

[zinc thicket]

What do you mean?

[molten gulch]

assigned male at birth?

[frail fjord]

like have you learned to be able to solve those types of problems by reading some books on those ideas

or like

u js did practice problems online

or took a class or sum

[fluid violet]

All mods are bitches smh

[molten gulch]

ohhh

SMH

[frail fjord]

wat

ohh

im blind

[zinc thicket]

I mean by practicing PYQs, Using books and to some extent lectures helped

I watch Micheal Penn Maths for rigour

And Titu Andreescu Problem Books for intemsive practice

[molten gulch]

removed comment

[fallow cypress]

? where did someone say sir

[molten gulch]

In the person's username

[fallow cypress]

It's also just used in Indian English as an honorific

For example to refer to teachers

[molten gulch]

oh true, I did forget that 😭

[gray gazelle]

Can anyone recommend me some books? i want to start being that guy that reads books! Maybe queer topics would be interesting or like fantasy stuff with dragons and vampires or something! :D

[frail fjord]

alr thx. just asking cause im tryna start doing amc comps from this yr onwards and wanna practice stuff

[misty galleon]

Hello I'm looking for a really nice quality PDE book, any recs?

I was hoping for one that just has as much as possible starting from the basics and branching out really far

I finished ODE not too long ago and whatever the next step should be I'd like it to start there

[molten gulch]

Evans

make sure you know some measure theory going in

[misty galleon]

I know a tiny bit I think?

could you throw me an example

is that like topologies and stuff

[high fjord]

Like measures

Like an intergral with respect to a measure

[vital bane]

Strauss PDEs

[fair fiber]

damn uve already done PDE? bro's defo getting that phd

[vital bane]

Are you looking for a book that teaches you different methods to solve PDEs or are you looking for a pure math book that systematically studies the theory of PDEs?

[vital bane]

I haven't done PDEs

I've only skimmed Strauss 😔

[fair fiber]

average mathcord user recommending books they basically haven't read

[vital bane]

Name one book I've finished

[fair fiber]

meditations by marcus aurelius

[vital bane]

false

[fair fiber]

um

bhagavad gita

[vital bane]

I've never even looked at a single page of that book

[fair fiber]

Quran

[vital bane]

Same goes for that

[fair fiber]

oh i know

re zero light novel 1

[vital bane]

The Alchemist by Paulo Coelho 🗣️🔥

[vital bane]

same goes for that

I actually read the WN for Arc 1

[fair fiber]

light novel 2

[vital bane]

This I think is the only book I've finished

actually no

I've finished one other book

Emotional Intelligence by Daniel Goleman

holy hell I've read 2 whole books during my life

I'm actually so smart

[fair fiber]

2 books is enough if one is d&f and the other is rudin