book-recommendations

[wet sentinel]

i would say these are calculus, intro real analysis, linear algebra (proof based and maybe computational), intro abstract algebra and maybe things like discrete math (elementary number theory etc..)

[trail void]

have u read bretscher on linear algebra friend?

otto bretscher

[wet sentinel]

no now is the first time i am hearing of it

i was using linear algebra by werner greub

[trail void]

i grabbed howard anton, bretscher but i will do axler after real analysis or along

[trail void]

do u think it replaces axler or?

[wet sentinel]

yes i do, i dont really like axler's book tbh

[trail void]

why not if i may ask? is it cuz of the determinant thingy?

[wet sentinel]

though i have to say this, this book is a hard hitter

but i liked it

[wet sentinel]

tbh i dont really know how to explain that lmao. But i didnt like the style of writing in general

although i tried it a few years ago so i dont even remember any details

i tried it for a very short time and stopped since i didnt like it

there is also linear algebra by friedberg insel and spence

its a good book too

#book-recommendations message

and here is a list of linear algebra books with descriptions

[trail void]

friend

after real analysis do you recommend numerical analysis or complex?

or do you recommend abstract algebra and topology instead

[fair fiber]

Do abstract algebra

[trail void]

and then topology correct?

[fair fiber]

It doesnt matter

But sure

[molten gulch]

complex, topo, and alg are all good

[trail void]

in what order?

[fair fiber]

It dont matter

I recommend algebra to get a taste of something very different

[mellow wren]

it's good to know some topology for complex

algebra isn't really related to the former two at first

[trail void]

preliminaries for abstract alg is linear alg and proofs i assume alongside some real analysis?

[fair fiber]

Honestly

You dont need real anak at all

[mellow wren]

you don't need any real analysis for abstract algebra

[trail void]

amazing

[fair fiber]

Lin alg helps with mathematical maturity but its not ne essary

[trail void]

do u think i shld do linear algebra before multivariable calc?

[mellow wren]

yes definitely

[trail void]

but in the book im using by anton and later by bretscher, it says calculus is required for alot of problems

im assuming its only single variable?

[fair fiber]

Fa sure

[mellow wren]

yeah so think of it like

multivariable is like linear algebra + single var calculus

[trail void]

damn so me doing linear algebra before multi variable calc is basically like a huge advantage

[fair fiber]

Idk man id say more like 80% calc and a bit of lin alg

well hmm

[fair fiber]

Nah i kinda agree with this for vector calc

[mellow wren]

yeah you really shouldn't be taking multivariable otherwise lol

[fair fiber]

Crazy how some unis teach mvc before lin alg

Some profs need to be beaten up fr

[trail void]

thats what confused me

[trail void]

you needa get hired

[fair fiber]

Fr make me national head of education

[trail void]

i enjoy self studying mathematics but i hate being taught

maybe i dont enjoy most professors out there

but i think self studying is overall more enjoyable

[gray gazelle]

i still haven't finished a single math book front to back

i want to do that for knuths concrete mathematics

[trail void]

i feel like ur only supposed to do 80%

[gray gazelle]

i mean they wrote the whole book

[trail void]

yes but like 20% is really repetitive often

[gray gazelle]

mm maybe so

[trail void]

if its not go ahead

[trail void]

whats special abt it

over discrete math

or any logic and set theory book

[hidden fractal]

Most people don't

Consider that most university courses only cover a portion of the assigned textbook

[gray gazelle]

https://www-cs-faculty.stanford.edu/~knuth/gkp.html

[trail void]

why is this tho

[trail void]

oh yes ik abt the book but im asking what makes it special over

lets say discrete math books or logic and set theory

[hidden fractal]

Not all of the content is equally important and it may be optimal to only cover the most salient topics on a first read, so as to not get bogged down in unimportant details

[trail void]

youre supposed to cover the rest on your own later or?

[hidden fractal]

You're not really "supposed" to do anything other than what you want to do

If you want to know all of the stuff in a book, you can read the whole thing

[trail void]

are you expected to

[hidden fractal]

No

[gray gazelle]

i guess i am just biased to knuth, didn't even consider other books

i think that it also prepares you for taocp which is something i'm interested in

[trail void]

me too but i heard its for later

theoreitcal cs

[gray gazelle]

i'm not sure, i don't think it requires prereqs other than like sheer determination

i haven't looked into it in awhile

[trail void]

i think ill read him after analysis and cs fundamentals

[gray gazelle]

i think it is a difficult book so it probably helps to study proofs and other math before working through it

[trail void]

whats your favourite shoe brand

[cursive burrow]

algebra book i need learn algebra better

[vital bane]

I suppose you mean elementary algebra

I don't really know a book for that

[molten gulch]

Artin is quite good for algebra

[vital bane]

I think he means elementary algebra

[cursive burrow]

Im 7th grader so

[vital bane]

Yea I realized from your name and from your about me🗿

[fair fiber]

@outer helm

c'est ton frère wesh

[outer helm]

i blocked him

annoying kid

manifold who agrees 😭

[fair fiber]

what'd he do?

[rigid trail]

never too early to start dummy foot 😁

jk, honest advice would be to hop on khan academy prolly

or really any of the free resources on the internet

[trail void]

ngl overhyped

[rigid trail]

it's aight

[fair fiber]

nah

honest advice is to just relax and enjoy life

because by the time he graduates college

it'll be 2035

Chatgpt 13.0 will be out

and will do anything he can do but better

[trail void]

ngl i doubt ai will progress in pure math as much

in the next 8-10 years

[fair fiber]

A few days ago, a UCLA professor just used chatgpt to generate the key idea in solving and optimisation problem

[trail void]

was it sucessful?

[fair fiber]

yes

[trail void]

suprising

now ask ai to visualize and analyze basic euclidean geometry problem

a one that isnt on the net

[fair fiber]

alpha geoemetey could probably destroy it

[trail void]

another ai?

[fair fiber]

deep minds ai

[fair fiber]

alpha evolve already discovered an improvement from straasens algorithm despite humans failing after trying for 50+ years

[rigid trail]

i think one area it could maybe be useful in is translation of written natural language proofs into truly formal proofs

[trail void]

time to head into ai research n engineering people

🤣

[rigid trail]

like lean/coq/other tt's

[trail void]

perhaps

but depends

[rigid trail]

like

10 years is a long time

[fair fiber]

we know

[rigid trail]

i think llm's may be able to do more useful stuff by then

[fair fiber]

exactly

there are so many different methods and types of ai that are being worked on rn

[rigid trail]

current llm's are not really trained for pure math specifically, it's just picking up on it from whatever math literature it happens to come across

[trail void]

always bet on the human spirit

[rigid trail]

even still

gpt is not totally totally ass

even rn

[fair fiber]

forget got imagine the most advanced unreleased models

[trail void]

its as useful as an 11 year old

[rigid trail]

nah it's more useful than an 11 year old

it can find math forum posts

[trail void]

thats if youre willing to overlook its countless mistakes

[fair fiber]

a ucla math professor used it to solve an unsolved problem xd

[rigid trail]

it can find relevant material p quickly

[trail void]

that i agree with

[rigid trail]

well yes you need to be trained in math yourself to be able to use it effectively

[trail void]

do you think cs majors are going homeless due to their inability to create unique code which isnt available on the net

[rigid trail]

to see the bullshit when it arises

cs majors are cooked

[fair fiber]

they're finished

[rigid trail]

i think that's an obvious enough point

[fair fiber]

in 2020 i said cs majors would be cooked by late 2024 i wish i was wrong but i gotta say i told u so to all the cs majors

[trail void]

i just think they dont read that many books lol

[gray gazelle]

i think we have barely taken advantage of the findings of cognitive scientists on optimal learning

[trail void]

send books

[fair fiber]

true

but it's kinda wasted now

cuz ai will make humans near obselete

[gray gazelle]

that is a pretty awful viewpoint

but a shared sentiment among many i bet

[fair fiber]

awful yes
realistic yes (when it comes to knowledge)

[trail void]

just hop on semax

get a prescription of semax and adhd meds xD

Sanjay Sarma @gray gazelle

he has a book

on it

[gray gazelle]

ah

[trail void]

Grasp - The Science Transforming How We Learn

As the head of Open Learning at MIT, renowned professor
Sanjay Sarma has a daunting job to fling open the doors of the MIT
experience for the benefit of the wider world. But if you're going to
undertake such an ambitious project, you first have to How do we learn?
What are the most effective ways of educating? And how can the science
of learning transform education to unlock our potential, as individuals
and across society?

[gray gazelle]

brooo

[trail void]

hi vro

planning ahead

[gray gazelle]

nooooooo 😭 😭 😭

[lost arch]

what to read on linalg after one's done FIS?

are there any further general courses or people take special courses after finishing FIS, like multilinear algebra etc

[molten gulch]

for multilinear I feel like most people learn some in a grad course on algebra or in a (good) multivariable calculus course or differential geometry or such

[lost arch]

i was just wondering if there are books that teach about the same stuff as in FIS, but like deeper or from other points of view

i heard of Kostrikin-Manin, for example, maybe there are others alike?

[molten gulch]

greub

[lost arch]

is that suitable for study though? i thought that was an encyclopedia or something

[tender river]

https://web.stanford.edu/~dkim04/writings/LinAlg.pdf

[slim lodge]

cgp books for year 1-10 maths

for problems Abacus eolve

[odd mountain]

Hi Someone use Anki

[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/

[lost arch]

thanks

[gray gazelle]

http://cognitivemedium.com/srs-mathematics

[magic garnet]

anyone have a textbook on real analysis (I just finished linear algebra) im pretty new to higher level math

[odd mountain]

Can you explain the article for me sorry i dont understand

[trail void]

when should one read mangatiana robdera

[molten gulch]

rudin

[rigid trail]

abbott, ross, rudin are all solid (least to most technical)

[trail void]

what should one read after abbott?

ross and then rudin?

got u

[rigid trail]

Personally would struggle through Rudin after abbott

Ross is nice but if you alr did abbott then I don't see a strong point

[trail void]

better alternatives to rudin?

[rigid trail]

Rudin is very good

It's just hard

Would recommend starting with Abbott if you are new to more rigorous math

it's a lot more friendly

[fair fiber]

bro first finish abbot and algebra and allat 😭

[magic garnet]

wait i found this tho

wjich i thknk is better for me

[trail void]

always be 10 steps ahead

now i shall be quietly observing for new books..

👻

[molten gulch]

mecore

<@&268886789983436800> pirated book repo

[zealous coyote]

We cannot allow this, sorry

[magic garnet]

oh my bad

[zealous coyote]

@magic garnet Just fyi, piracy is against discord ToS so we cannot allow it on this server. Please don't ask for or post pirated resources here.

[chrome wasp]

You couldve just sent name and author?

[magic garnet]

ya its all tge math u missed by garrity

[prisma ibex]

dose somwon haw ri gore book fro ri gore menster?

[old elk]

First Jay Cummings, then Mangatiana Robdera along with Ana Alves' book, and finally you try your hand at Sohrab.

Then move on to a more rigorous one. There are many people here who believe they have the same abilities, but that's not really the case. That's why I've been struggling on my own as a self-taught person, since I didn't learn much in my mathematics degree, unfortunately.

You have enough examples and solved problems to start developing your intuition.

[wet sentinel]

Which rudin are you talking about?

If baby rudin then I wouldn't really recommend doing it after Abbott

Like either do Abbott or rudin

Or some other intro analysis book

But doing both Abbott and rudin would be a waste of time imo

[viral orchid]

Looking for a good textbook on classical model and proof theory, ideally one that fixates on godel, tarski, and lob
Preferably, it should go up to type theory and modal logics

Ive been studying off a logic handbook, but ive been made aware that there are many weaknesses in my understanding

[prisma ibex]

what handbook wass it

[viral orchid]

gabbay and guenther 2nd edition

Which, ngl i loved it, but its definitely meant for people who already know logic

[fair fiber]

instead do topology with us

[cunning elk]

how about you actually read the article first

[remote sparrow]

the conventional choices for mathematical logic books typically use hilbert systems as their proof system, which is helpful for doing metalogic, but unwieldy for deriving formulas within the system, so while you nominally see some proof and model theory in conventional introductions to mathematical logic, hilbert systems are not typically the main focus in a dedicated proof theory textbook. i haven't seen any book that covers everything you ask for, at least in real depth.

[viral orchid]

what about with model theory and proof theory in first order languages then

[remote sparrow]

#book-recommendations message

they all get to godel's incompleteness theorems

[viral orchid]

well, i want a book that actually proves results about these from semantic interpretations, endertons doesnt go at nearly the depth im looking for

[remote sparrow]

what do you mean by "proves results about these from semantic interpretations?"

never even mentioned

[fair fiber]

Why are we learning his theorems if theyre incomplete?

[viral orchid]

im looking for something that constructs \models, shows how to extend canonical models, gives results on this extension, etc

[remote sparrow]

https://math.stackexchange.com/questions/4073243/motivation-behind-the-canonical-model-in-modal-logic

[viral orchid]

yeah stuff like this

[remote sparrow]

is this what you're talking about?

i haven't seen stuff about that in any intros

seems specific to modal logic

[viral orchid]

yeah, its a basis for modal logics

but we do this in first order theories

[remote sparrow]

idk...maybe read a modal logic book for more details after reading an introductory logic book?

[viral orchid]

Well, im looking for a particular book well beyond the usual introductory logic books like enderton

Does enderton ever actually define the \models relation?

[remote sparrow]

is there a reason you think he doesn't?

[viral orchid]

Im just asking

Because that relation is absolutely necessary for what im aiming to learn

[remote sparrow]

pages 23 (for propositional logic) and 81 (for first order logic)

[remote sparrow]

which is?

[viral orchid]

the end goal is algebraic semantics

[viral orchid]

ill give enderton a read, then

[remote sparrow]

no clue about that, might want to ask #foundations or #theoretical-cs

[viral orchid]

a bit sad it stops at the skolem functions

[fair fiber]

Bro i sent that ages ago

Did u just scroll up reading for hours

But ngl yes

Because hyouka is so ass

Bro was trying to clipfarm me

[remote sparrow]

mq 🤝 bussy beaver

[fair fiber]

Who is bussy beaver

[remote sparrow]

@still panther

[fair fiber]

Sour drop 👟 Sweet rise

[remote sparrow]

am i kicking sweet rise

[rigid trail]

:(

Bocchi is peak tho

[remote sparrow]

https://tenor.com/view/bocchi-bocchi-the-rock-bocchi-the-fumo-kita-fumo-gif-12872356873536297071

[twilit solstice]

https://tenor.com/view/sayaka-saeki-sayaka-sayaka-saeki-saeki-bloom-into-you-gif-16713469423269275294

Ahh. I love you to internet potato.

would not have made sense to a medieval peasant.

[agile spear]

guys pls tell me someone read powerless in here bc no one ik read it and it makes me mad bc i luv it sm

[vital bane]

He did say that

[remote sparrow]

super late response but i guess i'm biased to stories with chessmaster or chessmaster-esque characters, like Overlord, The Saga of Tanya the Evil, A Practical Guide to Evil, Nebula's Civilization or The Last Sovereign (NSFW JRPG that recently left early access on Steam). besides that, i like more grounded, character-driven dramas or stories with political intrigue, like Osora, Proof of Dignity, or the The Spark in your Eyes. i try to read whatever looks good to me though, and i'm not completely against power fantasy slop.

https://www.webtoons.com/en/fantasy/the-spark-in-your-eyes/list?title_no=3210

quite good and probably outside of your comfort zone

@fair fiber

[ionic osprey]

do you follow Pale Lights?

[remote sparrow]

no

[worldly brook]

this inner product -external product lingo pisses me off

what even is a vector projection

what can I read to finally learn all the "inner product", "outer product" stuff

I just remember that the cos between the 2 serves a good metric of distance cuz of the curse of dimensionality over high dimensional spaces

but this justification with inner vector product stuff seems interesting

[cursive rivet]

this'll be in basically any linear algebra textbook (though very few people use the term outer product), friedberg insel spence is a common recommendation

[worldly brook]

alrighttt, thanks

out of curiosity, is it doable to learn linalg without performing the math by hand?

[cursive rivet]

what do you mean performing by hand?

[worldly brook]

right so

[cursive rivet]

learning is an active process; you need to do things that build on and enhance your understanding

[worldly brook]

usually I would just read some linalg, then it would ask me to perform some matmul multiplications by hand

with is and stuff

I solve a few, get tired, and go do something else

[cursive rivet]

like, you can do those kinds of things only a few times and get used to them and not really have to practice them again

[worldly brook]

I like proofs

but doing the exercises really makes it a hassle to go through it tbh

[worldly brook]

I see

[cursive rivet]

and there are more abstract approaches that are heavier on proofs and dodge matrix operations as much as possible (though they are fundamentally unavoidable in most modern math)

[worldly brook]

I mean why even bother doing something u can plug in a modern calculator and get out a result 😭

that's not really active learning, that's just mindlessly moving numbers to reach a trivial answer

[cursive rivet]

well, having to write a lot of matrix multiplication algorithms for a class was greatly aided by having an intuitive understanding of how various elements of a matrix contribute to a product

[worldly brook]

know about any good proof focused linalg book?

[cursive rivet]

FIS as stated above is a common good one

my personal favourite is linear algebra done wrong by treil, which is a bit easier I think

but more explicit with matrices than some of its peers

[worldly brook]

just need the intuition, can't be bothered to get tired doing mindless calculations

if I wanna do any of that, I'll figure it out then or feed it to a computer

[worldly brook]

I'll try out that one then, thankss

[vital bane]

intuition and computation go hand in hand

So don't be scared to do a few computational exercises, they're helpful

[crude stump]

Where can I study the method of exhaustion that Archimedes used?
I wish to understand it, in depth with examples

[manic cairn]

do calculations when you get stuck on something else you currently want to do

for me i find myself ping-ponging between homological algebra and vector calculus/physics, because homalg tends to work more on the abstract nonsense part of my brain, and when that gets tired, i’m willing to compute a bunch of integrals

if everything is tired, history and english

[vital bane]

What about computing simplicial homology of some spaces

[slow roost]

I noticed there are some really cheap paperback FIS Linear Algebra books for sale through amazon, and I wonder if they're trustworthy. $25 vs $150 from Pearson. Is this some kind of scam or counterfeit?

[sage kelp]

Sus

[slow roost]

yeah, seems too good to be true

[sage kelp]

Unless it’s a copy that is falling apart 😆

[violet pollen]

Hey, just wanted to ask for some book recommendations for getting back into math and useful math for programmers. I've been a developer for 4 years but never went to Uni. My math background is weak and I could probably improve my quality of work by also improving my math background.

From a friend that went through computer science Uni I got recommended:
https://link.springer.com/book/10.1007/978-3-658-05620-9

Its a German book and it seems too advanced for me. I am sure I lack a lot of fundamentals, so that's why I wrote "getting back into math". To make it worse, I have ADHD so I have trouble with extremely dry books. Maybe someone has 1 or 2 good recommendations that would help me. Much appreciated!

[gray gazelle]

hi

can't comment on the book u sent link to

i don't have access to it

but i think u might benefit from first going through smth like Pre calculus

then getting into discrete math

[worldly brook]

if you're doing programming, it might be worth looking into discrete mathematics

[gray gazelle]

also its quite close to what he might have been doing

[stray veldt]

if you want something german, i think you'd be happier with something like "Mathematik für Informatiker" by Teschl
i think it has less strong requirements than something like Papula (which is a book for engineers) and probably more interesting given your background
while i think it could be tough if you didnt do math in a while, its possible

[gray gazelle]

so it would not feel

boring

[violet pollen]

Doesn't have to be German, but I'll check on this one either way, thanks!

[lost arch]

hey guys, does anybody have a recommendation for a statistics book after one's finished doing Ross' First Course in Probability? I'd like statistics to be treated on a similar level as that of Ross'

[light shuttle]

does anyone know how good these books are and if they aren't, any substitutes that could take their place

[hybrid sigil]

it's probably "International Edition", i.e. copies that are made for sale only in India, Nepal, Bhutan, Pakistan and maybe some other countries - those books are usually paperbacks and they are much cheaper than normal editions, but the content is the same. Usually they have a blurb somewhere on the cover "not for sale outside of countries X, Y and Z"

for example, here is Artin's Algebra, normally super-expensive, but this is International Edition:

you can see the red blurb in top-left corner "Circulation outside of the Indian subcontinent is not authorized".

and this is FIS that you mentioned, with the same blurb:

this is the Supreme Court case about this matter: https://en.wikipedia.org/wiki/Kirtsaeng_v._John_Wiley_%26_Sons,_Inc.

summary can be found in this article from Biblio: https://biblio.co.uk/International_Edition_Textbooks

[lost arch]

if you don't mind I'll make sure people will see my question

[molten gulch]

Don't international editions also drop 1-2 chapters?

[trail void]

abstract?

[molten gulch]

abstract what

Yes Artin's text is a text on "modern" or "abstract" algebra

[hybrid sigil]

not sure, but I don't see this mentioned anywhere, people usually say that it's just paperbacks, black-and-white printing and cheaper paper

paperback is actually a plus for me 🙂

I like my books more flexible and easier to carry around if needed

[wary verge]

Does anyone have any good book recommendations 🥹

[cunning elk]

you're gonna have to be a lot more specific

what kind of books are you looking for

[wary verge]

Pre algebra

[molten gulch]

openstax

[wary verge]

Thank you

🥹✌️

[slow roost]

I see, that explains it! might take a chance on a copy soon, my old 4th edition is pretty beat up

[remote sparrow]

sometimes

[normal crystal]

there's no guarantee they're exactly the same
you have to look into what is said about the particular book

[gray gazelle]

This is actually incredibly interesting! Thank you!

[remote sparrow]

you can check against the table of contents or the pdf sometimes

[fair fiber]

Chipperpotato

/j

[normal crystal]

I think a more common problem is they change the problem sets
that alone isn't necessarily an issue for self-learning unless they pile on a bunch of errors
that's the problem with the CS APP global version

[normal crystal]

idk about FIS and Sipser
but those are books that are popular enough and been out for years, so it's probably known if there are differences

[surreal heart]

does anyone know anything about Programming for Mathematicians by Seroul?

I'm looking to get better at programming, ideally with some theoretical backing and with as much mathematical detail as possible, so any other appropriate recommendations would also be appreciated

[turbid arrow]

@gray gazelle recommend something bruh

[crude stump]

What is a good problem book to go with euclidean geometry? Apart from evan chen

[long cloak]

Hello guys, is there any book about Permutation and Combination?

[cunning elk]

plenty

finding one is left as an exercise (i promise it's good practice)

[long cloak]

I wanna have one, can you recommend for me?

[tender river]

theres probably nothing explicitly meant for highschoolers

you can follow the chapters in other typical highschool math books

[tender river]

but if you need one you can look at https://appliedcombinatorics.org/appcomb/

[cunning elk]

literally any standard introductory combinatorics text should have a chapter or two on them

AoPS intro to counting and probability is one example geared towards younger students

[crude stump]

I need the theory of combinatorics

[lost arch]

guys, what's the best book to learn Analysis from if my goal is to cover sequences, series, point-set topology (open, closed sets, connectivity, compactness, continuity), limits, differentiation in one and several variables, Riemann integration and integrability, multiple integrals, and some measure theory, Lebesgue integral.

i consider Tao's Analysis I, II appropriate, but i know there are many more books of the same level and with similar contents. If you know any good books, let me know, plz

I haven't seen multiple integrals covered in Tao's, though

[tiny gulch]

<@&268886789983436800>

[tender river]

unironically rudin covers all this lol

[tender river]

browder too https://link.springer.com/book/10.1007/978-1-4612-0715-3

[lost arch]

well, i heard chaps from 8th and on weren't so greatly written tbh

idk if it's just hearsay though

[tender river]

that's not been the primary reason one would not want to use rudin

[split portal]

Depending on what you know/are comfy with the other 8 chapters aren't great either.

A lot of the stuff you're asking for are also usually covered across several different courses which would typically use several different books/sources as well.

I personally like rudin, but I don't think it's that great for point set given that the whole thing is done in the context of metric spaces.

[outer helm]

yo does anyone have a good resource for topological groups?

[vital bane]

Like an introduction or...? For what purpose?

They're used in a lot of different places like Lie groups, Harmonic analysis etc.

(I say etc. but that's literally the only two places I know where they're used )

[hybrid sigil]

Pugh "Real Mathematical Analysis" covers all of that too, and seems to be quite popular (and also what I've bought for myself, but haven't properly started on it yet)

[pseudo hill]

"Younger students" im 18 doing pre algebra aops made me question my life

[vital bane]

You can learn whatever math at any age, it doesn't really matter 🗣️

[pseudo hill]

Hello, I’m a self-study type and like deep thinking. Topics:

Algebra: indices & surds, factorisation, polynomials (remainder/factor theorem, roots, Vieta), quadratics & graphs, partial fractions (simple/complex), rational functions, rational-exponential combos, binomial theorem (integer/real n), exponential & logarithmic functions, functions (domain, range, inverse, composite), parametric equations, advanced circles & tangents, sequences & series (arithmetic, geometric, convergent, binomial), summation techniques.

Trigonometry & Geometry: radians, sine/cosine/tangent, sine & cosine rules, advanced trig identities, inverse trig, multi-angle trig equations, graph transformations, coordinate geometry (lines, circles), 3D vectors (algebra, dot/cross products, unit vectors), lines & planes in 3D, angles & distances.

Calculus: differentiation (power, product, quotient, chain, implicit, logarithmic), stationary points, maxima/minima, curve sketching; integration (indefinite/definite, substitution, parts, rational-exponential, derivative recognition), areas/volumes; differential equations (first-order linear, separable).

Sequences & Series: arithmetic/geometric sequences, sums/sigma notation, binomial expansions, convergent series, Maclaurin/Taylor/binomial series, function approximations, links to differentiation/integration.

Problem Solving & Logic: proofs (algebraic, trig, sequence/series), vector proofs (perpendicularity, collinearity, angles), multi-step reasoning across topics, pattern recognition (hidden derivatives, sequence → series → approximation).

[fair fiber]

fr that's why i learned how to add fractions in second year of highschool 🔥

neamesis tries not to use 🗣️ emoji (challenge impossible)

[pseudo hill]

It gets more complicated the just skimming bro

Math and money is my depression no math knowledge i have nor money

[vital bane]

Same

[pseudo hill]

Pls someone

[fair fiber]

aops

[pseudo hill]

Pls no more

Aops literally doesnt teach just makes you question

We must learn then question

We cannot question before learning

[fair fiber]

you must learn through question🗣️

[split portal]

Are you asking for books?

Or just describing math you like?

[pseudo hill]

Asking for books

Textbooks

[split portal]

Anything specific? Your list of topics is kinda broad?

[pseudo hill]

I was studying aops 3 hours lmao still at chapter one

[pseudo hill]

Yea one minute

[fair fiber]

that's normal

it's a steep learning curve

there are so many questions you should be taking hours

[split portal]

Fwiw no matter what you do, in order to learn math you need to do problems. Over time the problems get harder. The aops books are kind of intentionally trickier since they are geared more towards kids into competition math.

As you go further in math spending long-ish chunks of time stuck on hard problems will become more common like mq is saying lmao.

[pseudo hill]

Proof, Logic & Problem-Solving
• Algebraic & trigonometric proofs
• Sequence/series derivations
• Vector proofs (perpendicularity, collinearity, angles)
• Multi-step reasoning across algebra, calculus, & geometry
• Pattern recognition and generalisation

Calculus
• Differentiation: power, product, quotient, chain, implicit, logarithmic
• Applications: stationary points, maxima/minima, curve sketching
• Integration: substitution, by parts, rational + exponential forms, definite/indefinite
• Areas under curves & volumes of revolution
• Differential equations: first-order linear & separable

Sequences & Series
• Arithmetic & geometric progressions
• Sigma notation and summation techniques
• Convergent infinite series
• Binomial expansions
• Maclaurin & Taylor series approximations
• Links between series, differentiation, & integration

Geometry & Trigonometry
• Coordinate geometry: lines, distances, midpoints, circles
• Tangents & normals to circles
• Trig ratios, radians, sine & cosine rules
• Identities (double/triple angle, sum-to-product, etc.)
• Inverse trig functions
• Multi-angle trig equations
• 3-D geometry: vectors, dot & cross products, lines & planes, angles & distances

Functions & Graphs
• Function composition / inverses / domains & ranges
• Graph transformations (translations, reflections, stretches)
• Parametric forms of curves
• Rational-exponential and composite graphs

Algebraic Structures
• Laws of indices & surds
• Factorisation and polynomials
• Remainder & factor theorems, Vieta’s relations
• Quadratic & rational functions
• Partial fractions (simple → complex)
• Exponential & logarithmic functions
• Binomial theorem (integer & real n)

[lost arch]

what's aops though?

[split portal]

A book series

[pseudo hill]

Yes its like 1k pages for pre algebra aops

[pseudo hill]

Art of problem solving

[split portal]

Honestly what you've listed has a lot of overlap with a typical precalc class

[wicked fractal]

This is just standard high school curriculum - the proofs

[lost arch]

Algebra and Analysis undergraduate books usually cover all these in the first few chapters

[pseudo hill]

What- they are very complicated dude

[split portal]

I was meaning to mention that you might be interested in this book: https://classicalrealanalysis.info/com/

[wicked fractal]

Sorry I didn't see all of it. Most of it is high school and there is some first year uni stuff

[split portal]

The analysis one

It's a 2 vol thing that probably covers more than what you want.

[lost arch]

me? are you responding to my previous request?

[split portal]

I've only really skimmed it but I liked the bits I read

Yes for your prev request

[lost arch]

thanks, I'll take a look now

[split portal]

It's also free

Kinda weird format tho

[split portal]

Besides the aops stuff you're doing now, have you done algebra/trig?

[pseudo hill]

Some of the hardest im doing is
Trigonometry (Advanced)
• Full set of trig functions (sin, cos, tan, sec, cosec, cot)
• Complex identities & transformations
• Expressions of the form a \sin x + b \cos x → R \sin(x \pm \alpha) etc.
• Solving more complicated trig equations

Vectors
• 2D & 3D vectors: magnitudes, unit vectors, position & displacement vectors
• Scalar product applications: angles, perpendicularity, projections
• Lines & planes in 3D: intersections, parallelism

Problem-Solving & Proofs
• Multi-step questions combining algebra, calculus, trig, and vectors
• Proofs involving sequences, series, vectors, and complex numbers
• Deeper reasoning: pattern recognition, linking different areas

Calculus
• Differentiation: parametric & implicit differentiation
• Integration: advanced substitution, integration by parts, rational functions, trig relationships
• Differential equations: first-order separable, applied contexts
• Applications: tangents & normals, rates of change

Algebra & Functions (Advanced)
• Complex numbers: Cartesian & polar forms, roots, conjugates, Argand diagrams
• Advanced rational functions & partial fractions
• Logarithmic & exponential functions at higher level
• Series expansions: binomial, Maclaurin & Taylor series (more manipulations, approximations)

[lost arch]

this one is crazy good though. I've managed to find the first 30-some pages and it's just what i needed, so imma probably go into this one

[pseudo hill]

Yes but very shallow understanding

But dude maclaurin and taylor isnt easy nor highschool im self studying anyways

[split portal]

Power series junk does pop up in hs for some folks

It's kind of regional

Some places cover more math than others

The basics are usually not so bad for power series. But you could spend your whole life studying things related to series.

You could do that with a lot of topics in math.

[molten gulch]

Is there active research in the theory of infinite series still?

(Well yeah if you count like zeta functions and such) but besidrs that

[split portal]

If you can do the problems in a typical precalc book (maybe with a little struggle) I wouldn't really worry about how shallow your understanding is.

[split portal]

I mean, there are series problems and examples popping up everywhere in math.

[molten gulch]

Fair fair

[split portal]

I don't think I know anybody who solely studies series. You absolutely meet people who have series stuff pop up in their work in various ways.

[pseudo hill]

Self studying for an exam which requires very deep understanding so i did this

[split portal]

Well if you are comfy enough on precalc material to do problems out of a typical precalc book then there isn't really any issue with your knowledge in that dept.

How about calc stuff? Can you say the same for a book like stewart?

[pseudo hill]

Asking me?

[split portal]

Yeah you

[pseudo hill]

Idk never read it did AP calc a bit

[split portal]

Ah well then why not do that next?

[pseudo hill]

But then switched ciriculim

[pseudo hill]

Too easy tbh went to calc bc too

But the overall depth learning etc didnt like it planning to go uni in uk

[split portal]

Well when you say too easy does that include everything out of a book like stewart's calculus?

[pseudo hill]

Probably not

[signal ocean]

i need a book that explains power series any recommendations??

[split portal]

Okay, well then you don't know as much calc as you think and you should probably just continue with it.

[pseudo hill]

Thats like uni level i think i was told many uni students use it

[split portal]

Stewart and larson are fine. Paul's online math notes are also good.

[split portal]

But if your issue is depth, then a university level book would be more in depth?

[pseudo hill]

Regardless it doesnt matter cause the continuation of it wont matter cause it i would have done only 3 ap meaning no good uni all education goes to waste

So i will probably read stewart and just not now

[split portal]

If you compare any of the "main" calc books you see at most unis they all look pretty similar to stewart so idk if I'd call it a waste.

[pseudo hill]

Gotta secure a uni that teaches strong math

[split portal]

A typical path in the US for ug math looks something like calc 1-3 -> lin alg + ode -> proofs -> upper div math.

[pseudo hill]

Not the book as the waste but continuing american circ tbh but i will still read

[split portal]

Fair

[pseudo hill]

Damnnn

Are in uni doot

I like de moivre theory

[split portal]

Upper div is usually some flavor of two sem abstract algebra, two sem real analysis, some electives, complex analysis and probably more lin alg

[pseudo hill]

Theorm*

Very cool

[split portal]

Yes I am in grad school

[split portal]

So like this kinda gives you a clearish path if you are in the us

If not, you can also look up the course sequence for math majors at a uni near you to see what the path you'd wanna do looks like.

Then you just pick books for each class.

[pseudo hill]

Uni near me only go to calc 2

🙁

[split portal]

That's probably not for a full math major then.

The community college I started at capped off the math classes it offered at lin alg and ode fwiw

[pseudo hill]

Very cool what lead to your hobby about math and understanding

@split portal

[split portal]

I just took a bunch of classes and really enjoyed it so I kept doing classes lmao

[pseudo hill]

I see

[split portal]

I started in cs which I knew required a bunch of math

Then as I finished at the cc level I decided I wanted to add math for a double major when I transferred to uni

[pseudo hill]

Ohhh very rigorous

[vital bane]

Actually diabolical, they should do, calc 1 -> proofs -> Lin alg + analysis -> algebra, topology, measure theory 😔

[fair fiber]

here is the ultimate path if you disagree you are wrong
Calc 1-2 alongside Linear Algebra
Calc 3 alongside intro to proofs and logic
Proof based linear algebra + Discrete Math
Real Analysis - Data structures and algorithms

[vital bane]

I need to learn linear algebra in 4 days

[rigid trail]

Linalg is not too hard to catch up on

[surreal heart]

This is our program except you just skip non-proof LA and ODE lol

[split portal]

That's probably pretty nice

[fair fiber]

in my program we don't really learn analysis then jump into measure theory

[surreal heart]

Yeah it's not bad, but it's kind of strange. You could get a math degree and never do any diffeq which is strange, I think

[vital bane]

What do you do?

[split portal]

Ah I thought you meant ode and la were still mandatory after proofs

Not doing la somewhere in ug math is not great

Ah hmm

I might still be misreading

[fair fiber]

we are supposed to learn real anal first sem but no one is ready so it's sort of a mix of calc and analysis

but 70-30 split

[vital bane]

[fair fiber]

and then there's no proper real anal so students jump into measure theory and get wrecked

[vital bane]

Best undergraduate program in Sweden be like

[surreal heart]

Sorry I wasn't very clear, theoretical LA is required but no diffeq is required anywhere

[vital bane]

Do they not learn calc in high school?

[fair fiber]

they do learn but very little

it's nothing like india

unless they take a gifted or accelerated program in hs they don't learn 20% of what you see in JEE

[fair fiber]

we don't got cmi fr

[vital bane]

[vital bane]

Please censor that word

j*e

[keen apex]

Uhh

Hi

I live in the asian subcontinent

And i want to learn the fundamental theorem of arithmetic in a highschool level

[high fjord]

You mean that theorem about unique decomposition to primes?

Its very simple

Any basic numebr theory textbook will have that

[prisma lark]

Hi
I need recommendations for intro group theory books

i can see rose, rotman, and pinter from some looking around

for context i've done the first 6 chapters of LADR and i really liked the style of the book

ik the premise of the book is not something i am going to find in groups but

just to give you an idea of what i like I guess

[shut geode]

gallian is the standard recommendation

[keen apex]

Like a deep dive into primes and stuff

[molten gulch]

It's simply the statement that any integer (or element of a factorial ring/UFD) can be written as a product of irreducible elements up to order. In the case of Z this is just a statement about how every nonzero number has a (unique up to order) prime factorization

[keen apex]

I know

Ive seen some interesting videos on this topic and i wanted to learn more about it

[vital bane]

Maybe try Burton's number theory book?

[tender river]

dudley is nice https://www.amazon.com/Elementary-Number-Theory-Second-Mathematics-ebook/dp/B008TVF6FQ

[keen apex]

Thanks :3

[tender river]

i like rotman and clark is good too https://www.amazon.com/Elements-Abstract-Algebra-Dover-Mathematics/dp/0486647250. pinter is commonly recommended too but never heard of rose

[keen apex]

Is this good for noobies

[vital bane]

I suppose

[keen apex]

What about The dudley one?

[molten gulch]

Ireland and rosen is good

[vital bane]

it might be better based on your background idk

[vital bane]

Which book? Classical Intro to Modern NT?

Or do you mean this one?

I don't think Ireland was involved in writing this though

[molten gulch]

I do mean classical intro to modern nt

[vital bane]

Bro is recommending an algebraic NT book to a high school student with no prior experience with either algebra or NT

🗿

[fair fiber]

I would not misgender them

[vital bane]

Bro is gender neutral bro

[molten gulch]

I will say if there's a problem thank you very much

[molten gulch]

This is fine usually

[mortal ore]

Yall is a banger

[vital bane]

Youse

[cunning elk]

btd6 reference username 😱

[hybrid sigil]

I use Pinter as an easy but fun book (it’s a cheap Dover paperback and really good: has plenty of exercises grouped in topics and conversational style), and also Herstein’s “Topics in Algebra” for something deeper, quaint and more old-school (it also has great exercises!). I also like Gallian (it’s more like a relatively easy, pretty, modern textbook with pictures, historical asides and many calculation exercises) and Dummit and Foote for its encyclopaedic coverage and still readable prose. If you like practice-based books where you need to prove a lot of intermediate theorems as exercises and work hard then Clark is another nice Dover edition which is cheap, short and sweet, but covers a lot of ground

I am also tempted by Artin’s Algebra, you may like it coming from LADR perspective, because it uses many examples from Linear Algebra. Also there is an MIT course which Artin himself teaches, it has homework exercises and reading assignments based on this book, which is handy if you are self-studying.

[fair fiber]

i don't think linear alg is that important for intro group theory

i think you'll see it more when you study fields or ring theory

[hybrid sigil]

I think he said that just to show which style of books he enjoys

Not because he thinks that LADR is important for studying group theory

[remote sparrow]

herstein is good, but i would note that it omits group actions. a modern book that does group actions early and frequently would be Algebra in Action by shahriar shahriari. it doesn't treat module theory, unlike herstein.

big thumbs up to pinter for beginners

a similarly elementary book is judson, which is free online, but leaves fewer important results as exercises

[molten gulch]

I forget, how much does artin use actions? I know it introduces them relatively early as it should, but how much does it use them after

[remote sparrow]

fk

meant to ping mods

[remote sparrow]

i did a ctrl-f search for action, which showed a few mentions, including one hit for "group action." however, it's not in the index, and i didn't see a formal definition for it in the text. however, lecture notes following artin definitely do

https://old.maa.org/press/maa-reviews/algebra-0

ah he calls them "group operations"

they're given a definition on page 176

[hybrid sigil]

What are the benefits of using group actions? Do they provide a nice framework for presenting or explaining some other material?

[fair fiber]

They lead to orbit stabilizer theorem

Which is one of many ways of proving sylow theorem

it also leads to cayley theorem

so it in general creates very useful tools to do important things like classify groups

[molten gulch]

He calls it a group operation

[hybrid sigil]

Pinter is also not big on group actions and orbit stabiliser theorem, he relegated them fully to exercises:

I liked explanation of group actions in Dummit and Foote

[fluid violet]

😭

I have recently developed a love for group actions

Helped me understand Yoneda

[cursive rivet]

I cannot emphasize this enough: group actions are 99% of the reasons people care about groups, even if they don't say the words "group action" in how they talk about them

[hybrid sigil]

OK, but can you elaborate? Why is it so?

[cursive rivet]

so to apply group theory to any other subject, the way you do it is you find some group lurking about acting on the things you care about

(typically acting in a way that is compatible with whatever structure you have)

this is analogous to how you prove Sylow theorems or use orbit-stabilizer to classify things in finite group theory, there are lots of natural actions of finite groups on themselves/on objects related to them

so you notice such an action and then you use it to guide how to think about your objects and decompose them (e.g. into orbits)

[remote sparrow]

besides being a useful tool for group theory qua group theory, group actions are fundamental concepts in representation theory

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

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

[cursive rivet]

so like, representation theory is literally the study of group actions on vector spaces, Lie theory is used in geometry by finding Lie groups (or algebraic groups in the algebraic setting) or Lie algebras acting on your spaces, harmonic analysis is primarily about topological groups acting on spaces, and so on

Galois theory is about actions of the Galois group on roots of polynomials

[hybrid sigil]

Thanks! Sounds exciting 🙂 I have to get deeper in my algebra studies (preferably in combination with some other field) to really appreciate that interplay though

Do group actions play an important role in algebraic number theory as well?

[cursive rivet]

yeah, through the Galois theory thing I mentioned at the very least, though I know very little number theory

Galois theory being the starting point of algebraic number theory

[hybrid sigil]

Cool. That’s my current program, i.e. the driving force behind my studies: to get to Galois theory and Algebraic Number Theory

Representation theory also sounds interesting but for that I’ll need more linear algebra I guess

[cursive rivet]

if you have taken a class/gone through a book in abstract linear algebra, you probably have enough to start out and learn as you go

e.g. at the level of Axler or FIS or Treil or Hoffman-Kunze or ...

[hybrid sigil]

Yeah, I’ve got Axler and Halmos

And Strang too, but I don’t really like computational stuff 🙂

[azure depot]

is anyone down to study lees smooth manifold together? I already went through the integration on surfaces in Rn part in zorich

[azure depot]

Modules may be seen as a ring action

[tiny gulch]

How

[gray gazelle]

You guys should read harry potter

[cunning elk]

and the principles of mathematical analysis

[fair fiber]

it seems like an appropriate textbook for anyone finishing pre calc

If u can read harry potter u can read pma🗣️

[echo dirge]

Does anyone have recommendations for books or resources to help me get better at this style of equational reasoning proofs? The resources offered by the professor are quite limited

[velvet flax]

i have a feeling that "introduction to mechanics and symmetry" is not an introduction to mechanics

[molten gulch]

This is basic logic, this should be covered in any "discrete mathematics" text

[old elk]

I don't recommend that demonstrative method. Sure, it generates logic, but it's better to learn at the conjunctive level.

You can look at Jay's book.

[molten gulch]

I believe the important thing here is that that is the professor's method may very much show up on exams

Also knowing how to manipulate logical expressions is quite important to do a few times by hand IMHO

-James

[echo dirge]

Yea it’s very specified to his method which makes it difficult to practice from discrete math books

[hasty sluice]

Isn’t that covered in discrete math?

[echo dirge]

Professor doesn't upload any material and I'm not able to travel to uni so I have to do it outside

that screenshots from like 5 yrs ago during covid lol

just wanted to know if anyone had good ones to use I've been using "a logical approach to discrete math" rn

mixed with the fact I kinda suck at it tbh

[hasty sluice]

maybe try Rosen

[echo dirge]

appreciate it, I'll give it a look

[fluid violet]

Well like it was thinking about how it generalizes Cayley. This isn't a novel view at all, and I don't think it particularly is a good pov on Yoneda, but it helped me because it came to me when I was thinking about group actions so I was able to think about it myself.

Left Group actions are just functors G->Set, and the Hom functor is the G action on G corresponding to left multiplication. Natural transformations between functors G->Set correspond to morphisms of G sets, and so you can state Yoneda for functors G->Set algebraically.

[tiny gulch]

Yes exactly

It says that the regular representation is a free G-set

Specifically, the free set on one generator

You can generalise this observation using coends

[zinc dove]

hi do any of you know any good books to study advanced math for year 11 HSC

my plan is to learn everything over the summer holidays

i’m in the southern hemisphere

[trail void]

its called pre calculus with some topics in calc 1, read axler alg and trig and then thomas calc

[zinc dove]

when winter starts for you

december

[neon bramble]

Any good channel (youtube) for game theory? (If there is a specific playlist then even better )

[zinc dove]

okay thank you hurray

it’s always just the opposite

so when autumn starts for you it’s spring here

march to may is autumn

june to august is winter

september to november is spring

they draw santa in speedos and everyone goes to the beach during christmas here

[trail void]

okay thats mad funny ngl

[zinc dove]

is it meant to be that much

is this how much people pay for textbooks

[remote sparrow]

no

i'm sure you can find a used copy that's sold at a much more affordable price though, or you can get it printed somehow

[trail void]

LOOKUP STEWART PRE CALCULUS

if U wanna buy 😭

[remote sparrow]

https://math.stackexchange.com/questions/3763425/is-basic-mathematics-by-serge-lang-rigorous

https://math.stackexchange.com/questions/3731176/rigorous-and-comprehensive-textbooks-on-precalculus/3731894#3731894

[pulsar veldt]

I guess Axler precalculus is a good one

[lean pagoda]

I'm not deeply familiar with the text but A Logical Approach to Discrete Math by Gries features this style of equational reasoning (edit: Sorry I should've read ahead, didn't see that you're already working with that text)

[pulsar veldt]

Proves every theorem (not calling it theorem), except two by what i remember.

Btw, I don't believe that overly rigorous textbooks are the best option for those starting to learn mathematics; they should focus on the didactic and learning.

[pulsar veldt]

No. It is an old book and Axler used many contents from this book on his precalculus book

Anyway you can always find great stuff for free

[molten gulch]

<@&268886789983436800> advertising distribution of pirated resources

[real marsh]

Hey so unfortunately we can't allow people to use this server as a platform to enable the distribution of pirated resources due to discord ToS @pseudo hill

[zinc dove]

you’re evil

[zinc dove]

what does that mean

[molten gulch]

How so? Any pirated resources on this server at all could mean discord makes an example of this place and shuts it down, according to mods it's happened before

[fallow cypress]

Solution is we move off Discord to a random IRC server

[remote knoll]

Don't discourage mod pinging. If the mod ping is inappropriate we'll say so.

My personal stance is that pirating textbooks is good, actually. But the stance we have to enforce on this server is that it is not allowed. Because if we don't the server could be shut down or forcibly removed from the current mods and owner.

[gray gazelle]

Lmao what the , forcibly removed from the current mods and owner?

Who takes control of it

If that happens

[hushed gazelle]

Has anyone happened to read Fomenko's Homotopic Topology book? I'm an undergrad and wondering what background I should read if I'm interested in the subject

[sacred goblet]

Harry Potter is good

[molten gulch]

Discord itself

[pulsar veldt]

Proving something and not calling it theorem, but a "result"

[trail void]

what if its just an pdf and not pirated?

how do yk its pirated

Like posting a pdf cannot be piracy, right? maybe sending to a link?

[mellow wren]

This is probably a subtle point but I think it's likely to be deleted unless it can be verified as non pirated

Like the issue is that discord can't say plausible deniability for hosting pirated shit on their website because they can get sued lol

[ashen flax]

its probably best to assume that if it Could be considered pirated it is to be considered so

[mellow wren]

There's some shit about this in the DMCA probably but I'm not too familiar with copyright law

[trail void]

im gonna go find discord tos rule on it and find loops around it so they cant ban me lol

[molten gulch]

Well if you find loopholes, I will report them.

[trail void]

i think u misread me

i dont mean im gonna do it

[hushed vector]

Ryan

[hushed vector]

sounds like a plan

but we need to build a distributed messaging app with functionality like discord but security like signal

Preferably in haskell or rust

[trail void]

i understand rust but why haskell dear friend?

[hushed vector]

because i said so
yk wha, forget rust

haskell supremacy

[trail void]

do it in arms

[hushed vector]

[because i like haskell and think imperative programming should not be encouraged]

[hushed vector]

(or we could move to matrix. but it isn't exactly decentralized)

and idk that much about its encryption sheme

[trail void]

i think signal is okay but its just not very well optimized

[hushed vector]

signal doesn't exactly have the convenience of discord lol

[trail void]

pretty much yes

but discord has pretty much turned against its userbase

[molten gulch]

I think convenience is a problem lmao

The harder it is to set up, the better

[hushed vector]

for whom is it better???

i tried to set up wireguard on my droplet for THREE days 😭

and because i don't know networking, i couldn't debug what went wrong 😭

(specifically DNS didn't go thru)

so i just gave up 😭

[fallow cypress]

Sharing a pdf of material you don't have permission to distribute is pirating

The copyright holder has the exclusive right to distribute, reproduce, etc. the material

[fluid violet]

K nerd

I don't know what probability has to do with anything here but go off

I only share cdfs anyway

[bright epoch]

does anyone know of a really good graduate level text on monte carlo methods

[hushed vector]

and who is the copyright owner?
that's right, the publisher

[fair fiber]

True sigma algebras know that pdf is equivalent to cdf

[fallow cypress]

Yeah but the copyright holder decides the license

[molten gulch]

The copyright holder is commonly the publisher as many authors give away their rights to the publisher during the publishing process and the publisher will almost always pick the most restrictive terms possible as that's the most profitable to them

[heady ember]

Self publishing ftw

[remote knoll]

Generally, it's obvious, if it's not obvious then we'll figure it out, if we can't figure it out, then probably not something that Discord would be able to figure out either.

The important thing is that the mod team makes a good faith effort

[glacial haven]

Does anyone have a pdf on like all of algebra? Like basic equations to abstract algebra

[molten gulch]

Doesn't exist, read openstax or lang's basic mathematics or something, then read artin's algebra for abs alg or something

[glacial haven]

yeah it's a specific request lol. I'll check those out though ty

[violet shuttle]

try reading literally all of the arxiv?

[glacial haven]

I honestly wouldn’t have asked if I knew what that was

[jolly dawn]

Marcel Berger's influential text "Geometry Revealed - A Jacob's ladder to modern higher geometry" seems very interesting as a survey in classical geometrical problems. I've looked through the book but idk what the prereqs are... any help would be appreciated 🙂

[hybrid sigil]

Danny Yee was also quite excited about it and put it n his “best books” section, here is the review: https://dannyreviews.com/h/Geometry_Revealed.html

[clever cypress]

any beginner friendly book recommendations for mathematical induction or number theory?

[tepid phoenix]

Can anyone recommend me any mathematics books on equation based

I am in 9th grade

I want learn the physics and qm equations

[pure grove]

wa hell nah

[pure grove]

maybe books are not the best to learn phsyics and quantum mechanics, even textbooks arent usually the best way to learn these things for most people

just look up study resources aand/or videos thats what i do and it works for me

[tepid phoenix]

[pure grove]

if you can find lectures from very good professors its best

[tepid phoenix]

[violet shuttle]

I mean, I know that people often say they can't learn so well from textbooks, and I believe them. But I have no clue what their problem is. To me... it's just... read??

[lean badge]

how do people learn from videos!

[cunning elk]

expect the knowledge to passively enter them via osmosis

[fair fiber]

expect elrichardo to teach me fr

[cunning elk]

me

teach

?

😭

i just flubbed an interview last week where i was supposed to do that

[hybrid sigil]

Mathematical induction is just one thing basically, not sure you need a whole book on that! Wikipedia article is quite readable: https://en.wikipedia.org/wiki/Mathematical_induction?wprov=sfti1

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

This quote from “Concrete Mathematics” summarises it quite well, and I always keep this in mind when thinking about mathematical induction

[pastel lodge]

Is there a book on how to write logix and arguments as math?

[gray gazelle]

sounds like

what proof/logic books

do

[fading bough]

I need a good book for 3rd year electrical engineering with lots of equations

[molten gulch]

Hammack book of proof, there's some pure logic books somewhere in pins but those probably require some maths you don't know yet

[molten gulch]

This is very broad, but have you tried kreyszig's advanced engineering mathematics or maybe some mathematical methods texts physicists use?

[worn prism]

The link for the abstract algebra book does not work

[molten gulch]

Which one?

[worn prism]

https://math.jhu.edu/~iyengar/df.pdf

[tepid phoenix]

Fr

[molten gulch]

You don't! Videos are entertainment unless they're proper taped lectures and you're taking notes

[trail void]

i like those little autumn lectures oxford and harvard and mit gives

theyre usually so nice

[remote sparrow]

<@&268886789983436800>

[worn prism]

What was it

[worn prism]

Videos can be extremely informative if they are properly structured and dense. Though maybe just less efficient in most cases.

But things like debates and podcasts and discussions have very little educational value, except maybe referring you to other sources which you then read

Not everyone is good at reading

[sterile gyro]

Debates have alot of educational value

If you actively engage

[pastel lodge]

I know basic algebra lol, thats it indeed. thank you

[molten gulch]

Do you know analysis and topology?

[pastel lodge]

The very basics of both

I was searching for a book that explains how you write logical arguments in math slang

Just for fun

[leaden hearth]

how to prove it

[pastel lodge]

Yes

How to prove the argument right or wrong

[molten gulch]

No that's the name of a book

How to Prove it by Velleman

[worn prism]

lol

[warm sigil]

🐧

[whole karma]

What if you want to visualize a concept in mathematics, can videos be helpful for that ?

[worn prism]

Why aren’t there books for bilingual people

Have some parts in one language and other parts in another

[pastel lodge]

Lol

[hushed vector]

why reduce the target audience??

[worn prism]

It might help bilinguals to get a richer understanding of the topic

[hushed vector]

wha-

[hushed vector]

ic
yet another troll

[lean badge]

might be useful for LLMs maybe?

[worn prism]

What?

[worn prism]

Oh yea

[timber mountain]

can someone find me a book for beginners at linear algebra

[clever cypress]

thats a beautiful quote thanks!

[molten gulch]

Friedberg insel and spence

[timber mountain]

thank

[gray gazelle]

why

not axler

[silk dew]

book

[vital bane]

FIS >>

[gray gazelle]

🗿

[daring wolf]

FISH???? real

[snow shuttle]

w

[fair fiber]

No it was fist

[austere cloak]

I recommend a good book I read recently, it's called: " Out of the Dust " ! It was written by: Karen Hesse.. -Ford

[austere cloak]

Its about an Teenager that is living in the Dust-Bowl in Oklahoma -Ford

In the 1930s -Ford

[fair fiber]

No math? Hell no

[austere cloak]

Oh.. I apologize. -Ford

[fair fiber]

Who is ford

[fair fiber]

And i was kidding

[austere cloak]

My name is Stanford, but I go by Ford.

We are an System, I am signing off as my alter signoff. -Ford

[fair fiber]

Bro is at stanford university

[fair fiber]

Wdym ?

[austere cloak]

A " System " is someone with DiD ( Dissociative identity Disorder ) -Ford

An " Alter " is an separate identity that the " Host " has. -Ford

DiD is what used to be called multiple personalities -Ford *

[fair fiber]

I see

Cool

[austere cloak]

I am an Alter based off of " Stanford Pines " from Gravity Falls -Ford

[fair fiber]

Are you the no 1 alter

Who is rank no 1

[austere cloak]

What does this mean and also I don't think it works like that. -Ford

[austere cloak]

It's a very emotional and very interesting read / story. I also would recommend the book: Guinness world records of 2025! -Ford

[molten gulch]

👀 another system :o

[austere cloak]

Yes! -Ford

Hello 🙂 -Ford

[molten gulch]

Hoi! -James

[trail void]

that is not the responsibility of the author, it is the responsibility of your state

to translate works properly and distribute them

or atleast allow private companies to do it for you instead

[broken badger]

I liked arithmetic by paul lockhart

[fading bough]

No, thanks

[cerulean sigil]

What advanced undergrad/beginner grad level books would ya'll recommend for math stats? Maybe from a more pure-oriented angle.

[fair fiber]

my professors book fr

a concise introduction to mathematical statistics

[foggy quest]

https://sites.math.duke.edu/~rtd/PTE/pte.html for probability

[cerulean sigil]

This is exactly the kind of thing I was looking for! 😍

[remote sparrow]

https://link.springer.com/book/10.1007/b97553

https://link.springer.com/book/10.1007/978-0-387-93839-4

[velvet flax]

is the eguchi-gilkey-hanson review a good-enough coverage of diff geo for physics

(if it helps, i only need enough to comfortable get through "intro to mechanics and symmetry" by marsden+ratiu

[naive lava]

Yeah it's good enough for most stuff

Although i don't think it has symplectic geometry which is what you want for mechanics

Maybe for that you can check our Arnolds appendicies

Okay i checked the book out

İt seems like it covers much of the math prerequisites there too

And i don't know your end goal but if it's just classical mechanics, bundles, connections, characteristics classes are a massive overkill

[keen canopy]

hi, any recommendation for numerical analysis ?

who gives intuition on ideas

[cunning elk]

not ascher/greif

suffering through that rn

[shell marsh]

does someone have this book

[primal pike]

Elemantary algebra by HS Hall and SR Knight

and also Higher algebra by Hall and Knight

[gray gazelle]

burden is solid

using it right now

[keen canopy]

🍯

[native cradle]

is real analysis via seqeunces and series a good read?

[molten gulch]

author?

[native cradle]

Charles H.C. Little

[open niche]

Any books for pre-uni?

[near jewel]

What level are you at? In other words, what are you learning at school?

[open niche]

Rn Im in 10th grade, Next we gon have trigonometry in maths. But I already can do Most, so any book suggestion would be fine

[near jewel]

If you're familiar with algebra (solving multiple equations), trigonometry, limits, derivate (the relations between the derivates and original function), then I think you could actually just dive into calculus.

[near jewel]

Is 10th grade the second grade in high school for you (total of 3 or 4?)?

[open niche]

2nd year highschool

Would have been 3rd but got nerfed by my health

[near jewel]

If you cover all of this, then I think you could just start with a calculus book. And also, if you're not going to study STEM related subjects, then you should focus on your current schedule and do math later as a hobby.

[open niche]

I wanna study EE later on, maybe Ill change the major, maybee

[open niche]

Do you still have some suggestions for those? Just to have it

[near jewel]

Spivak's calculus and Thomas's calculus are two calculus books that people like to recommend. If there's a specific EE at a university that you currently aim, you can take a look at their program and see what book they use.

[near jewel]

For EE, I recommend doing electronics now instead of math, so you can build up the interest and check if you really think this is something you want to do.

[open niche]

Ill check them out, thank you. In my area I have a uni but I think this more like civil engineering, sadly🥹

[open niche]

Alrighttt, thank you man. Great help

[trail void]

Ron Larson for Trigonometry,

goated book

[lost arch]

is there a book that contains only the results of linear algebra (with proofs)?
not a study book, but more like an encyclopedia?

[molten gulch]

There's Hogben's Handbook of Linear Algebra

which is just 2000 pages of results

oh wait but it doesn't have many proofs

just facts

[lost arch]

it's fine

thank you!

[fair fiber]

is there a good mathematical stats book ?

introductory, not requiring measure theory but not too applied either and one that nicely lays out definitions and structure

i've covered most of the first 4 chaps in Evans Rosenthal

[languid lotus]

For the Putnam and beyond book is there any pre requisites expected? If so what? Im taking linear algebra and took an ode class just curious if I should know more

[molten gulch]

Check the preface

[gray oracle]

if you really wanna challenge yourself, pick up either apostol or spivak

[gray oracle]

i'm curious if there's anything like this but updated aside from pins:
https://mathematics.gg/books

[molten gulch]

Not that I am explicitly aware of

[gray oracle]

aw rip

i'm surprised neither apostol or spivak is here:
https://mathematics.gg/books/calculus

[molten gulch]

That page hasn't been updated in a while to my knowledge

[gray oracle]

yeah 2022

[gray oracle]

@sage python revive this /s /hj

[shrewd dawn]

Does anyone have book recommendations

[gray oracle]

for what?

[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!

[shrewd dawn]

For reading

[gray oracle]

what

[shrewd dawn]

Stories

[gray oracle]

uh 🥀

Tends to be mostly math but feel free to ask about other literature (YMMV).

[shrewd dawn]

Tf are these responses gng

[gray oracle]

idk read james joyce

finnegans wake

ulysses

[shrewd dawn]

Like tf does it mean by “just ask your question” ? Ts is actually trying to rage bait

[gray oracle]

you didn't specify what you want to read about tho

[shrewd dawn]

I mean how can a bot try to rage bait

[shrewd dawn]

Oh yea u are right my bad

😂😭😇

Nah bot was trying to rage bait fr

[gray oracle]

i gave you book recs lol

try reading them

[shrewd dawn]

I saw

I’m looking them up 👀

[molten gulch]

You don't just ask for someone to give you resources, you should be specifying the domain in which the resources are to be provided

[shrewd dawn]

For real bro 😎

[remote sparrow]

casella and berger

[remote sparrow]

i guess bickel and doksum too

[sharp nest]

Hello

Here for some books recommendations

For stats and calculate and linear algebra

Calculas*

[native cradle]

proof based?

LADR4e for LA

Spivak for calc

[sharp nest]

Well for newbies

[pale geode]

I need a free material, not necessarily a book, to introduce me into Answer Set Programming.

[vital bane]

Peak username bro

[lean badge]

@gray gazelle
im not veryyy into art history—i study literature! but a few titles come up about fashion, literature and music

Quentin Bell's On Human Finery—not quite a chronological account, but i think it provides interesting cultural and sociological perspectives on dress as art and a social language; i think it makes for a good companion to more historical surveys like Laver's Costume and Fashion

The Norton Anthology to World Literature is a more canonical text covering a very vast time period (past 2000 years iirc), with pretty good intros to literary movements within their time (cultural, philosophical influences)
The Western Canon by Harold Bloom is much more controversial: he argues against feminist literary criticism, semiotics, Lacanian psychoanalysis and deconstruction (all of which i love!)—exclusions are quite telling, but i think it's a good exposition for aesthetics in lit
The Romantic Agony by Mario Praz—amazing analysis of erotic sensibility!!! this is very focused on the late 18th to 19th centuries, but i think more broadly it's quite incisive in how Romanticism influenced modernism

Music and Cultural Theory by John Shepard and Peter Wicke—it examines cultural musicology from ethnomusicology, neuroscience, structuralist theories and some semiotics, aiming to integrate musicology with cultural theory (as the name suggests) by showing how each informs the other. i think this is a great theoretical map of how to think about music as a cultural system if you're looking to make connections between disciplines
The Cultural Study of Music—ethnomusicology, a bit more academic, but it covers how music interacts w society, tech, ideology and culture! (actually i think this is less dense than Music and Cultural Theory)

[gray gazelle]

I’ll try to get The Norton Anthology

[gray gazelle]

Ts too funny

[brazen grove]

i am unable to choosethe right linear algebra book.... i considered linear algebra done right VS hoffman and kunze... can someone help please ??... i kinda of know the computational linear algebra in my physics courses as in how to work with matrices with numbers and i have intuition of linear transformation from 3b1b vids.... but what i lack is proof based approach that connects the general properties of linearity in various things i study in physics like linear differential equations, linear operators, and complex number treated as vector space element rather than a field, etc... i will also be learning complex analysis and multivariable analysis after linear algebra.. so something that helps that too...

[hybrid sigil]

why can't you just start with LADR, read a chapter or two and see if you like it or not? (after all it's a free book in Open Access)

you don't have to read a perfect book, a good book should be enough (and very likely there is no single perfect book)

then, if you like it, keep reading it. If not, start considering Hoffman and Kunze, read a chapter or two. How is that as an algorithm? 🙂

[brazen grove]

cuz i am wondering if there is some hidden gem out there out of many unknown linear algebra books

[hybrid sigil]

I think it's better to start reading some books and then eventually make your own mind about which ones you like and which you don't (and what is a gem and what is rubbish) - rather than agonise too long over which book to choose. LADR and H&K are both good books, recommended by many people, and your own considerations too, so you can't go wrong with them. There is also FIS and Linear Algebra Done Wrong (also free) if you want more...

[daring wolf]

just open any book and do it

[near jewel]

Requirement/practice is prioritized than theory. You should focus on problem solving, if you counter something you don't know, learn it, not that you learned something then you specifically do the problems.

[trail hemlock]

for ah the canonical intro at my school seems to be gardeners art through the ages.

[lean badge]

i'll read it!!!

[remote sparrow]

oh i had that assigned as my textbook for ap art history a long time ago

[trail hemlock]

its awesome i really liked it

[lean badge]

(im not familiar w art history in a general sense ahaha)

[trail hemlock]

for ap art history we used smart history which was peak

but with readings out of gardners

[remote sparrow]

we also got shown some vids from khan academy

https://www.khanacademy.org/humanities/art-history

[trail hemlock]

yeah that’s what those are

smarthistory makes the khan academy vids

[remote sparrow]

i had no idea

[shrewd dawn]

Should I take AP art history

[wind oasis]

Bro, everyone should read 'Infinite Powers' - this book is responsilbe for making me LOVE calculus

[trail hemlock]

if u want to yes

[foggy quest]

https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ is good, but most linear algebra books are pretty much the same

[trail void]

name of author?

[gray oracle]

steven strogratz

it's more of a history book than something that teaches you calculus

[languid lotus]

Any book recommendations for the Putnam test or other math competition

[trail void]

i like history dw

[gray oracle]

anything by art of problem solving (aops) is good for amc and the like

[trail void]

im pretty sure they stop at calculus tho

also arent they supplementary

rather than primary for learning

[gray oracle]

they don't have calculus yeah