book-recommendations

[odd cargo]

ive lowkey been getting paranoid at the possible fact that any type of impact to my head would immediately make me less capable of doing maths.

well its like 12 am right now and im having 12 am thoughts, but thanks for the input

huh

honestly, euler was a demon for being able to do maths even AFTER going blind

[wary nacelle]

What book should I read on graph theory? I know the basic concepts (vertices, edges, walks, cycles,...), some theorems (Mantel, Turan, Hall,...) and the representation of them as matrixes (adjacency, laplace, Markov,...). I want to get a deeper understanding though, most of my knowledge right now is just mostly memorization, I have trouble using them to solve problems

[mortal iris]

Bondy and Murty's Graph Theory (not Graph Theory with Applications).

[wary nacelle]

Thanks y'all

[mellow topaz]

I took a look at the Princeton book. I'm curious, have you read any other books from the "In a Nutshell" series?

[mortal iris]

Yeah. I've seen a few. Not in detail and for long. They're very handwavy when it comes to the math.

[marsh spade]

I really recommend how to kill a mockingbird

[mortal iris]

Back to trolling eh?

[cunning elk]

how about to revive a mockingbird

[mortal iris]

https://tenor.com/view/dragon-balls-dragon-ball-daima-dbz-dragonball-anime-gif-3850681190231257168

[gray gazelle]

No Such Thing as Perfect by Misako Rocks

[dapper root]

Hi Teto

[vital bane]

or more capable

[glossy pier]

Best algebra books for ermm algebra n stuff?

Like everything

Or books to self teach from algebra all the way to topology and all that jazz?

[harsh pagoda]

By algebra do you mean high school algebra or abstract algebra?

[glossy pier]

Both

[harsh pagoda]

Try Serge Lang's basic maths

It covers a good portion of high school maths not any abstract algebra though.

[glossy pier]

Bet thx

Im reading an algebra book rn its pretty basic but its my starting point

[harsh pagoda]

Yeah don't jump into uni maths make your fundamentals strong first

[mortal iris]

Hall and Knight's Higher Algebra for Elementary Algebra and more. Hold off until you're done with Precalculus before jumping as far as Topology. There's a ton of stuff in between the two.

[proper trout]

Can you recommend a precalc book or set of books that have full (possibly more in depth) coverage of elementary mathematics? I've seen your remark about Lang's basic mathematics not going too deep in some parts

[mortal iris]

Axler's Precalculus book is pretty good. A free alternative is Stitz and Zeager. Use Lang as supplementary reading if you will.

Alternatively you can pick up Loney's Plane Trigonometry and Elements of Coordinate Geometry along with Hall and Knight's Higher Algebra.

If you want rigorous options, then Dolciani's Modern Introductory Analysis or Daniel Kim's Advanced Precalculus are good bets.

[proper trout]

err

[sleek wigeon]

Good intro book?

[remote knoll]

That particular book is in the public domain, jfyi

You can just download a copy of it from project Gutenberg and see for yourself

https://gutenberg.org/files/41568/41568-pdf.pdf

That being said, an intro book for what, exactly?

[sleek wigeon]

"Mathematics," seemingly

[dapper root]

Jesus Christ if it’s public domain you need a more modern book lol

World domination.

That one’s reserved for my bedroom

[sleek wigeon]

I'm not really too interested in math past its (most general) use in contemporary modeling, analytic philosophy, and its life in humanities and posthumanities

Does it engage with the history of mathematics thoroughly?

And past just plainly laid out ideas in the history of mathematics for that matter?

The style of doing phil in undergrad is very apart from textbooks, as typically we read areas of disagreement instead of the large consensus of agreement, so I'm not much used to them

If there is a better one, and certainly a more contemporary one for that than Whitehead (though I'm sure he's great), then please do send it my way

I can imagine that, sounds like a plagued application if you aren't seriously rigorous

Actually I wonder how good this book from our department library is, if anyone is familiar with Kline?

Sounds good!

[odd cargo]

theres a dude out there who plays in the nfl who also has a phd in maths

its fascinating how the brain works lmao

[glossy pier]

Yeah my goal is to learn basically all of algebra calculus and then go onto analysis linear algebra topology etc etc

Or idk what a good roadmap would be to learn it all

[signal zenith]

Used to play in the NFL, and he’s a prof at MIT now iirc

He’s in combinatorics

Goat behavior

[ember lark]

This is a good book btw I recommend.

[wicked fractal]

Depressing title

[odd cargo]

bro secured his cognitive decline

[odd cargo]

push me to the edge

[signal zenith]

Idk, he’s way smarter than I’ll ever be

I think it’s fine to make general statements like professional football is bad for the brain but I would hesitate (and it seems a bit condescending/arrogant) to specialize it to a specific person who in this case is clearly very intelligent and accomplished

[odd cargo]

people are so up their own ass that they think "contact sports is bad for the brain" is a general statement and not an actual fact

i can guarantee, with 100% certainty that he has brain damage, and im even more convinced of this after confirming he was in the nfl.

[humble spire]

He deadass said that the reason he quit the nfl was to stop his brain from getting more damaged 😭

[odd cargo]

i just think its interesting, atleast in his case, how that brain damage manifested itself phenotypically

[signal zenith]

Bruh

This is just a very weird way to be talking abt a professor of math at MIT

Surely this guy has messed up phenotypes and is going to be dumb in the future like wtf are you saying bro

[odd cargo]

huh?

[humble spire]

What does being a professor have to do with cte?

Gng 😭

[signal zenith]

I don’t think you should speculate about the future mental decline of a specific real person who is almost surely smarter than both of you.

[mighty lava]

Could anyone recommend either books or courses for linear algebra? I dont want just surface level knowledge but deep understanding of the topic. I have gilbert strang's book on linear algebra and applications but its in greek and id prefer soemthing in english. Should i get the same thing or soemthing else or maybe just an online course?

[humble spire]

Gng ur like maliciously reading what i said. All i said is that the man himself said that he quit the nfl over fears of brain damage.

🥀

[odd cargo]

dont even engage

[signal zenith]

Yes, I don’t disagree with any of this. Cog explicitly said “he’s secured his cognitive decline.”

Obviously Cte is real. It’s toxic to speculate about the cognitive capabilities of a specific person.

[odd cargo]

Axlers book is free and in english

[signal zenith]

Especially when that person is smarter than both of you.

[humble spire]

Oh kk lol

[mighty lava]

Does it teach eveything from scratch?

[odd cargo]

you dont know what brain damage is

[signal zenith]

Ok man. Big smart guy talking shit anonymously on a discord server

Seriously

[odd cargo]

you'd need to supplement with an elementary linear algebra book

[mighty lava]

Such as?

[odd cargo]

find whichever one

[molten gulch]

Just use friedberg insel and spence's book

[odd cargo]

reply to him, not me

[tame tree]

no

[vital bane]

Instead you should speculate about the past mental decline of a specific real person (me) who is definitely surely dumber than both of you

[ember lark]

Linear algebra done right

Or fis

[ember lark]

Preferably this one

[ember lark]

No you dont

[ember lark]

Yes it does

If you would like to learn more about determinants then you'd need a reference but it starts from the ground up

[tame tree]

gaussian elimination bruv

computing inverses

[ember lark]

It teaches everything in the book from scratch

[tame tree]

like every concrete tool

[ember lark]

It does not assume previous linear algebra knowledge

Etc.

[tame tree]

i get you like axler but its objectively not a good place to start

[ember lark]

You misunderstood the question

It teaches everything from scratch

[tame tree]

i mean its obvious that theyre asking about “everything” in a typical intro course but ok

[ember lark]

No not really, I interpreted the question as "does it assume no prior knowledge," to which the answer is yes

[mighty lava]

I only know about very introductory things and maybe a little about vectors so I’ll check reviews on each of the books I was recommended and I’ll choose one. Thank you!!

[ember lark]

Many, many universities disagree with you BTW. I don't know how you got "objective"

[molten gulch]

If FIS did some proper multilinear (and maaaaybe cleaned up a few proofs) instead of leaving it to a tiny bit after the determinants chapter I'd never even think about using something else

[tame tree]

because classes have handouts and lectures

[shut geode]

many universities disagree with you as well!

[odd cargo]

you're welcome to do what ever you like man

[proper trout]

What's the prerequisites of Daniel kim's? Ive already done Lang's Basic mathematics. Looks like a good follow up

[ember lark]

I'm aware, ive already completed linear algebra. From my first-hand experience with ladr you don't need to know any prerequisite material in linalg to be able to read the book well; it's disingenuous to say you do, because axler writes explicitly that you don't

This book starts from the beginning of the subject, assuming no knowledge
of linear algebra

[ember lark]

Right, well, I'm still not sure where you got "objective" from, considering the abundance of people who have used ladr as their first read of linalg and liked it

[signal zenith]

Plus, classes using other books isn’t proof they think LADR is bad

It just means they like other books more

[ember lark]

This is still tangential to the question of whether or not ladr starts from scratch, which he does

[lost arch]

is LADR missing something a typical intro course would teach?

[ember lark]

It doesn't cover gaussian elimination

[rain nova]

I've realised that the best way to learn linear algebra is to learn functional analysis. Trial by fire as they say

[ember lark]

Ladr is pretty functional analysis pilled

[signal zenith]

Axler is an analyst isn’t he

[ember lark]

Not sure but he has a measure theory book and has done stuff with harmonic analysis last I checked

[tame tree]

imo a first course should always tie back to and emphasize concrete computations

[mortal iris]

Effectively no prerequisites then.

[signal zenith]

I think LADR is kinda designed for a lot of american systems where it's expected that a proof based class is the second linear algebra class you take after having already done one with a lot of computations

[tame tree]

axler does not adequately cover all the stuff about solving systems of equations, computing inverses, taking det, change of basis, etc that any good student of linear algebra should be able to do

[tame tree]

yes, which is why i personally would not recommend it as a first read on the topic

[signal zenith]

yeah fair

[tame tree]

FIS marries computation + theory in a more wholesome way

LADW too

[mortal iris]

Aye. A first course needn't be completely non-abstract considering that the basic idea behind Euclidean vectors and Linear equations are typically introduced in high schools. It can and should include the abstractions and computations both.

[tame tree]

ideally people even also take like a class in highschool that does coordinate geometry like in the A level curriculum

[vital bane]

I like FIS and Hoffman and Kunze better than Axler

Axler is a nice book but not for a first exposure to the subject imo. For that Hoffman or FIS is more suited

It's like a fun book you can check out after you've learned LA

But I used it as a first course

I still can't do proper computations 🥀

[tame tree]

my use case for axler was as a supplement/second read for my linear algebra class

[mortal iris]

Don't get me wrong, there's stuff to like about Axler, but idk. It's got a very "Bro, you should do this because it's beautiful!" vibe lol.

[signal zenith]

I don't dislike Axler but I don't love it (to be honest, my view is that textbook doesn't matter too much for the core basic subjects; maybe at first, but you'll see them again and again so many times that eventually which way you see them first doesn't really matter)

[tame tree]

yea pretty much

[vital bane]

It has an agenda (it's too analyst pilled)

and I love analysis

[tame tree]

tbh it does have a very annoying “exercises that make you do stuff that the book develops in a subsequent chapter” thing going on

[vital bane]

3rd edition is actually bad imo (regarding the lack of treatment of determinants), 4th edition seems better

[vital bane]

I don't find that annoying actually, it's a nice thing that D&F also does. If I get multiple exposure to a certain thing, it makes it easier to understand

[signal zenith]

4th edition has a multilinear algebra chapter right

[vital bane]

ye ye

[mortal iris]

Not by much. You can literally read the reluctance of his covering determinants lol

[vital bane]

I regret using Axler as my first LA book, should've gone with HK my goat

[lost arch]

Kostrikin & Manin enjoyers here? anyone??

[tender cobalt]

ladw is goated

[night prism]

LADR- LAundry done right

[mortal iris]

Los Angeles Done Right*

https://tenor.com/view/trump-donald-trump-thumbs-up-good-yes-gif-13303990716584415679

[night prism]

🙌🥳

[ember lark]

based

[ruby star]

any good books for learning fortran?

[molten gulch]

Tbh I don't mind when books are authors introducing a topic because they find it interesting, sometimes it leaks through and is infectious however I found axler's writing style to be my least favourite part of his book...and some of his notation

[mortal iris]

Not the topic introductions themselves, but the approach he tends to take. That's where my criticism lies.

[molten gulch]

I do not like his approach much either

[narrow gull]

LADR: Linear Algebra Done Rong

LADW: Linear Algebra Done Write

[midnight thunder]

i think munkres point set Topology first chapter is decent, I'm not sure why someone would want to read an entire book on naive set theory

[night prism]

I think Halmos is the standard rec for that; I once found an exercise book to accompany it at the library, but forgot the name

Actually yeah, star makes a good point; intro chapters in many algebra or analysis texts may be enough?

[midnight thunder]

yeah

try to check out munkres or maybe some other books like dummit and foote for these basics

[steep garden]

alr alr thanks a lot both of you 😃

[sage python]

It also doesn't do enough analysis

[heady wren]

Prefaces, summaries and introductions are the best parts of math books

[mortal iris]

Halmos's Naïve Set Theory.

[shut flare]

mmm

I dont know my level on mathematics

[mortal iris]

Wtf is that username lol

[shut flare]

ignore

[mortal iris]

Another option dedicated to problems is this. Covers a lot of ground.

[steep garden]

oh thanks for that ‼️

[mortal iris]

Can also add the first chapter of Hammack's Book of Proof.

[full pike]

Oh, I see

XD

[heady wren]

🤣

there he is, the dude

[full pike]

😂

[heady wren]

man o' probabilities, with his atomic dice

ready to wage nuclear destruction on it

@full pike get the damn math discussion role, dude

The crime should be paying this much

[visual delta]

I've already read through completely another analysis book, but it might be needed for a class.

I think "International version" includes the US anyway.

Okay.

[mortal iris]

Bruh why lol

[gray gazelle]

Hi! What kind of math books or what math foundations must be strong for rf engineering?

[ruby star]

real analysis course i'm planning on taking still uses it lol

they aren't updating the curriculum to python til next year

[mortal iris]

Real Analysis using Fortran? Wtf?

[ruby star]

oh wait sorry numerical

[mortal iris]

Aah

Julia is the new Fortran by all counts lol. They should really switch smh.

Fortran use is very niche today.

[ruby star]

yeah i’m aware

but i hear it’s fast enough

[mortal iris]

So do you need a book for Fortran or Numerical Analysis or both?

[mortal iris]

So is Julia and is far more readable and has a lot more functionality too.

[ruby star]

fortran currently, i haven’t started numerical analysis as of yet

[ruby star]

oh i’m sure, i’m planning on learning julia in the near future but apparently i have to sidequest fortran first 😅

[mortal iris]

Fortran For Scientists & Engineers is your best bet imo

Yeah this was gonna be my rec if @ruby star asked for the numerical analysis stuff. That said, the theory for the basics are better covered in FNC.

That's true with any programming language.

Bruh. It's for a course. I doubt anyone wants to do anything with Fortran unless it's about cloning legacy code.

Aah. I highly doubt a course on numerical analysis would go that far tbf.

They're neither too deep into programming nor too deep into analysis.

Unless it's a graduate level theory course lol

Aye. I was just wondering ggs

[ruby star]

ooh alright, thanks!

i was going to ask them next week but i wanted to get a little bit of an overview first

[mortal iris]

Aye but a typical numerical analysis course wouldn't even go into LAPACK or BLAS or similar stuff besides using the libraries afaik.

That's my experience of having been through a similar side quest. Worst choice to stick with that course lol.

[frigid pollen]

Hi! Do you know any good books(Or a series.)focusing on undergraduate/bachelors' maths?(Pure, preferably deeper than what I need for Computers/Physics but still on that level.) Thank you!
(It needs to be free, or on Kindle Unlimited.

[mortal iris]

Everything is free if you know how xD

[mortal iris]

Also the things you need for CS or Physics can be pretty different. Physicists don't do much discrete math. CS ppl don't do much geometry. Emphasis on much. This is the undergrad context ofc.

[mellow topaz]

https://tenor.com/view/giftok-a-quiet-place-shushing-shaking-head-john-krasinski-gif-5875589853894697240

[mortal iris]

https://tenor.com/view/witch-wandavision-magic-power-scarlet-witch-gif-22433186

[mortal iris]

Last two sentences.

[vital bane]

This is true actually, learning analysis from Axler's LADR is very difficult

[median fossil]

But not much harder than learning LA

[jolly dawn]

The preface to Axler LADR says it's for a second course. Why did you use it for a first course?

[vital bane]

Because what the book considers a first course and what I consider a first course are different

The contents in Axler is elementary linear algebra first year UG stuff

[jolly dawn]

damn, some people are just built different

[vital bane]

similar to FIS and Hoffman and Kunze

[vital bane]

but these are much better

[jolly dawn]

I'm using Artin for a more abstract treatment of linear algebra, but it still doesn't cover a few things like dual spaces orthogonal complements, and generalized eigenspaces... I actually need 3 courses on LA

[mortal iris]

Depending on where you are from, you may have seen Euclidean vectors, systems of linear equations and matrices in quite some detail in high school. It makes no sense to have a redundant course covering all this with just some itty bitty extra stuff in first year undergrad if that was the case.

[vital bane]

The only thing you need is Hoffman and Kunze 🙏

[jolly dawn]

ahh I see

[vital bane]

It has abstract treatment + all that

[trail void]

hello where is the catboys department of mathematics

[jolly dawn]

well I madde decent progress already so might as well keep going

[vital bane]

https://tenor.com/view/felix-gif-20630474

[mortal iris]

https://tenor.com/view/crusch-re-zero-anime-nightgown-gif-24879337

[hoary ingot]

What is a good book to learn trigonometry?

[mortal iris]

Loney's Plane Trigonometry

[hoary ingot]

Thanks

[tulip lion]

Hi, can someone please suggest a good book for Group Theory problems. I want rigourous treatment problem that test my concepts fundamentally rather than computational problems. I did my theory for John B Fraleigh and found the problems to be rather meh and computational. I want theoretical problems since I am prepping for my end terms.

[mortal iris]

Herstein's Topics in Algebra is quite well known for its problems.

[tulip lion]

Thanks a lot <3

[tulip lion]

what do the # in the problems mean, I got what the stars mean through the prefacec

[mortal iris]

If you're looking for something even more challenging, you can take a look at Gorodentsev's Algebra 1.

[mortal iris]

I have no clue. It's been a few years since I used that book and only for problems. Ig you'll find out while solving one of them?

[molten gulch]

What numbers I assume they're just problem numberings?

[heavy idol]

the # means they were added in 2nd ed

[molten gulch]

Ah good to know!

[heavy idol]

and usually involve some basic matrix knowledge, which they dont assume in 1st ed

[torn blade]

where to find exercises on the following topics (analysis on Rn, no metric spaces/topology):

Compactness

Functions on compact sets

Differentiation on Rm to Rn

Higher order derivatives on Rn to Rm

Inverse and Implicit function theorems

[hasty sand]

you want exercises on compactness without any discussion of metric spaces, nor topology ?

that seems weird

[mortal iris]

This is by far the weirdest request I've seen here lol.

[torn blade]

there’s no way this is the weirdest

[merry sphinx]

spivak calculus on manifolds and munkres analysis on manifolds maybe, but idk about the no topology part

[torn blade]

tbh we did do topology in an earlier unit so its like it can contain topology stuff

[mortal iris]

Both definitely require some topology

[torn blade]

its just specifically focused on Rn now

i know topology

[mortal iris]

Then basically any multivariable real analysis book with such problems would do

[torn blade]

any specific reccs?

[mortal iris]

Zorich's Mathematical Analysis has what you're looking for, but for Compactness and Functions on compact sets there's a mix of general Topological Spaces and R^n in his books. See Volume 1 for the Calculus on R^n without getting into this territory. The general stuff is in Volume 2.

[fervent marten]

Does anyone suggest a book to learn about machine learning? I’m completely new to this.

And a good book about linear algebra for beginners

[mortal iris]

Practical or mathematically fine shizz?

[odd cargo]

Coming back to this cause i just re-read the preface and Axler himself states: "you are about to teach a course that will probably give students their SECOND exposure to linear algebra."

[ember lark]

note how it says "probably," while the statement about it building linear algebra from scratch is completely definite with no ambiguity

he does not assume you took a course in linalg already

[odd cargo]

im just curious where he states he assumes no knowledge of linear algebra, because those two statements are contradictory.

[ember lark]

but the nature of the text and public perception of pushing determinants to the end makes people see it more suitable for a second course

which is true

but it does not assume prior knowledge of linalg

[ember lark]

you can ctrl f what i quoted

and again, since i've read the book front to back, i can tell you that you do not need a prior course in linalg to read it without problems

they're not contradictory statements; a book can be (more) suitable for a second read while starting from scratch

[odd cargo]

considering how determinants come at the very end, it seems to me that it would be ideal to have taken a prior course

[ember lark]

and why is that?

the book is designed with axler knowing that he pushes determinants to the end

so none of the initial chapters use anything related to determinants

[odd cargo]

you dont think determinants are crucial in developing intuition?

[ember lark]

no? determinants are extremely unintuitive

it takes a lot of work to go from the traditional definition of a determinant to showing det(T) = 0 implies T is not injective, and people end up blackboxing it because of that

[odd cargo]

this doesnt make sense to me, ill just read FIS

[mortal iris]

That's probably cos you read Axler lol

[signal zenith]

Yes and no, determinants aren’t great on their own

[odd cargo]

also shilov is really good

[signal zenith]

Multilinear algebra is better

[mortal iris]

And on this note, they are, but I think what Axler is going for is attempting to avoid some of the cop out uses of determinants in constructing things related to linear transformations.

[signal zenith]

But tensors get confusing without some mathematical maturity so I’m sympathetic to axler POV

[ember lark]

i dont think one could reasonably produce a connection between the leibniz formula for the determinant to det(T) = 0 <=> T is not invertible on the spot

[jade kernel]

yall should read mushoku tensei

[ember lark]

meanwhile the theory of minimal polynomials and invariant subspaces are easier to think about

but, again, this is still just a strawman

the original person asked if ladr builds everything from scratch

to which the answer is yes, axler does not assume prior knowledge and explicitly says so in his preface

so i don't care for debates on whether or not axler is a suitable first-choice read

[mortal iris]

Hehe, although his determinant front and center approach is something that needs to be treaded with caution as well.

[mortal iris]

At the end of the day it's down to taste, but that's a weird attitude to have on pedagogy, just saying.

[ember lark]

i don't care about that debate right now because that's not what was asked lol

[mortal iris]

Aye. I should read about a pervy old man banging the shit out of kids in his new reincarnated body lol.

[odd cargo]

this might be L glaze right here

[ember lark]

everyone seems intent on injecting their own personal biases in their response to this, because the answer is objectively "yes," since axler himself confirms that he builds everything in his book from scratch (i.e., does not assume prior linalg knowledge)

[jade kernel]

Okay! I can't wait for your review on it

[mortal iris]

Nah. He's not wrong. It can be used for a first course and covers everything from scratch. Just that the way he does it is sus.

[ember lark]

right

[odd cargo]

he's highkey you with spivak

[mortal iris]

Buddy, I've read most of it. It gets a bit meh after the Orsted fight.

[jade kernel]

But the slice of life moments after orsted fight is so peak, and not to mention, the final battles

[ember lark]

my personal opinion is literally irrelevant to what was asked, i copy and pasted a quote from axler as my response. me liking ladr doesnt change the fact that ladr is built from scratch whether u like it or not

good day

[mortal iris]

You can't argue that Spivak is in any sense a bad book or a bad introduction to Calculus lol.

[tame tree]

the axler saga continues

[tame tree]

you know axler can just write whatever he wants in the book right

[mortal iris]

Chill buddy.

[odd cargo]

L glaze

[mortal iris]

I'll wait for your argument rather than the ragebait lol

[ember lark]

so you think he's lying...

[tame tree]

the fact that he writes that doesn't reflect the fact that most people would probably benefit from some more concrete stuff mixed in

[odd cargo]

im not arguing against it, i dont hate on spivak, i just dont like glazing

[tame tree]

idk i just dont see why youre so married to axler lol

[ember lark]

stop strawmanning, him building up linalg from scratch is completely irrelevant to whether or not it's suitable as a first read

[tame tree]

i mean you're the only one focused on that precise interpretation i believe

[odd cargo]

bro just move on

its all up to you if you want to use axler alone or not

me personally though

i would supplement everything

but thats just me

[ember lark]

you literally necroposted this conversation fyi

[mortal iris]

I ain't glazing. There are non-books per say that I'd rate above Spivak in terms of pedagogy. Though, Spivak's problems are still really well thought out imo. Pete Clark's notes are one. Heck, even mine are solid but they're for me. You can't just call a strong recommendation with reason a glaze lol.

[odd cargo]

i do have a habit of doing this so my bad

[ember lark]

Axlers book is free and in english
<Does it teach eveything from scratch?

what other interpretation is there besides "does ladr require prerequisite knowledge of linalg"

[tame tree]

you have to somewhat interpret things more charitably when answering questions posed by people looking to learn a subject for the first time

[mortal iris]

Usually the assumption is familiarity with planar and spatial euclidean vectors, systems of linear equations and matrix algebra.

[ember lark]

didn't he say he had some prior experience

[tame tree]

i missed that part

[mortal iris]

These are either high school material or first course material depending on where you are.

[ember lark]

never mind i might have hallucinated that

[odd cargo]

91 results is glaze

[tame tree]

when someone in the calculus channel asks "what's a good book", they're usually looking for something like stewart/thomas/larson and lots of time it would be unhelpful to steer them towards spivak or even a real analysis book

[mortal iris]

Huh

[surreal bay]

hello coming in2 ask
does anybody know any euclidean geo theory-based books that fit for olys / competitions in general

[ember lark]

axler does all of this besides systems of equations. i think his only blindspot is systems of equations/rref stuff

[tame tree]

which is a huge blindspot mind you

[odd cargo]

Coxeter has a good book but i dont know if it fits your definition of "competition"

geometry revisited

[ember lark]

fair enough

[surreal bay]

i mean

[ember lark]

but you both said "No" with no extra elaboration, while I said "yes" with elaboration on what i meant

[mortal iris]

On that front I pretty clearly ask them if this is their first exposure to Calculus. Where I come from, most ppl have seen Calculus in high school, at least single variable upto first order ODEs. So it's redundant to do all that all over again, poorly.

[odd cargo]

fyi i dont mind a spivak rec

[tame tree]

yeah, my example refers mainly to the people who just need something for like AP Calculus

[ember lark]

i think my response was fair /shrug

[odd cargo]

i dont think i ever said no

[surreal bay]

what would you define it as?
just so we’re in the same picture

[odd cargo]

im just arguing to argue

[tame tree]

sure, i don't think youre ultimately wrong at the end of the day, but the "everything" part there is slightly fudging things up

[odd cargo]

those olympiads do geometry dont they?

[surreal bay]

yes

[surreal bay]

for most yes

[odd cargo]

is that what you meant?

[surreal bay]

yes

[mortal iris]

Kinda one of the most helpful things to motivate linear structure.

[odd cargo]

try geometry revisited by coxeter, its pretty good.

[surreal bay]

what should i know before reading?
and is it ok to start from scratch w/ it?

[mortal iris]

EGMO for Olympiads.

Also Kiselev.

[surreal bay]

book 1?

[mortal iris]

The things not covered are a set of measure zero lol.

[surreal bay]

also what do you mean by EGMO?
because I’m thinking of the european math oly

[mortal iris]

Primarily 1. Some parts of 2 are also pretty useful to go through.

[mortal iris]

Did you try looking it up -_-

[surreal bay]

yes
i just got confused at the extra “for olympiads”

[mortal iris]

Literally what you asked for lol

[trail void]

European girls mathematical olympiads ofcourse

prepared to be womanized boyo

[mortal iris]

When it's 2026 and the young ones still use Google like boomers lol.

[trail void]

tech skills rely mostly on whether u learnt how to pirate or mod things as a teenager or not lol

[odd cargo]

dont brush off coxeter too quickly though, theres a lot of interesting info there

[mortal iris]

Honestly happening quite a bit these days with the rετarded gemini overview lol.

[trail void]

ughh i hate the forced ai feature

half of the time its just blatantly repeating reddit

i hopped on linux anyway it got me into needing programming

[mortal iris]

You can just add -ai at the end of your search prompt. This only works on browsers I think.

[trail void]

i think there is a feature to turn off the overview thingy its just that you have to turn it off everytime u use it

why are so many highschoolers getting into olympiads

oh yes i think it works for university applications well

[mortal iris]

Doesn't seem to work anymore

[ember lark]

[tame tree]

gemini is so dumb that i feel bad for it

[merry sphinx]

bros ai is cooked

[ember lark]

it pulled from reddit instead of mse so perhaps that's why

[surreal bay]

yes ofc
just not sure of what you have 2 know beforehand
& should i cover both books?

[sacred thicket]

pro tip add swear words. it scares the ai

[ember lark]

Truthnuke

[surreal bay]

[surreal bay]

longshot away from the EGMO sadly

[odd cargo]

sure

i dont think theres really anything you need to know before starting kiselev

[surreal bay]

i mean for coxeter

[odd cargo]

coxeter can be used to supplement kiselev

just make sure youre reading the right coxeter material

again, Geometry Revisited, and not Introduction to Geometry

the latter will probably do things to your blood pressure

[surreal bay]

you’re right/i just saw what’s covered in the ladder

[surreal bay]

are there some things that coxeter covers that kiselev doesn’t?

• with everything in mind i’m defo seeing the two today

[odd cargo]

id say a third of coxeters book is really just deriving theorems and applying them

shit you should probably know if you're doing competitive stuff

Kiselev probably flies over a lot of them

but kiselev is, in my opinion, is the more important book for you

[odd cargo]

let me rephrase, most of the book is dedicated to this.

all in all, one teaches you fundamentals (kiselev) and the other works as a book that could help you transition into the more "competitive" stuff

[surreal bay]

i feel like i just wanna say that I’m starting off from complete scratch in comparison to what’s usually covered in the “competitive” context — scratch in this context is circles , quadrilaterals , similarities — standard geo that a 16yo/ 10th grade curriculum would cover) +

[odd cargo]

those two books are all you need

[humble spire]

Egmo is a book 💀

[real marsh]

please don't filter evade.

[real marsh]

EGMO is both a book and a contest

[humble spire]

Nah but he was asking about oly geo books lol and he searched up the wrong egmo 😭

[surreal bay]

??the evan chen one??

[surreal bay]

i’m aware that you just said coxeter focuses more on the competitive context but just another thing
is it okay to alternate between the two while studying specific topics

[odd cargo]

up to you

would recommend you finish kiselevs geometry book though

its not even that long

maybe 250 pages

[humble spire]

Ye

[heady wren]

this only excludes pages with the word "ai" on the title from the search, but it doesn't disable the feature

[somber shore]

I want to max out my math chops for physics
I've done every single problem, from start to finish for: “Calculus For the Practical Man” and “The Book of Integrals” but nothing much else.
What's a good book for me to work on next?

[molten gulch]

zorich mathematical analysis 1 and 2 or amann and escher analysis 1 2 3, alongside FIS or hoffman and kunze for linear algebra and an abstract algebra textbook such as artin or hungerford or herstein

[night prism]

Oh you know herstein! Small book but such a nice writer

[tawny cosmos]

is Zorich mathematical analysis really a good book to learn analysis? im a math major btw

[molten gulch]

A hard book but yes from what I know, several other alternatives are also in the pins

[tawny cosmos]

ok thx

[steel cloud]

Which book will be best for reference with Atiyah's commutative algebra book?

I did the first 4 chapters and now I am on chapter 5 and target is do 1-8 chapters, now I want some reference too

[molten gulch]

Eisenbud

[mellow wren]

I am an endless fan of Matsumuras commutative algebra

[lost arch]

guys, good book on topology containing something on separation axioms, metrizability, non-Hausdorff space, pseudo-metric spaces and stuff?

[mellow wren]

Does Munkres not talk about these things?

[remote sparrow]

he definitely goes over the first two topics

[lost arch]

im using Singh, he superficially covers all of this but id like to know a little more

looking at Engelking now

[remote sparrow]

is there a reason you need to know those topics

[lost arch]

but if there's any alternative I'll look into it

[mellow wren]

Munkres is standard for point set

[lost arch]

actually just want to know more topology

i mean, in more generality

[remote sparrow]

mmm well there have been some relatively recent papers published in rings of continuous functions which falls under point-set but i don't think that really uses the latter two topics you mention

[lost arch]

because those topics are rather closely tied to nets and filters which seem to be of use in some of analysis

[remote sparrow]

i think a lot of research in point-set nowadays is in set-theoretic topology (as in using tools from set theory, as a field of mathematical logic, for point-set)

[remote sparrow]

you can look at willard for more on nets and filters

gillman and jerison is a good way to see nets and filters at work as well

most people's intended goals for their mathematical careers don't require especially deep knowledge of point-set

[lost arch]

yeah i know

its just for some reason interesting

yet i cant imagine myself learning alg top

[mortal iris]

This is an option, tho I don't think pseudo-metric spaces are covered in much detail, if at all. That said, I'm pretty sure Munkres covers these things as well?

[shadow vector]

Oh wow, this looks awesome

what are the prereqs?

[mortal iris]

For the topology part, Analysis. For the homotopy part, throw in Abstract Algebra as well. Ideally you should also know Linear Algebra before taking on smth like this even if not a strict prereq.

[shadow vector]

I know lin alg basic analysis and topology in the context of manifolds but no abstract algebra

maybe I can still take a look

[mortal iris]

You can still look at part one but better know at least some group theory before starting homotopy

[lost arch]

this text feels so light

the author explains things in a conversational tone

what a nice book

[steel stag]

Is "Introduction to proof theory" by Mancosu Galvan & Zach going to be an okay read if I don't have that much background in logic (eg, I don't know the proof of the FOL completeness theorem), or should I ready something else first

[limber trout]

Anyone know some exercises on complex analysis where I can get them?

[steel stag]

actually tbh, does anyone have a good text which teaches the proof of the FOL completeness theorem? i've been wanting to learn it for a while

[frozen perch]

I would imagine this is in any intro logic book worth its salt

I usually recommend Boolos

[glossy pier]

Im almost done with the practical algebra self teaching guide book, im thinking of moving onto one of these 2? Which one should i go with or is there another better one?

[mortal iris]

Very wildly different books. I advise you to use both. Hall and Knight would pepper you with problems, some routine, some hard. Dolciani will force you to be rigorous. You'd do really well if you can marry the approach Dolciani takes into the problem solving in Hall and Knight.

And to be fair, the problems in Dolciani aren't quite easy either. Just usually of a different flavor than Hall and Knight.

[glossy pier]

Should i read one first? Then the other? Both at the same time? 100 pages of one and then 100 pages of the other?

Sorry if i ask too many questions, i am simply excited

I heard maybe the hall and knight might be outdated idk

[mortal iris]

That's ideally not how I'd go about using two books for the same thing with different purposes. Work with the first 5 chapters of Dolciani first. These are fairly basic. Then compare the two books in terms of their contents and work on common material simultaneously.

[mortal iris]

Both are in terms of how some calculations are done, because these days ppl use calculators for them. Back when these books were written, people used tables.

[glossy pier]

Interesting

[mortal iris]

Content wise, they're not outdated for high schools. Though, Dolciani's approach is questionable if you're not certain about studying math in the future.

[glossy pier]

How so?

[mortal iris]

Go study the books, you'll find out in due time.

[glossy pier]

Thank you for your time, i hope i can quickly come back to ask for more recommendations

[mortal iris]

Don't rush it. Take a solid several months doing these before that I hope.

[whole karma]

Thanks for telling me, but i am a bit unsure about what exactly you meant by some terms, like what do you mean by level or amount of abstraction in this case and what do you consider "high school" math to be, so is it like :-
• Books like Higher algebra → book of proofs
Or
• Books like Elementary algebra → book of proofs ?

[pastel basin]

can u guys suggest me a course for algebra

[wraith girder]

linear?

check khan academy if that is the case

grant sanderson made a great course there

[steel cloud]

Okay

[steel cloud]

What background do I need for it?

[mortal iris]

I think I've explained myself quite clearly right after the part where I said that lol. Especially applies to part 1 of the book. If not, there are some easier to read books like Cummings' as well. Still, I don't think it's wise to go through such a book right after middle school unless you're obsessed with math. Idk why you're asking me what I consider to be high school math. It's pretty much standard across the globe, at least on paper with a few telling differences. The stuff in common is sufficient.

[mortal iris]

I'd still use a book primarily, no matter how good he may be.

[wraith girder]

wdym

he is an excellent "teacher"

i mean, his animations are golden

[mortal iris]

Did I claim he's not?

[wraith girder]

I mean, no..

IG

[mortal iris]

And he has a video literally telling you why you shouldn't believe in visualisations.

[wraith girder]

They are good for building intution

[mortal iris]

They're even better at building misconceptions

[wraith girder]

it depends on how you use them

[mortal iris]

Which is why have these things called books and do rigorous work.

[wraith girder]

Yeah, fair

You cant proof something visually that often

You need rigor for it

[mortal iris]

That's true of everything. Anything can be good if you use it right.

[mortal iris]

Often? Try never.

[wraith girder]

Personally, I like to think visually

I mean, I havent developed my thought process yet (in grade 9 here)

But, I derived the majority of my work for my rotation project without pen and paper

Obvioously, rigor is more tennable

But to get an idea of smth, better to imagine it first and then formalize

[mortal iris]

That's good for a 9th grader. You do you for now. I didn't expect I'm talking to someone this young since you brought up Linear Algebra. Most 9th graders don't know what that is lol.

[wraith girder]

I dont know linear algebra

[mortal iris]

There are things you simply cannot visually imagine

[wraith girder]

yeah

like 4D

or the intricate details of a shape

[mortal iris]

No. That's actually quite easy to some degree. There's far more interesting things.

[wraith girder]

You cant make a statement by imagining it

[wraith girder]

like what

my worldview is quite narrow at this stage

[mortal iris]

Doesn't really matter atp. It's alright. The entire point is, books, notes, pen and paper >> digital aids for the learning.

[wraith girder]

i want to know the "interesting things"

Even if I dont understand them

[mortal iris]

If you are using what's given in the text to think about how you would visualise and then try to be carefully checking things out, that would be more valuable than someone spoonfeeding you those visuals.

[wraith girder]

yeah

that is tru

But what about the reverse process?

[mortal iris]

So. Not really against visual intuition. More so against spoonfeeding.

[wraith girder]

Where you imagine smth and then write it down

[mortal iris]

As long as it's you doing it.

[wraith girder]

Ahh, thanks for validating the 4 months of work i have put in to my project

makes me feel better about it

[mortal iris]

There's this thing called an infinite dimensional Hilbert Space. We use it in quantum physics quite often.

[wraith girder]

so like a limit

where u keep shrinking

[mortal iris]

Not at all

[wraith girder]

but "aproach"0

or sorry

sorry

i mis spelled infinite as "infinitesimal"

srry my bad

yeah but continue onwards

[mortal iris]

Among other things, regular old 4d space is quite easy to visualise indirectly, but gets messy when it's something like our physical spacetime

[wraith girder]

ok, so you need an infinite number of parameters to define an object

how does that work

why would you want that

[mortal iris]

What are you getting this from lol

[wraith girder]

google says: "Inner Product (Angles/Length): Allows you to calculate the angle between two functions (functions can be orthogonal) or the "length" of a function."

google search

[mortal iris]

Don't bother. I already said it. Not relevant. You're in 9th grade. Enjoy what you're doing. You'll get here eventually.

[wraith girder]

hmm, wait cant u just measure the 'angle' using regular functional analysis, what's different aboutthis?

[mortal iris]

I only spoke about difficult things to visualise and where you might see them because you asked. Don't bother trying to find explainers rn. It will take a series of lectures to get there in a way that satisfies me lol

And in any case, not the right place to do it in #book-recommendations

[wraith girder]

i kind of get the quantum mechanics usage: like a particle can be in an infinite number of positions, and u represent each position with a probability

[wraith girder]

ok

srry then

[wraith girder]

one last thing, what if u have all the positions on independet axes and represent their probabilities on lets say the y axis

would that work

like how would u connect all the points when they lie on different axes?

[mortal iris]

You're pretty far away from being able to deduce or understand stuff about qm imho. Even many of your average physicists who work with it don't really get it right. So let that stuff rest until you're able to deal with it either in a lab or with pen and paper.

[wraith girder]

ok well a bit underwhelming

goodbye

..........................................................

[mortal iris]

Naturally. I don't like to give the pop science treatment lol. If you wanna talk about it, get to when you can understand most words spoken about it precisely.

There's a lot of time. Just have fun doing what you're doing now.

[signal zenith]

To do it rigorously you need at the bare minimum a lot of calculus and linear algebra knowledge.

9th grade you’re just not there yet, so learn those first

[mortal iris]

A course? Wdym by algebra? Could you be a little more specific? You have the pre uni role so I'm assuming high school stuff?

[pastel basin]

yes I wanna learn before joining my uni

cause I have weak foundation

[mortal iris]

Use books. What will you be doing in uni? Math?

[pastel basin]

yes

i mean we have m1 and m2 exam

exams*

related to maths

[mortal iris]

No idea what those are.

[pastel basin]

np

I'll figure it out

[mortal iris]

Not related. Are you studying math or something else? My rec changes depending on your answer

[pastel basin]

maths

[mortal iris]

Okay so you're gonna be enrolled in an undergrad programme for math so you need to review your basics. Correct?

[pastel basin]

yes

[mortal iris]

Use Daniel Kim's Advanced Precalculus or Dolciani's Modern Introductory Analysis. Supplement either book with Stitz and Zeager's or Axler's Precalculus.

[pastel basin]

okayyyyy

[unborn hazel]

I am going through book of proofs at the moment, I have completed the sets, logic, counting chapters and I am just about to finish the direct proof chapter. I was thinking of doing ladw after book of proofs, but I was wondering if it would be a good idea to do ladw alongside book of proofs at this stage? book of proofs is my first exposure to proofs and admittedly I struggled with direct proofs however I am feeling a lot stronger now. Contrapositive proof and Proof by Contradiction are the next two chapters.

[mortal iris]

Feel free to do so. Linear Algebra is one of those courses where people are given their first exposure to proof writing outside of a foundations course for a reason. As long as you understand the principle behind a proof by contradiction and a contrapositive already, it doesn't matter much if you're lacking the practice. If not, I recommend reviewing that and getting started.

[unborn hazel]

I will go through the Contradiction and Contrapositive chapters before hand, and then get a start on it. I am desperate to get started with some linear algebra haha. Also, how many books is too many at once? Should I limit myself to going through 2 at any given time, or is this down to personal preference.

[mortal iris]

Mostly preference, but realistically depends on whether you're in uni or doing pure self study.

[unborn hazel]

I'm dropping out of uni so its essentially pure self study atm. I think you were the one who suggested for me to do spivak calculus and to perhaps do spivak's book on mechanics alongside that. Would it be bad to start spivak calculus now, or should I just hold off and complete book of proofs and ladw. Then do spivak calculus and mechanics together?

[mortal iris]

Typically an average undergrad takes maybe 4-5 courses a semester. The first one typically includes Linear Algebra, Calculus, Proofs and maybe some computing. Some places might have some Geometry or Number Theory. Others may have a Physics course or so.

[mortal iris]

Iirc you have had exposure to elementary calculus already? The unrigorous kind.

[unborn hazel]

That is correct, a physicist taught us sv calculus and I have done a little bit of partial derivates but nothing i can remember icl

[mortal iris]

Ggs nws. I'd say hold off on Spivak's Mechanics then. You need to have a strong background in Calculus to handle that.

It (Part 1 of the book) can be done alongside Spivak's Calculus but you already have a couple of other things on your plate so it might be too much.

[mortal iris]

Instead just go with LADW, The Book and maybe use Pete Clark's notes on Calculus alongside Spivak (or alternatively Zorich's Mathematical Analysis instead of these two). I think that's a healthy combination if your doing self study.

If you want some physics flavour, you'll get that in Zorich' problems. Very rigorous but very accessible too. And it can and is commonly used for both Calculus and Analysis courses. You can check out the preface to see if you'd like to make it work.

[unborn hazel]

So do something like LADW + the book, after that do spivak/zorich + pete?

Also when you say to do spivak/zorich alongside pete how would you best study those alongside? Do I need to do x amount in one book then start doing the other, or should i be using one for questions and one for learning

[mortal iris]

I'd say you've already done enough of the book to begin with Calculus and LADW. As far as Pete's notes go, they are more concise so you can use them as an aide. Since you're not doing any physics anyways (and if you wish to) Zorich is the right call because it has plenty of pretty hard core application based problems that don't assume knowledge of anything beyond the textbook.

[fossil badger]

"Calculus Made Easy" by Silvanus P. Thompson is this a go to to learn all of calc

i learned calc in high school already which one for all calc 3

[odd cargo]

good book but you could definitely use a better one

and also if you mean single variable calculus, that is.

[molten gulch]

This is an okay text for reviewing single variable calculus, if you would like to learn "all" of Calculus, there sadly isn't a single textbook because "calculus" itself is quite expansive, if you just wish to review before moving on to something like proper mathematical analysis, I'd suggest reading through Thomas or Stewart and just doing exercises

[mortal iris]

In conclusion, go parallel from this point on, with the book, LADW and Zorich.

[fickle glacier]

Should i buy calculus by michael spivak or calculus by james stewart?

[surreal bay]

hello
i know ive been asking about practically the same topic these past two days but
does anyone know of any good alg books for competitive / oly math outside of hall & knight / AOPS?
not to insinuate that there’s anything wrong @ all with said book (what ive been sticking to so far)

[odd cargo]

Courant

[mortal iris]

Spivak. Stewart is a soulless (and imo useless) book. If you need to use something like that, feel free to "use" but don't "buy"

[odd cargo]

there is so much other higher algebra books out there

Theres Duval's Introduction to higher algebra

pretty sure its free as well

Chrystals Algebra P2 is also extensive

[surreal bay]

how do you think the two compare to H&K?

[odd cargo]

i dont know how to answer this question tbh

its all higher algebra lmao

i guess duval does utilise determinants a lot more

Chrystal is just the goat

[mortal iris]

H&K too easy for you?

[odd cargo]

bernard and child is also good

wilczynski's college algebra with application, also good.

[surreal bay]

i wish

[unborn hazel]

Thank you for all of your help. I appreciate it a lot :D

[surreal bay]

for higher alg in general?

[surreal bay]

content wise:
do you think the books cover roughly similar content?

[odd cargo]

For everything, im pretty sure the title states that its relevant to higher classes of secondary school to college

[odd cargo]

no

not exactly

[mortal iris]

Then why you looking for alts? Right place to be imho. Since you're doing the Olympiad prep, I should also suggest working with Functional equations using this book.

[odd cargo]

Also, use those olympiad books

like arthur engels book

or math olympiad treasures or whatever

[odd cargo]

https://tenor.com/view/eyes-wide-shut-stanley-kubrick-movies-tom-cruise-kubrick-gif-27061482

[fickle glacier]

i cant find it in my country

[odd cargo]

then go spivak

[fickle glacier]

alr, but i had read in the internet that "Spivak’s is basically an Introduction to Real Analysis "

so i was thinking it wouldnt be that good as a calculus book

[fickle glacier]

👍

[tame tree]

its proofy calculus

not full “real analysis”

[odd cargo]

well, isnt that what you would want, ideally?

[fickle glacier]

idk, i just know that real analysis is really hard

(im not in college yet)

[molten gulch]

It depends

SOme find it easy

some not so much

[odd cargo]

its perfect

[fickle glacier]

alr guys thx for your help 🙏

[odd cargo]

spivaks calculus, that is

[fickle glacier]

and precalculus what books do you guys recommend?

i studied precalc with a local textbook so idk if it was a good book

[odd cargo]

what does local mean

[surreal bay]

late reply mb
i feel like i do wanna see my options & what book is good for which / what it focuses on (not to undermine H&K ofc since it’s an obvious choice)

• going 2 look into the book u linked :>

[fickle glacier]

a textbook from my country

i'm not american

[odd cargo]

where from

[fickle glacier]

Brazil

[odd cargo]

oh

[somber shore]

Advanced Calculus by Fredrick S. Woods: Yay or Nay? And why?

[odd cargo]

try stitz and zeagars precalc, its freely available online

[odd cargo]

yay or nay for what

[molten gulch]

Whether it's good or not

[somber shore]

The book

[somber shore]

Yeah

[odd cargo]

yea but are you just reading the book or are you using it to prepare yourself for something

[somber shore]

Self study

[odd cargo]

what

[somber shore]

I want to self study beyond AP Calculus

[fickle glacier]

self-taught

self study = self taught

hes asking if it is a good book for learning alone without help from someone

[molten gulch]

Just use zorich or amann and escher's analysis volumes if you've done calculus and some proofwriting practice

[odd cargo]

if you're prepared to pick that book up then go ahead

[fickle glacier]

Which PDF should i download?

[molten gulch]

3rd corrected

[fickle glacier]

alr thx

[nimble yoke]

hey guys, i am planning to apply to UTokyo for grad school and their math entrance exam seems typical 😅 been a while since UG maths so a bit rusty. can anyone suggest resources to revise/practice?

here are the previous year papers:
sample - 2025
other-papers

Appreciate any leads!

[jolly dawn]

Honestly when i was preparing for MOs, the biggest mistake i made was not consulting sources in english. The wealth of information is insane, and you can literally train yourself to IMO level from AOPS website. I used japanese books and they were very poorly written

[jolly dawn]

Are you applying from overseas (to school of mathematical sciences)? In that case they say in their website that they examine you through your CV, rec letters, and other documents. You dont take an entrance exam. Thats only for students applying from japanese unis

[somber shore]

My physics teacher has one and asked if I want to have it

[fickle glacier]

whats an MO?

[jolly dawn]

Mathematical olympiad

[fickle glacier]

oh

thx

[nimble yoke]

yes. as far as i have read, the mathematics exam is a general requirement for master's admission for all.
its written at the bottom of this page.

[fickle glacier]

in my country the name is "Olimpíada de Matemática"

[jolly dawn]

We might be thinking of different departments. My bad

Im also applying to Utokyo and no exam for math department (still low acceptance rate)

[nimble yoke]

oh, this is the special selection process.

[nimble yoke]

yeah i guess. its not there for dept of mechano informatics. here.

[jolly dawn]

Yeah

[harsh pagoda]

Any complex analysis text that does the subject with a topological flavour ? Something which explores connections between complex analysis and topology , an example of such a connection is the winding number.

[peak lodge]

Is calculus by spivak a good book to start calculus as someone who basically has 0 calc knowledge

[odd cargo]

try and see

[peak lodge]

I read a bit and feel more lost the more i read

[odd cargo]

then dont touch it until youre ready for calculus

go do some proof writing exercises and revise your algebra

[fickle glacier]

derivatives are really simple actually

[rich sun]

until you come across the different kinds of derivatives

[pine tundra]

Which ones?

[molten gulch]

Zakeri

[molten gulch]

Gateaux probably

[harsh pagoda]

There are a lot of them. Exterior derivative , radon nikodym derivative, frechet derivative
, etc

[harsh pagoda]

Thnx

[pine tundra]

I thought you were talking about the ordinary derivatives but with weird functions, my bad

[night prism]

Anyone here worked from Marsden’s analysis book?

[remote sparrow]

https://maa.org/book-reviews/commutative-algebra/

https://maa.org/book-reviews/homological-methods-in-commutative-algebra/

saw these reviews for ferretti's commalg books

[humble spire]

Try apostol

I am doing it right now after pre-calculus math and even if it takes a bit of effort in understanding how he does things it is readable

Just google things where needed

[gray gazelle]

idk, I am going into calc 3 and we are using thomas calc. generally people do some calc computation course before doing real analysis or whatever. depends on your goals I guess. what are you trying to accomplilsh?

[mortal iris]

Ahlfors, to a degree.

[mortal iris]

Financial derivatives too lol

[whole karma]

Oh yes i just had little confusion with what you meant by "high school level", I initially thought about a specific level. Thanks for your clarification.

And yes, i have heard a lot about Cumming's proof book being more easier for very beginners, The amazon editorial review said "Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy.", considering all that, Cumming's proof book seemed very promising though the downside for me was that it is quite expensive while Hammack's book of proof is completely free. Several months ago i was thinking about to go for "how to prove it by Velleman" but i later heard that book of proofs is easier for beginners than how to prove it and so i have thought about reading it before "How to prove it" and maybe reading in this sequence may help in grasping Velleman better and may also help for revisiting the topics :-
Book of proofs --> how to prove it

what do you think about reading these two ?

[whole karma]

I wanted to ask that is there something special about Cumming's that Velleman does not have ?

[mortal iris]

Why would you sequentially go through two books that do pretty much the same thing?

[mortal iris]

More friendly writing style. Takes time to get you up to speed on the basics.

[whole karma]

I was thinking about reading both may act as revisiting the topic, and i would get to experience different problem sets and explanations.

[mortal iris]

Horribly redundant. Just pick one of those books and start working instead of over thinking what to use. They're not that different.

Figure out the rest later.

[whole karma]

Oh. Does Hammack's book or proofs have it ? or it is more like Velleman-style ?

[mortal iris]

Read it and find out yourself! If you like it, stick with it, or do the other one, or the extra other one. They are not that different.

Pick one and just begin.

[whole karma]

But what do you think about revisiting chapters ?

[mortal iris]

Who cares? Pick one. Do the work and then figure out whether that's necessary later

[whole karma]

Yeah

[mortal iris]

What knowledge do you have? Are you comfortable with reading mathematical statements? Writing basic proofs? Working with inequalities?

And what is your goal? Do you intend to pursue math or not math as you go ahead?

[mortal iris]

Spivak I'd argue is a little more readable. Apostol is quite nice in itself tho.

[marsh spade]

@mortal iris STOP TALKING ABOUT MATH IN A BOOK RECOMMENDATIONS CHANNEL

[mortal iris]

<@&268886789983436800> he's back. Did this the last time too.

[marsh spade]

what bro come on

[mellow rivet]

Dude you are a known troll

[marsh spade]

I will stop for real

[mellow rivet]

You spammed nonsense the last time as well

[marsh spade]

@mellow rivet I will stop for really, trust, please

[mellow rivet]

If I had a say in it idve muted you for pinging me with that instead of a reply message icl

[ember karma]

I do have a say in it

[mellow rivet]

I can't just modping for low quality troll users pinging me in the future though...

[mortal iris]

I'd not do it if it was the first time.

[ember karma]

If they keep going after you after you ask them not to, you can

[mellow rivet]

I mean I also just dislike users pinging me like that as I actually have real conversations in this server and enjoy responding quickly

[mellow rivet]

Wait repeatedly pinging isn't something mods will just tell me to block for? I swear other mods did that

[mortal iris]

Also the unsolicited dm

[mellow rivet]

Repeat troll and being uncivil

[ember karma]

If someone's deliberately trying to annoy you, and won't leave you alone, I would not be happy about that, at least you can also ModMail too, I promise you won't get bitten (well at least not too painfully )

[ember karma]

noted, thank you

[mellow rivet]

Yay i won't get told off because I dislike blocking

[ember karma]

You still should block them, but nonetheless, they still should leave you alone whether you block them or not

[mellow rivet]

Many quality users unfortunately seem not to agree

[lost arch]

the guy has a football club pfp, leave him alone 😭 😭 💀

[mortal iris]

It's alright. Seems like he's been left alone either voluntarily or by force lol.

[hybrid vapor]

Is the latest edition of textbooks always the best?

[cunning elk]

no

a lot of computation slop textbooks just get new editions for the sake of getting new editions

[hybrid vapor]

Any proof-based/rigorous algebra, geometry, trigonometry, or precalculus textbooks?

[molten gulch]

lang's basic mathematics and https://www.stitz-zeager.com/

[humble spire]

Proof based is daniel kim advanced precalculus

But i think theres barely any computations

[gray gazelle]

good resource, I might check this out

[gray gazelle]

did you work through all of these books?

oooh there is even latex source code I am hoooked! (thank you thank you thank you!!)

[hybrid vapor]

The Stitz-Zeager book is cool and funny lol.

The website is unpolished tho

[little ridge]

Can yall explain how to do this one?

[mortal iris]

This is #book-recommendations. Ask in #calculus

[little ridge]

Alr mb

[mortal iris]

Daniel Kim's Advanced Precalculus or Dolciani's Modern Introductory Analysis.

I would recommend supplementing with Axler or Stitz and Zeager for calculations. It's not enough to say 2+3=3+2. You should be able to tell both evaluate to 5.

[remote sparrow]

#book-recommendations message

[hybrid vapor]

Yeah, if it works it works, right? 😅

[remote sparrow]

@mortal iris have you seen pamfilos' books on euclidean geometry?

[mortal iris]

Oh yeah. Came across this a few months ago. Incredibly comprehensive from the looks of it.

I went through some chapters. Very well written too.

[next saffron]

Read my status

[mortal iris]

Go be vain in #chill

[wraith girder]

hey @mortal iris

what would be the best book for learning G.A

like for someone who has done Linear Algebra

[harsh pagoda]

GA meaning?

[wraith girder]

Geometric Algebra

Like if u want to learn it visually

[harsh pagoda]

Oh like Clifford algebras

[wraith girder]

If that's a thing

[wraith girder]

yeah

but that is a specific sub-field right

[harsh pagoda]

Try this Source: LMU München https://share.google/uppGHqMfHT4WIbPaW

[wraith girder]

okay

taking some time to load...

internet problem perhaps

[harsh pagoda]

It's by Douglas Lundholm and Lars Svensson

[wraith girder]

okay

Are there any other works from the authors on G.A

[harsh pagoda]

Same authors?

[wraith girder]

yes

[harsh pagoda]

Don't know

[wraith girder]

okay

loaded

[blissful turret]

do you guys compete

[wraith girder]

Do I need to learn rotors and spinors seperately before diving into this

I can't see rotors under the table of contents

sorry if I am asking for too much, but is there a more general source for learning G.A that doesn't start with Clifford Algebra

[harsh pagoda]

No it's defined in page 63

[wraith girder]

okay

that's all

thanks

[harsh pagoda]

You would need to know linear algebra pretty well before starting also knowing some multilinear algebra, like tensor products helps

[mortal iris]

If this is what you mean then Artin has a well known book, but it's not visual in the sense of having a lot of pretty diagrams.

Macdonald has a couple of books covering linear algebra and calculus from the GA perspective. They're very introductory so that might be a good place to start.

Ik of a pretty decent physics oriented book on the subject tho. That said, I've not really used much of any reference for this stuff besides the Chrisholm notes.

Unless @wraith girder you're talking about learning the basics of Abstract Algebra through pretty visuals. That would be a very different thing.

[west wing]

Guys can you recommend me some books of math that i will need as a cyber security engineer?

[gray gazelle]

what is a cyber security engineer? like you engineer secure hardware? interesting

oh it's more about protecting an organizations security in terms of networks and such .. i see

[west wing]

I don't work yet I'm just planning to start learning, probably i would like to be penetration Tester

[west wing]

Yeah, exactly

[west wing]

Actually there's hardware security engineer, too

[wraith girder]

I am learning G.A as I want to be able to model physical systems in the future, so from that presepective, your reccomendation would be much appereciated.

[west wing]

What is GA?

[wraith girder]

Geometric Algebra

It is like a generalization of sorts of Linear Algebra

[west wing]

And what is it used for?

[wraith girder]

Umm, a lot of things

But

Its better if u search for it yourself, my answer will be inaccurate

but of the top of my head, i think maybe functional analysis and clifford algebra for rotations

[west wing]

Okay, thank you, I'm just curious

[wraith girder]

No worries

[mortal iris]

Doran's Geometric Algebra for Physicists then. The notes are solid too. Keep them handy.

[wraith girder]

ok thanks!

[mortal iris]

Particle physics, general relativity, computational geometry and graphics, etc. right off the top of my head.

[wraith girder]

I must ask, do I need any prior like extensive physics knowledge to start this book

[west wing]

Ty

[wraith girder]

I would be interested in the prerequisites besides linear algbera and multi-linear algebra of course

[mortal iris]

Some introductory calculus based physics should be good enough.

[wraith girder]

okay.

[mortal iris]

It would be good if you knew multivariable calculus too ofc. Tho it is developed in the geometric algebra perspective in the book.

Don't expect a lot of rigor btw. There is some axiomatic exposition but at the physics level of rigor.

[wraith girder]

oh, that's ok then

Ok, thanks!

[mortal iris]

Not a great idea to send friend requests to ppl you've spoken to for like one pair of sentences.

[west wing]

I just did that bc I thought from your upper messages that you know about math and could be helpful, i wasn't chatting

[wraith girder]

Oh and I also have to ask, Can I hope to learn the basics besides the higher level details or cliffodr algebra and functional analysis in one month?

[mortal iris]

Most ppl on here know plenty of math, many more than me.

[west wing]

Okay, i apologize if that bothered you

[mortal iris]

There's not much to Clifford algebras if you know what algebras are and have seen quaternions before. More or less gets you into the basics. Functional Analysis on the other hand first requires you to know measure theory to even begin.

[mortal iris]

Not that it bothered me, but idek you lol.

[wraith girder]

I am not planning to dive into functional analysis

not at all

[west wing]

Do you know any books about discrete Mathematics or Number Theory?

[gray gazelle]

i'm doing Rosen's Discrete math and it's applications in my discrete math course

[mortal iris]

Was gonna recommend this

[gray gazelle]

Rosen also has a number theory book(?)

[mortal iris]

Idk. I was talking about Discrete Math.

[mortal iris]

For Number Theory, try Silverman. Well written

[gray gazelle]

there is a chapter on number theory in the discrete math book by Rosen

[mortal iris]

Burton is good too but might be too dry

[mortal iris]

I mean, elementary number theory typically does fall under discrete math.

[balmy root]

Burton dry? No way. It has history.

I mean the history's quite dry.

But still, it is refreshing

[mortal iris]

Great book, but the way it's written might be dry to someone who's not used to reading proper math texts

[balmy root]

What about Classical Introduction to Modern Number Theory by Rosen

[west wing]

Okay, thank you for helping

[mortal iris]

Haven't read it. Idk

[mortal iris]

I really like your username lol

[balmy root]

Randomly thought of it.

[wraith girder]

oh yeah @balmy root

I posted an explanation of my method in #chill , you can check it out

[thorny nest]

is it possible for someone with bachelors level math knowledge to get familiar with these topics at a level greater than or equal to of an economics major without any background in economics…

[frozen perch]

You could just do the same thing they do, and study economics

See if you can find a list of textbooks for an econ major somewhere

[mortal iris]

Isn't this just some calculus, statistics and game theory?

[thorny nest]

hmm , ill try that

[thorny nest]

it is somewhat (idk)

like wth is monopoly, that cant be a real topic lmao

[mortal iris]

Not reducing the subject to that ofc but the topics listed.

[mortal iris]

Sole domination of a specific market, vaguely speaking.

[thorny nest]

yeah but the thing is

they make it quantitative in the tests

[mortal iris]

Yeah. There must be a working threshold of sorts to define a monopoly in some model.

[thorny nest]

i saw a college suggesting david m burton for number theory and discrete math

i can understand it till the 8th chapter after which it just went all out with cryptography and stuff

can yall suggest any other books like that

not much solving , just need reading material

[mortal iris]

No learning math without solving problems

If it's more exposition you want you can take a look at Keith Conrad's blurbs but I strongly recommend going back and solving problems in Burton and proving stuff if you haven't.

[thorny nest]

damn alr

cant run away forever

[jolly vector]

can anyone give me an intro on how anything above high school probability works? like mdf, pdf, cdf, expectations, joint probability and types of distributions?
any good intro books and youtube vids are also appreciated. thanks a ton

[mortal iris]

Do you know Calculus?

I'm assuming you do since you mentioned things that typically require knowing it.

[mortal iris]

Best place to start. The course has a free book, lots of problems and accompanying video lectures too.

[tame tree]

just study probability this shit is fake anyways

"market structure under perfect competition" my sides

ok maybe im being too harsh, but you shouldn't really have a problem with studying it considering it's mainly just learning like vocab if you have the math down

[short fable]

Mathematically speaking these models seem simple, and IMO don't even go into Y3 or Y4 econs, which tend to either get mathematically harder or get closer to reality with more econometrics that cares about measurement (and not just basic wide differential equations with assumptions never met in practice)

[swift dragon]

any calucalus basic s recommendation

[real matrix]

Philosophy books for people who wanna read

[trail void]

Depends what kind of economics

i grew up reading adam smith for fun so honestly other than the maths it was actually very pleasant\

[trail void]

The Penguins classic kant is a bit misformated, look out for that. Since you're reading Machiavelli, read "On Livy" by him + "History of Florence" otherwise youre never really gonna understand him

[real matrix]

I see

Atm I'm busy with research papers

[trail void]

try to read about roman myth and Tacitus too as these play in hand for machiavelli

i dont know why people think machiavelli is some figure like marcus aurelius absolutely not

the amount of reference and background u need to fully comprehend is alot

Aristotle the metaphysics is nice but make sure you read plato too

and since ur reading plato read thucydides too

i have a friend who did a super deep study on machiavelli

shes from a rich family and they basically hire her for advice

[trail void]

incase u want my rec for adam smith

[trail void]

Salas, Hille, Etgen's "Calculus One and Several Variables" 10th Edition

[blissful kernel]

Hi, how many hours do i need to study (in total or per week) to finish the intro to counting and probability by AoPS?

[trail void]

this depends person to person

[night prism]

@mortal iris any experience with Hardy’s “Pure Mathematics?” Have stumbled across a hard copy and keen to read it

[trail void]

take as much time as you like but ideally 2 months or less if youre already somehwat familiar

[blissful kernel]

How many hours per month?

[wraith girder]

Would this be the recommended chat to share a physics proposal?

[trail void]

upto you

ideally 1-2

per day

[blissful kernel]

Thank you

[shadow vector]

🤨 What about the channel name "book-recommendations" makes you think that?

[terse sorrel]

Any recommendations to learn number theory to prepare for Olympiads, such as the British Math Olympiad 1 and 2?

[remote knoll]

No clue about specifically the BMO, but there are past exams available online for free. Why not try your hand as a few of them, and see what you need help with?

https://bmos.ukmt.org.uk/home/bmo.shtml

[terse sorrel]

ok

[thin fern]

Is Spivak recommended for someone already very familiar with basic calculus and is already past beta functions, gamma functions, Taylor series, ordinary differential equations, etc?

[odd cargo]

might as well jump directly into analysis

[thin fern]

I considered it because I wanted to brush up my basics but didn't want to just go over the same definitions and methods of solving derivatives and differential equations and all because I already know how to

would it still be a waste of time as opposed to just doing analysis?

[odd cargo]

all up to you

[thin fern]

I meant to ask whether the book dives into the more advanced concepts in Calculus as well

I did look at the contents

It's not very detailed

It just says integration and differentiation

[slim helm]

spivak proves a lot of the computational machinery as an intro to analysis, so the new thing you'd be learning is how to prove all the stuff you already know to be true. i honestly think it's more of an intro to analysis book more than a calc book

[thin fern]

Yeah

I'm an engineering undergrad

and our math professor never did really explain what exactly makes a function homogenous, exact, etc

even though we deal with homogenous ordinary differential equations and exact and non exact and non homogenous ones

not knowing the exact criteria for those really bugs me

because in brief, he just told us that homogenous differential equations are those that have every term to have the total power to be the same

But I know that that's not true because a lot of equations involving trigonometric functions (which can be expanded into a series, so every power won't be the same) are homogenous

And I wanted to know the reasoning behind it

[slim helm]

you may want a book centered around DEs then, im sure the math nerds here have found one that states these terms rigorously

[thin fern]

Any that you recommend?

[slim helm]

no, my university lecture notes were really good but i'm not allowed to give them out

[thin fern]

aw okay

[slim helm]

do a ctrl-f or wait for someone else perhaps?

[thin fern]

I shall, yes

[molten gulch]

For rigorous ODE there's arnol'd and Teschl that I know off the top of my head, for PDE there's Evans and Taylor's 3 volume PDE bible but both of those require some solid measure theory and functional analysis

[thin fern]

this will take a long time to do (my semester with these topics will end before I finish these)

[cunning stirrup]

Can anyone find a reference for discrepancy of non-trivial zeta zeros modulo tZ?

Maybe I'll make a script

[mortal iris]

Don't like it, but sure, you do you. Btw it has no exercises iirc.

[night prism]

I think the “examples” are actually the problems

[mortal iris]

Why would you share a proposal of any kind on discord lol, let alone on #book-recommendations

[mortal iris]

Oh no. Nvm. The no exercise one was his number theory book. Not this.

[mortal iris]

I'm not sure if either rigorous calculus or analysis are suited to you if that is the case.

[mortal iris]

Because these are little things that you can find with a simple search.

[mortal iris]

That's a very bad prof tbf. Makes me wonder if they even have a proper math background lol.

Exactness tho is more so a condition on the equation (it is still a property of the functions) rather than there being some type of exact function.

[humble spire]

I have seen fis recommended a lot for lin alg

I was wondering about it's explicit prereqs?

[molten gulch]

An ability to write proofs

And high school arithmetic/"algebra"

And a stomach for (very mild) abstraction

[humble spire]

Alr

Tysm!

[mortal iris]

@humble spire this is not a strict requirement because ppl often use courses like linear algebra to introduce students to writing proofs outside of a foundations course. But better if you're already comfortable.

[humble spire]

Ty for the notice!

[molten gulch]

<@&268886789983436800> pirated books

they cannot

[outer crystal]

sorry

thank you

[real marsh]

Allg just be careful in future :)

[outer crystal]

will do

[mortal iris]

Just FYI. If you didn't get the textbook from the author's or publisher's site (without institutional access) or a preprint server like arxiv (uploaded by the author), then it is most likely pirated.