book-recommendations

[gray gazelle]

in that case

Weil - Basic Number Theory

[dapper root]

Bruh

[craggy sapphire]

@dapper rootu know any?

[dapper root]

No I don’t

I don’t do number theory but I do know the hard books when I see them

[craggy sapphire]

yea this guy wants me to learn from a lemma theorem book

😂

idek how people learn from books like those

[gray gazelle]

jokes aside Davenport(?)

[dapper root]

I think any book you’re dealing with is going to be definition theorem proof

[craggy sapphire]

the only books like that are uni level books afaik

[dapper root]

But just… not like those two books

…

Number theory is kind of a university level subject

[craggy sapphire]

how? it's usually on high school math comp exams and stuff

let me check khan academy

nothing 😦

[solemn rover]

i learned basic number theory out of Numbers, Groups and Codes

@craggy sapphire

it's free also

[craggy sapphire]

Thanks. Is it newbie friendly?

[solemn rover]

it's newbie friendly

this is not a prank answer

number theory is a pretty advanced topic so newbie friendly and "solid treatment of number theory" are kind of mutually exclusive, so this is arguably a very superficial intro, just scratching the surface.

but it is newbie friendly

not sure how useful it is for comp math. i've never done any of that kind of comp math stuff

[craggy sapphire]

yea thanks a lot read the first few pages looks really good intro.

[junior merlin]

http://www.hpmor.com/ not math, but great

[smoky zephyr]

literally posts harry potter in #book-recommendations

[solemn rover]

no

it's not harry potter

it's worse than that

[crystal lion]

percy jackson guys 👍

[fervent lava]

In middle school I read all the percy jackson series even the ones involving the roman side.

then I read the Egyptians ones by the same author. I haven't been able to find more books like that since then. I used to rush home from school just to read it.

All I demand is a proper movie on those book similar to Harry Potter. The movie on lightning thief was interesting but it sucked according to the books.

[smoky zephyr]

how about that, i just checked the channel description and this channel isn’t just for math books

[fervent lava]

Same I had to double check first before going on about Percy Jackson.

[fathom elk]

How come I cannot find an explanation of Zadeh’s Extension Principle online? I read that it is well known, but cannot find it on StackOverflow or Reddit. Can someone recommend a reading?

Never mind. removing zadeh's name worked

[gray gazelle]

Oyestein Ore's An Invitation to Number Theory seems to fit the bill

It's a part of multitudes of brief volumes written with high school students as the target audience

[fluid nebula]

Hello there,
I was wondering which books should I read to understand the behavior of hysteresis curves in terms of differential equations.
I already know how to fit DE models to lab data. I want to have better insights into the mathematics of DE that governs the phenomena.

PS: Thank you.

[gray crystal]

Math comp books you encounter will also be of this form at some point

If you want specifically for beginning math comp number theory
I'd recommend Paul Zeitz's book, art and craft of problem solving

If you want something harder, you can try this book called Modern Olympiad Number Theory

[remote nova]

Hey folks, I'm looking for texts on special functions, and on hyperbolic 3-manifolds

Anything on algebraic number theory would be great, too

[split portal]

How do DF, Jacobson and Artin compare for self studying algebra? I just finished Pinter's book and I'm curious what book would be most beneficial to follow that book with some time in the future.

[remote ginkgo]

honestly, i like rotman's Advanced Modern Algebra the most

it's the most clearly-written i've seen

i have not checked out jacobson though

though lang is quite good too

[split portal]

What's the difficulty jump from Pinter to Rotman like? I will probably buy a copy of it either way since I know I've seen it mentioned a couple times too.

[remote ginkgo]

well

i must be honest

the difficulty is about the same

in terms of clarity of writing

however the topics are obviously more involved

just grab a pdf and skim some sections (see for example the Homology chapter)

[split portal]

I'll poke around in it :)

[dense wren]

how is brown & churchill's complex analysis book? I was able to pick up a 3rd edition for $5, but i guess its on its 9th edition now. Does anyone know how if theres a huge difference between the two?

[broken meadow]

its a nice book

not designed to teach it very deeply

[iron granite]

Does Pugh get Dedekind cuts right?

Because it seems too simple.

And I understand it.

[sage python]

@remote nova hahaha I've got something for you

This is in my "I should read this eventually" list

https://link.springer.com/book/10.1007/978-1-4757-6720-9

[remote ginkgo]

theres enough difference in the 8th and 9th editions to be annoying if you are in a class using one or the other

so i would imagine its pretty substantial, going back to the 3rd

[remote nova]

Actually, this is the book I'm trying to prepare for

I've got it checked out from the library and on the table upstairs

[slender dragon]

Best book for Abstract Algebra

https://www.google.com/url?sa=t&source=web&rct=j&url=https://csclub.uwaterloo.ca/~pbarfuss/18093757-Fuckin-Concrete-Contemporary-Abstract-Algebra-Introduction-by-Nicolas-Bourbaki-Junior.pdf&ved=2ahUKEwiA8LGg_qj0AhWmSTABHYIsAtIQFnoECAcQAQ&usg=AOvVaw2wAONMZdPN245ttBijWfm8

[remote ginkgo]

LOL

thats an amusing one

ive seen it before

[slender dragon]

Yes, but it's not fake I think (I read some proofs not all the book lol) hahha

[remote ginkgo]

yeah its fine

its totally fine

A proof of this fuckin’ theorem is given in some other
mother fuckin’ freaky math book by some mother fucker
FUCKIN' ALGEBRA
67
asshole, using the fucky fact from fucking analysis that a
sticky cubic real fucked polynomial has a sucky real root.
It could be fucked by some fucky unsucked theorem that
the pounded complex sexy roots of so real funky-fucky
polynomials occur in unfucked conjugate pairs

[slender dragon]

😂

[remote ginkgo]

i once wrote P[R] to denote the polynomial ring with real coefficients

and i want to die because of that fact

i literally was so sleep deprived i could hardly hold my eyes open and had to do a pop quiz

[sage python]

@remote nova so if you want a raw algebraic number theory book, there are a few choices

Neukirch and Lang are prob the titans here. Vibe I get is Neukirch has more AG, Lang has more analysis. Milne is also an alternative, has a volume on intro stuff and one on class field theory

At lower level, people seem to like Marcus for its exercises. Samuel's "Algebraic Theory of Numbers" is what my undergrad used for that class

I don't know dedicated books about hyperbolic 3-manifolds though, maybe some general "Hyperbolic geometry" book? And about special functions... I've heard @marble solar shill for "A Course in Modern Analysis" by Whittaker and Watson (modern = 115 years ago lol) which seems to do such stuff

In that general vein, there's also a book about the 2D case

"The Spectrum of Hyperbolic Surfaces" by Bergeron

I reference that a fair bit rn

[remote nova]

Thanks a ton

[gray gazelle]

anyone read Thomas Jech?

[solemn rover]

yes.

it was a long time ago tho.

[frail sail]

oi fellas recommend me some physics texbooks. Right now im doing precalc (will be doing calc in a few weeks) and basic physics such as mechanics, waves, optics and circuits. Any textbook recommendations to strengthen my physics

[solemn rover]

the one i learned out of was fine

standard textbook for freshmen

[frail sail]

whats it called?

[solemn rover]

"Physics for scientists and engineers" by Randall D. Knight

sorry i edited the post

ok we are good lmao

[frail sail]

👍

[smoky zephyr]

https://tutorial.math.lamar.edu/classes/calciii/3DSpace.aspx

does anyone know a book explaining stuff like this, but more detailed?

[quick hornet]

what do you mean by "stuff like this"

thats just standard calc 3 content

so any multivariable calculus book

if you want exposition on ℝ³ (and ℝ^n) more specifically with none of the calculus content

just explaining vectors and etc.

the first few chapters of a linear algebra textbook

(a non-proof-based one is more likely to focus on ℝ^n specifically)

[smoky zephyr]

ok thanks

[subtle siren]

I don't know how good Paul's notes are on R^3, but they seem fine. Seeing as the topics are labelled, you can try to google specifically if you think the notes there are lacking on any specific topic

[smoky zephyr]

yeah some of the sections in there just didn’t explain what exactly to do before i got some questions on it

maybe i didn’t think hard enough, idk

[main void]

Hi guys,
Any algebra book with a categorical perspective? Serge Langs “Algebra” does this a bit, but I was looking for something else

[quick hornet]

aluffi does elementary algebra (like first group/ring theory course level) categorically

any text written for advanced graduate courses will use categories where appropriate

but maybe not a fully categorical perspective unless youre doing like

homological algebra

[gray gazelle]

I think the usual suspects for commutative algebra use some diagrams as well

[main void]

yeah looking for ring/field and module theory type stuff so i ll take a look at aluffi

[storm sleet]

Everyone has an opinion on aluffi, I personally like it, but I know some people have mentioned the exercises leave a lot to be desired

[main void]

issue is im defo not at graduate level lol, its just that I have a group theory course with a categorical perspective I really enjoy so i was looking fir an “extension” of this

[gray gazelle]

Extending to more abstract nonsense

[main void]

oh wait a sec I already have aluffi on my computer, completely forgot about it lol

[main void]

heck im a math student, thats all i do anyway lol

[sage python]

How much categorical stuff actually appears in intro group theory?

Aside from just saying oh blah is a category/morphism/natural transformation, maybe free vs forgetful are adjoints, and Yoneda possibly

[solemn rover]

very little in my experience

[split portal]

The undergrad set theory book, the big grad set theory book or some other book by Jech?

[gray gazelle]

the big one

[split portal]

Ah, I have a copy but haven't worked seriously out of it.

If it's like the small undergrad one I bet it's excellent.

I know I've seen the big one get recommended more than a couple times in diff places.

Also whenever I do poke around in it it seems very clear and well written. Though that might not count for much.

[main void]

I guess not really intro but group actions have nice categorical interprentation as functors, G equivariiant morphisms can be seen as natural tranaformations

Also, free actions are left adjoints of forgetful functors. Free abelian group is a left adjoint, etc etc etc

Also I guess its just nice to have a new perspective on already known concepts (group quotients etc)

[rocky nebula]

any good textbook to learn the induction principle?

[abstract ginkgo]

Hey man! https://www.youtube.com/watch?v=sraSn2MPCfU here is a video which I have reccomended to many friends of mine.
If you are looking for examples, you can look this up https://math.usu.edu/rheal/online1050/Precalculus/Section_8.5.pdf

[rocky nebula]

thank you!

[gray gazelle]

this sounds more like

trying to phase group theory things in the language of categories to have more examples for category theory

rather than making use of category as a tool

but if there is some nice application of category theory to group theory that makes something easier to understand than without using category theory

i’d love to hear it

[gray gazelle]

is mathematical analysis by tom apostol a good book?

[little horizon]

Anyone know a wheel algebra book

[marble solar]

It's hard to get a good text on hyperbolic 3 manifolds. You can look at them from different aspects, I think a good starter book on 3-manifolds are: Thurston's Three-Dimensional Topology and Schulten's Intro to 3 manifold topology

[halcyon hornet]

Thomas Calculus or Stewart Calculus? I want to study Physics after this and also do Spivak after this because Spivak will be rigorous for first.

[fluid bay]

probably just try spivak first tbh

[sinful glade]

try the aops calculus book actually that's quite nice

[halcyon hornet]

Uh no.

Not AoPs for Calculus.

I used AoPs Algebra 1, PreAlgebra and half of Algebra 2.

[forest sleet]

Why not for calculus? I thought it was much nicer to read than mainstream calculus books

[halcyon hornet]

AoPs is competition math.

I do not want to get Competitive even in Calculus.

[gray gazelle]

anyone has some short gentle soft introduction to honological algebra for undergraduate

[solemn rover]

rotman!

it's not short.

but it does start from a pretty accessible place

[gray gazelle]

id like one that does it in abelian categories tho

[solemn rover]

it's really not hard to translate it all into the language of abelian categories. furthermore by the freyd mitchell embedding theorem, to prove something in an abelian category it often suffices to prove it for modules

that said, the standard textbook by weibel does abelian categories, it is neither soft, nor gentle, nor for undergraduates

i think you should be aware that "uses sophisticated categorical machinery to treat things in full generality" and "gentle, soft, for undergraduates" are slightly in tension

[halcyon hornet]

Does Stewart Calculus cover Multivariable Calculus? Or does Thomas Calculus cover Multivariable Calculus?

[solemn rover]

yes.

stewart does

idk about thomas

[halcyon hornet]

Oh thanks!

So after Stewart I can study real Physica and more Analysis, Linear Algebra and basically higher mathematics?

[gray gazelle]

If you wanna study real physics you sign up for lab courses, friend

[iron granite]

induction by titu andreescu

[slender dragon]

Just read Spivak or Apóstol instead of Stewart

[halcyon hornet]

@solemn rover.

[iron granite]

Thomas does cover Multivariable Calculus. It's a good book.

[halcyon hornet]

Oooohh thanks!!!!

Both are pretty similar, right?

[gray gazelle]

Instead of picking up Stewart I suggest you try Spivak

[halcyon hornet]

I do not really have all the prerequisites down well.

Like I am not so fluent in Trigonometry, Geometry and some parts of PreCalculus

[gray gazelle]

I worked through Stewart and it has lots of redundant exercises and lacks rigour

spivak calc on manifolds i heard is good

yeah it's in my list

[halcyon hornet]

So that is the thing.

I will check Spivak after Stewart.

[gray gazelle]

I sent you a mse post. It contains a very good reading list for precalc.

[gray gazelle]

That's unnecessary. You can jump right in with Spivak.

[halcyon hornet]

Ohhhhh.

I will check it out.

[halcyon scaffold]

Thomas is very wordy

[scarlet steeple]

I also lack in hs geometry, I want to go through euclids elements though and relearn it from there.

[mint isle]

If you want to get your concepts clear inside your head then you have to choose this Larsen

Larson

[halcyon hornet]

Damn.

[past ice]

Spivak requires the same or even fewer prereqs than Stewart, and out of the two, Stewart probably expects more fluency with trigonometry right off the bat. If I recall correctly, Spivak develops the trig functions rigorously halfway through the book in a purely analytic way, and before then he only relies on their very basic properties for some examples. Waiting to finish a whole other nonrigorous calculus book before Spivak seems like a waste of time if your goal is to read Spivak. You will not learn rigorous math from Stewart, nor will you gain much mathematical maturity.

[halcyon hornet]

Oohh.

[burnt vessel]

I would say going through elements itself is probably not incredibly helpful in learning modern geometry, although there are some great companion texts that put Elements in more modern terms.

[halcyon hornet]

My goal is not Spivak.

My aim is to study Real Physics with Mathematics, and study Higher Mathematics.

I can do analysis after Calculus anyway, and Linear Algebra.

Also, Spivak is very rigorous people say.

But I do not understand challenging problems at my level itself.

Also I am not Terence Tao like prodigy, I just skipped some stuff, I am in 8th grade.

If still Spivak will be not too irritating, frustrating, un-do-able, challenging af, etc., then till me and Spivak it is then.

Because I do not have much budget left RN for 2 books, I bought lots of book already(Story books, Some Pop-Science and mostly Olympiad Mathematics).

@past ice.

[burnt vessel]

I would argue you'd be better off getting the prerequisites down. It can be very difficult to jump into higher math and physics without them. But, that said, Spivak is a fine text to start with, it will get you what you need.

[solemn rover]

Calculus is a prerequisite for any kind of sophisticated physics, and definitely a prerequisite for analysis.

It's not a prerequisite for linear algebra. You might be able to read the book by Lay on linear algebra now, if your algebra is strong.

[halcyon hornet]

Exactly.

That is why I need to do Calculus, for Physics and more lit af/cool Mathematics.

[solemn rover]

Stewart is the book studied by like 90% of college freshmen who take calculus. Spivak and Apostol are more sophisticated and deal with rigorous proof, whereas Stewart is easier and teaches you how to do more computations

[analog pollen]

just do spivak

stewart is a waste of time if ur going through spivak anyway

[halcyon hornet]

Oohh.

[fast zealot]

Any good recommendation about the history of some famous mathematicians? I get really interested in them

[karmic thorn]

This isn't about history of mathematicians per se, but development of mathematics itself.

[fervent lava]

The people who are recommending spivak left and right have you actually gone through the book? It is a genuine question. I just have a feeling that people who haven’t gone through it are like someone who doesn’t take care of his health then proceeds to recommending someone else the best way to get healthy. Note I have nothing against spivak.

[dapper root]

Nope

I mean my recommendation is to just do a shitty calculus book like Stewart then just go do real analysis

Lol

[surreal phoenix]

if I had a buck for every time someone recommended spivak for a first course in calculus

[fervent lava]

I did a shitty calculus 1 course now I doing abbot understanding analysis.

[surreal phoenix]

It's like recommending Rudin for a first course in analysis. It's doable, surely, but why?

Torture?

[dapper root]

Yeah I feel like that’s better lol, Like just go learn how calculus operates so you know what shit should be

Then go show that it actually is

[brittle latch]

baby rudin has not been helpful in my analysis class tbh

[burnt vessel]

Spivak isn't great, but it gets the job done. I feel like that in combination with all of the online resources about Calculus gets you a pretty good understanding of the subject

[gray gazelle]

hey, what do you think is the best book for general topology and what for geometric topology?

[burnt vessel]

But if I had to do calculus over, I'd just use online resources and skip paying for a textbook and class altogether lol. I got almost nothing from my calc classes, except calc 3

[brittle latch]

obligatory 3b1b recommend

[fervent lava]

I haven’t done topology but I have seen people here recommend topology by munkres

[gray gazelle]

i absolutely aggree, textbook isnt necessary for calculus. in fact, i didn't even use a textbook for real analysis (though i did have some great lecture notes from the professor=

[fervent lava]

There also the one by lee called topological manifolds, there Hatcher point set topology notes in #book-recommendations .

[gray gazelle]

yeah, it's the most recommended one, im wondering if there is some less mainstream but great book you would recommend

[fervent lava]

I am not adequate to answer that.

[gray gazelle]

or anyone else whos online

[brittle latch]

go see what MIT OCW might have

as in, find a class on topology on there and see if they have any notes or a textbook they follow and try that

also mainstream books are usually mainstream for a reason

[dapper root]

If you are interested in geometry try Lee’s Introduction to Topologcal Manifolds

It doesn’t cover as much general point set as something like Munkres

But it covers what you need for differential topology / geometry

[fervent lava]

Lee 3 books is what I plan to go through in the future.

[gray gazelle]

i'm using my professor's textbook, i find it great with lots of pictures and intuitive explanations, but its very brief and has almost no exercises, so i would like if there was some more detailed option that goes slower

[dapper root]

And it introduces topological manifolds so you’re already seeing some amount of geometry in a sense

[gray gazelle]

his book only has around 80 pages

[dapper root]

Lee’s book is very un-terse

I find it a bit too verbose at times

[gray gazelle]

oh great i'll take a look at it

i mean my professors book is also written very verbose

i imagine it's just his flow of thoughts

[dapper root]

How is it 80 pages then

[gray gazelle]

idk hahah it's so unusual

it's 80 pages, full of pictures

but he also has all the theorems and short proofs

for intro to geometric topology, this is the syllabus: Quotient topology, continuous maps on
quotients, projective spaces. The Brouwer fixed
point theorem, the Jordan theorem, the
Brouwer invariance of domain theorem.
Simplicial complexes and polyhedra,
subdivisions, picewise linear maps, the Euler
characteristic. Topological manifolds, one and
two dimensional manifolds, classification of
compact, boundaryless surfaces

does lee cover that too or should i take a look at another book

[dapper root]

I think it does like most everything in there

It might be just a little lacking on the AT part like simplicial complexes and Euler characteristic stuff

[gray gazelle]

ok i can always look somewhere else if it's just one topic thats lacking

[dapper root]

I think he only talks about CW-complexes?

[gray gazelle]

ok thank you for your help

[brittle breach]

General Topology by Stephen Willard
Has an understandably and in-depth treatment of point set topology. Lots of exercises

I continued reading it because of how good the writing was.

I was originally looking for more geometric top stuff

[remote nova]

I would generally suggest Hatcher's notes for a brief study (and do problems, as I think there are a few), and then for further reading/reference you can look at another text like Munkres.

You can also go through the first chapter of something like Bredon's Topology and Geometry or the second chapter of Principles of Mathematical Analysis. Again, brief studies and should help you out for basic stuff.

[torn aspen]

May I have a recommendation for a book on group theory? I'm about undergraduate level in mathematics although I'm still in highschool, so looking for some extra reading to expand my horizons

[manic cape]

Any good algebra book should have that covered

I believe there is a list pinned in this channel

[torn aspen]

I’m assuming this is abstract algebra

[manic cape]

Yes

[torn aspen]

okay, awesome, and also how much should i expect to be spending?

I don’t see any books on algebra in pins?

[burnt vessel]

Id recommend Fraleigh. Its the book Im currently using in my 4th year abstract algebra course.

Which you can get for like $20

[torn aspen]

does it explain from basics?

[gray gazelle]

Armstrong

[burnt vessel]

Depends on what you mean by basics. It doesnt explain all of set theory no, but yes it starts very fundamental

[torn aspen]

prerequisites?

[burnt vessel]

Set theory, functions, and some linear algebra/vector spaces in the later chapters.

But if you just want to know the fundamentals of group theory, really just set theory and functions

[torn aspen]

how much set theory do i need?

i’m just a highschooler dipping my feet into maths thats not calc or alg or geometry

[burnt vessel]

A decent amount. You need to understand binary operations over sets, subsets, and what a set is. Group theory(and most of other modern mathematics) is built upon set theory

[torn aspen]

Okay, so I’ll likely be wanting set theory first

[burnt vessel]

Yes, if you haven't got experience with that yet, I would recommend learning it before delving into most higher level math topics.

[torn aspen]

is there any books on that you’d recommend

[surreal phoenix]

most introductory books offer a section or two on set theory anyway to make sure you're prepared, but try Naive Set Theory by Halmos

[burnt vessel]

tbh for the fundamentals of set theory, you probably don't need a textbook. Khan Academy or some other online resource likely has great explanations on it

[torn aspen]

what do you define as fundamentals?

[surreal phoenix]

Khan has videos on set theory?

[torn aspen]

In the UK, we do a bit of set theory in school

[burnt vessel]

Yeah last I checked they do. I remember tutoring someone and finding them

[surreal phoenix]

Xetrov you probably already know most of what you need, just an extra bit of refining

[burnt vessel]

They at least have stuff on like what a set is, how to union and intersect sets, and most likely functions as well

[torn aspen]

ok

can do all that already

[surreal phoenix]

Oh sweet, I guess that makes sense since school covers set theory to some degree

[burnt vessel]

I do kind of wish there were like a more refined version of Khan Academy for upper level topics tho lol

[surreal phoenix]

Imagine.... Life would be so much easier

[burnt vessel]

Like if I could just watch a Khan Academy on all of Galois Theory..

[torn aspen]

i’m having to purchase books for quantum mechanics

[orchid musk]

Does the edition of Gallian for abstract algebra matter all that much?

[torn aspen]

Expensive

[orchid musk]

Right so I’m just wondering if the content isn’t all that different across the editions

[torn aspen]

Oh no, I wasnt saying expensive to you

[burnt vessel]

For the most part content doesnt differ between editions of textbooks. Mostly correcting small errors and mixing up problems

[torn aspen]

I’m just saying higher level textbooks are bank breaking

[orchid musk]

Dover for the win

[torn aspen]

should i learn set theory to a greater depth first

[burnt vessel]

I havent bought a single textbook since my freshman year of college

[surreal phoenix]

you don't need too much

[burnt vessel]

You just need to refine the fundamentals of what sets and functions are

[orchid musk]

Have you taken an intro to proofs class? Sometimes called discrete mathematics?

[surreal phoenix]

If you wanna go overboard for set theory itself, that's fine, but you won't be using much of that for a while

And like I said, you'll probably find a preliminaries chapter covering set theory in many introductory textbooks for any field that uses it

[torn aspen]

Okay, I've been told that group is built on set but I won't necessarily need it. Do I take the plunge or stay in shallow waters for now?

ok

[orchid musk]

Xetrov if you haven’t read a book on proofs I’d recommend starting there, it’ll also have the required sets and function prerequisites

[torn aspen]

on proofs?

[surreal phoenix]

Oh yeah, if you're not used to proofs, it could be a tough ride

[torn aspen]

I'm fine with proofs

[surreal phoenix]

Done any proof based courses?

[torn aspen]

nope

[orchid musk]

You can take a look at Richard Hammack’s book of proof, free online

[surreal phoenix]

Well, I won't discourage you from trying, but I suggest getting more familiar with that part

[torn aspen]

but school in the uk also has a whole module on it

[surreal phoenix]

What kinds of proofs did you do

[torn aspen]

if that's enough lol

[orchid musk]

If you understand it you can skip it but at least check if you’ve learned it before

[torn aspen]

Let me get the syllabus

[burnt vessel]

Yeah group theory relies on having good knowledge of logic(ie proofs) and set theory. It'd be challenging to explain some of the concepts without them

[torn aspen]

one that pops up the most is induction though

[surreal phoenix]

well you seem to have some level of familiarity, so you might be fine

Give it a shot

[stray veldt]

(if you want a intro proofs review, check #proofs-and-logic message)

[torn aspen]

we've not done any logic though

its all in words

[gray gazelle]

Any book about propositional logic, first order logic or both?

I'm interested in reading some in detail

[foggy relic]

whats a good book to learn mathematica

[burnt vessel]

Depending on your familiarity with programming in general I can only really recommend their documentation. Its really good.

I also read that as mathematics at first and was SUPER confused

[halcyon hornet]

Very well then as you all said, I will start with Spivak instead of Stewart. So I will be ready to bang my head so many times!

[karmic thorn]

@gray gazelle This might come in handy

[craggy sapphire]

I want to go through spivak, but I don't feel like I am mathematically strong enough yet to go through that book. Is there any prerequisite material that I can go through that might prepare me for Spivak's calculus

[halcyon hornet]

Damn you guys were right Spivak start's right through the basics.

Literally starting with grade 5 stuff.

And skipping around here and there much okay.

[gray gazelle]

i hate your naivete

i hope you enjoy reading and learning it

[halcyon hornet]

Oh wait I am too early to judge.

[gray gazelle]

can you stop ghost pinging goddammit?

[halcyon hornet]

Just on page 11.

[gray gazelle]

just read and learn till the end

blocked

[halcyon hornet]

Hush thank god.

[prisma snow]

You were quite rude, and you know that, that's why you deleted your message.

[halcyon hornet]

Oh.

Well.

FYI.

You do not know our previous chats.

What she/they has DMed me.

And a bit of the previous stuff in the server too.

[halcyon hornet]

This was nothing in front of that.

[prisma snow]

Okay?

[halcyon hornet]

I am generally not rude to anyone nor block or like to be blocked by anyone in this server.

[prisma snow]

About Me has blocked me too, so it's not like I want to stand up for them. Just saying there's a reason you deleted your message.

[halcyon hornet]

Oh.

Okay.

I just wrote "Can you stop being irritating goddammit".

[craggy sapphire]

spivak prerequistes pls

[halcyon hornet]

And I do not think this is that bad.

[halcyon hornet]

#book-recommendations message

Check out the Prerequisites section in Thomas Calculus. Enough I think.

Also, what level are you at?

[craggy sapphire]

I've glazed over the problems in spivak and there is no way that I am solving those with my current knowledge

[craggy sapphire]

uhhh are you familiar with uk education system?

I mean, I know calculus

[halcyon hornet]

Then Idk I have not even started Calculus.

[gray gazelle]

you aquire the knowledge by reading th book first

[craggy sapphire]

yes ofc, but is there any point even going through the book when i probably won't even be able to get started on most of the problems

hence why i was wondering if there is any other book where i can develop the type of problem solving skills that spivak demands

instead of just being thrown straight into the deep end

[gray gazelle]

theres only one way to check - read and understand like just the first chapter and see truly if you cant solve them.

[halcyon hornet]

Depends on your goals.

For Engineering, Physics or So, Stewart's or Thomas is enough.

For Mathematics, Spivak they say.

[gray gazelle]

A standard Pre Calculus course should suffice to tackle Spivak. I am working through it myself and it doesn't really assume you know anything besides PreCalc.

If you wanna refresh your precalc concepts then I would recommend Axler's text on the same. It's quite concise and doesn't throw a lot of redundant computational problem at you like most other American textbooks do.

[gray gazelle]

Also you want to familiarize yourself with proofs for which refer to this

[craggy sapphire]

How do you tackle all the proofy type questions with only PreCalc?

Oh

thx

[gray gazelle]

you will get used to proving things after a while

[craggy sapphire]

the only proof technique i am fine with is induction

and perhaps direct proof

but everything else is a blur lol

[gray gazelle]

I don't think you should spend time with big books about proofs tbh

[craggy sapphire]

How big is that book you linked?

[gray gazelle]

Just use them as reference

[gray gazelle]

that one is a brief and very good handout

I used it myself

[craggy sapphire]

Alright. I'll give it a shot. Thanks for all the help

[gray gazelle]

np :))

You can also find proofs in precalc tbh. Like say you wanna prove an inequality $a<b$ holds. One way to go about it would be to assume that $a\geq b$ and then logically deduce a contradiction out of that assumption

[hasty eagle]

死んでいる

[gray gazelle]

This method is called proof by contradiction

Anyone has got a nice pdf for geometry (just 1, 2 and 3 dimensions, mainly) which starts from the very basic in a rigorous way?

I have found some already which seem nice, but I'd appreciate any suggestion

High school geometry?

[halcyon scaffold]

You could try Hilbert's foundations of geometry

[gray gazelle]

Yeah

[halcyon scaffold]

If by geometry you mean euclidean geometry

[halcyon hornet]

Euclid's Elements .

[gray gazelle]

I don't quite know what you understand by highschool geometry, but I suppose? Just basic 2d, 3d geoemtry and with rigour etc

[smoky zephyr]

2000+ year old book lol

[gray gazelle]

The problem is, I don't know how to read geoemtrical proofs I think

Neither write them

Although I haven't studied Geometry much but Kiselev's 2 volumes on geometry are quite standard

You can also refer to Coxeter's Geometry revisited

I just know cartesian coordinataes (which do suck in some cases) and the basic high school stuf

[gray gazelle]

Yeah

[halcyon hornet]

Ghost pinger who.

[halcyon scaffold]

IMO this is very outdated and not really rigorous by today's view.

[gray gazelle]

geometric proofs are quite simple and ||cute||. You would get used to it after you grind on some problems.

[halcyon hornet]

Oh oh.

[gray gazelle]

Me, wanted to ping the message above yours, sorry.

Thanks

[halcyon hornet]

Okay no problem.

[wintry edge]

Long shot, but does anyone know if there exists some pdf of the book "an atlas of graphs" by Ronald Read online?

I might have to get it at a library as it seems pretty hard to obtain

[flat bay]

Any good linear algebra books for beginners?

I don't really like my current book

[frosty girder]

i liked Friedberg, insel and spencers book

[flat bay]

"Linear Algebra: Pearson New International Edition PDF eBook" is this the correct one?

[frosty girder]

This one

[flat bay]

[frosty girder]

uhm uhm
u can still get the book if u know what i mean

[flat bay]

this better make me a god

[frosty girder]

u can check the book out and then decide if u want to buy it or not

[flat bay]

gonna give it a read

Thanks for the tips

[frosty girder]

[gray gazelle]

Get an earlier edition

[iron granite]

that's 18000 rupees, and it's like half my quarter-annual school fees.

[frosty girder]

,w 300 dollars to INR

[hasty eagle]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Samsyet#6969

[frosty girder]

it should be 21k

[frosty girder]

also ur school is expensive

[iron granite]

LKSEC, one of the top schools in the country. /s

Wait, is this doxxing?

[frosty girder]

yes lol

[frosty girder]

i was in the "worlds biggest school" for about 4 years

[sage python]

@iron granite welcome to the self dox gang

[iron granite]

Happy to be here.

[frosty girder]

am i in the gang as well?

[nocturne sky]

Anyone got a recommendation for a calculus book?

I’m a hs student and I’ve gotta self study calc - I’m already pretty familiar with broader concepts and I use calc pretty often in problems I come across, but have never sat down to really learn it.

I’m gonna be taking the BC exam in may. Should I grab something more suited to that or one of the ones in #books-old?

[solemn rover]

Stewart should be fine.

[gray gazelle]

Japanese final exam textbooks

[manic cape]

Any recommendations for probability theory or a roadmap for studying modern probability?

I don't have any background with the theoretical stuff

[gray gazelle]

i liked A probability path

[marble solar]

Rick Durrett's probability book looks good

[slender dragon]

Spivak

[surreal phoenix]

please stop saying spivak, he needs a book for freakin BC calculus

[slender dragon]

Someone says Ruin and you don't say nothing 🧐

Spivak is difficult yes, but it's more accesible than Rudin, Apostol or related books. I would say

[surreal phoenix]

Oh no, I just assumed that one's a troll reply from how absurd it was

You're right for sure, but it's still overkill for BC calculus

[slender dragon]

Yes, maybe

BC Calculus is High School?

[surreal phoenix]

Yeah

[remote ginkgo]

Khan academy

Books take way too long

[surreal phoenix]

Professor Leonard

[remote ginkgo]

If you're just doing calculus, proofs are likely beyond you

Leonard is too slow

Grind the exercises on khan

Consult vids only as needed

[gray gazelle]

yeah I would say just do the problems and listen to the teacher, if theres a particular topic you struggle with, either look in your school textbook (or any other) if you have one, or on the internet

[remote ginkgo]

Do lots of derivatives

Wolfram alpha has a problem generator

Do endless derivatives

Master them

[gray gazelle]

wait what, aren't derivatives just around 5 rules constantly applied?

i would say do endless integrals

[marble solar]

Spivak

It's unironically the best Calculus book

[remote ginkgo]

People mess them up

Constantly

You did too, you just don't remember it

[gray gazelle]

ok, but still, i would say for one derivative, you should do at least 30 integrals to be somewhere equally good at both

[remote ginkgo]

Well he's not there yet

[gray gazelle]

oh i havent read that

i just thought he wanted general calculus advice

[remote ginkgo]

One should learn calculus by reading euler

[slender dragon]

🧐

I tried. I got bored

In the first page

[lime seal]

[slender dragon]

Who wouldn't want to read his book?

[sage python]

Spivak is the correct answer for someone who wants to learn calculus and proofs simultaneously

[nocturne sky]

Yeah I mean that sounds like a good choice honestly

The stronger knowledge of calc I have the better

If I was just worried about the exam khanacademy might be aight but I’d like to learn higher level math and shit so having that duality is probably helpful

[sage python]

If you have no interest in proofs it's too much of a diversion to likely be worth it. If you're more advanced it's probably too basic and you can jump to analysis

[nocturne sky]

Nah I’ve hardly done any proofs and I’d like to be able to and eventually I’ll take analysis and shit which the proof writing from spivaks would help a lot with I assume

[orchid musk]

Is there a point in doing Spivak after Abbott?

[slender dragon]

I don't think so

[broken meadow]

No

[remote nova]

Introductory text on automorphic forms?

[remote nova]

Have you seen Zorich's Mathematical Analysis I, II texts? It seems like a really good alternative to Spivak, though it is a bit large. I've only seen a few people say they like it, but I've also only seen those review for the book.

[remote nova]

No, but in general I'd say they exist for two different purposes. Spivak is for learning calculus with a rigorous foundation. Abbott is a really caring introduction to mathematical analysis. In other words, Spivak tells you how to do calculus and know what you're doing. Abbott is built for the second purpose, but removes the concern for the first purpose.

[orchid musk]

Hmm okay, thanks

[sage python]

Goldfeld-Hundley is good as an intro, Bump is more advanced, Bergeron is more the real side, as well as Iwaniec

[slender dragon]

These seem very good too.

[misty wyvern]

Spivak is really well-written, the only alternative I would consider is Apostol

[dapper root]

I’d recommend these two as a combo

[junior merlin]

calculus early readers edition

[brittle breach]

is there a AG version

[brittle latch]

i know a well renowned doctor in the field, i hear goes by the name seuss these days

[past ice]

Zorich is great but it's way harder than Spivak.

[fervent lava]

I know I should not be doing this until I finish my 2 book I have but I was wondering what would be the multivariable analysis book after I finish doing understanding analysis abbot and friedberg linear algebra. Looking online I hear of calculus on manifolds, vector calculus, linear algebra, and differential forms by hubbard, and there also another one called analysis on manifold forgot the author.

[glad prairie]

READ SPIVAK READ SPIVAK READ SPIVAK!!!!!

[glad prairie]

[manic cape]

[gray gazelle]

Guys , is IA Maron calculus good for competitive exams like JEE

[brittle breach]

why such a strong recommendation

[foggy relic]

Spivak is godly

but it will make you cry

[brittle breach]

calc or calc on mfds

[foggy relic]

mfds is very difficult fwik

[brittle breach]

not sure if ryc response was for plegasus question or the earlier question

[foggy relic]

perhaps both

[halcyon hornet]

You too Ryc?

[glad prairie]

no i think spivak is silly

i would just use paul's notes or stewart or something and then move onto an actual analysis textbook afterwards.

well

what i actually read was this and i liked it a lot but it's kind of old and not very modern https://calculusmadeeasy.org/

paul's notes + 3blue1brown is probably optimal

[sage python]

Eh if you want proofs

Then I prefer Spivak -> Royden tbh

Like if you're taking ordinary calc and then decide wait I like math

Then no need for Spivak, just do Rudin-level analysis

But if you know you want proofs why waste a bunch of time doing it half-assed

[glad prairie]

because if you try to do it full assed you'll end up very confused

[halcyon hornet]

You too!!!!

[sage python]

Not necessarily, Spivak succeeds fairly often lol

[halcyon hornet]

Daymmmm.

[halcyon hornet]

I see I see.

[glad prairie]

citation needed

i have never heard someone actually say they learned calculus from spivak

[sage python]

Many people at UChicago lol

[glad prairie]

only people grinning and going "yeah, i totally had a great time learning calculus from spivak" while hiding an obvious grimace

[sage python]

Since that's how it's taught

[halcyon hornet]

So just do Calculus from anywhere but well, and then do Analysis from good sources and really well, Ryc? .

[solemn rover]

hahaha

[glad prairie]

that's what i would do

[solemn rover]

i'm grimacing rn at this convo

[halcyon hornet]

So the pattern continues.

[sage python]

Do whichever you prefer at the end of the day lol

[glad prairie]

whatever, everyone has their own opinions on this

[halcyon hornet]

The people with honorable role, or rather, people with more experience say that while the others say SPIVAK SPIVAK.

[solemn rover]

O.o

[sage python]

Yeah v inexperienced tru

But yeah my overall thing is, I enjoyed it, and some people say it's too hard to start with but... Just toughen up a bit and it's not lol. It's not for everyone

But it works for its crew fairly well so to suggest it's categorically bad is pretty dumb

[solemn rover]

we're talking to an 8th grader dami

[broken meadow]

i didn't even know calculus existed in the 8th grade

probably

kek

[halcyon hornet]

[fervent lava]

I did not even know there was more math after calculus in high school.

I thought calculus was the end goal of things.

[solemn rover]

no offense dude i'm just suggesting that maybe a book meant for college freshmen at very competitive colleges is not good for a random 8th grader

you have not yet been accepted to the University of Chicago, so i'm not sure why i would recommend a book for you based on the University of Chicago's preferred teaching materials

[halcyon hornet]

Thank you for adding the word random.

There are other 8th graders who are doing Topology and Advanced Physics and so many competitions and all, and I am no what like them, yet.

[solemn rover]

i'm not trying to denigrate you

now i feel like an asshole

fuck you dami

[halcyon hornet]

Dude what.

[halcyon hornet]

You are not.

You just did what I would have liked.

[broken meadow]

this is very difficult to parse

[halcyon hornet]

Nvm.

[sage python]

Clerk I wasn't actually responding to the suggestions to Senku here lol

I was responding to the sentiment that Spivak is not suitable at all

Which was more ryc

[karmic thorn]

Spivak might be a challenging read for you as it stands, Senku, but that should not hinder you from trying to read it. The best thing to do here is to pick any calculus textbook you can find, read it, and see if it clicks with you.

[sage python]

I'm not suggesting Spivak is the be all end all. For some people the extra effort of having Spivak as your starting point isn't likely worth it

[halcyon hornet]

Yes I have understood the way to study Calculus right now.

[karmic thorn]

[frigid comet]

https://images-na.ssl-images-amazon.com/images/I/51abyqKuy8L._SX322_BO1,204,203,200_.jpg

[broken meadow]

rip that rat

lmao

[sage python]

I think if someone's really unable to approach Spivak at all, at least given sufficient effort

[sudden kindle]

In 8th grade I learned about the quadratic formula

[halcyon hornet]

PIN THIS PIN THIS.

[broken meadow]

mouse

[fervent lava]

I hate cats, is there one for dogs.

[sage python]

Then maybe they're not ready for calculus

[halcyon hornet]

#cats.

[sage python]

But it might be that you could start with calculus but you'd be faster if you did Paul's notes then analysis. In which case maybe that's the better option

[sudden kindle]

Learning calculus is overrated

[sage python]

This is all geared toward math people who eventually need to learn the theory. If you don't then Spivak's main selling point isn't worth much

[sudden kindle]

Learn combinatorics and some group theory

[halcyon hornet]

[sage python]

And maybe you'd rather learn proofs through linear algebra or some other subject and then just jump right to Rudin tbh

[halcyon hornet]

Then Become a professional counter and puzzle maker.

[sudden kindle]

I count for a living

[fervent lava]

that what you recommended on some reddit post. The guy had the same name as you.

[halcyon hornet]

How many worshippers do you have then?

[sage python]

I kinda like linear algebra more than calc because the logic is easier

Like calc has nested quantifiers

Which take a minute to wrap your head around

And I think there's less of a gap between practice and theory than there is in calculus

[halcyon hornet]

I will study the theory well, build the intuition, do exercises and solve problems.

[halcyon hornet]

For Calculus.

[sage python]

Definitely hard disagree with the nonsense about calc 3 before linear algebra

That this is apparently common suggests to me that a lot of people who design curricula are kinda smooth brained

[halcyon hornet]

Proofs come after Calculus then .

[sage python]

Proofs come whenever you want them to come lol

Don't underestimate or overestimate yourself

[frigid comet]

I hope the proof for my current problem comes soon.

[halcyon hornet]

Are you scientifically speaking or joking here, because brains should be soft and wet instead of rock hard.

[halcyon hornet]

What is that, may I know?

[sage python]

Smooth brained is an expression for stupid, the joke being that you're smarter if your brain has more wrinkles

[halcyon hornet]

Oh okay.

[sage python]

@frigid comet btw got a toy problem finally

Bounding spherical functions

[frigid comet]

It's a microlocal scattering theory problem, related to the nonlinear time dep. schrodinger eq.

nice

[sage python]

For now an easier case which might already be publishable. Eventually gonna generalize quite a bit

[frigid comet]

have you solved the easier case yet? what is the actual problem?

if it takes a while to describe, i'll read it a little later. have a meeting shortly.

[halcyon hornet]

Oh damn I understand nothing.

Never-mind I need to learn A LOT of stuff before to understand that.

[sage python]

Nah he just gave the easy case Friday lol

[frigid comet]

🐱

[sage python]

Paper by Cowling and Nevo that I could improve upon and/or generalize

They do it for complex ss Lie groups

For now just SL(2,C) and SL(3,C)

[ripe granite]

Why is nobody recommending "Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 "

Everyone at harvards learned calculus from that book

[sage python]

Hmm, how does that compare to Durrett?

I used Durrett kinda and liked it

[fervent lava]

why aren't people recommending stewart calculus? I heard if you do every problem in the book you be better than most mathematicans.

[covert lotus]

Hello, any good book that explains how to partition an integer into "n" parts where we specify the decomposition content (for example 3+2+1=6) (I need it for some very big numbers...)
I guess some good book on combinatorics or number theory?

[sage python]

Stewart isn't really anything special as far as calc books go, def not enough to justify its price

Just pick up any $50 calc book and the quality is practically the same

I didn't know about the non-standard terminology bit even, that's a double oof

[fervent lava]

I am shocked how overpriced it is.

stewart book.

[sage python]

Also "better than most mathematicians" claim is pretty garbo lol

[solemn rover]

overpriced?

how can a book be overpriced if doing every problem in it makes you better than most mathematicians

[karmic thorn]

Miklos Bona, A Walk Through Combinatorics, Chapter 5 or 6 I guess.

[solemn rover]

surely such a book would be worth a fortune

[covert lotus]

Thanks

[sage python]

Being the best mathematician isn't worth that much money is the thing Clerk

[halcyon hornet]

[ripe granite]

idk dami you get a lot of money if you win the breakthrough prize

like 3 mil

[halcyon hornet]

What.

[frigid comet]

until stewart calculus edition 15: early transcendentals version drops and a new wave of mathematicians overtake you

[broken meadow]

fetal transcendentals

[frigid comet]

actually, without checking. how many distinct versions of stewarts calculus books do you think currently exist?

[ripe granite]

6

[fervent lava]

a lot.

[frigid comet]

I would think closer to 20

[broken meadow]

we will make the distinction between early transcendentals and the normal one right

[karmic thorn]

They have distinct covers

[broken meadow]

i think around 20 as well

[ripe granite]

[broken meadow]

since there are 10 or so of each kind

early and normal

i think the last one i saw of each was 8 or 9

so maybe by now we're at 10 of each

[karmic thorn]

Seriously, why do some authors have such a temptation to keep pushing new editions with almost nothing new?

[fervent lava]

and there no difference with each version except fancier cover. maybe that were the 200 dollars is going.

[ripe granite]

idk I never read stewart

I learned calc from khan academy

[karmic thorn]

There are some standard textbooks here running in 50+ editions

[ripe granite]

khan academy is very good

[broken meadow]

i learned from school and khan academy

[karmic thorn]

I learnt from a mix of school, Khan, Thomas, winging it

[broken meadow]

and then at the end i did several exercises from the "problems plus" section of each problems part in stewart

[halcyon hornet]

You used Thomas?!!?

[karmic thorn]

Yeah

[ripe granite]

Thomas is good

[karmic thorn]

Even MIT OCW a bit

[fervent lava]

those authors are actual mathematicans that are scamming the system. Alright let make the instructor require the students to get the new version each year.

[halcyon hornet]

Better than Stewart?

[karmic thorn]

And Herb Gross' lecture series 😌 Love the man

[ripe granite]

never read stewart so idk

[broken meadow]

Thomas has an actually okay proof of the divergence theorem for its level

[halcyon hornet]

Nvm I will buy Stewart or Spivak since school library has Thomas and I am going to school from next year I guess.

[sage python]

Are they scamming the system or are they using the system to scam students?

[fervent lava]

using the system.

[ripe granite]

youre not in school?

[halcyon hornet]

Corona.

[ripe granite]

ah

[halcyon hornet]

So online school.

[ripe granite]

[frigid comet]

So I think there are 9 editions of calculus, each with an "early transcendentals" version, thats 18 already. Then there"s essential calculus, at least two editions, each with an early transcendentals version, thats 22. Then theres "Calcululus concepts and contexts" at least 4 editions, "Brief applied calculus", and two "biocalculus" books, giving a preliminary count of 29.

I haven't checked this too carefully though.

[ripe granite]

[fervent lava]

it every similar to my other books for other course. We must buy the new edition which isn't available online yet for free, just the old edition.

[halcyon hornet]

Daym sire.

I do not understand the hate for Stewart.

[karmic thorn]

Christ

[sudden kindle]

I learned calculus from mooculus

[halcyon hornet]

Me leaving the chat bye-bye.

[ripe granite]

moo

lol

[frigid comet]

well publishing 29 essentially identical books to beat the used book market and build a fancy house for himself is one reason at least.

[halcyon hornet]

[karmic thorn]

Stewart empire will collapse!

[frigid comet]

https://tenor.com/view/pirate-cat-cute-kitten-gif-15214073

[fervent lava]

only illegal if your not caught.

[halcyon hornet]

Oh.

[ripe granite]

illegal pdfs

gasp

lol todd-meister owned

[karmic thorn]

Yeah, you'd be better off trying to actually dig in.

Don't fall into analysis paralysis.

[ripe granite]

wise old slim

[sudden kindle]

Do a healthy bit of everything

Analysis, algebra, geometry, its all the same thing

[ripe granite]

[halcyon hornet]

I do literally the same thing for anything new I am trying to learn, so get good resources first and then study it all.

[ripe granite]

someone sully bomb

[sage python]

There's a case both ways

[halcyon hornet]

Now you are going to get Sully bombed.

[fervent lava]

wtf a sully?

[sage python]

Not a sully bombable suggestion tbh

[halcyon hornet]

Yes yes I agree.

[sage python]

Maybe like

[ripe granite]

someone sully bomb dami

[sudden kindle]

Linear algebra > calculus

[sage python]

Idk Senku do you say crank shit a lot? Be honest

Idk you well so I have no idea if you're one of the server cranks

[halcyon hornet]

What is crank shit?

[sage python]

I don't think you are but whenever someone young is shooting high you have to wonder

[frigid comet]

we need a definitive server crank list

[ripe granite]

senku is not a crank

[frigid comet]

with tiers and colours

[sudden kindle]

I'm just kidding, linear algebra = calculus

[ripe granite]

senku go learn calc

just pick a book

[halcyon hornet]

Yes sir!

[sage python]

If someone needs to get their ego toned down a bit I will say they should do calculus first

[karmic thorn]

Don't spend so much time looking for the "best" resources that you compromise on the time that could have been spent learning. Get a rec, run with it. If it doesn't work for some reason, ask around again. @halcyon hornet

[sage python]

Because if you don't know what you're doing calculus will make that painfully obvious and humble you a bit

[sudden kindle]

Whst

[halcyon hornet]

Okay!

[sage python]

Otherwise it's a matter of preference imo

[ripe granite]

wtf js tbhs

[fervent lava]

"to be honest" i think.

[halcyon hornet]

.

[ripe granite]

ignore it

[orchid musk]

yeah don't get "paralysis by analysis" jumping in and getting your feet wet is more important

[sage python]

People who think they can prove big unsolved problems that are way over their heads

And just end up blabbering idiotic shit about the zeta function or whatever

[halcyon hornet]

Yes I do not think that, definitely not.

[sage python]

Yeah then just do what you want

[karmic thorn]

I'm something of a crank myself

[orchid musk]

dunning kruger at its finest lol

[gray gazelle]

even if you want the best resources, i would suggest paul's notes for a beginner, they are very beginner friendly and also 3b1b Calculus videos are very good with paul's notes atleast for a 8th graer i guess

[sage python]

Dunning Kruger is fine if you're right lol. People rarely are with math especially lol

[gray gazelle]

i dont think you can get any "better" resources than these

eventually the content is the same

[sage python]

Paul's notes strike me as the smoothest way to do it and it's free

[gray gazelle]

yeah

[sage python]

Otherwise grab the first calc book you see that's not too expensive and just roll with it

If you really need a physical copy that much

[gray gazelle]

its just that 3b1b provides some intuition and for a beginner that is the best yo can get

[sage python]

(Also get it smoothest? hahahahaha)

[orchid musk]

also realize learning isn't a linear process, somedays you'll be able to proceed and learn much more than other days in the same amount of time

[gray gazelle]

i bought a physical copy and realised i cant keep 2 notebooks and 1 book on my desk at the same time 💀 because its too small

[gray gazelle]

i also have my monitor on it so

keyboard too

😔

[ripe granite]

maffz

[manic cape]

thanks

[gray gazelle]

lol as if i got 50000 currencies to spare

[ripe granite]

do not bring up ipads

people will start asking about which version is the best one instead of learning calc

[fervent lava]

intuition for calculus, isn't calculus itself the intuition.

[gray gazelle]

kinda

but you need some form of where it came from as a begginer

that moment when your savings total up to 1/3rd the price of an ipad

[sage python]

F in respects

[fervent lava]

I finally found a book for multivariable analysis, functions of several variables wendell fleming.

[sage python]

Does it cover wending numbers of curves?

[fervent lava]

basically equivalent to hubbard book but not the extra linear algebra in it.

that is what I was looking for, since friedburg covers that for me.

[karmic thorn]

Do introductory books on algebraic topology assume you know category theory?

Or do they introduce whatever notions are necessary on the go?

[remote nova]

Most books won't do the former

[karmic thorn]

Like, they won't use categorical jargon?

[remote nova]

They often teach you what it means

[karmic thorn]

Sounds good.

[subtle siren]

Billingsley is probably standard for advanced probability.

There are actually a lot of more recently-published probability books (Billingsley, Feller are really old), but I don't know of how good they are, because I don't really read advanced probability

https://math.stackexchange.com/questions/156165/good-books-on-advanced-probabilities
This SE post recommends Klenke, Kallenberg, and also Resnick as already mentioned above

[karmic thorn]

@livid garnet Please don't post pirated books here, Discord disapproves. And of all things you chose some literature...

[livid garnet]

im like 90% sure copyright has expired on labyrinths

[karmic thorn]

||The copy you shared explicitly mentioned not sharing without permission, I think.||

It is unfortunate that publishers continue to leech off of these works

[livid garnet]

that restriction doesn't apply anymore once the work is in the public domain

[karmic thorn]

Then probably share the version that doesn't stipulate a copyright

In any case

Why post that out of the blues lmao

It isn't even math I suppose

[livid garnet]

its a really good book

I reccomend it

[livid garnet]

magazine, radio, or television review, no part of this book may be  
reproduced in any form or by any means, electronic or mechanical, including  
photocopying and recording, or by any information storage and retrieval  
system, without permission in writing from the Publisher. ``` is an incredibly standard disclaimer to put with copyright information

its like the blue screen fbi warning on films from a certain era

[karmic thorn]

Ah, okay, my bad then.

[hollow spoke]

Any review about TM Apostal Mathematical Analysis book .

[frosty girder]

I would say its a pretty good book

i am doing it myself, and i like it quite a bit

[hollow spoke]

Thankyou for your response

[frosty girder]

[marble solar]

Name a better Calculus book

[glad prairie]

it's the best calculus book, that doesn't mean that it's the best book to recommend someone who wants to actually understand calculus for the first time

it's the best book for a second read, or even if you've seen the ideas before elsewhere and are really comfortable with all the prereqs

NOT the best general use book.

[marble solar]

I disagree, I think it's fine for a first read under guidance

[quick hornet]

sorry liberals, best calc book is

[marble solar]

I learned Calculus through Spivak my first time through

I had an experienced instructor who was sure to give us plenty of computational homework so we learned how to take derivatives and integrals quickly

But we also learned how to prove things at a basic level

[gray gazelle]

Anyone read p-adic numbers and their functions by Kurt Mahler?
Working through it now and it's dense but yummy, it's so cool how much general stuff there is besides the g-adic/p-adic stuff

My community college library has a very small selection of math texts and this happened to be one of them which is very lucky

[gray gazelle]

12 pages long

that's too short

I prefer calculus for dummies

[marble solar]

This is pretty neat

[quick hornet]

why would your calc book have more than 12 pages, calc consists of like 4 definitions and 3 facts

[marble solar]

lmao

[quick hornet]

• limit/continuity
• derivative
• antiderivative
• definite integral
  and then:
• all these are linear
• MVT
• FTC

thats literally it

[gray crystal]

Can someone recommend me a book for rep theory of groups
In particular, one with some nice problems (say equal to or slightly harder than Herstein level)
I've tried Steinberg but it has too few problems and most problems seem to be just calculations

[sage python]

First part of Fulton and Harris

[pine trellis]

#1: nG

Think about it. None of us understand what he does so the only proof we have that he's not a crank is faith.

[subtle siren]

Risky click of the day

[broken meadow]

calculus.pdf

[solemn rover]

interesting read

[polar tulip]

looking for an intro to brownian motion at the early grad/advanced undergrad level. Assuming a general measure theory background is fine

[quick hornet]

tracing mathoverflow gives me https://arxiv.org/abs/1802.09679

that is to say, a lot of mathoverflow posts cite it as a reference

idk if thats because its good or just because its convenient

but probably worth a look regardless

[polar tulip]

this looks great, ty!

[sage python]

@polar tulip smh not reading Lawler

[halcyon hornet]

GG.

[subtle siren]

Both Pitman and Yor have huge reputations, that's probably why
After taking a look, it looks really comprehensive. Wow

[subtle siren]

I don't think that arxiv is an intro as much as it is a serious comprehensive recent review. A more typical intro might be one of the textbooks

[storm hatch]

Do you guys have any recommended free ebook in the topic of number theory for year 12 or high school student, because when i searched at google it was all for collage

[solemn rover]

you could try "Numbers, groups and codes", that's what i learned out of in college. i don't remember how good it was.

[twilit crystal]

Nothing on #books-old for stats and probs?

[gray gazelle]

Could someone recommend me a problem book on elementary number theory (prime numbers, divisibility, Eulers theorem, Fermat...)? With challenging but doable problems. (first year undergrad)

[karmic thorn]

@gray gazelle Here's a rather big list

[gray gazelle]

@gray gazelle

oh it pinned

whatever

thanks!

[subtle siren]

What level? If undergraduate, probabilitycourse.com and its textbook.

If graduate, scroll up

[twilit crystal]

thanks

[twilit crystal]

does it cover triple?

I'm not sure what level

im asking for a friend, he is a programmer, but kinda bored and is looking for learn some probs and stats

[twilit crystal]

by scroll up you mean the brownian stocahstic proc?

[subtle siren]

This is advanced probability

Brownian is specific to Brownian, it's a core stochastic process for sure but it's not all of probability

[subtle siren]

What do you mean by triple?

[twilit crystal]

thanks

[twilit crystal]

In probability theory, a probability space or a probability triple {\displaystyle (\Omega ,{\mathcal {F}},P)}(\Omega ,{\mathcal {F}},P) is a mathematical construct that provides a formal model of a random process or "experiment". https://en.wikipedia.org/wiki/Probability_space

[subtle siren]

That's typical in a measure-theoretic course, or essentially advanced probability

[twilit crystal]

Ah I think that's too advanced.

[subtle siren]

That's weird, I don't know why you would need to care about the probability triple unless you are into advanced probability

[twilit crystal]

I think that's coz I'm weird lol.
I don't care about advanced rigor, but I care about the "true" narrative of math.
I want to have a feel of how things are actually defined, minus suffering the proofs

[subtle siren]

"true" narrative of math is very difficult to say. If you want conceptual understanding of things I think you might want to search for different books to find a fitting style than to really have someone else find it for you, unless you specifically can define "true" narrative for others to help you

[twilit crystal]

I think I like something like Terrence Tao Analysis 1. self-contained, no pre-req, gentle on proof, but solid conceptual understanding.

[subtle siren]

I think the undergraduate stuff might still work. They don't define it but there's a still a lot of conceptual ideas

Essentially most probability textbooks could discuss some form of the triple or aspects of it, but generally only advanced textbooks care about exact definitions since they want to be axiomatic and build up

[twilit crystal]

I see, I'll start with this: probabilitycourse.com thanks

[craggy dome]

Are there any good lectures on analytic number theory online? Would really appreciate it 🙂

[halcyon scaffold]

by lecture do you mean videos, lecture notes or books?

[craggy dome]

Videos if possible

[gray gazelle]

Oyestein Ore's Invitation to Number theory might be a suitable read. It's written with high school students in mind.

[solemn rover]

i learned basic probability and statistics out of the book by Hogg, Tannis and Zimmerman

[junior merlin]

@gray gazelle all ebooks are free if you try hard enough

[solemn rover]

numbers groups and codes is free online

[smoky zephyr]

can you guys recommend a multivariable calculus book that is very detailed in the multiple integrals section

i absolutely suck at these

[gray gazelle]

I think there is spivak's calc on manifolds, maybe that'll be good

[surreal phoenix]

I think that might be a different kind of detailed than he was looking for

[smoky zephyr]

this is definitely not for me

by detailed i meant, explains everything

because with double integrals i basically have no clue what i’m doing

[surreal phoenix]

I learned them from professor Leonard, see if that helps

[smoky zephyr]

well i don’t usually use youtube videos but this one time might be an exception

i’ll try it

woah these videos are like 2 hours long, don’t know if i can do that

[gray gazelle]

yea that's the problem with em imo

just too long

advanced calculus by folland

[surreal phoenix]

They're full lectures, so if you're already familiar with the ideas, you can skip to the examples

Either way, highly recommend them

[smoky zephyr]

tterra, do you think that will be a good book for someone that understands basically nothing about double integrals

because i’ve been insanely lost after i’ve gotten to this point

[gray gazelle]

[surreal phoenix]

I don't think advanced calculus is what he's looking for either

[gray gazelle]

the book has many examples and exercises

[surreal phoenix]

just basic stuff you'd find in a multivariable calculus course

How rigorous is it though

[gray gazelle]

yeah, advanced calculus (the book) is basic stuff you'd find in a multivariable calculus course

[surreal phoenix]

Usually advanced calculus means analysis, so maybe that's where I'm confused

[gray gazelle]

depends tbh, I have a book called advanced calc which has stuff like PDE's and multivar

[surreal phoenix]

Oh I see, nevermind then

[gray gazelle]

the book is rigorous.

[surreal phoenix]

Well then it's probably more than he's asking for

Might overwhelm him

[gray gazelle]

rigor != absence of computation and worked examples

you can have both, you know

[surreal phoenix]

yeah, but its presence isn't something he's asking for, either

[gray gazelle]

so they can skip those parts, then?

you don't need to read every part of a book

[surreal phoenix]

still, if you're not even sure if it'll help with his problem with double integrals, why recommend a rigorous book

[gray gazelle]

how can i be absolutely certain any of my recommendations will help anyone?

rigorous book or not

i just chose one i liked and found helpful when i learned that stuff

i don't know quantum well. i can't pick a book specifically tailored to their interests and past education

[surreal phoenix]

Impossible, of course, but still, it's like recommending spivak for someone that doesn't get derivatives. Sure, it works, but it'll probably end up confusing them more

Well, either way, this discussion is getting off track, you can try it and see if it works for you, quantum

[quick hornet]

this is gonna sound a bit elitist but like

what is there to get confused by if youre doing double integrals nonrigorously

you literally just... integrate twice

wrt different variables

[surreal phoenix]

not sure myself tbh, but hey

[quick hornet]

i feel thats why a more rigorous recommendation makes sense

[surreal phoenix]

How come

[quick hornet]

if a student asked for more detail i'd assume they want rigour

since there isnt really much more detail in a nonrigorous course?

[surreal phoenix]

If he has a problem with something you find so simple, I don't think complicating it more is his remedy

[smoky zephyr]

there are questions i know how to do and questions i have no clue how to do

[surreal phoenix]

I don't think rigor is the problem here

[gray jungle]

most calculus books fit that

[surreal phoenix]

he can't do some computations, he doesn't need rigor

[quick hornet]

idk, thats weird to me

what type of questions are you getting stuck on?

[gray gazelle]

.

[surreal phoenix]

Give us an example, quantum, can you do that

[gray jungle]

i was looking for a good calc 3 book as well
settled with jerrod marslen and alan weinstien calc 3 book+munkres for more rigorous reference

[surreal phoenix]

Munkres has a calculus book?

[gray gazelle]

oh no

[surreal phoenix]

or are you talking about his topology one

[gray jungle]

analysis on manifolds is along calc 3

[surreal phoenix]

I see

[smoky zephyr]

@quick hornet stuff like this