book-recommendations

[outer turtle]

i see

thanks!

:D

[tribal crow]

[remote sparrow]

try cummings

#book-recommendations message

<@&268886789983436800>

The sophisticated language is necessary to express new ideas. Of course, I'd criticize books that only apply this language to "obvious" ideas and don't give examples that show why precise definitions are necessary.

It might interest you to read Hamkins' Lectures on the Philosophy of Mathematics for a discussion of the purpose rigor serves for mathematics.

#book-recommendations message

[outer turtle]

ty!!

[ivory shore]

I'm gonna write it down, seems interesting book

[normal crystal]

he has some lectures for it on YouTube

[ivory shore]

Got it

Do you have the pdf format of that book?

[torn blade]

every other question is asking for lin alg book recs lol

[molten gulch]

Yeah

[tribal crow]

calculus and linear algebra book reccs are super common

[normal crystal]

they're ready to tackle Calc and Linear Algebra
but not ready to use the search functionality

[timber mesa]

there's also a very good LA pin #book-recommendations message

[tribal crow]

<@&268886789983436800>

again?

<@&268886789983436800> here, once again

[tribal crow]

<@&268886789983436800> again

[sleek python]

Is it the same person again and again

[tribal crow]

different accounts

[sleek python]

Same content? Seems like it may be a new tactic to have multiple bots join

[tribal crow]

different promoted product, but they all pretty much look the same anyways

[modern ruin]

oldest trick in the book

maybe we’ll end up getting a new automod pattern soon

[heady ember]

What do you need there that isn't covered

[vital bane]

Tensor products for one and multilinear forms and some more stuff that I'm not exactly sure about because I haven't studied QM and GR yet

[heady ember]

That's not linear algebra anymore. Fight me

[vital bane]

honestly that's debatable

[heady ember]

There's a reason I put sotrue

And my point still stands: Physicists likely won't care for the proofs.

[vital bane]

no, of course not but I was talking more about the content than the proofs

[vital bane]

Spivak out here putting open problems in his intro analysis book titled "Calculus"

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

[leaden valley]

Are there any mathematical prerequisites to this book or is it purely philosophical?

[remote sparrow]

nothing deep, but a general familiarity with practicing proof-based mathematics would make some discussions more enlightening

[upper gazelle]

can someone rec a book about complex numbers and other algebra stuff at a math olympiad level (AIME)

[leaden valley]

Thank you, one of my top interests after pure math is the philosophy of it, like Platonism and Wittgenstein.

[slow roost]

I've tried to read the Tractatus a few times. It starts out so clear. The world is everything that is the case. Yes, I'm on board, let's go. But then it gets, uh... hard to follow

his Philosophical Investigations is more readable and quite a delight

[remote sparrow]

https://press.princeton.edu/books/hardcover/9780691202815/sourcebook-in-the-mathematics-of-ancient-greece-and-the-eastern

TIL a new katz sourcebook has been published

[slow roost]

ooh, cool title

[dreamy cove]

any good book with problems in combinatorics and probability

that would be useful in competetion math?

i am willing to learn things i have basic knowledge of those i believe

[sand path]

Any noticeable difference between Spivak’s 3rd and 4th edition Calculus text ?

[leaden valley]

I think titu Andreescu’s book called combinatorics for undergraduates

Don’t know what the others think

The book is used by participants in the international math Olympiad

https://mathematicalolympiads.wordpress.com/wp-content/uploads/2012/08/a_path_to_combinatorics_for_undergraduates.pdf

[leaden valley]

I think the statement “the world is everything that is the case” is much deeper than what others think it is.

[dreamy cove]

hell nah why does it talk about rings gang 😭

but the problems look cool tho

[leaden valley]

Can you screenshot the page?

[dreamy cove]

will see if it is above my paygrade

cant send pics

in this channel

[drowsy nacelle]

Send in #chill

[leaden valley]

Just send it to me in dms

[dreamy cove]

page x

[leaden valley]

Or in chill

[dreamy cove]

in introduction

last part

i mean its not really relevant i guess in the context

still i had a mini heart attack

[leaden valley]

It’s not relevant no

It’s just the introduction

[dreamy cove]

yeah

[leaden valley]

Plus this is an advanced approach, the book is for undergraduates

[dreamy cove]

yeah makes sense

maybe any easier book slightly?

[leaden valley]

I know “concrete mathematics” by Knuth is a good book for undergrad combinatorics

[dreamy cove]

actually the problems look some of them at least doable

ill try and see

will let you know if i could find any use of it

[leaden valley]

Again you can ask the others since I don’t have that many books on combinatorics/discrete math

@dreamy cove there is a book that just compiled problems in combinatorics with no explanation of theorems

It’s good to work through once you get a good idea of combinatorics

[dreamy cove]

name?

[leaden valley]

For example one of the problems is find the number of subsets of N=(1,2,3……..2000) whose elements sum up to a multiple of 5

[dreamy cove]

multinomial theorem somehow?

im thinking

name of the book?

[leaden valley]

102 combinatorial problems, again by Titu Andreescu and Feng

[leaden valley]

The answer to it is shocking

But you can see that it includes powers of 2

[drowsy nacelle]

This is a nice problem

uses ||generating functions||

[leaden valley]

Because the subset (5,10,15…..2000) is a set where all subsets satisfy the requirement, so we need the power set of it

At least that’s what I think

[leaden valley]

Yes

[dreamy cove]

okay thanks

i think that book is easier than this is hard af

ill try that one and see if i find any use of it

[leaden valley]

It is separated into basic and advanced problems

The example I stated is in the advanced section

[dreamy cove]

ohh

[remote sparrow]

https://www.amazon.com/Visual-Complex-Analysis-25th-Anniversary/dp/0192868926

https://www.amazon.com/Visual-Differential-Geometry-Forms-Mathematical/dp/0691203709

can anyone attest to the quality of the paper for those who have bought either of these books?

if it's just average, i'll have them printed with lulu

[dreamy cove]

ok wow that first chapter is really good addition or multiplication

i really like that grid square problem

[slow roost]

I didn’t hear about that new edition of VCA! I have an older one as well as VDG, and the paper quality is good

[remote sparrow]

what's the texture of the paper like

is it like, thick, glossy, rough, etc.?

can you upload some pictures?

also is your copy of visual differential geometry a hardcover or paperback

[remote sparrow]

probably the main changes to be aware of is that figures and theorems are now numbered, and figures have complete captions

[slow roost]

it’s not thick but not too thin / cheap feeling. And not glossy

I have them in paperback

[vital bane]

Yoooo let's goooo

wtfff

Foreword by Roger Penrose!!

that's insane!

[summer lagoon]

Hello, do you guys know a good book or article that introduce translation surfaces?

[leaden valley]

Yeah that’s cool

This complex analysis book is visually oriented so there are some better complex analysis books

Not saying that visual stuff is bad it’s absolutely essential

[ivory shore]

Hello! any real analysis book recommendation?

Someone told me Real Analysis by Folland it's good

I've finished studying "Understaind Analysis" by Abbot and i want to take a step into real analysis

[heady ember]

Folland's text is not for an introduction to analysis.

It covers measure theory and should only be read after learning intro analysis.

[ivory shore]

Would you mind suggesting an appropriate lecture for me?

[tender cobalt]

he did say he finished abbott

[tender cobalt]

I think you can start Baby Rudin now

"Principles of Mathematical Analysis" by Walter Rudin

[merry sphinx]

I mean, rudin does cover roughly the same lvl of stuff. Probably just skim the 2nd chapter of baby rudin and the 7th, do some exercises and then folland should be fine

[heady ember]

Oh my bad, then: I somehow missed that.

If you finished Abbott, you can probably hop into measure theory without issue.

[ivory shore]

thx, i'm gonna check it out

[old elk]

Hi guys anyone here, have you read this book by chance, I am studying line integral for homotopy theory in algebraic topology, and I would like to review a little, with a good construction and formation of the line integral theory.

[leaden valley]

Beginner-

Baby rudin (Rudins principles of mathematical analysis)

Bartle’s introduction to real analysis

Abbott

Moderate -

Papa rudin (Rudins real and complex analysis)

Dieudonne Modern analysis

Advanced (measure theory introduction)

Royden’s real analysis

[molten gulch]

Papa rudin goes over measure theory, does it not?

[sage kelp]

Any recommendations for books that talk about hemicontinuity and continuity of correspondences?

[old elk]

yeh

[remote sparrow]

https://measure.axler.net

[fresh skiff]

not mentioning folland, axler, schilling (if i spell correctly) seems unfair.

even there are few more (i dont remember authors name)

[leaden valley]

That’s interesting, didn’t know Axler wrote a real analysis book. I really enjoyed his linear algebra book.

[leaden valley]

Where would you place axler in my list: beginner, intermediate or advanced?

I excluded some books from the list to make it short, since it can get really confusing if you give a lot of books, one will not know where to start and which book to choose

[remote sparrow]

it teaches measure theory

and elementary functional analysis

there are a couple of scattered extra topics

[fresh skiff]

its measure theory so in middle one (but this varies from person to person, maybe some find it hard but usually easier than others)

[remote sparrow]

e.g. an intro to measure-theoretic probability

[remote sparrow]

https://sites.math.rutgers.edu/~greenfie/mill_courses/math503a/instruct.html#text

this man has

not much said but apparently he thinks there's at least one nice proof

you might find zakeri useful to reference given he has a very geometric/topological take on complex analysis

[vital bane]

and complex analysis

[gray gazelle]

Have any of you taken for credit math courses online in the US? Have you found any places online that are asynchronous and inexpensive? I have heard that netmath is good but I am not a fan of the system they use and also seen that John Hopkins has an online masters degree but it's quite expensive. Community college locally only offers the basics.

[normal crystal]

what level are you looking for?

[gray gazelle]

Calc 1 thru like multivariable, linear algebra, stats, if get beyond that probably coursework in dynamical systems/more advanced topics

[remote sparrow]

i wonder why needham chose this specific vegetable to illustrate intrinsic geometry

[cursive orbit]

a lot of community colleges should offer most of those topics

[molten gulch]

Oh...OH WHAT

[normal crystal]

it depends why you're doing this
you could self-learn and credit by exam the intro courses
for junior/senior courses, idk, maybe state schools have something

[willow saffron]

mind you I just opened the chat

[gray gazelle]

any recommendation to understand maths from the very basis? don't have a lot ot background but I'm eager to start learning

i've been learning some logic and set theory but wonder if there is some kind of "golden" book to approach them

[mortal ore]

Do you have a goal in math

Or do u just wanna learn it in general

[little kiln]

Does anyone have any book recommendations on Combinatorics? particularly a book that would ease me into it and also teach graph theory with problems. Apologies I know this is probably a big ask.

[analog lava]

is there a textbook that teaches representation theory with a more geometric/topology view?

I think there has been a connection between categorical rep theory stuff and knot theory for example and i was wondering how would one get to learn about this

what path

[sudden kindle]

Thats crazy 💀

[slow roost]

I guess most vegetables are more uniformly curved

that one nicely illustrates positive, negative, and zero

definitely funny

[last cipher]

Any good mathematical physics books or applied math books in general?

[molten gulch]

Check the pinned messages

[serene schooner]

where can i read principhia mathematica?

[molten gulch]

archive.org

[serene schooner]

thanks

page 1/512

[dusk hemlock]

A WILD POWER OF 2 APPEARED!!!

[serene schooner]

I'M ON THIRD VLOUME

ok i found the 1

[remote sparrow]

gamelin

[marble solar]

For most people, stein and shakarchi vol 2

[mortal ore]

How should i read a textbook?

Im going through Lang's Undergraduate Algebra right now to prep for summer

and i hope to absorb all the info well enough

but theres so much

[fresh skiff]

Can i do Linear algebra problems in Berkeley problems in mathematics?

after studying Linear algebra from FIS

or maybe i need more background

[willow merlin]

Which books have lots of examples of minimal polynomials and relates them to diagonalization?

[remote sparrow]

can you tell us how you perceive your current linear algebra textbook to be deficient for this purpose?

[willow merlin]

my current book is anton and doesn't even mentioned them

perhaps i am using an old edition

which book do you use for linear algebra?

[vital bane]

probably because of how much curvature it has

why did you think he chose that vegetable

[tender cobalt]

[dreamy cove]

ayooo

[remote sparrow]

the minimal polynomial is discussed in chapter 7 of friedberg, insel, and spence

https://www.statlect.com/matrix-algebra/minimal-polynomial

also there's an article here

it's also discussed in garcia and horn

[pallid quail]

what's FIS tho

[remote sparrow]

look up

[fresh skiff]

Fridberg, Insel and Spence

[remote sparrow]

https://www.mathpop.com/

[pallid quail]

yeah i got it

[remote sparrow]

sad there's AI slop on the front page of spivak's publishing company now

[pallid quail]

well you wanna do berkley ones ?

im interested

[vital bane]

Fried Rice, Ice Cream and Sauce

[fresh skiff]

Doing math with an empty stomach moment

[vital bane]

I actually just had lunch

[remote sparrow]

@loud cradle apparently weintraub has another linear algebra book that i was not previously aware of

it has incorporated his previous treatments of the JCF algorithm, presumably in a more refined way

https://old.maa.org/press/maa-reviews/linear-algebra-for-the-young-mathematician

@sage python

<@&268886789983436800> gambling ad

[night gorge]

Cheers

[leaden valley]

Wtf why would someone advertise gambling

[remote sparrow]

to make money

[remote sparrow]

@static prism this linear algebra book does certain things in a way that might interest you

[fresh skiff]

https://bookstore.ams.org/view?ProductCode=AMSTEXT/57

this books seems good as well

[little kiln]

Apologies for replying again but I'm still wondering if anyone has any recommendations?

[gray gazelle]

its the best activity you can do

[remote sparrow]

A Walk Through Combinatorics by bona

[vital bane]

truly spoken like a Genshin Impact player

[gray gazelle]

never played

[little kiln]

Thank you

[delicate rover]

Hi

Can anyone give me good headstart for fluid mechanics and topology?

[keen orbit]

are there good playlists on youtube about riemann integrals in real analysis ?

[gray gazelle]

learn in general!

[old elk]

I have already read a section of the book, it literally explains everything in a summarized and clear way but it has no basic to difficult exercises, I think I will keep looking for the right book.

[leaden valley]

Is there a better book on abstract algebra than dummit and Foote

[timber mesa]

check the pins, there's a big list of abstract alg books somewhere

[leaden valley]

Thank you

Tbh I don’t know why I asked this because I am not struggling with dummit and Foote

Just that it’s wordy

But it’s interesting so far

Just wondering if there is something better

I already have the book by artin but didn’t read it yet

[old elk]

You should read Artin's

I have Foote's, Gallian's and Thomas Judson's, but I'm more partial to Foote's.

I can recommend other books, in Spanish and Portuguese if you wish.

[velvet gyro]

Anyone read Kolmogorov’s Foundations of the Theory of Probability?

would it be overkill or the opposite?

[peak raven]

Not reading author name

[earnest wolf]

i recently asked for an ODE book / lecture notes and was suggested two good resources (Paul's notes and Boyce's book), thanks to Sour Drop

but unfortunately they lack the discussion and practical examples of 3x3 systems of ODE's

how do we, for example, solve x' = Ax where A is 3x3 and has a triple-repeating eigenvalue? or a double-repeating?

so looking for this kind of stuff

[leaden valley]

Bro

Are they translated

And are they good

[old elk]

This I have for abstract algebra

[ivory shore]

Tenes una biblioteca ahí

[old elk]

jajaja, no soy amante al algebra abstracta, pero me gusta las palabras que usan xde

[ivory shore]

No sé absolutamente nada sobre álgebra abstracta pero parece linda materia

[leaden valley]

I am going to assume you didn’t read all of them

[ivory shore]

he's crazy if he read all of them

[earnest wolf]

reading cover to cover math textbooks is usually not very efficient

[old elk]

This is correct

[ivory shore]

damn, now i know why i'm not learning anything

[old elk]

To the eye I kept the ones that looked from the easiest to the most difficult, some have what others don't, others have different exercises like topological etc, those are the ones that have interested me because they are not confined to one area.

[old elk]

Que nivel estas?

[ivory shore]

i do the same, i'm aware i'm not gonna read all of them but step by step i'm learning and even more

[ivory shore]

básico-intermedio, no soy estudiante de alguna carrera de Matemáticas/Física, soy autodidacta

O sea, estoy estudiando ingeniera aeronáutica y eso me ayudó mucho

[old elk]

In what area of mathematics do you focus?

[ivory shore]

At this moment i'm studying analysis (Abbot, Spivak, etc) and Fourier Analysis

I like ODE's, PDE's, complex analysis, etc

Tools that help me in my career because we study them a lot but I'm studying them in a math way

theorems, definitions, proofs, lemas

[fresh skiff]

Yay. Algebra lover

I love algebra as well

[cobalt arch]

Where did you find the Lanski book as a pdf? I can't find it online. I don't want a pdf, I already have it as a hardback, but I am asking to know where you found it

[south elbow]

What are some good resources to read to become intimately familiar with tensors? Penrose diagrams look like nonsense to me right now and I want to know more about them

[earnest wolf]

Oh
I think I found what I need

[old elk]

It was hard to find it, literally that book is a beast for people who want to specialize, it's like a dummit but harder haha.

[gray gazelle]

Munkres for Topology

[remote sparrow]

https://bookstore.ams.org/stml-82

@fierce hedge

[keen orbit]

sorry for jumping in like this but rn i am studying portuguese since i will study in brasil so if you have good recommendations for abstract algebra in portuguese i will be grateful

[keen orbit]

also if anyone knows about this

[old elk]

That interests me, what university are you applying to, my friend?

I am aware of the books they use in Brazil.

[keen orbit]

i came to brasil about 2-3 months ago so right now i will temporarily get into a university called cruizero do sul so that i can do the transfer exam to university of sao paulo (usp) in april-may

if that doesnt work then i will try entering using fuvest at november

are you perhaps studying in brasil too ?

[old elk]

No, but I am going to apply to sao paulo and the university of campinas in the middle of the year and at the end of the year to see if I pass for the other year to start.

[keen orbit]

ohhhh do you mean the transfer exam by middle of the year ?

[old elk]

Arnaldo's elementary algebra
Elon lages's real analysis
Adilson's algebra
Elon lages's analysis in several variables
Oliveiro's functional analysis

[keen orbit]

tysm

[old elk]

No, admission test for the master's program

[old elk]

If you need the pdfs, I have them

[keen orbit]

ohhh master's program

i am applying as an unergraduate

[keen orbit]

if you please can you send them to me?

[cobalt arch]

Harder than Dummit and Foote? I don't think so, it is more introductory in nature

[old elk]

I was going to buy it, but I hesitated, so I went for the Foote, although I'm still considering it.

[opaque magnet]

Hello guys any recommendation for introduction/elementary geometry book please ? (i'm an absolute beginner) i'm currently on this book: Basic Math & Pre-Algebra For Dummies i'm studying math from 0 (i already basic arithmetic knowledge) i'm an auto didact i plan to Do Basic Math & Pre-Algebra For Dummies > Algebra I > Geometry > Algebra II .

[solid grotto]

Can you share ?

[old elk]

Which one do you need?

[old elk]

Do you need the pdf?

[vast jackal]

you can do a much better job by going to aops series if you can tackle hard ones

[vital bane]

Springer UTM made in china

[lilac raven]

any thoughts on complex variables with applications by silverman?

my school’s first year grad complex analysis is using that

[remote sparrow]

never heard of it

https://link.springer.com/book/10.1007/978-0-8176-4513-7

this?

seems a bit soft for a graduate class

https://www.amazon.com/Complex-Variables-Introduction-Applications-Mathematics/dp/0521534291

this might be more appropriate for a grad class that wants to emphasize applications

[lilac raven]

yeah i was expecting something like this, ahlfors, or maybe stein since that’s what the class used in the past

it’s like a weird half lebesque measure theory (royden) and half complex analysis course tho

with an emphasis on holomorphic functions, residue theory, and conformal mapping so i think maybe it’s just the later chapters in the book?

[cobalt frigate]

Guys the 3 little pigs is a good book

Very educational

[trail hemlock]

LMAO

[cobalt arch]

No thanks, but you can tell me, if you want, from where on the internet you got it

[old elk]

In a telegram group, although I haven't checked if it's on the genesis page.

[quick hornet]

pls no discuss piracy

daddy discord doesnt like it

[last cipher]

Would it be possible if you provided me with 5 and 2?

[cunning mirage]

good books for jee adv ?

[quiet trench]

Anybody have a good textbook that theyt reccomend for algebra 1?

[earnest wolf]

the guy just self-published

I'm surprised that springer didn't sue for using "their colors"

[vapid pollen]

https://qr.ae/pYwzZq

[cunning mirage]

thx 🥰

[vapid pollen]

I've got one more wait

https://www.quora.com/What-are-the-books-for-the-JEE-which-have-a-theory/answer/Apurba-Chowdhury-1

Check these out

[cunning mirage]

basically cengage

[leaden valley]

What’s the backstory

[earnest wolf]

#math-discussion or #discussion

[sleek python]

Oh shit I thought I was in chill

Sorry

[old elk]

guys I am looking for a book
that explains the equivalence relationship
and equivalence classes.

[graceful moon]

Any introductory algebra book will do that. Dummit and Foote or Artin are the classic recommendations

Liebecks a Concise introduction to pure mathematics talks about them IIRC and that’s a very very approachable book

[slow roost]

Stewart & Tall - The Foundations of Mathematics

[viscid moss]

Any Books for calculus/advenced calculus plz ?

[torn blade]

i recommend Stewart’s calculus book

not sure what “advenced” calculus is tho

[slow roost]

Spivak

[viscid moss]

Tysm

[jaunty vault]

What [books] are unlocked after Spivak's Calculus is completed?

[molten gulch]

most intro real analysis texts I guess but you could do complex variables if you wanted (assuming spivak covers partial derivatives and line integrals), maybe some other stuff too

[jaunty vault]

okay thanks

[molten gulch]

I would also recommend waiting for other people's opinions

[old elk]

In my opinion, a book of calculus in several variables, I know one called vladimir, but in this case I would use one that is portuguese which is the book of analysis in several variables by elon lages lima.

Then you unlock complex variable after they define line or contour integral.

[fast summit]

Any good proof books?

[molten gulch]

hammack's book of proof https://richardhammack.github.io/BookOfProof/Main.pdf

[fast summit]

Nah I didn’t like that one

It assumes you know linear algebra

I’ll probably read it after the summer when I’ve taken lin Alg and diff eq

[molten gulch]

Not really, it assumes you know what a vector space is at some points I think

but that's about it

[fast summit]

R^n mappings too

But that’s some advanced calc 3

[molten gulch]

Nope

[molten gulch]

R^n maps ae just multivariable functions

Just running away because you see something you think is related to some advanced class you haven't taken yet isn't gonna fly

[fast summit]

Negative Nancy headahh 😂

[fast summit]

My school rotates calc 4 Lin alg with calc 3

I have not done any work with multi variate

I just want a book to read while I’m In spain next year bro 😢

Damn are you making your own book?

[molten gulch]

An example of a multivariable map (f\colon \mathbb{R}^{3} \to \mathbb{R}^{3}) could simply be some map, say (\begin{bmatrix} x \ y \ z \end{bmatrix} \mapsto \begin{bmatrix} 3x \ 2y \ 4z \end{bmatrix})

[hasty eagle]

James (The Cat Collective)

[fast summit]

Is that a scalar

Lowkey

[molten gulch]

Next year is a long time, you could EASILY learn the material

[fast summit]

Wait I’m dumb

Nvm

[fast summit]

Alr I’ll try

[molten gulch]

Recall that (\mathbb{R}^{3} := \left{\begin{bmatrix} a \ b \ c \end{bmatrix} \colon a, b, c \in \mathbb{R}\right})

[fast summit]

Do you have any nice stats or probability books that go past ap stats

[hasty eagle]

James (The Cat Collective)

[molten gulch]

All of 'em use some nontrivial amount of calculus

[fast summit]

It’s alr I’m in calc bc rn

Idk if that’s enough though

[molten gulch]

I do not know how much calc BC covers, I only started taking calc after getting to uni

[fast summit]

It goes through calculus 1 and 2

The major uni topics it doesn’t cover is integration via trig substitution, and the root test for convergence

But i have finished all the homework and material and need something to do

[molten gulch]

Also please keep in mind here that I'm not considering cauchy sequences for defining the reals, any topological properties of R, etc... which should be done in a proper definition

I'm also not explicitly considering the euclidean norm

[fast summit]

It’s good because I don’t know any topology or complex analysis 😂

[molten gulch]

Cauchy sequences are real analysis

not complex

[fast summit]

Oops my bad

Don’t know that either

[molten gulch]

I'd recommend first getting your mathematical wheelhouse in order

before doing anything

[fast summit]

???

[molten gulch]

Because you keep mixing up fields and definitions

[fast summit]

Well I haven’t taken any of that before

You need to learn proofs for real analysis don’t you?

[molten gulch]

Many people learn proofs alongside it

I learnt proofs with linear algebra last summer -Ryan

[fast summit]

Nice 👍

My high school teacher for math will do calculus 3 senior year so I don’t want to learn that myself since he’s a cool dude and I want to do that class with him

[molten gulch]

I'd recommend picking it up early, it'll give you an edge, also learn your convergence tests and trig sub

[fast summit]

Ok I feel a little bad for him for doing that, but I don’t know what I’d do senior year since I works the full calculus sequence and linear algebra so I thing real analysis would be my only option, and they don’t offer that at any community colleges near me so I’d have to drive an hour everyday to go to a class

[molten gulch]

I mean, if you pick it up early, you can still go to class, it'll basically be a free credit, won't it?

also many unis will require you to take some form of proofwriting class to do RA afaik

[fast summit]

Oh you mean just get s a basic grasp?

[molten gulch]

ye

[fast summit]

Ok I can do that for sure 👍

I’m going to try to learn trig substitution tonight then I guess, thanks for the help! 😄

[molten gulch]

IMO it's not a difficult method, just...tedious

[opaque magnet]

Hi guys i'm getting into algebra soon are Elementary Algebra and Intermediate Algebra from OpenStax a good textbooks to study to build strong skills in algebra to tackle Pre-Calculus and Calculus later ? (I plan to use stewart book's later for pre-calc and calculus subject i'm also an auto-didact)

[rigid trail]

The textbook you choose doesn't matter too much for learning algebra

Just be sure to practice a lot

And I'm not sure what "pre calculus" is

[vapid pollen]

Just sharing quora posts brother, I am not in a position to give u my experience

I'm a JEE2027 aspirant, so I shared these to see if they could help!

[cunning mirage]

-_-

[vapid pollen]

Wish you all the best on ur JEE journey

[cunning mirage]

ok np

[vapid pollen]

lol 💀

[vapid pollen]

Take care, also

[cunning mirage]

yeah i needed this

[vapid pollen]

U can go to the jeeneetards discord server and ask people there for recommenda

[vapid pollen]

🫂🫂

[vapid pollen]

Lot of people there who could help you!

More than I can

[cunning mirage]

yeah i know

[vapid pollen]

Okay goodluck! Take care 🫂🫂

[opaque magnet]

it's is basically algebra and trigonometry before heading into Calculus if i'm not mistaken but thank's

[rigid trail]

How is it different than just trigonometry

[opaque magnet]

i think you just should have some knowledge of trigonometry before going pre-calculus from what i have read, subject: College Algebra and Trigonometry and Pre-Calculus are overlaping from my understanding so it's basicaly the same idk it's a bit confusing to me also but i'm not there yet i'm soon to algebra I

it's just different from school to school from what i understand, i'm french also so the subject aren't even named the same in my language but i learn math in english.

[rigid trail]

You mostly just need a lot of practice in algebra, then understand some trigonometry

Then you can learn calculus

I'm not sure what pre calculus is for

[opaque magnet]

Here my roadmap for now
• Pre-Algebra
• Algebra I
• Algebra II
• Trigonometry (Basics)
• Precalculus
• Calculus
• Discrete Mathematics
• Linear Algebra

[opaque magnet]

It's basicaly a review of Algebra and trigonometry from my understanding

[rigid trail]

So you don't really need a book for it

It's just a course that they make students take to refresh on the topics?

[opaque magnet]

Yeah i think's so

[rigid trail]

Also you don't really need trigonometry, it isn't quite a prerequisite for calculus

But it is good to know, along with some geometry

[opaque magnet]

I will need it for programming project

[rigid trail]

The only actual prerequisite for calculus is a strong understanding of basic algebra

[opaque magnet]

i prefer to learn math correctly and have decent foundation on the subject

[rigid trail]

What programming project needs trigonometry? Are you doing game or graphics dev or something

[opaque magnet]

yeah

I'm learning

was learning C++ but i want to understand math behind problems and actually learn math since i messed up in shool years ago

now i have full time ahead, no work so i study alot and i'm actually liking math for the first time

[rigid trail]

Nice

Well you don't need math to learn C/C++

[opaque magnet]

but i have so much math to learn

i know

[rigid trail]

I'm interested in graphics programming in C

If anyone knows some good books I'd appreciate it lol

[opaque magnet]

but once I tried to solve any problem involving little math i was getting really anxious and didn’t know what to do and mind got blank

so that's why decided to learn math and actually use my brain

ok need to sleep it's 6 am i've been up since 16 hours

[opaque magnet]

What level of math you have currently ?

[rigid trail]

I'm studying math as an undergrad

Studying real analysis and diffeq as a first year

[opaque magnet]

Nice, i’m self studying at home i don’t have lecture or teacher but only my brain 😄 and i study in english which isn’t my native language

[rigid trail]

You got this, it is definitely possible

I also was self taught until I started university

[opaque magnet]

So cool, yeah plenty of good resource are in english

That’s why i made the jump

[hearty canopy]

Anyone read dune messaih ,how is it

[opaque magnet]

Good luck for the degree, i hope you will get there ! I’m going to sleep have a good day/night

Thank’s for the talk.

[lament thistle]

hello, i need a book about basic aritmetics for my son. can someone recommend me one?

please

[trail hemlock]

aops has a prealgebra book which i think is nice

people say lang's basic mathematics is good but after looking at it recently i think its boring and there are a lot better choices.

[slow roost]

I mean

how could that material not be boring?

at least it actually explains it well

what books do you think are better for this?

I'll check out the AoPS one

[trail hemlock]

for prealgebra i think khan academy is prob the best. aops prealgebra is good, also david morin has algebra books that are rly nice

[trail hemlock]

yeah i mean it’s a good book, i just don’t think 6th grade me would have sat through it or paid any attention

[slow roost]

this is true, the writing style is for people already at a solid level

[trail hemlock]

the morin book in particular i like because it has “more than 100 original math limericks”

[slow roost]

that's fun

[tender cobalt]

Any algebra books that start with field and ring theory?

[slow roost]

there are books on just rings or fields, but I've not seen a general algebra book that skips doing groups first

ring theory kicks off with a lot of direct analogs of results from group theory to rings

fields are a pretty different feeling thing, you use more linear algebra to develop the theory and it feels different

[remote sparrow]

i don't think any introductory abstract algebra books start with field theory, but Algebra: Notes from the Underground by aluffi, Abstract Algebra: An Introduction by hungerford, and A Concrete Introduction to Higher Algebra by childs do rings before groups

[slow roost]

neat! I love Aluffi's Algebra Chapter 0, I'll have to check that one out

we used Hungerford's Algebra in my grad algebra sequence. Nice challenging book, super thorough

I wish I worked harder on algebra back then. Trying to improve it these days

[vast jackal]

YouTube should suffice like the organic chemistry tutor but if you want him to learn more, khan academy or prealgebra aops should do

[vital bane]

bro you gotta focus on one book

I see you asking for book recs 3 times a day, you gotta lock in and finish Shifrin first

[astral temple]

I learned random calculus stuff on YouTube but I want to make sure I learned everything properly does anyone does anyone know a free book that has all the topic of calc 1 and 2 and maybe 3

[gray gazelle]

Calculus by Spivak is usually recommended. This is the first book I found that is free. https://openstax.org/details/books/calculus-volume-1/

Calculus is mostly the same everywhere so it doesn't really matter imo

[astral temple]

Ok

[vital bane]

I would recommend the calculus books by Open Stax

https://openstax.org/details/books/calculus-volume-1

[tender cobalt]

Facts tho youre right

[unborn ingot]

If u people have a hard time finding learning materials,here’s a site I used its all free

called vdoc.pub

[fathom wharf]

im taking bs mathematics and we have this subject called elementary analysis I, II, III. what is it and can I have a book recommendation for this

[lilac raven]

what’s the course description

it’s most likely real analysis (rigorously defining convergence, continuity, differentiation, and integration) but the rigor of it depends largely on your school

[undone prairie]

guys do u know a book for self study of number theory?

[tender cobalt]

looks just about what i need, thanks

[uncut salmon]

Is there any recommendations written somewhere for point-set topology? I didnt find anything in the pinned messages.

[uncut salmon]

Thank you, it's probably the book that I'll use eventually, but I was curious to know other books.

[uncut salmon]

Do u think it's THAT good that using another one wouldn't make sense?

[vital bane]

you could check out Lee's Topological Manifold book as well

Lee's Quadrilogy of Manifold books are all the craze these days in the server

[solid goblet]

I used Manetti

[uncut salmon]

Ok thanks for everyone, I'll check them out!

[naive lava]

they are AMAZING

i did not read all of them but, BUT, compared to spivak, i prefer them

[vital bane]

🤨

[naive lava]

for diff manifolds

[vital bane]

I will not stand for Spivak slander

you shall be executed summarily!

[naive lava]

look, i love his calculus textbook, but diff geo's are just too wordy (rudin enjoyer slander)

[vital bane]

of course...

I like words on a page 🗿

[naive lava]

i believe no textbook can talk enough to make you grasp a subject like a teacher does, soo, i just prefer him throw theorems to me and i can figure out the rest

[vital bane]

why not both

[naive lava]

like i have never used any math textbook that gives me good enough intuition and a way of thinking by words, it's always from problems or self exploration

[naive lava]

wdym

[vital bane]

Both good exposition and self-exploration through good problems

that's what Abbott does amazing book

insanely well written

[naive lava]

i don't think good exposition exists tho

[lilac raven]

aside from munkres, i hear good things about this one

[vital bane]

reading that book is basically like having a teacher sit right next to you, who gives you good problems

[lilac raven]

https://www.maths.ed.ac.uk/~v1ranick/papers/morris.pdf

topology without tears

[vital bane]

that's because you've only read Rudin type books 😔

I hear Tao is a great expositor of Analysis

like his measure theory books and his analysis books

[naive lava]

no, i've looked at abbot too, but i believe what he makes up in exposition, he loses it from other ways

[naive lava]

my friend used Tao but later said he'd prefer something like rudin

because i believe power of books like his comes also from a refernce viewpoint

for example, i would never ever care for the proof of bolzatno weiretrass theorem, but if i need it, i can just look it up and it'll be the easiest thing ever

or just in general things you don't need to learn

[vital bane]

but that proof specifically has some nice ideas

[naive lava]

sssssh, don't let them know

anyhow, here's a review of lang's algebra: One of the exercises in an earlier edition was “find a book on homological algebra and do all the exercises.”

[vital bane]

classic

oh he removed it in a later edition?

[naive lava]

i think he just points to a certain book rather than just saying find a goddamn book and learn

[gray gazelle]

Munkres! Also, Topology and Groupoids by Ronald Brown.

[fresh skiff]

hearing the later book for first time

seems a nice book

[gray gazelle]

Yeah I heavily recommend it if you’d like to learn some alg top too!

[fresh skiff]

yeah

i will consider it

soon i will start top

[normal crystal]

we need to get you a Ronald Brown Enthusiast tshirt

[gray gazelle]

So true

[remote sparrow]

https://math.stackexchange.com/questions/184338/book-with-lot-of-examples-on-abstract-algebra-and-topology

[remote sparrow]

@loud cradle i received my copy of the second edition of garcia and horn's linear algebra book

[slow roost]

they are goated, but I'm not sure what trying to learn topology for the first time from Intro to Topological Manifolds would be like. For the very ambitious and hard working, it could work out. I recommend Munkres, Crossley, or Mendelson

[orchid echo]

I’m pretty sure Lee says that his topo manifolds book is not the place to learn topology

Like in the book

[slow roost]

that sounds right

[loud cradle]

nice, i forgot this exists... taking a look at the preview on amazon i like the list of content added in the new edition:

[slow roost]

it still gives a pretty solid review / overview of the necessary parts of it for his purposes in the first few chapters

[dim sierra]

I had Garcia as a professor before he's the goat

such a nice guy

[remote sparrow]

https://global.oup.com/academic/product/an-introduction-to-module-theory-9780198904908?lang=en&cc=us

not yet released but leaving this here

[dreamy cove]

any got any book recommendations for hard linear algebra problems?

[fresh skiff]

it depends upto your background

[dreamy cove]

i know some matrices, determinants, vectors, 3d geometry thats pretty much my linear algebra knowledge

not super indepth but i have some idea

[slow roost]

Golan - Linear Algebra a Beginning Grad Student Ought to Know

has a LOT of exercises, including plenty of challenging ones

[fresh skiff]

Probably try Fridberg for proof base linear algebra, if you want something more challenging try axler.

[fresh skiff]

Will it be worth using this book for problems ?

[slow roost]

I don't really know what people really want to know when they ask a question like that

will it be... worth it? To do problems in a math book?

worth... what?

are you wondering if the price of the book is reasonable?

what would constitute it being worth it?

[dreamy cove]

im more for doing problems than proof to be honest

[dreamy cove]

will look into it

nope the contents are too high level for me as of now

[slow roost]

you did ask for hard!

[fresh skiff]

i mean spending time

[slow roost]

that depends on your own values and goals, right?

[fresh skiff]

fridberg will be a better choice

[fresh skiff]

makes sense.

Like i wanna go into Algebra side (like alg geo etc)

[dreamy cove]

okay!

[slow roost]

I wholeheartedly recommend FIS. It's what I learned LA from

[dreamy cove]

umm i dont think you guys understand lmao im not tha tgood at math yet

im looking for hard problems that use elementary things?

[slow roost]

I get you better now

[fresh skiff]

and it is what i am studying
really a GOAT

[dreamy cove]

yea

[slow roost]

I wouldn't dismiss a book like FIS for being proofy. It's really well written and has a lot of elementary / computational problems

it may be a challenge for you (most likely will) but you might like it

[dreamy cove]

hmm

[slow roost]

what have you been learning it from so far?

[dreamy cove]

just teachers and shit

[ivory shore]

does anyone have the book titled "Fourier Analysis and its applications" by Gerald Folland?

[serene igloo]

Does anybody know a book with plenty of differential equations?

[fresh skiff]

a differential equation book
(book with title Differential equations)

[molten gulch]

yes, why

[lilac raven]

Thoughts on pde by Strauss?

[molten gulch]

heard it's good

[thorn cloak]

I used it for my undergrad course. It’s good but i personally like PDEs by Choksi more

Theres a lot more content though so you might need to be selective

[tender cobalt]

Any rigorous ODE books?

[tribal crow]

Arnold comes to mind

my class uses Hirsch, Smale, and Devaney though

also fairly good, imo

[tender cobalt]

whats the difference between that and arnold

[tribal crow]

the difference is that I have not read Arnold, but am reading HSD

I’ve heard good thing about Arnold though, so I figured I’d give it a shoutout

[ivory shore]

Could you pass it to me?

Please

[molten gulch]

No, providing materials in this manner is piracy and is not allowed in this server

[ivory shore]

Oh, i didn't know

My bad

[lilac raven]

i think brown has a grad course in odes, you could probably check what book they use

[candid mountain]

I wanna learn calculus all . is there any book which covers full calculus ?

[tender cobalt]

Thomas' Calculus

And James Stewart Calculus

[candid mountain]

ok . thanks for your suggestion . I have decided to go with stewart calculus

[fresh skiff]

arnold requires measure theory from the reader iirc

[tender cobalt]

I saw in preface it said elementary real analysis and linear algebra

[fresh skiff]

I see. But iirc it requires MT
Maybe I mistaken idk

[hearty steppe]

what are the most self contained texts for bifurcation theory and perturbation theory?

Anyone familiar with this? https://www.google.com/books/edition/Bifurcation_Theory/5CfrBwAAQBAJ?hl=en&gbpv=1&pg=PA1&printsec=frontcover

[vale venture]

I feel we have to convince our libraries to get this, have you looked into it ?

[slow roost]

I read Baez' article in it, which is characteristically really great

https://arxiv.org/abs/2304.08737

haven't looked at the rest yet

[haughty parcel]

Hi people! Can you give me a list of books from arithmetic to calculus that explain in detail the why's of procedures instead of being like recipe books?

[opaque magnet]

Are OpenStax books Pre-Algebra 2e and intermediate Algebra 2e a good resources ?
I'm going to use other resources for further but i wanted to know if it's any good for algebra learning ?

[normal crystal]

yea, they're fine
most of the books at that level are similar

[mortal ore]

the problem with this is that its the "why" is usually pretty difficult

i.e. learning long division in 4th grade vs doing modular arithmetic and euclidean algorithms in number theory in college

also calculus vs analysis

[ivory shore]

In my case I use chatgpt for recommendations , I specify what I want and you can check them out one by one

I did that, for example, to study Fourier Analysis

[molten gulch]

ChatGPT hallucinates book names

[exotic belfry]

and quotes

[ivory shore]

It's not the best tool but it's helpful if you are lost

[opaque magnet]

Ok thank's man, for further study I will use stewarts or sullivans books for pre-calculus and calculus, an introduction book on trigonometry about 250 pages before heading in pre-calculus

[gray gazelle]

greetings my friends

could anyone please recommend me resources for studying the various indeterminate forms in limits and techniques to solve questions related to them (with derivation of the formulae used as well)

[abstract copper]

any springer coupon?

[scarlet terrace]

any calc textbook should do, like stewart

[burnt marsh]

hi guys! I'm in HS rn and i wanna explore more complex math. could someone recommend me books or resources that'd be a good starting point? Thanks again.

[dreamy cove]

resources with good questions on conic sections?

[ruby plaza]

should i read the books of the giants like Euler and Gauss. Like it might be interesting from a history point of view but is there any real advantage

[tender cobalt]

you can start with khan academy, do their precalculus, algebra II, trigonometry courses and then you can go read some calculus book. it's what i did. Or you can also start off with some precalculus book to teach yourself some trigonometry algebra along with some vectors which can help you learning calculus . Lemme know if you need any recommendations for them.

[burnt marsh]

sure i'll check out Khan Academy. And yeah can you recommend some books to start with calculus? i know the basics for school but thats about it. Thankyou!

[haughty parcel]

so i should stick to textbooks that teach procedures till i learn about logic and number theory and such in order to understand all of those procedures?

[shadow otter]

if you keep on practicing it kinda comes to you

[dreamy cove]

make sure u are good at algebra to not get kicked by calculus

most people rush that and jump into calculus and when its time to apply everything from before they cant recall

[tender cobalt]

for calculus, most popular one is Calculus by James Stewart, but I personally really liked Thomas' Calculus and it has much better content. before starting calculus you want to be familiar with trigonmetric identities, logarithms and exponential function, but i guess you can start without and be fine, although going to be a bit harder

[mortal ore]

Yeah

[cobalt arch]

I think there is an advantage, namely, simplicity and axiomatization. Such books by the masters are more likely to be written in simple yet rigorous language and they are axiomatic in nature. Read this for more: https://mathoverflow.net/questions/28268/do-you-read-the-masters

Yet some people might disagree, it is up to you to think through it and decide

[dim sierra]

I don’t think that’s the case at all

Papers by Gauss and Riemann for example are notoriously difficult to read. In fact Gauss had the habit of never revealing the way he thought about things or the intuition behind them - he would just give the results and the proofs. His definition of composition of binary quadratic forms for example isn’t simple at all, and seems totally unmotivated. Riemann also writes extremely densely

In general famous historical books or papers are quite difficult to read - if you want to read Gauss’s geometry stuff you can check out Volume 2 of Spivak’s Comprehensive Intro to Diff Geo. I’m sure there are commentaries on his other works as well but idk about them

[buoyant dawn]

hello people! i was wondering what the general consenseus is here on the best books to start on combinatorics?
i've done a good bit of it in a high school setting before, of course, but that's very different from a college setting specially as a math major so i'd like a book that starts from the start. i already searched up "combinatorics" in this channel and also did my own research and downloaded a lot of books, but i wanted to ask again anyways to get some second opinions! please give me recommendations :>
(p.s., i'd also appreciate the same for stats & probs, but i've already ordered the blitzstein & hwang textbook lol)

[tame tree]

walk through combinatorics by bona

[quiet mural]

heyy..am new here : )

[fresh skiff]

I think you have already mentioned this in some other channel

Like a few hours ago

[quiet mural]

ohh..may be i forgot 🥲

[cobalt arch]

I am talking mostly about their more accessible works instead of papers like Disquisitiones Airthmeticae by Gauss or Elements of Algebra/Analysis of the Infinite by Euler. I am pretty sure there are places where their exposition could have been much better and their notation modernized but there is a lot to glean from these books and this can be said about more modern books as well. I have read parts of them and I am planning to read them in their entirety. But that is just my preference and other people might agree or disagree with that. I explicitly said to the person who asked that it is best to think independently and come to a conclusion regarding what they want to do.

[fresh skiff]

Thats fine

[dim sierra]

Yeah I wasn’t attacking you sorry if it came off that way, just disagreeing

Which of their works are the more accessible ones, by the way? I’m interested in reading them too

[buoyant dawn]

that one seems to be quite liked here! can you tell me ab it?

[tame tree]

its very problem oriented

[remote sparrow]

there are also solutions included to many problems in the book

[buoyant dawn]

hmm, so its beginner friendly and has a lot of good problems with solutions?

i think if i mix that with something like Principles and Techniques of Combinatorics by Chuan, which from what ive seen seems to more rigorous and proof-y, it should do me well for the next semester

any other good more rigorous books, though? :>

[buoyant dawn]

skimming through it rn, bona seems positively lovely!

[sage kelp]

Does anyone have recommendations for a textbook on convex functions? I found Convexity by Eggleston, but it seems to be a little outdated.

[sand path]

Recommendations for Linear Algebra text that are more Physics/Application focused

[graceful moon]

My recommendation is to read the pinned document in #proofs-and-logic written by Loch, and then just dive into an introductory textbook in whatever you want to learn, and you’ll learn to write proofs through doing the problems

There’s also the book of proof, which is an entire book dedicated to it, but I’m not sure that’s needed

Something like Liebecks a concise introduction to pure mathematics could be a nice read if you don’t know which area of maths you’d like to learn about

I often recommend that last book to highschool students who are thinking about maths at uni, it really gives you a taste of the different kinds of things you’ll be doing

[dim pendant]

Instead of your basic subject books that have titles like "Abstract Algebra" or "Theory of Complex Functions of Many Variables", what more specialized books do you guys enjoy? I'm looking to acquire a few more here and there but my favorites are "Primes of the form x² + ny²" and the big three book series on elliptic curves.

(I am not interested in combinatorics, probability, or statistics)

[north summit]

Is someone familiar with the measure theory book by axler?

[cobalt arch]

It depends on the mathematician but there are many good books that are accessible. Like I said their published works, especially the ones that have been translated into English are mostly accessible. However Euler was a very prolific writer and his Opera Omnia is certainly going to contain books that aren't as accessible but it is still worth going through the ones that have been translated like Elements of Algebra, Analysis of the Infinite and Foundations of Differential Calculus which should be read in the way I have written them. Gauss' Werke contains his first volume, which is Disquisitiones Arithmeticae, and the rest. There are many other mathematicians which have written books and can be found easily. Now not all of them will be as accessible but that is something to be expected. You have to find the books that are at your level or a bit higher or even lower (if you want to revise said material in a unique way).

[slow roost]

I should have some more books like this.. here are a few favorites
Gardner - Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
Rucker - Geometry, Relativity, and the Fourth Dimension
Conway, Berkelamp, and Guy - Winning Ways for your Mathematical Plays
Scorpan - The Wild World of 4-Manifolds
Gompf and Stipsicz - 4-Manifolds and Kirby Calculus

honorable mention to Smullyan - What is the Name of This Book?

which is more about logic than math

[fresh skiff]

wow i love title of these books

[valid narwhal]

Probably irrelevant but how can you tell whether a PDF/eBook is pirated or not

[normal crystal]

clue 1, you didn't buy it

[naive swift]

i'm not sure if this is the right channel but is there a solution manual (official / non-official) for the 4th edition of ladr? i was only able to find solutions for the 3rd edition

i think i found one: https://github.com/motivationss/Linear_Algebra_Done_Right_4th_ManualSolution

[small perch]

does anyone know any good introduction into higher or enriched categories?

[burnt marsh]

okay! thanks again

[vital bane]

@remote vortex

[graceful moon]

Do you care much?

[vital bane]

i hear Axler's measure theory book is very good

[vital bane]

Linear Algebra and Its Applications by Gilbert Strang

[quiet mural]

heyyy

[valid narwhal]

definitely not, but I have huge respect to the authors so I'll find non pirated copies. Can't afford to buy one cuz there's no way I can convince my parents to buy me an undergrad textbook when I'm in highschool

[graceful moon]

The authors don’t see much of that money, the publishers do

[valid narwhal]

should I care?

[normal crystal]

understandable
if you want open education resource textbooks, those exist

[valid narwhal]

they do but I prefer some textbooks over others. especially more rigorous ones

[signal mountain]

either a textbook is available for free or its not
if its not then any copy youre gonna find is a pirated copy...?

just pirate now and if its brings you value youll keep it in mind for years to come, buy it when you can

[normal crystal]

if you want ones that aren't open but aren't willing to pay
then you already know the answer

[valid narwhal]

that's probably true. most of the tb I got is from some website where they've hidden it to secretly that I had to type specific code for that book in a discord server for the bot to send me a dedicated link for download 😔

[livid lintel]

Oh.. that’s the fake zlib site …

[valid narwhal]

I just hope that I'm not doing any harm to the author. idrc about the publishers. they get enough money for doing nothing particularly intellectual

[valid narwhal]

sounds good

[graceful moon]

I can’t make that call for you, wanting to support the authors is a very valid and novel thing. Just maybe look at how much of that cut they actually get.

There’s also websites like openstax with a bunch of open source text books

[ornate frost]

Anyone has recommendation on a book which has a complete treatment of propositional logic? (i.e., its main theorems are also discussed not only its axioms/building blocks)

because I read a book on judgmental aggregation which already discussed the building blocks

[rough nymph]

Is Spivak's calculus book good or is it bait?

And lang's book

[tender cobalt]

its really good

[rough nymph]

a lot of mixed opinions online, but I trust u

what about Lang?

[marble solar]

It is the book that mathematicians teaching Calculus wish they could use for their class, or the one they wish they wrote as it contains exactly the insights, caveats, and exploration of the ideas behind Calculus

Lang wrote a lot of books. Most of them are bad, few are good

[rough nymph]

wow

[rough nymph]

His Calculus book specifically

[tender cobalt]

I am not sure about his calculus book

[marble solar]

🤷‍♂️

[tender cobalt]

its very minimalistic

doesnt really have much content

[marble solar]

I'll say the Lang books that I've heard as being good, I have not heard Calculus mentioned

[tender cobalt]

but spivak you can close your eyes and read it

it's solid and remarkably good

the explanations are so good

[rough nymph]

ahh okay

[tender cobalt]

i wish i learnt calculus with it, i want to "unlearn" calculus and learn from spivak lol

[rough nymph]

okay ill use spivak then, thanks for the help guys

[marble solar]

It has mixed opinions because it's not really a first book for Calculus for those that aren't dedicated

It's difficult. Very difficult. I learned Calculus from Spivak as a freshman

[rough nymph]

I am a first-time calculus person

[rough nymph]

oh man....

[tender cobalt]

the benefit of that struggle is that your background will be solidified so well that you can start on some real analysis book without any hassle

[rough nymph]

It sounds great, I just hope I don't get crippled on the way because I don't have calc experience

First sentence: The title of this chapter expresses in a few words the mathematical knowledge required to read this book.

I hope this is a truthful narrator

[tender cobalt]

yes

one thing you can do is get yourself familiar with basic derivatives and integration formulas

from youtube

actually that wont probably help it just gives some experience

But dont worry, you will be fine if youre hard working

[rough nymph]

@tender cobaltDo you have tips for self-studying? Do I just read the book page-by-page and write notes? Or how would you do it

[tender cobalt]

read the book page by page, take notes of every important details (like definitions, proofs)

and when copying down the proofs, make sure you understand every single line you copy down

if you dont, move on to next line

and ask that line you didnt understand in math discord server or math stackexchange for help

the best advice is keeping up consistency

[grim ore]

@tender cobalt :o

[rough nymph]

No book specific but:

How do you guys manage multiple books studying in parallelly?
1h Calculus -> 30 min Logic -> 1h Linear Algebra?

i.e.

Or do you try to do one chapter each

[mortal ore]

I kinda just treat it like a video game

I just do it when I feel like it

Which ends up being hours a week

But

If ur passionate about smth it'll come naturally

[ivory shore]

It depends on how hard each one is but practically, yes. To be exact 1 hour for each

[graceful moon]

I do a chapter each (might not be a full chapter), just like one class a day

[vital bane]

in my experience doing multiple books at once is not a good thing, and 1 hour of math is not at all enough time

just focus on 1 book, finish it, then maybe think about doing 2 books at once

[royal scaffold]

imagine if colleges were structured this way

academic year split into 15 parts ;__;

[restive falcon]

Does anyone know any books on infinite combinatorics?

[gray gazelle]

anyone have a rec for a calc textbook covering 1 2 and 3 others than stewarts?

[vital bane]

what is that?

combinatorics of infinite sets?

[slender cargo]

Any good book to skim for undergraduate probability theory? I'm taking a course on Real Analysis (the measure theory kind) and I wanted to skim an undergraduate probability theory book, one that does not use measure theory (I've never taken an actual course)

[remote sparrow]

https://stat110.net

https://www.amazon.com/Mathematical-Statistics-Applications-Dennis-Wackerly/dp/0495110817

this one is more concise (has both probability and mathematical statistics)

ross is popular too but i just really like blitzstein and hwang

[slender cargo]

Much appreciated!

[tender cobalt]

huh

[buoyant dawn]

everyone ive talked to seems to love that book lol

btw i know this is a bit off topic since its not a book but, on the subject of undergraduate first courses in probabilities, theres like 6 videos of a 16 video oxford lecture by matthias winkel available on youtube, does anyone know if the rest of the lecture is available anywhere?

[vestal niche]

https://www.amazon.com/Ordinary-Differential-Equations-Universitext-Vladimir/dp/3540345639

Greatest ODE book of all time

[gray gazelle]

Anyone here knows any introductory book on elliptic functions which can be read by someone in highschool? Preferably one also focusing on the history.

"Elliptic" meaning related to ellipses, not elliptic curves, the works of Legendre Jacobi and Abel.

[vital bane]

Arnold W

[vestal niche]

Warnold

[tender cobalt]

manifolds ❤️

[rigid trail]

pog

im glad i got that book instead of my course's "required textbook" thats some long ass thing

[tall herald]

Looking for a foundational document for algebra similar to what Euclid's Elements is to Geometry

Reccomendations plz

[vestal niche]

Like a historical document?

That stuff's probably in some ancient Arabic

[gray gazelle]

what counts as algebra?

[vestal niche]

ODEs - Arnold + Hirsch et al
PDEs - Haberman + Strauss
Basically how I'm approaching these topics

[tall herald]

What??

You guys don't have anything??

[vestal niche]

Wdym by anything?

[vestal niche]

Are you looking for a historical document?

Or a modern textbook?

[tall herald]

THE foundation of algebra

[vestal niche]

So a historical document?

[tall herald]

What do you guys do all day if there isn't a foundational text? Like what is the field based off of?

In Geometry, there is a physical book containing all of the arbitrary assumptions and axioms you must make for geometry as a field to work. There is no text like this for the arbitrary assumptions and axioms of algebra?

[gray gazelle]

Have a look at Ankitung zur algebra

by euler

[vestal niche]

If you want to read a textbook that builds modern algebra from the ground up then you can read Dummit & Foote's Algebra

[gray gazelle]

Perhaps thats what you are looking for.

[gray gazelle]

Btw Euclid's elements most definetly is not that work

[vestal niche]

Artin's Algebra also works as well

[vestal niche]

Yea Euclid just made basic geometric observations and built on from there

[sweet wharf]

Any books for JEE aspirants

[gray gazelle]

@vestal niche Were you in TUM?

[tall herald]

Not foundational

[gray gazelle]

Nvm weird question

[vestal niche]

What's TUM?

[tall herald]

Dude this is like having a religion without a holy text wtf

You seriously have no foundational document?

[tall herald]

Then geometry has interprative axioms and is invalid by result of this?

[gray gazelle]

Which algebra? the moving stuff here and there or modern algebra?

[vestal niche]

Gonna be honest chief I have no clue which algebra you're even talking about

[tall herald]

Or at least, the conclusions reached via interpreative axioms

[tall herald]

Doesn't the field build upon itself

[vestal niche]

Yea we have field axioms and all that in algebra

[gray gazelle]

Elaborate, I dont get you.

[vestal niche]

Yes

If you want to learn more, read Dummit & Foote

[tall herald]

If there is not ONE set of axioms, then these axioms can differ depending on who you ask. Since every single piece of geometry ever done is based upon axioms, the validity of every single geometric conclusion differs depending on who you ask. If there is no solidity, it is invalid. Geometry, assuming interpreative axioms, is invalid.

[vestal niche]

Maths and religions are two completely different entities with completely different practices

[tall herald]

Math and classical, formalized religion based upon a holy text are the same

[gray gazelle]

There's never ONE set of axioms.

[vestal niche]

No

Mathematicians have argued over choices of axioms

[tall herald]

You make axiomatic assumptions, then work off of them. (2+2=4), (linera algebra)
A Christian makes an axiomatic assumption (the existence of God) then works off of them (doing as God teaches).

[tall herald]

Every time an axiom changes, every conclusion made by virtue of that axiom is now invalid

[gray gazelle]

Well Christians don't do it very well.

[gray gazelle]

so?

[vestal niche]

https://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis

[tall herald]

Yes, if there is a foundational crisis, any conclusion reached by using the axioms is invalid until the axioms are solidified

[vestal niche]

We have figured that out using logic and set theory

[vestal niche]

So the modern axioms of mathematics are built upon these two

[gray gazelle]

what do you mean by axioms being "solidified"?

[vestal niche]

Hope this answers your questions

Now if you're looking for a text to learn the axioms of algebra, then read the first couple of chapters of Dummit & Foote or Artin.

[gray gazelle]

@tall herald Let me ask you a question, if a line intersects one side of a triangle then does it necessarily intersect the other? provided that the side that it intersects is not a part of the line.

[tall herald]

One, solid set of axioms that do not change and are not interprative

[gray gazelle]

That's not possible ig

[vestal niche]

You can see how algebra is built upon a set of axioms

[tall herald]

I cannot answer this question, as the axioms which it has been predicated on are subject to change. We do not know what a triangle is, and as you have not defined it, I cannot answer the question. We do not know what intersection is, and since you have not defined it, I cannot answer the question. We do not know what a line is, and since you have not defined it, I cannot answer the question. We do not know what sides are, and since you have not definedi t, I cannot answer the question.

[gray gazelle]

@tall herald do you know about the continuum hypothesis? have a look at it.

[tall herald]

What is a line? Euclid say it's a thing with breathless length, but according to you, these are not universal and unchangign axioms

[tame tree]

Why on earth did you take your inane ramblins to this channel

[vestal niche]

What?

[gray gazelle]

bro since you mentioned the elements i assume you agree with it?

[tall herald]

Not anymore if there are other accepted foundational documents

[gray gazelle]

so the issue is over.

[vestal niche]

Huh?

[tall herald]

Yeah the whole field is a sham

Obviously it has applicability in life but if they can't even agree upon axioms to work upon no intellectual conclusions can be valid

[vestal niche]

@tall herald Brother calm down

[gray gazelle]

either you are 12 or you don't know much about math.

[tame tree]

Literally every mathematician agrees upon ZFC unless their work involves some deeper scrutinization of these axioms

[tall herald]

LMFAO

Dude

[vestal niche]

I don't think they know what logic and set theory are

[tame tree]

By which I mean working in logic

[tall herald]

"Literally every....Unless...."

[buoyant dawn]

lmao, i mean thing is euclidean geometry is a very different field

[vestal niche]

@tall herald Just learn logic and set theory

[buoyant dawn]

and arguing over axioms is definitely part of the charm :>

[tame tree]

anyways please dont continue clogging up this channel with this absurd know nothing discussion

[tall herald]

I have a philosophy degree

I did 4 years of logic

[tame tree]

Yeah that's not mathematical logic

[tall herald]

Define mathematical logic

[gray gazelle]

Ha ha, me after reading descartes.

[tame tree]

No thanks you can just google

[vestal niche]

Dude you're just trolling at this point

[tame tree]

again, stop clogging up this channel

[vital bane]

I found the problem

(jk)

[tall herald]

Lmfao no I get you

[gray gazelle]

define define?

[tall herald]

Im in law school

So thankfully not just that

[tall herald]

Providing a true statement predicate that applies to every instance of the object in question

Also guh I took set and model theory for, like, 2 years

[gray gazelle]

Define true?

[vital bane]

Define define

[tall herald]

Do you think we just...give up after sentential and predicate logic? That we just sit there and twiddle our thumbs?

[vital bane]

oh you already did it

[tall herald]

Providing a true statement predicate that applies to every instance of the object in question

Yeah lol

[tall herald]

This one's a bit harder

But, antithetical to mathematicians, I will make an original thought not owing to ever-changing axioms

[gray gazelle]

Anyways guys have a look

[gray gazelle]

Axioms change but the results dont.

[tall herald]

I would say to be true, an object has to not be contradictory to physical reality

[tall herald]

??????????????????

If I changed the legal system and the laws themselves, would people still get convicted for the same crimes?

If I were to make murder legal, would people still go to jail for murder?

[buoyant dawn]

https://cdn.discordapp.com/attachments/986583006502342677/1337103391540645909/image.png?ex=67a63a12&is=67a4e892&hm=602147520885f61398bb8ed317737dfc50b0ad0687e38550d32ccc987c278c33& this is golden honestly

[tall herald]

This is the most mathematician shit I have ever heard

[gray gazelle]

depends on how you change the laws

[buoyant dawn]

...welcome to the mathematics server? thats what we have here lol

[tall herald]

No I get what he's saying, people tend to just stop after Sentential 2

I did predicate 1-4 and sentential 1-6, but yeah we had to take set and model

[buoyant dawn]

axioms are very different from laws, example of axioms changing but the results not changing would be like

[tall herald]

I also went to all of our math mondays which was a neat perk

[buoyant dawn]

how the universal set isnt a set in any of the axiomatic approaches to set theory

[tall herald]

Axioms are the laws that cause mathematics to function in (xyz) way

[buoyant dawn]

in zfc we say it just doesnt exist and i believe in von neumman they call it a class (?)

[gray gazelle]

if you get from "Every murderer will be hanged" to "every murderer will be hanged after he is made to eat pizza" that isnt the same as "Every murderer will get a scholarship"

[tall herald]

You and Turqoise are disagreeing with eachother. In sentence A you have changed a law. According to turqoise, axioms =/= laws

[vestal niche]

Take a break y'all

[buoyant dawn]

bc we are different people :p

[gray gazelle]

im not talking to him

[tall herald]

I do have to go thank you all for the discussion though

This is very important

[vestal niche]

Go outside

Breathe some air

[tall herald]

Change doesn't happen without disagreement have a good day

[gray gazelle]

Anyone here knows any introductory book on elliptic functions which can be read by someone in highschool? Preferably one also focusing on the history. urgggghh please.

im supposed to study for my exams lol

[vestal niche]

Bro no change is happening from a Discord server

[gray gazelle]

ok then

but im getting a boo

k

[vestal niche]

McKean and Moll came up quite often from what I've heard

You may also want to look at Lang

[gray gazelle]

Isnt complex analysis necessary there?

[vestal niche]

Expository wise he's one of the best (in any topic)

[vestal niche]

You can Google/Deepseek through anything you don't understand

But usually Lang will make the concepts as clear as possible to the widest possible audience

[gray gazelle]

Yeah I love Lang

He's nice despite being a Bourbakist

[vestal niche]

Lang and Lax are the two best math writers I've ever read

[gray gazelle]

But then some people hate him.

and he was an AIDS denier

[vestal niche]

I mean he was apparently a jerk irl

Doesn't take anything from his mathematical writing ability tho

[gray gazelle]

His shouting in class to attain understanding is a cool quote

[vestal niche]

Now that I've read Arnold, Lang - Lax - Arnold is my current top 3

[gray gazelle]

I read his Math! Encounters with hs students its so well written

[vestal niche]

Yea Lang's just an amazing writer in general

[gray gazelle]

how long do you think Lang's intro to linear algebra should take?

[mortal ore]

Idk i tried lang for abstract algebra

He was super boring

[gray gazelle]

oh well lang's elliptic functions are the number theory ones

[vestal niche]

I mean math books aren't meant to be exciting if you think about it

Lang's books explain complex topics well - that's what he's known for

[vestal niche]

Which is all that matters in a STEM book really

[mortal ore]

That's not true

I'm using gallian instead and it's much more motivated and interesting

I've heard gallian isnt very in depth though

So I might use artin as a supplement

[vital bane]

False

math books can be super fun to read

there are good books and there are bad books

[vital bane]

eh I wouldn't say that

it's enough for UG algebra

[mortal ore]

Thats what I was thinking

[vital bane]

but yea Gallian is super fun

[mortal ore]

I'm doing a class with gallian this summer

Then I'm using dummit and foote for graduate algebra in fall