book-recommendations

[woven hill]

A drawer

Not too small

Not too big

Js the perfect size

And underdesk as well

Really cool table

10/10 would recommend

You could get one of those bed tables

Like the small ones that you put over your lap

A big one

Why don't you use that thne

Damn

[quick ocean]

Guys, one of my cousins is going to Warwick for Math and Stats this September. He asked me for something I had to get an opinion on. I didn't understand where to ask so I just chose this channel, if there is another one more appropriate, I can write in that channel as well.
He did his 12th in IB, international baccalaureate. What he said was that in IB atleast, the secret hack and insider's tip to success is just past papers and question practice. From experience I told him that this is the case for higher education as well. He then told me that for different subjects, there's like a holy grail of a guidance book from which if you do questions, that's the best, like Tsokos in IB physics, Hodder in Math, etc.
So he asked me, for Warwick Mathematics and Statistics UG, is question practice and previous year question practice the "hack" and if so, which would be the best books, the "holy grail" of texts to practice from?

[cerulean steppe]

Past exams and reading and doing exercises from a good book on the subject is the hack

[wary locust]

hey guys, ive written the jee exam and want to progress further in math (ive never wanted to limit my math there but i never had the time cuz of other subjects) but now im going to college and will have time for math alone, so id like to know if theres any advanced calculus books that can teach me either in a different way or a different difficulty

(multivariable calc too)

[rich sun]

spivak

[trail hemlock]

also a book called honors calculus by maccluer which is worth checking out.

[warm knoll]

hey

[warm knoll]

can someone help me find Game Theory - Michael Maschler, Eilon Solan, Shmuel Zamir

2nd Edition

oo

ok

[vast leaf]

Not a book but https://tutorial.math.lamar.edu/ is pretty good

[cerulean steppe]

there are some good notes here for beginning undergraduates up to graduate students: https://mtaylor.web.unc.edu/notes/

[normal crystal]

imagine how rich he would be with a referral code

[cerulean steppe]

everything is free, so where would the money come from?

[normal crystal]

the imagination

[limber talon]

Hi math friends, what prerequisites would you recommend to go through Vakil’s FOAG text?

[hearty steppe]

Hey anyone else had a chance to work through this? https://books.google.com/books?id=9bavEAAAQBAJ&newbks=1&newbks_redir=0&printsec=frontcover&pg=PA2&hl=en&source=gb_mobile_entity#v=onepage&q&f=false

[remote sparrow]

https://www.rxddit.com/r/PracticalGuideToEvil/s/1iJDYvs2g7

@glad rampart

[glad rampart]

yoooooo

any news on the physical version?

thats what im hyped for

[slender wasp]

If you wanna do pure math next, you can look at Spivak. If you wanna do more applied/engineering maths, maybe Apostol Calc I and II are better. They do Apostol for first year undergrad math in IITB for example, in their engineering programs. Not sure what they do in their pure math programs, can try looking up the curriculum on the website.

[humble spire]

wait this was published 💀

i am insanely behind on catching up with this

[humble spire]

a physical too?

lowk time to buy 🔥

[heady ember]

By "some" I suppose you mean Axler

[steel cloud]

I want to do measure theory, I did undergraduate, I did real analysis, metric space, topology, abstract algebra, which textbook will be good for me?

[normal crystal]

is that a real person or a comic book character

[remote sparrow]

folland

[heady ember]

Some recs I have seen people give

• Folland
• Bass (free)
• Dietmar A Salamon

[steel cloud]

Okay thank you

[heady ember]

Also see this

Has anyone seen Ibrahim Assem and Flávio U. Coelho An Introduction To Module Theory? What do you guys think of it?

Well, not that I'll be reading commie alg anytime soon, but I'm just curious.

[quick ocean]

Could you share names of good books

[torn crypt]

Title page?

But I’ve never seen that one, the placement of V feels odd tho

[torn crypt]

Hrmmmm

[wary locust]

noone really does pure math early on here cus its not valued much in this country

same with me

ill check out apostol tho

ill do a chapter using the pdf before getting the book

[vital bane]

Check out Measure Theory by Donald L Cohn

[hearty pawn]

any book like to get started into the complex math stuff?

like

some niche theme

[wooden minnow]

any book recs that serve as a great introduction to category theory?

[steel cloud]

Okay

[tiny gulch]

Depends how much background you have

For the gentlest intro probably Eugenia Cheng’s “the joy of abstraction”

If you’ve got a bit more maths background then probably Awodey’s or Leinster’s books

Even more and Riehl’s is goated

If you have some programming background then I’d heavily recommend Bartosz Milewski’s “Category Theory for Programmers”

His video series of the same name is excellent too

[steel cloud]

Does anyone maintain book library on some online cloud?

[still panther]

i just keep my stash on my pc

i found that maintaing a dropbox is more troublesome than just redownloading shit i wanted to read

i keep the list of the books i want to read in a spreadsheet though

[steel cloud]

Oh

I want a big library where I can easily download, I know there are some online websites but I don't know I think that's not working now

[wooden minnow]

I'll go check Awodey and Riehl to see what fits right for me, thank you!

[ember junco]

any books to master undergrad math as a cs major

[ember junco]

+1

[torn blade]

ive heard good things about “A concise introduction to pure mathematics” by Liebeck

idrk anything that introduces alot of topics at once

Napkin by Evan Chen is good actually

[cerulean steppe]

which subject?

[cerulean steppe]

real analysis + multivariable calc and diff geo: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[molten gulch]

It doesn't cover any material in enough depth imho, better to start with a real analysis book or something

[hearty pawn]

Alright, thanks

[torn blade]

yh it’s not a “real” textbook but it’ll give you a sort of roadmap for pure maths

[patent iris]

hello, i just graduated from high school. I need resources to self-learn linear algebra & calculus (for graphics programming & making AI). I am watching 3blue1brown's linear algebra videos and they are great. I was able to apply them with programming too. However, even though they are great I am sure they dont dive deep enough and I couldn't understand some parts.

What resources would be best for me?

[molten gulch]

Friedberg Insel and Spence's Linear algebra if you want theory + computations; Lay Lay Mcdonald if you only want computation bashing

[steel cloud]

Anyone read the Topology a geometric approach by Engelking?

[cerulean steppe]

https://www.math.brown.edu/streil/papers/LADW/LADW.html or https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[half void]

Jerrold marsdens books are pretty good.

[trail hemlock]

i like royden 5th edition. cohn is great as well, but I found the problems to be too easy and a bit boring. but cohn is very nicely written, and u can always get problems out of papa rudin.

[ember junco]

thank you

[thin sparrow]

Hi, can anyone recommend a book on geometry or trigonometry? I think my foundation is weak.

[humble spire]

Gelfand trigonometry was a lovely read

[hearty pawn]

bro

this guy

[humble spire]

?

[hearty pawn]

he told me to write i am dying or sum now i cannot write in discussions

[humble spire]

What

[hearty pawn]

nevermind figured it

[humble spire]

Kk lol

[thin sparrow]

Thank you for the recommendation!

[outer helm]

does anyone know of a good category theory book in French?

[real ravine]

I am in high school yet but i found some calculus resources https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/pages/textbook/ https://tutorial.math.lamar.edu/ https://mrherlaar.weebly.com/calculus-12.html https://www.youtube.com/@DrTrefor/videos

[topaz rampart]

does anyone have any recs about youtube channels or books about topology?

for a beginner in the concept

[timid lion]

my school recommends Gamelin & Greene Introduction to Topology

[trail hemlock]

Kelley's general topology is good imo

[vital bane]

Also check out Khan Academy and Open Stax's Calculus books and Stewart's book

and for multivariable calculus: https://www.damtp.cam.ac.uk/user/tong/vc.html these are great

[native elk]

guys i want to begin studying computational complexity, more on the theory side, like np completeness, proof complexity instead of sorting algorithms, efficient matrix stuff. i heard ppl saying Arora & Barak is best, is that true?

pls ping me:)

[steel cloud]

Oh thanks

[lavish orbit]

Wanting to get into numerical analysis of PDEs and FEM, any good recommendations?

[remote sparrow]

@willow pecan

[spring wing]

Any Good book for calculus?

[daring wolf]

stewart

or thomas

they’re very standard texts to calculus

[spring wing]

Alright brother

[timid lion]

@marble solar why do you not recommend it?

[vital bane]

meet me outside

[tender river]

wdym by beginner? what is your current math background?

[native elk]

hey its a crime nobody mentioned m.a.armstrong basic topology

its the book im currently studying topologt

absolute gold standard
--------------i am a separation line------------

somebody please, computational complexity theory books

i saw the article on this in princetons companion and was like

is Arora & Barak good enough

[timid lion]

Sipser is ok

[native elk]

what is the difference ppl seem to think that A&B is objectively the best for selfstudying

[timid lion]

Sipser is a survey of theory of computation, it is better for automata theory and computability theory than for complexity theory

[normal crystal]

there isn't much overlap
do Sipser first if you're interested

[native elk]

survey?

[timid lion]

survey course is a brief look into the field. like first-year classical physics is a survey course

and most high school courses

[native elk]

thanks so much

[timid delta]

Best set theory book to get that out of the way asap?

[timid lion]

introductory or more advanced?

[timid delta]

For Topology

I was thinking about Jech? Or maybe Halmos? No idea, my set theory is pretty basic

I'm starting to have problems with Topology for some things I should already know

[daring wolf]

I think the first section on Munkres topology is enough.

they cover some set theory

[timid delta]

Yeah, but I do want to learn a bit more

[torn crypt]

If you want like, proper set theory, Jech is good?

[tender river]

the first chapter of dugundji

[torn crypt]

But there’s a lot of “tilts” to the theory and sub-POVs and such

[timid delta]

I see

I will try Jech

[steel cloud]

For multivariate which book is good?

I know metric space and linear algebra

[torn crypt]

The start is fairly general stuff, so you can change book after learning some, or stop when you’re satisfied

[vital bane]

first chapter of Munkres should be enough

[torn crypt]

Yes, but hey chapter 4 of jech is nifty

[vital bane]

Is this big jech or baby jech?

[timid delta]

Is there any difference

[timid lion]

multivariate stats? or calculus

[steel cloud]

Multivariate calculus

[timid delta]

Calculus of several variables

[timid lion]

Stewart is good for intro

[timid delta]

Yeah

Sorry my best friend got my phone

She's a silly

[timid lion]

I have also seen Hubbard & Hubbard Vector Calculus recommended, i plan to read it

[timid delta]

And a troll

[timid lion]

this as a second course/book*

[torn crypt]

Yes

[tender river]

#advanced-lounge message theres this but idk it. Only multivar i know is the differential calc sections and the first integration chapter of munkres: analysis on manifolds and i dont like that book

[vital bane]

baby jech is UG set theory , big Jech is graduate set theory, i think you need to know measure theory and topology for that

[vital bane]

You can check out Hubbard and Hubbard and Zorich @remote sparrow recommends that one

[ancient creek]

If you want proof intense, exercise based I am reading mathematical analysis 2 by Zorich

[heady ember]

Do you know basic analysis?

[vital bane]

yes he knows single variable analysis

Are you going to recommend Henri Cartan's book?

[heady ember]

Yesn't

[heady ember]

You can use

1. Henri Cartan Differential Calculus
2. Coleman Rodney Calculus on Normed Vector Spaces
   for a treatment of derivatives and stuff on normed vector spaces.

For integration in maximal generality, measure theory:

1. Folland
2. Bass
3. Dietmar A. Salamon

If you want to stay within the confines of R, then

1. Folland (not his measure theory book; iirc its called Advanced Calculus)
2. Michael E. Taylor

just some recs I have heard others give through time

[steel cloud]

Yes

And what about baby Rudin for multivariate?

[heady ember]

Nothing short of terrible, from what I have heard.

[steel cloud]

Thank you

[daring wolf]

baby rudins multivar is shit

[rich sun]

it's for babies

[surreal crow]

I will reccomend Newton's book principia

[vital bane]

Have you read it?

[vital bane]

Do those books cover divergence and curl?

[heady ember]

Uhh Folland and/or Taylor do iirc

In any case, you can just learn about them more generally in diff geo

[willow pecan]

Iserles has a nice book

[lavish orbit]

ahhhh wait this looks perfect
awesome
tysm

[orchid otter]

Is Div grad curl a good one?

[molten gulch]

We used it, liked it

[old elk]

Sit down and study, basically there are no tricks, just take a break and that's it.

[quartz ridge]

Book recomandations for Analysis 2, Analsysis 1 and Calculus for self study [I'm 11 th grade by now (I know, I'm not cool)]

?

[tender river]

theres a few books mentioned here #book-recommendations message

[foggy quest]

the one here is good: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/. You will need to supplement chapter 4 with multilinear algebra chapters from https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ or Lee's Introduction to Smooth Manifolds

[young thorn]

hey

can i know some good books for abstract algebra

i have covered things mentioned in
abstract Algebra: Theory and Applications by Thomas Judson
i need something on upper undergrad level

[marble solar]

The presentation of material is formatted poorly, and it doesn't develop the concepts as well as Munkres. Kelley is a more classical book, but most people use Munkres today for a reason, it's really good

[timid lion]

i see, perhaps i'll use munkres instead

[remote sparrow]

dummit and foote

[willow merlin]

which book explains orthogonal decomposition

[molten gulch]

anything on linear algebra I assume

[willow merlin]

you assume?

open your favorite la book and show that it includes it then

[humble spire]

https://math.libretexts.org/Courses/Irvine_Valley_College/Math_26%3A_Introduction_to_Linear_Algebra/03%3A_Eigenvalues_and_Eigenvectors/3.05%3A_Orthogonal_Projection_and_Least_Squares/3.5.01%3A_Orthogonal_Decomposition

or js watch a yt vid

[willow merlin]

is math.libretexts your favorite linear algebra book?

[humble spire]

no

if it works though I dont see why you wouldnt use it

most books explain it the same i think

[willow merlin]

which books

i have seen you before, are you from the chemistry olympiad discord server

[humble spire]

yes lol

[humble spire]

idk rly

i would trust libretexts though

or check the pins

there are a bunch of open source la books

[willow merlin]

https://textbooks.math.gatech.edu/ila/ila.pdf

this is the source of the libretext page

like it cited this one

i will use it, thanks

[willow merlin]

yeah, thanks, i just find it funny people say "every linear algebra book in earth"

like i tried to look for it in axler 4th edition and didn't found info explaining it

[trail hemlock]

you assume?

[pine tundra]

I found it, actually

Page 188

[willow merlin]

is an example of one orthogonal decomposition

[humble spire]

kk lol

[humble spire]

mhm

[pine tundra]

Well, you have to know that Axler is an unconventional LinAlg book, for example he doesn't use determinants

[willow merlin]

yes

[heady ember]

Free ({}\neq{}) open-source. To be open source, the source files (e.g. the {\TeX} files) must be available at no cost, which I don't think is very common?

[hasty eagle]

grass

[humble spire]

oh yeah

mb

[glossy mango]

Guys is james stewart's book a good place to start learning calculus??

[rich sun]

It's certainly not a bad place to start learning calculus

[glossy mango]

thanksss for ur response

[buoyant dawn]

recs for learning bayesian data analysis? both the theory side and practically implementing it ideally with python as thats what most of the uni here uses. hit me with as many as u got pls 🙏
ive been reading bda3, sivia and kinda skimmed through a bit of bayes rules although it was kind of childish

[buoyant dawn]

(but also adams' calculus is a lot better imo)

[glossy mango]

oooohh i'll check it

[blazing rune]

Have you looked at Martin? Bayesian Analysis with Python: A practical guide to probabilistic modeling is pretty good and uses industry-standard packages like PyMC.

[buoyant dawn]

i have not, ill take a look at it ty!

[buoyant dawn]

oh just to narrow things down a bit my probability project is about modelling a one parameter thing so atm i dont rlly care for the multi-parameter stuff and more advanced material these books may contain (and i havent even taken prob 2 which teaches like covariances and stuff like that yet lol), although as im very interested in this topic pls do feel free to recommend more advanced books still i just wanna know the general gist of the literature on this topic :)

[young thorn]

how is langs book?

someone recommended me lang

would it be a great jump from the book i did or is it approachable

[daring wolf]

Lang? is that guy serious

Langs book is for graduate

ah

wait

theres undergrad book but just get dnf because it has more exercises from the ground/trivial examples so you can understand from them

[young thorn]

well i have done some the book i mentioned above
its introductory undergrad level

but yea i think he meant langs book for grad one

[daring wolf]

in D&F if you think you are comfortable with concepts so you can jump those trivial exercises like

show a operation is commutative/associative etc

then you can just omit it

[young thorn]

but again i have no idea what prereq would be to read that book

lol

[daring wolf]

Lang grad algebra requires undergrad algebra

sometimes more than that

[young thorn]

well any precursors to that ? cuz eventually i wanna read that book

like books u recommend before reading langs grad text

[daring wolf]

It has been used in some grad algebra courses, but since there are a lot of greater books than langs algebra there is no point to read it over

[young thorn]

ohhhh

[daring wolf]

But still i think lang is great references or some purposes

[young thorn]

well what should i read then ? considering i already know introductory undergrad abstract algebra

dummit foote?

[daring wolf]

what

D&F is undergrad algebra

[young thorn]

i havent looked at the book

[daring wolf]

undergrad = someones doing their balchelor degree

grad = master or phd

[young thorn]

yea i know about that but i have no idea about D&F;s content

[daring wolf]

I dont think DnF is great to learn more concepts because

while it has some comalg homalg, rep theory

the comalg, homalg sections arent good

[young thorn]

well then what would be good replaement for it ?

[daring wolf]

getting a comalg/homalg book is better than reading this

[young thorn]

aaaah

[daring wolf]

but homalg? usually introduced after you learn algebraic topology

[young thorn]

yea

[daring wolf]

comalg? If you are comfortable with ring/modules theory then you can start with it

but idk what is good book for intros

[young thorn]

hmm sounds good

thanks

i might look at D&F for once then

[young thorn]

are you

not me , i mostly did a lot of competition problems

mostly for IMO but now i wanna do some college maths

before college

i wanna be prepared

[normal crystal]

real shame Chipper
cryin' shame

[steel cloud]

Okay thank you

[crisp widget]

What are some good linear algebra books to self study with, for context I already took an linear algebra course for engineers but I want to go deeper into linear algebra, but I’m having trouble finding books with solutions

[daring wolf]

It is (nearly) impossible find official solution for undergrad, or higher level books

you should find unofficial ones

and learn more linear algebra, you mean proof-based or?

[crisp widget]

Yeah, I want to get into proof based maths more

[daring wolf]

Some linear algebra books that are free online are for example Linear Algebra Done Right by axler and from some other author, linear algebra done wrong

there are other books (not free) like friedberg, hoffman

[crisp widget]

Ty, I’ve been looking into those already but ig solutions are hard to come by so I’ll just have to yolo and hope I don’t completely misunderstand concepts

[native elk]

ramsey theory recommendatons pls

and tell me what math background i need to study it

i searched and every textbook is like $200

[broken bramble]

you could try schaum's outline of linear algebra: https://www.amazon.com/Schaums-Outline-Linear-Algebra-Outlines/dp/1260011445

it's got 600 practice problems with step-by-step solutions

not sure if it's at the level you're looking for though

[normal crystal]

in epub😬

ok
I promise
I'll stop
after the summer

[torn crypt]

I’m afraid I dunno any great Ramsey books. there’s a book about nonstandard methods in analysis, number theory, combinatorics which mentions some Ramsey stuff. Some Ramsey stuff I remember in Halbeisen’s combinatorial set theory, but idk if that’s the right kind of combinatorics for you.

But do consider posting that inquiry in the #combinatorial-structures as well since there’s few who are really into that stuff, your question might get buried

Unless like @dense seal knows a book or so

[heady ember]

You don't need solutions: just check your own work.

[native elk]

np, i'm not that into combinatorics anyways, ramsey theory seems like a niche subject

[rocky berry]

can anyone recommend good book for self study discrete mathematics

for beginners

[devout plank]

hi

[fresh skiff]

Hello. Welcome to the mathcord

[devout plank]

thanks for welcoming me

[meager dagger]

cat_lurk~1

[rocky berry]

Guys??

[elder stratus]

bona - a walk through combinatorics

knuth - concerte mathematics

[timid lion]

hi

[normal crystal]

Epp or Rosen
or MIT Math for CS

also, why do people never search

[lament remnant]

https://www.cambridge.org/highereducation/books/an-introduction-to-mathematical-reasoning/884E620008388D6452ED9707CBEA0BF0

[rocky berry]

because i believe there are more experience ppl here than me.

[normal crystal]

I meant search in this channel
the same questions are asked daily

[rocky berry]

ohh my bad, i will try next time!

thank u btw im really started to get indulge in that book by rosen

[normal crystal]

it's ok
everyone does it

[normal crystal]

I probably prefer Epp
but it's a matter of taste
there's also Discrete Math with Ducks

[rocky berry]

can u please elaborate epp it will be easier to find book with correct name.

seriously there are lot of resources which makes u confuse sometimes xD.

[normal crystal]

https://letmegooglethat.com/?q=epp+discrete+math

God dammit
that actually fails 🤡

[rocky berry]

that was a prank xO

[normal crystal]

it shows up top hit when I search direct though

[rocky berry]

u did search for me xD

[normal crystal]

weird
I clicked again and it works
anyway, there ya go

[rocky berry]

yeah it worked now!

firstly i was getting some warning websites from US epp personal site bla bla

[normal crystal]

yea, it was something like government agencies or whatnot
idk what happened

[floral lantern]

What kind of linear algebra course?

And what kind of matrix algebra

[drowsy thicket]

I'm not sure about Strang but that sounds like something one would usually learn in linear algebra, not algebra

[quick ocean]

Math and Stat

[dense seal]

Uhhhh there's uhh IDR what it's called it might just be called Ramsey theory lemme double check

Haven't read it but I think it's "standard"

yeah Graham, Rothschild, and Spencer

[dense seal]

This is just the publishing industry tbh, most advanced math textbooks are going to be like this.

[torn crypt]

Noted

[dense seal]

For background I think if you've done like a proof based real analysis course you should be good? Like the pre-reqs I don't think are intense.

Maybe some elementary number theory idk how much they go into that angle though.

[native elk]

yea im aware all the books are super expensive

[hidden grove]

hey guys

is chat alive?

[hidden grove]

what books do you recommend for undergraduate mathematics?

Specifically algebra and linear algebra.

[tender river]

rotmans algebra books are my favs for algebra

for linear algebra theres a review here #book-recommendations message

[granite olive]

Recommendations for a book on plane curves in R2, their differential geometry

[granite olive]

Artin algebra, hoffman and kunze linear algebra, sheldon axler ladr, halmos fdvs, herstein topics in algebra

[hidden grove]

Do they cover algebra not found in school? And how large are the books?

Sorry for the late reply

[molten gulch]

If you think algebra is just manipulating expressions and solving polynomials, you're in for a massive wake up call

[granite olive]

Algebra not found in school? Not sure what you mean

[humble spire]

Different algebra from school

[molten gulch]

They mean arithmetic and basic number theory and stuff like what some call "precalculus"

[humble spire]

Dceently large books

[granite olive]

These are abstract algebra books. They cover groups, rings, fields, polynomial ideals etc i think. Its been a decade since i read fhem

[hidden grove]

Like sets and vectors?

[hidden grove]

Like 400 to 500 pages or over 1000

[molten gulch]

Depends

So-called graduate algebra textbooks are 1000-1300 pages long

[granite olive]

I think you need to be more specific what you are looking for

[hidden grove]

Damn

I guess these books are what I'm looking for

[granite olive]

What are you looking for? High school texts?

[hollow shore]

Hey folks. Any thoughts on Visual Group Theory by Nathan Carter?

[molten gulch]

I assume decent if used alongside a standard algebra text

[hollow shore]

hmm I see

[echo sedge]

i need textbooks for linear algebra

i am beginner

but i wanna learn all stuff

any suggest

i will learn it for qc [but its not imported, i will learn it independet of that.]

[molten gulch]

friedberg, insel, and spence; treil's linear algebra done wrong; axler's linear algebra done right

https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf
https://linear.axler.net/LADR4e.pdf

[echo sedge]

thank you

[fresh skiff]

Hi TCC, how is the study of IVA going so far?

[molten gulch]

good but taking a break, somehwere in ch2

[fresh skiff]

Wow

Interesting

I thought to pick this book after FIS and axler (atleast upto eigenvalue in axler) but now i have decided Lee's ITM and Algebra

[molten gulch]

nodnod

what algebra text?

[fresh skiff]

The main will be DnF (i will write solutions like higher, kinda inspired and find it in some way useful). Also will Keep some easier books like Artin, printer, or beachy

[molten gulch]

nice

[fresh skiff]

Thank you

[glossy folio]

i'm going to major in comp science, can anyone suggest math topics and books for it that i can 🙂

[hollow shore]

https://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf

[glossy folio]

thanks

[normal crystal]

he has supplementary material and videos for that and the advanced book
https://njohnston.ca/publications/

[normal crystal]

there is also a playlist for Vector calc based on Colley on his youtube I just noticed before

[topaz rampart]

lol whyre they calling it done wrong?

[digital onyx]

Is there any decent book to learn linear algebra combined with abstract algebra by finishing which, I can study very basic category theory

I heard by some math students it’s always nice to study category theory early and it doesn’t rely much on pde and basic category theory helps with abstraction.. however I am vary bad with linear algebra a

[molten gulch]

Just read a linear book and then an abs alg book, but I guess Artin's Algebra book has some linear stuff within it

[molten gulch]

I've always been told to hold off on cat theory as late as possible and until I have a repertoire of examples

[digital onyx]

And is it possible though I know not likely, to skip linear algebra (linear algebra is hard)

So learn it late?

[floral lantern]

abstraction without a need for it is useless!

[molten gulch]

Linear alg isn't all that difficult in the grand scheme of things and it's so fundamental I wouldn't recommend skipping it at all

[floral lantern]

also linear algebra is significantly easier than anything that comes after it

[molten gulch]

Also this, a million times this

[molten gulch]

I've found basic abstract algebra to be on par with linear so far tbh

[trail hemlock]

yeah as tcc said, artin is perfect for this

[placid lynx]

non standard analysis- alain robert, some great questions

[digital onyx]

I have been using linear algebra done right but never took any linear algebra course fbefore since I don’t have it in my curriculum.. it’s so abstract

[molten gulch]

Yeah that book is better for a second pass at the material, try friedberg insel and spence

Or if you want something that just does everything with matrices for eight chapters, there's always the college class favourite even though IMO it sucks; Lay Lay McDonald's Linear Algebra and its applications

or Gilbert Strang's books

there's also Treil's Linear Algebra done wrong, also free

https://www.math.brown.edu/streil/papers/LADW/LADW-2014-09.pdf

[digital onyx]

Okay I will try that one friedburg is it easier than done right? Which one is more understandable like actually not diving straightly into massive crazy computation

[molten gulch]

I mean, I enjoyed friedberg for linear; hated using Lay in class so I just learned out of Friedberg

Friedberg has a lot of theory but the exercises have a lot of computational examples too

One should be familiar with theory and computation

[digital onyx]

I actually have been studying linear algebra quite consistently for half a year never nearly as well as analysis goes.. I feel maybe I never took courses or it’s just different than more typical math (analysis is quite applied?)

[digital onyx]

That’s so true

[molten gulch]

I've always found linear algebra more concrete and easy to grasp than analysis but I do know this is very person dependent

[digital onyx]

I always miss something going computation and I just hate it then. I am doing some practice for computation these days hopefully they fix some issues of mine still shuffling, my method is too dumb and general

[molten gulch]

It's all about practice

[digital onyx]

I think it’s primarily because of the fact that economics rely on analysis less on linear algebra, so without course it becomes inaccessible I will take a course next semester if my self study doesn’t make any progress

Or should I study abstract algebra first to make thing easier I heard in frace they study abstract algebra at high school so maybe it makes things easier they all algebra right?

[molten gulch]

linear algebra can give you intuition useful for further abstract algebra

[digital onyx]

I do both them.. please god for the love the god make this work for me

[floral lantern]

i mean basic stuff ig

but stuff like advanced group theory (lots of counting) or galois theory is hard

even like intro ring theory can be nontrivial depending on how deep your class goes

[cunning elk]

axler's avoidance of determinants in LADR is baffling

like sure don't just turn everything into unmotivated det spam but

we use them for a reason

[digital onyx]

I only had this idea of skimming through linear algebra because the generating group is quite similar to generating sigma algebra (pretty much the same)and property verifying is very similar to that of verifying something is a sigma algebra but maybe not that easy

[regal marsh]

Hi ,can any senior here please suggest me some good book to start with calculus?

[digital onyx]

Spivak calculus or Stewart personally speaking Stewart is more friendly and somewhat more comprehensive

[molten gulch]

stewart or thomas

[regal marsh]

Thank you 😇

[regal marsh]

Thankyou 😇

[timid lion]

i read stewart and then spivak. spivak is a treat to read

[regal marsh]

One more doubt is that I get stuck in graph parts, any recommendation for that part? I am a begginer, I want to start with basics to go on olympiad level

[timid lion]

like how to read/make graphs? stewart has a lot throughout his book and you should play around in desmos/geogebra

[regal marsh]

Thanks alot 💙

[digital onyx]

Though don’t worry about calculus, it’s okay just to find a book and study you’ll be fine. You will have very general way doing integrals in the future so

When you’re deep into math you solve any integral with simple functions and convergence theorem without needing any integral techniques

Most important part in calculus is really what spivak’s book values, the series’ convergence, different tests and method to evaluating series. Even double triple integrals they are pretty much just another layer of applying Fubini tonelli. Which isn’t as hard as many techniques for evaluating integrals I would personally suggest.

Though, spivak as first book might be a bit hard

Stewart is better for more comprehensive approach, as it includes more topics in calculus.

[molten gulch]

plot x/y pairs, simple

[timid lion]

the way i think of it, stewart is for first course, spivak is for second course

[regal marsh]

Thanks again for your valuable advice. I don't know much about maths book, I suddenly got drawn to maths, & I really want to understand it, I want to have a solid base, for that any recommended book Or a channel to study from is what I am seeking. By any chance you know any lecturrs online?

[regal marsh]

I think I will try both of them.

[timid lion]

for calculus, khan academy is still good

beyond calculus i didn’t like

[digital onyx]

MIT opencourseware depending where you go, if you want to study mathematics then calculus is kinda useless since simple function + Taylor + convergence theorems + tonelli + fubini solves everything for you in the future

Otherwise you can go to khan academy as rose suggested

A strong base is favored

[timid lion]

i feel like i am learning it all over again but only the important parts while i am taking analysis lol

[regal marsh]

Actually I don't know much about mathematics , I have just started, I will keep this in mind. Another reason for me to understand calculus is because of Physics.

[digital onyx]

Then go with rose advice, khan academy and do a lot of practice for firm foundation.. you don’t need those tools I mentioned

[foggy gorge]

Do you guys know books with good logical puzzles?

Despite the Mathematical Circles one

[real stratus]

i found ch5 (limits) to be very unmotivated and the delta epsilon proofs were hard to understand there

[normal crystal]

like Raymond Smullyan/Martin Gardner
or less recreational
I think CRC Publishers has a series on Mathematics Puzzles you can look up the titles

[foggy gorge]

I'm rn reading "What's the name of this book?"

It is exhilarating

[digital onyx]

Takes time

[rigid trail]

pdf form?

i agree it's good

o

i dont have any

no

there's a math library with a lot of the springer books though

[tribal crow]

@regal marsh welcome to the mathcord!

@rigid trail and welcome to the mathcord too!

or I guess welcome back

[rigid trail]

hi im back again

[regal marsh]

Hiee ,Thanks
Glad to be here
💙

[steel cloud]

I did group theory, ring theory now i want to do a field theory and Galois theory, so which book is good?

[floral lantern]

The field theory and Galois theory chapters in dummit and Foote are good

Also Milne has great notes on field and Galois theory

The first 3-4 chapters will be most of a “standard” first course in algebra stuff

The back half has infinite Galois theory and other more advanced topics

[steel cloud]

Any other book?

[floral lantern]

Milne’s notes!

That might be best

Cox is also an option

[steel cloud]

Okay i will look at Milne's notes

Thank you

Any comments on Bogachev measure theory book?

I want to cover all these topics

[torn crypt]

It has chapter 1 at least I’m pretty sure, and a lot more. It should have a lot of chapter 2, but I forget if it uses the probability language anywhere really.

It has a lot in those two books, a lot

Maybe not what id use as to learn L^p spaces the first time around, but I think there’s a lotta stuff in those books worth knowing

[marsh ingot]

I recommend Cohn

[steel cloud]

So Bogachev is good for that ?

[steel cloud]

Okay

[marsh ingot]

Didnt check Bogachev enough to say if its good

[torn crypt]

It’s good, but idk if it’s the kind of book you want

[steel cloud]

so which one you refering here?

[remote vortex]

Bogachev doesn't cover probabiliity as such at all; Cohn has one chapter on it. If you want to cover both measure theory generally and probability specifically, then Billingsley's Probability and Measure might be worth checking out

[spare abyss]

Hi there. I'm preparing for University and the TOLC-S requires somewhat of all High School Mathematics with obvious elisions to reduce the studying load (Calculus is not needed). I usually look for classics as modern textbooks are usually bloated with images and the overall format of the page was never enjoyable for me to read (mostly due to the way the text layout. Does anyone know a book that doesn't waste time in images, chatters and terrible formatting and explain pre-calculus?

[vital bane]

<@&268886789983436800>

https://tenor.com/view/verne-stare-gif-24447130

[steel cloud]

okay thank you

[spare abyss]

Have i written anything against the server rules?

[digital onyx]

Is it still beneficial to learn probability 1 (elementary probability in lower division of math department) if perquisite knowledge suffices to study measure theoretic probability?
In typical math department, is linear algebra first or probability first? Which material to study for probability?
I actually want hand on approach, because I need to pass many math exam next semester and I probably don’t have time for a full rigorous setup for probability

[vital bane]

yes, everything you wrote was against the rules

[digital onyx]

Though not realistic, is there any material that prepares me to pass probability 1 exam very fast since I need to pass a lot of exams

[vital bane]

jk it wasn't in response to your message

it was in response to another message someone else posted

[digital onyx]

Is it due to his focus or language? I am kinda asking exam centered materials too these days but I have too many exams next semester

[topaz silo]

Neamesis was joking

[spare abyss]

Please don't cage me in non euclidean mandelbrot set...

[digital onyx]

Got it, I thought asking too exam centered material isn’t allowed.. to be honest I am almost mad these day I have 7 exams next semesters including a couple I never learned before so I am just asking more exam prep material 😭
I do have a break though

[spare abyss]

Besides, I was peaking into Mathematics for Calculus byJames Stewart | Lothar Redlin | Saleem Watson, yet it is full of images and sub paragraphs which occupy 70% of the page layout and is obnoxious

[edgy hare]

There is way too many autistic and literal minded people here to say something like that and not cause momentary pandemonium 💀:😂

[spare abyss]

I may be neurodivergent but I can hold myself 😆

[edgy hare]

For sure! I just thought it was funny how literally a bunch of us (including me) took it at first lmao

[timid lion]

it sounds like you may want a set of course notes more than a book

[digital onyx]

I just want to do problem instead of study, the time constraint made me in possession of no patience..
Maybe note is better I felt like tell me definition and how to solve exam

[molten gulch]

Wha-; what did they say that was against the rules? It seems like a bog standard request for a textbook?

[spare abyss]

As a reference I'm reading Feynman lecture for the time being, but even the analysis 1 book my brother used during CS engineering was concise without an a4 sized page having the same surface of an a5 in terms of text

[digital onyx]

Is it possible though or too unrealistic to think of passing exam by studying exam? I mean I don’t even feel realistic anymore with these many exams

[spare abyss]

Reading it on a kindle is impractical i'd say, the page is too 😅

[topaz silo]

Now you're just trolling

[spare abyss]

So repeating the test possible questions on spam? In that case you will study the test so regardless you will study for the exam

[normal crystal]

how are the Feynman Physics lectures an example of concise

[molten gulch]

?

[spare abyss]

I think I've used the wrong word...

[digital onyx]

That’s kinda what I have been doing just I can’t handle different type of questions..

[molten gulch]

I didn't see the comversation underneath

lmao

I was scrolled up to yesterday

[timid lion]

most course notes you find will probably be in text format, then you can make your own ebook i suppose

[topaz silo]

Ah i thought you saw it and decided to follow suit

[digital onyx]

So I kinda want to study only algebras and study probability exams to earn credit
Or maybe even more unrealistic, I study measure theoretic probability passing both elementary probability and that, so I can get double credits alongside linear algebra.. too hard.. no time no patient, almost no motivation anymore.

[molten gulch]

No

[normal crystal]

what exams are you talking about
placement exams at your Uni that will grant credit?

[digital onyx]

Abstract algebra linear algebra probability theory I think there are more but I barely look at them anymore since more I see them more depressed I am

[spare abyss]

It just looks dense and bloated but I suppose that's the standard, my high school textbooks had the same issue

[molten gulch]

God I hate books that dense

[digital onyx]

It’s really that I am not first year student so as advanced year I actually can’t do much at this point, or I study math as master which I am actually thinking (my exam schedule isn’t realistic)

[spare abyss]

Same

[molten gulch]

https://www.stitz-zeager.com/Precalculus4.pdf there's also this

[spare abyss]

Thank you!

[normal crystal]

that's not what I'm asking
I'm asking the nature of the exams
if the math department is offering exams to place out of a class and you can get credit
it's probably just the class final exam
which means you should study their syllabus
asking here to answer a vague question won't help

[spare abyss]

there is everything I need for the tolc-s! thank you Ryan!

[digital onyx]

You’re right! I should do that, sorry I am too desperate..

[normal crystal]

I didn't mean to sound confrontational
I'm just trying to say the answer to your question is probably simpler than you think

[digital onyx]

I understand and I admit you’re right. I got very little patience these days sorry

[normal crystal]

np

I'm sure they will definitely tell you what's on the exams etc
and there are probably previous finals etc floating around

[spare abyss]

Hard timing abstracting?

[digital onyx]

Too many exams, and never had a proper plan..

[spare abyss]

hah...

Yeah I see now

[toxic heart]

Do y’all think I should get stewards book for precalc? I heard his calc books are good aswell so might aswell get the precalc (this is for learning the subject)

[digital onyx]

Should’ve never thought about changing majors out of a random thought 😭

[spare abyss]

If you like verbosely dense books I guess

[toxic heart]

I mean do you think it’s understandable in general? Like do you think 14 year old me can read it😭

[spare abyss]

I usually stay away from those cause I get overloaded of useless stimuli/informations when reading high school formatted like textbooks

[spare abyss]

Regardless of your age you can learn anything, it just depends by cognitive development which leads to how you are growing and how capable your brain is to conceptualise things...

[digital onyx]

Stewart is relatively easy to read if you dedicate yourself to practice, it’s really well-written

[molten gulch]

I have always wondered why textbooks need so many images, so much color, tiny font text, etc... to motivate a topic

[spare abyss]

But if you want a tip from someone asking the very questions: stop asking, just study

[molten gulch]

Some color a-la Axler's LADR are good

[digital onyx]

Calculus is rarely intellectually demanding rather you have to get your hands dirty by practicing

[toxic heart]

I just want my money worth

[molten gulch]

but otherwise, it's SO excessive

older books never had it

[spare abyss]

We don't know how you approach Math, the interest can also be volatile, usual from teenagers, but calculus per-se is easy, very easy compared to analysis

Though again, you have plenty of energy, just do it and stop overthinking

[molten gulch]

Basic analysis is quite easy too

[digital onyx]

Because of some non math students study them, like some actually struggle with it I feel

[molten gulch]

I wouldn't call much of a UG math cirriculum difficult

[molten gulch]

I can motivate the same graphs and functions with nice derivations, some epsilon delta tricks, and nice theorems

[spare abyss]

Is that what every Mathematician says after solving 200 differential equations? 😛

[molten gulch]

ODE or PDE

[spare abyss]

PDE

[molten gulch]

because it's well known that most nonlinear nonseperable PDEs are quite difficult

[digital onyx]

True but you’re still educator, some can be really, slow in these things if you’re other department

Some think calculus is hell

[spare abyss]

To my knowledge, to find something easy you need experience so that most of the mental faculties and computations are automatic, hence the familiarity with that subject is built in your brain, like a module, and approaching new topics of said subject comes easier as your brain has routines to be more efficient in proccessing informations

I guess that's why I cannot understand literature in my 23s

[digital onyx]

The electronic resources is helpful, nothing better than a couple of practice while you’re browsing

[molten gulch]

You do know that PDE is not often taught with the generality of measure theory and functional analysis at the undergraduate level in most universities, atleast in the US, right? Doing so would be absurdly difficult as here some unis don't even have measure or functional analysis offered as an undergraduate class

[spare abyss]

For what Sabine Hossenfelder has been arguining on her channel PDE are probably not even the actual tool we need for advancing in physics

And most likely I'm confusing the 2, so take what I'm saying with a grain of salt

[molten gulch]

I respectfully disagree with her, and there are several other reasons why I don't like her but I won't get into that now

[spare abyss]

She looks to be the opposites of showmen like Mikiu Kaku so I'm happy for the knowledge and critic insight she brings up

At least when I watch debates with her involved she doesn't attempts to sell her books...

[spare abyss]

But yes, after all divergencies are what make critical thinking progress :P

[molten gulch]

I hate Kaku for...obvious reasons; but so much of Sabine's content just feels like clickbait or ranting; and neither is all too useful when you're even ACTING about being a popular science channel

[spare abyss]

What is mostly clickbait about it?

She seems to follow the papers she disgresses in a concise way

She surely is very ranty, I give you that, but is part of her scientific character I presume

[molten gulch]

Anything where she discusses AI, Strings, etc...

I don't know how accurate much of the stuff where she goes on rants about establishment physics is

[molten gulch]

Most of her video titles, thumbnails where she's sarcastically holding her head in hands, etc...

it's

it's offputting to me

[spare abyss]

Well string theory is not physics at all, and I'm linking to her argument of being unmeasurable for now. So all we have to do is being faithful to mathematical proofs which have nothing to do with Physics until we will be able to measure all these radiations Kaku is selling. Moreover research is centralised into particle physics and string theory, as she states by also revealing a confidencial email which "exposes" the research bubble the scientific community lives in

[spare abyss]

How do you gather the attention of as many people as possible who doom scroll on youtube...? yes that's the answer...

I think she is aware of that and over time is what her scientific persona became on youtube

And I don't enjoy the boomery format too, though she thinks in a critic way. Once I will get a bulk of 5 years of physics I will surely be entitled, to a small extent, to approach these arguments 😆

[molten gulch]

I believe there was a debunk somewhere of that confidential email but I genuinely do not remember where it was, I normally do not come prepared to discuss this much

[molten gulch]

This is exactly my issue

I prefer organic and truthful growth over clickbait

[spare abyss]

Oh it's fine don't worry

[molten gulch]

Clickbait is just gaming a broken system; it's so utterly stupid

[spare abyss]

And this is not the channel for discussing it

[molten gulch]

Yeah lol

we should move this to discussion 2 or something

[spare abyss]

Wait I got something for you

[brave pebble]

What are some good books to improve at proof writing

[molten gulch]

Hammack book of proof

https://richardhammack.github.io/BookOfProof/Main.pdf

[molten gulch]

You are aware that this trend started decades prior to the introduction of TikTok, right?

[vital bane]

a single picture can be worth a thousand words

[foggy gorge]

Do u guys know geometry books with exercises like this?

[molten gulch]

I have no issues with graphics per-se, though I do have an issue with the books with tiny highlighted text, four million colours, random images "related" to the field, like why do I need a picture of an aeroplane in a linear algebra textbook, it has nothing to do with the exercises

[cunning elk]

see also “an idealistic critique of stewart’s calculus”

[fluid violet]

Mfw cat theory

[flat forge]

what is the most basic book which can level up your geometry from scratch to olympiad level

[true silo]

Anyone know any good books to learn about Vieta Jumping or Fermat Method of Infinite Descent?

[vital bane]

I can understand if it's quite distracting for you but in my opinion it's fun to read! Besides, who doesn't love an aeroplane or a space shuttle or an astronaut on the cover of their LA/calc book

it's super cool

[molten gulch]

Makes sense

to each their own I guess

[vital bane]

When I looked at those covers what came to mind was "Well duh! Of course! You need Linear Algebra to build an airplane!"

[molten gulch]

true

[vital bane]

Though looking all flashy and stuff doesnt mean much if the content (exercises and exposition) is trash

[molten gulch]

yep

[remote knoll]

If anyone is good at LC Classification, I have a book I can't find the Classification of, (I'm finally organizing my collection), and I was wondering if anyone can help. It's called "Combinatorial Techniques" by Sharad S. Sane (ISBN 978-93-80250-48-9). It's not in the LC catalog search.

Failing that, what other methods for looking up LC Classification are there? If a book isn't in the catalog and the LC classification isn't inside the book in the copyright information, I'm pretty stuck at the moment.

[iron willow]

Hi

[molten gulch]

<@&268886789983436800> requesting pirated materials

[compact copper]

Hello, please do not request pirated material on this server. As a partnered server we are strictly bound by ToS which that violates.

[remote knoll]

...

I do dumb at all times and in all places

[iron willow]

Well thanks

[iron willow]

Sorry

[compact copper]

um... no problem

[iron willow]

Even you don’t have combinatorics for mathematical Olympiad by S Muralidharan

[remote knoll]

You know, I actually don't think I do.

[valid narwhal]

how good is friedberg's linear algebra

[remote knoll]

What's your background?

Looking at it, it seems to be a better "second pass at linear algebra" sort of book.

or for someone who has taken, like Abstract Algebra or a proofs course but skipped linear algebra (or otherwise have an advanced level of mathematical maturity for when you'd normally take linear algebra)

[whole sparrow]

Friedburg was the standard upper division linear algebra book at my school. It thought it was quite good.

[remote knoll]

that being said, I've never used it personally, so these are pretty surface level impressions looking at the textbook for a few seconds.

Depends on the timing

like, you still have to learn how to think in terms of mathematical rigor

yeah, you should definitely spam your nsfw scam discord where a moderator is talking

lol

What I mean is, sometimes incoming freshmen take linear algebra, and you can't necessarily expect an incoming freshman to have that level of mathematical maturity. Some do, but it's not something you can expect, yeah?

[normal crystal]

Chipper shared his naughty epubs again
didn't he

[valid narwhal]

highschooler with much interest in maths

should I give it a try

wanted to give myself a challenge over the holidays

have some experience with proofs

[remote knoll]

If you decide to use this book, I would strongly recommend supplimenting it with a more basic resource to give you some grounding in the material.

[valid narwhal]

Would you have any specific material in mind

[remote knoll]

GA Tech has a free online linear algebra "textbook" that's very good.

and more basic.

[valid narwhal]

Had a look into its contents. Is it the one bearing the name ‘interactive linear algebra’?

[remote knoll]

I believe so yeah

[valid narwhal]

Tysm i think it will be very helpful

[molten gulch]

we absolutely fucking loved it TBH

used it as our first linear book, though that's not super common AFAIK

[floral lantern]

Friedbwrg I think is more common than using a book like Axler as a first linear algebra course for math majors

Since it assumes no matrix algebra

[timid lion]

we have a course for lower-div/engineering using Lay, then the first upper-div math course is Friedman

[tender river]

So when I was taking Linear Algebra I asked Lang a question about my problem set, and he asked to see my book; which was Friedberg. He started reading it and then said "who is this asshole!! You can't introduce a variable without quantifying it!!" then he looked at the cover and said "hmm, never heard of him" and then tossed my book aside. I asked him what book he'd recommend and he said "mine, of course." I did look through his book, but still felt more comfortable with Friedberg.

some random reddit post

[valid narwhal]

I see

Ig its hard enough to keep me occupied

[fluid violet]

sounds pleasant

[broken meadow]

i used friedberg it was totally fine

[agile flume]

pq oogissimo?

[broken meadow]

it makes my name longer

[fresh skiff]

I love this book !! I am teaching myself linear algebra from this book

[flat forge]

what is the most basic book which can level up your geometry from scratch to olympiad level

[daring wolf]

Just ground up in your own skills

[normal crystal]

ixnay on the p...

🤡

I think there is a intl edition

do you not know what ixnay on the ____ means

[keen orbit]

People can afford it in one way or another

[cerulean steppe]

pirate it or use another book thats free like https://mtaylor.web.unc.edu/notes/linear-algebra-notes/

[normal crystal]

L
ixnay on the p...

[cerulean steppe]

or check it out from a library, like a university library

[normal crystal]

the pb intl edition is only 20$
but idk what they messed with

[slender wasp]

FIS Indian edition, new is $6. And it's better printing than most Indian/international editions, which can be terrible.

It's Pearson which usually messes something up, but surprisingly this one seems pretty good and complete.

[normal crystal]

6$ shipped where

[remote sparrow]

well they're supposed to be for international markets

that is actually not legally actionable in the U.S.

https://en.m.wikipedia.org/wiki/Kirtsaeng_v._John_Wiley_%26_Sons,_Inc.

it's not de facto unactionable, it's de jure

[limber fern]

Does anybody have any high school statistics textbooks? I am trying to apply to be a teacher and i want to see how a textbook of that level teaches the concepts

[normal crystal]

Triola Elementary Statistics is a popular algebra based stats book

[tribal crow]

I'm late, but I really like FIS

I think they do a great job explaining things (barring maybe their last chapter ), and their book is chock full of examples that I found super useful when learning

[limber fern]

Thank youu

[normal crystal]

but if you're applying to a specific HS
you can just check what they used recently

[limber fern]

Oh yeah that's true. I'm planning to ask around. Thanks so much

[normal crystal]

btw, Professor Leonard's Stats lectures are based on Triola 11th edition

[boreal schooner]

Can anyone suggest a good Real Analysis book to combine with Rudin

[vital bane]

Understanding Analysis by Stephen Abbott

[boreal schooner]

Other than that ?

[vital bane]

Tao, Jay Cummings, Bartle and Sherbert, Schroder, they are all good analysis books similar to Abbott and I think will go well with Rudin

[boreal schooner]

Ok

Schroder ?

[vital bane]

"Mathematical Analysis: A Concise Introduction"

[boreal schooner]

Ok

[remote vortex]

Spivak's Calculus is also a real analysis book despite the title; I'd compare it in scope and aims to Abbott

I haven't spent that much time with that book but it seemed on the level

[frozen perch]

Same story with Calculus and Analysis in Euclidean Space (which is heavily inspired by Spivak), it’s essentially developing multi variable calculus from a rigorous analysis perspective.

It bears a lot of the quirks of the author, but the use of sequences to do analysis is great

[gray gazelle]

Are you the real Galois?

[remote vortex]

Haunting the mathcord

[minor ibex]

Hey,

Wondering what book I should learn in order to make the transition between axler and roman in linear algebra. I know a lot of concepts crucial to start roman like tensors, bilinear forms, pseudo inverses, jordan form... are missing in axler.

I would like to cover these topics from a highly theoritical/axiomatic perspective in order to build strong structural foundations, so engineering-oriented books like FIS are not what I search for.

[slender wasp]

Apostol as well.

[native elk]

finite geometry and information theory please everybody! plus if you are studying any one of them tell me if theyre fun

ping me

[minor ibex]

elements of information theory by cover & thomas

it's the one I will study soon but it requires a solid grasp on probabilities

[fresh skiff]

Analysis by Amann

[daring wolf]

rudin pma along with rudin rca and rudin fa

[kindred mural]

hi guys, what is the best book to learn calc

is stewart good?

alright

i need to grind calc 2

is 2 weeks enough

okie

[viral moth]

ANOTHER acgn ???

[kindred mural]

what

[viral moth]

knew someone who went by that for 3 years

[kindred mural]

xd

cool

[fresh skiff]

worse combination

[pliant axle]

Any book sequence recommendations for diff geo? I just finished understanding analysis and going to do either rudin or Tao for a more formal pass. What should I do afterwards? (I know I need manifold calculus and differential forms but what else + books 📚) thanks in advance

Extra points if there’s a nice book for discrete diff geo

But idk if I have to know diff geo for discrete version

Discrete seems a lot easier since it’s all based on vertices instead of manifolds or whatnot

Excuse my lack of correct terminology ^^^

[daring wolf]

if you just want some basic dg on euclidean 1,2-manifolds, then get carmo dg on curves and surfaces or o’neill ig i dont know other ones

if you want to learn smooth manifolds i’d choose lee smooth manifolds then get a riemannian geometry/riemannian manifolds book

and probably a lot of riemannian geometry books contain some geometries 1,2 manifolds so you dont have to worry about not learning basic dg books

(it may not cover special ones that work on euclidean specific things)

[native elk]

what about finite geometry guyyyyyyyyyyys

[zealous ruin]

best book for practice of calc 1

[timid lion]

stewart

[signal canyon]

this calc1 calc2 stuff is equiavlent to alevel maths in uk? or?

dk any good books here so was wondering what the americans use

[timid linden]

some of it is, so calc 1 has limits and hyperbolic trig i think which isn't in uk a level maths. And calc 2 has improper integrals, polar coordinates, sequences and series (a level maths has some of this but not much) and vectors (again, a level maths has some of this) which isn't in uk a level maths

[signal canyon]

ah yh that stuffs probably firther maths

ill try learn further next year

[timid linden]

yupyup

[signal canyon]

alr thanks

[timid linden]

but yah most of calc1 + calc2 is covered by further maths a level in the uk

np!! ^^

[daring wolf]

Stewart.

[tropic frigate]

any book recommendations for practicing international math bowl OR some basic calc 2-3 material?

[timid linden]

(not a book, sorryyy) but https://tutorial.math.lamar.edu/ has some practice problems on it for calc 2 and 3. The only book i can recommend is Stewart's Calculus Early Transcendentals which covers calc 1 - 3 so if you only pay attention to the calc 2 and 3 parts there's exercises for those chapters

[peak dew]

Is there any major difference between FIS linear algebra book's fourth edition and fifth edition ?
I got it's fourth edition

[cursive rivet]

for discrete: https://brickisland.net/ddg-web/

for classical curves and surfaces, here's something I sent a friend a while back:

https://arxiv.org/pdf/2012.11814 is very explicitly geometric (so if you really like drawing shapes and thinking about them) and tries to not be very technical, but I don't love the writing tbh

a prof of mine really likes pressley, elementary differential geometry. its main drawback is it refuses to use any abstract linear algebra, so sometimes is far too roundabout.

have heard great things about o'neill elementary differential geometry from everyone i've talked to, but never read it. pretty similar to shifrin below I think

http://alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf
is my personal favourite, a bit short but covers all the fundamentals and is well-written

the most famous is do Carmo, differential geometry of curves and surfaces. I personally can't stand it, it's very terse and lots of typos, but other people love it it seems

For manifolds, just go with Lee or Tu (hard recommend Lee over Tu but people's tastes very) and then go learn some actual differential geometry with those prereqs you'll have

[lusty escarp]

https://x.com/AxlerLinear/status/1940214288448463270

Sheldon Axler (@AxlerLinear)

Hardcover print versions are on sale for $30 each (50% off) until July 4:
* Linear Algebra Done Right at https://t.co/Opj7aMS06F;
* Measure, Integration & Real Analysis at https://t.co/C12dQo9kzk.
Use coupon code FLSH50 at check-out to get the $30 price.

X · Jul 2, 2025, 1:01 AM

[vital bane]

CAT!

[true sail]

Hello, is there a book you could recommend me with examples and exercices on isomorphisms and homomorphisms between group-like structures?

[tender river]

#book-recommendations message

[timid lion]

no. there are inline edits, some revised proofs, different exercises

[true sail]

So, basically any of those algebra books?

[molten gulch]

literally any algebra book will cover homo- and isomorphisms

[verbal tiger]

Any recommendations on textbooks for Applied Linear Algebra? Something that includes PCA/SVD and other ML methods. I took an ML course in undergrad so it's not new to me, but it would be good to have a refresher

[tender river]

probably horn's matrix analysis or some numerical linear algebra books

[tender river]

there is also this https://web.stanford.edu/~boyd/vmls/vmls.pdf

[remote sparrow]

https://www.amazon.com/Matrix-Mathematics-Cambridge-Mathematical-Textbooks/dp/1108837107

[tender river]

and based on some past posts here watkins: fundamentals of matrix computations seems well liked too

[steel cloud]

Who?

Any advice for learning measure theory from Royden?

[true sail]

Thanks!

[coarse estuary]

Hey guys, I’m gonna start learning linear algebra in maybe a year or two and I’m wondering if anyone has a book recommendation. A friend recommended me “Linear Algebra Done Right” by Sheldon Axler, but it says in the preface that the book is meant as a second exposure to linear algebra and I was also disheartened by the lack of graphs/visuals. Anyone have a good book?

[molten gulch]

I hate graphs and visuals beyond what is absolutely neccessary, a lighter book which still expects mathematical maturity from the reader and covers most of the same material is Friedberg Insel and Spence's Linear Algebra

[steel cloud]

I think linear algebra done right is a good choice for beginners

[molten gulch]

It can be if you're able to jump into abstraction

[steel cloud]

But when does the Axler use abstraction?

[coarse estuary]

Yeah I’m using it to study pure math

I’m worried with axler I won’t be able to get a lot of geometric intuition for some of the concepts

I couldn’t find any graphs or pictures of any mathematical objects anywhere

Maybe they’re just well hidden 🤷‍♂️

[remote sparrow]

you can see there's a link right above the message ur replying to

[molten gulch]

IMO you don't need it a ton; I don't view math geometrically all that much anymore

Unless I'm explicitly doing geometry

but it ofc useful if doing physics and such ig

[coarse estuary]

I suppose

I’ll make sure to check out the book u recommended tho 👍

[steel cloud]

Great, thank you

[cunning elk]

sure a picture is worth a thousand words but I think their importance is highly overrated in lower level courses

bc people often will use that as a crutch to evade actually understanding the material

[cerulean steppe]

$a \cdot b = |a||b| \cos \theta$

[hasty eagle]

L

[cunning elk]

projections, right triangle trig

[cerulean steppe]

The simplest case is when $b = e_1$

[hasty eagle]

L

[cunning elk]

see: the average 3b1b comment section

[remote sparrow]

the algebraic definition extends the geometric notion

https://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality#Geometry

[clear jay]

https://store.bookbaby.com/book/python-and-math-essentials-for-machine-learning

[minor ibex]

Hey,

Wondering what book I should learn in order to make the transition between axler and roman in linear algebra. I know a lot of concepts crucial to start roman like tensors, bilinear forms, pseudo inverses, jordan form... are missing in axler.

I would like to cover these topics from a highly theoritical/axiomatic perspective in order to build strong structural foundations, so engineering-oriented books like FIS are not what I search for.

[remote sparrow]

everything you said was missing in axler is present in the fourth edition of axler

https://linear.axler.net/LADR4e.pdf

are you using an older edition?

also it would be a good idea to know some abstract algebra before going into roman

[minor ibex]

😮

[remote sparrow]

i'm also not sure why you said FIS is "engineering-oriented"

https://www.amazon.com/Linear-Algebra-2nd-Kenneth-Hoffman/dp/0135367972

hoffman kunze is good

[minor ibex]

I was trying to make a roadmap and someone recommanded me axler but had pointed out many topics missing, I assume he used another edition yeah

[minor ibex]

I mean it seems there is a lot of computation exercices and few hard proofs exercices

[minor ibex]

I'll check this out 👍

[minor ibex]

is a book like artin enough ?

[remote sparrow]

"computations" can be proofs in linear algebra if you're working with matrices

linear algebra proofs can be pretty straightforward

[remote sparrow]

sure

[minor ibex]

okay, I will definitely do the axler book before looking at other stuff then

At my uni we had 2 courses on linear algebra

one was heavily oriented on computation, the other one focused on vector spaces, linear maps, rank theorem...

[remote sparrow]

that's typical in the U.S.

[minor ibex]

I'm french but yeah my uni seems to be following this US thing

like we have calculus II, III

My goal is to master math in order to check advanced topics in quantum information

[trim kayak]

I have a strange recommendation. I took a course on teaching mathematical thinking through the local university as it's required to renew my teaching certification.

I have been reviewing my notes and looking for resources online. Can anybody recommend any books or other resources for teaching mathematical thinking to high school students? Thanks!!

[ripe pagoda]

AOPS has a pretty “creative problem solving” based curriculum to highschool math i think, i might recommend studying their curriculum somewhat? good luck

What book do i use to learn the atiyah singer index theorem? (my advisor does diff geo so from a diff geo standpoint would be good)
@slim nacelle im pinging you to make sure you see this

[trim kayak]

Can you send me a link to the curriculum or website? Thanks.

[ancient vine]

https://artofproblemsolving.com/wiki/index.php/Mathematics_books#General_Introduction_.2F_Multiple_Topics

[ripe pagoda]

it assumes enthusiastic learners btw

so your mileage may vary

[ancient vine]

how do you study a book of math.

[ripe pagoda]

i mean if you want to emulate the teaching techniques of it, you pay attention to how everything is formatted, in what order it is, and what parts are emphasized kinda

[ancient vine]

particularly a book that aims for the NMO

[broken bramble]

you can approach it either way. i think it's nicer to start with the geometric definition and derive the algebraic one

[sturdy shore]

Funnily enough, that formula can be used to define the angle theta

in a (I guess real) vector space where angles don't make sense a priori

[cerulean steppe]

it's a result in 2D. The dot product is defined by $a \cdot b = a_1b_1 + a_2b_2 + \dots + a_nb_n$.

[hasty eagle]

L

[frozen perch]

It comes out of the fact that the size of a vector is the square root of the sum of the squares of its entries

[mortal ore]

2-norm moment

[cerulean steppe]

it's not trivial. One way is via constructing a rotation $R$ such that $Rb = e_1$. Another way is to use the law of cosines

[hasty eagle]

L

[frozen perch]

(I hate the law of cosines, so I just drew the picture directly to get around it)

[cunning elk]

the “engineering student”-ification of lower division university math and its consequences have been disastrous

[timid lion]

yeah :(

[frozen perch]

Oh. Then there's gonna be a lot of this going forward

[cunning elk]

yall have to learn a lot of math but also lots of science specific to your field

so in professors’ eyes

some sacrifices have to be made in the rigor/actually explaining things department

the problem arises when

this treatment is the only available option even to non engineering students

[broken bramble]

it's usually derived from what i remember

it's the cross product that typically isn't

[frozen perch]

But it should be! To do mathematics effectively we should characterize our objects rather than construct them

The cross product of u and v is just the vector orthagonal to both with size equal to the parallelogram formed by u and v, with orientation chosen to match the right hand rule 😭

Not whatever horrible coordinate forumla it's usually taught as

[cunning elk]

the determinant abuse of notation 💀

[frozen perch]

Oh god, yeah. A useful crutch for calculation, but if that's the first thing you see of it ☠️

[broken bramble]

true but they should at least derive that formula after characterizing it

the cross product or derivations?

[frozen perch]

You can certainly learn how to use a cross product just with a lot of practice, but I think having that understanding would help get to that point faster

[broken bramble]

i disagree, i think when you drop weird formulas out of the sky it discourages a lot of people

not everything fits this mold but i think a good pedagogical strategy is: give a motivating problem, characterize a tool that would help solve it, and then derive whatever the formula is from the characterizing properties

like for the cross product the motivating problem could be calculating torque, you characterize it in the way link did, and then you show how its properties lead to the component formula everyone learns

that way its seen as actually being useful and its no longer mysterious

[cursive rivet]

that's unnecessarily reductive

I know plenty of engineers who enjoy this stuff, but care most about applications

[cunning elk]

yea wait until you get further into your degree before trying to make generalizations like this

in your first year you're not really doing anything substantial yet and people largely haven't figured out their precise interests

[clear jay]

Any book reccomendations for TMUA Prep?

[remote sparrow]

i've sold a few

but they were all duplicates so far

[arctic harbor]

what do you guys think of the art of problem solving series?

i'm looking at purchasing a copy of the pre-algebra and algebra textbok

[topaz silo]

Hallo, I want to learn the part of calc 2 that's in the screenshot, and all of calc 3, what books would be good for these?

[timid linden]

the book i used for calc is Stewart's Calculus Early Transcendentals which covers calc 1 through to 3, i think it covers everything in that screenshot

[topaz silo]

I see, thanks

[subtle swift]

Is this channel only for math related books or could i give other recommendations as well

[vital bane]

any books

Usually you can know what a channel is for by reading the channel description...which is for describing a channel

Classical Mechanics by John Taylor, engineering I don't know haven't studied it yet, for fantasy I'd recommend the novel series "Re:Starting Life In Another World From Zero" by Tappei Nagatsuki (there is an english translation available by Yen Press)

[hollow shore]

For fantasy, check out Dune by Frank Herbert

[vital bane]

There is a free web novel as well, translated by Witch Cult Translations https://witchculttranslation.com

Tong's lecture notes are also great for all sorts of physics http://www.damtp.cam.ac.uk/user/tong/teaching.html

[subtle swift]

Project hail mary

By Andy Weir

Just amazing

[proud osprey]

The trailer for the movie adaptation was released like yesterday

I liked the scifi parts of the book but the characters and dialogue were atrocious

[native breach]

Seconding Classical Mechanics by John Taylor, really wonderful textbook.

[pastel atlas]

Best book for Calculus, from scratch to advanced

[molten gulch]

Thomas or stewart are fine

[signal canyon]

any engineering students, specifically chemical, any good books i can read to put on my personal statement or js anything to help learn ab the coursework?

i hesrd its calculus heavy

[daring wolf]

just get stewart or thomas

and get some other books for advanced topics after you finish stewart or thomas

[pastel atlas]

What about trigonometry?

Thanks btw

@daring wolf you too

[daring wolf]

huh trig? just learn some from ur school curriculum and that is enough

[pastel atlas]

Well to be honest I am trying to self-study maths outside of school in general from scratch

Idk what books I should use, I wanna start from the beginning to advanced

[daring wolf]

I don't know any good books for trig since I just learned it without getting a book...

and the ones that I probably know aren't in English

[eager wigeon]

I think any kind of precalculus text should have enough trig to get you what is needed

[cunning elk]

precollege mathematics is so oversaturated online

that there’s bound to be something

[upper estuary]

Khan academy is good for trig

[wild maple]

yall do you know any good books on analysis?

[daring wolf]

rudin

and abbott

and see the pinged messages

theres a book review on analysis

[tender river]

#book-recommendations message

[cerulean steppe]

https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[hard mango]

Are there any good books on applied category theory?

[tender river]

googling gives you this https://ncatlab.org/nlab/show/applied+category+theory

(although the links to the lecture notes are dead sites)

[frank saffron]

There's one channel on yt, called the math sorcerer. The guy has some videos about good math books, there's one video recommending one book from each broad area of mathematics. At least i think those videos are pretty good

[molten gulch]

Math sorcerer has gone to shit now

[hard mango]

Ok thanks I’m gonna check it out

[frank saffron]

Why?😢 He became crazy? I don't watch his recent videos tbh

[signal canyon]

idk what it is

all he uploads is like

"go off the grid, do math"

and its js him babbling

his actual math videos r useful soemtimes

speaking on thsi, any good youtubers that ARENT organic chem tutor

i dont like him very much, as crazy as it may seem

[remote sparrow]

he sells a bunch of ai generated books of dubious quality at best

[mortal ore]

ai generated implies dubious quality

[frozen perch]

Anyone have any books they particularly like for number theory with cryptography? I’m going to be preparing lecture notes for such a course, so I’m poking around different undergrad resources

[remote sparrow]

@sturdy shore btw did you end up using zakeri; if so, how did you find it

[sturdy shore]

no, the instructor was using another book and following it very closely (lang) so I had to follow

I still read a bit of zakeri, thought some of the proofs were way better than proofs you'd find elsewhere regarding elementary integration results

[frank saffron]

holy shit lol. I find a lot of his videos interesting, he has good videos reviewing math books. I didn't see him selling those kind of book at least

[mortal ore]

it was a more recent development

unfortunately many of his book reviews ended up being very ai-derived and uninspired

at least recetly

[sturdy shore]

hot take? I thought that guy was always highly mediocre

[frank saffron]

Aw that's sad, didn't know that. Well, thanks for the warning

[mortal ore]

the worst part is that he now pumps out ai generated books and sells them to people as if theyre his

[sturdy shore]

never said much about the content, it always felt like AI lol

[signal canyon]

any good alternatives?

everyone js says the same thing

3blue1brown or organic chemtutor

[mortal ore]

for what

[sturdy shore]

like a yter reviewing math books? idk any

[mortal ore]

book reviews or general math topics

[signal canyon]

sorry

didnt specify

[mortal ore]

no dw about it

[signal canyon]

i dont know what the american ewuiavelnt is

but i think its like

calc1/2

level

[mortal ore]

yes

just introductory calculus

i recommend khan academy for those frankly

[signal canyon]

noted

[sturdy shore]

3b1b is goated

[mortal ore]

3b1b's essence of calculus is pretty good

[signal canyon]

yeah but he has very few specific videos

[sturdy shore]

khan academy is really good for the actual courses for w/e they offer

[frank saffron]

Just now i was watching his video "Legendary Calculus Book ", where he's reviewing apostol book on calculus, i was thinking of reading it

[mortal ore]

except for calculus 3 and linalg