book-recommendations

[halcyon hornet]

Oohh.

Yeah makes sense.

[grand thistle]

not much, only hte introduction and a bit of chapter 1

[halcyon hornet]

Is it fun?

[grand thistle]

very

[halcyon hornet]

Oh.

[grand thistle]

im really only reading it for fun

[halcyon hornet]

Do you get "Aha" moments?

Oh lol.

[grand thistle]

well, it's only been about 15 pages, but im pretty sure those moments are coming

[halcyon hornet]

Cool!

That is mostly what I want anyway lol.

[grand thistle]

it grabs your attention by introducing with some cool proofs

like the proof to why theres an infinite number of prime numbers

here

i don't exactly know what it's saying right now and how they got to that, but thats the good part of the book; it leads up to the technical stuff while keeping you interested along the way

[halcyon hornet]

Oooohh.

Any idea how much prerequisites are needed for the entire book?

[grand thistle]

probably just basic high school algebra

it really just builds from the ground up

[halcyon hornet]

That is really cool!

[grand thistle]

yeah it is

[tame plaza]

Any thoughts on Calculus Made Easy by Silvanus P. Thompson and Martin Gardner?

[gray gazelle]

iirc it uses infinitesimals

which is nonstandard calculus

@tame plaza

but take the opinion of someone who really understands calculus and and knows the difference between standard and nonstandard calculus

[tame plaza]

interesting

is non standard calculus easier than standard calculus?

[gray gazelle]

i have no idea

i was looking for a calculus book to read too and found that book

but it was very old+ had nonstandard calculus so i avoided it

[tame plaza]

1998 is very old?

are you talking about the 1998 version or the 1914 version? @gray gazelle

[gray gazelle]

either

the original text was originally published in 1910

[abstract walrus]

is Zuckerman's Number Theory worth going through the pain?

there are an unnecessary amount of questions on every topic

[sudden kindle]

Look at that beautiful elliptic integral on the cover

at least it looked like an elliptic integral 😬

[sage kelp]

Where can I find the basics of limits of sequences of sets?

[modern stone]

I’ve heard it’s good if you want to get an intuitive understanding for calculus, but it should be used as a supplement

[modern stone]

Yes and no.

Some proofs are easier if you use infinitesmials but it is harder to make non-standard calculus rigorous than standard calc

[tame plaza]

alright

[gray gazelle]

any cs book that goes over big O notation?

[uncut gale]

Hi, sorry for a general question, but rn im reading and solving exercises from Cauchy-Schwarz Masterclass and I really interested in books with the same approach - interesting problems lead to interesting results, that require little to none prerequisites.

Also, can someone recommend good statistics book/ problem book that has solution manual - Im sorta self learner unfortunately.

Sorta, that also has cool useful exercises

I mean, I started to understand calculus a little bit better by getting a grip on inequalities

oh, proofs from the book is awesome

yeah, partially

[gray gazelle]

3blue1brown has cool videos too

about hard problems

[uncut gale]

Concrete math goes over it in the last chapter

or are you interested in O notation for algorithm analysis? TAOCP then

[gray gazelle]

hold on

that's the million pages book right

[uncut gale]

yes, but it didnt meant to be read fully

its more reference book than anything

[gray gazelle]

i see

thanks

[uncut gale]

if you want textbook algorithm text - Cormen will suffice you

[gray gazelle]

i wanted a complexity book

and i found one

[tulip blade]

Basically any discrete math, algorithms, or complexity book. Id look at concrete mathematics by knuth. He has a good chapter on asymptotics.

[foggy relic]

do you need to learn that from a book

[gray gazelle]

No

[sage kelp]

Any introductory books to abstract analysis?

[solemn rover]

can you elaborate on what you mean? abstract harmonic analysis by folland is supposed to be really good

do you have background in analysis or are you looking for a first text in analysis

[sage kelp]

So I found this book Foundations of Abstract Analysis by Dshalalow and found the content quite interesting (the preface caught my attention also). Started reading it, but it feels like I need some additional resources. I already worked through Bartle & Sherbet analysis book, but still want to gain some more math experience. I have in mind studying some basic measure theoretic probability and functional analysis.
(This is the table of contents https://link.springer.com/content/pdf/bfm%3A978-1-4614-5962-0%2F1.pdf)

[gray gazelle]

Anyone know any resources on linear forms in logarithms?

[lime sapphire]

does anyone have an idea of resources i can check out to learn integration techniques usually found in competitions and integration bees?

[uncut gale]

i dunno about competitive, but try inside interesting integrals

[pale scarab]

Any good books on computational geometry?

[manic bay]

has anyone read the Algebraic Number Theory and Fermats Last Theorem is it a good book? \

[balmy prairie]

Does anyone know any big book(500+ pages) which contains basic math until complete middle school math?

I am currently in highschool and I am lacking knowledge of the basics, so it is giving me a lot of problems in understanding the advanced concepts. If anyone knows, please ping me.

[stray veldt]

i don't think there is just one book with the title "Algebraic Number Theory"

[stray veldt]

oh it's the complete title lmao

[manic bay]

yeah ahaha, have you read it?

[stray veldt]

no, not familiar with that one

[halcyon hornet]

This book seems rather unfamous.

[glad prairie]

Lang's Basic Mathematics is a big book that contains all that stuff. It might be a bit on the tougher side. I also don't really like Lang.

I prefer Gelfand's books, which cover a lot of ground but are split into a few pieces. They're also not super easy but they're very conversational and enjoyable. It's easy to find free pdfs of these books online if you want to test them out.

[stray veldt]

weird title though

[manic bay]

Yeah

Do you guys have any books on fermats last theorm?

[stray veldt]

depends what you want

there is a book called Fermat's Last Theorem by Simon Singh which talks about the history

[manic bay]

pretty much, a book on Pierre de Fermat and his theorms

[balmy prairie]

Thanks.

[stray veldt]

if you want to understand wiles' proof, a single book will not suffice

[manic bay]

thanks, I will check it out

Wow, this is exactly I what was looking for, Jeez Thanks

[halcyon hornet]

Got your answers, notcls ?

[manic bay]

Oh yes, really satisfied
I found a book that I was looking for in terms for what I wanted like the history, and how he created those theorems

[halcyon hornet]

[glad prairie]

i have singh's book, i should read it and pretend that's me learning algebra

[manic bay]

really is it good ?

[glad prairie]

i have no idea, i haven't read it

i picked it up from a used bookstore for a dollar

like 3 years ago

if i put this book on the "to read" list it's gonna be 5th or 6th priority at this point haha

[manic bay]

hahaha i totally know how you feel, I am like with everything its something I want to do, but I procrastinate

like it could be a good movie, and be will just be on my phone till 3 am

[sage python]

Stewart-Tall I've heard of actually

[rigid walrus]

Guys what's the best book for numerical linear algebra?

[karmic thorn]

Demmel, Numerical Linear Algebra

I don't know anything about this book but it has been suggested multiple times here

[modern stone]

You could also try Khan Academy on youtube. They aren’t really a book but they cover all you need

[balmy prairie]

I don't like videos because I think they are too slow. I am someone who's a fast reader and can easily grasp subjects, so that's why I am looking for books only.

[modern stone]

Understandable

You could take a look at Paul’s Online Notes

https://tutorial.math.lamar.edu/

[balmy prairie]

Thanks, gonna give a look.

[smoky zephyr]

@balmy prairie none of the stuff on there is middle school level

[balmy prairie]

There is one which is

Basic Mathematics

At least that's the stuff that's teached in middle school in my country.

[shy compass]

anyone know a good text which covers topological entropy?

[tame plaza]

like this? https://books.google.com.sg/books?id=Z9z7iliyFD0C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

[glad prairie]

yeah

[tame plaza]

ok

[shadow tusk]

do you not like Lang's basic mathematics because it's tough?

[glad prairie]

no, i don't like it because lang writes like shit

[shadow tusk]

lol

ok

[smoky zephyr]

doesn’t lang write a ton of books

or am i thinking of someone else

[solemn rover]

yeah.

he's prolific

can't think of anyone comparable that comes to mind

[gray gazelle]

I liked Basic Mathematics

It induced in me a sort of rigor fetish

[tame plaza]

someone deleted their comments ig

does this mean Gelfand didn't make any mistakes?

[uncut gale]

afaik his algebra book very good edited

at least in russian, i have a copy

[polar smelt]

One message removed from a suspended account.

[smoky zephyr]

i was saying none of the stuff on pauls online notes is middle school level

i consider middle school stuff to probably be algebra 1 and anything below

[polar smelt]

One message removed from a suspended account.

[fervent lava]

pauls online notes has a algebra course.

[smoky zephyr]

that’s algebra 2

[uncut gale]

Im sorry for repeating my question, but rn im reading and solving exercises from Cauchy-Schwarz Masterclass and I really interested in books with the same approach - interesting problems lead to interesting and useful results, that require little to none prerequisites. Something more combinatorial/probabilistic in nature

Also, can someone recommend good statistics book/ problem book that has solution manual - Im sorta self learner unfortunately.

[tardy shadow]

Quran

Good book

Author - god

[glad lark]

I have a very good mathematics book

problem solving stratergies by arthur engel

i cant understand much but its nice

putnam level questions

[uncut gale]

ooh, nice, thank you

[glad lark]

have u bought it?

[glad lark]

?

[narrow tide]

Wanted to ask about Complex analysis by lang

The contents seem promising

[glad lark]

ya i have bought it i can send u a few pages if u want to see more

@narrow tide

[narrow tide]

Thanks. How is it, I do have a soft copy just dunno if it's worth putting the time in

[glad lark]

actually i am a 10 class student so i just understand a few topics but it is worth trying

it has good level questions

[narrow tide]

Got it thanks

[glad lark]

np

[halcyon garden]

What are the prereqs to intro to modern dynamical systems katok and hasselblatt?

[foggy relic]

i tried reading some of it, it was ok

lang is the guy who spams books i think

[narrow tide]

Yep lmao

He's dead tho

[still umbra]

Best reference book for ~calc 2/calc 3

preferably dense or proof-heavy

Since I've done most of this stuff before, but I just forget random bits occasionally. e.g. Taylor's Theorem for example

[fervent lava]

Probably spivak calculus and his calculus on manifolds book. That what is recommended in this server by people.

[wintry quartz]

Whats a good book to get an introduction to category theory? And also if anyone has video lecture series they could share that would be highly appreciated

[humble bluff]

working mathematician thing

when I first saw it it looked really advanced

but read it nonetheless

[wintry quartz]

The one by Saunders Mac Lane?

[dapper root]

Category theory in context

Categories for the working mathematician is so much more than you need for a lot of purposes unless you plan to something insanely categorical

[halcyon garden]

Bump

[sudden kindle]

Bump

Bump

Bump - Automorphic Forms

[restive falcon]

what would be the reasons to use either rudin or pugh

for real analysis

[uncut gale]

use both tbh, rudin for exercises, pugh for explanations

[restive falcon]

i dislike flipping between books

as pdfs

but like

are there other advantages

of each over the other

[marble solar]

I prefer Pugh's text over Rudin's text for intro analysis because Pugh gives more examples, more exercises, and goes through things more thoroughly for students

It's good stuff that's on there

[restive falcon]

oh

ok

[marble solar]

Rudin isn't a bad text, and there's no canonically wrong choice

[restive falcon]

ah

[marble solar]

Some people like Rudin for his conciseness and precision, lack of extra fluff leaving you to figure it out

But for students, especially those without a mentor to help them, I think Pugh is superior

[uncut gale]

if you have time and patience -read pugh and solve exercises from both books

[restive falcon]

do they both cover basically the same content

[uncut gale]

rudin afaik is a covers a little more

[restive falcon]

oh

is rudin more technically precise

or sth

[hollow peak]

They both cover the same material equally precisely

Rudin is good for when you've done proof based math and are coming back to review and have the skills

[marble solar]

They cover the same

[hollow peak]

Pugh is good for first time learning

Lots of really nice pictures in pugh as well

[uncut gale]

my bad then

[hollow peak]

And it's still far from being easy if you're bored by abbott

[marble solar]

However, Pugh covers intro measure theory in a better manner

[tulip blade]

Theyre tons of very hard exercises in pugh

[frosty girder]

[marble solar]

Rudin's chapters on special functions, fourier, and multivariable stuff is pretty good

Probably better than what's in Pugh

[uncut gale]

is abbott good choice after spivak's calculus?

[frosty girder]

how many exercises would pugh have in one chapter

[tulip blade]

A lot

[marble solar]

No, skip straight to Rudin, Pugh, or Whitaker & Watson

[hollow peak]

Pugh covers everything at a reasonable pace

[frosty girder]

[marble solar]

A lot. 50-120

[hollow peak]

Rudin does it very quickly

[tulip blade]

I think both are fine. I really like the first 3 chapters of pugh tho.

[hollow peak]

So just skip Abbott if you can handle spivak

[frosty girder]

im doing apostols book rn, and every chapter (except for the second one) that i have seen has like 50+ exercises

[restive falcon]

I'll go through pugh probably

[frosty girder]

Ooo damn

[tulip blade]

There is a nice ebook for pugh available for free

[marble solar]

Which Apostol book? Calculus volumes 1 & 2? Or Math Analysis?

[tulip blade]

The rudin pdf is just shit

[restive falcon]

oh

[frosty girder]

mathematical analysis

[tulip blade]

U have to scroll.

[restive falcon]

in what way

[marble solar]

Apostol's book is like Rudin + Detail

[restive falcon]

oh

[frosty girder]

[marble solar]

It's pretty decent

[frosty girder]

im liking it so far

[tulip blade]

Pugh has table of contents on the side you can just instantly skip to wherever @restive falcon

[frosty girder]

the exercises are a bit too much for me at times

[marble solar]

It goes over a lot of neat things

[restive falcon]

oh

[marble solar]

I hope one day I can teach intro to analysis

[frosty girder]

[tulip blade]

Its not really a big deal im js.

[restive falcon]

yeah I'm used to no contents metadata
i read winning ways pdf

[uncut gale]

maybe lets do reading group on intro to analysis lol

[marble solar]

Nah, I don't have time for that

[uncut gale]

sadge

[marble solar]

I took intro to analysis 6 years ago

Wow!

Holy shit it's been 6 years

[hollow peak]

you can always post questions in the channels

[frosty girder]

Damn

[normal sandal]

I think I can TA a real analysis course in my second year

[frosty girder]

Ooo

[hollow peak]

I took real analysis last year

[normal sandal]

Have to actually get a good grade on analysis this year though💀

[frosty girder]

Idt i can join since well i would be super in consistent

[hollow peak]

this year I TA'd it which was fun

[frosty girder]

i havent taken analysis yet

coz im not in college

[marble solar]

I'm auditing/taking PDEs for the third time

[normal sandal]

yeah I think TAing is cool as shit

bit frustrating sometimes I'd imagine

[restive falcon]

I'll do pugh analysis

[hollow peak]

I made lots of comments about how measure spaces are just fancy topological spaces

[normal sandal]

I think we have to just help/check homework & midterms

[hollow peak]

I think that stuck with them

[restive falcon]

then knapp algebra i have

[frosty girder]

measure spaces in an intro course?

[marble solar]

THat's literally how Papa Rudin teaches it

[frosty girder]

[restive falcon]

is there a like
pugh 2

[hollow peak]

it totally makes sense to teach them as dual concepts

[restive falcon]

electric boogaloo

[hollow peak]

also then borel measures unify them

[marble solar]

No ~ if you're interested in going further in analysis, there's a lot of routes after pugh

You can learn fourier, complex, measure & integration, or PDE

[restive falcon]

because I'm very interested in complex analysis and holomorphic dynamics

[normal sandal]

ooh complex is fun

[marble solar]

Eventually, if you want to be an analyst, you learn them all

[restive falcon]

yeah

[hollow peak]

Jerry shurman's notes on complex analysis are great

[normal sandal]

I've heard stein & shakarchi thrown around a lot for CA? any good?

[hollow peak]

They're all online

[marble solar]

Great exercises, ok exposition

[restive falcon]

i have the stein real analysis pdf

[marble solar]

I'm a big fan of Marshall's Complex Analysis text, although it's a little wonky

[normal sandal]

Hm interesting ty

[restive falcon]

someone joked and told me it was a good intro book

and i believed them

[normal sandal]

I think might have to pair it with lectures for the best experience

[marble solar]

It is an intro to measure & integration

P:

[restive falcon]

anyway

yeah

[hollow peak]

measure theory and fine properties of functions by Evans

[restive falcon]

pugh seems fun

gotta do a physics exam see you all later

[marble solar]

So I'm auditing PDEs, and we're doing Linear PDE stuff. AKA Fourier, Sobolev, and all that shit

It's so different from Evans

[normal sandal]

Actually wrt to exposition, if a book doesn't have the best exposition / explanations do your lectures + paying attention in them help supplement that?

[frosty girder]

👋

[frosty girder]

[marble solar]

I did like 8 chapters of Evans only for it to all be useless

[frosty girder]

[hollow peak]

I can't imagine any treatment of linear PDE other than Evans

it is literally impossible

[marble solar]

Gregory Eskin, Lectures on Linear PDEs

[hollow peak]

[marble solar]

Goes more into distributional calculus

[hollow peak]

One of these days I'll read Taylor

[marble solar]

And tempered distribution

It's interesting because I always thought that grad PDEs would look exactly like Eskin's book

(Eskin is Emeritus at UCLA)

[hollow peak]

It would be nice to finally unify my understanding of weak stuff

[marble solar]

And I learned functional from one of Eskin's students (Joe Bennish, who is mentioned in the preface)

So it's like exactly how UCLA teaches PDE stuff still

[hollow peak]

Because of riesz, distributions supercede weak solutions, right?

[marble solar]

Something like that, I didn't get far in the functional route

[hollow peak]

I am so hype to actually take a class on functional analysis

[marble solar]

Wasn't too much my cup of tea ~ it was an applied course so we just used distributional calculus to do fourier and Boundary Value Problems

[hollow peak]

I know babby Hilbert space stuff

[marble solar]

That's basically what we did

[hollow peak]

but I am ready for the real deal

give me horrible topologies

[marble solar]

My friends that took functional said it was horribly boring

Because all you do is "Oh what if we have this norm, oh is this space complete? Did you remember to diagnolize"

etc.

[hollow peak]

I think that's interesting though

I find stuff like banach alagou interesting

[marble solar]

For like 2 weeks maybe

But 10-16 weeks of it?

[hollow peak]

Well there's more to it than just that

[marble solar]

Banach Alagou is interesting

[hollow peak]

Like, can't do functional analysis without convex analysis

and convex analysis is super cool

[marble solar]

Convex analysis is weird, I don't understand it

[frosty girder]

whats convex analysis?

[hollow peak]

hyperplane separation

[marble solar]

but then again, I don't understand PDEs

So

🤷‍♂️

[hollow peak]

roughly, analysis of convex things?

[frosty girder]

Convex things as in convex shapes? or convex functions?

[marble solar]

You can rephrase convexity in terms of acceleration being non-negative

Convexity of functions

[frosty girder]

so f''(x) is positive

[marble solar]

And you can do all sorts of estimates using random techniques

[hollow peak]

both, because the geometry of the overgraph of convex functions is equivalent to the convexity of the function

[frosty girder]

i see

sounds cool

[marble solar]

and by random techniques

I literally mean brownian motion stuff

[hollow peak]

a lot of very interesting stuff in math ends up relating to convexity, in particular convexity of norms

[frosty girder]

[frosty girder]

[hollow peak]

duality of Lp and Lq when p,q are holder conjugates can be seen as a consequence of convexity of Lp norms

and convex sets are just interesting in general

[frosty girder]

[hollow peak]

convex hull of finite set of linearly independent vectors is a convex polytope

then you can do Fourier analysis on these

[frosty girder]

i see, so will i have to learn this myself separately or do Functional analysis books teach this at the start or w/e?

[hollow peak]

The symmetries of the polytopes are reflected in Fourier transforms of their indicators

[frosty girder]

sounds cool

[hollow peak]

you just pick this stuff up over time

some of it just advanced real analysis, others are basic functional analysis

[marble solar]

You can also do discrete fourier analysis on boolean functions

[frosty girder]

I see

[marble solar]

in relation to convexity and PDE stuff

Which is what my research advisor does

[hollow peak]

that relates to PDE

[marble solar]

yUh ~ we got published in a good journal on the topic

I'm just trying to broaden my knowledge of PDEs before I actually hit the ground running with him

[normal sandal]

good luck!

actually doing research is scary to imagine

[livid ermine]

What do you mean when you say it is a "reading book" and not a "textbook"?

[civic carbon]

it's chapters are arranged to be compelling and interesting individually, rather than designed to form a comprehensive introduction to the subject.

[livid ermine]

I am reading miklos bonas book, and am almost halfway thru, was thinking about reading the van lint book afterwards

Are the topics not general enough to be put in an introduction?

I see the two books cover some of the same material

Although the wilson van lint books looks a lot more sophisticated

[civic carbon]

I would only say I wouldn't wnat to use the Van Lint/ Wilson book as a first text. And I would skip chapters of it that are not of interest to you. It also helps to have some experience with abstract algebra.

[vale marsh]

Are there any books that cover recursion with trigonometric functions per chance?

[restive falcon]

where can i get a pugh pdf

or will i have to sail the high seas

[forest sleet]

if your university has springer access it should be available there

[restive falcon]

I'm not in university

...

[forest sleet]

used on amazon might be cheap

or there's a (probably very small) probability your public library might somehow have a copy

[restive falcon]

nvm

it's on scribd

[forest sleet]

if you ever want a hard copy it looks like it's $10-12 including shipping used on amazon/ebay

[restive falcon]

yeah

i mean this pdf is a bunch of bad page scans

on double page spreads

but i can't complain

[snow plover]

dees nuts story is my maths book

[foggy relic]

https://smartmanmaths.files.wordpress.com/2017/11/real-mathematical-analysis.pdf

(lmk if i need to delete this)

[grand thistle]

as someone whos never done linear algebra before except some basic matrix and vector stuff that came up in precalc and algebra based physics and whos had very minimal exposure to proofs, what linear algebra textbook would you guys recommend?

i have axler's linear algebra done right (3rd ed) and strang's linear algebra (5th ed) downloaded

[quick hornet]

do you want to be exposed to proofs, or would you rather a less proofsy treatment of the material?

[grand thistle]

im debating between those two

[grand thistle]

i guess i wouldn't mind the proofs

im reading through How to prove it first just so i can get a feel for what may come up

[quick hornet]

then both those are fine, honestly the lin alg book you choose isnt tooooooo important

if you go with axler, just use another source for determinant stuff

[grand thistle]

i heard strang is more matrix based and axler is like more algebraic

[quick hornet]

axler hates the determinant for understandable reasons but takes it pretty far

[grand thistle]

ah i see

[quick hornet]

kinda stunts its treatment

and yeah, that is true

axler tries to develop the linear-algebra-is-about-vector-spaces angle early

rather than about matrices and vectors

[grand thistle]

he introduces determinants in the last chapter

seems kinda late

im leaning towards strang right now

[quick hornet]

he avoids it since he thinks its very unmotivated and, in practice, acts more as a "trick" than a tool for actual understanding

this is... not false

but i still think he covers it too late

i mean, my honest recommendation is you try both books for a bit

see what gels with you better

[grand thistle]

i see

thanks

also when should i start

after i read how to prove it?

[quick hornet]

i honestly think you could skip most of how to prove it and be fine

skim anything you already know, work up till chapter 5 or so, decide if you need more from there

[grand thistle]

i was thinking just working up to chapter 3

then looking at chapter 6

since mathematical induction is supposedly very important

but thats about it

[quick hornet]

oh chapter 6 is induction? definitely learn that then

sorry its been a while

thought that was chapter 5

[grand thistle]

this is the contents

do i need relations and functions or am i fine

[quick hornet]

jeez i forgot how long that book takes to get through its material

uh you should have intuition for like, how functions work, but every lin alg book im aware of kinda handholds you through that

so you can probably get away just skimming that section

relations probably wouldnt come up

[grand thistle]

right

so just up to chapter 3

and chapter 6

skim through 4?

[quick hornet]

sure, honestly even that might be overkill

linear algebra is a very natural setting for learning proofs

so you might wanna study it concurrently

good source of examples

and intro proofs textbooks are very slow paced in general

[grand thistle]

well im kinda busy with school i dont think i have that much time

im also self studying calculus which was one of the main reasons why i was reading how to prove it

[slender dragon]

I would recommend Hoffman and Kunze or just read Axler book

[grand thistle]

since epsilon delta was kinda confusing when i first started out and i wanted a better intuition for derivations

[grand thistle]

hmm i see

ill check those out

[fossil arch]

Is there a proper probability (and statistics if possible) book that teaches measure theory too? Or at least as much is necessary to understand (so self contained I guess)

[fossil arch]

Oh never mind maybe? Lol. I'm taking my first course on probability and statistics this coming semester and from what I read on this server I thought probability uses measure theory a lot and that they're connected?? So I assumed like any undergrad math probability class would have that, but when I was scrolling through recommendations here I'm getting the impression that only graduate level books use it, so it wouldn't be appropriate for me

If anyone has anything to clarify or add I'd appreciate it
If undergrad probability is better taught without it then I guess my question would change to "what's the best 'mathy' probability book for an undergrad-level first course?"

[sage python]

@fossil arch so the thing about probability is that in general it uses measure theory

But you can study certain classes of spaces without the full power of measure theory

[fossil arch]

I guess it's the weird spaces where measure theory really comes in handy huh?

so it wouldn't add anything to not-weird spaces?

like is it unnecessary/overkill for a first class

[quick hornet]

overkill yes

or like

it depends what you mean by "first class"

if your "first class" is called "probability theory and measures", yeah thatll use measure theory

but "probability and statistics"? really overkill

[fossil arch]

okay nice the latter then

[quick hornet]

just accept that theres a sense of "we can measure area of really weird sets in R^n in a sensible way"

and thats all you need

[fossil arch]

so then what would be a good book to learn from

[fossil arch]

yes

I've seen a bit about it

[quick hornet]

this measurement agrees with your intuition in most cases so

shouldnt be a problem

[restive falcon]

thanks

[smoky zephyr]

blue

[restive falcon]

woah

blue

let's gooo

[gray gazelle]

Hey. Can I get recommendations to learn stats. I have not studied it more than high school level basics. Would be nice if it involves computation since I will be studying data science. Also I am not used to reading books so a book-lecture pair would be ideal. Or mooc.

[subtle siren]

https://www.probabilitycourse.com/

Alternatively
https://online.stat.psu.edu/stat414/
https://online.stat.psu.edu/stat415/

[subtle siren]

Although if you follow this, I'd recommend R instead of minitab

[gray gazelle]

Anyone in cs who benefited from concrete Mathematics by knuth?

[tulip blade]

Yes its a very popular book.

[gray gazelle]

Does it have any prerequisites?

[tulip blade]

Not really. Having calculus is helpful and being familiar with writing proofs.

[gray gazelle]

Alright, thanks

Hi. Is there some analysis textbook that also covers Dirac delta function, gamma function, fractional derivatives?

[subtle siren]

Fractional derivatives is very specific

[crimson cipher]

Hello, anyone have recommendations for graduate (module based) representation of finite groups texts beyond the standard (Serre/Fulton&Harris) ones? Two I've seen,
Weintraub’s Representation Theory of Finite Groups: Algebra and Arithmetic
&
Sengupta's Representing Finite Groups: A Semisimple Introduction
both seem nice but I haven't seen many reviews online so I was interested if anyone here had experience with either one of them

[gray gazelle]

Means?

[crimson cipher]

Fractional derivatives are normally a niche topic not covered in general textbooks, however a quick google finds me this which covers all the topics you listed https://www.wiley.com/en-us/Mathematical+Methods+in+Science+and+Engineering%2C+2nd+Edition-p-9781119425458

[gray gazelle]

Thanks

[subtle siren]

There are books on fractional derivatives but yeah, niche.

On this I'd also like to ask for resources on Z-transforms, or related transforms. If possible I'd like an applied-math perspective, but if you think I should learn complex analysis then you should recommend it

[fossil arch]

Yup ok I took a look at some others I saw here and Ross is definitely the one for me, thank u

[gray gazelle]

what would be a good book for intro to complex analysis?

Syllabus:

Curves and surfaces in space. Submanifolds. Local parameterization. Arc length. First fundamental form of the surface. Surface area.
Scalar and vector fields. Gradient, curl, divergence and Laplacian operator. Curve and surface integrals. Gauss theorem. Stokes theorem and Green's formula. Application.
Holomorphic and harmonic functions. Cauchy-Riemann equations. Integrals of complex functions. Green's formula. Cauchy formula. Development in a power series. Uniqueness theorem. Cauchy estimates. Liouville theorem. Fundamental theorem of algebra. Open mapping theorem. Maximum principle. Laurent series expansion. Classification of isolated singular points. Meromorphic functions. Order of zero or pole. Residue theorem and applications. Argument principle. Rouché theorem. Holomorphic functions as maps. Conformal maps, elementary examples. Schwarz lemma. Holomorphic automorphisms of the disk and the plane. Riemann mapping theorem. Laplace transform. Elementary properties. Inverse formula.

I'm looking for either main textbook or supplementary book, any recommendations are wanted

the books our university lists are:

T. M. Apostol: Calculus II : Multi-Variable Calculus and Linear Algebra with Applications, 2nd edition, John Wiley & Sons, New York, 1975.
J. E. Marsden, A. J. Tromba: Vector Calculus, 5th edition, Freeman, New York, 2004.
L. Ahlfors: Complex Analysis, 3rd edition, McGraw-Hill, New York, 1979.
J. B. Conway: Functions of One Complex Variable I, 2nd edition, Springer, New York-Berlin, 1995.

[shrewd dew]

Hi! I'm currently mainly interested in two areas. Number Theory and Algebraic Geometry.

In the case of number theory, I really like the topics covered in Cox's book Primes of the form X^2+nY^2. The thing is that I don't like the book so much. So I would love to study some of this topics from different sources. This topics include Class Field Theory and Complex Multiplication.

In the case of Algebraic Geometry I've already work through Fulton's Algebraic Curves and attended to another course based on Hartshorne's first three Chapters (although I have to go through those things 100 times until i understand them). I would love to relate algebraic geometry and number theory studying ¿arithmetic geometry?.

Any recommendations for these topics.

Aside for the algebraic geometers: What books do you like that serve as an alternative for Hartshorne? I'm currently working through Vakil's Rising Sea and I really like it.

[misty wyvern]

Check out Qing Liu's Algebraic Geometry

I probably shouldn't recommend anything since I know approximately 0 alg geo but it's often used an alt that's not Hartshorne or Vakil

[sage python]

Re AG: honestly if you're liking Vakil prob just go with it and don't get other recommendations. Feels like with AG there's no "grand slam" winner, like Rudin in analysis. So I feel like it's easy to hear someone who dislikes your preferred book and you start to doubt your choice even though it fit you well. That said, my impression of the big 3 is:

Hartshorne is the standard. His first chapter is a mess, it seems like a complete slog to work through, and apparently its pov is becoming dated now. Also if you like arithmetic it apparently doesn't do enough with non-Noetherian things.

Vakil is more modern, self-contained wrt commalg, and better written, but unfinished, and similar to Hartshorne, a lot of material is in exercises, which can be good or bad (more practice but also is much slower.

Liu is more self-contained wrt commalg and does things in a bit more generality for arithmetic types. Also probably the one that's easiest to work through semi-efficiently. But he only does Cech rather than sheaf cohomology. Which feels like a major omission (apparently Grothendieck said that sheaf is what's actually going on, Cech agreeing in nice cases is an accident).

[restive falcon]

is rudin good for complex analysis

or is there better

[lapis sundial]

Stein Shakarchi is pretty popular for complex analysis and has a good amount of detail

[south salmon]

^

Rudin is a little

[lapis sundial]

i liked lang too personally but idk what the consensus on it is

[marble solar]

Marshall's Complex Analysis book

[marble solar]

Marshall's is good

[gray gazelle]

guys

what math book should i get?

for the foundations

[smoky zephyr]

be more specific since #foundations is a thing and you definitely don’t want stuff related to that

[gray gazelle]

Foundations as in "Logical Foundations" or prerequisites for something like Calculus?

logical @gray gazelle \

sorry for the ping bro

dont kill me for it

It's okay :)

[gray gazelle]

If you are looking for introductory logic Paul Teller's 2 volumes called "A Modern Formal Logic Primer" is nice.

[smoky zephyr]

they were looking for the calculus stuff

[smoky zephyr]

that’s why i said this

they said that in #chill

[gray gazelle]

Lmao

[smoky zephyr]

not sure why they didn’t respond lol

[uneven plover]

Any book which has from basic calculus to advance?

[gray gazelle]

@uneven plover do you want it to be proof based?

[uneven plover]

Hmm fine

[gray gazelle]

@uneven plover also what does basic mean here

[uneven plover]

Umm from like starting?(not precalc) like yk limits then differentiation like that

[gray gazelle]

If this is your first time going into calculus I wouldn't recommend it to be proofs based

Do lectures interest you?

There an MIT OCW on calculus that is very good

[uneven plover]

No I want a book

Also not first time but I prefer from basic

[pure iris]

howard anton

calculus

[wise umbra]

Hello, concerning Liu it seems a really good book but one downsides seems to be that he does not mention much/any results concerning the functoriality of the constructions

Or the general functor of points

I would recommend a mix of Vakil/Liu/Stacks project for reference
Maybe you could also take a look at Algebraic Geometry II by Mumford (and someone else I forgot)

If you want to follow one and only one book I don't know what's best, different books covers different things
Nevertheless, Liu's seems focused on the arithmetic applications

[grand thistle]

i wanna switch from stewart

its kinda boring

any books recommended?

ill refer to it for formulas and some stuff ig, but i dont really like how it's written honestly

its like a bit dry

im looking at apostol rn

seems interesting, introduces integration first

also has some linear algebra in it

it opens up with some basic set theory and proof techniques

which is also good

[coral narwhal]

apostol has like 2 calculus books and 1 analysis book

[grand thistle]

im talking abt the calculus book

volume 1

[coral narwhal]

by 2 books I dont mean volume 1 and volume 2 btw

he has a calc book with the name (calculus with linear algebra) or something like that

but yeah that is a nice book

the one you are using

[grand thistle]

stewart?

[coral narwhal]

apostol

[grand thistle]

oh

i have the pdf

i think i might go through this part

just for fun

and to help me with understanding proofs and logic bettter

and to see if i like his writing style

[shrewd dew]

thank you for your answer

[shrewd dew]

thanks

[shrewd dew]

thank you

[gray gazelle]

https://ocw.mit.edu/courses/mathematics/18-014-calculus-with-theory-fall-2010/index.htm

This course follows Apostol. I thought it might be helpful.

[grand thistle]

ah right thank you

i didnt know that

18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

hmm

how much is elementary calculus

just basic differentiation and integration?

should i know like series expansions and things like that?

[smoky zephyr]

elementary calculus is probably just derivatives and integrals

[grand thistle]

weird how it defines integrals before limits and derivatives

but i guess it's good to see from a new perspective

[smoky zephyr]

[gray gazelle]

Advanced calc textbook that’s online?

[modern stone]

Spivak, Apostol

[gray gazelle]

Ok thanks

[modern stone]

In the case of calc textbooks I think you can find all of them online

[sage python]

The second author of AG2 is literally screaming rn

[sudden kindle]

AG2

Mumford's books are do good

MASSIVE + respect

[gray gazelle]

hey guys!

any calculus book recommendations?

[dapper root]

Realistically, whichever one you can get your hands on easiest. I’m sure others will chime in on the relative strengths of different texts but intro calculus books all cover virtually the same material

If you have a choice, I’d suggest just reading a bit of each and pick the one you liked the most

[dense pewter]

I think it also depends on what you want to get out of it

[marble solar]

I like Thomas' University Calculus for a first read

If you're up for a challenge Apostol's Calculus or Spivak's Calculus are fun

[foggy relic]

spivak is good

[foggy relic]

spivak

[icy knot]

There’s a lot of price gouging on Apostol and Spivak’s books otherwise I’d already have either one.

[marble solar]

Just go to local bookstores

See if you can find a used copy

I found Apostol Volume 1 & 2 for $2/each

Spivak's Calc on Manifolds copyright might expire in 2035

[wind coyote]

Good afternoon. Does anyone have in physics the book "Calculus" by M.Spivak? I bought it a long time ago and the first day I opened it I found a strange word, which has nothing to do with mathematics, and I would like to know if it also says that in its editions or if it only happened to me in the Spanish version. Thanks

[novel obsidian]

Has anyone read Aluffi's intro to algebra book called: "Algebra: Notes from Underground". If so, how does it compare to other intro to algebra books, like artin or allufi's "algebra: chapter 0"

[astral meadow]

Hello! Would anyone know a good reference that deals with Hausdorff dimension of fractals? Something very simple that just defines the thing and gives examples of computations, and explains the box-counting method. I'm looking for a gentle introduction for students of mine that know basic linear algebra and series, and I'd just like them to understand the definition in order to do the computations, either by hand for the Koch curve (for instance) or by a machine for a Julia set they'd have to plot. Thank you!

(ideally it should avoid talking about measure theory and that stuff)

[slender dragon]

It's the theory on Integration. The bad part of that is that to calculate integrals is very hard (Compared to the usual methods).

[grand thistle]

you can find pdfs online

[grand thistle]

ah i see

does it use like riemann sums

[wooden hawk]

does anyone know where i can find a lot of calculus problems online with detailed steps on how to solve promblems

[slender dragon]

Yes

[gray gazelle]

need help 1-2 hours weill pay

[fervent lava]

Maybe Paul online math notes.

[grand thistle]

find a pdf of stewart

stewart might be boring as hell but at least it has a lot of problems

it really emphasizes the calculations

[restive falcon]

try rudin he has a nice approachable style /s

[misty wyvern]

Rudin is actually good, ignore the naysayers here.

He's the only basic analysis book i still keep on my shelf because hes better to reference than anyone else

[restive falcon]

i know he is

but he's not the best for approachable analysis

[tribal kernel]

Not saying this is inexpensive, but you can purchase all of Spivak’s diff geometry and his calculus book directly from the publisher, Publish or Perish. It’s a strange process, but you have to email them and tell them what you’re interested in, and they will send you a PayPal link. It’s about $50-$60 per diff geometry text.

[foggy relic]

libgen?

or do u need physical copy

[quick hornet]

i have a copy, what part do you need?

(i dont know what you mean by "in physics" but i assume you mean "a physical copy of")

[brittle latch]

wh-

im jealous

my local bookstores are mostly kid oriented

what if kids are masochists

[cyan prism]

pdf google

[gray gazelle]

vs b-ok.as

[gray gazelle]

ok thanks bro

[paper stratus]

abbott is much better at the complete beginner level

[misty wyvern]

FWIW I started with Rudin and I'm no ultra genius.

I thought it was fine.

[paper stratus]

disclaimer: this is my view from skimming abbott and I've never opened rudin, I've just heard stories about it.

[misty wyvern]

And legitimately, at some piont in your math career you will look back at Rudin and think "all that shits trivial".

This is like debating which calculus book is the best

My answer is "the best reference" because pedagogy barely matters at this level

[slender dragon]

Why should be Rudin the best reference?

[misty wyvern]

I have no idea why, it's just the one I find most useful to reference.

More complete, sharper proofs, etc.

Guess I always approved of Real and Complex & Functional just covering a ton of stuff.

Though unlike Principles, RCA and Functional can still be quite challenging to a professional mathematician

If you're an analyst you'll take to them well but less analytical folk won't find them as easy as Principles

[wind coyote]

hello! it doesn't matter if it's physical or digital. One thing happens to me ... In an exercise there is a word that has nothing to do with mathematics. It is a word that I do not want to mention here because not it is suitable for everyone. (If you want, we can talk in private and I'll explain in detail) I would like to know if this word It is poorly translated from English to Spanish (I have it in Spanish) or if it is also written in English.

The version is the "third edition" is the red cover

[marble solar]

yUh, RCA is brutal lol

I have a first edition

Not recommended

[quick hornet]

whats the exercise? i'll check for you

[gray gazelle]

bro

calculus is the best maths topic lol

linear equations are so boring tbh

[quick hornet]

ah

the 2 fields of math

calculus and linear equations

[slender dragon]

Calculus to me is the most boring

You need to see more math. In the future you'll see probably 👍

[gray gazelle]

Hey

Yeah dead

Btw I'm new to this channel and can you recommend me some maths books for starters

Not the hard ones though

[smoky zephyr]

that is very vague

you’ll have to be more specific

[gray gazelle]

I'm sorry but like something for a student in 9th grade

[subtle siren]

Is 'how to prove it' a book for 9th graders interested in math

[gray gazelle]

Oh well thank you

I just searched the author of the book you are talking about is Daniel J. Velleman?

[smoky zephyr]

yes

the beginning is pretty boring be warned

[gray gazelle]

Okay thanks

[subtle siren]

I was asking but seems like no objection to my suggestion

[smoky zephyr]

oh

i don’t know either lol

@gray gazelle if you don’t understand don’t worry it might not be made for someone with your current knowledge

i haven’t actually read the book just the first few pages lol

[gray gazelle]

Oh okay lol I'm just gonna try reading it.

[crude sable]

another sam?

[tidal oar]

Hey how Is Graph Theory book by Reinhard Diestel...?

[karmic thorn]

Good

[tidal oar]

can you review for me two playlists a little ,of which one should i follow for graph theory please....?

[karmic thorn]

I'm not sure if I can judge them, maybe look for any that you find easier to follow and covers a broader variety of topics.

[tidal oar]

the thing is it is completely new for me , so want to get best i can , i don't even know on what bases should i judge it...

[tidal oar]

r u experienced in graph theory..?

[karmic thorn]

🤷‍♂️ I don't think it should matter much, most learning would come from solving problems from a textbook anyway

[karmic thorn]

Not at all, only familiar with the superficial terminology

[wind coyote]

It's page 214, exercise 56. The 4-6 fisrt words

[red sleet]

hiii can someone please recommend books to learn more about math, i'm a senior

i want to pursue maths for higher studies and i'm looking for something that could help build my basics well? i know high school math well, i guess

[wooden hawk]

go to Aleks use one of their higher ed programs, I'd start simple, and if that is to easy than up the annie until you kind find waters where you understand but are learning, end of the day, college is gonna push u towards calculus so sharping your algebra skills and trigonometry is gonna help.

i mess read the question, i skim a lot its a nasty habit

but it's advice id give to myself in ur spot

[red sleet]

thank you!

[hearty thistle]

Hey, recommended books for a high schooler wanting to do CLEP (College Level Examination) Calculus? Khan Academy can't be my only source.

[worldly oriole]

Thomas' Calculus could be a good starting point as it goes through the basics without skipping over too much rigour

[hearty thistle]

Does it have all the coursework involved in CLEP?

[worldly oriole]

Ah, I'm not sure about that. I'm not very familiar with CLEP

if in doubt you can skim over the contents page of the textbook

[hearty thistle]

Wait a minute, which book would you recommend cover all these topics? this is what the CLEP syllabus utilizes

[worldly oriole]

any calculus textbook should cover all of these, Thomas' certainly does

[tulip blade]

I am

[quick hornet]

this?

(the page numbers are different in different languages but this is close) \

nothing weird about that in english

probably a weird mistranslation

[peak dragon]

does someone knows about a book about quantum algorithms and quantum computation? smth like Skiena's algorithm design manual or Sipser's theory of computation books?

[wind coyote]

not really, the exercise is about L'Hopital

[quick hornet]

ah, i see what youre talking about

its 53 in this edition

and is indeed a bit vulgar in english, though not really considered rude

slight nsfw language

[smoky zephyr]

never expected to see that kind of language in a math book

[modern stone]

Very poetic

[gray gazelle]

spivak moment

[sudden kindle]

What are some standard number theory topics/ books for graduate students?

[sage python]

Hmm

How's your AG?

[sudden kindle]

I'm curious what is considered "standard" for graduate student in number theory

[sudden kindle]

Learning AG right now

[sage python]

Hmm so in general there's raw algebraic NT, class field theory, basic analytic number theory

Elliptic curves, more generally abelian varieties

Diophantine geometry (rational points on varieties)

Modular and Automorphic Forms, Langlands program, Galois reps

Arithmetic dynamics

Obv the basic analytic NT can go multiple directions as well. Distribution of primes, bounds for L functions (which links to elliptic curves, langlands, tbh everything)

Also Shimura varieties

There's some yoga I think between algebraic K-theory, Brauer stuff, Galois cohomology??

A lot of different areas and they vibe in interesting ways

[sudden kindle]

Yes, and CSAs and quaternion algebras, thats my impression

[sage python]

Arithmetic/Diophantine geometry I put in one word but obviously it's massive

As well as modular/automorphic forms. You could go into detail for instance about modularity-type stuff, bounds on Maass forms, higher rank stuff (eg Siegel modular forms), quantum chaos, reps of reductive groups, cohomology of Shimura varieties and arithmetic groups, subconvexity, foundational langlands

Number theory is v big lol

[misty wyvern]

Number theory was a mistake

[sage python]

Ur left pinky was a mistake

[gray gazelle]

What foreign books that got translated into English do yall like?

I'll start with gelfand's books

[sudden kindle]

I think I will read Neukirch

Algebraic Number Theory

[sage python]

Neukirch is quality

[gray gazelle]

And Im sure theres a number theoretic proof of this as well

[sudden kindle]

Neukirch seems to emphasize the geometric perspective in algebraic number theory

Which is something I'm really a fan of

[indigo relic]

Linear algebra books recommendation?

[foggy relic]

his language is so concise but also so funny

for like a formal book

[indigo relic]

I'm familiar with it just i want a reference to review it when i forget something

[indigo relic]

if you talking to me then yeah

[foggy relic]

oh sorry i said that in response to TTera

[dark veldt]

is geometry for enjoyment and challenge good

[foggy relic]

do you want a book for this?

also which type of geo

theres euclidian, differential, algebraic, etc

[dark veldt]

there is a book called geometry for enjoyment and challenge

[foggy relic]

oh sorry i thought that was a subject

looks like a euclidian geometry book to me right @dark veldt ?

if thats what youre trying to learn, idk anything abt this book but the AoPS Introduction to Geometry is amazing for that subject as it proves (almost) every theorem, explains most of the motivation, and has very hard problems

[dark veldt]

what is euclidean

[misty wyvern]

It means Euclid made it, you're welcome

[foggy relic]

the normal geometry they teach in high schools

[dark veldt]

yea

my high school uses it for this year

like with the proofs and stuff

[slender cargo]

Just wanted to give my thanks to this channel for the book recs. I've started learning pure math on my own after having been away from college for some time (what confusing times those were). It's been good fun. I'm working on the beginning of Artin's Algebra at the moment

[dapper root]

ALGEBRA

[slender cargo]

The farthest I got in pure math in college was a quarter on Rudin's blue book. I never took a class on modern/abstract algebra, so I'm excited to learn it

[modern stone]

The book is on Euclidean Geometry?

[solid idol]

Need a book recomendation for pre-calc. Stuck on it for a while.

Tag me.

[modern stone]

Necessarily book or it could be also a video series?

[solid idol]

both.'

I would liek to know both but if you only know video series/book then please do.

[modern stone]

well i’ve heard in terms of video resources Khan Academy and Prof Leonard are very good

[solid idol]

Aight thanks. Book resources?

[robust mortar]

These notes can be useful https://tutorial.math.lamar.edu

[solid idol]

Thankyou verymuch!

[iron granite]

I recommend Elementary Geometry From An Advanced Standpoint by Edwin E. Moise. Literally constructs geometry from algebraic notions.

[near spindle]

is this book good

[modern stone]

Yes

For getting an intuition for calculus

But it is not enough

[near spindle]

intuition?

eh

[gray gazelle]

Uhh

It's non standard calculus

Uses infinitesimals

[near spindle]

wdym by "standard calculus"

[gray gazelle]

AFAIK it uses infinitesimals instead of limits

[near spindle]

oh yeah i didn't see a single limit in it

[modern stone]

@near spindle don’t worry though. infinitesimals are very good for getting a “feel” for why theorems should be true even if they aren’t rigorous

[near spindle]

alright

do you have other book recommendations? @modern stone

[modern stone]

For calculus?

[near spindle]

yes

[modern stone]

I suppose you are a beginner

[near spindle]

yes

[modern stone]

I’ve heard Stewart is standard

[near spindle]

oh

what do you prefer

[modern stone]

well, what I know about calc is mostly from watching youtube videos and reading threads/articles online 👀

[near spindle]

oh

well i won't have internet after a while so

(no computers too)

[modern stone]

well, other good recommandation is Spivak’s Calculus

But it is more rigorous than Stewart so it could be hard for a beginner

[modern stone]

If you are an absolute beginner this might be good to give a taste for calculus

[near spindle]

well i need more than that

so stewart it is

[robust mortar]

yo :letsfuckingoooo:

[robust mortar]

just want to point out just in case: infinitesimals are rigorous afaik

[foggy relic]

ye

[tawdry orbit]

Has anybody here read "A course of pure mathematics" by G.H Hardy? I'm reading it right now, and I'm not sure what the prereq is. His explanation of why 2 is an irrational number wasnt clear. I read the explanation in Abbott's understanding analysis and Baby Rudin. I can't go much further in baby rudin because its hard, and i only used it because i wanted to reas about why 2 is an irrational number. I do like Hardy's writing, but his explanation on some things aren't very clear (keep in mind this is the first chapter, i havent gotten further). Is there any other book that serves as an intro to pure maths?

[dapper root]

2 isn’t irrational though…

Do you mean sqrt(2)?

[night knot]

it's √2 yeah

@tawdry orbit the text's saying if √2 were actually rational, it'd have some corresponding simple fraction m/n - squaring and shifting would show that m is an even number, and applying this substitution shows that n is also even, which contradicts with the idea that the fraction was simple to begin with

you could try Spivak or something else if you're interested - are you mainly looking into Analysis or Rigorous Calculus right now?

[forest hill]

is there any good book for reviewing multivariable calculus? maybe up to stokes theorem

[tawdry orbit]

Yeah. I made a mistake

[tawdry orbit]

In abbott, he started by saying that let (p/q)^2 be = 2. He also stated that p and q were odd numbers. After that, he explained that p^2 = 2q^2, and q^2 = 2p^2 because of that it means that p and q are both even numbers, which contradicts the original statement that they were both odd numbers. I understood his explanation, but from Hardy's explanation, i couldn't even tell when he had proved that the square root of 2 was irrational. Have you read his book, and is it worth pushing through? If i skip some chapters will i be missing somwthing needed from the previous chapter?

Also, my school library doesn't have Spivaks calculus.

[night knot]

I'd say go with Abbot and try Hardy later?

I have Hardy on my reading list but I can't really tackle it right now due to being busy with other books

so someone with more awareness of Hardy would be better suited for answering

[modern stone]

Yes I know non-standard analysis and the whole spiel

But I can guess that Thompson takes a more “hand-wavery” approach to infinitesmials

I could be wrong though

[modern stone]

Nice

[robust mortar]

Ah could be. After all seems like small book.

[tawdry orbit]

Ok, thanks. I think I'll go with Abbott.

[mellow bison]

I’m prob stupid but why odd numbers

[forest hill]

i believe usually you say p and q are relatively prime

[mellow bison]

Ok

Is it because it would be in simplified form then?

[foggy relic]

yeah, its a proof by contradiction

you start by saying that there is a rational number p/q squared that equals to 2, where p and q are relatively prime. then, you can show that p and q are both even which is a contradiction, which hence makes sqrt(2) irrational

[mellow bison]

How would you prove sqrt(3) is irrational?

Like u can’t do the same approach

Since it’s multiples by 3

[night knot]

You technically can

[lapis sundial]

You can do the same thing pretty much

[soft drift]

anyone recommend books on game theory

[foggy relic]

yeah u can, this time its just that p and q are both divisible by 3 hence a contradiction

i recommend looking up proofs of irrationality of pi,pi^2,and cos(1)

very cool shit

[crude sage]

I'm trying to choose between Tao's Analysis I and Spivak. My impression is that Tao is more rigorous but places less emphasis on exercises. Does anyone have any recommendations?

[marble solar]

No, Spivak is easier to read

Tao is more rigorous, but I don't think he's necessarily conveying the ideas any clearer

[gray gazelle]

I tried Spivak and got stuck on Tuple definition

[smoky zephyr]

a tuple is just a vector

an n tuple is an n dimensional vector

[gray gazelle]

Ok but the norm confused me more

Why is it under a radical?

[smoky zephyr]

it’s just the pythagorean theorem

[gray gazelle]

Oh

WHAT

you can generalize that? Dangggg

[gray gazelle]

anyone recommend me a probability and statistics book to get references ?

[wintry garden]

Can anyone recommend me a book on classical/modern geometry at a university level?

[gray gazelle]

if you mean synthetic geometry, maybe Hartshornes Euclid and beyond

[wintry garden]

I'll give this a try, thank you.

[gray gazelle]

no u

[dapper root]

I am still in shock Hartshorne has a Euclidean geometry book, seeing someone recommend Hartshrone for geometry and it not being an act of condemnation to the incessant hell of hartshorne exercises is startling

[frosty girder]

Lmfao

[full linden]

can anyone provide good webpages from professores with lecture notes?

[crude sage]

Interesting, thanks!

[restive falcon]

what's wrong with hartshorne exercises

[karmic thorn]

This very strongly depends on the topics you're interested in, do you have something more specific in mind?

[dapper root]

The fact they take hours and hours to do

You just have to try them yourself to truly understand, or just see enough people complaining about them

[marble solar]

Just read EGA

[restive falcon]

are they like
really interesting problems

[marble solar]

They're problems you normally wouldn't assign

In fact, Hartshorne's text is a simplified version of EGA

So you just read EGA, and there's that worked exercise, but you have to know some french

[restive falcon]

oh

so it's just like

really difficult

[dapper root]

Like 2/3 of the content is just in the exercises

Which are infamously hard

[restive falcon]

lmao

[full linden]

goal: Lie groups and algebras. Alg. geometry and Alg. Topology

[gray gazelle]

Is there a free online *textbook that covers linear algebra with lots of practice problems? I am in my senior year of high school and the coursebook provided by my teacher is not so clear

I have tried Khan Academy but I do not find the practice problems sufficient enough

[analog pollen]

you can get every textbook online for free

but you can check out schaum's outline of linear algebra

has alot of problems

solved ones too

[gray gazelle]

You can?? I am a really poor student with a poor libarary

Please tell me how

uhhh

Schaum's outline - I'll note it down!

[analog pollen]

libgen

and sometimes you can also just find the pdfs online

[gray gazelle]

Thank you kind soul, I will immedietly check it out now

[analog pollen]

np

[dapper root]

Pls don’t discuss piracy publically like this, discord TOS prohibits it and it my result in the server being shut down

[analog pollen]

oh sorry didnt know that

my bad

[marble solar]

I really like Stillwell's Naive Lie Theory, although it's at a very beginner level

[tawny copper]

what are good introductions to (elementary) combinatorics? Specially with nice exercises

I'm not too interested to learn a lot of combinatorics right now, I'm just interested in learning the basic tecniques of proofs you would encounter in (elementary) combinatorics

[gray crystal]

Try A walk through combinatorics - Miklos Bona

[tawny copper]

Thank you. Looks interesting

counting is super cool, but I don't even know how to count

[abstract walrus]

If I already have a fair amount of knowledge about Number Theory should I continue with Adler or Titu

[gray gazelle]

Olympiad purpose?

[gray gazelle]

Is internet archive considered piracy here.

[gray gazelle]

Now I don’t know whether internet archive is considered piracy here, but if not, then you can find an excellent collection of mathematics (and for that matter, of every subject) textbooks there (many of the respected textbooks)

@gray gazelle holy crap , another Devansh

[sage python]

web.archive? I have no idea how you'd find books on there tbh. Maybe if a prof had it up and took it down.

In any event what matters is that you follow discord TOS

[gray gazelle]

Hi I’m Devansh too

[gray gazelle]

I think you are referring to the way back machine. Internet archive is not way back machine

There is a particular experience of searching at archive. Means there is no smart searcher, so if you write a letter incorrectly in name, then you would miss it. Some books have only author’s name as title. So you have to search up many elements of the book if it does not work. The number of respectable books like Graduate Texts in Mathematics is large, but it takes time to be able to search. Till then, I would recommend searching on Google: [book name] archive.com

[gray gazelle]

Hi. Indians on server?

[gray gazelle]

Yes

I’m Indian too

[maiden slate]

many

[frosty girder]

too many

[abstract walrus]

Ahaha aren't there a lot in the Olympiad server as well

[abstract walrus]

Mhmm

[gray gazelle]

https://artofproblemsolving.com/articles/files/MildorfNT.pdf

Yes some NT should be enough for Olympiad style books, though it is hard to say nowadays what they use at IMO.

[gray crystal]

You can also check out Modern Olympiad Number Theory

P good at all levels, freely available
and written by a friend

[abstract walrus]

Yeah i tried Khurnis book

[abstract walrus]

So neither?

[gray gazelle]

I should say that you may read one book (there is also the one of Ivan Niven, which might be better) and then look at this handout, or other MOP handouts.

[harsh coyote]

any books reccs for beginner undergrad math

that we can self-study before uni?

[night knot]

Good recommendation for Algebraic Topology?

Also dumb question, do I need a full background on Topology or Algebra beforehand? I need alg top for some CS stuff

[tulip blade]

Is there anything in particular you are interested in? Also, are you familiar with writing rigorous mathematical proofs?

[harsh coyote]

calculus

[gray gazelle]

Spivak's calculus

[harsh coyote]

not anything except basic proofs in my pre-uni curriculum

[harsh coyote]

thank u

is pdf available online?

[gray gazelle]

No

@harsh coyote if you want lectures you can check mit OCW

[harsh coyote]

thank u

[abstract walrus]

zuckerman? that book had way too many questions

[gray gazelle]

Yeah. Hmm… I think you have to do at least 3000 problems before GM in IMO. I left trying IMO because I hated the syllabus and questions, so I was reluctant to open zuckerman. I would say, do it for theory, as well as the 2 star problems of zuckerman (some are from IMO)

[abstract walrus]

what's GM sorry?

[gray gazelle]

Gold Medal

[abstract walrus]

ah

also Andreescus/Adlers book is built more around Olympiad anyway so how is Zuckerman better

[gray gazelle]

Olympiad books are hard to understand. Besides, I cannot guarantee that they will give the better theory, and definitely they will exhaust their usefulness in future

Zuckerman is more standard oh built for students.

[abstract walrus]

hm fair point

thanks I'll just do the asterisk questions in zuckerman then

[gray gazelle]

Two asterisk

[gray gazelle]

And MOP handouts of Reid Barton, Yufei Zhou, Thomas Milford, Kedlaya, Naoki Sato (whoever you find) will give you killer tricks for harder problems. They sometimes use Higher techniques like Bezouts Theorem, but definitely not in the absolute detail of them. I believe doing this will give fair amount of comfort and confidence in even the hardest problems

[lime sapphire]

what is it about rudin that makes it so famous? is it just that good or is it just one of those old books people keep going back to for tradition's sake?

[restive falcon]

it is very good

has a lot of content

is very dense

and offers minimal intuitive explanations

[tulip blade]

A little of both. Its notoriously difficult so a lot of math majors look at it as a challenge to read it.

[jolly summit]

Sorry for bothering you but what did they recommend to you?

[quick hornet]

rudin also simply a very very good reference text

pedagogically it blows but the layout is very good if youre like 'i need to cite this super simple result on x subject', its very easy to find in rudin

and rudins proof is typically very succinct and clean

its almost like an intro analysis encyclopedia

[misty mason]

Yes on libgen

[polar smelt]

One message removed from a suspended account.

[gray gazelle]

Aluffi

[solemn rover]

is this like, systems of linear equations

[brittle breach]

I prefer lang

[gray gazelle]

thats too advanced for undergrad i think

[dapper root]

I think “extremely basic” combined with “algebra 2” meant they wanted a book like, for 10th grade math

[smoky zephyr]

carla is a troll

[subtle siren]

Any undergrad book

If you're in HS, it's good to look at undergrad

[gusty jasper]

Does anyone know any books that help visualise group theory? I'm not sure what level i'm at (Final year undergrad), but i've covered action groups, orbit stabiliser theorem and Sylows theorems.

[tulip blade]

Visual group theory by carter

[polar smelt]

One message removed from a suspended account.