book-recommendations

[dapper root]

This is just in contrast to like A&M where you like have to just learn all of that

[sudden kindle]

CA fan

[dapper root]

If you want to not have a bad time trying to do AG

Ya know?

[flint forge]

Okay but chmonkey the user clearly was interested in category theory so your response was just kind of weird lol

[heady ember]

[dapper root]

Max

[solemn rover]

Yeah i know what you mean. I think I just have the suspicion that people don't view category theory as a legitimate subject of mathematics the same way they view differential geometry, rather they view it as a language

once you learn the language you're good to go

[dapper root]

I guess that’s true

[quiet forge]

I definitely feel this way.

[solemn rover]

Sure, ok.

[flint forge]

you don't even know any category theory CV

[quiet forge]

I have tried reading The Rising Sea several times.

[dapper root]

That isn’t a category theory book lol

[quiet forge]

I usually crawl away in terror after a couple of pages.

[dapper root]

And even ignoring that, repeated attempts to learn a subject then to stop doesn’t invalidate it as a field of study, it just sounds like you’re scared of it lol

[quiet forge]

Of course.

I'm petrified of it.

Seriously.

I had terrible experiences in all my algebra-flavored courses (except an algebraic number theory seminar that, alas, had no homework) in graduate school.

My commutative algebra professor legitimately traumatized me.

[solemn rover]

to be fair, Ravi Vakil is a flesh eating demon who is hiding under your bed right now

[quiet forge]

Every time I get stuck or confused, I have a panic attack and can only think "I'm a useless menace".

[dense seal]

oh cool, free algebraist, I always wanted one.

[quiet forge]

And I no longer have patience to endure the frustration.

I'm too sore.

[dapper root]

What are you even trying to say?

[sudden kindle]

CV u should see a therapist maybe

[quiet forge]

I have algebra PTSD.

[dapper root]

You said that you think category theory is less of a subject to study than like diff geo

[solemn rover]

Well, learning to fight back against those negative thoughts sounds like an important skill

[dapper root]

And now you’re saying you’re afraid of algebra, I just don’t see the connection

[tight crag]

Omg clerk I like Troelstra so much

[quiet forge]

I said I agreed I felt CT was like a language.

[tight crag]

[quiet forge]

While it is certainly a subject, it feels more ambitious than that.

It strikes me as being more of an alternative formalism for math in general.

As opposed to set theory.

It isn't just a subject in its own right; it remakes other subjects in its own image.

(At least, from what I've seen.)

[tight crag]

Category theory seems to work really well for simplifying things

[dapper root]

Yeah so like

[solemn rover]

what are you looking at by troelstra

[dapper root]

This is annoying because to my knowledge you don’t know much category theory, so saying that is just kinda silly

[tight crag]

Constructivism in mathematics

[solemn rover]

oh nice

yeah ok.

[dapper root]

Like, even though I don’t love category theory with all my heart, there’s undeniably purely categorical things that are powerful and show that it’s way more than just a language with a few bells and whistles

[solemn rover]

when i said i couldn't get through one of his books i meant

[dapper root]

Like the adjoint functor theorem is one that comes to mind immediately

[quiet forge]

I don't deny that.

[quiet forge]

IMO, being a language is a more powerful / "better" thing than being a "subject".

A language is a subject that unlocks new subjects.

[dapper root]

Which is why it seems disingenuous to express an opinion without qualifying it at the very least that this is how you feel about it. Particularly when you’re telling someone “the thing you enjoy and study to me feels like less of a legitimate subject than something else”

[solemn rover]

"Basic Proof Theory" and "Metamathematical Investigation of Intuitionistic Arithmetic and Analysis"
Both of these start out ok but eventually just get obscenely technical

[quiet forge]

Totally.

[solemn rover]

Really good results in there but the proofs are technical!

[quiet forge]

I skimmed through the first part of that passage, and shouldn't have. I was focusing more on "category theory as a language" rather than "Category theory as illegitimate for study".

[trail kernel]

I had a dream that I was recommend a good book about tensors but then I woke up and realized that such book doesn't even exist

[blazing canopy]

usually tensors are covered in a general algebra book

[trail kernel]

what books for example? I didn't see them in my abstract algebra or linear algebra books

[tepid hare]

has anyone read Linear Algebra and it's Applications by David. C Lay????

[shell geyser]

I used it and I personally think it's a decent book. Has a decent amount of applications and covers everything you'd need to know for an introductory course. That being said I didn't enjoy chapters 8 to 10 all that much and they probably don't need to be covered in a first course. If you're more mathematically inclined though maybe you'd enjoy a more theoretical book like Friedberg's Linear Algebra.

[gray gazelle]

@stray veldt any good language theory book for second year CS?

Like a first time studying it

[stray veldt]

i honestly have no idea

[limpid bear]

you could try "Theory of Computation" by Sipser, it's a classic recommendation (also it's the only book in English on the topic I remember off the top of my head)

also the guy has a course on MIT opencourseware if that's a format you prefer

[gray gazelle]

Thanks

[gray gazelle]

hello

can you recommend good self study books for rigorous probability theory

more geared towards theory than applications

• stochastic processes

[tepid hare]

I am recently doing this book. And according to my exam syllabi ...i only need to cover chapter 1-5 ....I think it's a beigneers book which you can do by urself .... After this for advanced algebra i will pick friedberg

[tepid hare]

U did this for University algebra?

[shell geyser]

Nah I was self-studying while in high school. Did chapters 1 to 9.

[tepid hare]

Oohhh nice! Which country?

[tepid hare]

Y also did friedberg? Wat r ur reviews on that book?

[shell geyser]

Uh I'm from Singapore. I just like studying stuff for fun.

Ah no I haven't finished Friedberg. Just heard pretty good things about it. I read the first chapter and it seems good, but it's pretty hard. Definitely try something else first.

[tepid hare]

Studying stuff for fun is gr8!

[gray gazelle]

I'd say keep on with friedberg

it could be hard at first but it certainly is a good book

and it requires pretty much no prereq

Id recommend checking out some proof books tho

I’ve read friedberg, it’s awesome

[shell geyser]

I think it depends on what you want to do to be honest. Here I think Friedberg is used for a second course.

[tepid hare]

Can I do friedberg by myself? Without my professors help?

[gray gazelle]

Sure

[gray gazelle]

yes you can

I did

it has solution manuals

[gray gazelle]

Plenty online yeah

also it is pretty famous book so there are many resources

It’s like somewhat of a Spivak but for linear algebra

its much easier than spivak tho in my opinion

[tepid hare]

Goot to hear! For basics of linear algebra i am doing David linear algebra...and I rhink those basics concepts will help in friedberg

[gray gazelle]

Yeah of course

[tepid hare]

Yeah 👍

[gray gazelle]

theres another book that I'd recommend as reference

one by hubbard and hubbard

its not exactly linear algebra book but it is very very wellwritten

[tepid hare]

I will check this too ,🙂👍

[tepid hare]

😄

Thank you guys !!! @gray gazelle @gray gazelle @shell geyser

[shell geyser]

Ah I have heard of Hubbard & Hubbard. Should probably give that a read at some point.

[tepid hare]

For calculus i am doing Calculus by M J Strauss and Paul online maths notes

[shell geyser]

It's the one that covers multivariable, linear algebra and some differential forms right?

[tepid hare]

Btw have u heard of algebra by axler? Which is best in these 2 ?

[gray gazelle]

yes

it also covers multivariable analysis

[heady ember]

Differential forms

[gray gazelle]

Is this book good ?

[gray gazelle]

most indian textbooks are pretty goodf

like I haven't seent bad ones

[gray gazelle]

👍

[alpine moth]

i need a book to study for math logic problems

i need to do a high level test of math logic to enter a university what you reccomend

[mossy portal]

what prerequisites(if any) are needed for dynamical systems and time scale calculus in general? any books recommendations?

ive done single variable calculus and thats abt it

[subtle mango]

good textbooks for differential equations?

one i have in mind rn is Arnold

[tepid hare]

S.L ROSS?

[runic hatch]

Differential dynamical systems by Meiss is also decent imo

[hearty sluice]

geometric group theory/hyperbolic geometry books?

Looking for recommendations for a reading seminar I will run next semester

(target: grad students)

[gusty smelt]

not a book but for ggt msri's "notes on hyperbolic word problem" might be good for what you are looking for

[hearty sluice]

Note sets are good too!

[hearty sluice]

I can't find anything with that exact title, is it "notes on word hyperbolic groups"?

[gusty smelt]

oh yeah thats the one i think

[old elk]

OH NO!

I don't understand Apostol

[solemn rover]

Rough

What are you having trouble with

is it anything we can help with

[old elk]

I think I have a lot of empty space of knowledge but .....
I will start with Calculus II
I will be around here asking questions every day

[livid ermine]

van dalen logic and structure

[vital bane]

make sure you really understand the basics and the prerequisites before moving on the the next thing or else you might be struggling

[tepid hare]

Then I'm glad that i didn't chose this for my course. Instead I chose Calculus by M J Strauss with Paul online notes

[heady ember]

Choose Spivak

jk

[tepid hare]

Yeahhh and for that ig Paul Dawkins Online notes are best

[tepid hare]

Heard of this but never read. I think this book is quite tough

[heady ember]

Im doing it for fun

[tepid hare]

For fun is nice lol

[coarse frost]

[tepid hare]

@heady ember hey can u help me with my prblm? I asked it here like 3 hours ago and still no reply :(

[vital bane]

did yoh start preparing yet?

[coarse frost]

for?

jee?

kinda

[vital bane]

entrance exams lol

[coarse frost]

im chilling rn tho

[vital bane]

discord preparation

Lol

[coarse frost]

[vital bane]

Lmao

i read daminark as denmark lol

[sage python]

Are you prepping for the backflip you'll have to do in a couple minutes

Honestly I should be king of Denmark

[coarse frost]

thonk

[vital bane]

backflipping into to cmi

[coarse frost]

no im not preparing for that

[vital bane]

I agree

[coarse frost]

[vital bane]

not preparing for cmi?

why not?

[coarse frost]

u will become king of denmark when u teach me maths

[vital bane]

you wanna be a algebraic geometer?

[coarse frost]

i cant
i already gave the exam

lmao

[coarse frost]

kinda

[vital bane]

oh lmao

[coarse frost]

i wanna become an expert in every field

[sage python]

Ayy

[vital bane]

you'll need to live until 1000 years old for that 😔

[sage python]

Jack of all trades gang

[coarse frost]

[vital bane]

so if you really wanna do thaf

[coarse frost]

yessir

[vital bane]

i suggest doing research in reversing aging tech

and epigenetics

and then once you crack that

start math stuff

since you can live much longer

ez 😎

[sage python]

Or just be fast

:)

[remote ginkgo]

this is wrong

obviously there will be no way to stop aging

[vital bane]

lol being fast? kinda cringe

[remote ginkgo]

the correct solution is to transfer consciousness to a machine gradually

[sage python]

Shyshu tbh I'm kinda figuring out AG as I go

And lately haven't looked very much at it

[coarse frost]

[vital bane]

it might seem like that, but it's actually possible

[sage python]

That said it's a cool subject

[remote ginkgo]

no

you are wrong

[sage python]

And eventually I'm just gonna be like

Today I will learn it

And then learn it

[coarse frost]

and then teach me

[vital bane]

read the research papers bruh, we've done it in yeast

[heady ember]

"Eventually"

[remote ginkgo]

yes in yeast

[sage python]

What are you trying to learn now?

[coarse frost]

im still quite far from actually doing AG

im currently busy in uni entrance stuff

[remote ginkgo]

but u wont ever do it in people

[coarse frost]

i will be free by august latest

[vital bane]

and in mice we've slowed dowb aging considerably

[sage python]

LMAO

Look at this nerd

[remote ginkgo]

u might slow it a bit.

[vital bane]

ok

[coarse frost]

then i will start grinding analysis and algebra

[coarse frost]

who

[sage python]

You

[heady ember]

[sage python]

Imagine unironically having entrance exams

[coarse frost]

[vital bane]

yes you need to start grinding anal

real anal

complex anal

fun anal

[coarse frost]

i need to get into uni

[vital bane]

yea india is sad

[remote ginkgo]

honestly its good

im glad they have them

[sage python]

Simply be so based you get in without

[vital bane]

bruh

[remote ginkgo]

are they really hard though.

[vital bane]

no

[remote ginkgo]

ok thats bad then

[coarse frost]

yeah im not based enough

[remote ginkgo]

they should be really really hard

[vital bane]

they're not actual hard, they're just bullshit hard

[coarse frost]

they are hard

not for the right reasons tho

[remote ginkgo]

they should be brutal

[vital bane]

exactly

[remote ginkgo]

entrance exams should be like putnam

[sage python]

Lol, idk if I feel like performance on timed exams should be the primary basis for getting into school

[coarse frost]

trust me they are

[sage python]

Like

[remote ginkgo]

i dont trust u

[coarse frost]

having to do 75 questions, 25 from maths, phys chem in under 3 hours is horrible

[vital bane]

I wish they had undergraduate math and physics but they have bullshit highschool math

[coarse frost]

ik

its not a good metric

[remote ginkgo]

u should have to solve an open problem

[coarse frost]

but i cant change it rn

[remote ginkgo]

to get in

[coarse frost]

definitely not at this point in my life

[sage python]

I'm pretty up there in terms of being good on the spot etc

[vital bane]

why? you're going to school to learn things, you're not going to school to become a professional test taker

[sage python]

And still I feel like eventually it's not an important skill lol

[vital bane]

yup

[sage python]

I do think reading is a good skill though. And I recommend rereading

[remote ginkgo]

the most important skill is seeming unrelatable to the average person

[vital bane]

like if you go into industry or academia solving problems in a timed manner is absolutely useless because the problems you encounter will take days or weeks or even months

[coarse frost]

the kinda reading u do is closer to mugging up than learning

here for uni exams

[sage python]

No I'm joking that Neamesis over or under negated my sentence

[heady ember]

What's mugging

[remote ginkgo]

what im about 2 do 2 u

[vital bane]

what

[sage python]

It's when you mug someone

[remote ginkgo]

https://tenor.com/view/cat-pet-snail-gif-25646449

[vital bane]

just memorizing it

[heady ember]

Ah

[vital bane]

instead of actually understanding it

[sage python]

Also this is books rec

[vital bane]

Lol yeah

[coarse frost]

learning rote learning things

[coarse frost]

fuck

#discussion

[vital bane]

shit

[sage python]

Shyshu when you finish studying for g

Read Schroder Mathematical Analysis

[coarse frost]

schroder?

i was reading apostols analysis

[sage python]

That is now the official Daminark™️-endorsed real analysis book

[coarse frost]

hmmmmm

[vital bane]

publish research papers when you're 16

[coarse frost]

i mean, have u read apostol?

i liked it quite a bit

[vital bane]

apostol seems pretty good

i havent read it yet tho

[coarse frost]

and i also have its hardcopy, which i really like in a book

[vital bane]

lmao

[sage python]

Fair

Idk Apostol too well

Feels very old school

[coarse frost]

i have read 4 chapters properly, but i have to do more problems in them later

[coarse frost]

[sage python]

But pretty comprehensive

[coarse frost]

old school as in?

[vital bane]

the only analysis book i've read is abbott

[coarse frost]

i mean he covers a fuck ton of stuff

[vital bane]

and it was pretty good

[heady ember]

Why do you like Schroder

[sage python]

Like it's written for boomers

[vital bane]

but i've only read the first chapter though

[coarse frost]

u have completed analysis

[vital bane]

anyone over 20 is a boomer

[coarse frost]

i wont say that ig

[vital bane]

only the first chapter

[coarse frost]

oh lmao

[sage python]

So anyone who enjoys Apostol probably doesn't understand why a slice of bread falling and bass boosted words are the peak of humor

[vital bane]

also I can proudly say that now I know how to quantize the classical harmonic oscillator

[vital bane]

what if they did

[coarse frost]

No i definitely understand that

[sage python]

Wait you do semiclassical analysis?

[coarse frost]

smh

semiclassical analysis as in?

[sage python]

Sounds like a contradiction Shyshu

[coarse frost]

maybe ur assumed result is false

[sage python]

Maybe ur a dork

[coarse frost]

no u

[vital bane]

no me

[sage python]

Fuck

[coarse frost]

[vital bane]

No wii

oui

[sage python]

Anyway my case for Schroder for those who don't already have something they vibe with

Namely grass asked

[coarse frost]

i guess i can check our schroder later on

[vital bane]

schroder? isnt that like a thermodynamics book?

probably a different schroder

[sage python]

I feel like it's basically the best of Spivak and Rudin put together

[coarse frost]

is it good for a reference book?

[coarse frost]

hmmmmm

[heady ember]

[sage python]

It starts off quite gentle apparently

Like during proofs it has boxed off commentary

[heady ember]

Apparently

[vital bane]

one reason i like apostol is it's kinda comprehensive

and i love that in a book

[coarse frost]

that is based

[night prism]

I’m finding D&F to be quite shit too

[vital bane]

but-

[vital bane]

it's the bible

[night prism]

At least compared to expectations

[vital bane]

the bible

heresey

[coarse frost]

yeah its comprehensive and still very good at explaining it all imo

[night prism]

Yeah, just like Apostol

[coarse frost]

no its artin

artin is the bible

[night prism]

For you birds to keep chirping

[coarse frost]

smh

[vital bane]

d&f is the bible

[coarse frost]

that is very based

damn

[coarse frost]

no.

[sage python]

Yeah so I feel like it almost is easier to start than Spivak

[coarse frost]

commentary is always based

[heady ember]

[sage python]

These boxed comments get less frequent the further you go because it's assumed you're getting better at things

[coral narwhal]

check out jacobson :)

[coarse frost]

apostol would be perfect if it had commentary

[coarse frost]

thats fine really

[vital bane]

[coarse frost]

they are mostly needed early on

[sage python]

Yeah

[heady ember]

As a person doing Spivak, you have intrigued me

[sage python]

And then the second factor is

[coarse frost]

[sage python]

The contents subsume Spivak cup Rudin

[heady ember]

Time to find a pirated totally legal copy

[sage python]

And then some

[vital bane]

sloth are you a grad student?

[night prism]

His was better; I’ve settled on Rotman’s group theory course

[sage python]

Despite being shorter than either lol

[heady ember]

Wait what's subsume

[sage python]

Nah I'm first year at CMI

[remote ginkgo]

i FUCKING HATE d&f

[night prism]

Thank you

[remote ginkgo]

lang is the one and only

i can read it like a novel

[night prism]

Lang is very good too

[remote ginkgo]

and it goes way deeper and broader

[coarse frost]

hmmm

[vital bane]

cmi as in...? clay mathematical institute or chennai mathematical institute?

[remote ginkgo]

and i share a birthday with lang

[coarse frost]

apostol covers a fuck ton of shit

[night prism]

Rotman is sharp too

[sage python]

Chennai lol I wish I was at clay

[remote ginkgo]

rotman is very uhh

lame

[coarse frost]

jesus the kids at cmi

im not good enough

[remote ginkgo]

i have it on my desk rn

[vital bane]

Lol nice we have two students from cmi here!

[coarse frost]

[remote ginkgo]

lang beats the living dogshit out of it

[coarse frost]

sloth is a grad student

[remote ginkgo]

i dont thing anything touches lang as a first graddy daddy algebra text

[coarse frost]

i will do artin and then lang

i guess

[remote ginkgo]

u could consider aluffi first.

[karmic thorn]

@sage python what's your take on Amann-Escher

[coarse frost]

or might just do comm alg straight away

idk

[sage python]

Idk it too well

[remote ginkgo]

wait shyshu

[coarse frost]

idk about aluffi

[vital bane]

i say that you are good enough but if you really think you're not good enough then get better

[coarse frost]

[remote ginkgo]

are you grad student

[karmic thorn]

Three volumes but it's pretty extensive

[sage python]

Tbh I just saw Schroder and was like

[coarse frost]

im a hser

[night prism]

Lang is good, I’ll admit; more a matter of I started and don’t want to change anymore

[sage python]

Yeah this is it

[remote ginkgo]

yeah

[karmic thorn]

Nice

[remote ginkgo]

dont do comm alg first

[coarse frost]

Lmao

rude

[remote ginkgo]

you will not have any success

[coarse frost]

comm alg after artin

[vital bane]

yes he is

[coarse frost]

[coarse frost]

wtf i didnt even know myself

[vital bane]

Lol how?? i even started off with saying you are good enough lmao

[remote ginkgo]

i dont really like how artin writes, but i havent read his algebra text yet

[coarse frost]

[remote ginkgo]

but yes

[coarse frost]

i liked what i have read of it nicely

[sage python]

What what did you read of him?

[coarse frost]

and i think it will be enough to start with comm alg

[vital bane]

sloth where are you from?

[remote ginkgo]

galois theory, his gamma function book, and some other thing i cant place atm

[karmic thorn]

The preface

[coarse frost]

[remote ginkgo]

lol

[sage python]

Jabalpur

[vital bane]

jabalpur?

where is it?

i mean

which state

[karmic thorn]

Lmao

[remote ginkgo]

kentucky

[vital bane]

ah yes

jabalpur in kentucky of course

[night prism]

Lol

[coarse frost]

[sage python]

Yup

[coarse frost]

wha-

[sage python]

We got all the KFC here

[coarse frost]

how do know what jabal pur is dami

lmao

[remote ginkgo]

they live together

shyshu x dami romance

[vital bane]

in madhya pradesh? nice, how is it there? or rather how was it since you're in cmi now

[coarse frost]

(jabalpur is very close to where i live)

[sage python]

Oh shit

[night prism]

He can see you

[coarse frost]

lmfao

[remote ginkgo]

this is the book recommendations channel

[vital bane]

time for sloth to 1v1 shyshu

[remote ginkgo]

so in the interest of recommending books

[sage python]

Tru

[remote ginkgo]

i will recommend...

[vital bane]

death battle

[night prism]

Anyway

[coarse frost]

nooo

[remote ginkgo]

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

[sage python]

But yeah Lang's a decent follow-up to Artin

[coarse frost]

yeah

[remote ginkgo]

"decent"

i think u mean

[coarse frost]

dami what book would u recc for comm alg

[remote ginkgo]

mind warping light emitting genius beauty.

[night prism]

Perhaps there should be a “thinking about reading [this]?… read [that] instead” thread

[coarse frost]

thats not ataiyah

[remote ginkgo]

say atiyah

say atiyah

[coarse frost]

oh atiyah

sorry

[remote ginkgo]

say atiyahhhh

[heady ember]

How much does Schroder cover compared to Apostol

[coarse frost]

hmmm

lemme check actually

[heady ember]

After quite a bit of pain and persistence, I finally found a nice totally legal copy that is doesn't have the boxes messed up

[coarse frost]

holy fucking shit

thats a lot of things

thats amazing

[coarse frost]

of schroder?

send it to me please ty

[heady ember]

Should I try to do it

I know most basic stuff in Cal I and II, though I haven't done extensive practice for like IBP and series and im doing Spivak now

[heady ember]

Sure, I'll pm you then since its not allowed here

[serene reef]

Stick to what your doing. Switching is annoying.

Hmm 🤔 spivak com? Which spivak is this?

[heady ember]

Spivak's Calc

[coarse frost]

ty!

[serene reef]

I didn’t know spivak had a calculus book. Wow.

[heady ember]

You need to accept my friend req in order for me to pm you first kek

[coarse frost]

u can pm me directly tho

cant u?

i accepted it anyways coz why not

[heady ember]

Nope i tried

[sage python]

Okay measure theory books review time

[sage python]

So I should start this by saying that one awkward thing in calculus and analysis is that people have very different levels of background, and this makes books pitched weirdly. For instance, if you've done Spivak, Baby Rudin will contain a fair bit of repetition, but at the same time has too much additional stuff to just skip.

So one thing I'll keep in mind here is where a book is situated

[vital bane]

stein and shakarchi?

I've only heard about them though

[lime sapphire]

looks applied

[sage python]

Real Analysis (Measure Theory) Book Review

Royden and Fitzpatrick - Basic flow is Lebesgue measure on R -> topology/functional analysis -> general measure spaces. Not entirely a fan of doing Lebesgue measure alone and repeating yourself in general, but some vibe with it. You can read it after Spivak Calculus, and since it does all the content of Rudin 1-7 that's not in Spivak already I actually think something like this is a better followup.
Edition story is weird: first three editions are what everyone knows (standard for the subject along with Big Rudin), and only had Royden. Third apparently had bad editing. 4th adds a lot of functional analysis content with some light casualties, still disgusting errata. Apparently what's in print now is the 4th edition "Classic Version"; idk what that means.

Stein and Shakarchi - 4 volume series, first 3 are mostly independent. I think on paper all that's assumed is linear algebra + Spivak-level calculus, but unlike Royden there isn't a cohesive treatment of even Baby Rudin level topology (pretty much does what it needs as it goes, and isn't really enough). Volume 3 is the real analysis content. Also starts by doing Lebesgue measure on R^d before general measures, the merit of which is up to you. Holds off on L^p spaces/functional analysis until volume 4 (except for L^2/Hilbert spaces). Seems like the quality of writing and of the problems is quite good.

Schilling - Presents measure theory in general from the start, though it emphasizes the example of Lebesgue measure starting early. Mostly needs Spivak Calculus + "basic notions" of linear algebra and calc on R^n, though I wouldn't feel comfortable saying that . Has a probability vibe, and gets results like Radon-Nikodym, weak (1-1) and strong (p-p) bounds for Hardy-Littlewood maximal function, Lebesgue differentiation, and Calderon-Zygmund, using martingales. Which is wild.

Big Rudin (first 9 chapters) - Pretty much the book on the topic along with Royden until recently. Intended to follow up chapters 1-7 of Baby Rudin. It makes the objectively bad weird choice to only talk about Caratheodory wrapped up in Riesz rep. Does a bit more on L^p spaces and functional analysis than Stein-Shakarchi 3, but not much: it also has a followup on functional analysis (bit different angle than Stein). I haven't read it myself to say much about its level of conciseness, one of my profs said "If you miss a comma you miss a theorem"

Folland - Approximately the same background as Big Rudin. I feel it's a bit more... "systematic" than Rudin: does Caratheodory standalone, and does topology straight up. Talks a bit more about L^p spaces and functional analysis than Big Rudin, and also has some basic distribution theory (which grandpa Rudin tbf has more of) and probability, though not the complex analysis.

Bass - Designed for grad students who need to pass an analysis qual: all vanilla proofs, tons of problems pulled from quals at different schools, and affordable on a grad student budget. Topic coverage pretty similar to Folland, with slightly different organization.

I'd peg the last two as the correct choices for those who have the background

[vital bane]

spoken like a true 4th year grad student

[green herald]

whos read gamma mathematics bfore

[mossy portal]

😅

[mossy portal]

not sure if any linear algebra is required but would appreciate a book recommendation for my question above

[vital bane]

you might have better luck asking in the #dynamical-systems channel

[mossy portal]

thank u

[sage python]

Ah there was a part 2 but I dozed off

[heady ember]

[rain hound]

Looking for a good comprehensive book on graph theory. I would like it to also extensively cover “directed graphs”, because those pop up all over the place.

[hearty sluice]

undergraduate or graduate level

[rain hound]

Graduate level

[hearty sluice]

have you checked out "graph theory"

the yellow book

[sage python]

You prob wanna give the author lol

[hearty sluice]

Diestel or Bondy/Murty

[rain hound]

His graphs are undirected

[hearty sluice]

the entire book?

[rain hound]

Well I haven’t read the entire book but that’s how he defines graphs initially

[hearty sluice]

That's how a generic graph is defined

youre gonna have a hard time to find a graduate textbook on graph theory, for only digraphs

maybe some set of notes?

[rain hound]

Welp

Yeah I’d be happy with some course notes tbh

[hearty sluice]

@indigo kindle any ideas?

[sage python]

Maybe Diestel graph theory?

[hearty sluice]

That's the first one I recommended

[rain hound]

If worst comes to worst I’ll probably just learn graph theory as best I can from Diestel and try to abstract the results to directed graphs where I can

Thank you for the suggestions guys

[sharp latch]

Diestel graph theory is mega based

But if you’re looking for an undergrad text with applications to computer science you’d probably be better off with West

[coarse frost]

probably just edit this bit into the original message

coz its pinned

[sage python]

Honestly I might expand them both since there are more books and I'm worried about character limit but

[coarse frost]

hmmmm

u have nitro

u got a big limit

[sage python]

Oh shit

[coarse frost]

like 4000 characters is enough

[sage python]

I didn't realize your limit went up

[coarse frost]

lol

yeah

it does

it doubles

and if ur message is too long, discord tells u how long it is

[hallow bramble]

Hi guys! I'm new here and I'm loving the community for far.
Well, I'm looking for a reference about scientific research methods in mathematics. Any suggestions?

[sage python]

@glad prairie what do you think lol

[coarse frost]

so u can cut that much part out into the adjacent message

[sage python]

Schilling is the one where I found out about this martingale business

[glad prairie]

Damn nice

one sec

should you put a little title at the top of the post

since no one will see what you posted above in the pin

@sage python

[coarse frost]

that would be nice to put in each of the message that has book reccs

[sage python]

Done

[glad prairie]

I like it a lot dami

although

I am personally convinced that folland is far and above the best option

and i feel like having it second to last in the list and also not shilled super hard kind of undersells it

while royden is first and is imo meh

[sage python]

I guess I'm keeping with the theme of the others where it's less advanced to more advanced

[glad prairie]

but that's just my taste

i see

i didn't know that was the organization

[sage python]

It's not strictly that but it's sorta like

Okay Royden's kinda the undergrad book at this point

[karmic thorn]

No Tao

[sage python]

I originally posted just the first three as "the real analysis books that frontload Lebesgue measure and then repeat themselves"

And then I was gonna do the other 3 right after but fell asleep lol

Hmm idk Tao too well

Also omitted Wheeden-Zygmund actually

[sage python]

Bit weird at a glance lol

It's basically Stein but talks a lot about Jordan measure for some reason lol

[karmic thorn]

Yeah the preface does say it's based off of S&S volume 3

There's also a very extensive 5 volume treatment of measure theory that apparently dives into more advanced (set-theoretic?) side of things, I can't remember the author though

[sage python]

Oh I heard of that

Fremlin or smth

Idk it super well

Yeah I didn't include Tao, Wheeden-Zygmund, Fremlin, or Barry Simon for not knowing them well enough

[karmic thorn]

Yes!

Also Knapp's Basic Real Analysis

[sage python]

Oh tru

[vital bane]

a 5 volume collection of just measure theory?

goddamn

that must be for those people trying to rigorize the path integral or something lol

[karmic thorn]

Yes

[sick wigeon]

Does someone know of a rigorous ODEs book other than Arnold which is not a full fledged dynamical systems book?

[karmic thorn]

I think there's one by Simmons, another by Rota. I'll have to look up the book titles.

[vital bane]

do you mean the "Differential Equations with Applications and Historical Notes" by george simmons?

[slim peak]

Viorel Barbu's book

[sick wigeon]

I will look it up
Thanks!

[sick wigeon]

Simmons didn't feel like a rigorous text iirc
I will look up rota
Thanks!

[scarlet sierra]

What's a brilliant book for logarithms aimed at beginners?

[quick hornet]

beginners to what? to the concept of logarithms?

[uncut zealot]

Try "Introduction to Exponential Inverses" by J. D. Logarithm; it's a classic.
Or openstax and khan academy, which are both free.

[loud cradle]

there's also https://www.amazon.com/Logarithmic-Containing-Logarithms-Trigonometric-Examinations/dp/1362571210/ref=sr_1_3?keywords=Logarithm+Tables&qid=1655256994&sr=8-3 but watch out, there are a few typos

[scarlet sierra]

Thank you

[scarlet sierra]

Basically a book for dummies

From concept to advanced

[scarlet sierra]

Cheers pal

[gray gazelle]

Any thoughts on P-Adic numbers and Analysis by Koplitz?

[quiet forge]

It's not bad, though it's at an advanced level for someone who hasn't taken real analysis yet.

[solemn rover]

When you say "watch out, there are a few typos" do you own a copy of this book

It looks like you're recommending just a literal table of log values.

This won't help someone learn what logarithms are. It's just a list of numbers which would be useful to engineers who need to know what the values of logs are. And they can just use a calculator for that.

[gray gazelle]

What level of analysis is sufficient? Like after reading Tao? Or something more rigorous?

[quiet forge]

It's more about that nebulous concept known as "mathematical maturity".

The ability to fill in gaps for yourself.

Etc.

[gray gazelle]

I see

[quiet forge]

Also, which Koblitz book do you mean?
There are two.

[uncut zealot]

This one

[gray gazelle]

"p adic numbers, p adic analysis, and zeta functions"

why is one easier than the other?

My only reason for asking this is because I wasn't able to get my hands on Gouvea, but I was able to get my hands on Koplitz

So is there like a drastic difference between the two in terms of subject matter/difficulty?

[quiet forge]

One sec.

[quiet forge]

I have this one, it's a graduate text.

The "basic" material would be that from Chapter 1.

[gray gazelle]

Hmmm yeah the difficulty increases a lot after chapter 1.....

I'll try to see if I can get Gouvea somehow, but Koplitz was the only one I could find on the web

[old elk]

Pls

[crimson leaf]

#❓how-to-get-help

[blazing canopy]

I am looking an upper-level undergraduate probability book that has a decent number of computation-oriented exercises and "word problems". My usual reference is Grimmett and Stirzaker because they have a ton of exercises, but many of their exercises are more mathematical in nature (proving convergence of something, deriving some estimate, etc) rather than a concrete probability application. Any suggestions?

[grave thorn]

can vouch for this one

[grave thorn]

Maybe probability models by haigh

iirc it doesn't use measure theory

[loud cradle]

no, i was being a smartass 😁 - I don't think anyone would actually use a table of log values these days

a similarly antiquated book along those lines is "A Million Random Digits with 100,000 Normal Deviates", published appropriately enough by the Rand Corporation: https://www.rand.org/pubs/monograph_reports/MR1418.html

[solemn rover]

Ok, I can take a joke, I just was not totally sure whether it was a joke. Being a wiseass is acceptable

[sage kelp]

What are good precalculus and calculus books that are rigorous enough but that don’t contain zillions of mechanical exercises either?

[shell geyser]

Hm off the top of my head I can really only think of the AoPS books as not having many mechanical problems. Possibly Serge Lang's Basic Mathematics, but I think that's more a review of precalculus mathematics than an actual textbook.

[solemn rover]

In my opinion the harm of 'mechanical exercises' is often exaggerated. Conceptual understanding is a key skill we want to build but so is computational fluency, the ability to competently work with this stuff. You need both.

[tepid hare]

Has anyone read Introduction to Real Analysis by Bartle and Sherbet? Is it sufficient to do for graduate level courses?

[sage kelp]

Yeah, I believe there should be some kind of balance between conceptual understanding and mechanical exercises. I gather the most popular book is Stewart, but there are just tons of exercises

[shell geyser]

I mean you don't need to do all of them. Or even most of them.

I think you'd actually be dead if you did all 100+ exercises in each of the sections of Stewart.

[sage kelp]

What’s AoPS?

[shell geyser]

Art of Problem Solving. I believe their books are targetted at advanced high school students.

[sage kelp]

I saw someone suggesting Velleman’s Calculus book as being somewhere kind of in between Stewart and Spivak

And then Shifrin Multivariable Mathematics

[crimson leaf]

I usually just find a syllabus for my book then do the problems they recommend

[heady ember]

Spviak

[gray gazelle]

@wet furnace what book did you use for linear algebra, asking since I think your cool and smart

[wet furnace]

I think it was lay when I took the course and then I fooled around with shaum's linear algebra book I found randomly in someone's old bookshelf and took, looks like this: https://i.ebayimg.com/images/g/0RwAAOSwf5ddaTw7/s-l500.jpg

idk I think the thing is once you know some linear algebra everything starts to look like a vector space and you use it every day and get good

I thought that little work book was fun and had a lot of fun problems in it, but that was a long time ago idk what I would think of it now

[gray gazelle]

interesting, thanks for responding

[wet furnace]

you're welcome

[junior mantle]

does it matter if I get an older edition of a book? since its cheaper

so like 3rd edition instead of 4th

[stray veldt]

most of the time not really

new editions mostly fix typos, sometimes there is a new chapter or slight rearrangement

[primal mica]

Name checks

[gray gazelle]

older editions sometimes have more resources with it

like solution materials

so sometimes it could be a better choice

unless you hate old fashioned designes

[junior mantle]

i actually like the fancy look of older math books

[runic hatch]

It depends on the book I’d say

[solemn rover]

Bonus points if you can tell me what my name is a reference to

[gray gazelle]

I like universitext, gtm designs

[foggy relic]

What is the prerequisite for Fulton's algebraic curves?

[gray gazelle]

https://www.amazon.com/Problems-Mathematical-Analysis-Student-Library/dp/0821820508

has anyone used this book before

if so is it any good

[indigo kindle]

you should probably look for a book on network science if youre doing stuff like centrality measures and the like

maybe https://www.amazon.com/Complex-Networks-Principles-Methods-Applications/dp/1107103185 for instance

[gray gazelle]

I barely started AoPS book and im already enjoying it, are there any other good books like these of aops that someone could recommend?

mostly high school stuff
college algebra, precalc geometry and such; calculus books i would like recommended too after i get done with these

[tepid hare]

No it dosent! I m currently doing David c lay 3rd ed and it's 5th ed is available on Amazon. Not offline.

I usually buy older ed books not latest eds becoz i get it's solutions easily online

[tepid hare]

Anyone? Any reviews?

[wanton pier]

New here. What's a good math book for someone who never really got past algebra 1? I've been having an interest in programming(starting with python) and you need to master A1 to begin with...

To elaborate, I started with "Homework Helpers Algebra", but the book has quite a few typos and inconsistencies. Wondering if there's a better choice out there

[crimson leaf]

For algebra 1, algebra 2, geometry, trig, and pre-calc (even though it isn't a book) I would suggest khan academy

[junior mantle]

its A transition to advanced mathematics

the one by Zhang

[brisk ice]

I suppose for your own self study you might be able to look up the new edition and find an erratum and just go along with the old edition. However, if you are using for a class it might be annoying or impossible to do work if you don't have access to the questions and the profs just assigns pages and question numbers from the new edition.

[smoky surge]

Anyone have a recommendation that they like for abstract algebra with a focus on group theory does anyone have a rec?

[foggy relic]

you could just read from your physical older book and then find your required problems in a pdf version

[hearty sluice]

any of the standard algebra books should be fine

just ignore the parts that arent about groups if you prefer

[wanton pier]

Thanks

[smoky surge]

Awesome! I Thanks

[pearl path]

the fourier analysis guy recommended one book

[smoky surge]

who?

[pearl path]

"galois theory" by harold m edwards

also, I have a group theory folder in my computer

lemme send it to you in dms

[smoky surge]

awesome thanks

[rain hound]

Thank you. It’s for CS and mostly for complexity/algorithms stuff. But this is cool too.

[gaunt bobcat]

Well it isn’t actually a book recommendation, it’s rather a resource recommendation. I’m learning calculus from Paul Dawkins notes, but there are not much exercises (imho), do you have any good resource for exercises with solutions?

[tepid hare]

I m also doing paul's notes along with a standard reference Multivariable calculus by M J Strauss which have decent exercises. I found this great maybe this work for u too ;)

[subtle mango]

khan has exercises for most of the stuff on paul's online math notes

not sure about diff eqs, havent looked into it on khan

[crimson leaf]

Alternatively you can always find a stewart book and solution manual somewhere online that has tons of exercises the solution manual will work through the problems typically

[remote ginkgo]

no

try aluffi

[hearty sluice]

Maybe not a great idea if the user does not care for category theory

otherwise, it is a really great resource

[haughty anvil]

is the richard ruczyk book about algebra and geometry

good?

"The art of Problem Solving" Intro to Geometry

[indigo kindle]

maybe try sedgewick and wayne?

or introduction to algorithms, clrs is a well known one as well

I forget which one I used

sipser is also a good first theoretical cs book

[gray gazelle]

Also sipser has an MIT ocw course

[rain hound]

Thank you. I am reading all of those, but not for graph theory. They’re good books for the material they cover. I wish to get into geometric complexity theory, and the problems involved are just so difficult. I want to learn all the math I can that can possibly give me some edge to make the problems involved approachable or doable. And regrettably circuits are not undirected graphs lol.

[gray gazelle]

yo, can yall recommend any books/resources on set theory? thanks :D

[heady ember]

Enderton's Elements Of Set Theory

If you want it done axiomatically

[crimson leaf]

@uncut zealot Sorry for the ping but I was curious, what makes Pinter so good?

[rain hound]

Halmos’s naive set theory is pretty good for motivating everything and explaining clearly imo.

[gray gazelle]

hmmm thanks yall

[indigo kindle]

sounds tough. havent read it, but this may be worth checking out? https://link.springer.com/book/10.1007/978-1-84800-998-1

[rain hound]

Thank you! The table of contents sounds like exactly what I want. Here’s to hoping the authors didn’t write like Rudin.

[indigo kindle]

good luck!

[solemn rover]

This is naive in my opinion. Category theory doesn't magically solve away all of a first semester algebra class. You really cannot just say "no, try aluffi" without further explanation and expect to be taken seriously just because it introduces categories, morphisms and functors.

Can you give me a categorical proof of the classification theorem for finitely generated subgroups over a PID, or the Sylow theorems? what are the aspects of solvability in a group that cannot be cleanly understood without a 100 page preface on category theory?

There's not something substantial missing from Dummit and Foote that impedes the presentation. They still discuss universal properties of the tensor product

[coarse frost]

:artin:

[remote ginkgo]

i dont like dummit foote

especially not for a first touch on algebra

i havent really seen a great first book

[remote ginkgo]

i havent met many people irl that do frankly

i dont think the categories intro in aluffi is really the selling point

i'd like a nice easy intro book to rec people

but i havent read many

there is always pinter but i feel it stops short

[sage python]

If you go back in pinned messages I have a fair bit of commentary on algebra books lmao

[coarse frost]

dami should just start covering all the books in the topics he knows about in #books

[stray veldt]

[shell geyser]

So I wanted to pick up a differential equations to start slowly preparing for a university course. The reference text from what I've gathered is DiPrima & Boyce, which I don't think covers all the topics. Namely, I couldn't find:

Lipschitz condition, Picard's method of successive approximations, Existence and uniqueness of solution, Gronwall’s inequality, Continuous dependence on initial value.
Is there an ODE book that does these topics? In addition to the standard computational topics.

[runic hatch]

Differential Dynamical Systems by Meiss covers all of that, although it doesn't have much of the standard computation stuff (by computation I assume you mean finding explicit solutions for certain ODEs by say integrating factor or separating variables)

for reference everything you listed is in Chapter 3 of the book

[shell geyser]

Ooh neato. Thanks.

[halcyon hornet]

Any Good(And Rather short to study and online form preferred) Recommendations For elementary Number Theory?

[hollow shore]

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

[slate snow]

Hecke - Lectures on the theory of algebraic numbers

old but classical

[gray gazelle]

btw what is your opinion on serge lang's undergraudate analysis

tho I've already done analysis i'd still like to hear some opinions aoubt it

[uncut zealot]

It has an accessible writing style, there are plenty of exercises on interesting topics that dive deep into various things without generally being too hard.

I think he also does a decent job of motivating most definitions and theorems.

[slim peak]

Viorel Barbu's book.

[sage kelp]

Any Calculus books similar to Velleman's Calculus: A Rigorous First Course?

[alpine rover]

what's the best/most used abstract algebra textbook at the undergraduate level?

[crimson leaf]

Cool, thank you!

[gray jungle]

ive been enjoying artin

[tepid hare]

idk about most used but i like gallian.

[alpine rover]

thanks guys

[dense fern]

Heyo
Does anyone here know where can i find any good books for starting learning parameter problems? Even the easier ones.
There's just one year of school left for me and the final math exam has one parameter problem. Sadly, they just don't teach us that in school. 😔

[tardy walrus]

What do you mean by parameter problem? Like in Hebrew

[dense fern]

Hey, i'm from russia, not israel, just learning the language
I mean smth like that. (Find every value of a for the system to have solution/s)

Etc

[tardy walrus]

Ah okay, so khan academy probably has good resources on this.

In this case, notice you can subtract 2x from both sides on the bottom and you get:
x^2-2x + y^2 + a^2 = 2ay
So
y + y^2 + a^2 = 2ay
And then you’d use the quadratic formula to solve for when there’s a solution for y (and also using the quadratic formula, or finding a minimum for x^2-2x, solve for which ys the first equation has a solution for x)
It’s all about manipulating equations, so I’m not sure how much new material you’d have to learn, it’s more of mastering older material

[dense fern]

Thanks
Never heard of it before, just opened their website
What's the course to pick though, i just can't understand?

[dense fern]

Yeah, I've noticed the main idea of getting rid of x^2-2x but just got stuck then 💀

[tardy walrus]

I’m not entirely sure, I’d try searching for systems of equations

[placid pollen]

We used that book for our first courses in diff. equations. Sucks for theory, but the conditions for using the methods are clear. Like an engineering book I guess

[finite thorn]

Is Basic Number Theory by Andre Weil a good introduction book to the topic? If not can I be recommended some other options?

There are only a few books that are in English in my university library, so no guarantee I can find the book

[hallow oriole]

it's fine

there are literally like a hundred good number theory books lol

[sharp latch]

If duhon is looking for an intro to elrmenatry number theory then it is not fine

[hallow oriole]

oh

i didn't read the introduction word

oops

well

uhh ive heard good things abt apostol

although not sure on how friendly it is

[smoky zephyr]

tensor products
yes very introductory

[willow ridge]

That’s analytic nt

[willow ridge]

But they actually are

[finite thorn]

Yeah I guessed it'd be more elementary than this seeing as it has basic in the name, rookie mistake. Idk of any books that could be what I want tho

[warm glen]

im pretty sure basic number theory is a bit of a misnomer

it's not elementary number theory, it's class field theory

unless thats what ur looking for

[foggy relic]

see burton maybe

leveque ive heard is good

[shell geyser]

Yeah from what I've seen it looks like an engineering book. I'm not a pureblooded mathematician though so I don't mind engineering books. I think the caclulus and linear algebra books I used were also engineering books (Thomas and Lay respectively.)

[dapper root]

This book is very far from basic

It adopts a very highbrow approach to the subject, if you’re taking your first foray into the subject I don’t think it’s a good introduction

Oh whoops, countless people have already said this 😅

If you have an abstract algebra background, I think Neukirch is a very common recommendation for algebraic number theory

[delicate hemlock]

does Hovey cover enough stuff about model categories for me to have a rough idea of what's going on when i see them in papers? skimming the table of contents, I don't see much emphasis on the localization stuff (especially not as much as in hirschhorn but i'm not reading all of that) but i'm mostly looking to just get the main ideas to learn how it's used in practice

[heady ember]

Try Michael Taylor's books on PDEs
(jk actually don't)

[flint forge]

more than

By localization do you mean like

Bousfield localization and such?

[delicate hemlock]

yeah that kind of stuff

[flint forge]

honestly this material is not written down well basically anywhere to my knowledge lol

I always end up using lurie as a reference

[delicate hemlock]

[flint forge]

the 1-categorical situation is like

a lot of folklore afaict

Maybe Ravenels paper that is called like

"on the bousfield classes of blah blah"

[delicate hemlock]

idk, i think i remember reading a mathoverflow thread about how model categories are the "local" version of infinity categories

[flint forge]

is a good place to look

[delicate hemlock]

hmm ok i'll def check that out

[flint forge]

idrk how to parse this tbh

I got

literally every word in the title wrong

https://www.jstor.org/stable/2374308?seq=1

but thats the paper

[delicate hemlock]

yeah me neither lmao, i think the point was that it's good to get your hands dirty with model categories first before concerning yourself with other higher algebra

bet, thanks

[flint forge]

oh

was that peters post

[delicate hemlock]

yeah that sounds right

[flint forge]

i disagree with the sentiment tbh

but nothing wrong with using model categories

I just don't really think that one needs to be super well versed in e.g. hovey to read something like lurie

[delicate hemlock]

fwiw, i'm trying to learn model categories alongside homological algebra

i'm mostly interested in the big picture stuff of homotopy category vs derived category and someone else suggested looking at model categories so

[flint forge]

Yeah thats for sure the right direction

Also like

the model category stuff in particular elucidates a lot of the computations you do in homalg

like projective /injective resolutions are given a homotopical description

[delicate hemlock]

oh yeahh, i remember skimming something that showed you can compute ext with projective or injective resolutions as a kinda natural corollary of how model categories are defined

[calm saffron]

imagine learning math when u won’t win fields medal

[dapper root]

Wait isn’t this by definition tho?

Or maybe you mean the balanced part where you can compute it in either variable?

[delicate hemlock]

yeah, i meant the balancing thing

[dapper root]

I see, yeah

[delicate hemlock]

still haven't actually learned all the theory of derived functors but i'm so excited for it

[flint forge]

if you view ext as being a homotopically derived hom then its a lemma

arguably this is a more natural definition of ext than defining it by how you compute it, at least in my opinion

I guess you could also take Ext to be defined via sequences of actual extensions

in which case this is also a lemma

but not related to homotopy theory

[gray gazelle]

Has anyone here seen advanced calculus by buck?

[sage python]

Garbage

I've been victimized by it for a bit in my analysis class

And it's garbage

[sage kelp]

Any opinions on Marsden and Weinstein's Calculus 1-3 books?

[gray gazelle]

Oh okay

[gray gazelle]

How about hubbard hubbard

I think i asked sometime ago but i forgot so i ask again

Apologies for that

[gray gazelle]

I want alternatives to rudin chapter 9-10

Or spivak

I just need to learn enough material for smooth manifolds

So yeah I was wondering if the book is rigorous enough

Yep i meant that book

You mean hubbard?

How about studying appendices

Would that be enough

Oh okay

Maybe I should go for spivak then

[runic hatch]

Spivak is pretty short

[gray gazelle]

Ive heard that its pretty difficult tho

And has some errors

But its from amazon review so it might not be correct

[runic hatch]

I’ve heard about errors too yeah

An alternative is munkres analysis on manifolds

[gray gazelle]

Thats the reason why im trying to avoid it tbh

[runic hatch]

Covers essentially the same material but in more detail, and didn’t seem to have any major errors from my reading

[gray gazelle]

Also about exercises

[runic hatch]

Exercises in general felt a bit too easy tho

[gray gazelle]

Does the book heavily rely on exercise

[runic hatch]

For his AoM

CoM is pretty reliant on exercises

[gray gazelle]

Maybe I should go for munkre thrb

En

[runic hatch]

Yeah maybe

I think it’s decent enough

[gray gazelle]

Which chapters do you think i should study over vacation

[runic hatch]

What’s this in preparation for

[gray gazelle]

When i plan to take manifolds diff geo and real analysis

In future

By real analysis i mean one with measure

[runic hatch]

Hm probably just try to go for as much as you can imo

Main thing is to get multivar differentiation done

[gray gazelle]

I dont think doing the whole book would be realistic

Maybe up to fubinis theorem

[runic hatch]

Fair enough

[gray gazelle]

Also about duistermaat kolk

Ive heard many good things

[runic hatch]

Yeah that should suffice for most measure books

[gray gazelle]

But have been told that it is very very challenging

[runic hatch]

I haven’t read that one

[gray gazelle]

Oh okay

Thanks for answering

[runic hatch]

So I can’t give my op on that

Nw

[gray gazelle]

apart from aops, any other good books on combinatorics, trigonometry, algebra, number theory, geometry ect(high school / olympiad stuff).. that include hard problem sets and good explanations of concepts with the "why's" behind the explanations and not just how's?

[hollow shore]

Zeitz's The Art and Craft of Problem solving is nice

[gray gazelle]

thanks i will look into that one too

if anyone has books for this to suggest please do

[languid galleon]

Can anyone recommend books which cover content from 5th till 12th grade? Mainly books with exercises and eventually solutions? Basically everything pre university

[runic hatch]

It’s not a book, but Khan Academy should contain everything you’re asking for

[gray gazelle]

what are some relatively unknown books

that you find to be great

for me it would be freitag's complex anlaysis and j yeh's real analysis

[languid galleon]

Yeah but khan academy does not have many exercises afaik :/

[gray gazelle]

anyone else got something to recommend? making a reading list

[shell geyser]

If I'm not wrong Khan Academy has practically infinitely many exercises. The way the thing works is that even if you do the same topic again, it will generate different questions every time. So you can always repeat if you need more practice.

[languid galleon]

TIL, thanks!

[devout depot]

Yeah its true

[hollow raft]

Any algebra 1 textbooks? I realize that because of my self teaching technique I know a bunch of random parts of it but not enough to say i know it lol

[sage python]

I don't know any books unfortunately but the Khan Academy suggestion is overall a good one

[hallow oriole]

aops is decent

[halcyon hornet]

AoPs Introduction to Algebra.

[hollow raft]

Okii ty

[stark kestrel]

I am looking for book(s) suggestions on (1) vector fields and spaces, (2) mathematical optimization, and (3) the mathematics of waves. Would appreciate your help!

[orchid yoke]

Hello, I want to start learning about graph theory. Can someone suggest me a great book about it ?

[stray veldt]

have you looked at diestel?

[crimson leaf]

How do Diestel and Bondy & Murty compare?

[restive falcon]

are there any books on discrete calculus

[hearty sluice]

@indigo kindle

[indigo kindle]

afaik b&m is a less dense, more applied

diestel is heavier, lot more emph on the graph theory

diestel is also more modern

talks a lot about neat stuff like graph minors and infinite graphs and such

no like algorithms or complexity really, except in notes

so

depends on what you want to study ig

i do love me some diestel tho

[crimson leaf]

Guess I'll just have to read both then eventually

I'm interested in algorithms and their design but also learning more about extremal graphs and combinatorics, along with Ramsey theory, and knowing more about graphons

Also would you guys say Peter Cameron is a fine first intro to combinatorics or something lighter first

[indigo kindle]

diestel has sections on both, and a crap load of exercises

have not read cameron :/

generatingfunctionology is a great read though 😁

[crimson leaf]

I was interested in that one as well! Figured I should read some analysis and combinatorics first though lol

[hallow oriole]

can someone rate/give alt recs to the following book list: for someone who knows single-var calc
Calculus by Spivak
Multivariable Mathematics by Shifrin^
LADR^^
LADW^^
baby rudin*
Mathematical Analysis: A Concise Introduction by schroder*
Algebra by Artin(?)
Fraleigh(?)
dummit and foote(?)

meant to be read in roughly sequential order

rudin is there more as a reference and bc i wanna give it a shot

money isn't a concern

well

it is

but like some is chill ya?

[uncut zealot]

Those are all good books for learning single-variable calculus

[hallow oriole]

thank god

[hallow oriole]

o ya question marks are for ones im very unsure in

esp dummit and foote

[runic hatch]

I’d recommend Jacobson over Artin/D&F tbh if you already did linalg book before reading an algebra one

[hallow oriole]

oh yeah im not sure on the linalg books either

both ladw and ladr seem to have people who absolutely hate em

[crimson leaf]

I got recommended Fraleigh but I haven't read it yet considering Pinter instead

[runic hatch]

I liked H&K myself

[night prism]

If money truly isn’t a concern, I can recommend what’s been working for me: buy about 4-5 books you like that present a topic in slightly different tones and levels.. This especially helps big time if you’re on your own

[crimson leaf]

Yeah having multiple books is really good for when you get confused

[flint bay]

D&F is based to have as a reference bc like 70% of the book is examples

which u need for algebra

[rain fjord]

Find the books and download off of zlib for free

That’s better way

[hallow oriole]

i like physical books

[rain fjord]

You could print them

And get them bound

[hallow oriole]

print em where

get em bound where

[rain fjord]

Any ol print shop

They should do bounding as well

[hallow oriole]

well, it's a good idea

the issue is my parents being very strictly anti-piracy

[rain fjord]

Also most of time printing from online book is cheaper than buying books themselves

Can’t be that strict

Mine let me do this process for college precal book

Which cost 300 bucks

If braught hardcover

[heady ember]

$300