book-recommendations

[gray jungle]

i mean i dont know how you were doing it neam but thats not exactly true

you can absolutely study multiple topics at once, in fact thats basically the college experience.

as long as you realize that more topics will require more time of your day

i have rarely studied one topic at a time

[tender cobalt]

Ye thats why I decided to follow that pace of taking 3 courses at once for a semester (4 months of algebra, linear algebra, and topology)

[gray jungle]

but if its a side thing you do on top of college classes sure

dont add pressure

[vital bane]

self-studying is different from attending lectures and doing selected homework problems

lack of discipline mainly and doing like 4-5 books at once

[gray jungle]

not needed, you can mimic a course in your self studies.

[vital bane]

why?

[tender cobalt]

consistency is hard in self study

[vital bane]

I like to do all the exercises

[gray jungle]

like i just set goals on each book and try to achieve them, i certainly dont do "all" exercises.

[tender cobalt]

what books

[gray jungle]

like this week i wanna progress this section and that section from this book and that book.

as long as my schedule is free it works out.

[vital bane]

Abbott, Axler LADR, Taylor CM, Griffiths EM

and D&F a little bit

[tender cobalt]

The balance between math and physics is always so hard 😭

[vital bane]

now I am purely focusing on Abbott

[vital bane]

this is indeed what I do

[gray jungle]

like we kinda meme about it neam but if you werent so set on doing all abott exercises, you'd have been done with it a year ago

you dont need to master a topic while studying it

cause you'll go back to this stuff with time

[vital bane]

even if I were set on doing every single exercises I could've been done with it a year ago (I wasted so much time in various different ways)

[tender cobalt]

if i study 3 subjects at once

should i study all 3 of them each day?

like allocating say 1 hour for each

[tender cobalt]

relatable

[vital bane]

but I can only speak from personal experience, and from my experience it's a good idea first do one book, finish it, then you can think about doing 2 books at once

[gray jungle]

just keep in mind the average student taking real analysis would be doing it in 3 months, and each 2 weeks they have to be done with a section, so as long as you set similar (but more generous) expectations, you can do a lot of progress.

[tender cobalt]

i was supposed to be finished with shifrin now, after 3 months you told me to lock in and do shifrin LOL @vital bane

[gray jungle]

picking good exercises to do is important, cocat had a good message about it.

[gray jungle]

how you do that is up to you, personally i dont like doing multiple topics a day.

[vital bane]

if I were just doing Abbott and had discipline, I could've absolutely done Abbott in 3 months, like did you see the speed with which I was going through Axler

[tender cobalt]

how fast did you finish axler

[gray jungle]

well you need to find a balance too, burnout happens

[tender cobalt]

ah i see, so what if i target like finishing each chapter of 3 subjects in two weeks

[gray jungle]

i know you are prepping for a important exam now so for sure dont stress

[vital bane]

I didn't entirely finish Axler (I dislike chapters 8 and 9 and 10), but I finished like 2 chapters in one month? something like that

[gray jungle]

i mean depends on the chapter, i know books who's chapters are 2 months worth of content

[tender cobalt]

linear algebra is easy to absorb ngl

[remote sparrow]

keep in mind this is 3rd ed

[vital bane]

yea it's 3rd ed

4th ed has improved

[tender cobalt]

right

[gray jungle]

if you're unsure slender, find a course online and follow their calender

MIT OCW for example

thats what i used to do

[vital bane]

yea you can do that too

and instead of doing all the exercises in the book, you can also do a mix of their assignments and the interesting exercises in the book

[gray jungle]

topology for example

[tender cobalt]

yea thats what i am planning to do

[tender cobalt]

my problem is i barely do exercises

[vital bane]

but why I follow just the entire book is I simply have extreme greed for knowledge

[vital bane]

yea doing exercises is where 70% of the learning happens

[tender cobalt]

yea thats what i realised

I am planning to finish Roman's linear algebra first half in 4 months

[gray jungle]

if your ass is free after abott and the MS exam you should let me setup a measure theory group for you and grass + others @vital bane cause aintnoway you spending 2 years on that

[vital bane]

From Munkres:

[gray jungle]

you gonna be doing graduate math you need to be swift

[vital bane]

🫡 I'll let you know

[tender cobalt]

yes i had to do a lot of exercise from set theory chapter and after that i "understood" stuff

[gray jungle]

thats true

[vital bane]

btw James

[gray jungle]

i would go as far to say as 90%

[vital bane]

how long do you usually spend on an exercise before moving on?

1 hour? 2 hours? 2 days?

[gray jungle]

well im a very obsessed and stubborn person

[vital bane]

sometimes I've spent 5 days (though of course not literally 5 x 24 hours)

[gray jungle]

so i keep doing it till its done

i get really mad when i cant solve something

that i should be able to

and i have spent days on exercises before

i just usually do other stuff on top

[vital bane]

But wouldn't that detract from the time limit you've set yourself (for finishing a particular book)?

[tender cobalt]

Is it possible to finish Jacobson basic algebra I until galois theory chapter in 4 months? @gray jungle

[gray jungle]

well usually i do solve it eventually so i never had that problem

[vital bane]

you should stop worrying about time limits, and realize that you can learn math even after O-levels

[gray jungle]

and obviously i have seen solutions

none of us can always accept the defeat

and then i get mad anw cause i should have solved it

♻️

[vital bane]

yea it's so frustrating when you've spent 3 hours just coming up blank on how to proceed just to look at the solution and it was so obvious

[gray jungle]

good advice, just get started with it be consistent and you'll finish it

[vital bane]

consistency is extremely important, don't neglect consistency (like me )

[gray jungle]

it happens, uni pressure and mental health can stop someone

but eitherway this is not the place to discuss this

[vital bane]

#self-pedagogy when?

I think it should be a channel imo (But this isn't a place to discuss that either )

[dusk hemlock]

that's just every channel other than #math-pedagogy

[dusk hemlock]

#『meta-discussion』

[gray jungle]

didnt we discuss that?

[vital bane]

oh did we?

[gray jungle]

someone mentioned some problem about JEE and exams and i forgot about it

like people missusing it

maybe im forgetting

actually i think maybe it was about a channel for standarized exams, so maybe you're idea isnt bad neam

[dusk hemlock]

yeah

[gray jungle]

do bring it up, only issue i see is that these things can be asked in #advanced-lounge usually

[dusk hemlock]

specifically banning standardized exams there in fact

[heady ember]

Not really: ||just don't do Phy*ics||

[heady ember]

Me in the jungle trying doing math

[heady ember]

Same here

[grim ore]

@tender cobalt realistically, I have been only working through one text book this semester and ive only gotten to chap 5, skipped 4 tho

AoE by Silverman my beloved

Like, reading texts take time

Also if you are a student and doing jobs/work outside of that or have other responsibilities

Like Neamsis said, either do 1 text with passion, vigor, and enthusiasm, or do >2 texts with half assed attention and most likely will end up in burnout (from experience)

Same thing with classes btw, i cannot imagine doing more than 2-3 math classes in a single semester

Not that I dont like the content, but math is awfully (or blissfully) has a lot of content to absorb

[tender cobalt]

Youre right

[tender cobalt]

Right

[vital bane]

@remote sparrow buying up books be like: https://tenor.com/view/the-library-grows-the-library-הספרייה-גדלה-gif-3134347585434305444

[molten gulch]

I see, makes sense, thank you sourdrop

[gusty coyote]

some one have any advice in calc 2 books ??

if you have for calc 3, 4 and 5 I would b pleased

I mean the best for self learning !

[vital bane]

Lmao what's calc 4 and calc 5

[gusty coyote]

calc 4 is calc 1 and 2 in n dimentions

[gusty coyote]

calc 5 is EDOs with complex numbers

well , in my coutry we refer to those like this

[vital bane]

that's a weird naming scheme

[vital bane]

that's fair

[gusty coyote]

hehe , how u call it bro?

I thought it would be de lol

[vital bane]

usually in this server I've heard calculus in 2, 3 and n-dimensions refered to as calc 3

I have heard "calc 4" once, and it was probably used to refer to an ODE course, not sure

[gusty coyote]

I see

probably the right thing is to give 2,3 and n dimentions in calc 3

[tender cobalt]

real

[gusty coyote]

I think here bros divide it

[tender cobalt]

Me too

[tender cobalt]

Imagine calc N

[gusty coyote]

calc ngl

[tender cobalt]

@vital bane What do we get as N approaches infinite

[naive lava]

behold, calc 77: global analysis

[tender cobalt]

calc 69420: Horn's Lemma

[vital bane]

I will learn global analysis one day

[naive lava]

hopefully me too

[subtle violet]

macroglobal analysis

[gray gazelle]

microlocal analysis is impossible

[dapper root]

true

[grim ore]

Of course

[slate pilot]

Calc infinity: the theory of everything calculus

[warm fiber]

Can anyone recommend a book for starting out with combinatorics?

[dusky flare]

<< Introduction to Combinatorial Analysis by Riordan >> is quite good i had it recommended to me a few times

<< Combinatorics: A Guided Tour by Mazur>> is also decent

[remote sparrow]

https://www.amazon.com/Walk-Through-Combinatorics-Introduction-Enumeration/dp/9811277842

an older edition is just as good

[jade terrace]

Does anyone recommend books for starting proof-writing?

[rocky path]

i personally read Richard Hammack's Book of Proof for free online it was very good imo

not an expert tho

also anyone got advice for books on analytic number theory

[molten gulch]

hammack is good

[heady ember]

Yeah its comfortable

[timber mesa]

the usual recs are either Hammack's book or Velleman's How to Solve It

another one I skimmed one time is Transition to Advanced Mathematics by some other authors

that one is a bit too verbose for my taste

basically skim different books, see which one vibes with you most and follow that one

that goes for studying any subject

[iron pulsar]

yesss

ty. i notice they're sorted alphabetically rather than by date read

it's this this week then? curious

i like that you seem to have very modern taste

a library seems important for me to match pace 😅

i really like the Montessori method also

i wonder what i'm reading this week

it's about like working backwards from functioning adults rather than forward from kids, if that makes sense

[iron pulsar]

maybe this

counting femicide - catherine d'ignazio

that seems like an interesting read. i feel curious to read it, especially if i can find a pdf

anyway, counting femicides for me this week. @ me if you wanna yap books c:

[final swallow]

Can someone recommend an undergrad proof-based book on elementary classical/euclidean geometry (not two column proofs)

[royal frost]

Hello friends. Does anyone have a good book for AMC-10 only

[vague granite]

evan chen EGMO is standard, but it depends on how much background you have

[rocky path]

would euclids elements count lol

[earnest marsh]

hi guys, so one of my relatives helped me get this book called "Algebra and trigonometry with analytical geometry" by Earl W Swokowski. Is it good to study these topics?

And what other books should I get to deepen my knowledge in algebra, geometry, probability, basically all the things covered in precalc

And I got james stewart's calculus book too for later, is it a good book?

[molten gulch]

it should suffice fine

[tepid wind]

May I ask in hs competitions, may it happen that problems link combinatorics and geometry, or combinatorics and number theory?
If yes, can someone recommend a problems textbook, not for one branch, but one that links branches?

[normal trench]

gosh I hate that book

[marble solar]

It's a decent enough book

It's not horrible but it's not great

[normal trench]

it's really really not good for self study imo

AOPS calculus is just so much better

stewart is rife with rambling and an excessive amount of rote exercises

[keen orbit]

what are the prerequisites to study analytic number theory / algebraic number theory and what are some good book recommendations for these 2

[marble solar]

So it's not a good book for self study because there are better books? Or it's not a good book for self study because of rambling text (such as?) Or it's not a good book because there are many practice problems?

I think Stewart is a fine book. There are lots of resources available for it, and many classes use it. The advantage is that there are lots of varying levels of practice problems

[earnest marsh]

cool! and is there any books for precalc you recommend?

[marble solar]

I don't know any good pre-calc books

Mainly because I don't know any pre-calc books

[still panther]

calculus is a stupid subject and everyone should just do real analysis

[dim sierra]

That makes literally no sense

[abstract copper]

What chapters are necessary for DF algebra?

I mean the ring theory part

[loud cradle]

it's very good for (finite) group theory if you can deal with the old-school use of mappings on the right.. i would not recommend it for ring theory as he treats this using a weird intermediate notion of "x-groups"
i didn't read the field theory chapters so can't comment there
on a related note, his "finite group theory" book is really good

@tender cobalt ^

[still panther]

you get me

[naive lava]

not the hatcher

[timber mesa]

diffgeo and algtop don't sound like they lend themselves to that kind of pedantry lol

[molten gulch]

yes but they have ✨ categories ✨ /j

[graceful moon]

Unsure what you mean, Hatcher is the most complete and rigorous text I’ve ever had the misfortune pleasure to read

[molten gulch]

I cannot tell if you're being serious or not

[still panther]

also who "studies category theory to formalize set theory"

ETCS is ass sorry not sorry

[keen orbit]

Any recommendations ?

[normal trench]

to be fully honest, I only read a significant portion of the multivariable calc section, and remember it being way too rambly. Also, having too many practice problems is more detrimental than you may think, because it makes doing a chapter's exercises very intimidating and make it difficult to pick problems that will help you improve and understand the material better in a sea of exercises

[sudden kindle]

I'm the 25 yo prover now

[normal trench]

I just think AOPS does pre-undergrad math so well

I love the series a lot

[floral lantern]

Hatcher 😨

[heady ember]

John M Lee has such a book iirc

[naive lava]

Hartshorne

[grim ore]

??

[naive lava]

he has an ecludian geo book too

[grim ore]

the more you know

Geometry: Euclid and Beyond

[molten gulch]

I believe John Lee and Robin Hartshorne have both authored texts pertaining to Euclidean Geometry.

[naive lava]

that book is really great imo

historic notes are presented too

I wish my journey with him ended right there

[dim sierra]

What does that mean 😭

[naive lava]

Hartshorne has another book I'll prolly read

and it's one of the most brutal math book afaik

[fresh skiff]

Oh, i mistakenly thought of his AG book

💀

[naive lava]

that's what i'll have to read unfortunately

[fresh skiff]

What, you are studying AG?

[naive lava]

I will

[fresh skiff]

Damn

How lucky

[naive lava]

turns out

you need to learn math to become a math phy

[fresh skiff]

But using Hartshorne might be a bit dry way (I haven't even studied AA yet but this is what i come to know tho my folks)

[grim ore]

Id recommend the Shafarovich series

[naive lava]

my advisro said that's what i'll read

[fresh skiff]

His volume 1 and 2 right

[naive lava]

he sent me a list

[grim ore]

Basic Alg Geo 1-3 goes through each chapter of hartshorne

[naive lava]

and like

god damn

[dim sierra]

Oh I thought you were talking about LEe

[naive lava]

i think he hates me

[grim ore]

@fresh skiff Whats wrong with Shafarovich

[fresh skiff]

Good luck dogu

[dim sierra]

You know I heard that Hartshorne still shows up to the AG seminar in Berkeley, and he only signs copies of his book which are well used LOL

[grim ore]

Hartshorne is not terrible after having some background in the topic, I felt like I was able to read it decently through after my trials with shafarovich BAG

[fresh skiff]

Wait?
I haven't even studied abstract algebra, so i am no one to make issues with shafarovich

[gray gazelle]

anyone has like physics notes or smth one can refer to self study physics!

[naive lava]

not notes but i can reccomend books

[grim ore]

Oop my bad, i thought the emoji was saying BAG was scary

[gray gazelle]

oh sure

please

[grim ore]

imo its really approachable and at a ug/grad lvl

[fresh skiff]

AG enjoyer
(AG is one the area in math i love most even haven't studied it, but always wanna study)

[naive lava]

soo what do you wanna study

[fresh skiff]

Oh lol

[naive lava]

AG sounds really really cool tbh

[gray gazelle]

really like i think focus on prolly mechanics and just general basic stuff then move onto to the classical mechanics really may be i can just go straight to classical too i think

[fresh skiff]

I see. Maybe
D&F (group rings and fields) -> Shafarovich works

[keen orbit]

what are the prerequisites to study analytic number theory / algebraic number theory and what are some good book recommendations for these 2

[fresh skiff]

So true

[naive lava]

u can do directly to CM, Taylor is a popular choice

[keen orbit]

anybody has an idea about this ?

[naive lava]

it has both newtonian and lagrangian approach

[final swallow]

i'm not looking for algebraic geometry 😭

[gray gazelle]

i was trying to go through this university physics... its absolute dog water

[gray gazelle]

ohhhh

[grim ore]

definitely possible to go from Alg to shafarovich's works, but you may need to also pick up on some supplememental material

[naive lava]

he has a euclidean geo book too

[grim ore]

the comm alg in both hartshorne and shafarovich are rightfully assumed to be known

[final swallow]

oh

[grim ore]

meaning, you may come across a big theorem like Nullstellensatz and it just be used in a proof or stated without proof

which is in a general comm alg text

Id recommend Eisenbud

Thats my go to comm alg

[fresh skiff]

Ah yeah commutative alg.

[fresh skiff]

People also recommend MA (Micheal and athiya)
Sorry if i spell incorrectly

Iirc Eisenbud is like a gate from alg to AG

[grim ore]

Atiyah is common supplement, i just personally like Eisenbud a lot more, both arent bad though

Eisenbud does do a lot more things geometrically compared to the former

[grim ore]

So I can see this being held true, and is also explicitely stated in the text many references to AG

[cursive orbit]

🤓

[fresh skiff]

Got it. Thank you Zyphen

[gray gazelle]

hello guys

i just finished 10th grade and i want to get into mathematics

what are some books i could use to progress

[molten gulch]

Hammack book of proof

[gray gazelle]

okay

also are olympiads proof based math?

[floral lantern]

Yes, but the emphasis isn’t really on the proof writing and ideas as it is to problem solving.

[marble solar]

There are plenty of courses online that follow along, and no one is expected to do all of the exercises in a book. I think having a lot of problems is a plus, rather than a minus.

Stewart's calculus isn't really that verbose, it's very computationally oriented

[real marsh]

My stance on ag books is the one you learn from is the most god awful piece of writing to exist, and every other book is purely inspired prose

[rocky path]

What are the main prerequisites you really want to focus on for ag

[real marsh]

Comm Alg, Galois Theory
You also need to like know basic point set topology stuff
You should also learn basis category theory
Depending on how deep you want to go, learn some homological algebra

[normal trench]

maybe I'm just a fool for this, but when I open the exercises section and see almost a hundred rote exercises, it just makes me not want to start at all

I feel like almost nobody really needs that many exercises. I like books that select a small and useful set

[heady ember]

Isn't that like 700 pages of comm alg

[heady ember]

Oh you need Galois Theory for AG?

[remote sparrow]

you only need about half for a first course

if you want a modern atiyah & macdonald, there's altman & kleiman

free online

has all A&M problems and more with solutions to all of them in the back

[real marsh]

It comes up

[remote vortex]

<@&268886789983436800>

[vital bane]

didn't know Outsider hated AG

[remote vortex]

Definitely, it's too close to category theory for my liking

[heady ember]

You prefer dogetory theory?

[remote vortex]

||owltegory||, need you ask?

[dusk hemlock]

LOL

[vital bane]

Grass have you come across disjoint unions in your set theory books?

[heady ember]

The only set theory book I have read is Enderton, which, no, doesn't talk about disjoint unions.

But I know what they are.

[vital bane]

The first time I encountered this was when I was reading about tangent bundles I think?

I think one characterization is that they are a disjoint union of tangent spaces

[heady ember]

Why are you reading about tangent bundles when you haven't finished intro analy

[vital bane]

you don't get it grass

I was reading about tangent bundles before I started intro anal

[heady ember]

Going off on a tangent will only make it harder for you to finish A🤖

[vital bane]

and besides the physicist way to learn diff geo is without analysis

[heady ember]

Yeah sure; the uncivilised way of the barbarian.

[still panther]

even Devil can quote scripture, doesn't mean he understands it

[vital bane]

mfs when they find out about experimental verification of predictions:

[heady ember]

Experimental verification to understand math

[vital bane]

what?

[heady ember]

What

[vital bane]

okay it's not that complicated

it's just labelling your elements before you take the union

[remote vortex]

Yep, you just artificially modify your sets so that they're guaranteed not to have elements in common.

Although when I hear "disjoint union", my immediate thought would just be "union of sets which are pairwise disjoint", not a special operation.

[vital bane]

same

[still panther]

all sets are disjoint until proven otherwise

[molten gulch]

same

[lapis heart]

multiverse union

[grim ore]

Yes, and I love it

[grim ore]

lmfaoooooo

[real marsh]

A solid example is everyone who was in a schemes class I took hates Mumford's book now and thinks Hartshorne and Vakil are great books

[molten gulch]

LOL

[grim ore]

i meannn are they wrong tho, mumford's red book is kinda atrocious, but i also love their geometric proofs

even calling it a red book is wack at that

[real marsh]

it used to be red :(

[grim ore]

now its blue and yellow

[real marsh]

The red book is a very comprehensive text, I think my main issue with it was just being outdated and sometimes it was unmotivated

[grim ore]

honestly it just was a bore to read, or even skim at that

[real marsh]

yeah

but like for instance the main critique of vakil is that it's too exercise heavy, which once you know some ag isn't an issue anymore, and the main critique of hartshorne from what I can tell is it's too terse, which after reading mumford is no issue

[molten gulch]

I was JUST about to say this lmfao

[grim ore]

the main complaint i hear of vakil is the monologue and blocks of text

[real marsh]

huh interesting

tbf my main complaint of ag in general is an abundance of yapping

[remote sparrow]

i heard gortz/wedhorn is good

[grim ore]

^ that

idk maybe my trauma from hartshorne has affected my cognition, but i cannot stand texts that just yap even if its not AG

[remote sparrow]

yapgebraic geometry

[grim ore]

Like i lowk do like dense texts

[vital bane]

bro: I like dense texts
the density of bro's texts: Q in R

[grim ore]

lmaooo

[remote sparrow]

why aren't you reading matsumura then

[molten gulch]

why is everything a fucking exercise /lh

[grim ore]

i just got exposed to eisenbud first

[remote sparrow]

i have no stake in this either way

[grim ore]

tbf, not that its great, but most of the time (atleast good texts) would set you up far enough to being able to prove the theorems on your own

Worst case, just use a supplement

Like most of these texts that were stated have literal theorems -that other texts would state and prove in the chapter- as exercises

[real marsh]

An experience I had while writing my first report for a class was realising that whenever an author leaves something as an exercise that actually means they were too lazy to type up the proof. So Vakil is lowkey relatable

[molten gulch]

I assure y'all, my humour isn't USUALLY this bad

[molten gulch]

I agree

[grim ore]

Literally this, and I hate this with a burning passion, especially if they dont set you up for it cough Miles Reid

Monologues with no direction with exercises feeling like theyre completely unrelated to the text you just read and went through

[remote sparrow]

i heard reid's uag isn't great, but i've pretty much only heard positive things about uca

[grim ore]

And the frequent drop of "exercise left to the reader" without anything except just the statement

[remote vortex]

Well, not always, ||sometimes the author themselves can't prove it so they present it as an exercise||

[real marsh]

I have done this once

[molten gulch]

I just skimmed one section and I saw him say something along the lines of "everyone knows that....[nontrivial thing]" and leaves it at that

[grim ore]

Its not a terrible text, meaning the exposition is great, but hte proofs and exercises are hard af

[molten gulch]

I forgot the page though 😭

[grim ore]

LITERALLY AND I KNOW WHAT YOU WERE PROBS ON TOO

Like i thought it was a joke but his ass was not joking

[molten gulch]

lmaoooo which section

I saw that and instantly closed it lmao

[grim ore]

His lectures are recorded, but worst quality even for the time it was recorded

Like artin's lectures are older than his but even they have better quality

[grim ore]

Not as bad as having a qual question for a theorem a prof just proved in their paper released a month prior

[molten gulch]

I'M SORRY WHAT

I thought most qual questions were pulled from textbook, homeworks, exams, lecture examples, etc...

[grim ore]

A professor in our dept did that around 2-3 years ago and a lot of grad students dont like him

[molten gulch]

also maybe should we move this out of book recs

[crimson halo]

Anyone know of a book that would be good to give a quick treatment of ODEs for a pure math grad student who's mostly just interested in understanding enough for geometry and morse theory?

[shell gale]

Anywhere where i can learn to demonstrate any surface (2D)?

maybe 3D too

and all theorems and stuff

[prime hound]

Would anyone have good book recommendations for the Schwarz Christoffel transform along with Cauchy's Residue theorem? I'm trying to learn about these subjects to use conformal mapping to create custom airfoils (not joukowski).

[heavy vault]

Is there a standard textbook to study for Oxford mat exam

Do I just use aops or smth

[cursive orbit]

ahlfors should cover both topics

[prime hound]

Awesome, thank you

[uncut salmon]

Good and complete lecture notes on qualitative study of ODEs?

Even if it's only about first order ODEs

[heady ember]

Arnold ODEs?

That's a common rec for rigorous ODEs

[uncut salmon]

Thx

[dim sierra]

yeah that book is so fire I’m reading it rn as well

[cursive orbit]

🤓

[vital bane]

which chapter are you doing rn?

[dim sierra]

Chapter 1 😂

Like 35 pages in

[vernal tinsel]

Apostol analytic number theory, Marcus number fields

[dim pendant]

The prerequisites really depend on the level you're studying at. Some books on algebraic number theory only require a first course in algebra, perhaps not even up to Galois theory, and perhaps some number theory. Others expect you to know real and complex analysis, as well as topology. This is because a lot of books that call themselves "algebraic number theory" do a lot of class field theory, not your basic, really old stuff. For analytic number theory you should be able to get by with complex analysis and the first half or 2/3rds of a course in elementary number theory.

So a good basis for studying these areas will be (1) complex analysis, (2) a first course in abstract algebra, (3) some elementary number theory

[jade meadow]

I feel like learning galois theory is really useful for understanding number theory, the more I learn

[dim pendant]

I fully agree that for a mature study of alg NT, one should either know GT, or have a resource handy as required

I can't speak to ana NT, but I'm sure it shows up, even if only for the nerdy graduate kiddos

[fleet wyvern]

guys what book do you recommend on learning how to be stupid?

[still panther]

you can take a shot at writing your own i think

[fleet wyvern]

nah thats lame

oh ho ho ho

[wooden spoke]

What are some good introductory texts for differential geometry?

[naive lava]

do carmo is popular

[dim sierra]

I think you should check out Tapp

[tender cobalt]

Presley

Guys any good courses/lectures I can use along with Jacobson Basic Algebra I?

[cursive orbit]

🤓

[dim sierra]

damn this alphyte guy loves me so much

[cursive orbit]

John M. Lee Introduction to Smooth/Riemannian Manifolds

but low-key Loring Tu's book series is better

[naive lava]

could you call it an intro if it's 800 pages

[naive lava]

maybe artin's book for motivation

is's an ug book but it has nice stuff

[tender cobalt]

That's not Introductory diff geo text that's a manifold text no?

Same with tu

Introductory diff geo mostly means diff geo of curves and surfaces no?

[naive lava]

he also has a riemann geo book so ig that counts too

[tender cobalt]

3d diff geo stuff

[tender cobalt]

Ohh

[cursive orbit]

idk intro diff geo could mean introduction to modern dg or classical dg

[slender cargo]

I've heard that it's better to do a course on curves and surfaces first to build intuition for a course on smooth manifolds

[tender cobalt]

True

[naive lava]

mfw physics textbooks start with non-embedded manifolds

[tender cobalt]

Any good lecture videos for abstract algebra

[cursive orbit]

I think as long as you know like standard topology then you should be able to reasonably follow a manifolds book thl

[tender cobalt]

Yeah true

And some analysis

[gray jungle]

https://www.youtube.com/@richarde.borcherds7998

very good series on groups and rings

[cursive orbit]

damn he changed his name from BORCHERDS to Borcherds

[tender cobalt]

Thanks

[normal horizon]

What art of problem solving book should I start off with

[dim sierra]

What’s your background?

[remote sparrow]

i really like the pictures

mfw when there's pictures in diff geo

[dim sierra]

Lmfao

Yeah one of the only books that has color

[karmic onyx]

i should've asked him to sign mine

[dim sierra]

You haven’t even opened it bruh

[deep moat]

If you're new to mathematics, I suggest you start building your foundations with AoPs: Pre Alg and Introd. Algebra

You can do the road map that is already provided by AoPs

Pre Alg -> Algebra -> Geom -> Counting & Prob -> Number Theory

If you know about Alcumus, then its a good place to find a lot of problems and grind on them. It's similar to I XL's problem gen, but Alcumus is more about foundation + problem-solving ability. In addition, it already provides a well-detailed solution. Some cases, the solutions are not that detailed, so you can ask ChatGPT to explain it to you (the o3/o1 models should be good)

[normal horizon]

Idiot freshman

[dim sierra]

I think starting with algebra is fine, if you find it too easy you can always go up to something harder

What Shawn said above is also good advice

[normal horizon]

Ok thanks

[deep moat]

Highschool?

Yeah, you're gonna have a lot of fun when it comes to math in hs haha

[dim sierra]

oh if you’re in HS prealgebra might be helpful as well idk

[deep moat]

prealg ~= algebra

but in the pre alg section it introduces a lot of concepts

nt, stats, and geom

which is like a kickstarter

[dim sierra]

yeah u right

[normal horizon]

Yes im that young

Taking pre calc rn

[deep moat]

Welcome to Highschool!!
Highschool is pretty fun

[deep moat]

tf?

[normal horizon]

I took ig math 2 in 8th

Because they put me in the “advanced” classes

[deep moat]

oh, I see, then you have a good foundation in math already.

[crimson pasture]

guys I wanna pull the trigger on reading about algebraic geometry, what book should I read, vakil rising sea? or something else?

[deep moat]

If thats the case, you can use pre calc of AoPs(?) however AoPs is competition based book and not a course-course book

[normal horizon]

I don’t really know

What to pick

[deep moat]

Can you specify what you're looking for?

[normal horizon]

Do you know what math league/math counts is?

I suck at that

[crimson pasture]

so rising sea?

I also have a copy of hartshorne from my dad

[normal horizon]

I might just take the into to algebra and work my way up

[deep moat]

Oh, so you're getting in competition math. I see..

Below are some materials/resources that I can give to you.

Focus on the problem-solving part and have a good foundation

Introductory Books

• AoPs (Prealg, Algebra, Geom, Counting & Prob, Number Theory)
• 1001 Algebra Problems
• How to solve it by G. Polya

Resources for practice:

• Alcumus
• CEMC

I suggest you start of with Algebra (assuming that you have a strong background in the prealg phase), if its too advance, I suggest you start building your foundation with prealg. Afterwards, you can go and read the other books.

Read 1 book at a time, and make sure to not multi-task

You can spend around 2 hours or more depending on how badly you want to get better.

You can use ChatGPT or Deepseek to help you with each topic and problems to guide you, but please do use them for educational purposes only and do not cheat your way through.

[normal horizon]

Wow

[crimson pasture]

do khan academy I self taught myself completely with khan academy from a young teenager to calculus

[normal horizon]

Might do that so I don’t have to beg my mom to buy me a 55 dollar book

[deep moat]

I don't know anything about algebraic geom, but as reddit user said:

Most people nowadays learned from Hartshorne's book. I did this as well, with supplements from Vakil's FOAG for commutative stuff that Hartshorne doesn't cover thoroughly. Liu's book is good if you have a more arithmetic personality, and I've heard good things about the book by Bosch. (Namely, it may be friendlier than the aforementioned books.)

[deep moat]

||you can pirate aops books with libgen||

[crimson pasture]

haha sounds good but theres ways to get books for free legally, many books are availible free legally online

[deep moat]

most of the books that I have stored in my pc came from pirating HAHA

[normal horizon]

I used to do that with Wii games when I was a 7th grader lowkey BUT they were worth like a doller

[crimson pasture]

okay im not gonna be chicken and im gonna jump right into it thanks best of luck to you

[normal horizon]

I’m bouta be smart

[crimson pasture]

yes my friend stay studious

[deep moat]

Enjoy the process!

Math is fun

[normal horizon]

Thank you guys for the help

[deep moat]

make sure to understand each topic and don't do any rote memorization

[normal horizon]

❤️

[crimson pasture]

youre the coolest dino in my eyes

!

[normal horizon]

I picked my roblox User to be that in 4th grade

Lol

Alr bye ima get reading off cool websites that have free books

[heady ember]

Don't share pirated sites/resources here.

[deep moat]

Oops

mb

HAHA

[crimson pasture]

my bad

[deep moat]

sorry sorry

[crimson pasture]

RUN

[heady ember]

[deep moat]

🏃‍♂️ 💨

[normal horizon]

I aint do nothing so I’m good

Alr bye

[crimson pasture]

bye bye

[keen orbit]

alright tysm

[keen orbit]

ohhh i see, then i think that i will probably start with algebraic number theory after i have done these along with galois theory to get in with a stronger background and be able to delve deeper into the subject

tysm for your help and recommendations

[keen orbit]

do you know more resources so that i can have more options to choose from

(even if they require more prerequisites than these)

[rocky path]

what are good books and introductory abstract algebra, and what prerequisites would you recommend?

[cursive orbit]

do you know linear algebra?

[heady ember]

Look in pinned

[remote sparrow]

#book-recommendations message

[wispy bison]

You can also try reading that one chapter in dummit and foote which introduces algebraic geometry using polynomials over the complex plane first, but doesn’t introduce sheaves, to complement vakil’s approach, which jumps right into sheaves in the second chapter. Evan Chen’s Napkin also introduces alg geom

[crimson pasture]

im already familiar with sheaves, im a big boy

[crimson pasture]

have you read atiyah macdonald commutative algebra

people say the exercises are excellent im thinking of using it in tandem with vakils rising sea

[wispy bison]

No

I have a copy of eisenbud which I read the first chapter of and not much else

and I also just started learning about alg geom, just wanted to mention some other resources

[remote sparrow]

altman and kleiman is basically A&M but updated

also has solutions to all A&M problems

[vital bane]

oh hell yeah

[remote sparrow]

https://www.youtube.com/watch?v=iImXmmcoPho

[pine lark]

Hello everyone! I am in class 9...... I wanna learn mathematics from basic (as my grade) to advance level (I wanna participate in math olympiad). Please recommend me some great books that can stay with me in my journey of mathematics. I love Mathematics. When recommending the books, please at the last of book name, include the outcome I will have after mastering the book. Please, help me in my journey of mathematics.

[pine lark]

I need books for ALGEBRA, GEOMETRY, PRE-CALCULUS, CALCULUS......

[deep moat]

@pine lark

Some of these resources can be found online :D
For obeying the rules in this server, I would recommend you to do your own research on how to get these books!

In fact, everything you need for comp. math is in the AoPs curriculum. However, if you're looking for something more fast-paced (removing the necessary details and the important ones), go I recommend AMC 8/10 Books by OMEGALEARN!

[pine lark]

Thanks a lot! Sir.

[deep moat]

In addition to help, you can ask in #competition-math!

[leaden panther]

Guys is Gamma function defined for negative integers

[inner needle]

The usual definition isn’t, but you can extend it to negative numbers as long as they’re not integers

[vital bane]

Sour Drop looking at this bookshelf:

https://tenor.com/view/the-simpsons-pathetic-principal-skinner-gif-13486077408184960752

[crimson pasture]

no it has poles there

[grim ore]

My “bookshelf” is just more so a stack of textbooks i’ve collected over the past 3 years

It stays in my closet

I wish for the day i have a bookshelf in my office space

[fleet wyvern]

princibal skinnyer

[tender cobalt]

Marsden Tromba Vector Calculus

[pale scarab]

I only have a few physical books. PDFs on the other hand are out of control..

[grim ore]

I use icloud, and just delete the folders if not in use

I did this method on all my systems previous and current even when on windows and linux

[cursive orbit]

proving something is "well-defined" usually means proving it exists and is unique

in this case though, it is a bit vague as you are averaging over the natural numbers, which is not in general well-defined, so you have to pick a sensible definition yourself here too

[cursive orbit]

I think discrete math is a good starting point for trying to build up mathematical maturity

[full marsh]

What happened to chill and math discussion channel?

[wraith cave]

you have the studying role remove it in #info

[full marsh]

Ohh thank you

[trail maple]

are people still reading the original texts of philosophiae naturalis principia mathematica or euclid's elements?

[vital bane]

probably a very small number of people

because

1. they're very old
2. most people don't read Latin or Greek

[vital bane]

@remote sparrow I have a devious idea

Step 1: buy a springer book, read it in 90 days
step 2: return it
step 3: return to step 1

[round axle]

bruh math isnt even intimidating its just overwhelming to start

like what book do i read first

https://tenor.com/view/adventure-time-jake-the-dog-existential-existential-crisis-gif-22706230

where do i begin

no gifs is insane

absolute madness

[vital bane]

we shall begin at the beginning

numbers and shapes

[round axle]

yeah

sounds wise enough

[vital bane]

Are you a high school student?

[round axle]

do i think in sounds and shapes or numbers and shapes

because if the sounds of numbers hold the meaning of numbers

[vital bane]

what math do you already know?

[round axle]

that would mean

oh thats a hard question like doing math i suck at conceptualizing math im good at cuz i like physics

so i learn concepts as i go

[vital bane]

I like physics too

[median saffron]

neam in book reccomendations first timw

[round axle]

oh and

i do some electrical and robotics engineering very basic hobby stuff tho

[vital bane]

water beam here likes physics too

[vital bane]

very cool

[round axle]

so i have to know like

electricity related math

so like

basic calc i can conceptualize and whatnot algebra

[vital bane]

nah you're just unfamiliar with it for now, you will learn how to conceptualize math

[round axle]

integrals are the area under the curve

derivative etc

[round axle]

yeah i gotta actually discipline now tho

[median saffron]

[round axle]

ive hit a point where i cant just bs my way thru physics and engineering

[vital bane]

so you know calculus?

[round axle]

like

conceptually

i cant rly solve an equation or whatever

i know

like 2 things maybe

ask like basic things

definitions/vocab is what im talking about

[vital bane]

okay then I suggest you start off with this https://www.khanacademy.org/math/precalculus

[round axle]

literally thats it

[vital bane]

🫡

[round axle]

oh i did like a little of that

limit

s

and basic stuff

[vital bane]

do all of it

[round axle]

but thats not

what im looking to know

nah

thats me procrastinating ^

my mind weaponizing itself against me because it doesnt wanna go thru the discomfort of learning something new

i know this feeling all too well

[vital bane]

yea it's hard to learn something new because that's pushing yourself out of your comfort zone

but if you can persist, no one can stop you

[round axle]

from a physical lens ur literally forming new neural connections which means u have to stray from ur fundamental level of energy

[vital bane]

you see, learning math is like a ladder, without the lower rungs, you can't really climb up to the higher rungs, so if you want to learn all the electricity math (like vector calculus so you can learn electrodynamics and stufff) then you have to learn precalculus, then calculus and linear algebra, then vector calculus and ODEs

[median saffron]

being good at maths ≠ being good at physics unfortunately

[round axle]

right

[vital bane]

but it helps a lot

[round axle]

im good at physics

but

ive hit a stalemate

because i cant read the equations

or any of the math anymore

meaning i cant start to conceptualize it at all

im literally blind

it hurts

[vital bane]

then

we'll start right here

from square one...no

from zero 🔥

[round axle]

zero doesnt exist

[vital bane]

sotrue

[round axle]

only infinitely approaching 0

come on

were mathematicians

lols

[vital bane]

I would suggest finishing this 100%, and then doing khan academy's calculus course along with James Stewart's Calculus book

[round axle]

alright do u mind if i use our dms as like a mentorship thing cuz i need math friends

most my friends are from like

spiritual/esoteric circles so they barely know physics let alone math how i need for my growth

[heady ember]

"Just read Rudin bro. He gives you a rigorous treatment of the reals."

[round axle]

some are very smart tho

[vital bane]

RCA

[heady ember]

Oh no a crank

[round axle]

lols

im right tho

[vital bane]

you can use this server we are all friends

[round axle]

not asking u to believe me

tru

just gotta

take it out of my junk folder

put it above the rp servers

lmfao

[median saffron]

sour drop presence

@remote sparrow what books would u recommend for multi var calc im looking to get into it soon

[remote sparrow]

hubbard or shifrin

[vital bane]

what kind of multivar calc book though?

for physicists or for mathematicians?

that matters

also don't forget to use da GOAT along side your book of choice http://www.damtp.cam.ac.uk/user/tong/vc.html

[median saffron]

are these ur standard calc3 books normal difficulty

[remote sparrow]

no

[median saffron]

is it rigourous

[remote sparrow]

yes

[vital bane]

not Zorich?

[median saffron]

lot of proof stuff in it?

[vital bane]

are you looking for proof stuff?

or applied stuff?

[median saffron]

i dont like proof

[remote sparrow]

not many routine exercises

[vital bane]

Then I think Tong notes + Khan academy is perfectly fine for multivariable calc

if you want extra exercises, check out 1st chapter of Griffiths EM

[remote sparrow]

linear algebra has more straightforward proofs

[vital bane]

Tong covers some tensors as well

[median saffron]

i dont think khan will be enough

[vital bane]

it will be

if you combine it with David Tong's notes (they have exercises as well)

[median saffron]

id rather just have one book that has everything tbh

[vital bane]

🗿your wish has been granted

go wild

1300 pages

[median saffron]

noooooooooooooooooooooooooooooooooooooooo

[vital bane]

one book that has everything

everything from basic precalc to tensors and group theory

[median saffron]

mvc for mathematicians not for physicists!!!!!!! ill learn how to apply mvc to physics in my physics course next year anyway so its chill

[vital bane]

[median saffron]

[grave raven]

same 😭

a lot of shits start spamming out of nowhere

[tender cobalt]

😭

[heady ember]

https://tenor.com/view/obi-wan-so-uncivilized-attack-of-the-clones-star-wars-gif-19823075

Go back to your harmonic oscillators, you fility Phy*icist.

[median saffron]

WOW.

[grave raven]

jokes on you, i'm a math major

[heady ember]

https://tenor.com/view/marauder-doom-false-idol-doom-eternal-doom-slayer-gif-26144059

[grave raven]

i agree but i'll still stick to my opinion

[lapis kiln]

Physics slander is unreal

[vital bane]

I will help you to see, slayer

Doom Eternal was GOATED

so was Doom 2016

Doom The Dark Ages? Haven't played it, so I don't know

[heady ember]

#discussion

[vital bane]

my favorite channel, No Access

[vast jackal]

discussion is idk

[vast jackal]

hey guys what's your experience with aops books with like 1 chapter and how long does it take you to finish?

for me my max is 1 chapt per day

[abstract radish]

Many years ago, probably in the timeline 2015-2018, I found a mathematics pdf online. I had it downloaded. I wasn't as knowledgeable enough with math back then. I want to see it again. I don't know what I did to lose it. I don't have it in my drive. I don't remember anything about the book except for a few things. I remember seeing "Tel Aviv" whether it's the origin of publication or the author's university, and it's introduction I think starts with listing symbols and their meaning like ∃, ∀, iff and the likes. Maybe anyone recognizes my description of the pdf

if not found on the intro, it's on the appendix or last part

[still panther]

that narrows it down only very slightly, most math texts have a symbol index of some kind

[abstract radish]

the title might be just "Mathematics"

from what i remember there's no front cover image. Just a text front

[jade meadow]

I think you are describing what might be the most generic book of all time lol

[wraith cave]

try looking at tel aviv’s proofs textbooks

[subtle violet]

[abstract radish]

i found my notebook where i copied the symbols index

from that pdf

[tender cobalt]

i decided to buy Jacobson I & II (For Abstract Algebra)

i have these books currently:
Roman + Axler (Linear Algebra)
Munkres (Topology – point-set)
Pugh (Real Analysis) and Shifrin (Calculus on Manifolds)
Tu (Intro to Manifolds)

i am thinking to buy two more books to complete my arsenal, any suggestions? thinking an algebraic topology book? and some other book i dont know what it should be

[naive lava]

ahlfors? rudin or folland maybe? cartan? Hartshorne?

maybe spivak?

what type of book do you want?

rotman has a nice alg top book btw

lee's manifold books are good too

[tender cobalt]

i was just checking it out

[naive lava]

milnor wrote some fire stuff back in the day

[tender cobalt]

my goal is alg geo and diff geo

i was thinking about folland RA but i dont know if i will need it for diff geo

[tender cobalt]

Topology from differentiable viewpoint?

[naive lava]

well than you're prolly gonna need a complex analysis book

for alg geo

[tender cobalt]

ah right a complex analysis book, what i go for? Stein Shakarachi?

to complete the arsenal

Is rotman better than hatcher

[still panther]

anything but hatcher

[tender cobalt]

everyone hates hatcher LOL

[naive lava]

rotman has a categorical pov which i prefer

hatcher talks too much

[tender cobalt]

so after some jacobson II that should be easy right

[naive lava]

it's kinda hard to actually read

[naive lava]

it is also an intro to cat theo so it should be all good

[tender cobalt]

Hatcher?

[naive lava]

conway is a popular choice

ahlfors is great

gamelin is also nice

[naive lava]

yeah cos he talks too much

[tender cobalt]

which one do you think ill like

[naive lava]

what did you like previously?

since you're becoming a geometer, probably ahlfors is the most geometric one

i've also almost finished it and it's a great fun

not dry

filled with actually fun stuff

[tender cobalt]

i never touched complex anal

[naive lava]

hmm

then idk

gamelin presents itself as a ug textbook

but covers almost a superset of ahlfors

[tender cobalt]

which one will i like if i like jacobsons writing style @naive lava

[naive lava]

i think you should check out all of them to see which one you like the best

[tender cobalt]

good idea!

@grim ore yo zyphen, is gamelin enough for the complex stuff needed in AG

[grim ore]

Im going to go for the general answer, and say that gamelin is a good text for complex

It more so also matters for what are you pursuing in AG?

[tender cobalt]

idk being able to read Hartshone or Silverman?

[grim ore]

bruh, dogu just told you gamelin is nice lmao

[molten gulch]

for hartshorne I always thought what you really need is algebra

and some topology

[grim ore]

So AG is roughly split up into different ways to look at problems and different problems

There is complex ag, and scheme theoretic ag

[molten gulch]

yeah

[molten gulch]

is there any place you tend to need both?

[grim ore]

I think it would be better to say, what are you planning to study, and find out how to look into where you want to go

[tender cobalt]

i want to understand algebraic number theory and FLT proof

(big ambitions...)

[grim ore]

Hodge Theory is one of them

[molten gulch]

ah yep expected that

Where does one learn the complex geo side of things? Huybrechts? G&H? AFAIK for schemes most people do like shafarevich or hartshorne or gortz and wedhorn, etc....

[grim ore]

tbh since you mentioned silverman, thats kinda an entirely different subfield of its own called arithmetical geometry

[tender cobalt]

ohh 😭

bro aint this shit legit millenium problems territory

hodge theory, arithmetic geometry

[grim ore]

Yes lol, Voisin too, but this is kinda the extent of what i know about complex ag. I havent explored far enough in complex

[molten gulch]

Ah okay, that makes sense, ty

Asking mainly bc like...hodge theory stuff and complex manifolds seem really cool

[tender cobalt]

okay so if i learn alg geo and riemann geo then i can do complex geo right

[molten gulch]

oh also yeah, how much diff geo is needed

[grim ore]

to me the intersection between complex and scheme theoretics are really different

take that back, i assume that diff geo is more on the scheme side because of what im familiar with, but huybretchts does a lot of lin alg and complex analysis focus

voisin doesnt go into diff geo, but more with complex manifolds and kahlers

[naive lava]

complex manifolds are usually tought after real manifolds

[grim ore]

so because they do manifolds i assume that there will be diff geo but tbh idk

^

[tender cobalt]

okay guys im getting gamelin since it doesnt assume analysis

[grim ore]

Yeah gamelin i think just takes after calc iii

[tender cobalt]

Rotman for alg top gamelin for complex anal

[grim ore]

Just making sure, are you planning for the futuee

[tender cobalt]

yes

okay so books buying:

jacobson basic alg I
jaocbson basic alg II
rotman alg top
gamelin complex anal

[grim ore]

Did you take ug algebra?

jacobson is a grad lvl text

and i know you are going through munkres point set rn too

[abstract radish]

I found it. But only saw one with the two pages of notation. it's Differential and Integral Calculus, I
Lecture Notes (Tel Aviv University, Fall 2009)

[abstract radish]

I found the complete one! 🙏

[karmic onyx]

Not true at all wtf

Just not well used bc peter didn't use hartshorne

[dim sierra]

lmao

[karmic onyx]

Some people are so unhinged tho, you ask a question and their reply is a hartshorne problem

Im tryna be that guy

[dim sierra]

It’s so intimidating when people do that

[karmic onyx]

bro why are you active

cooked

[dim sierra]

I think I yapped too much in the diff geo channel

[molten gulch]

Why did you post this clip in BOOK RECOMMENDATIONS

[tender cobalt]

nope, thats why i will do jacobson basic algebra I

he introduces stuff from scratch and very self contained

[dreamy ledge]

Dr. Seuss - Green Eggs and Ham

[plush rain]

<@&268886789983436800> user who does nothing but advertise this yt channel, also this particular channel has been spammed in this server before abt 7 months ago

[timber mesa]

they've been muted already

good point about the channel though I thought that looked familiar

[plush rain]

ty

[remote sparrow]

not everyone; it's just polarizing

[dim sierra]

Hatcher is goated smh

[karmic onyx]

Cap

Among us when he sees a confusingly written proof that's 3 pages long but it's formatted as a single paragraph

[dim sierra]

hatcher is good

[karmic onyx]

Yeah I think I've hated on it too much

Its not that bad + others are probably worse (can't confirm tho)

[dim sierra]

Others are definitely worse in my experience

I wish Hatcher did more smooth manifolds stuff tho

[karmic onyx]

I wish Lee talked about sheaves more

[slow roost]

anybody have thoughts on Bosch - Algebraic Geometry and Commutative Algebra? seems like a pretty nice recent book, getting into schemes right away after the first half on commutative algebra

[dim sierra]

opinion rejected

[slow roost]

it looks to be closer to something like Hartshorne than Vakil, but maybe somewhat more readable than the former, idk

[plain barn]

any recomendations for algebraic topology?

[tender cobalt]

i asked for some

And i got suggested Rotman

better than hatcher apparently

[plain barn]

just saw hatcher cited above and found the coincindence funny

cus a friend of mine suggested hatcher just to then tell me that it's very badly written

lmao

but that all other options seem worse

[tender cobalt]

ye apparently the proofs are just chunks of paragraphs

[tender cobalt]

rotman too?

[plain barn]

idk didn't ask

[molten gulch]

all alg top books kinda meh

afaik

just check dami's pins

[tender cobalt]

hows Bredon

[molten gulch]

idk I haven't read it

[naive lava]

just get may's combo and start smoking 12 packs a day

[molten gulch]

lmfaoooooo

may's book is uh

isn't it just a bit too efficient for a first pass

and by a bit I mean like...incredibly

[naive lava]

I've mentioned this quote and i will again

[molten gulch]

wait whose quote even is that

[naive lava]

I can only speak for Peter May’s style because I know the man and attended many a lecture from him when I was at Chicago—once an audience member asked if he could draw a picture of what he was describing and he drew a commutative diagram. Homotopy theory as a whole is sometimes pretty visual and often abstract, Peter May is almost never visual and typically hyper-abstract

[naive lava]

some redditor

but I find this hilarious

[plain barn]

ALGEBRAIC TOPOLOGY HAS CATEGORY THEORY??

[gray gazelle]

There’s better AT books imo

[naive lava]

yea alg top is basically functors from groups to topological spaces

[plain barn]

that's amazing

[tender cobalt]

category theory originated from algebraic topology

[plain barn]

I thought it was from algebraic geometry

[gray gazelle]

T&G is good…

[tender cobalt]

whats that

[molten gulch]

I've seen that quote before, also something on MSE about students in his class not being able to compute pi_1 because thy were too deep in theory or smthn

[molten gulch]

yes

[gray gazelle]

From Top to Grp or other algebraic categories, typically

[molten gulch]

that's why cat theory exists in the first place

[gray gazelle]

E.g. Fundamental group(oid), homology, higher homotopy groups, etc.

[gray gazelle]

Topology & Groupoids

[molten gulch]

but apparently that's turned into uh...whatever the fuck this is

I know this is all homalg, I'm just riffing

[naive lava]

https://www.reddit.com/r/math/comments/1j991lq/how_visual_is_homotopy_theory_today/

this post?

[plain barn]

D:

[plain barn]

well after this at least I know I don't want hatcher

[naive lava]

ok nvm that wasn't here

[plain barn]

I fucking hate my eyesight (visual stuff)

[molten gulch]

this was the reddit one, but I saw something else on MO or MSE once, I forget

[dim sierra]

Like?

[gray gazelle]

The aforementioned T&G

[dim sierra]

What’s that

[tender cobalt]

who's it by

[gray gazelle]

Ronald Brown

[gray gazelle]

among us, ^

[dim sierra]

Bruh

That’s way too algebraic

Get that outta here

[gray gazelle]

[trail hemlock]

thats hilarious

holy shit

😭

[trail hemlock]

now do it without quiver.

[molten gulch]

I didn't draw that one lmfao

[trail hemlock]

yeah ik, but could u imagine

jus take away my drinking water atp ✌️😭

[remote sparrow]

it's standard pretty much everywhere (in part, presumably, because it's legally free online); many places that write qual problems for alg top use hatcher for inspiration @tender cobalt

i would also assume it's comparatively more suitable for a more diverse audience; both geometers/low-dimensional topologists and algebraists would take a class in alg top

the former group might not need to see the category-theoretic formulations right away

despite its polarizing exposition, usually hatcher is regarded as a good source of exercises

[tender cobalt]

i see

any input about Rotman

[plain barn]

hum

[cursive rivet]

I have heard this described by friends as "globally good but locally terrible", which I agree with. its choice of topics and coverage is really great (and basically takes the approach I think most courses should take), but the overall writing is soulless and incredibly terse to the point of not explaining anything

[tender cobalt]

ohh i see

thanks

[remote sparrow]

i heard the exercises aren't very hard or insightful, but the exposition is pretty clear

[tender cobalt]

works for me 🔥

[dim sierra]

So true, I couldn’t understand something once in my class and tried Bredon and thought “wtf”

Why is he ZOOMING

[cursive rivet]

depending on your specific needs, I think the second half of Lee's topological manifolds book is really good to get your feet wet, though it doesn't get as far as you'll need for a full course in algebraic topology

[tender cobalt]

I'll check that out as well thanks

that should be like putting emphasis on manifolds right

might be good for transitioning to his smooth manifold book

[plain barn]

huh I was thinking of going with bredon because of my interest in lots of subjects and on differential geometry

also his preface really attracted me

why is the common opinion really apparently "all algebraic topology books are bad but some aspect is good"

rotman is also attracting me

in the preface

[remote sparrow]

@pliant wadi and @fallow cypress worked through rotman before hatcher i think, so they can probably speak to this

[naive lava]

like imagine asking your analysis teacher to draw a picture of a function and he just writes exp(x^2 - 4) on the board

[trail hemlock]

😭

[remote sparrow]

imagining the picture is an exercise

[trail hemlock]

thats acc a pretty solid exercise

i think rudin had "draw a picture" as an exercise for smth

[naive lava]

imagining the commutative diagram is the exercize

[naive lava]

btw do you know any problem book to supp rotman with?

[remote sparrow]

hatcher i guess

[naive lava]

I can't escape hatcher

[remote sparrow]

maybe someday someone will write a better book

or hatcher comes out with a second edition

[plain barn]

I started reading a bit of rotman and and getting really attracted to it

maybe this is it..

[remote sparrow]

https://mathoverflow.net/a/8571

@naive lava

[naive lava]

he's busy finishing the 1st ed

[remote sparrow]

hatcher's answer recommending tom dieck

written in 2009
still hasn't gotten around to writing a second edition

[naive lava]

he'll scratch that i bet

[molten gulch]

I think he even split out his chapter on spectral sequences originally to be its own book, then left the chapter, then said he'd merge it into his alg top book...and then never finished it

[dim sierra]

bro the tom dieck book is SO algebraic holy

[naive lava]

then had a k-theory chapter

[molten gulch]

oh yeah

[naive lava]

anyhow im gonna go and imagine a commutative diagram

[modest glade]

how good would you guys say the princeton companion is for a broad introduction to mathematics in general?

if it is even used like that

[silver stirrup]

what would be a good resource for group actions?

i feel like artin just blitzes through them

and herstein doesn't even cover them at all

[dim sierra]

Dummit and Foote does plenty of that

[silver stirrup]

most recently, I wanted to solve a problem about finding finite index subgroups of some given group, and i think the solution involved counting transitive group actions, but all my research came from this one keith conrad handout, and i'd like to just have more comprehensive knowledge

oh ok ill look at that

[remote sparrow]

shahriari's Algebra in Action

https://www.cambridge.org/highereducation/books/actions-of-groups/9E2CF39D99D882E664FFAB8547B39469#overview

idk whether this book is good but i saw this when i googled "books covering group actions"

[latent hull]

Does someone knows a mathematical book about origami?

[karmic onyx]

hartshorne is pretty readable in my opinion (or at least the small portion that i've read until now is), i think the only "issue" that i've heard some people have with it is that a lot of important ideas are taught via exercises instead of in the exposition, so you end up having to do a large percentage of the exercises to understand enough.

i have not seen the book you are asking about in particular, but i'll skim it to see