book-recommendations

[marble rock]

i thought ireland rosen wasx ANT

[civic carbon]

It is not

[marble rock]

cool

is the text cool?

i think i can read it

judging by contents

i know no NT

[civic carbon]

I don't have a lot of recollection of what was in it.

[tranquil ocean]

Yeah you can read it without any NT knowledge

[civic carbon]

but I know it was elementary number theory, and pretty good for looking up that content

it's what we used in my undergrad course I think

[marble rock]

nice zeta

it says grad texts at the top 😄

is it supposed to be grad or is it like advertisement lmfao

[civic carbon]

I would not take too seriously when a yellowbook says it is for undergrads or grad students. It's not like a hard and fast line

[tranquil ocean]

You definitely could

[civic carbon]

I wouldn't, though

[tranquil ocean]

Yeah, there are maybe a few number theorical facts that could be helpful to know, things like the multiplicative group of a finite field is cyclic

[civic carbon]

but if you know that, you can leisurely read through an elemtnary number theory book rpetty quickly, and that will give you the background

it's not that you can't understand the material, but rather that the motivation is super important to understanding the historical development

and also it is good to understand what questions algebraic number theory can and can't answer, but that requires a broader context

[tranquil ocean]

Yeah, it wouldn't be too hard to read the first six chapters of ireland and Rosen or something

[civic carbon]

Yeah, that's basically what I'm recommending

I wouldn't worry about it too much, how fast the book is won't change how fast you read it

[tranquil ocean]

The chapters are all really short, its not actually that much material

[civic carbon]

I would recommend a lot more than the first six chapters of Ireland and rosen

but definitely skip chapter 9

[tranquil ocean]

Yeah, I forget what exactly is in the chapters

[civic carbon]

I would skip 9 (Cubic/Biquadratic reciprocity), 14 (Stickelberger's theorem), 15 (Bernoulli numbers), and read the rest of it

it will give you a good lay of the land, even has a short introduction to algebraic number theory

but will also igve you an idea about analytic number theory and arithmetic geometry and how these areas intertwine

and I think that scaffolding is important

I'd recommend it. You don't have to carefully study it. I'd do some exercises, not necessarily a ton. But just get a sense of what the big theorems and questions are.

and if a section goes over your head, just go to the next one

[tranquil ocean]

I've only read the first eight chapters and have studied alg NT pretty well without any difficulties, but yeah, I think I'd recommend to read more too

[civic carbon]

you definitely don't need it all, but I think the "brief outline of each area of number theory" format is great

Number theory, more than a lot of areas, is driven by its history. "Why on earth does anyone care about X?" is a question where understanding what came before really helps.

But a lot of the motivation in algebraic number theory is "If these slight generalizations of the integers work like the integers, we can trivially prove Fermat's Last theorem"

and then crawling into a darker and darker hole of realizing that they do not

but then finding their own beautiful structure

[tranquil ocean]

(Marcus's Number Field's first chapter has a great overview of this)

[civic carbon]

oh yeah, definitely, I love that book

I also reocmmend the article "What is a reciprocity law?"

as a good read that gets you quickly into the kind of innocent looking questions

I mean, FLT is totally insignificant an unimportant mathematically.

but it was immensely important historically, and indirectly led to the act that we have computers that work

and many other things

[marble rock]

number theory seems cool

but isnt it all just

tricks

in problems

[civic carbon]

I would say that number theory has a lot of structure that takes its time revealing itself to you.

a lot of the "tricks" mathematicians knew turn out to have explanations that fit into a grander theory

like, for example, if m and n are both the sum of two squares, so is m*n

and there is this heinous formula for writing (x^2+y^2)*(w^2+z^2) as an explicit sum of two squares

and everyone knew this, and used it

but it turns out from the right point of view, this formula falls out for free

so the way I think about it is that in number theory, you are always seeing shadows

and what at first appears to be a weird trick, often turns out to be a shadow of something deep and profound

[marble rock]

yea i got it

cool af

is it beautiful tho

[civic carbon]

haha well I hope so!

For me, I think Faltings theorem is a good illustration of the deep structure of number theory

[valid moth]

what is the statement of it?

[civic carbon]

So, associated to every two variable polynomial is a compact surface, that is a sphere, a torus, a two holed torus, one of those things

and the number of holes is called the genus

and Falting's theorem says if you look for solutions to your equation in the rational numbers, then if the genus is 0 there are infinitely many, and if the genus is 2 or more, there are only finitely many

so, for example, just by looking at x^7+y^7=1 and knowing this way of associating a surface to it, you know it has at most finitely many solutions in the rational numbers

"Geometry determines arithmetic"

it is just the Riemann Surface associated with it. Which is the solutions to the equation over the complex numbers.

so the global structure of this analytic object is dictating the arithmetic properties of the equation.

(this took until the 1980s to prove, btw)

(but it was conjectured from the early 1900s by Mordell)

(so you can tell a number theorist is older if they call it Mordell's Conjecture)

[tranquil ocean]

@gray gazelle Sticking to irreducible plane curves, you have the fact that the genus is equal to (d-1)(d-2)/2 where d is the degree of the curve

[marble rock]

why do i think AG has alot with NT

isnt AG NT but over Z

[civic carbon]

(though you have to be careful, because if the plane curve isn't smooth, then you have to do a bunch of... blow ups and that changes the genus)

(but the point is well taken, it is easy to calculate this thing)

yes, exactly

and the degree of y^2x^5 is 7

a lot of algebraic geometry exists specifically to do number theory

(not all of it, by any means)

[dapper root]

: (

I can’t really deny it tho lol

[civic carbon]

I mean, stuff like Hodge Theory and what not can exist off in another dimension and pretend they have nothing to do with number theory

and "classical" algebraic geometry is definitely a thing of its own.

My first algebraic geometry professor could not do anything about number theory to save his life, but god bless him... he tried

[valid moth]

@civic carbon oh that's pretty cool yeah

[civic carbon]

(But the same would happen to me if you tried to make me say more than two sentences about Hodge theory)

[frigid comet]

say exactly two sentences about Hodge theory then.

[civic carbon]

"Hodge theory exploits the fact that algebraic (surfaces?) have two entirely separate (co?)homology theories, one coming from the analytic structure, and one coming from the algebrogeometric (best adjective) structure. Although the two structures are isomorphic by GAGA, there are non-trivial maps between them."

that's my attempt, how did I do?

[frigid comet]

haha I think that is pretty good, but I don't interact with Hodge theory at all :p

[civic carbon]

if I could instantly understand the contents of any textbook, I think I'd pick Griffith's and Harris' Algebraic Geometry book

I don't think I can make it ten pages in without getting lost

[marble rock]

im going to grow up

and solve hodge conjecture

screenshot

this

[frigid comet]

If you broaden that to allow a series, I would probably take Hormander Vol 1-4

[dapper root]

I’ll be basic and say EGA

[flint forge]

i'd pick "How to play poker"

[frigid comet]

you won't get the millenium prize if you use stockfish for it @marble rock

[marble rock]

🐶

[civic carbon]

there's also that impossible curves book

[flint forge]

is that true gomez

[civic carbon]

that would be a good choice

[tranquil ocean]

I'd say I'd love to understand the whole proof of FLT

[civic carbon]

it has two volumes, so it might be a good choice

[frigid comet]

idk, you'd have to ask the clay math institute

[tranquil ocean]

Which is probably a lot more than just a book but

[ionic wren]

I’d also love to say that

Can’t tho lmao

[frigid comet]

ivrii's monsterbook would also be nice

[flint forge]

i'd understand rudin's analysis

[frigid comet]

lol max, that is easily attainable

[civic carbon]

oh the scary one?

[flint forge]

gomez im sorry

but i just cannot remember the implicit function theorem

every time i read it

my brain just deletes it

[frigid comet]

haha what about the inverse theorem

[flint forge]

i forgot it as I'm reading it

[frigid comet]

if you know one you just need to get good enough at using it

[civic carbon]

Every time I have to pick up big Rudin I am filled with immense sadness

[flint forge]

uh thats like, jacobian is invertible implies locally invertible right

[ionic wren]

He is referring to proto-human circa 300k bc rudin @frigid comet

[frigid comet]

yeah exactly

[flint forge]

okay yeah that one i got

[frigid comet]

that's easy to remember right?

[flint forge]

oh man

[frigid comet]

yeah

[flint forge]

the fucking rank theorem

[ionic wren]

Wdym

[flint forge]

the way rudin states it

is like a full page

[ionic wren]

Lol

[flint forge]

i forget it as i read it

[frigid comet]

how does rudin state it? when I hear rank theorem I think of Lee's version

[flint forge]

i can find it ig one sec

[frigid comet]

oh is this in the multivariable sec of baby rudin? yea don't read that

[flint forge]

ok looking at it now

its not as bad

but still

look at that

i cannot comprehend it

[frigid comet]

lol yeah I get where you are coming from

[civic carbon]

I remember distinctly being in homological algebra, and the professor writing some horrible TFAE statement on the board, and saying that he was going to go on the proof, but when we got sick of it we could tell him to stop and he'd move on. And then he said "So the proof revolves around this commutative cube..."

and it was like "stop"

[ionic wren]

Lol what

[flint forge]

lmfao

[frigid comet]

commutative cube haha

fuck that

[ionic wren]

what the hell does that mean

[flint forge]

commutative c u b e

im ok w that actually

my brain vibes w it

i can picture it

[frigid comet]

exactly what you think it means

[ionic wren]

What does commutative cube mean

[flint forge]

simply observe that the following commutative dodecahedron...

[marble solar]

a cube with commutative diagrams

[ionic wren]

Wait

Ohno

I understand

[flint forge]

my brain is like

just big enough

[ionic wren]

Like

[flint forge]

to picture the triangulated category axiom

[ionic wren]

I know what you mean

But

[flint forge]

commutes

[ionic wren]

Yeh

I get that diagram

[civic carbon]

that's a beautiful diagram

[ionic wren]

Ya

[flint forge]

its the braid axiom for triangulated categories

[ionic wren]

It looks like a braid too

[flint forge]

with T(-) being the transition

[civic carbon]

I can't make it very far into sentences that involve the word "category"

possibly related to said homological algebra class

I remember clearly one day when I understood what yoneda's lemma said, and it made sense

but then it was gone

[ionic wren]

When the world needed him most

He vanished

[flint forge]

lol

to be entirely honest

i still find the slogans dumb

[ionic wren]

Wdym

[civic carbon]

and the most frustrating part is that I've spent serious time trying to get it, because everyone syas algebraic geometry makes so much more sense if you understand these things, but my brain does not bend that way.

[dapper root]

I think that depends on the level you’re doing it at

If you’re like still at “I’m doing hartshorne” I think it isn’t that important

[flint forge]

zeta im barely capable of rembering the definition of differentiable in R^n

[dapper root]

But I’m still there so what do I know

[flint forge]

dont worry

[ionic wren]

Lol

[dapper root]

I can remember it when going into R

But R^n to R^m I’m like

Uhhhhhhhhhhh

Something matrix

[tranquil ocean]

I could write down the statement of yoneda and yet I still have no idea why I should ever care

[flint forge]

tbh you probably shouldnt

[dapper root]

It can matter

[flint forge]

in general people should care less about the yoneda lemma

[dapper root]

But it also can not matter

It probably won’t matter for most people

[flint forge]

as far as I am concerned yoneda is basically at the same level of 'whoah' as the fact that all groups embed into a symmetric group

[tranquil ocean]

I mean, I felt that yoneda was sold to me as like, the fundamental theorem of category theory

[dapper root]

But I think the people for whom it matters try to convince everyone else that it matters a ton

[flint forge]

no

its not

yoneda just gives us a nice cocompletion

actually

I think Yoneda => that group theory theorem

so its actually a generalization

yeah

[ionic wren]

Ngl max I don’t know what you mean by cocompletion

[flint forge]

i mean thats reasonable you dont know category theory

[ionic wren]

That’s cocorrect I do not

[civic carbon]

I really wanted to make hocomology

[ionic wren]

w h a t

[pale mica]

cocomology

🍫

🍵

[ionic wren]

hocopocomology

[civic carbon]

I'm pretty sure cocomology is a beach boys song

[pale mica]

Owomology

[ionic wren]

NO!

[dapper root]

I only do mology

[cloud trench]

Is there any good book on generating functions for solving recurrence relations?

one that explains it slowly and simply

[hollow current]

try this mb

[gray gazelle]

Guys what do you think is a good calculus text? I want something better than stewart or Thomas because I learned everything I learned really rigorously(I learned single variable from mit ocw and a lot of rigorous physics). I consider apostol or spivak but I don't want to spend too much time so something in between would be really good. Btw in what depth does apostol cover linear algebra?

[wooden sparrow]

@gray gazelle I just heard someone suggest spivak. But I didn't read it.

[gray gazelle]

I know about spivak but i am thinking of something easier because I am doing this for contest physics. But I really can't stand Stewart and Thomas and Larson and textbooks like those.

But I might just go with apostol. It is really good for me(it suits my learning style) . But I fear it will take too much time

[hollow current]

Thomas and Finney Calculus is nice but as i see u don't want it

[gray gazelle]

Is it like Stewart?

[hollow current]

i haven't read stewart still

[gray gazelle]

Is George Simmons calculus good?

[hollow current]

Btw, also u can look and Edwards and Penney Calculus

https://www.amazon.com/Calculus-6th-C-Henry-Edwards/dp/0130920711

[gray gazelle]

OK thanks for suggestions

[soft drift]

esgnto6👍

[calm crane]

cocomology $\cong$ mology

[hasty eagle]

ariana:

[broken meadow]

coco

[radiant crown]

(co)²

[flint forge]

This makes me so uncomfy hahaha

m o l o g y

[calm crane]

oh crap i thought this was chill not book-discussion xd

[strange osprey]

Any good math formula books?
Need dem juicy formulae

Round 2

[main flax]

go look up a detailed anti derivative table

[valid moth]

lol

@strange osprey you play chess?

[strange osprey]

No, used to. Why?

Why are you asking? @valid moth

[valid moth]

there's a fairly active chess community here

#chess-go-shogi

check it out, if you start playing again

@strange osprey

[strange osprey]

Fairly active? Now that's what I call honesty instead of being scammed.

[warm socket]

I believe ramanujan's notebook might be a nice "math formula book"

[tight crag]

Lol

Are math formulas inherently interesting without context?

[cold lagoon]

🤔

[calm crane]

physwiz, you really should consider getting some proper book to study from instead of being obsessed with formulas. Sure it is helpful to like go i want to understand some formula as a goal but you shouldn’t spend all your time caring about these.

[zealous elbow]

You need to understand the logic behind the formulas or else it's meaningless

[lost fjord]

wait who deleted my message?

[crude lake]

just mem every formula you can

you'll eventually be better than terry tao at math

solving math problems is really just testing every possible combination of formula/method application

[gray gazelle]

[restive raptor]

[crude lake]

just min max, prune and go in for lethal

you can easily mate a problem in 20-30 moves thsi way

[main flax]

what are you talking about

[gray gazelle]

mate a problem

[dapper root]

@crude lake Brb gonna set my quantum computer to just try everything

It’ll become@better than Tao

[molten wave]

can we use this channel according to its title

[crude lake]

no

[dapper root]

Oh my b I didn’t even notice what channel it was

[strange osprey]

Okay

Ariana

Scrap the formula books. What about a level mathematics books?

[main flax]

how much math do you know and what do you wish to learn more of?

[strange osprey]

Any math that I could possibly apply to physics.

[valid moth]

i recommend algebraic number theory then

[strange osprey]

Is that a level?

[ionic wren]

he's jokin

well

[valid moth]

it is a level

yes

not sure which though

[strange osprey]

I just wanted a level mathematics textbook.

[gray gazelle]

oh he means A-level

[strange osprey]

I already have a physics a level.

[gray gazelle]

like the course

right?

[strange osprey]

Yes

Year 12 and 13

[gray gazelle]

year 13

[strange osprey]

In GSCE curriculum school.

I am in year 9

[gray gazelle]

right

well as i said i'm not sure of any textbooks specifically for A-level maths but you should try the mit ocw single var course

it's good to be passionate about maths but you need some kind of direction

[strange osprey]

Much better if I Google it. This tells me nothing.

I am not passionate about math.

By the way.

As you can see from my name. My passion is clearly physics.

[gray gazelle]

right

thank you for the clarification

[main flax]

but your profile pic is an inaccurate representation of an atom, almost in every way

[strange osprey]

[ionic wren]

actually

its on a display

of many

many

authentic

atoms

[main flax]

can

you

type

in

full

sentences

please

[strange osprey]

Hi anakin skywalker

!

What direction were you talking about? @gray gazelle

[gray gazelle]

like

a bit of structure

[strange osprey]

Example

[gray gazelle]

because it's really easy to just stuff around and get nothing done

[strange osprey]

What is stuff around?

[main flax]

what's a good intro galois theory book?

i kinda don't want to do d&f

[sage python]

I learned out of lectures that followed D&F, Lang might be okay too

[main flax]

alright

i'll read into lang's, ty

[sage python]

Milne's got free online notes and they're probably good

[main flax]

i googled, looks good

thanks again

[tranquil ocean]

@main flax why :(

[main flax]

because i hate d&f with passion

it's good but it's so dry

and 8 examples spanning over 5 pages is not rly fun to read, but if i skip them i feel like i'll be missing stuff

[tranquil ocean]

Wait, don't examples make things less dry?

[ionic wren]

Dummit and Foote isn’t especially dry I don’t think

[main flax]

idk man

i just don't enjoy it as much as other texts

[marble rock]

same publius

turns out math books are way fun

but df is just bad

its in between the 'terse advacned text' and the 'intuitive fun text'

[main flax]

i can't pinpoint exactly what i don't like, but i don't like the book

[marble rock]

the bad part

[main flax]

i still have nightmares from chapter 10

[marble rock]

modules?

[main flax]

yeah, fucking hated those

[marble rock]

yea i did them p fast didnt care tbh

[main flax]

it was mostly absolutely my fault, i didn't realized that i had to do exercises before moving forward

[marble rock]

was jusut cool seeing lin alg stuff

[tranquil ocean]

Idk, I'm using the book for two classes now and have liked it

[marble rock]

@main flax tbh no lmfao heres my take : not doing exercises is perfectly okay

jk lmlfao

[main flax]

anyway i'm being very butthurt about this book

[marble rock]

yea same and i cant really switch cuz rest of texts use category language

which idk

and jacobson turned out to be the same of df really

[main flax]

i never tried jacobson

[marble rock]

just paragraphs of writing

[main flax]

too many choices

ah

[marble rock]

yes herstein is the good df

[ionic wren]

I found jacobson reallly dry tbh

[sage python]

Dummit and Foote is licking the desert lol

[marble rock]

same

yea jacobson is imo overhyped

but idk

[sage python]

Like he just takes

So

Fucking

Long

To say stuff

Jacobson is the best intro algebra book lol. Maybe Lang

[ionic wren]

What do you think of artin as an intro algebra book dami

[sage python]

Artin's the correct book if you don't know linear algebra

[marble rock]

maybe lang?

maybe lang best intro algebra book?

[gray gazelle]

[sudden kindle]

Yes saracino is a good book!

[strange osprey]

@sacred wagon Yes, I am good at calc.

Integral and differential. Have also done some partial derivatives.

And partial integration.

[ionic wren]

Wait

Partial integration

What’s that

[strange osprey]

Now, I am learning some advanced integral formulas.

I don't want to sound like a showoff again.
No, I haven't done linear algebra.

[ionic wren]

Sorry I have never heard of partial integration

[strange osprey]

Wait what?

Type in google

!

Aleph null

[ionic wren]

Do you mean integration by parts

[strange osprey]

Uhh...I will double check whether partial integration exists. I swear I saw it somewhere.

Partial integration not integration by parts.

I am a former prodigy now.

[ionic wren]

Can I have a link to something about partial integration

[strange osprey]

https://www.cliffsnotes.com/study-guides/differential-equations/review-and-introduction/partial-integration

[ionic wren]

That’s typically just called

Integration

[strange osprey]

Mindblown

Well...I am only 13. Why the rush at learning college syllabus though it is extremely fascinating and maybe a bit complex for a small brain like me.

Perhaps I am just pessimistic.

Okay

Got it

Yes sir

[coral snow]

if you would recommend a linear algebra textbook to an absolute brainlet, what would you recommend?

[north spire]

Linear Algebra by Klaus Janich

[coral snow]

emphasis on absolute brainlet btw

[north spire]

It's 200 pages or so of rigor and memes. It was fantastic

[coral snow]

i'll check it out

wait a sec

is it this

[north spire]

yea

[coral snow]

it starts with sets and maps

lul why are systems of eqs in chap 7

[north spire]

It's meant as an abstract introduction to linear algebra so it begins with vector spaces. Some other abstract introductions do this differently, though.

[coral snow]

i just wanted to learn lin alg for physics purposes lul

[north spire]

The guy was teaching physicists and mathematicians. This book is based off of his lectures.

The only thing about this book that's "bad" is the lack of problems. That can be remedied by a problem book in linear algebra. A good one that I've worked partially through is Linear Algebra: Problems Book by Ikramov.

[coral snow]

is there any prerequisite knowledge i need to start this

other than low level HS stuff

[north spire]

i mean, do you have, like, basic knowledge of what sines and cosines are?

if you do, then you're good

[coral snow]

well then, guess i'll give it a shot

[north spire]

cos he uses that in constructing examples of rotation matrices

but well, it's not strictly necessary. He also uses an integral as an example of an inner product but that's just a one off example and you can come back to it when you learn about that stuff later

[coral snow]

why would you recommend this over, say, strang's intro to lin alg or georgia tech's interactive linear algebra textbook

[north spire]

i've used neither of them. I haven't even heard of the latter.

[coral snow]

ah, fair enough

https://textbooks.math.gatech.edu/ila/index.html

this one's the one by georgia tech

[north spire]

let me see

[coral snow]

im not sure if it's healthy for me to be using this many resources

[north spire]

I mean, why not? Use LA by Janich and use the georgia tech thing for geometric visualizations of what you're doing. Janich does have that but, for the most part, it is a theoretical text.

The georgia tech textbook seems to give you access to nice illustrations. Only thing is that the chapters in that book don't match up with those in Janich's book.

[coral snow]

but yeah, i'll keep this in my resources just in case

thanks

[north spire]

yea i mean, just read what you enjoy reading. If strang's style is something you like, read that instead

for me, the reason i started using LA by janich was because it was one of the recommended textbooks on ETH Zurich's Linear Algebra 1 website. I believe it was the only one that was translated into English at the time

[coral snow]

eth zurich, nice

wait, can you link me that?

[north spire]

http://www.vvz.ethz.ch/Vorlesungsverzeichnis/lerneinheit.view?lerneinheitId=125021&semkez=2018W&ansicht=KATALOGDATEN&lang=en

[coral snow]

thank goodness it's in english

oo they mentioned friedberg insel and spence

anyway, thanks for this suggestion

[north spire]

the language of instruction is german so they most likely use the german texts

[coral snow]

i mean, the site is in english

the titles seem german so i'm not touching those any time soon

[north spire]

but they're also slowly recommending their students to read english textbooks too

yea janich has been translated and the translation is pretty good. I believe it was done by Silvio Levy

uhhh wait

huh it doesn't state the name of the translator. I'm probably thinking of another translated text

but yea, this one was great

[gray gazelle]

FINALLY

Im on the last chapter of baby rudin, The Lebesgue Theory

[lavish gorge]

did you do all the exercises?

[gray gazelle]

Yes

should i start with papa rudin after completing the last chp?

[steel viper]

You can if you want

But there are other fun things you can do

[gray gazelle]

like?

[steel viper]

I mean, lots

[valid moth]

like analysisn't

[steel viper]

Intro abstract algebra is cool

go away arch

smh

[valid moth]

hey that's what i meant

try artin or jacobson

[gray gazelle]

yeh im reading LA by lang

[valid moth]

or LA sure

not sure how good his LA book is though

i think i didn't hear very good things about it

[marble rock]

can you read lang if ur a beginner?

[gray gazelle]

and general topology by willard

[steel viper]

lang has published like 8 thousand books

[marble rock]

algebra

lang

[valid moth]

again you probably know enough pointset from rudin chp 2

[steel viper]

if you mean his linear algebra book then probably

[valid moth]

so you can just do AT

[marble rock]

algebra lang

[steel viper]

the grad algebra one?

[valid moth]

after you learn algebra

[marble rock]

yes

[valid moth]

instead of doing like a pointset book

[steel viper]

i dont think anyone learns from lang

[marble rock]

yea ever1y just says its refrence

[steel viper]

ew

[marble rock]

wait

arcshys

[steel viper]

begone u AG goblin

[gray gazelle]

wat books should I refer for algebraic topology?

[marble rock]

rudin chap 2 topology

topology text?

[steel viper]

hatcher or bredon

[gray gazelle]

yes

[marble rock]

ppl say classic AT is hatcher

[gray gazelle]

rudin' chp 2 was awsum

[marble rock]

lmfao

[steel viper]

bredon has a good chap 1

which like

[velvet briar]

Yes lol. That's one of the best books that currently exist

[marble rock]

i was thikning of learning AT as like an intro to math for me

[steel viper]

does all of point set

[marble rock]

but point-set was just too boring for me

and di thought iw ouldnt enjoy AT anyways

[velvet briar]

Hatcher's AT

[steel viper]

huh

[marble rock]

i was fooled with the pictures

[steel viper]

AT
intro to math

?

[marble rock]

i meant like real math

[velvet briar]

Every course is an intro if you work real hard

[marble rock]

yea

hahaah

but i meant like actual hard math

and the lcosest thing to me is AT

just learn point-set

[velvet briar]

Problem is, AT uses point-set as a language

[marble rock]

AG would tkae a whole other text on comm alg

yea

[velvet briar]

You might not get why we care about AT unless you see some of the problems that point-set sucks at solving

[marble rock]

i just liked the cool pictures

and like the cool terms

glue wedge

lmfao

u do this in math cool curious

lmfao

stupid motivation but /shrug

[velvet briar]

But then again you like groups a lot so AT is a natural choice haha

[marble rock]

hahahaha yea

i relaly wanna know wahts ' the fundamental group '

[steel viper]

loops

up to homotopy

qed

delete them

they are trash

fuck your specs

[velvet briar]

Take a shape. Pick out a point on it.

Now, draw a line on that shape that starts and ends on that point. If you draw two lines, they are "the same" if you can stetch/deform one into the other. We say these lines are the same up to homotopy.

Now, the construction of these lines puts a group structure on your shape. For example, the 2D circle gets a fundamental group Z.

[marble rock]

lmfao

this sounds cool by default

i didnt know math can be this cool

like u can actually see stuff in this shit lmfao

[flint forge]

i think we should get rid of all spaces with nonabelian fundamental groups tbh

[velvet briar]

It turns out that the group tells you lots of topological properties right away

[marble rock]

yea

how does the group structuree look like

i dont know what the 'construction of the lines'; mean

[flint forge]

do both loops

you have two loops

you do one

and then the other

this is a third loop

[marble rock]

mmmmmmm

[velvet briar]

Still thinking about the circle
1 loop + 1 loop = 2 loops

1 + 1 = 2

The integers lol

[marble rock]

wtf boys

ye ayea

i get it yea

[velvet briar]

Do one loop, but then loop back
1 - 1 = 0

1 has an inverse

[marble rock]

and like the goal of this

is to classify topological spaces

or like shapes basically

[flint forge]

yes

[marble rock]

so what happens if the fundmaenta lkgroup

is iso to some other fundamental gruop

of another shape

[steel viper]

up to h o l e s

[flint forge]

but it's not strong enough to classify them fully

[velvet briar]

The bae result is that this is conserved over homeomorphism, so it captures topological properties

[marble rock]

so what happens if the fundmaenta lkgroup
[7:27 PM]
is iso to some other fundamental gruop
[7:27 PM]
of another shape

i wonde

r

[steel viper]

technically nothing

you need stronger conditions

[pale mica]

gruop

[velvet briar]

If it's not iso, these shapes are not homeo

[flint forge]

With Algebraic Topology

[steel viper]

but if pi_1(X) is not isomorphic to pi_1(Y) you know that X and Y arent htpy

dang

sniped

[flint forge]

you don't get much information

from two spaces having the same invariants

you get a lot from two spaces having different invariants

[marble rock]

@steel viper idk what htpy means tbh

oh

okay

[flint forge]

There are some theorems about when two spaces having the same invariants allows you to say something useful

[pale mica]

Homotopy I think

[marble rock]

yea

so so the stronger link is 'homotopy

'

ig

which is something similar to isomorphic

ig

[flint forge]

well

All homeomorphic spaces

are homotopy equivalent

but not the other way around

[gray gazelle]

how many pages does bredon's geometry and topology has?

[marble rock]

yea

[gray gazelle]

its a 84 mb pdf*

[steel viper]

many

[marble rock]

so is the donut coffe one

an example

[velvet briar]

π1(Circle) = Z
π1(Line segment) = {e}
The circle is not homeo to the line

[flint forge]

That is a homeomorphism

[marble rock]

yea

yea yea

[flint forge]

homotopy is way weaker

for example

take C minus the origin

this is htpy equivalent to a circle

but is not even close to homeo

[marble rock]

okay

yea

i thought it would bes tronger

thats why its useful

ig 😄

[flint forge]

no

[marble rock]

to classify things up to homotopy

and saay which are same whichia re not

which*

[flint forge]

Yeah no

classifying up to homeo

is a really hard problem

for example, one of the millenium problems was

prove that every manifold homotopy equivalent to a sphere

was homeomorphic to a sphere

this problem took several authors

and many many years

[marble rock]

does htis mean

[flint forge]

and was finally solved by perelmann

[steel viper]

ultrachad perelman

[marble rock]

everything is a sphere

lmfaao

[flint forge]

no

[marble rock]

this is the perrelman stuff

lmfao now i know

[steel viper]

[marble rock]

oh oh

yeah

sorry i missread

the homootpy prt

[flint forge]

(when I say manifold here I mean closed manifold)

hahahaha

theres a problem n hatcher

[steel viper]

lmao

[marble rock]

cool shit boys col shit

[flint forge]

where you have to write out

and explicit htpy

sounds cancer imo but

[valid moth]

Perelman's proof of Poincare: "draw a picture."

[velvet briar]

Big thing is that yes, without this method, point-set sucks at proving homeomorphism. This gives a great and easy method to say lots quickly

[marble rock]

yea

[flint forge]

uh

[marble rock]

okay

[flint forge]

thats pretty false imo

AT says basically nothing about Homeos without a lot of effort

i.e. the poincare conjecture

[velvet briar]

Well, more like "non-homeos"

[flint forge]

not even that

it can't detect homeo within a htpy class

AT is about htpy

not homeos

[velvet briar]

I agree

[flint forge]

At least the invariants are

Ofc people still care about homeos for some reason

[marble rock]

yea boys anyways that sounds cool as shit

is there a shortcut for learning point-set

wihtout analysis

[flint forge]

Sure

learn point set

[marble rock]

oh yea

[flint forge]

there is no analysis in point set lol

[steel viper]

yea wut

[flint forge]

fellas, is there a way to learn PDEs without learning Categorical Biology?

[steel viper]

no.

[marble rock]

ask in #book-recommendations

[valid moth]

you should know some algebraic sociology beforehand

[marble rock]

the algebr aneeded for AT isnt that much right?

just GT?

[steel viper]

btw @flint forge isnt generalized poincare stronger than "homotopy n sphere implies homeo"

[flint forge]

uh you can generalize to diffeo

you any other category

i think its wide open in PL?

[steel viper]

[flint forge]

the generalized Diffeo version is false in general

but we are pretty close to understanding when it is false

[steel viper]

thats woke

isnt only n = 4 left

[steel viper]

oh diff isnt settled

[quick hornet]

nah its settled

its false

read the image smh

:^)

[flint forge]

https://en.wikipedia.org/wiki/Exotic_sphere#Classification

I gave a talk on some of the stuff in here

its cool

[steel viper]

wtf gaurav literally just talked about S_n and A_n all lecture

are we going to finish what he wants to cover?

today we did just the thing pointed to

and these arent the final notes

[flint forge]

did he prove things?

[steel viper]

yeah

[flint forge]

classic. mistake.

[steel viper]

[flint forge]

im so mad my foot is still too injured to climb

oh wrong channel

[steel viper]

how did u hurt it

also yea

lets move lol;

[calm crane]

wait wtf

groups
group actions
frickin rings and modules in a section and then categories

[winged gust]

Hey all. Does anyone know of books that are written like "A Book of Abstract Algebra" by Charles C. Pinter?

The way I would describe it would be, a chapter per idea. For example, Operations are the first practical chapter, it's 6 pages long. Then "The Definition of Groups" is 11 pages, then "Elementary Properties of Groups" is 8 pages, etc. They're all pretty self contained (tending to use only ideas introduced in prior chapters). Mostly the meaty bits of the chapters end up being the exercises. I'm still working through it, but I find I really enjoy this kind of structure for mathematical topics as it allows you to explore the ideas in isolation of other ideas (at least, IMHO). The book winds up having a lot of chapters, but I actually don't mind that.

One thing that I find it's lacking is a list of answers to all of the questions, as there are trickier exercises that I'd like to sanity check if I got right or not.

[dapper root]

I can't provide any sort of other book like that tbh, but in general not many books will include full answer keys / even any answers

Often an answer key doesn't exist, and on the internet there will be problems you won't find solutions for. Some of the most used books like Rudin have had answer keys made because of their widespread use, but don't count on it. It's just a reality of the field, which kind of sucks 😦

[north spire]

Hey all. Does anyone know of books that are written like "A Book of Abstract Algebra" by Charles C. Pinter?

The way I would describe it would be, a chapter per idea. For example, Operations are the first practical chapter, it's 6 pages long. Then "The Definition of Groups" is 11 pages, then "Elementary Properties of Groups" is 8 pages, etc. They're all pretty self contained (tending to use only ideas introduced in prior chapters). Mostly the meaty bits of the chapters end up being the exercises. I'm still working through it, but I find I really enjoy this kind of structure for mathematical topics as it allows you to explore the ideas in isolation of other ideas (at least, IMHO). The book winds up having a lot of chapters, but I actually don't mind that.

One thing that I find it's lacking is a list of answers to all of the questions, as there are trickier exercises that I'd like to sanity check if I got right or not.
@winged gust There are answers available online. Someone solved most of the problems in, like, the first 13 chapters so I usually check my solutions against theirs for simple exercises. For proof questions, I usually post my proofs on stackexchange for others to check.

Usually, though, answer keys/solution manuals don't really exist for these books. You just get a feeling for when your argument is correct in most cases. Then, for tricky problems, you just let others check your proof.

[winged gust]

Just found https://www.reddit.com/r/math/comments/5wv91o/similar_books_to_pinters_abstract_algebra/ seems like there are a few books on different topics that are similar in style. It seems like ABoAA can be classified as an IBL (inquiry based learning) text. Also taking a look at http://danaernst.com/resources/inquiry-based-learning/ as it's a link that was posted there related to all of this.

[dapper root]

I belive the text "Combinatorics through guided discovery" falls under that umbrella then

If you want to learn combinatorics, it's also available freely online

http://bogart.openmathbooks.org/

Legally, might I add

[winged gust]

Nice, thanks for the recommendation, checking it out

[dapper root]

I worked from it for a little bit

Then got sidetracked lol

[winged gust]

Then got sidetracked lol
@dapper root I know the feeling, lol

[tranquil ocean]

There's also a book by Murty called problems in modular forms, but that's probably a bit beyond what you're looking for

[dapper root]

Zoph with the modular forms NT shit at all times

haha

[winged gust]

@tranquil ocean what's a modular form?

[tranquil ocean]

uh

[winged gust]

Yeah, taking a look at Wikipedia, that's a bit out of my league for now.

[tranquil ocean]

It's an important number theorical object that people study

They were a large part of the solution to Fermat's Last theorem for example

The book itself on problems in modular forms doesn't require too much though

[marble solar]

Spivak's Calculus has a lot of solutions in the back

And a solutions manual you can buy separately

If you don't know a lot about analysis, Spivak's intro text is a great way to learn

Hundreds of exercises

[winged gust]

@marble solar Thanks for the recommendation, I'll check it out

[dapper root]

I haven't done Spivak, but I've gotten the feeling that if you're gonna do Spivak you might as well do some easier analysis book

But that might be total bs, idk

When I did analysis I had done calculus before

It was like the non-rigorous one, but I did up to multivariable stuff and like Green's, Stokes (not general), divergence theorem etc.

[marble solar]

The great thing about Spivak's Calculus is no matter what level you're reading it

You'll learn something

It's akin to the feynman lectures

[pulsar aurora]

Debatable. While I didn't get into the core aspects of Spivak's, I felt like I was learning stuff in a vacuum, especially when I had no calculus background for context. I inevitably gave up on it

[dapper root]

I guess my thing with Spivak is if you want to learn calculus to use as a layman, I don’t think you need to fuck with epsilon’s and deltas

If you want to do that and be rigorous, why not just do analysis

It’s this weird middle group where I’m not sure why you would want to go through it

[pulsar aurora]

🤷 I am learning from Apostol currently, but I started using it when I had no knowledge of calculus what-so-ever, so it was helpful

[north spire]

If you want to do that and be rigorous, why not just do analysis
most analysis books require that you have a background in calculus so that you can see where things are going

[dapper root]

Apostol is an analysis book right?

[north spire]

apostol's 2 calculus books, i assume

[dapper root]

most analysis books require that you have a background in calculus so that you can see where things are going

Yeah I agree with that 100%, but I feel like speed running an easier, non-rigorous treatment of calculus and then doing analysis is gonna be better. It seems weird to spend a lot of time doing it really rigorous, to sort of redo that when you do analysis

But idk, I acknowledge I might be totally wrong here

[pulsar aurora]

Yes, Apostol's Calculus. not his other stuff

[north spire]

It's probably a taste sort of thing. My analysis prof sent us, essentailly, a copy of a set of notes he made on rigorous single-variable calculus so we could finish that before we start analysis this coming semester

[pulsar aurora]

personally, I'm not about optimizing my study time. 😛 I simply wanted to have more context in calculus than what I'll probably get in my community college calc classes

[dapper root]

That’s fair, I guess

I also come from a weeeeird place

I think most math majors hated calculus because it was non-rigorous and they were like “why does this work!!!”

But I had absolutely no issues just doing it and being like “okay haha chain rule go brrrrrrr”

[north spire]

Also, like, my analysis course doesn't cover geometry while my prof's stuff covers analytic geometry in R^2 and R^3 pretty rigorously. There's some merit to being introduced to epsilons and deltas in rigorous calculus, alongside the geometry

then, just go straight into the rigor in analysis, without holding back

[pulsar aurora]

I'm not a math major, but that said, I consider myself really shit at math, and felt I needed the extra rigor. 😛 That said, it's interesting stuff to me too

I never studied any other analysis book, but Apostol sets it up with a lot of calculus-centric context starting with the problem of areas and Archimedes's method of exhaustion which lays the context for summations then into Integrals.

Sure, you don't need any of that to learn it, but I found it very helpful in connecting the dots

Especially with all the geometric intuition he provides

[north spire]

i mean, yea use what you enjoy reading

i didn't like apostol very much. So, I just used something different. I did like courant though

[pulsar aurora]

I couldn't find any copies of courant to check out. Apostol jived positively with me and I just kept going

But yeah, I don't think there is a singular text to rule them all. There may even be an optimal way of learning, but people here seem to like Spivak, so it gets suggested a lot to those transitioning

[dapper root]

Do you mean “may not even be”

I don’t think there is, if it exists it surely has to be person to person

[pulsar aurora]

No, I said what I mean.

Optimal can be varied on the goals. In school, you don't ever touch all chapters of a textbook, and generally hone into the 'main points' just enough to get your ass moving, at least, in my experience.

[north spire]

There isn't a singular text to rule them all. People make different recommendations precisely because one text worked better for them than another did.

[pulsar aurora]

I'm sure some of the things I"m learning in Apostol could be cut, and I'd still advance fine into other areas of mathematics

[marble solar]

Spivak can be used as an intro to analysis book. He actually debated whether or not to call it Calculus or intro to analysis. He decided that he wanted his target audience to be students interested in mathematics and wrote it for them. You can look at the exercises that he gives and compare them to Rudin's. The only thing that Spivak doesn't really do is use topological concepts

[dapper root]

I really feel like introducing basic topological concepts is so helpful tho

My analysis textbooks first chapter was like topology and limits

[marble solar]

Yeah it is, but at which level? When you're first learning calculus it isn't

[dapper root]

It didn’t explicitly describe it, but it talked about open, closed, etc for what it is in a metric space

[marble solar]

He wanted it to be accessible to someone that didn't know higher mathematics, but valuable for someone that does

[dapper root]

I mean, yeah, but that makes me hesitant to suggest it as a first analysis textbook

[marble solar]

I mean when learning any subject you should have 3 books

One at your level, one below your level, and one slightly above

How may different ways are there to approach AG?

Well you can build up from algebraic curves, to schemes, and go on from there

Or you can start from a differential geometry/complex analysis point of view

etc. Getting different viewpoints is where you get breadth

[dapper root]

That’s all fine and dandy, but in practice it really usually seems to be only one method with how it currently is taught, at least in the US

Which is sad, but I do see the point you’re trying to make

I’ve never really done that tho, but my method is probably pretty atypical. Maybe a lot of very high-achieving people do similar stuff (eg jump into stuff way above your level and flounder for a while), but it’s rough

[marble solar]

Yeah I did that too, my prof. described it as "Running around with your pants around your ankles, and when you're not doing that you're shooting yourself in the foot"

[dapper root]

It’s worked tho ¯_(ツ)_/¯

[marble solar]

Yeah, I read through most of Jacobson's Basic Algebra volume 1 at CC

It was rough, but very rewarding

[dapper root]

I wish I did math earlier

I spent too long just doing nothing and thinking I was hot shit because I didn’t have to try in calculus and diff eq

[pulsar aurora]

I wish I felt I was hot shit. 😛 That said, I also have a decade of not doing math, so I also acknowledge my personal limitations. Why I picked the slow and steady. Plus, Spivak was just too much and too little

[sudden kindle]

@dapper root that's a common feeling. As long as you're working hard now, thats all that matters. Dont get too hung up regreting your past

[dapper root]

I kinda got over it

And then met hsers doing AT and got it again

LOL

Such is life

[pulsar aurora]

You should be bigger than them. Just beat them up to feel better

[sudden kindle]

Who cares honestly. We all have own own individual paths through mathematics. We shouldnt feel bad about where we are in comparison to others. No ones better than you for knowing more mathematics. Really the only reason we're walking here is because we enjoy it. So enjoy your journey and help others on theirs too! ^^

[dapper root]

Yeah, but the reality of like... getting a job weighs heavily on these sorts of things. I do it because I enjoy it, but wanting to turn it into a career means at some point you have to come face to face with the reality that it turns into a competition about who gets hired as a tenure track prof, who’s a lecturer, and who is stuck at a community college

[pulsar aurora]

Don't get a job doing math .boom, problem solved. 😛

[dapper root]

If your goal is to make a living doing research and being at a university these things matter

If only it were that easy neveza, if only

[pulsar aurora]

how so?

[dapper root]

This also devolved from book discussion

[somber mica]

I’d just like to add that teaching at community college can be a pretty sweet deal

In my experience the students at CC are a lot more modest and dedicated than the ones you meet at uni, on average

But if your goal is to do research then that’s probably not much of a comfort

[marble solar]

switch to math or gen?

[tight crag]

@dapper root when you start out with math the important thing is developing your mathematical maturity, much moreso than studying advanced cool topics

There are a lot of high schoolers studying AT and the like on this server and other servers, but they usually neglect a lot of fundamental things

[sage python]

Let's move to #math-discussion

[hearty steppe]

That being said Liquid I’m all ears for more suggestions on developing mathematical maturity. I don’t even consider it an age thing but just intellectual naivety of the subject matter at large.

Do you think that a text like Velleman’s How to Prove it and one’s personal flavor of exploring mathematical analysis in decent depth (my case so far is Abbott and I will also check out Schroder) is enough?

[tight crag]

Honestly it just seems to me that you develop mathematical maturity by
1)doing math
2) talking to people about math and getting feedback
3) doing the above 2 things for an extended period of time

[compact snow]

agrees.

[gray gazelle]

agrees

[gray gazelle]

Halmos. Naive Set Theory.

Opinions? It's very cheap.

you could probably get the same sort of thing from the first part of munkres

but really just use libgen and see if you like it

Definitely a fair call.

Next is, how to get extra time in the day to read math books? Anyone? 😐

[pulsar aurora]

Depends on your life schedule. If a student and worker, yeah, it's difficult, and generally I reserve it as supplement or on the side. However, if it's summer break, and just working... You can easily reserve an hour or two

[marble rock]

just asking on recommendations on how to proceed

learn topology from hatcher notes ( point set )

or proceed with field theory and galois theory ( df )

[white cradle]

learn topology from sutherfeld imo

[marble rock]

is it easier/harder

i think point-set is just oging to be meg aboring

mega boring

and i know no analysis

and dont want this to be in the way

[gray gazelle]

do rudin then

[marble rock]

its too boring form

for me

[gray gazelle]

how is rudin boring

you need to get really into the exercises

[gray gazelle]

@sacred wagon @pulsar aurora Thanks for your advice. I do put in daily consistent hours. I wish I had student time. I work full time, parent, and as covid passes will attempt resume a virtual part time job (in terms of hours) of semi competitive training. Really, the latter is the only flexible commitment.

Something I am getting used to is how long it takes to read, ha.

[pulsar aurora]

You may have to make compromise. I have no children, and work relatively part time. So more time to do things

That is something I will have to deal with as i get back on the career horse of working 40 to 45 hours again

[gray gazelle]

Luckily my current role has an excellent absence of overtime, so I'm trying to take full advantage of that. Good luck. I don't miss 45-50 hour weeks.

[pulsar aurora]

I miss the office work. But eh, I decided to go back to school and not many jobs are flexible for that

Either way, I keep the mindset of selfeducation a long term and not a short term race. This means slowly chipping away at a subject even if it takes over a year for a semester worth of progress

[gray gazelle]

I agree. It certainly is a marathon, although probably more enjoyable than long distance running 🙂

[gray gazelle]

Pirate your books guys

Invest in an ipad or something with a pencil and pirate your books on library genesis

[quick hornet]

we're aware, yes.

[civic carbon]

Also, wehn you're a postdoc or whatever the college will pay for your books

[marble solar]

I've seen publishers send books to profs to try to get them to use it for a class

completely unsolicited

well, unasked for

definitely solicitation going on

[civic carbon]

oh yeah, that definitely happens, and you can request books for course review too

[hearty steppe]

Rudin I think I might still use for problem sets. It is too dense and old school for me. I kinda was able to get halfway thru chapter one but the material is just so dense to the point I can have a problem interpreting it as someone new to analysis.

For now I am gona stick with Abbott and Schroder

[gray gazelle]

What are some good online chess books?

Free

[gray gazelle]

What do you guys think of GH Hardy's  A Course of Pure Mathematics.

Just got it recently

[main flax]

is that a book for a first semester analysis?

[gray gazelle]

ight thanks

[main flax]

np

[hearty steppe]

What I find amazing is that there seems to be so many books on analysis that have different flavors unique to everyone. May be like that for other math subject books but what is special about analysis is that it seems to me that it is the bread and butter that makes sense out of even the more complicated formulas and what to do with problems where just using the standard general formulas doesn’t work without some technique based manipulations.

[marble solar]

Yeah, there's a lot of ways of teaching analysis

One of these days I'm gonna sit down and learn PDEs but I know not when

[pulsar aurora]

I've yet to do analysis. Sort of excited to read those books.

It'll be a bit though...

[dapper root]

If you've done any rigorous calculus that's honestly kinda analysis

If not, then that's cool too

[sage python]

Eventually someone should like, write up the union of Spivak, Baby Rudin, Calc on Manifolds well

And then make it into a single two volume thing

This is the conclusion I have come to. Rudin's too tricky to start with but then Spivak -> Rudin is a decent bit of overlap, Spivak -> Spivak is good but you miss some stuff

[limpid gazelle]

Spivak’s calculus on manifold chapter 4 is hell

[sage python]

Glancing through it now, first part is multilinear algebra which is tbf tricky

[limpid gazelle]

The hard part starts at the second section

For me

[sage python]

Quality chapter. Might be on the tough side but quality

[limpid gazelle]

It’s a list of definitions that make stoke’s theorem possible

[marble solar]

the guy wrote it when he was 24

cut him some slack!

[hearty steppe]

Who wrote what when they were 24

[limpid gazelle]

spivak I assume

[hearty steppe]

Oh wow, that’s impressive

[limpid gazelle]

Huh interesting Spivak also has a book called "A Comprehensive Introduction to Differential Geometry"

[marble solar]

Yeah 5 volumes

I've read volume 1 and parts of volume 2. Excellent books

[limpid gazelle]

Nice

How do they compare to Lee's Smooth Manifold tho?

If you've read them

[marble solar]

I haven't used Lee at all

I've used Warner, Petersen, Schulten's, and Spivak for manifold stuff

[rapid grotto]

it seems to me like spivak's introduction to differential geometry is perfectly accessible if I have a solid grounding in point-set topology

or maybe not even that

[marble solar]

I recommend some background in differential geometry of surfaces

Like Schaum's outline level

[sage python]

That way you'll find out the subject sucks and avoid it

[dapper root]

😱

[flint forge]

it really is truly cursed

me and dami agreeing on something being bad

means it really is bad

oh

thats not differential geo tho

[valid moth]

integral geometry when

[marble solar]

I mean you don't "need it" but it helps build intuition on the relationship between topology, surfaces, and geometry

I'm a firm believer of getting your hands dirty with computation and lots of examples

As much as I hate it

[sage python]

I think in this case it kinda depends on whether the person is gonna stick with manifolds/differential topology or do diffgeo

I think curves and surfaces help to do Riemannian stuff but if it's raw manifold theory then not as much really

[marble solar]

That's a fir assessment

fair*

[raw herald]

Algebra books good for self study as a supplement to dummit and foote?

[steel viper]

There is a pin

https://discordapp.com/channels/268882317391429632/716264872018706443/718931426346795099

@raw herald

[ionic wren]

It’s true iirc the first thing artin actually does

Is define a matrix lmao

Like in the book

Yep

[marble solar]

https://www.math.ucla.edu/~rse/algebra_book.pdf

Here's a book from my algebra prof that he's been writing for a while now

It's pretty good, if you find typos just email him

[ionic wren]

Btw you prolly know this but be careful not to accidentally dox yourself

The organization looks nice

By that I mean the table of contents

I think it’s a bit wierd to have half the book

Be additional topics category

[raw herald]

why is it so bad to dox yourself most of us do it everyday on other social media platforms lol

[ionic wren]

I don’t have any such social media

So it’s prolly just a personal view

@marble solar also there aren’t any exercises I can see?

[raw herald]

I like that book!

[marble solar]

There's lots of exercises in Elman's text

[ionic wren]

Wow so I’m blind

I looked to the end of one chapter

I couldn’t see any

[marble solar]

The additional topics category is stuff that doesn't fit into the one year course at LA

[ionic wren]

Wait so where are the exercises then

[marble solar]

They're embedded at the end of the sections

e.g. pg 64

[ionic wren]

Ohh

[marble solar]

pg 59

etc.

[ionic wren]

Oh I see

I’d maybe suggest have a link in the contents to the exercises but it doesn’t really matter ig

[raw herald]

I'm powering through trying to learn as much algebra as I can before I get to purdue because everyone there is an algebra-something researcher lol

[ionic wren]

Personally I actually like that format your professor uses

[marble solar]

His lectures are perfect

The book is just typed up lecture notes

[ionic wren]

Lmao really

[raw herald]

ucla really has some fire math authors

[ionic wren]

Is this book gonna be sold or

[marble solar]

Eventually he's gonna publish it