book-recommendations

[fast wasp]

or exercises

[cedar flume]

Book recommendation for real analysis pls

[cedar ridge]

Spivak/Apostol

[loud cradle]

at what level? there is a pinned message with recommendations for lebesgue-enabled analysis

[grave thorn]

what level book?

[grave thorn]

as bungo mentioned, specify the level; if undergraduate Rudin is always a good pick

[cedar flume]

This are the topics I've

[cedar ridge]

This ain’t Rudin content 🥸

[versed cypress]

Has anyone tried Calculus from the Ground Up (Jonathan Bartlett)

Or has anyone gone through it and how did they find it

[fast wasp]

Great, but that's what I meant

[vital bane]

yes

a book full of integrals

[fast wasp]

[vital bane]

"Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions)" that's the actual title

[fast wasp]

hahahahaha tks bro

[hallow oriole]

devilishly seductive 😈

[fast wasp]

[fast wasp]

so sexy

[sage kelp]

The way of Analysis

[icy knot]

Beginner: Understanding Analysis

[fierce hedge]

@remote sparrow Did you buy the gamelin and greene book?

[grave thorn]

It quite literally is

[icy knot]

Intermediate: Introductory Real Analysis, Kolmogorov

[remote sparrow]

not yet

[cedar flume]

Ok thank you

[limpid gazelle]

What's a good book on zfc?

[late plinth]

that looks like a fun book
idk how practical but def interesting

[vital bane]

I mean it's not for math students though, they dont really evaluate integrals that often, they're more worried about how to integrate like idk a functor or something lmao

but it'd be useful for physics and engineering students

which a part of me is

[fluid bay]

integrating a functor

[late plinth]

i mean ya, thats what i meant

[vital bane]

[late plinth]

idt i touched an integral in a while but it just seems like one of those cool things to have on ur shelf

[vital bane]

those measure theorists are wild

they'll turn anything into a measurable space

[remote sparrow]

enderton's set theory book

for an undergraduate treatment

hrbacek and jech i've heard is also good

[limpid gazelle]

Oh I'm looking for something that talks about zfc using model theory, not just the axioms and rigorous set theory

Sorry should've specified

[manic cape]

As a math student, i could definitely use a book like this

integration is too hard

[vital bane]

yea knowing how to integrate stuff using special functions and hypergeometric functions would be pretty cool

[late plinth]

Symbolab is too op

[hallow oriole]

fuck symbolab

we stan my boy https://www.integral-calculator.com/

easily the best free integration solver

and it's not even close

well

ig wolfram alpha is better

but that's not rly a fair comparison imo

[crimson leaf]

Disagree this one has steps for free which makes it better

[hallow oriole]

the thing is that wolfram does more things that js integration

and wolfram can evaluate some integrals that this can't

[cobalt maple]

Hey, could anyone recommend a book for algebraic geometry that covers the following:
Algebraic sets, affine and projective varieties, fundamental properties
of varieties. Sheaves and locally ringed spaces. Morphisms of varieties, birational maps and blow-ups. Smoothness and singularities. Hilbert polynomials and Bezout's theorem.

[indigo mesa]

https://www.mathematik.uni-kl.de/~gathmann/de/alggeom.php the 2014 version covers all of that

[cobalt maple]

Oh wow, I'd actually been looking at the newest version of that

Ah, I see the 2014 version doesn't require prior knowledge of commutative algebra

[indigo mesa]

yes

his commutative algebra notes are pretty neat as well tho

in case you're looking for something there as well

[cobalt maple]

I see. I'd like to learn some commutative algebra before the course too. Do you think it would be better to learn it separately or in the context of one of these notes maybe?

(A friend said he fiends it easier to learn comm alg in the context of other stuff)

[indigo mesa]

You should definitely take a look at his comm alg notes then

[stray veldt]

you can also check out the algebraic geometry book by Perrin

proving bezouts theorem in full generality is not that easy and this book basically sets out to do it from scratch

[indigo mesa]

I've been reading them and they motivate the connection between geometric and algebraic objects a lot

[cobalt maple]

I see. Thanks. I'll try both.

[dawn mirage]

hey guys, now that the illegal z-lib is gone, what other ways that I can get free math books, asking for legal advice kinda, been a while since I've last tried to read.

[grand thistle]

the other one is still up ||library genesis||

[orchid mortar]

From a library if your library has them. Also depending on topic it might not be impossible to get good free resources

[dawn mirage]

I see, I'll be sure to avoid that.

[dawn mirage]

Sadly, no good libraries around me .

[grand thistle]

yeah stay safe on the internet make sure not to do any illegal things

[dawn mirage]

[low marsh]

guys im new to this server and just look the doubts of other people for fun but 90% of them just seem to pass over my mind....any book which can help me cover these?

i mean i think that the language used in the questions in my country is really different from the one thats used in others..

[paper ice]

You mean the help channels?

Naturally they cover a large amount of mathematical topics so you are not going to be able to help with every unless u are really advanced

[mossy flume]

^^

If you want to learn more math, of course you're in the right place

@low marsh what sort of math have you covered thus far?

[paper ice]

I'm liking this book so far, it's a fun one

[mossy flume]

Jay Cummings has a nice Twitter acct

[paper ice]

I hope that's not sarcasm, enough things have been ruined to me beacuse of political or otherwise shady backstories, lmao

[gray gazelle]

hi

[tawny copper]

I use libgen, works fine for me

[slender cargo]

Going through Abbott's Understanding Analysis and I am appreciating this book much more than when I was in college

[remote sparrow]

https://tenor.com/view/tommy-wiseau-oh-hi-mark-hey-mark-gif-17296134

[slender cargo]

oh I heard of that book

it's like 600 pages long

a lot more motivation than usual

[remote sparrow]

nice

how is it

can't find a pdf to evaluate for myself

[foggy relic]

for analysis i like browder

[vital bane]

yea it's very nice

which chapter are you at?

[slender cargo]

Ch. 1.5 Cardinality

going through the problems in that now

fun stuff!

[remote sparrow]

could cummings be an abbott contender?

[vital bane]

abbott is more of a gentle introduction to analysis

it only covers anal in R

[vital bane]

nicee im goinf through problems in 1.2 gonna come to 1.3 maybe we can dp abbott together

[slender cargo]

[remote sparrow]

in the rectum? i mean where else would anal be

[vital bane]

[slender cargo]

gentle is what I want. I'm just self studying for fun now

[vital bane]

I'm self studying too but for becoming a serious math student one day

[remote sparrow]

but i mean is cummings similar to abbott

[vital bane]

and do stuff like fun anal, harm anal

[remote sparrow]

is what im wondering

probably true imo

[vital bane]

I found a video

let me share it

[remote sparrow]

math sorcerer right

i shared his video a couple days ago here

[vital bane]

https://youtu.be/oE3Q7EoYT4U

Lol yea

I havent watched it yet

[fickle whale]

I've read cummings

[vital bane]

is it similar to abbott?

[fickle whale]

Most of it anyways

I haven't read Abbott

[vital bane]

abbott is very good for beginners and self-learners, and I'm in the intersection of those two things

[fickle whale]

I liked Cummings but I don't have anything else to compare it against

[vital bane]

oh wait your name reminds me

dual of a geometric algebra

[fickle whale]

I'd say it's good for those two things

[vital bane]

[remote sparrow]

@vital bane have you heard of zorich

his analysis volumes have many physical examples

[vital bane]

no

[vital bane]

huh

[fickle whale]

Cummings has a lot of great jokes in it

"Great"

[vital bane]

Lol that's good

[fickle whale]

Which made it more interesting to keep reading

But also stupid stuff like

[remote sparrow]

i have a draft pdf of his proofs book. the jokes are pretty corny but some are cool

[fickle whale]

Using social media logos to number equations in a proof

[vital bane]

[fickle whale]

It's a good laugh and it makes you double check what you're reading

[remote sparrow]

cummings is a young guy too

[foggy relic]

contender for worst book in analysis?

[fickle whale]

That topic has some nuance I shan't discuss in this channel

[vital bane]

okay shall I ping you later in the bivector server?

[remote sparrow]

it's reasonable. abbott is just pitched lower than tao or rudin

[fickle whale]

sure, I can get fact checked there too. Just like last time

[remote sparrow]

doesn't make abbott a bad book

[foggy relic]

abbot is not reasonable

it is a bad book

[vital bane]

name 3 things that make it bad

[foggy relic]

name 3 things that make it good

it covers no content

[vital bane]

mfw u sound like geogristle

[foggy relic]

and its entire tiny contents can be in 20 pages

im not

[slender cargo]

? you might as well say that Rudin covers no content. might as well skip to a highly condensed paper on measure theory

[vital bane]

this

[foggy relic]

Rudin is very good

but it wasn't a good fit for me

so i used mostly pugh/browder

[vital bane]

abbott + apostol is for me 😌

[slender cargo]

if I keep enjoying this I'll do Munkres Analysis on Manifolds later

[vital bane]

[slender cargo]

will learn about metric spaces eventually

[vital bane]

apostol has metric spaces

[remote sparrow]

i doubt invictus has read cummings

but it's probably not up their alley either given their comments on abbott

[remote sparrow]

hubbard and hubbard also covers multivariable analysis. lacks some theoretical exercises since it's also meant for a rigorous multivariable calculus course (though all the sophisticated proofs are also in the appendix), but it's good.

[slender cargo]

yeah I looked into that

it seems to mix computations with proof exercises

[remote sparrow]

yep

[slender cargo]

tbh I got the feeling it was trying to do everything at once. it felt confusing

but I've no idea

[remote sparrow]

yeah you can google his two analysis books or search zorich in the discord search bar

[gray gazelle]

I read, but I have this feeling that I'll forget what I'm reading anyway

And that gives me an existential crisis

[grave thorn]

Idk whether a "highly condensed paper on measure theory at the level of Baby Rudin" exists

[gray gazelle]

Bogachev Measure theory?

[slender cargo]

I was just trying to make a point that having a lot of motivation in a book isn't necessarily bad

even if the content of the book could be fit in 1/10th the size

[grave thorn]

Rudins measure theory section is bad lmao

[gray gazelle]

Oh I misunderstood the question

[slender cargo]

yeah I've heard. I'm going through Abbott's Understanding Analysis now and I'm really liking it. another might claim that it's low level and deficient in how much material it covers, but that's okay to me

[pale quarry]

Book recs for olympiads guys?

From scratch

Just assume I don't know anything

I'm a 10 year old with no capability of articulating olympiad problems, assume that

[sturdy shore]

excluding the chapters that people generally skip in rudin (like the measure theory one), the difference in material covered between Abbott and Rudin shouldn't be so significant...

of course, how it is covered is, but saying Abbott has no content is weird af

[pale quarry]

And give me book recommendations for the math olympiads

[slender cargo]

that's the impression I had. Abbott doesn't cover metric spaces until a section near the end, but that's the main difference

[wispy timber]

book rec for levy processes?

[remote sparrow]

a possibly apocryphal story i heard about rudin was that he wanted to add more pictures to PMA but the publishers said that would drive up the costs, so he decided not to do it

and watching a rare video lecture by rudin himself, it doesn't seem like he was opposed to motivation and meeting pedagogical needs

also evidenced in the 3rd ed. of rudin, where he defers the dedekind cut construction of R to the end of chapter 1, citing that this way was more pedagogically effective, albeit not logical

[vital bane]

but remember you can just glance at what you've read to remember it, it's not like completely wiping your memory

[vital bane]

I know right

[grave thorn]

Schilling has nice notes on levy processes

You can find them on arxiv

[remote ginkgo]

LMAO

mods

[wispy timber]

tyvm

[pale quarry]

I'm 15 dude

I just

Don't know

How to do math

[hasty turret]

Articulating Olympiad problems is very easy

Solving them is not

[pale quarry]

My capabilities match that of a 10 y/o

[pale quarry]

Same difference

[remote sparrow]

articulating fermat's last theorem is easy. proving it is not. a problem statement and its solution are distinct.

[pale quarry]

Cool

How do i solve shit, in simpler terms?

[remote sparrow]

you can google evan chen. he has made some material for olympiads

though i'm not sure why you want to go into an olympiad with that sort of defeatist attitude

olympiad problems are designed to be solved in a fixed amount of time

these competitions don't take geniuses, just plenty of practice

if this is to stand out on your college applications or whatever, then i would discourage you from participating

[foggy relic]

i have not

but if you're comparing it along the lines of abbot i have little reason to think its any good lol

[remote sparrow]

i have not read cummings

i am asking if it is like abbott

cummings' style is more conversational and informal based on reviews and reading a draft copy of his proofs book

[foggy relic]

looking at the toc, it seems like the bare minimum

[pale quarry]

?¿? You can put that on your college application? I don't even wanna pursue maths I just like the challenge

I'm planning on doing law why would I put a math competition on my application

[gray gazelle]

😭 someone call the police pls lol

[dawn mirage]

Icic, thanks!

[hallow oriole]

anna's archive

note: i cannot personally verify that it is completely legitimate

use at your own risk

i have downloaded a book and virus scanned it and it came out fine

use at your own risk

be safe on the internet

[crimson leaf]

How about we don't share piracy sites on here

Probably best suited for dms

[hallow oriole]

oh yeah btw for anyone who didn't know generatingfunctionology has a legal free pdf online maintained by the author

https://www2.math.upenn.edu/~wilf/gfology2.pdf

it's a really nice book!

[crimson leaf]

Yes very thankful to upenn for hosting it this many years after his passing

[hallow oriole]

yes!!

• wilf is one of my fav mathematicians for no reason besides his book and that he helped make the calkin-wilf tree!

[low marsh]

in 10tg grade at the moment and covered algebra and geometry... functions and calculus and various topics such as limits, matrices etc still remain untouched

i mean i really want to dive very deep into math so from where should i start?

[gray gazelle]

True

[sudden dock]

you can start from a College Algebra or Trigonometry book. If you don't like books, you can go for Khan Academy

[vital bane]

do everything in khan academy calc ab, bc -> linear algebra -> multivariable calc

then a proofs book, then analysis, algebra and topology

after that you can start diving deep into math

[low marsh]

@vital bane @sudden dock to be honest..i prefer books over videos so thanks for your recommendation

[vital bane]

why not both

[sudden dock]

Now, If you are looking for an Algebra book, I would suggest College Algebra by Robert Blitzer, It's good written, the text is not very hard to understand, Questions at the end of each section are not very hard, good for improving basic concepts. P.S Don't waste a lot of time on questions, they are repeating

[hazy elk]

You can try AOPS books too

[vital bane]

"multivariable mathematics" by ted shiffrin

it has both linear algebra and multivariable calculus in n-dimensions and a bit more

[sudden dock]

.

@vital bane You can't suggest a 10th grader multivariable calculus and linear algebra

[vital bane]

spivak's calculus then

it starts off from functions and limits

[gentle arrow]

honestly i would do proofs concurrently idk

[vital bane]

I guess?

[gentle arrow]

basically a requirement to read higher math textbooks

[vital bane]

unless it's written for physicists

[hasty turret]

Actually why not do Olympiad stuff

That's a good intro for proofs, unironically

[vital bane]

putnam

[tawny breach]

Hey guys. I've spent the past half year refreshing myself on Algebra 1-2, Trig, Geometry. I'm now looking to get into calculus. After a bit of research it seems many people suggest moving past pre-calc, directly into calc 1. I'm not looking to rush my learning would this be advised? and if so what calc books can anyone recommend to start with as there seems to be a lot of options?

[gentle arrow]

good algebra/trig skills pretty much allows you to skip precalc

[hazy elk]

I think if I had a choice as a highschooler, I would probably read Axler and Abbott

[hasty turret]

I guess AoPS is a good starting point

[low marsh]

Actually my concepts for algebra and quad eqn are pretty solid so I'm looking looking for a book that has questions which require high thinking

[grand thistle]

ive seen people recommend serge lang's "Basic mathematics"

[low marsh]

i did solve aops questions available on their website (i know those questions are different from the books your referring to) when i was preping for olympiad so...yeah i did like the difficulty of those questions

[sudden dock]

Watch this video https://youtu.be/OmJ-4B-mS-Y

[low marsh]

Ok now im noting all these books and imma try them all to see which one fits the best

[low marsh]

Ookay.

yea i watched it... i think im only aware of the numerical mathematics and that too...only around 40% knowledge of each topics..

[gray gazelle]

Ted Shiffrin

[low marsh]

i think the book he was talking about is called multivariable calculus and not multivariable mathematics right?

[sleek canopy]

godel escher bach is a thinking man's book

[remote sparrow]

hubbard and hubbard's multivariable calculus book is also good if you want a hard copy that's cheaper than shifrin

[random roost]

It would be nice to have books recommended here be cleanly organized by topics over at https://learnawesome.org/

[vital bane]

[vital bane]

no no it is called multivariable mathematics, it's called that because it teaches you linear algebra and multivariable calculus (in n-dimensions a.k.a in R^n) cocurrently, ted shiffrin says that's how it should be taught, which I kind of agree with

[low marsh]

ah i see..my bad

[gray jungle]

Whats a topology book with cool exercises

[gray gazelle]

Engelking's General topology has cool exercises

[hazy elk]

How are the excercises in Dugundji like?

Is it too terse for a first read?

@gray gazelle

[gray gazelle]

well I didn't say you should read it, but the exercises are cool

[hazy elk]

Oh I thought it was your canonical suggestion for a general topology book?

You're talking about Dugundji right

[gray gazelle]

ah no. It's reference text and it's hard

and terse

[gray gazelle]

yes but it's still challenging to read

even though more relaxed than Engelking

that's why for example Munkres created his books, as an introductory text to oppose the existing ones

to be more introductory

I recommend starting with something about metric spaces tbh

[gray gazelle]

oh wait.

I thought you were talking about Engelking, I misread

[gray gazelle]

exercises are okay but they can be a bit boring imo
I don't think it's too terse, but it's probably better to start off with something like metric spaces

[hazy elk]

I see, even the ones in Munkres are kinda boring no?

[gray gazelle]

I think so. I guess there's not much fun in doing exercises from topology unless it's something harder than usual

[vital bane]

infinite dimensional point set topology then

[void pasture]

Is there a book or guide on trigonomtric functions and identities aimed at first year uni students? My book only covers sin, cos, tan, sinh, cosh, tanh and some of their identities. For instance, today I was challenged with the integral $\int{\frac{1}{\sqrt{1+x^2}}dx}$ which was solved by using the identity that $1 + \tan^2(x) = \sec^2(x)$, which my textbook does not cover, it doesn't even cover sec(x)), yet there have been several integrals that can't easily be done using these identities that it does not cover. On a side note, the identity are easily derived based on the content htat the book has provided, but it doesn't help when I get questions like this where knowing the identities straight up helps a lot

[hasty eagle]

Chippotle Maths

[gray gazelle]

that exists already

well, infinite-dimensional topology exists

[lapis sundial]

tbh you might be better served just by looking at trig substitutions

[remote sparrow]

csc = 1/sin and sec = 1/cos. (sin x)^2 + (cos x)^2 = 1. you can easily derive 1 + (tan x)^2 = (sec x)^2 by dividing through that identity by (cos x)^2. you just need to remember what csc and sec mean.

you can look at paul's online math notes for trig and his trig cheat sheet if you need it

[willow pecan]

It's fine

[void pasture]

Thank you, Sour Drop. I'll check Paul's notes now. I wish you a sweet day, Sour Drop.

[remote ginkgo]

tychonoff product

[remote sparrow]

https://mirtitles.org/

https://archive.org/details/@mirtitles

https://twitter.com/MirTitles

the person running the blog archives some soviet-era math books published by mir

[fierce hedge]

We used to have maths seminars using Mir titles. Good books

[fierce hedge]

Also, is it just me or is everything in French for some reason?

[remote sparrow]

just recent blog posts indicating a french copy of a mir book has been uploaded

gotta scroll down

a very small number of titles is texified

mainly the physics titles

[neon tiger]

need a book on geometry with ques going from easy olympiad level to very difficult ques

[remote sparrow]

evan chen wrote a book on olympiad geometry that could help

[brave yew]

i'm going through paul eccles introduction to mahematical reasoning

what books should i go over next to further mathematical maturity?

[steady orchid]

war and peace

is gud book

[brave yew]

did that one 2 weeks ago

what else?

[steady orchid]

48 laws of power

oh wait u want books on math?

[dense glen]

Yes it is good book

[remote sparrow]

You can go anywhere you like once you've finished an intro to proofs type of book. An intro to proofs course is somewhat like an English composition class, a class primarily to learn how to read and write effectively. You may be assigned some light readings to respond to, but the substance of the content is given less attention than in how you respond to it. So after finishing an intro to proofs book, you should move on to studying topics more deeply, keeping in mind how to communicate your ideas with appropriate rigor. Given you mentioned that you failed real analysis twice, you can choose to postpone it for something else if you'd like to build more confidence. However, gentle books on real analysis could be those by Abbott or Cummings. Maybe you could do linear algebra, elementary number theory, or combinatorics.

[brave yew]

i've gone over the topic, it feels like i'm not qualified

it's the difference between going over an intro to proofs class and going through a weeder class

being able to say, read HOTT comfortably is different than reading an intro to proofs book

[remote sparrow]

Well, I've heard a lot of praise for Cummings, and I'm wondering if I should add it to my library. $15 seems like a pretty reasonable price, and I'd love to hear a review from you if you feel like you succeeded with it.

[brave yew]

so this?

https://www.amazon.com/Proofs-Long-Form-Mathematics-Textbook-Math/dp/B08T8JCVF1

i mean i have polya, but math books are traditionally so concise

[remote sparrow]

cummings' real analysis book

but you can pick up his proofs book if you want

i liked reading a draft copy i found on the internet

That said, you can go wherever you want after finishing an intro to proofs book. You do not need to keep reading these books if you can competently complete them, and you should not stay stuck there. If needed, you can always turn back and review these books. But there is no royal road to science; you have to struggle with the material. Mathematical maturity is not built by idling on introductory material (not to be confused with revisiting material from a fresh or more advanced perspective); it's by actively engaging with new ideas.

https://www.amazon.com/Real-Analysis-Long-Form-Mathematics-Textbook/dp/1077254547

Failing twice is not an indication that you can't gain mathematical maturity. Part of maturing is failing. There are all sorts of reasons people can fail a class, and it is almost never, if at all, because they are inherently stupid. You can succeed.

[orchid mortar]

fml I failed at my econometrics class because I can't math stats and linear algebra properly

[formal kernel]

its okay bro

[shadow magnet]

Guys pls help me with this h\w

I don't get the concept

Oh ok

[grand thistle]

has anyone tried halmos's "Linear Algebra Problem Book"? I'm looking for a mostly problem based book that will drill into my head a lot of the linear algebra i forgot

[mystic orbit]

LOL

@ TTeppa

Can you elaborate btw?

I'm bored so I was looking at the pins

Wanna chess?

Bruh

Turbo nurd doesn't know chess?

Wtf

I should prolly ping Nami if I want an answer lol

But he mod so

W/e, I'll ask later

I wanna know why doe

Especially since tterra swears by the book

Ye, everyone knows rudin goes to shit after chapter 8

Some stop at chapter 7

Got incredible exercises tho

It's the book i was using before taking a break

Lmao

Yeah, the proof for the inverse function theorem was fucking despicable

[minor knot]

[sage python]

Yohan's assessment is likely correct. I haven't gone in detail through Spivak for differential forms but since the book is short in general it's likely on the quick end.

Rudin's proof of inverse function theorem I thought was fine no?

Like Rudin chapter 9 overall is a bit awkward, like he sorta does this thing where he includes the bare minimum of linear algebra he needs within the chapter and... eh

[fierce hedge]

How's apostol compared to Rudin?

[sage python]

But Rudin chapter 10 indicates to me that Walter Rudin did not understand differential forms

Probably fine?

[vital bane]

what is the dummit and foote equivalent for analysis?

like a huge 1000 page analysis reference book starting out from intro analysis and going to more advanced topics like diff geo(yes not exactly analysis), measure theory etc.?

im just curious if such a thing exists

[stray veldt]

amann escher

[vital bane]

oh I see it's split into 3 books?

[stray veldt]

yes

[vital bane]

okay thanks

[placid pollen]

I know a 5 book series, I will tell you later since I can't remember

[vital bane]

simon?

"a comprehensive course in analysis" by barry simon? ryc and slurp (or gmod) or someone else were talking about it a few months ago

[placid pollen]

No that's grad analysis damn looks good tho

[scarlet steeple]

what is the best abstract algebra book out there?

[gray gazelle]

opinion based

[sudden thorn]

guys
can anyone Suggest me a combinatorics book?(I want it to prepare for AMO)
(I totally mastered the basics and rn I am looking for problems of a similar level to the jbmo)
But most of what I found The author does not explain the motivation that helped him solve the problems

[vital bane]

but yea there's no absolute "best" it's subjective

[heady ember]

Dummit and Foote more like damnit it thick

[placid pollen]

My plan is this. I would get an easy intro and applications book and a grad level exposition. Thomas Judson for the first (currently using for undergrad, but the professor uses others), Lang's Algebra for the second thing. So undergrad intro and grad reference, then if you're interested in a particular topic, you grab something about that particular topic and check Lang as a second view or summary on the same topic. If you feel lacking severely in a particular undergrad topic you check the undergrad book to get a warm up.
Dummit and Foote as far as I know covers both purposes, which is why I'm not interested in it. A book should serve only one purpose if it's going to sit at my book shelf, otherwise I have internet

[scarlet steeple]

why? is Langs Algebra not sufficient as a main text?

I was going to do an intro book and then use langs book for more advanced alegbra

[placid pollen]

You can try, it's probably the only algebra book you will need. It's just that if you feel tired or don't want to put in the time of checking by yourself, because his exposition is brief, then maybe you need motivation from an undergrad course to be seriously interested.
And by "motivation" I mean knowing specific algebraic structures and examples which are elementary. In Lang's algebra I've seen him use analysis examples which you might not know so the example wouldn't land as enlightening yet

So I'm not saying just algebra books are gonna land you in Lang's algebra, you need some grad analysis to realize why some algebraic structures are cool. (Banach algebras? I'm out of my depth here. It's just the way I see it as an undergrad)

[scarlet steeple]

Ok I see interesting...

like how much analysis

i know real analysis

up too real analysis*

do i need functional, harmonic e.t.c?

[placid pollen]

Inspiration from functional analysis a little, but not strictly needed since you're going to work the algebra rather than the topological or analytical properties; harmonic it's actually something people study once they get the basics of grad algebra and analysis. Topology, Analysis and Algebra are usually the main courses you take at the same time in grad school because each one appears as an example or inspiration for the other, they are very related to each other.
I mean first semester is usually real analysis, algebra and topology afaik, so you can get the basics of algebra without the other two, but it's assumed you took undergrad courses about the other two.

[scarlet steeple]

@placid pollen thanks for all this advice, ill put it to good use

[icy knot]

I’m going to go against the grain and offer Hoffstein’s Mathematical Cryptography book. @scarlet steeple

[pine sun]

Some good Analysis 1 books?

#books-old

[broken meadow]

#books should have a few too

(pls send me reviews)

[crimson leaf]

Guichards book is free and isn't hard if you want something more difficult you could try Bona walkthrough combinatorics or combinatorics graph theory by Harris et all. If you really want a challenge there's Stanley but afaik that's usually a first grad level course in enumeration

[sudden thorn]

thnxx

[remote sparrow]

https://www.youtube.com/watch?v=2hgqiU9tg2c

[icy knot]

Glad to see Professor G getting recognition. #The Math Sorcerer Amazing instructor!

[remote sparrow]

you had a class with him before?

[turbid pasture]

:))

[sudden dock]

Doing Seeing and Understanding Geometry.
~ Harold R. Jacobs

Is this book any good? Is geometry worth 700 pages? My goal is to be able to do competition level problems.

[fluid bay]

i think the standard geometry text for olympiads is evan chens book

"euclidean geometry in mathematical olympiads"

[sudden dock]

even though Evan Chen mentions that there are no prerequisite for reading his book but I have read some reviews which say that its better to have some basic geometry knowledge before reading Evan Chen's book.

so I'm a little bit confused now

[gray gazelle]

two pages aren't equal

one might take you a minute

another an hour or two

[sudden dock]

I didn't understand.

[icy knot]

Yes. I took calculus and differential equations with him. Professor Gabilondo.

[vagrant sedge]

Hi. What is a good book that has chapters talking about open sets of regular boundaries (like Lipschitz boundaries, C^1 boundaries, etc), Green's theorem, and things like that?

[fringe kayak]

Hi,

I have to pick a general topic for a year three of bachelor's projet.

I've been particularly interested in the Commutative Algebra and Galois classes I've taken. I Also particularly enjoyed differential geometry and its applications on topology via the Poincaré-Hopf theorem, although I have not fully completed this class yet.

These classes were very introductive and the project's goal is to allow me to dive further into one of them 💕

In Commutative Algebra I've read about flatness. In Galois I've loved Galois's transcendant extensions but I also started reading about differential fields ; while the topic seemed quite complicated I found very exciting the idea of bringing differentiation into algebra.

I would like to hear about your opinion as an Algebra and Geometry enjoyer, of what you think would be an interesting general concept of study for my project. And if you have any books/editor that have made you love those topics 🙂

I think I would love to see how commutative algebra and Galois could do when put together but I'm not sure they can come together

[gray gazelle]

Make a logical argument before pinging me thrice. You’ve communicated 0 things in English that are worthy of being interpreted.

[orchid mortar]

Keep your wars to DMs

If you have nothing positive to say

Say nothing

[gray gazelle]

Which is what I have been doing in the ~2 weeks you have been seething over my message.

Ok.

[orchid mortar]

You can try #math-discussion and actually the advanced topics channels instead. I don't think #book-recommendations is the right place for this

[fringe kayak]

thanks for your advice, i hope copy pasting my message won't spam

[orchid mortar]

It isn't but uhh, don't get your hopes up for replies I think #groups-rings-fields is the relevant advanced math channel but don't tell them I sent you because I know 0 pure math

[remote ginkgo]

ur a freak dude

[gray gazelle]

Evan Chen’s Euclidean Geometry can be read by anyone with eyes that are capable of reading this message.

[remote ginkgo]

evan chen is not good

because he didnt practice enough or spend time on interesting topics

bad parenting ig

[gray gazelle]

This is not about his napkin book. Basic comprehension skills would have told you that. IMO Gold is enough of a feat to show that he practiced enough Euclidean Geometry.

[remote ginkgo]

nope

[remote ginkgo]

once again as always u completely miss the point

[gray gazelle]

As always? I do not know you, and I forgot you exist until I saw you mentioning me.

[remote ginkgo]

well, i'm afraid that's not true

who cares

the question should be whether the pedagogy is good

[gray gazelle]

Jech “Set Theory” can be read profitably by anyone who can read

The ZFC stuff gets a bit hairy, but the good student can read it with basic proof knowledge.

[gray gazelle]

I doubt you can go from proofs to P Adic Hodge Theory

[gray gazelle]

Your other recommendation is a bad recommendation. Use Munkres.

[gray gazelle]

This is a biased roadmap. It’s whatever though, I do not care.

[mystic orbit]

dude can't write two words without sass jeez

[gray gazelle]

I would recommend doing very difficult integrals as found on the stack. You can find them on the stack exchange, past Putnam or MIT Harvard competitions, and graduate Physics textbooks.

A good book would be Boas’s book for Engineers and Physicists.

Then doing the “math methods” version for physics fields if you want to be an “integral master”

[gray gazelle]

Good recommendation for once +1

[orchid mortar]

[sturdy shore]

he is blessing us, the pedestrian mathematicians

[gray gazelle]

If you wish to quickly dive into Hartshorne, just use Atiyah. Eisenbud makes elliptical insinuations on what is elementary and what is required from a CA book, it is the Vakil of CA books, except, unlike Vakil, it does nothing well.

[mystic orbit]

what's a good intro to algebra book btw?

[gray gazelle]

D&F or Artin (if you have not seen Linear Algebra or you are not confident). Mostly DF, but Artin is for high schoolers to first year undergraduates.

Otherwise, I would argue that I dislike the concrete approach by Artin, when looking back

It still works though.

I have never read it, unfortunately.

My friend has learned Algebra from it, and she knows her stuff

So I’m sure it is usable

[mystic orbit]

how about aluffi?

I saw it mentioned a couple of times

[gray gazelle]

I’ve actually learned Category Theory before I learned any other pure maths, so I didn’t see the need to read something like this

I didn’t check anything it

[slender cargo]

wtf is going on

[mystic orbit]

I see

[gray gazelle]

The only Algebra books I’m familiar with are: D&F, Artin, Lang, Bourbaki and that is the order I recommend them, although some nuances are lost with this simplistic orderings which I will elaborate below 👇

[fallow cypress]

I'm fond of both D&F and Aluffi

D&F is a classic

[gray gazelle]

D&F is great for the motivated student who wants fun, engaging problems on strictly Abstract Algebra, and it is a good encyclopedic reference. Out of all these books it has the best basic Algebra & Galois Theory.

Artin. The first book I learned Abstract (& Linear) Algebra from. I’d say the problems are just right below D&F due to the nature of them, but he does fun things with matrices and has a novel view. I recommend this to any highschooler who knows proofs.

Lang. The first step into chaos. My third book on Algebra. The text itself was easy enough, pretty succinct and gets a lot done. However, the exercises are beyond boring and, although nontrivial, felt forced. I learned Homological Algebra here as I worked through Weibel’s Hom Alg book.

Bourbaki. Do not read this book. You will die. I knew infinity categories, 4x algebra courses, and I still found it weird with notation and style. I’m not sure who this book was written for

[hazy elk]

Even Hatcher thinks Munkres is a pedestrian treatment, Dugundji ftw

[gray gazelle]

Hatcher’s AT is the definition of Pedestrian.

May’s AT book is much better

Especially if you include both volumes, it covers much more

[indigo mesa]

They just have different approaches

Hatcher is better for people who haven't had a first exposition to AT imo

[gray gazelle]

Honestly, I think Hatcher didn’t work out for me because of the groundwork I did before even approaching it

I didn’t do the classical Algebra + Topology —> Alg Top roadmap

I still used Hatcher for simplistic viewpoints on things May finds nontrivial, but he is too Russian in writing style if that makes sense

[indigo mesa]

It does make sense to me, and i agree but i disagree with generally calling may a better book

[viral roost]

everyone, bourbaki set the standard for basically every mathematics book in existence

its role is historical, whether you should read it is another discussion

[indigo mesa]

Hatcher is a lot more approachable

as a first AT text

[viral roost]

the lie groups and lie algebras volume still holds up

[gray gazelle]

For sure. For reference I knew AG & Higher Topos Theory before AT, so that definitely might have played a role in why I was annoyed with his writing style, so I redact my original statement because it’s not fair I judge it as pedestrian because it wasn’t written for someone with the background that I had

[fallow cypress]

anyone have recs for papers on stochastic blockmodeling

[viral roost]

how does that work, the HTT book relies heavily on knowledge of simplicial sets and results from AT like classifying spaces

[gray gazelle]

I knew simplical sets, but not AT.

[fallow cypress]

I'm trying to figure out where to start learning about it

[gray gazelle]

I went from ordinary category Theory to simplical sets & model category to infinity categories to higher topos and im currently on higher algebra

[indigo mesa]

Well yeah with these prerequisites the groundwork in Hatchers book becomes fairly trivial i suppose

[indigo mesa]

AT?

[viral roost]

stochastic block modeling probably

[indigo mesa]

Oh i didn't see that message

[viral roost]

Hatcher often dominates the reccs, I'd like to present some alternatives so people know they exist:
Bott and Tu differential forms in algebraic topology
Rotman algebraic topology
Munkres algebraic topology
Whitehead elements of homotopy theory
May a concise course in algebraic topology

[gray gazelle]

Learn any algebra you need while doing Calculus

[viral roost]

from what little I've referenced of Brown's topology and groupoids it's also interesting

[indigo mesa]

Bott and Tu as a first AT course?

[viral roost]

well yeah, it teaches poincare duality, char classes, homotopy theory, spectral sequences

if you manage to get past the intro

[indigo mesa]

Maybe add Tammo Tom Diecks text

[gray gazelle]

If I ever want to review elementary algebraic manipulations, I would do impossible integrals.

[viral roost]

AT is inspired heavily by differential forms and electromagnetism

so you can come up with explicit calculus representatives of AT invariants

that's also why physics produces so much AT, even currently with TQFT

[indigo mesa]

It has a lot of great content i agree but i'm not sure if i would recommend this to someone who hasn't done any AT

[viral roost]

why not

it is just calculus

it doesn't assume any AT at all

[indigo mesa]

But my opinion there is limited tbf i only read small parts of it for the seminar report of a friend

[viral roost]

well consider reading more of it

if you are familiar with the subject it shouldn't be a huge time investment

[indigo mesa]

It's not quite what i'm interested in rn but i'll probably get back to it at some point

[gray gazelle]

To learn Physics just open any book on QFT and do all the exercises.

Prerequisites: Advanced Quantum Mechanics, Advanced Math Methods, All of Undergraduate Physics

[viral roost]

are you for real

hard to tell

[gray gazelle]

I recommend Zee for a more elementary outlook. I recommend Schroeder for a legitimate course, and Weinberg if you want to get your feet dirty

Admittedly, I did not do Weinberg because I am not a mathematical physicist

[cinder trellis]

Shrooberry is the sully meme in the flesh

[viral roost]

Everything he just said is wrong lol

[gray gazelle]

How?

Ahlfors Complex Analysis

Honestly, if I had to pick one book to give you, and no other book, it HAS to be Gritth Harris’s book.

Honestly, I think brilliant.org is better than khan for developing problem solving

[dense seal]

Anyways this has been fun, but please stop giving advice... You've clearly followed a highly nonstandard path through mathematics. this path is not only extraordinary narrow but potentially discouraging to younger inexperienced students so we will not condone it.

[gray gazelle]

I got introduced to Mathematics via Mac Lane Saunders “Categories for the Working Mathematician”, but my best friend read “HoTT” and he is more in love with maths than me. Any foundations book is fine.

[gray gazelle]

So I’ve been skimming through intros and such of most of which I was given and so far yours has actually been the clearest intro lmao

[hasty turret]

Wait this is not a meme?

[cinder trellis]

“I’ve seen some terrible recommendations by people who have no credentials to give those recommendations. This is a rather pedestrian discord for pedestrian mathematicians it seems.” -Shrooberry

[gray gazelle]

Thank you

I really like how he sets it up for complex Algebraic Geometry

[mystic orbit]

this has to be pin worthy

[gray gazelle]

After Griffiths Harris, you can get to the cool stuff

Like Voisin’s book

[restive falcon]

not here

[sturdy shore]

definitely here

[cinder trellis]

Shrooberry the type of person to numerically label their cereal so that they can eat them in an arithmetic progression

[restive falcon]

they probably don't know what that is

[gray gazelle]

That’s all recommendations I have today, I have to get back to work

👍

[mystic orbit]

👋

[restive falcon]

specifically because it looks like actual advice

[cinder trellis]

RIP whoever your boss is lol

[sturdy shore]

it is funny how he said the good student can read Jech - Set Theory with basic proof knowledge and everyone skipped over it like that is a normal thing to say

[hasty turret]

What's the difference between a "normal" mech book and a "math methods" book

So do you just add rigor in the latter?

[restive falcon]

math methods is not mechanics lmao

[remote ginkgo]

hi heliogristle

i get the pun and i dont like it

no

[orchid mortar]

The introduction textbook was meant I suppose?

[restive falcon]

we finally meet

[hasty turret]

airgristle

[remote ginkgo]

at last

aquagristle where

[gray gazelle]

Math methods in classical mechanics is a springer textbook. I am not sure if the PDF is legal, but it exists.

[sturdy shore]

I am very confident that is not the one they meant

[remote ginkgo]

that books good shrooberry

u got some good recommendations

[gray gazelle]

It is

[remote ginkgo]

some.

[orchid mortar]

Well it goes in with the flavour I suppose. Just ask people to read the absolute latest

[remote ginkgo]

im looking for a cheap place to buy arnolds Dynamical Systems IV

if you know somewhere

amazon is over $100

[gray gazelle]

No, I meant the graduate textbook.

[hasty turret]

So a math methods book won't teach me mechanics?

[orchid mortar]

[remote ginkgo]

wrong

[orchid mortar]

Why do you want to be taught mechanics

[hasty turret]

I mean I want a rigorous formulation of mechanics and I just want to know if math methods is supposed to be that

[remote ginkgo]

it is

the book shrooberrys talking about is what you want

[restive falcon]

i would advise you not to listen to anything geogristle, ker, or shrooberry says

[orchid mortar]

I think any analytical mechanics textbook should be rigorous enough for their needs

[remote ginkgo]

dont listen to heliogristle they literally obsess over antagonizing me

arnold is a master

yep

the pictures are great

[viral roost]

arnold is the foremost classical mechanist in history

[remote ginkgo]

yea a bit

yep

[hasty turret]

I see

[remote ginkgo]

its not hard to follow him though

[viral roost]

he created symplectic geometry

it's his

[remote ginkgo]

the hardest thing he will say is something like

[viral roost]

he's also very geometric, lots of pictures

like his ODEs book

[orchid mortar]

so now I know who to blame for all this symplectic manifold nonsense on Wikipedia

[gray gazelle]

Almost any book for Arnold is a banger.

[remote ginkgo]

"newtonian laws are invariant under action of the galilean group"

if you know what a group action is, ur fine

u will be ok.

[viral roost]

or if you can write down the matrices of them

[hasty turret]

I see

[remote ginkgo]

^

do not EVER listen to heliogristle

they exist to stifle us

[hasty turret]

I know

[orchid mortar]

This sounds like Landau but worse

[remote ginkgo]

it is

but it is more explicit about the mathematical objects

[dense seal]

.pin

[restive falcon]

you know i have a life outside of mathematics

[viral roost]

also why am I on that list

[remote ginkgo]

i do too

[viral roost]

he seems like he doesn't but it's all rigorous

[remote ginkgo]

you just got cancel cultured

[viral roost]

bruh

ally literally doesn't know anything

[remote ginkgo]

ik

lol

[steel viper]

Drake what is your mathematical background

[hasty turret]

Linear algebra

[flat lantern]

came to watch the circle jerk

[steel viper]

and physics background

[hasty turret]

And abstract algebra

[gray gazelle]

I think Landau Lifschitz would serve as a good course in Classical Mechanics.

[remote ginkgo]

im here to rotate the circle jerk and observe its symmetry

[restive falcon]

moth thank fuck you're here

[slender cargo]

[remote ginkgo]

^ this is an unsocialized behavioral activity

[slender cargo]

these recommendations

[forest sleet]

Math methods is probably like Bender Orszag, not a specific physics topic

[remote ginkgo]

just get arnold its good

[forest sleet]

for classical mechanics you can try Arnold's classical mechanics (should probably be on SpringerLink) or Spivak physics for mathematicians

[hasty turret]

Physics ,I am familiar with Newtonian mech

[remote ginkgo]

not spivak

[hasty turret]

I have no idea what else exists

[remote ginkgo]

spivak is a strange man

@hasty turret arnold tells you basically everything

[gray gazelle]

After Classicsl Mechanics, I recommend dipping your toes into Sakurai’s QM books.

[remote ginkgo]

u can read landau 1 simultaneously if u want

[flat lantern]

if you're reading books rather than papers then you will never learn anything

[remote ginkgo]

wrong

[hasty turret]

I mean I know what group,group actions,rings and ring actions are

[gray gazelle]

I pick up new books because I don't want to read what I already am reading

[flat lantern]

journal articles are acceptable but you're on thin fuckin ice

[gray gazelle]

I don’t recommend this at all.

[slender cargo]

if you're not learning things in complete generality then what are you even doing

[remote ginkgo]

ok, this has gotten stupid

i'm out

[flat lantern]

call me the moon lord cause there's some lunatics in here

[gray gazelle]

How are you supposed to learn from papers without doing books?

[orchid mortar]

Shrooberry do you have an econometrics recommendation

[steel viper]

Landau is probably fine from what ive seen

[hasty turret]

Ok,ig I will try Arnold

[steel viper]

With arnold i think people often recommend an intermediate mechanics course beforehand but ymmv

[remote ginkgo]

arnold is a good supplement for landau

[hasty turret]

If it's too hard, I will do Landau

[remote ginkgo]

bc it makes explicit some things

i think landau is a bit harder than arnold

bc u have to actually think about the physics

[hasty turret]

Learning mech for fun

[forest sleet]

quantum mech is fun

[gray gazelle]

I think no undergraduate physics textbook is worth looking at

[orchid mortar]

🧐

[slender cargo]

..............

[orchid mortar]

My econometric request was denied

[steel viper]

coincidentally i think the same except about your messages

[hasty turret]

Latter

[flat lantern]

I agree. I recommend watching "SciShow" videos for physics knowledge and revision

[hasty turret]

I know there exists Lagrange shit. I have literally no idea what that means

[restive falcon]

i would instead recommend not doing physics

[gray gazelle]

it means you study physics using Lagrangian

[orchid mortar]

IDK if this is supposed to be troll but I really like Action Lab's vids

[remote ginkgo]

just read arnold

its piss easy

focus

[hasty turret]

Wtf are there a million mech books

[gray gazelle]

Goldstein has some very annoying exercises.

and Hamiltionian mechanics means you study physics using Hamiltionian
easy

[remote ginkgo]

yes, theyre all bad except arnold and landau

[gray gazelle]

^

Geogristle has good takes sometimes

[remote ginkgo]

i always have good takes

[indigo mesa]

[remote ginkgo]

🏌️‍♂️

no refutation, just angry emojis

smh

[indigo mesa]

I'm just enjoying the show

[restive falcon]

you literally recommend lang algebra I don't have to give justification

[remote ginkgo]

?

whats wrong with that

[dense seal]

your takes are extremely narrow and pointed to one particular branch of mathematics and one particular application of mathematics

[remote ginkgo]

how

i really dont think thats true

[remote ginkgo]

if u could give me some real constructive feedback i can fix it

no we are discussing the meta aspect of book recommendations

[gray gazelle]

this is an equivalent of a burning trash can

[restive falcon]

for example, you include almost nothing related to logic on your reading list

[remote ginkgo]

yes a burning trash can containing dummit & foote

[indigo mesa]

nice hat blitz

[remote ginkgo]

wut

[flat lantern]

I agree with gristle on this one

[remote ginkgo]

my reading list is not "for the general mathematician"

[gray gazelle]

thanks, you too

[viral roost]

if helio could stop harassing and gaslighting us that would be great

[flat lantern]

you guys can't just claim something's bad without explaining why

[indigo mesa]

thank you

[hasty turret]

Who is your reading list aimed at?

[steel viper]

harassing
gaslighting

[orchid mortar]

can I ask for econometrics recommendations

[gray gazelle]

Learn Differential Geometry from the latter two of the Lee series and “Riemannian Geometry and Geometric Analysis”

[remote ginkgo]

mathematically-heavy engineering & dynamics adjacent ppl

[flat lantern]

getting gaslit by a highschooler
intellectual giants

[remote ginkgo]

im pretty sure they have been a highschooler for 10 years now

[flat lantern]

true...

[gray gazelle]

Lee’s book is rather rudimentary, so if you finish it quickly then ask me again for my secret collection of DG books.

[remote ginkgo]

lee is bad

[restive falcon]

[orchid mortar]

of all things I didn't expect #book-recommendations to become #chill

[flat lantern]

I agree with gristle on this one

[gray gazelle]

I agree

[flat lantern]

I disagree with shrooberry on this one

[gray gazelle]

If he just wants something demotivated to learn General Relativity, that is easy and quick though

[remote ginkgo]

same

lol

[restive falcon]

i cannot believe you continue to allow yourself to be trolled by a 16 year old

[remote ginkgo]

your words look the same as an 80 year olds

[steel viper]

Lees smooth manifolds is quick?

[gray gazelle]

Learn PDES. I recommend Evans book, but others recommend Taylor’s 3 vol series.

[forest sleet]

I like Lee's smooth manifolds

[remote ginkgo]

i hate it

[dense seal]

exactly, but you no where acknowledge this, instead you pass off your list as being "the fast track" for mathematics, when there is a painful lack of combinatorics, tcs, advanced topics in ring theory, probability & statistics, etc.

[forest sleet]

nice reference for differentiable manifolds

[slim nacelle]

Lee has a lot of issues

[remote ginkgo]

we chose to omit certain things on purpose

the intent is not to be comprehensive

[gray gazelle]

you mean errors? Those are just on the pirated copies I'm pretty sure

[steel viper]

Lee is like

Very wordy

[slim nacelle]

Lee is the Vakil of DG

[restive falcon]

your words look like they've been thoroughly checked to make sure they're contrarian enough

[steel viper]

I think the reality for most physicists is that they hack in the diff geo needed as they go and then backfill with increasing rigor later

[remote ginkgo]

well if you dont have anything non-straightforward to say

why say anything

[steel viper]

like

[gray gazelle]

“Curvature in mathematics and physics” is another decent one

[hasty turret]

Ok,I guess 2nd stage is where I am at

[steel viper]

if you're goal is just to learn the requisite diff geo for GR

[hasty turret]

Thanks

[forest sleet]

for GR there is O'Neill semiriemannian geometry

and Wald

[steel viper]

why not just read carroll or wald

[slim nacelle]

imo Tu's differential geometry is maybe better if you're looking towards GR

[remote ginkgo]

sternberg

[gray gazelle]

https://www.elsevier.com/books/semi-riemannian-geometry-with-applications-to-relativity/oneill/978-0-12-526740-3
I was going to mention this

[steel viper]

is this the intro to manifolds book

[restive falcon]

so you waste time reading my messages

[steel viper]

or does he have a separate diff geo

[gray gazelle]

Yes

[dense seal]

you have not addressed my main concern. you litterally claim:

Whether you are a student in STEM, an industry professional, or an academic researcher, the knowledge we emphasize will elevate your capabilities to new, otherwise unreachable heights. We seek to curate pure-mathematical resources that have been historically demonstrated to have real-world ramifications
And yet these other fields of math have real-world ramifications. You present your list as the end-all-be-all but that is excruciatingly not the case.

[slim nacelle]

"Differential Geometry (Connections, Curvature, and
Characteristic Classes)"

[steel viper]

i see

[gray gazelle]

Sternberg’s Curvature book is top tier.

[remote ginkgo]

thats not on the same page

[remote ginkgo]

:/

we have a discord where we talk about other topics

that arent on the list

the list isnt that...

this is a strawman

[dense seal]

I know you banned me from it for talking about other topics

[gray gazelle]

What list?

[restive falcon]

the only other thing on the website is the fast track

[remote ginkgo]

i didn't ban you

[steel viper]

personally if i spent all my time arguing with high schoolers about book recommendations and losing i would simply stop running a math themed cult but idk thats just me

[remote ginkgo]

it is, but wasn't

[flat lantern]

weak grindset, moth

[remote ginkgo]

^

absolutely pathetic

[gray gazelle]

gristle i was hoping that as someone else who enjoys differential geometry you'd be a little more based than this

[remote ginkgo]

than what

[restive falcon]

wow you are still responding to my messages I'm impressed

[remote ginkgo]

im petting my dog

im just unphased really

ppl get mad i exist

[steel viper]

i dont think anyone cares abt ur existence in the abstract

[gray gazelle]

lets follow the channels topic next time, aight?

[steel viper]

they just get mad that ur annoying

[flat lantern]

keep yo head up high king....

[remote ginkgo]

i find you annoying, moth

what now?

[restive falcon]

I'm not mad I'm just wasting your time

[remote ginkgo]

you gonna keep being nasty? mean?

huh?

[flat lantern]

fight fight fight fight

[gray gazelle]

Stop disturbing this channel and move to a more pedestrian channel

if you guys want to argue, do so about books and their recommendations please

#chill

[steel viper]

and that u misrepresent mathematics in a way that could probably actually harm someones math education if they get duped into following ur """"fast track""""

[flat lantern]

A MORE PEDESTRIAN CHANNEL

LMFAOOOOOOOOOO

[remote ginkgo]

you are being willfully ridiculous

[restive falcon]

who is the maths cult leader here

[flat lantern]

I agree with gristle on this one. Logic stinks.

smelly

[viral roost]

what exactly is the cult

[gray gazelle]

@dense seal can you calm those people down please

[viral roost]

shut up and read?

[gray gazelle]

maths cult?

i'm interested

[bold knoll]

Thanks!

[restive falcon]

hi ker how's the cult

[gray gazelle]

No problem!

[viral roost]

I don't know I just read

haven't talked to them

[gray gazelle]

If you finish it quickly, then let me know so I can introduce you to some more rigorous books.

[restive falcon]

sheafification

[remote ginkgo]

now i see what ur doing

[flat lantern]

my favourite STEM cult is "kurzgesagt" I buy all their calendars and I'm building a little shrine to the bird

[remote ginkgo]

ur procrastinating studying for your finals

[zealous light]

I think a concern people are having is the ambiguity on your anticipated audience for your list. I’m not really at liberty to say anything about the validity of the list or anything, but the definition of “mathematical scientist” on that page may not strictly mean someone interested in math physics like it seems the fast track is suggesting people learn

[remote ginkgo]

shameful, heliogristle

[flat lantern]

I'm procrastinating learning block theory

[viral roost]

it's not really ambiguous

[flat lantern]

but who has finals in decemember dawg

[viral roost]

you learn calculus, you learn linear algebra, you can approach more general things

[remote ginkgo]

^

[restive falcon]

my predictor exams are in like may

[viral roost]

those are books that relate and build off of each other

that's all

[restive falcon]

what are you talking about

[lapis sundial]

Yeah

[gray gazelle]

bruh just play minecraft frfr

[flat lantern]

true!

[lapis sundial]

Minecraft is applied block theory

[remote ginkgo]

you literally cant make a reading list without 50 people creating a lynch mob and coming to cancel you @viral roost

[fallow cypress]

Can we use this channel for book recommendations

[lapis sundial]

So it is worse

[gray gazelle]

I read this list. It is bad, but it is not the worst I’ve seen. I would maybe add some infinity categories and more pure math, but that wouldn’t be useful for the average scientist. Eh. It does what it does.

[crimson leaf]

Me omw to my final right now

[flat lantern]

freako creepo schooling

[viral roost]

they are really putting a lot of interpretation into it

very creative

[remote ginkgo]

yeah, all of it silly

[crimson leaf]

Gotta get a 10% on this final and I'll get an A

[lapis sundial]

Gl

Lol

[gray gazelle]

i have a quantum final in like 30 minutes

[flat lantern]

"decomposition of non-semi simple modules" is the one sentence description

[restive falcon]

maybe there's a reason people don't like your reading list

[viral roost]

I think it's just you

[remote ginkgo]

yeah

[crimson leaf]

Thanks it's gonna be a lot of work hope I don't forget my name

[viral roost]

you don't have to like it

I would like it if you left us alone though

ty

[gray gazelle]

I think I should make a reading list

[viral roost]

go for it

[restive falcon]

we would all like it if you left this server alone

[viral roost]

I have been here before you

[restive falcon]

but you don't seem to be doing that

[gray gazelle]

Wait, who even is heliogristle?

[remote ginkgo]

i would like it if i had some caffeine

[slim nacelle]

people point out that gristle's list comes off as annoying because it's inappropriately overconfident and self-important
gristle responds to this criticism by being inappropriately overconfident and self-important

[gray gazelle]

I thought they were a geogristle friend

[viral roost]

I thought we were cool

what's up

[flat lantern]

KILL!!!!

[hasty turret]

Is this a right moment to ping Moderators

[remote ginkgo]

gristle is actually inappropriately overconfident and self-important

append this

[zealous light]

I’m not trying to be a part of the lynch mob as much as trying to parse the argument people are making in some coherent way.

The ambiguity I was referring to was after what would be considered the basics of a second year undergrad (algebra/complex analysis) because it seems to be primarily focused on math phys

[gray gazelle]

Is geogristle, not friends with heliogristle, why do they have similar names?

[viral roost]

I think it's a form of attempted bullying

[gray gazelle]

to build a minecraft beacon of height h you need $\sum_{i=0}^{h}(2i+1)^2$ total blocks

[hasty eagle]

arthur-caruso

[indigo mesa]

lmfao

[flat lantern]

bullies u

[restive falcon]

it's a good joke

[gray gazelle]

they already know

[flat lantern]

I am a moderator

[lapis sundial]

Hydrogristle

[stray veldt]

lets get back to the topic of this channel; you can take your personal argument to DMs

[viral roost]

I was on topic, there is no argument other than my request people leave me alone

[fallow cypress]

Anyone familiar with stochastic block modeling?

Looking for expository paper recs

[gray gazelle]

I could make a case for Zorich being a better book than Rudin to be fair

that message is so old

Reply to comment earlier that I lost track of:

I don’t think proof courses offer anything novel. If you want to learn proofs open any book on intro-level books and solve appropriately. Or just read Halmos in about 3 hours and that is a decent profit

Blitz, thank you for upvoting, but your recs seriously need revision

I didn't ask you. I know they aren't the best

Do any of you know some good books on stoicism

[gray jungle]

I've used munkres before and so far Engelking had much more interesting exercises which is what i was asking for sir

[stoic hedge]

Hi, does anyone have a recommendation for a book to study math,( I want to advance, my class's pace is very slow) with some interesting questions which challenge your thinking and are not like school textbooks(I'm in 8th grade)?

[gray gazelle]

What kind of math. School math you mean?

[stoic hedge]

Sort of

[fallow cypress]

Not a book but I am very fond of Khan Academy

[stoic hedge]

But a book which also challenges your logic, and doesn't require you to simply solve the same question 100 times

[gray gazelle]

So, maybe you'll feel comfortable trying to solve some olympiad questions? It seems like you want a challenge

[stoic hedge]

I studied physics with it, it was nice, but I can't be consistent if something is online

[stoic hedge]

Maybe, can you recommend websites/books to get questions from?

[gray gazelle]

nah I never did it myself. But people here will gladly recommend you some books on the topic of mathematical olympiads, I'm sure

[remote sparrow]

Relatable

[mystic orbit]

I was recced marcus aurelius's "meditations"
haven't read enough to give my own opinion tho

[fallow cypress]

Do you want to do stuff of a topic related to what you are learning in school or completely different?

[stoic hedge]

Ok ty anyway, so anyone, if you've got any suggestions of such books, pls send them

[mystic orbit]

oh, there is a timer now, I guess that's a good idea but it's a little annoying

[stoic hedge]

Not necessarily something which is related to school, but can be related to it

[gray gazelle]

Reced?

[mystic orbit]

recommended lel

[gray gazelle]

Oh ok

[fallow cypress]

Any intro number theory or discrete math book would probably be interesting if you want something to challenge your logic, won't be related at all to what you're doing in school though

[stoic hedge]

Ok thanks

[remote sparrow]

https://urss.ru/cgi-bin/db.pl?lang=en&blang=en&page=Catalog&list=6
https://urss.ru/cgi-bin/db.pl?lang=en&blang=en&page=Catalog&list=5

apparently this place sells some mir books, at least according to someone in math sorcerer's comment section

the website is pretty poorly organized though, no option to search for english titles only

the older catalog items tend to be in english though

the newer ones in spanish

[slender cargo]

I feel like advancing through Khan Academy would be good? Just keep going until you get through Calculus, and then proceed from there. Basically skipping grades if you're that motivated

[spare ridge]

aren't you in high school

[willow pecan]

Moth is no longer in high school

[spare ridge]

it's a joke

he will always be in 9th grade in my mind

[spare ridge]

#❓how-to-get-help

[gray gazelle]

the slow down was put here because of off-topic discussions

don't start again

[spare ridge]

aight

[mystic orbit]

it's they. it's right there next to their name :headslap:

oh, the slow down is lifted?

nice

[cedar ridge]

jadore math dissy drama

[gray gazelle]

does anyone know a good place to buy walter rudin's principles of mathematical analysis for cheap? I tried on buying on amazon and waited for weeks and still didn't get it so i refunded.

[remote sparrow]

sounds like you were just unlucky, but you could try abebooks

[warped cedar]

Does anyone know any books that do a good job covering least squares regressions? Looking for something to help some kiddos

[solemn forge]

A colleague of mine works on that sort of stuff. I asked him a lot of questions about community detection and so forth once and with respect to stochastic block modelling he said the following looked like a pretty comprehensive review (I think this is the one he linked me to, but I can't find the original email): https://appliednetsci.springeropen.com/articles/10.1007/s41109-019-0232-2

[fallow cypress]

ooooh omg thank you so much!!!!

[solemn forge]

Cheers

[somber basin]

Six of Crows by Leigh Bardugo

[placid pollen]

Use bookfinder.com to get a list of prices for different stores. I bought his Functional Analysis textbook for 40$ which might be a bit overpriced for some but I just love his style. (biblio.com I find it better than abebooks if you're from outside the US, I will say there's a bit of policy problems in eBay and some US based stores, a bit justified since some people in need exploit the refund option from Mexico)

[crimson leaf]

addall is a good site as well as a kind of a search engine for used book

[gray gazelle]

You can always borrow something from your uni's library.

[placid pollen]

I've gathered a good reading list+guide for basic undergrad, advanced undergrad and basic grad. But I'm going to use it selectively when someone asks about a topic to make an interactive impression.
[<--- really needs friends ^^^^^^]

[willow pecan]

Uh huh ok

[remote sparrow]

just dump the entire thing here and it might get pinned by mods

[willow pecan]

Might being the operative word

[remote sparrow]

even so, your post is going to get logged for discord search

might help someone

[fathom monolith]

I would look at it. I studied CS with an emphasis on the C and not the S, so I like looking at resources where people collect a bunch of what they see as "Important" resources. Lets me feel like im getting the math degree I really wanted 😌

[placid pollen]

alright I'll post it, I was afraid of editing it a bit more but I forgot you can edit discord messages anyways

[gray gazelle]

Don't we all

Friends are nice when you don't have them you know

When they live in your imagination

[hasty turret]

So like Computer Engineering?

Or was it software engineering?

[hallow oriole]

best way to get friends is to be sm1 worth being friends with! dropping the whole list is the best way to prove that!

you know what to do ^-^

[placid pollen]

Sorry, I started the list because it was fun, but it ended up being an essay.

Sounds very pretentious, but it's because I don't want to be responsible for burned out intelligent kids.

The more I think about it, the more I think it's irresponsible to just put a list out there without much of a guide.

I love the MAA guides for example, I recommend checking their book reviews before trying to read something. I feel much more at peace just redirecting people there if they want to read book 'x' than redirecting them to books 'yz' which I like.

But still, I don't feel at ease being responsible for recommending MAA guides just like that. I will too expose the common pitfalls those guides could have.

One of the authors (I don't know if it's only one or many) is more of a software engineer than a Mathematician, he (IIRC) says he's a Math book reviewer by hobby. Which might be easier than having to work through a book in the heat of a grad education, so he might overlook the perspective an undergrad or grad school might have. I don't think he lacks the 'empathy' though (I think there was a better word for 'being in your shoes', but I will just say empathy.) That 'pre-perspective' is important when trying to read a book. It's not the same to read as a reference, as a first read, or as a problem book, or as a `cool book' (Halmos and Rudin enter in this last category with some of their books.)

There are also reviews from old mathematical magazines which I find very, very on-point every time I check one even if they are probably different magazines. Reviews of old mathematical magazines have been just good in my experience.

(I will probably post the essay/guide when it's done, but it's green as of now. It will show personal biases that I will be ashamed to have shown later. Alternatively I could just polish reviews of individual books and let the essay sit there as a long-term project.)

[fallow cypress]

Plus, if you have any reviews of individual books, you can submit them to be published in #books :)

[remote sparrow]

fast track guide

where else have i seen those words before

best not to label these sorts of guides as a streamlined curriculum

choosing books is a highly personal process

maa reviews are good

one small thing for anyone reading this, BLL+ (basic library list) doesn't necessarily mean they're right for you

those are just books that maa thinks libraries should acquire, and libraries generally want books that meet some criterion for longevity

for example maa favorably reviews tao's analysis books but it's not a BLL+ book

[fallow cypress]

Yeah "fast track" is misleading

Book reviews are welcome though