book-recommendations

[karmic onyx]

yeah it doesn't look bad, fairly standard for a course in commutative algebra + a first semester course in algebraic geometry (so your favorite commutative algebra book + chapter 2, some of chapter 3 in hartshorne). the ordering is a bit different than the first course that i took (a little odd that they don't find a use for a discussion of proper morphisms until the very end), but it seems like a perfectly reasonable book to use. it's definitely terser than vakil's text, but not as terse as hartshorne in places, so the reader experience will be different than vakil, who has a ton of diagrams and stuff everywhere (also, vakil covers some "less important" stuff before some "more important stuff" later on). a similar comparable book (and perhaps more standard text) is gortz and wedhorne, which my course used alongside some notes by clausen and hesselholt, which are well organized, but personally felt a bit hard to read/reference since every section is just a wall of text. overall, your text probably fine, i'm just yapping too much, sorry

[remote sparrow]

https://www.youtube.com/watch?v=K1cFredFaDM

[karmic onyx]

i should conduct an experiment on how much algebraic geometry i can learn while "safely skipping" understanding spectral sequences. already been through 2 reading groups which go over them but could be safely skipped because they "aren't super important"

[trail hemlock]

i love this guy

[graceful moon]

As much as I joke about Hatcher (and I genuinely dont think its a particularly great book) I do think its better than Rotman, Rotman is nice to supplement because the exposition is generally good but its just so slow

and he just does some things kinda weirdly. While I am not even remotely close to an expert or even respectably competent in AT I can defiently agree with the take that there are no good AT books, you just pick which one seems the least bad to you

[gray gazelle]

Y’all should just read T&G fr..

[graceful moon]

Are you on Browns payroll or something

[marble solar]

Any opinion on Spanier?

[karmic onyx]

A book I've heard about this is origametry by Thomas hull, but i haven't read it myself, so no idea how it is

[heady ember]

Oh really? Lol

[trail hemlock]

ok so not exactly it was 5.22 (d)

guess i was thinking of smth else

[remote sparrow]

@solemn rover

[heavy vault]

i dont know if this is in a specific book but ik theres some stuff on how adding origami operations to euclidean geometry allows you to do new stuff like trisect an angle

https://www.youtube.com/watch?v=RxYlKzi7BUU this looks good from his summary so yea id say try this ig

kinda tuff title too

origametry

[cursive orbit]

🤓

[karmic onyx]

shut the fuck up

[tender cobalt]

Yeah me too here

[random oar]

hello guys I'm a cs student, learning probability, where can I solve questions? I know about Sheldon Ross book, but are there other resources too? and is Sheldon ross good book?

[remote sparrow]

https://stat110.net

[stable flicker]

Ross' first book is taken to be very easy by most math standards.
There are a lot of probability textbooks. Like a lot.

[karmic onyx]

if you just need probability for cs, try Jean Walrand, Probability in Electrical Engineering and Computer Science: An Application-Driven Course

[deep moat]

I second this!

Stat110 is really nice

[stable flicker]

wtf til gatech's ila is written in xml??????

https://github.com/QBobWatson/ila/blob/master/src/matrix-mult.xml

[random oar]

okay thanks

[stable flicker]

@remote sparrow Any notable things missing from this list?

[remote sparrow]

for what purpose

[stable flicker]

for listing purpose
but yeah the number of open source books out in the wild is exceedingly small

Under "probability" alone I have 858 Files, 62 Folders

Interestingly I think there's very few open source pure math books

[karmic onyx]

what's the list of

i'm confused how something could be missing

[stable flicker]

It's of open source books

It doesn't have to be free, it has to be open source (which usually means it's free)

[karmic onyx]

what is an open source book? like contributers are allowed to edit it?

or just that it's free

[stable flicker]

one that let's you see the source

It's not difficult to understand

[karmic onyx]

i see

[stable flicker]

For example VCA is not an open source book because I got no clue how the author drew anything

[karmic onyx]

what is vca

[wispy bison]

You might try Origametry by Tom Hull

[stable flicker]

https://global.oup.com/academic/product/visual-complex-analysis-9780192868923

[karmic onyx]

oh

[karmic onyx]

i suggested the same thing lol

[wispy bison]

oh just saw that

[stable flicker]

You can start writing an open source book I can star it on github

[wispy bison]

oops

[solemn depot]

for amc, aime, usajmo etc is aops books all that you need?

[graceful moon]

Can’t say I’ve looked at it in all honesty, I probably should though, it’s potentially the nice middle ground between the very slow pace of Rotman and the rather quick pace of Dieck that I’d like

And well it just isn’t Hatcher

[plain barn]

hmm

well I kinda like slow stuff so I'm going with rotman

I was also attracted to bredon but taking a surface look it does indeed seem horrible to read

like there are whole sequences of pages with 50 definitions one paragraph 23 theorems

[gray gazelle]

Can anyone recommend me a good and bulky statistics textbook that includes all concepts in AP Stat plus more?

[final swallow]

Does ap stat cover only hs statistics

I'm not that familiar with American educ terminology

[silk patrol]

#math-discussion message
Any advice would be appreciated. Would a pre-calculus textbook be more ideal/comprehensive starting point to fill in my knowledge gaps?

[final swallow]

What's your current background?

[gray gazelle]

Yes, it includes one and two-variable data (normal distribution, residuals, regression models), data collection, probability, random variables, and probability distribution, sampling distributions, inference for categorical data: proportions and chi-square, and inference for quantitative data: means and slopes

It’s taught at the high school level but might include some college topics

[final swallow]

I have Elementary Statistics by Mario F. Triola and books like it should serve you well

I don’t really know a lot of stats books so idk if there exists that is better

[silk patrol]

I work in epidemiology - so a reasonably good level of statistics knowledge. But I'm missing essentials like a proper calculus education, and I think it's holding me back from progressing my understanding of stats

[silk patrol]

^

[gray gazelle]

That looks good, thank you for helping

[final swallow]

If you have taken a proof based class and calculus you can try a mathematical statistics book instead

[gray gazelle]

Do you have any specific title by chance?

[final swallow]

Mathematical Statistics and Applications by Wackerly

Tbh i have only skimmed the contents of the book and not actually read it

But it looks good to me so far

[final swallow]

I think you can go straight to many calculus concepts without taking a precalc course assuming you have a decent grasp of high school algebra

You'll need some trig tho

But you probably won't need the skill of fluently manipulating trigonometric identities

[silk patrol]

Algebra I'm ok with. I worry that there is gaps in my knowledge though, and I'm not sure how important the concepts are. Things like surds for example I have no clue. I also think my geometry understanding is bad, because whenever I watch 3blue1brown videos and he mentions stuff like 'the derivative of sine is cosine', it doesn't make a lot of sense to me, even when I see him visually show how it makes sense.

[gray gazelle]

This looks like it can definitely suit me, I prefer the higher mathematical basis compared to how other stat books teach. I think this will be very good, thank you for sharing this.

[final swallow]

Nice

[silk patrol]

slight tangent, but would you guys recommend textbook/study approaches over online resources like khan academy?

[final swallow]

I don't know anything about epidemiology so I can't recommend a specific book tailored to it

But as far as i know there exists books like calculus for biology/calculus for life sciences

[silk patrol]

The level of maths needed for epidemiology is pretty basic. 99% of it is fundamental statistics, which imo you don't need to know things like calculus for. But to get into the more advanced levels of statistics you need a more rigorous maths background

[final swallow]

I think most standard calculus textbooks (Stewart, Larson, Thomas) could do the trick—they cover almost everything from single variable calc to multivariable to differential equations although that might be too much?

If you're not a fan of modern heavy textbooks then you can try older ones(e.g. Calculus with Analytic Geometry)—they basically cover much of the same topics but more concisely

And are probably much cheaper

Then there are also calculus books tailored to biology like Calculus for Life Sciences by Sebastian J. Schreiber

[silk patrol]

I don't mind heavy ones - I'll probably use a digital version so I can work on my laptop and take notes by hand

work gives a free subscription to o'reilly learning, so might have a look through their library. They have quite a lot of books like 'calculus/maths for data science'

[vast jackal]

hey by any chance you're a Pinoy right?

[final swallow]

Yes

[vast jackal]

ohh

umm what major did you get?

[final swallow]

Quite obv from my pfp

[vast jackal]

I'm a Pinoy too lol

[final swallow]

Let's talk in #chill

[vast jackal]

alr

[grim ore]

this is a graduate level book?

[tender cobalt]

i heard i can start from there though..

i also read from preface it dont assume any previous algebra

[grim ore]

You can definitely start from there, but Ug textbooks are meant to build foundations and help mathematical maturity. You can definitely use a grad algebra textbook to teach a ug class, but it the pacing, rigor, and even the foundations that it just takes for granted vs a ug text is important to consider

most ug and grad algebra texts start in the same place but starts introducing details that a ug text doesn’t

Hell me going through grad hungerford for qual exam, it literally went through groups in like 30 pages compared to a whole third of the text, around 100+ pages in the ug version

[tender cobalt]

is it a bad idea then to start from here

😵‍💫

Jacobson: Extremely clean writing, my personal favorite. Prefers to explain things in English rather than symbols. Covers an interesting/non-standard set of topics. For this you want some LA going in.
i just saw this in the pinned messages too

[grim ore]

Imo, to be frank, I think you should try building your mathematical maturity, which purely means you can think logically and attack problems based on what you know and proof writing skills

[tender cobalt]

how to do that?

[grim ore]

Really just pursuing any ug text at a time. I feel like we have talked about this already specifically about algebra too?

yes we have

If you want the ug experience learning some grad lvl topics, read D&F

It’s slower paced and drawn out but it will also go over those grad lvl topics while still teaching you foundations

[tender cobalt]

alright thanks i will check out both D&F and Artin

and try to get good "foundations"

[tender cobalt]

I thought learning things in less pages would be faster

[fresh skiff]

D&F with some basic book as reference maybe Farleigh

[slender cargo]

Number of pages doesn't matter. If you're taking 8 hours to understand 5 pages versus 4 hours to understand 10 pages that explains the same material, then the bigger book might be better

[vital bane]

Why do you need to go faster though

you really need to get rid of this mind set of "I gotta go fast" and take your time with the basics

if your basics are really strong, then you will have a far easier time learning the more advanced subjects like functional analysis and differential geometry

and spectral geometry

[trail hemlock]

strong ahh

[fading void]

humble pi: a comedy of math errors
pretty interesting book

[grim ore]

📠

[remote sparrow]

daminark was a very strong student that attended one of the best math programs. he is not the norm

[vital bane]

and he doing all the book reviews

[tender cobalt]

how to be a very strong student

😭

[vital bane]

take your time and not rush things and do lots of exercises

that's how you become a strong student🗿(lifting weights also helps in becoming a strong student)

[naive lava]

u start nicotine

[gray gazelle]

☠️

[past dust]

How’re the books the calculus with analytic geometry by lewis leithold and calculus by adams

[solemn rover]

Rotman is easier than Spanier and a good introduction.
Spanier is really a great book in that it's extremely precise and clear, which is the polar opposite of Hatcher.
However, there are a number of critiques that I will put out there.

1. It's too comprehensive in some parts, particularly it gives an encyclopedic treatment of singular cohomology, going into too much detail so that you can have trouble getting the main ideas. One needs to carefully read the chapter intros where he highlights the main ideas and focus on them. Or one needs to follow a semester course in topology and read only the topics discussed in the course.
2. It's too general in some parts and you don't get as much intuition as if the less general but more concretely accessible theorems were taught. Poincare duality is better learned from Bott-Tu. The Leray-Hirsch spectral sequence is better learned in a book on sheaf cohomology such as Godement. Obstruction theory is better learned from Hu. The cap product is studied as a map H^n(X; G) \otimes H^m(Y; G') -> H^{n+m}(X x Y, G''), where G, G', G'' are modules and we assume a given bilinear map G \otimes G -> G; one can easily miss that this makes H*(X;R) into a graded ring.
3. It's a bit older and if it were rewritten today I think it would have been better to use simplicial sets rather than simplicial complexes.

But it's very rigorous and detailed. The treatment of covering spaces and fibrations is good, the treatment of homology of simplicial complexes is good, and so on.

[keen orbit]

try changing your username to daminark

[dim sierra]

What’s the title of the book by Hu to learn obstruction theory?

[solemn rover]

"Homotopy Theory"

[dim sierra]

Thanks

[dim pendant]

I find Jacobson quite nice. It's no nonsense, clear, and efficient

Oh well I guess that might actually make a book less accessible to undergrads

[rocky path]

Do any of y'all have recommendations on books that cover quaternions in depth in the context of pure mathematics? Most of the books on the subject are primarily focused on the applications of the subject in robotics, comp sci, etc, and understandably so. But i really want to read about the deeper mathematical properties of these numbers

[remote sparrow]

https://jvoight.github.io/quat.html

[rocky path]

oh hell yes.

tysm

[foggy quest]

see chapter 8 of https://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2018/04/linalg.pdf

[rocky path]

holy shit L from classic manga and anime death note

say your classic line

[foggy quest]

what is it

[rocky path]

you decide

[foggy quest]

No, it would be a problem if you were Kira. Because you're my first friend ever.

[rocky path]

https://tenor.com/view/clapping-clap-applause-standing-ovation-gif-15648815

no embed perms😔

[iron pulsar]

im reading grit - angela duckworth. anyone is welcome to join me ☺️

[old elk]

grit angela?

book?

[iron pulsar]

https://www.goodreads.com/book/show/27213329-grit

it supposedly has growth mindset insights

[old elk]

my mother told me one thing: study so that you can defend yourself in life with something.
my advisor told me one thing: Don't stop, don't stop.

now I say to myself don't get distracted by what is on the internet

[honest pilot]

Can anyone suggest me a book to start number theory?

[remote sparrow]

#book-recommendations message

[honest pilot]

Thank you

[fresh skiff]

hey, sorry for random ping.
Do you know video lectures on set theory ?

[remote sparrow]

https://ocw.metu.edu.tr/course/view.php?id=270

https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf

[fresh skiff]

Thank You

[heady ember]

https://www.youtube.com/watch?v=OcTVKWq1nUk&list=PLWSTDG33fdNBqApiDLuLnRzOin1TYrNGn

[fresh skiff]

why it looks so horrible

[heady ember]

Wdym. The thumbnail?

Oh btw I sent that as a nonserious rec.

That's grad level stuff

I only know the one Sour Drop sent for lectures on set theory, for ug level.

[fresh skiff]

yeah i seems like. I saw this video and i was be like : Is this set thoery

[heady ember]

Yeah I mean it has forcing in the title

You should be scared

[fresh skiff]

yeah i was a bit confused why such title lol

[fluid zealot]

so guys i was thinking to start learning logic where should start from ??

[past dust]

How’re the books the calculus with analytic geometry by lewis leithold and calculus by adams

[livid tide]

I've taken a break from math for like 6 months but I'm trying to get back into hobbies and habits recently

I want some recs on algebra / category theory something I can obsess over

Ideally with cool problems to solve

(Advanced) Algebraic structures was my favorite course of my undergrad

And I wouldn't mind going over similar content again I've forgotten a lot

[naive lava]

if you like algebra

and want something like cat theo

why don't you look at algebraic topology?

[livid tide]

Took an alg topology course and that was really really interesting too

Professor was meh but id be more than down to self study

Going to abstractmaxx good

Although i don't know where to start in looking for books

So instead of recommendations advice on that is also appreciated

[graceful moon]

You could look at some homological algebra stuff

Weibel is really good, rotman is solid if a little slow

[old elk]

I have this collection chosen in such a way that I can advance in algebraic topology from the easiest to the most difficult, I still have to place topology by Stefan Friedls.

I would really recommend first going through the theory of vector calculus and analysis in several variables, and then algebraic topology and then homological algebra, so it would be a good line for understanding, if you are more into geometry and analysis.

I love Stefan friedls' topology book, but I really don't have any goal to start learning his notes.

[dapper root]

Lmfao

Are you planning to read 21+ textbooks on AT?

[molten gulch]

that is a LOT of topology books holy shit

[silk patrol]

I'm considering having a go at "No bullshit guide to math and physics - Savov"
But i've seen mixed reviews. Some say it's brilliant, some really slate it. Any opinions here?

I mainly want a book to help me fill in gaps in my knowledge of highschool and early-college level maths

[scarlet geyser]

hello guys

i need best functional analysis book

someone have any offer ?

[gray jungle]

do you have a certain goal from learning functional analysis? whats your motivation? more importantly do you know measure theory?

[fresh skiff]

James be like : I can smell fun anal

[gray jungle]

Basically a lot of different FA books are targeted at different people in mind, some requiring more prerequisites than others, hence my questions.

[scarlet geyser]

I am a 3rd year university student and that's why we are taught that subject.

[gray jungle]

have you taken a course in measure theory?

[scarlet geyser]

no

[gray jungle]

Then i recommend "Introductory Functional Analysis with Applications" by Erwin Kreyszig

[scarlet geyser]

okey thx

is meausre theroy imprtant thing for FA ?

[gray jungle]

incredibly

a lot of the most important spaces you work with are measure theoretic (i.e L^p spaces)

[scarlet geyser]

I will definitely take the time to study measure theory in parallel.

[gray jungle]

but you can do a lot of FA with some blackboxing

[scarlet geyser]

ha okey thx for info

[scarlet geyser]

our fist lesson is 1.1. Set Concept is this dif or same ?

[gray jungle]

im not sure whats that referring too, do you know what the following lessons are called?

[scarlet geyser]

sry but i dont understan what you say ?

[gray jungle]

im saying the lessons name doesnt say much because it sounds as if they are introducing sets, do you know the name of the other lessons? (1.2, 1.3 ...)

[scarlet geyser]

ahhhh okey

[gray gazelle]

Topology and Groupoids is a very algebraic AT text

[scarlet geyser]

yes absoultly 1 min

[gray gazelle]

First 5 chapters are mostly point-set though

[remote sparrow]

#book-recommendations message

[scarlet geyser]

Equivalent sets , Countably infinite sets və ya Countable sets, Continuum-sized sets or Sets of the cardinality of the continuum

[gray jungle]

Then it sounds like your course is gonna go through measure theory before functional analysis.

because those are preliminaries to measure theory

[scarlet geyser]

aa okey i got this

and do you offer for this subkect FR book erwin ?

because my subject fr consist of this lessons

omg i dont know i am madnes off university sometimes come borig

[gray jungle]

since it seems they will do measure theory first, a better book for you to use is "real analysis" by Royden

a similar but harder book is "real analysis modern techniques and its applications" by gerald folland

[naive lava]

dude has my dream library

[torn blade]

as a first AG book do i need to supplement Vakil with a commutative algebra book (Atiyah)

[nimble osprey]

Hey can someone tell me which is the better between thomas and Stewart calculus

(please)

[naive lava]

Absolutely 0 difference

[scarlet geyser]

Understanding Analysis" by Stephen Abbott i reed this book. okey i change thx my man for information

[naive lava]

just pick the cheaper one

[nimble osprey]

Huh ok might as well get thomas

It’s cheaper

Thank you!

[gray jungle]

stephan abott is more elementary, its not measure theory or functional analysis 👍

[scarlet geyser]

ha okey thx

[molten gulch]

<@&268886789983436800> scam

[naive lava]

mf u beat me to it

[rocky path]

sorry if this is a common question but what's the best linear algebra book for someone who wants to get deep into the theory and not so much the applications?

I read the pinned post on lin alg but it seems like pretty much everything has some kind of drawback that makes it not as good

[marble solar]

Have you been through the basics of linear algebra already?

[jade meadow]

axler I would guess

[marble solar]

Like a first course that's computational oriented, and a little bit of proofs? In the US, it'd be a lower division linear algebra class

[jade meadow]

the book Linear Algebra Done Right

[rocky path]

no, but I'm pretty quick to pick concepts up

[marble solar]

A good book would be David Lay's Linear Algebra and its applications. Another great book with many examples is schaum's outline to linear algebra

You can skim over the applications part of the book if that doesn't interest you, but some of them are interesting

[slender cargo]

Axler's Linear Algebra Done Right (after a first course) or Friedberg Insel Spence are the most common texts used, from what I've seen. However, don't view these texts as the end of the story. Get a good exposure to linear algebra from such a text, but then the story goes further in module theory, which requires going through group and ring theory first. I think why each of those linear algebra texts has a "drawback" is because it's better to see some of the material later in the context of modules.

[jade meadow]

hmm but is it 'right' to learn vector spaces first on their own instead of learning ring theory first and realizing them as a certain class of R-module

[rocky path]

I'm leaning towards hoffman and kunze rn but that might be a mistake

[jade meadow]

(jk of course it's right lol)

[rocky path]

scam

[cunning elk]

fuck off scammer

<@&268886789983436800>

[rocky path]

<@&268886789983436800>

[slender cargo]

Yes! But I think some people might be too concerned that they pick the perfect linear algebra text

[cunning elk]

ik they use FIS for undergrad linalg at Yale

[marble solar]

Trust me it is a mistake to jump straight into hoffman and kunze. It really does assume that you know the basics of matrices, row reduction, column reduction, determinant operations

[cunning elk]

that’s what my friend there told me

[rocky path]

gotcha

[cunning elk]

at my uni we used this absolutely dogshit “textbook” for an intro linalg class that was all computation bash no rigor

[marble solar]

It's not that you're unable to pick up the concepts, it's just that hoffman and kunze (and other second books) don't teach the basic computations that you need in order to understand what they're trying to get across

[cunning elk]

said textbook was also incredibly poorly written

[jade meadow]

you could also start with what's his name's mit lecture videos https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/

[rocky path]

makes sense yeah

[cunning elk]

strang?

I feel like his lectures are kinda overrated

too much stream of consciousness for my taste

[naive lava]

mayybe lax?

[marble solar]

Big fan of Daiv Lay's book for the first linear algebra. It has plenty of proofs, plenty of computations

Lots of exercises, and only the last two chapters are application oriented

David Lay's*

[old elk]

The books are a bonus, there are some that explain better than others, basically it is impossible to read all 21 books unless you are a prodigy and have some gift or talent, which I clearly do not have.

[rocky path]

god i wish there was a textbook store near me

would be fun to window shop

[cunning elk]

your local university maybe?

[marble solar]

I don't think a prodigy can read 21 books in a short amount of time, nor at the same time

[rocky path]

Maybe

[naive lava]

textbooks are expensive and almost all the money goes to publisher not author

[cunning elk]

this is why I always roll my eyes at the random AoPSers that go “should i read 1638481957294839938 textbooks this summer to make IMO”

they’re being completely unrealistic by saying stuff like that

[marble solar]

I've never heard someone say that. One thing I was told in undergrad is to find 3 sources on something you really want to learn. One book below your level, one book at your level, and one book at a higher level

[cunning elk]

man i sure wish someone gave me that advice lmao

[dapper root]

It would also be a massive waste of time to read 21 books on a subject

[rocky path]

So out of all the books people have recommended so far I'm thinking either david lay or friedberg insel and spence

[marble solar]

And then you bounce around topics as it's relevant to what you want to learn. I'm not sure it's good advice either. I think just going with the lecture notes & following along in class is better than finding "the perfect book"

[still panther]

hoffman and kunze seem pretty elementary to me (in the sense that they start from first principles)

its not roman

[marble solar]

I mean it does start at elementary matrices, but a beginning student needs to do many examples of row reduction, column reduction, determinants and computational problems to get a good long term handle on linear algebra

As important as linear algebra is, we shouldn't rush beginning students to advanced topics too early. Some extra time spent on linear algebra is hardly time wasted if they're interested in mathematics

[still panther]

just pick up a problem book alongside it then, i dont think the textbook needs to spend its time to have 10 examples of the same thing

[old elk]

If you can if you like the subject :D

[marble solar]

Do you know of a book that gives 10 examples of the same exact thing at the linear algebra level (other than maybe schaum's)

[still panther]

h&k even has a review paragraph where they reiterate all the common techniques you should apply to solve different elementary problems which i think is already pretty generous

[gray jungle]

i mean you're just gonna be learning the same thing multiple times from most of the books, its better to have a main book and use references to suppliment them instead.

[molten gulch]

<@&268886789983436800> another scam

[still panther]

its not a scam its a 50 dollar certificate for a math book on steam

[full cairn]

wow, people are so generous nowadays

[molten gulch]

lol

[still panther]

steam for math books would be kinda fun

showing off hardest exercises you solved

getting platinum in niche fan favorites

[gray gazelle]

Code forces is closest it gets to that

[rocky path]

went to a local university library so i could casually browse and flip through books but the mathematics section was under construction so i could only ask for specific books which kinda defeated the purpose of my visit

[graceful moon]

Doing every problem in Harthshorn just for the steam achievement

[grim ore]

No turning back - 2000 points

[naive lava]

oh wow this steam achievement comes with a fields medal next to it

best bundle ever

[graceful moon]

It’s the motivation those lazy geometers have needed

[scarlet geyser]

hey brother a lot of thanks i learn chapter 2 for tomorrow lessons book is soo good and understable 🙂

[molten gulch]

What material does your course cover

Provide a syllabi, in the original language if not English

[scarlet geyser]

Measure theory

[molten gulch]

That is not a syllabus sheet

[scarlet geyser]

oh sry but syllabus is not in english

[graceful moon]

There’s got to be a good book on AT between them

[tardy oasis]

📚

[mighty tartan]

Discussion

[remote sparrow]

📖 📕 📗 📘 📙 📚

[remote sparrow]

bookscussion

[rain nova]

WHERE IS THE ADVANCED CHANNEL

[stuck zephyr]

gone

[marble solar]

you got april fools'd!

[wispy bison]

You can also look at https://measure.axler.net

[wide dock]

what should i refer for grade 12 olympiad

[tender river]

#advanced-lounge

[sudden shale]

Is there a website or free pdfs with problem sets to work on? Someone asked this yesterday but deleted their question.

I speedran trig on Khan academy and am now suffering in calculus with how shallow my trig is. I need to practice

[carmine lodge]

Good morning

[remote sparrow]

bookscussion

[naive trellis]

book rec

[sudden shale]

I agree. I’ve seen everything once but I’m not intuiting anything.

It was perfect for relearning algebra (it’s been many years), but material new-to-me is getting harder

[sudden shale]

I think I just need more practice. I can do the steps. I’m not understanding the why.

Khan Academy didn’t drill that much on identities, and I’m now I’m struggling with derivatives for trig functions.

[deep moat]

In times of these kinds of scenarios, I often ask ChatGPT o3 for them haha

[tender cobalt]

chatgpt 4o, o1, o3-mini these models are really good with highschool mathematics, and 1st year mathematics

like calculus etc

only issue is proof based math

[mortal ore]

It struggles with calc 3 from my experience

[tender cobalt]

which model

[mortal ore]

Whatever the public model of gpt is rn

[tender cobalt]

yeah that's 4o-mini , the free version

it sucks a lot

[deep moat]

I recommend for an Introductory book like Schaum's Outline in Trigonometry . (Book I found online)

[mortal ore]

Would the paid version be that much better?

[tender cobalt]

yeah

[mortal ore]

Interesting

[tender cobalt]

it's a LOT better

[mortal ore]

I likely won't pay for it but that's pretty cool

[deep moat]

o1 is good for Calc 3

[tender cobalt]

you should be getting 4o like a few messages per day in free version

[deep moat]

Afaik, o3 has like an unlimted input of images

for free users

[mortal ore]

Wdym

[tender cobalt]

ok wait

@mortal ore try switching your model

to 4o or o1 or o3

and give it a calc 3 problem

[mortal ore]

Eh that's too much effort, I don't use AI anyways

I'll take ur word for it

I haven't needed it since calc 3 lol

[sudden shale]

I’ll try it out. Thanks

[tender cobalt]

useful if youre a loner like me who dont got friends to ask for help🥲

actually this server is decent for asking for help

[mortal ore]

I'm not anti-ai or anything, it's just not relevant to my areas of study (math and philosophy)

[deep moat]

Now I remember why I dislike trigonometry

Not anything personal, I just don't like the subject! HAHAHA

[rugged field]

Where did latex testing disappear

[mortal ore]

Luckily it's not that deep math-wise

As in there's not any more that you have to learn after calculus besides complex number identities

I give it terminology only

No images

As in algebraic descriptions of the information it's working with

[sudden shale]

I’m having more fun with calc

I want to get into graphics programming eventually. I can’t stay doodoo at trig

[mortal ore]

Better hope ur good at linear algebra

[sudden shale]

I find linear algebra fun too. It’s pretty interesting from a programming perspective

[proven lantern]

Hello. I would like a book recommendation on Complex Analysis. I did first chapter of Ahlfors and found it to be a bit verbose and easy. Would prefer something harder, but not that hard to require lots of prerequisites(such as Roger Gay). Thanks in advance.

[remote sparrow]

can you tell us your background?

[proven lantern]

I've done Zorich's Mathematical Analysis book 1 (roughly equivalent of whole of Rudin's PMA).

[remote sparrow]

try looking at freitag and busam

https://link.springer.com/book/10.1007/978-3-540-93983-2

the paperback has gone on sale for $16 before so keep an eye out

[proven lantern]

Thanks. I got the digital copy, looks great.

[graceful thunder]

Naw dawg whats going on

Whats general now

And what is that simplified ahh logo

[proven lantern]

Stack of books, this is book recs channel.

[proven lantern]

General's #discussion

[graceful thunder]

Ok thanks

[naive lava]

ahlfors picks up the pace around ch 2-3

maybe keep reading it a bit

if you like the content

[proven lantern]

Nah I think I will go for Freitag. It seems more favorable.

Thank for the advice anyways.

[tight crag]

Bots being on top is crazy

[median edge]

cats

are on top

[onyx anvil]

hello

[deep moat]

o/

Hi!

[mortal sandal]

April fools is messing with my brain

[stable flicker]

[empty mortar]

[gray gazelle]

What tf happened to this server

[earnest wolf]

what

not possible

all of our bots are she/her

[stuck zephyr]

april fools

it'll be easier if you just read the channel description

or the emoji

I think only #april-fools-2025 is a new channel

[hollow shore]

where is the feet channel?

[fresh skiff]

Why playing with channels😭

[native cradle]

Helpful is yellow now

Wth

[tender cobalt]

[merry sphinx]

straight up thought some ppl were just given the role today

[gray gazelle]

o3 mini high >>> 4o

[gray gazelle]

I can't find it either

[gray gazelle]

I haven’t seen you in this channel(I can only assume this is “book recommendations”) in awhile

[tender cobalt]

<@&268886789983436800>

[gray gazelle]

learning calculus want to do discrete mathematics! any recommendations

[earnest wolf]

I also need it

[spring epoch]

Boo

Did I scare you

[fading mortar]

Are there any books on the various philosophies regarding the nature of numbers, sets or other basic mathematical objects?

Also books on authors efforts on trying to define a number through logic (cantors) or rigorous proofing (like peano axioms)

[marsh ice]

Bertrand Russel had a book on the philosophy of math

It was ‘intro to the philosophy of math’ or something

He gets into the idea of sets, numbers etc and what they mean semantically

[gray gazelle]

WHERE IS FEET CHANNEL

[warped sage]

Whoever took my pic perms away is gay

[stuck zephyr]

https://tenor.com/view/epix-image-perms-gif-20444679

[hearty prawn]

https://tenor.com/view/chico-chico-lachowsi-francisco-lachowski-dalit-indian-gif-14481150343048856079

[gray gazelle]

Cantor tried to define numbers through logic?

I thought that was primarily Frege

[shadow lantern]

Please somebody recommend me a book that could explain division of fractions. I can't get my head around it. I want to know why 1÷3 is 1×(1/3). Why (3/2)÷(4/5) is (3/2)×(5/4). How to visualize fractions, how i can apply it in division,multiplication...

[fading mortar]

I don't remember but cantors was something like every number is a set containing that numbers of Units I guess

Like the number 2 is a set with 2 units in it which can be anything (the units can be any object real or abstract)

[sudden kindle]

Fulton & Harris is actually a really great book

[fading mortar]

I'm not experienced in this so I maybe wrong, I saw a kitfine's tedex talkin this so

[remote sparrow]

good to know

actually who should know representation theory

[fading mortar]

You can do that by breaking down division into repeated subtraction, or thinking of it as the inverse of multiplication and then making it into repeated addition maybe?

[gray gazelle]

Division is just multiplication by inverse

the inverse of 5/1 is 1/5

inverse of 5/4 is 4/5

[sudden kindle]

Wdym?

[remote sparrow]

thinking of whether i should buy it since a new paperback copy is 55% off on amazon, but i'm wondering if i should save that money for something else since rn my plans are moreso towards logic

[shut shale]

that's one of those operations imo which is easier to think of in actual language or pictures. 1/3 means how much is a share if you cut 1 up into 3 equal pieces. It stands to reason then that 1 * that proportion will be a single piece.

a book is not the right medium to learn that though, it's too fundamental. No need for a book.

just watch some youtubes or something until it makes sense

there's no difference between understanding division and understanding divisions of divisions imo

[sudden kindle]

Rep theory is cool and yummy

Do u like lie groups

[shut shale]

it might help you to view integers as fractions and do a practice problem or two (e.g. 3/1 / 4/1 instead of 3/4

[remote sparrow]

don't know what a lie group is

i see this concept come up in mathphys sometimes

[sudden kindle]

Yeah, its very relevant to math physics

[shadow lantern]

Thank u all, i think I'm getting it slowly xd... lot of drawing tho...

[neat matrix]

gemini 2.5 pro

[remote sparrow]

what about other areas of math

@mossy flume

[mossy flume]

why ping

[waxen thorn]

wheeeeeee

[remote sparrow]

do you know what other areas of mathematics rep theory gets used in

[mossy flume]

oh uh

algebraic combinatorics is a big one

algebraic complexity theory to a large extent if we want to get to really modern stuff

both of these use very combinatorial aspects of representation theory (mostly focusing on S_n and GL_n)

low-dimensional topology according to my roommate also has lots of rep theory (of a very different non-combinatorial flavor)

idk anything about that stuff

[remote sparrow]

[mossy flume]

if you want a nice intro to the combinatorial stuff

https://link.springer.com/book/10.1007/978-1-4757-6804-6

I like this book alot

very approachable and well written

@sudden kindle also likes this similar text

https://link.springer.com/book/10.1007/978-3-030-98025-2

which I personally haven't looked into

but I can't imagine it's bad

can't go wrong either way

having solutions included I guess is a plus

seems light on any of the symmetric function theory though

which is a shame

[thick quarry]

Bro where is this ping?

[tender river]

there is no ping

[thick quarry]

I litteraly have one.

[cold elbow]

skill issue

[viscid comet]

I am at the tail end of an undergraduate complex analysis course and it honestly has been one of my favorite math courses yet

Where do you suggest reading for further discussion on analycity specifically or complex analysis as a hole?

[dense grotto]

every channel dead

[dense grotto]

imagine getting fooled this hard

[remote sparrow]

what book did your course use?

[viscid comet]

Saff's

Fundamentals of Complex Analysis with Applications to Engineering and Science

[remote sparrow]

do you know real analysis

point-set topology can be helpful for certain books as well

[viscid comet]

Yes

Currently in real and I've taken a point set topology course as well

[remote sparrow]

try looking at freitag and busam and/or zakeri after you finish real

maybe stein and shakarchi for the problems too

gamelin has some extra stuff beyond a first course

[tacit hollow]

Hello everyone,
does anyone happen to have any good resources on differential equations. My professor keeps skipping material, and we just hit laplace transformations. I can’t make heads or tails what’s being talked about in the textbook.

You’re amazing in advance.

[vivid vigil]

change this goofy server icon pls 🙏

[tender cobalt]

Paul's online notes is really good for differential equations. And there's also a nice book by Zill, "A first course in differential equations with applications"

[haughty dagger]

did my acc get hackeed

i saw notif sometime back

and it disappeared

without me clicking on it

[lime vessel]

It's trolledge day

Maybe they set up a script to ghost ping the whole server over 24 hours

[gray gazelle]

no

[burnt delta]

It’s not even April fools anymore

[civic peak]

Can’t fool us anymore

[fresh skiff]

Grass this green looks good on u

Green color

[heady ember]

Orange ||doesn't look good|| on you ||||

[fresh skiff]

True
Idk why so awful color

[deep moat]

woah

hello book recoms!

[strong island]

9th grade, giving up on school, so I just want to return to the one thing that's easy for me and makes me feel good.

What're the best books for:

Algebra 2
Trigonometry
Precalc
AP calc
Calculus
Intro physics
Etc

If there's one thing I'm going to be good at (besides reading and writing), it's math.

[stuck zephyr]

I think you can use khan academy for those topics

if you want I can give you the books i used or textbooks

[tame ingot]

Any suggestions on convex optimization that is not the standard Boyd & Vandenberghe?

[vivid ridge]

I got a recommendation: the Pulse series by Patrick Carman

[fleet wyvern]

books for all of you (recommendation):

Math

ik im onto nothing ik

[dim pendant]

You got us

[gray gazelle]

yo guys

what resources should i use to learn calculus

ive considered MIT opencourseware but an instruction book would be nice imo

[tender cobalt]

Stewart or thomas calculus

[deep moat]

Haven't read a calculus book, but from what I've heard, Stewart is more famous and a go to calculus book

[sweet ingot]

Do it have Calculus 1,2, and 3?

[deep moat]

I don't think so?

Calc 1 yea
Calc 2 idk
Calc 3 I guess Evan Chen's notes?

[sweet ingot]

Its sad how when people mean Calc, they most likely mean 1

😔

[deep moat]

Because Calc = Calc [{1,2,3}]

Calc has 3 variations so you gotta be specific

[stiff crow]

calc 1 and 2 covered but also most of the stuff for 3 but not like in depth

[fading mortar]

If you're into learning about math as a subject, and not just doing questions, i.e. learning it as a tool, check out various pop math books like The book of numbers by John h Conway, Infinity and the mind, story of √-1, what is mathematics by r courant, mathematics from the birth of numbers, princeton companion of mathematics

For algebra, algebra by serge lang, and elementary algebra for school (algebra 1) and higher algebra (2) both by hall and knight

[molten gulch]

They're not variations, just breakups of material nto differential calculus, integral calculus, and multivariable (differential and integral)

And fwiw stewart covers all of them

[fading mortar]

What are some really good algebra 1 books?

[molten gulch]

Abstract Algebra 1 or Middle/High School algebra?

[molten gulch]

Serge Lang as a first abstract algebra book is way too difficult

like WAY too difficult

[fading mortar]

High school algebra 1 and algebra 2 for +1 and +2

[fading mortar]

I see

[molten gulch]

OpenStax has some textbooks on it, when we were in school we just went off our teachers notes and didn't really use books

[molten gulch]

Gallian, Fraleigh, D&F, and Artin are IMO much better

[fading mortar]

I'm trying to collect all information i can collect on all of mathematics as I learn,
Thanks for this, do you have any other textbooks or pop math books in which I can find something? Thanks a bunch!!

[molten gulch]

Absolutely no popmaths, I hate that stuff, but I will feel good listing textbooks if I know you have the prereqs for them lol

I don't want to just give book names and you jump at them without knowing the prereqs

[fading mortar]

I have passed high school, and have completed my regular textbook which has algebra 1 in it (functions aren't taught yet)

Though I do have little info bits in advanced topics here and there

That's why I'm trying to comprehend them fully with a good source

Thing is, I'm not only trying to do questions while learning math, if you get me, I'm trying to understand the subject like why, what how etc etc, that's why I dont mind if the topics go little beyond my prereqs or even go beyond math itself (philosophy as in case)

I see

Nah nah it's okay, I understand

I like anything from which I can learn something "new" from

[fading mortar]

I appreciate the efforts, but I would also like the list as it would let me discover more things I can learn, thanks

[iron pulsar]

finished

i love deliberate practice.

[molten gulch]

How did you get through highschool without covering functions?

I am...a bit astonished

[iron pulsar]

i love "i put in effort, therefore i am passionate." i love cultivating passion and grit.

maybe i could read Grit again

[fading mortar]

Oh it's just how it is in my country

We learn algebra 2 after 10th (hs)

[molten gulch]

Ah here alg 2 is taught in 9-10th grade (US)

[fading mortar]

Complete alg2? As in inverse trigonometry too?

[molten gulch]

Yes

[fading mortar]

Okay so, what's the best textbook for algebra 1 and 2? (Of US)

Okay weird question but what is the best source (not just a book) from where I can learn pre algebra?

I've heard about Libre texts website

Also this video https://youtu.be/VXzm8ReImG0?si=vW3bGtt_HqsPs3Tx

[molten gulch]

Again, openstax textbooks should be fine at this level, I just must ask, why are you discussing analysis and abstract algebra without a solid grounding in these elementary topics? It just seems like you'd be setting yourself up for disaster. There's also no royal roadmap of mathematics, the further you go, you'll realize that everyone has their own favourite books and eventually, while there's still some semblance of a tree for some.things, it becomes much much murkier

[rocky path]

start with zermelo fraenkel set theory and work your way up /j

[civic peak]

Or first order logic. Whatever floats your boat

[remote sparrow]

https://www.rxddit.com/r/math/comments/1jq17n7/are_textbooks_meant_to_be_read_or_referenced/

[gray gazelle]

Start with Foundations Of Arithmetic by Frege, clearly..

[real marsh]

I didn't find Lang terrible as a first abstract algebra book, I just found you had to be good at ignoring the boring content

[civic peak]

For a first abstract algebra book I found Hungerford’s ‘Introduction to Abstract Algebra’ ( not his ‘Algebra’) to be great. Now that I’m doing more than just basic group theory/Galois theory I find it quite useful (I think it’s more a mathematical maturity thing for me)

[slow roost]

my first was Herstein, Topics in Algebra

it's pretty old but nicely written. But the convention he uses for writing functions is unfortunate

[still panther]

follow it up with "a course in arithmetic" by serre

[vital bane]

But there are absolutely great popmath and popscience stuff out there, you just have to search for them

Like Abbott's Flatland

[vital bane]

my condolences

[vital bane]

this

[fleet wyvern]

im broke

i ment dumb

[remote vortex]

A very nice book in similar vein is The Shape of Space: https://www.amazon.com/Shape-Space-Chapman-Applied-Mathematics/dp/0824707095

[vital bane]

Interesting, I shall check this out

[gray gazelle]

what is a good first book for a gentle introduction to harmonic analysis?

or if I need Fourier analysis first maybe that (I don't know the distinction very well)

I stumbled upon S&S Fourier analysis book, is that a good choice?

[vital bane]

afaik, fourier analysis is your classic fourier series of functions and fourier transform on R and R^n, but harmonic analysis is like doing fourier analysis on compact topological groups and stuff

[vital bane]

I've heard good things about that book

[gray gazelle]

So if I don't know the details of Fourier transform (just a surface level understanding) then I probably need Fourier analysis first

[vital bane]

I would say so, yes

[gray gazelle]

which stewart book should i use

i went to the website and theres 12 books

also ive got practically zero idea of calculus

i just got out of 10th grade

so would this book still be ideal

[gray gazelle]

so do you start with sets

[fading mortar]

In 11th, we starts with sets yes, then functions, trigonometry, PnC, Probability, calculus 1

[gray gazelle]

also wtf is alg 1 alg 2 calc 1 etc

[gray gazelle]

zamn same

[gray gazelle]

since when did chapters start having numbers

[fading mortar]

Algebra 1 is simple algebra like polynomials functions etc

[gray gazelle]

ye so which one is relatively recent

[fading mortar]

Algebra 2 is advanced algebra

[gray gazelle]

bwuh

[fading mortar]

Calculus 1 is introductory int and dif I guess

[fading mortar]

Where are you from

[gray gazelle]

chicken butter masala country

the one which was colonized for <200 years

nvm doesnt narrow it down

india

[fading mortar]

Oh, same, so everything you learn in 11th except calculus (limits) and PnC, is all algebra 1 in American system

[fading mortar]

I knew from the first response don't worry

[gray gazelle]

dawg

i thot i knew algebra

[fading mortar]

I don't know tbh

[gray gazelle]

apparently i have covered algebra 0

[fading mortar]

Nah I thought I did too

[fading mortar]

That's pre algebra

[gray gazelle]

me when weekly humbling in everything known to man

[fading mortar]

Like basic arithmetic and things

[gray gazelle]

hmm

[fading mortar]

Man, I just experienced the same thing yesterday here

So I've been trying to find information related to the definition of numbers and other mathematical entities

Turns out, there's none

[gray gazelle]

so im gonna do alg 1 and precalc + calc together

would that work

[fading mortar]

Yes that's 11th syllabus (ICSE)

[gray gazelle]

man

wish god dropped a universal math book

[gray gazelle]

what are you using for calc

[fading mortar]

That too, again, I got to know that everyone apparently has "choices" and there's not one single best math book for anything like alg1 2 or anything

What I'll be doing is writing my own, after reading all which are generally used

[gray gazelle]

bond?

[fading mortar]

Ah I see, I don't know calculus yet, so thanks ig

[gray gazelle]

so transcen is precalc?

stewart

[fading mortar]

Ian stewart?

Lol

He's a really great author

[fading mortar]

If you want to revise your uh

Basics*

You can complete elementary algebra by hall and knight

It's american type Algebra 1 book

Contains functions and all

Great book,
Has like 6k questions if you like to speedrun carpel tunnel

[vital bane]

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

[gray gazelle]

james

[trail hemlock]

ts boook is so peak

[cobalt arch]

Any good books on computing any kind of limit? I don't want a calculus book, I want something which has a more rigorous exposition of limits and deals with any kind of limit. There are some limits which I don't know how to compute and the books I have on them are not exhaustive nor do they treat these special cases.

[remote vortex]

Well, for a rigorous exposition you want a real analysis textbook (such as Abbott's Understanding Analysis), but I don't think you'll find a book that would give you methods you compute literally any kind of limit.

[cobalt arch]

It might have been an exaggeration to say any kind of limit. I would be happy with a book dealing explicitly with most kinds of limits. Do you know of any such book? I know a lot of real analysis books but not one that deals explicitly and exhaustively with these kinds of limits.

These limits aren't that hard to compute but I can't compute them and I want to find a reliable way to do so, as it would be the case in a book.

[remote vortex]

Have you got any examples of the kind of thing you're talking about?

I certainly rate it highly, it's very lucid and approachable, especially compared to something like Rudin's book (which covers more material but is much more dense and expects much more effort and experience from the reader)

[cobalt arch]

I can't paste the image here

[remote vortex]

Try in #calculus

There aren't many, but I liked the ones I saw.

[vital bane]

There arent many? each section has around 10, so each chapter has 40-50 exercises

[cobalt arch]

I posted it, any thoughts? I know they might seem elementary but still I can't compute some of them

[vital bane]

A lot

check my thread for proof

[remote vortex]

Just don't check how long it has taken

[remote vortex]

I stand corrected then!

Anyway, the exercises tend to be quite good because they test understanding, like asking the reader to consider what would happen if we relax the assumption of a theorem, or whether an object satisfying certain conditions can exist.

(so then the exercise becomes about constructing such an object or proving that it's not possible)

[vital bane]

and coming up with invented definitions like "clompact" and "vercongence" and asking the reader to analyze the properties of the objects that have these properties quite instructive

they test understanding

Understanding Analysis

[still panther]

[whole matrix]

Atomic habits by James Clear

[fading mortar]

Best books for pre algebra?

[hollow shore]

Hello. I am looking for brief and efficient treatment of standard Olympiad math topics with little less bloat. If you know any books matching this description, ping me.

[naive lava]

which olympiad?

[hollow shore]

RMO level

@naive lava I meant, math olympiad at the regional level

[naive lava]

pick ur titu andreescu book

all of them target slightly different audiences

[hollow shore]

is there um

one which covers every topic?

[naive lava]

you cannot get ready to an olympiad with just one book

[hollow shore]

I am not preparing for the olympiads lol

[naive lava]

then what r u doing lol?

[hollow shore]

But an exam with a olympiad flavour

to get into uni

I need a primer of sorts

[naive lava]

then what are the topics

[hollow shore]

Number Theory, Combinatorics, Algebra, Geometry (Plane and Analytic) and little bit of Calculus

[naive lava]

if you want compact and precise

u can check out putnam and beyond

but that's a hard book, u should keep that in mind

[hollow shore]

alright

[fading mortar]

What's the best pre algebra, and algebra 1 books of all time?

[tender river]

For you probably the book your school uses?

[wraith cave]

at that stage you can just ask anyone over 20 or go on khan academy

[fading mortar]

I'm not trying to learn, I'm just asking for the books you guys prefer for pre alg

[high fjord]

None

Waste of paper

[wraith cave]

yeah in math it only has exercises for precalc and most of the calc courses

• a few others

but nothing in linear algebra and differential equations

i haven’t continuously used it

i used it back in grade 6 to learn html and algebra 1

and used it last year to learn calc 1-3

[vital bane]

Learn linear algebra and offer to make a linear algebra course for Khan Academy

https://tenor.com/view/thanos-gif-25117042

[gray gazelle]

Wrong channel

[tame tree]

khan academy is already non profit

[gray gazelle]

[cunning elk]

“nonprofit”

and yet it keeps pushing that ai slop nonsense

[slow roost]

the first example Lang gives of a group is "Let G be a group and S a nonempty set. The set of maps M(S,G) is itself a group." yeah why bother starting with an actual example of a group, right?

[fading mortar]

Are openstax books worth it?
What about the everything you need to ace ___ series?

[remote sparrow]

nonprofit =/= has zero revenue

[molten gulch]

what is M

[cunning elk]

don’t confine yourself to one source

[remote sparrow]

if you are an element in M(S,G), you are a function that maps from S to G

[cunning elk]

I browse openstax/libretexts sometimes if im looking for good worked examples even outside of math

and the “everything you need to ace X” sounds sus just from the title

[slow roost]

correct, and this is a group because given maps f,g: S -> G, we can define a map (fg): S -> G using the group structure of G, i.e. (fg)(s) := f(s)g(s)

it's just such a weird case to use as the first example of a group

[remote sparrow]

they are fine

https://www.hachettebookgroup.com/imprint/workman-publishing-company/page/workman-brands/big-fat-notebooks/

[gray gazelle]

Lmao

[broken bramble]

most math books are horribly written

there are very few gems

[lusty elk]

I think a better example is what Herstein starts with: the set A(S) of all bijections from the set S to S. A(S) forms a group under function composition. I like this example cuz a group is (intuitively) the set of permutations of an object, and permutations are formally bijections from a set S to itself.

Herstein is very well written imo

I believe Jacobson Basic Algebra I also starts with a similar example

[slow roost]

it's a automatically a better first example of a group by virtue of it not mentioning "a group G"

[lusty elk]

yeah lol

[hollow scarab]

The logic book

[tawny crater]

looking for an undergraduate level, preferably a chatty textbook (not terse) which discusses topology with the use of filters

ive been reading munkres but my professor is a set theorist and this discussion is completely absent from munkres. (there is a two page "supplementary excersizes" part about nets)

[tropic nacelle]

@earnest iris someone recommended Blitzstein for prob and stats

no idea who that is, but there you go

[earnest iris]

Nice, ill check it out

[tropic nacelle]

https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit

ah found it

that's like 2 semesters of university statistics

[remote sparrow]

#book-recommendations message

probability != statistics

[tropic nacelle]

look at the content in the book though

[earnest iris]

If there is one that gives a more high level overview for statistics that would be greatly appreciated
I am mostly learning for fun and to understand the power of statistics

[tropic nacelle]

I mean I use them interchangeably because at a basic level they focus on distributions and so on

[remote sparrow]

i own the book

[tropic nacelle]

if they want to learn how to do ANOVA, preferably in R, or something

then they should specify

you're missing the context of our previous chat in the help channel

#help-11 message

[manic cairn]

have you tried asking your prof?

[tawny crater]

hes not the most approacheable

if all else fails

[still panther]

a dry one

[gray gazelle]

How's the book named "Mathematics for non Mathematicians".

[remote sparrow]

only one i know is willard, who is on the terse side

you can also look at folland's chapter on topology i think

[pliant wadi]

Contravariant right derived functors are absolutely killing me rn, any lecture notes/expository paper on it y'all like that I can refer to?

[vital bane]

I think you mean MGS, Metal Gear Solid

[remote sparrow]

[remote sparrow]

alternatively, monosodium glutamate

https://tenor.com/view/uncle-roger-msg-bae-gif-8759410599062906315

[heady ember]

https://tenor.com/view/metal-gear-rising-mgr-metal-gear-gif-7216811852594003147

[remote sparrow]

but it's not completely unrelated if the gif is from the same franchise

[heady ember]

That's why I sent an MGS gif

[tender cobalt]

fr

[vital bane]

MGR:R*

[iron pulsar]

i did it 🥳

[vital bane]

I am passionate, therefore I put in effort...

[iron pulsar]

and i put in the effort, therefore i am passionate

[vital bane]

is this the book you mentioned?

[heady ember]

[iron pulsar]

https://www.goodreads.com/book/show/27213329-grit

[jade tundra]

for garde 8

anyoe wanna be friends dm me

[surreal mango]

How is this book?

[iron pulsar]

i liked it

[regal juniper]

Who's Got any recommendations textbooks for linear algebra

[steady meteor]

I've been looking into the same and keep seeing Gilbert Strang's book recommended. He also did the 18.06 MIT OCW course recordings that are on YT, so my plan is to watch his course and get his book.

[regal juniper]

Have any idea what the book is ?

The name

[regal juniper]

Okay thanks for the extra information i'll check that out too

[steady meteor]

Linear Algebra and it's applications by Gilbert Strang

[regal juniper]

alright give me a quick second to get the book

[grand cloak]

Excuse me. Anyone here familiar with Brannan's Geometry? I'd love to discuss projective geometry. Thanks ✨

[regal juniper]

Got one of his books want it?

[steady meteor]

For real?

[regal juniper]

Add me I'll send it there

[steady meteor]

Sent you a friend request, you're my new bff lol

[uncut salmon]

Guys what's an idiot-proof book of algebraic topology (in particular about coverings)? I'm not understanding things about Galois coverings and friends.

[iron pulsar]

i like the section on grit constituents (interest, practice, purpose, and hope) and development (exploration, spotting and streching on weaknesses for a few hours each day, observing how the task connects with and contributes to other's wellbeings, and deepening the belief that sticking with things can improve future outcomes).

i could read the book again to learn to identify cultures for growing grit, since the third section concerned growing grit from the outside in.

[molten gulch]

friedberg, insel, and spence is quite good

[dim sierra]

that or axler. the latter is free

[strange tree]

Principles of Mathematical Analysis
Textbook by Walter Rudin

[molten gulch]

axler doesn't cover much of the matrix algebra some might want to know if they're just starting out

[vital bane]

FIS is much better in that regard

in every regard 🗿

[craggy sage]

Hello, any recommendations for hard math books that match JEE syllabus?

I'm not preparing for jee but it will be nice if I automatically prepare for it while studying maths on my own

[merry sphinx]

reference book, maybe

[manic cairn]

use serge lang’s basic mathematics

[regal juniper]

are these authors?

[naive lava]

a walter rudin book

[grim ore]

Dense?

[slow roost]

yes. Commonly referred to as FIS for short

[grim ore]

Dense textbooks dont have much exposition if at all, which is why they arent great for self study, but great for references as [kugelblitz](#book-recommendations message) mentioned

Is there a reason why you want to specifically read dense texts?

Honestly, I like dense textbooks too but for me its moreso finding them through word of mouth, either here, or stack exchange

If there is a field of math you are wanting to look into, i might know one in there

[slow roost]

I don’t recall ever seeing a textbook that is literally just definitions, lemmas, theorems, and corollaries

I’d be interested to see one

[grim ore]

tbh, if you are looking at the ug lvl, it would be hard/rare to find dense textbooks in that

[molten gulch]

rudin, axler(?), lang(?)

[remote vortex]

I wouldn't call Axler particularly dense

Rudin, certainly

[grim ore]

Rudin def

I mean, I think they want something specifically without much exposition, right?

[slow roost]

I think a word like ‘terse’ hits on what they’re looking for more than dense

[grim ore]

Yeah youre right

[slow roost]

or ‘difficult’

[grim ore]

Still, in terms of terseness, idk if there is any ug texts like that

[slow roost]

yeah not so much

try some grad books

Matsumura - Commutative Algebra comes to mind

[grim ore]

I think thats too far esp since they asked for a lin alg text

But yeah, would be terse lol

i guess for a regular grad algebra text that is terse/dense would be grad hungerford lol

[slow roost]

Serre - A Course in Arithmetic is another really terse and tough one

I’m fond of grad Hungerford, it’s what I used

[grim ore]

Lang's lin alg text iirc wasnt terse in the same sense that they wanted, but its pretty brief with some embedded exposition

[slow roost]

It is definitely more terse than D&F

[merry sphinx]

damn, never been hyperlinked before

[slow roost]

for linear algebra they might like Shilov

[grim ore]

lmaoooo

[molten gulch]

oh I meang lang's grad alg, though he does speak a bit in it

[broken bramble]

can i ask why?

math seems basically useless if you don't have any intuition

[slow roost]

read Bourbaki

[remote vortex]

Russell's Principia Mathematica

[regal juniper]

What's that

[slow roost]

Friedberg, Insel, and Spence - Linear Algebra

[signal mountain]

sounds like a reference

oh whoops someone alr said that haha

im blind

[iron pulsar]

https://www.goodreads.com/book/show/6271219-problem-solving-101 im reading this rn. it's tiny. 111 pages. super light and clear. fun

[limpid monolith]

complex methods book for phycisit plspls

[tender cobalt]

you could check out Roman's Advanced Linear Algebra for really a dense linear algebra treatment

not much intuition in the book

[iron pulsar]

i liked it. i found it helpful.

i liked the logic trees, root cause analysis technique, and pro and cons table. i liked the pleasant real-life stories they told, the principle of problem solving as partly thinking and partly acting, and the digestible, empowering language c:

i liked it

i really like improving my problem solving skills. i'm a problem solver

[molten gulch]

it also moves super fast and is abstract

[vital bane]

in the preface he says it's helpful if you've taken a course in linear algebra already

it's in the name "Advanced Linear Algebra"

[gray gazelle]

any recs for a introductory probability/statistics textbook, but that uses measure theory all the way? i found "probability and measure" by billingsley but idk if it's what i'm looking for

[tender cobalt]

yeah

[vital bane]

@remote vortex might have recs (but some of them might be in Polish )

[vital bane]

half of it is module theory

[tender cobalt]

Yeah and technically you start start linear algebra there if you have enough "mathematical maturity"

[tender cobalt]

only two chapters

[vital bane]

the mathematical maturity in question:
a course in linear algebra

[tender cobalt]

i dont think you can read roman even if you master axler

[vital bane]

yea you'd need some algebra

[tender cobalt]

its not like its fully based on algebra either

The most proofs in the book are like set theoretic

😭

[vital bane]

huh?

[tender cobalt]

yeah

[vital bane]

set theoretic?

wdym?

[tender cobalt]

the proofs are similar to poinset topology

[vital bane]

[still panther]

it just skips the first half (or even all of it depending on your course) of a linear algebra course in the prologue and calls it preliminaries

[molten gulch]

ehhhh

[still panther]

which is good

[vital bane]

topology proofs are similar to analysis proofs

[tender cobalt]

also AA material in the book is self contained

[vital bane]

can you give an example of a proof from the book?

[tender cobalt]

Wait let me show

[still panther]

that... would be really surprising

[tender cobalt]

check theorem 1.2

man the entire book is spammign set theory

[tender cobalt]

no

only metric spaces stuff are similar to analysis proofs

otherwise

its all mostly set theory

and thats what roman does, spam set theory

there is also zorns lemma spam quite often

[vital bane]

it's probably because the theorem itself is set theoretic in nature lol

[molten gulch]

lattices need set theory? all of math is set theory?

[tender cobalt]

see other pages

everything is set theoretic

like the set theory stuff you see in pointset topology

[vital bane]

but all of math is set theoretic

[tender cobalt]

finite sets countability etc

functions etc

[tender cobalt]

yes

[still panther]

thats not what set theory is about

[molten gulch]

Yes because we're looking at properties of vector spaces in depth?

[molten gulch]

BUH

you did not actually just-

[tender cobalt]

bruh axler definitely doesnt spam set theory much

neither abbott

[vital bane]

Ah yes how set theoretic

[tender cobalt]

idk im probably confusing

[still panther]

you can know if your text is interested in set theory by looking if it defines what cofinality is and proves Konig's lemma in the preliminaries

[vital bane]

Yooo Riesz Representation Theorem 🗣️🔥🔥🔥🔥

DA GOAT

[molten gulch]

yes this is most definitely analysis

[tender cobalt]

idk why yall simp analysis so much

😭

[vital bane]

we simp all the fields of math

they are all goated

[molten gulch]

Have you not heard our analysis rant

and our number theory rant

we have.....issues

[tender cobalt]

I simp everything EXCEPT discrete math (combinatorics etc)

[vital bane]

but analysis and geometry are extra goated 🗿

[molten gulch]

BUH

[floral lantern]

number theory my beloved

🤩

[tender cobalt]

geometry is goated af and is THE BEST if its not olympiad geometry

[molten gulch]

Astrid is gonna make sure you have a bad day for that one

[floral lantern]

minkowski's theorem

[molten gulch]

We're slowly coming to realize that it's best to let those enjoy what they enjoy

[floral lantern]

😔

[vital bane]

combinatorics is also goated, have you heard of combinatorial commutative algebra? it's a field where you use commutative algebra to study combinatorics

and vice versa

it's crazy

[tender cobalt]

yes that stuff is good

[vital bane]

I wanna study it one day

[tender cobalt]

but

[floral lantern]

algebraic combinatorics

[tender cobalt]

olympiad combinatorics, graph theory etc

[floral lantern]

😨

[tender cobalt]

NOPE

Algebraic combinatorics, sure

algebraic graph theory, sure

[vital bane]

graph theory is goated

[molten gulch]

buh graph theory shows up everywhere

[tender cobalt]

combinatorial topology (algebraic topology's old name), sure

[tender cobalt]

ik

[molten gulch]

You need basic graph theory for that\

[tender cobalt]

i just hate the olympiad style one

yes

but i just hate olympiad math

[molten gulch]

which is so-called olympiad style

[vital bane]

combinatorics have nothing to do with olympiads though?

[tender cobalt]

what

what you on bro

olympiad spams combinatorics

😭

[vital bane]

or rather the other way around

[molten gulch]

You do know that the olympiads generally pick specific types of problems to give people because they're easily tractable, right?

[floral lantern]

I will say oly combo is like

fine

compared to the rest of oly

[vital bane]

besides olympiad problems can be quite fun

[floral lantern]

there are actual problems and ideas there

and a lot of oly combo kids can almost immediately start succeeding in research because of the skills they learn in oly

[still panther]

combinatorics is at the D tier