book-recommendations

[tulip blade]

Construction of reals is pretty boring.

[quick hornet]

in any case, though, i wouldnt buy more books

you can, er, find them if you know where to look

and are fine with a pdf

[cursive orbit]

Is it just me or is this statement contradicting itself?

I disagree with the people who say this book is not for people who have never seen calculus before. Quite the contrary. This is the book you want so that you don't have to unlearn what you were taught in calculus to move on to higher math.

[gray gazelle]

Premise : I disagree with people who say this book is not for people who have never seen calculus before.

[prisma snow]

No, it is not contradicting itself

[cursive orbit]

oh wait

I'm blind

[prisma snow]

It is saying if you use another calculus book, you will have to unlearn what you learned in that book first.

But not with this one

[gray gazelle]

S1 : Quite the contrary. This is the book you want so that you don't have to unlearn what you were taught in calculus.

[cursive orbit]

I didn't see the double negative

[gray gazelle]

Me neither.

[primal summit]

Can u even do analysis on the long line with its usual topology?

[quick hornet]

i have 0 intuition for the long line

but id wager no

[grave egret]

agreed.

[prisma snow]

Bravo. You are both correct.

[marble solar]

Not preferring Ahlfors

[sage python]

Didn't you say you liked Marshall anyway?

[marble solar]

Marshall is pretty good

But I'm saving that for the summer since that has the most intense problems

I'm doing Ahlfors -> S&S volume 2 -> Marshall

Once I get most of the exercises solved in Ahlfors I'll move on

and yes, if I get stuck longer than a few hours I go on math stack. I have nothing to prove to anyone

And I don't need to waste weeks thinking up a clever substitution

[marble solar]

I really like Garnett & Marshall's book Harmonic Measure

[sage python]

Oh nifty

[marble solar]

yUh

Garnett pulled final questions from Harmonic Measure

You can guess how the final went

I think the average was below 30%, and I got a 40%

The super star analyst got a 75%

[tulip blade]

Opinions on fourier analysis book by stein and shakarchi

[marble solar]

Very good

You should work through it

[lapis sundial]

s&s expensive cri

[marble solar]

Just take it one volume at a time

[tulip blade]

yea I am

I want to do arithmetic combinatorics and fourier analysis comes up a lot so Its probably a good idea.

[foggy relic]

can anyone recommend a good calculus based introductory statistics book? the one im considering is "An Introduction to Statistical Learning: With Applications in R"

[split bluff]

yeah reading Spivak to learn calculus is like studying car mechanics to drive a car

[foggy relic]

libgen

[crystal lion]

if you wanna become a car mechanic you should study car mechanics

if you wanna become a mathematician you should study the "mechanics" behind calculus

idt anyone is telling engineers to go study real analysis

[split bluff]

i think one should know what a certain thing does before studying it rigorously

at the end of the day, math is a tool to ease real life reasoning

[crystal lion]

99% of the server would like to have a word with you

[foggy relic]

bump

[foggy relic]

another book i think is good is "All of Statistics: A Concise Course in Statistical Inference"

[tiny karma]

Sorry for the belated reply, my background so far has been going through the first two years of mathematics for typically every STEM major.
-Differential & Integral Calculus
-Multivariable & Vector Calculus
-Linear Algebra & Differential Equations
I have yet to take a proofs class but shall in the upcoming academic calendar.

[past ice]

Spivak is how math majors should be learning math anyway. You don't see an analogous computational and proof-devoid abstract algebra course before you start learning it rigorously. Why treat calculus/analysis like this?

[crystal lion]

i think it's more in the sense that computational calculus is preparing you for that rigor jump

and once you've taken a rigorous course you don't need to "ease yourself" in again

also idk wtf proof-devoided abstract algebra would be

[past ice]

well anecdotally, computational calculus courses don't seem to reliably train any of the skills required for rigorous mathematics

[crystal lion]

like what would be the analog to "computing integrals" in abstract algebra

[crystal lion]

no I meant specifically real analysis

[past ice]

the kind of integrals people spend months computing in nonrigorous calculus classes seem to exist only in the american education system. People who study math in Europe are equally confused on how American math undergrads spend months computing integrals without proving any theorems

[crystal lion]

maybe it's like

for the mast majority of people

they have to take some math class after precalc in hs

and in no way are they prepared for the level of rigor you're alluding to

this is bad but computational calculus seems to really fit in with the rest of courses in american hs math education

[foggy relic]

checking if a group satisfies associativity

maybe

[crystal lion]

lol like

checking (n choose 3) products in a group of order n?

oh boy

[foggy relic]

more lol

[crystal lion]

computational calculus is the peak of the "memorize formula and apply it 50 times" attitude

[foggy relic]

cough cough ap stats

[past ice]

well I definitely agree that the issue with math education is pretty foundational and not easy to fix. But I'm also skeptical about how well computational calc transitions aspiring math ppl into the rigor. Pretty much every math major I've talked to who went through the computational calc/lin alg/ode sequence feels like they were just picked up and placed in the deep end when they took their first rigorous course (at my school, there is an "intro to proofs" course that every math major has to take, and it has the reputation for being very difficult).

[foggy relic]

by computational calculus, do you mean like evaluating tedious integrals

i only learned calculus because I needed it for a pre-requisite, so I did 3b1b/khan, which is computational mostly. nowhere near the level of say spivak

[lament sage]

here's my hot take

education system bad

[foggy relic]

how is that a hot take?

[lament sage]

exactly

[foggy relic]

the educational system is just doing boring and easy things 10000 times

ex: in my precalc class today the teacher told us how to multiply matrices and then made us do like 20 on our own which was very boring. I would have much rather wanted to learn say how matrices came to be, why you multiply it that way because of vectors, etc

[past ice]

I think d/dx was just noting in a cheeky manner that this same conversation happens pretty often. But I'm always happy to rag on the garbage education system so I'm not complaining lol

[foggy relic]

[crystal lion]

the infamous "intro to proofs" course

[foggy relic]

isnt that like what is induction, what is proof by contradiction, etc

they dont teach any math in it afaik

[past ice]

yeah, imo it's something of a band-aid for the lack of rigor up to then, but a pretty effective one.

[lament sage]

I don't know how it is in other countries but here most people can barely tackle computational calculus

let alone a rigorous proof based one

[crystal lion]

it's a half ripped band aid at best

i feel like (purely speculation bc im not in college) most ppl develop this level of rigor on their own to get by

[past ice]

well if we're being generous we can say it's a very good band-aid applied to a severed limb lol

[crystal lion]

if your limb is severed you need stitches or some shit

not a bandaid

ok that's not very important lol

[past ice]

that was what I did and anecdotally that's what the most successful students seem to have done. The capacity to self-learn is perhaps the best predictor of success in a rigorous math program.

[foggy relic]

which country are you in?

[foggy relic]

which grade

[crystal lion]

2nd

[foggy relic]

you're in 2nd grade?

i find that hard to believe

[crystal lion]

oh I meant

12nd

typo

mb

[foggy relic]

12nd

cool

im in hs also

[karmic thorn]

I see. I think Abbott's Understanding Analysis might be a good starting point, or you could check with the recommendations/reading list of your real analysis class.

Rudin is not great on pedagogy, and Tao barely has any computational problems.

[gray gazelle]

I am looking for "AGS Pre-Algebra" and "AGS Algebra".

[wooden sparrow]

[gray gazelle]

If anyone can help me, pls text me

[quick hornet]

wow vakil really branching out

[tiny karma]

The one that's taught with at my institution has terrible ratings.

[tiny karma]

Oh, understood !

[tiny karma]

I'll make use of this suggestion, thank you !

Is there a different text you'd recommend after I've gone through a proofs class ?

[karmic thorn]

Perhaps you could use Rudin alongside a pedagogically sound textbook then. There are far too many analysis books out there, but imo Tao+any book with good problems should be a nice combo.

[tiny karma]

Gotcha, thanks !

[karmic thorn]

No worries; goodluck!

[gentle sapphire]

Anyone has any experience with Moschovakis’s Notes on Set Theory? Looks like a good read.

[vocal parcel]

What would be a good starting point for Olympiad level math and physics for me? I'm already prepping for JEE and I kinda wanna start preparing for the Olympiads too?

[stray veldt]

there is an olympiad server in #old-network

[vocal parcel]

alright thanks

I'll check that out

[frigid comet]

artofproblemsolving is an invaluable resource too. there are lots of books but which ones would depend on your level etc.

[gray gazelle]

Nothing offensive, but does Olympiad help ppl improve math?
What happens to math olympiad winners, do the really takeup math later?

[molten mountain]

I know a person who did take math later who really enjoyed participating in olympiads... Ig if you have a zeal for it then it'll help you... Just participating for winning prizes may not help ig

[quick hornet]

if by "olympiad winners" you mean top performers in the IMO

many of them do end up going into math, yes

and they typically do very well

not all do though

some went into another STEM field or whatever

as for whether the olympiad helps with higher math: yes, but not as efficiently as just studying that higher math directly

[final goblet]

Which is the best book for set theory and.. also for Euclidean geometry?

[quick hornet]

how deep of a dive do you want into set theory?

do you just want "the basic terminology/techniques required for the rest of mathematics" or do you already know that and want a dedicated treatment of the subject for its own sake?

if the former, most introductory-level proofsy math textbooks will have a section on it; munkres' first few chapters come to mind, or any book on proofs (like velleman)

if the latter, halmos' naive set theory is a good starting place

(despite being "naive", it develops everything formally from a variant of ZFC, it just skims over some regularity stuff)

as for euclidean geometry... honestly i think most people will recommend you just read an annotated version of euclid lmao

euclidean geometry isnt studied too much for its own sake outside of the context of some higher-level geometric or logic techniques

so lower-level treatments are considered more of a historical curiosity

which is why people will typically recommend euclid

there does exist research into euclidean geometry on a higher level (see tarski's work on it, for instance), but that has heavier prereqs

[and AFAIK, that body of work hasnt really been collated into a single resource and is mostly spread between various papers by tarski/hilbert/etc, although i may be wrong on that point]

[frigid comet]

It helps with developing "clever" problemsolving. Olympiad calibre students are often able to prove technical lemmas quite quickly/creatively (indeed some putnam and IMO problems are spawned from simple cases of lemmas in papers). This is only one aspect of research mathematics though, and success in olympiad math is neither a necessary or sufficient condition to succeed in research math.

[candid obsidian]

can someone recommend textbooks on string theory?

[gray gazelle]

introductory set theory book?

[gray gazelle]

Scroll up and you can see namingtons opinion on that

Ohh nice nice

[willow pecan]

You can ask for books on string theory in the physics discord, helpfully linked in #old-network

[gray gazelle]

I second Naïve Set Theory

[gray gazelle]

Prerequisites are quantum field theory and general relativity. You got those?

Also, yeah, phys Discord is probably better, you can ping me there if you want

[candid obsidian]

can i study it from somewhere? like a textbook?

i'm starting from scratch with a high school calculus knowledge

or i guess it qualifies as early uni

[gray gazelle]

qft and gr are very advanced physics

You absolutely need an undergraduate in physics to even attempt any meaningful string theory

[candid obsidian]

so there is no way i could study it on my own?

ok then

thank you all for your help anyway

[gray gazelle]

Unfortunately no, sorry

Unless you want to commit several years

[gray gazelle]

You could! You’d just have to commit to learning, well, physics as a whole

[candid obsidian]

yes, thank you, can you recommend a text book?

[gray gazelle]

If you just want to learn a bit about string theory, the popsci book The Elegant Universe by Greene is fun

[candid obsidian]

i'll probably start there, then see if there are any textbooks

thanks

[gray gazelle]

If you want to start out learning physics, I recommend Young and Freedman’s University Physics

[candid obsidian]

thank you so much my man

[gray gazelle]

No problem! If you ever need help + have questions, the Physics server in the #old-network (i haunt there most of the time) will be happy to assist!

[candid obsidian]

ok

[sinful pewter]

sometimes they move on to see real math, and they hate it and reject it

[marble solar]

@sage python I had enough points from my credit card to get two free books from amazon

I ordered my physical copy of Marshall

Thinking of ordering Rick Durrett's Probability

[sage python]

@marble solar hmm

I feel like since Durrett offers his book free anyway

There's probably a better use of that second slot

[marble solar]

I don't do well w/ PDFs

I do also need to learn some functional stuff

[sage python]

Gotcha, so is Durrett a book you consult frequently?

[marble solar]

No, but I am ignorant of probability

So UT Austin has 7 quals you have to pass

Each equivalent to 1 semester of material

My thinking is like

Real, Complex, Fcnl, PDE, Probability

Will be the first ones I tackle

What you thinking @sage python? should I just grab Haim Brezis?

[sage python]

Yeah I'm thinking

If you're mostly doing PDE stuff then yeah Brezis might be a good functional book. Alternate option is Buhler-Salamon if you want to do more spectral theory

But less Sobolev spaces

I guess like, a good rule just for your eyes' sake is, buy the books you think you'll be reading the most

[marble solar]

I like hunter and nochtergale for applied functional

[gray gazelle]

Guys I'm looking for a good translation of Euclid's Elements.

Have you already a suggestion for it?

[sage python]

Hmm, so where do you think you'll most likely be next year? All factors taken into consideration, what's the "default" plan? And what research area will that entail?

My logic is you'll have quals one way or another. But if you anticipate that your research will involve a lot of X, then buying a book on X is the best idea long run

[marble solar]

There's a good chance I'll end up at one of Austin, A&M, or Irvine

At A&M/Irvine I'll be working with the people I know which is a mixed bag of

Functional, PDEs, Probability, and Harmonic Analysis

A&M would be more on the functional side, Irvine more on the probability side

both in harmonic and PDEs heavily

I don't have any experience in pure functional or pure probability

I took an applied functional class that was solving Boundary value problems

And I did random matrix theory as my first probability class

[sage python]

Maybe Brezis + Durrett was the strat instead of Marshall

Nah jk

I imagine complex could still kick in a fair bit in that kinda stuff tbh

[marble solar]

Yeah, and Marshall's approach is pretty unique

With lots and lots of problems

I'm about halfway through Ahlfors

[sage python]

Is it a more analytic angle?

[marble solar]

It's very geometric, very analytic

Lots of pictures, angles, analytic expressions, clever limits, etc.

I mean I learned all my complex analysis from Garnett

So it just goes hand in hand with that

[sage python]

So in my mind I'm thinking what to get depends on what you pair with what

Like e.g. Brezis is prob the functional book best tailored to you

But if you're also getting Evans

[marble solar]

I already have Evans

[sage python]

At some point in life

[marble solar]

I've worked through the major chapters important to me

[sage python]

Yeah then I imagine the Sobolev space/PDE material in Brezis is largely redundant right?

[marble solar]

Yeah

I can link the syllabi for Austin

https://www.ma.utexas.edu/academics/graduate/preliminary-exams/prelim-courses-syllabi/probability

https://www.ma.utexas.edu/academics/graduate/preliminary-exams/prelim-courses-syllabi/applied-math

So if I prepare for Austin quals, then I'll be ready for Irvine and A&M quals

https://www.ma.utexas.edu/academics/graduate/preliminary-exams/prelim-courses-syllabi/analysis

Here's the analysis one as well. I'm probably just using the S&S series, Ahlfors, and Marshall to prepare myself for that one next August?

Since that's the one I'd be most prepared for, and then see how I feel on either applied or probability

[sage python]

Yeah hmm, I guess idk if you buy math books somewhat frequently then don't overthink this decision, you've got Marshall, get either Durrett or something in functional. If you have Evans then within functional get something that maybe does more spectral theory or stuff like distributions/harmonic

Maybe S&S 4 lmao

Actually tbh I like S&S 4 as a choice here

But yeah I think you could just knock those 3 out in one go

Maybe first focus on analysis + applied? Probability is probably the one you'd have to go most out of your way to do

[brisk ice]

@sage python can you let you or any for that matter know if any of these books on this list are good

https://hnarayanan.github.io/springer-books/

if you scroll down to the math/stats section

managed to snag all of them at the time but not sure all this stuff seems pretty advanced

oh well i do see linear algebra

[sage python]

Idk most of these books tbh

[brisk ice]

:/

[sage python]

Grafakos Fourier is supposed to be good

Fulton and Harris is a classic

Axler I don't like

Lee Smooth Manifolds is pretty good, perhaps a bit drawn out for my tastes

[gray gazelle]

god particle

name of the wind

a wise man's fear

DAYLIGHT

[willow pecan]

?

[gray gazelle]

they are great books

[willow pecan]

Oke

[marble solar]

I already own this

[marble solar]

I get math books when I have spare change lying around that I may spend

[sage python]

Gotcha

[sage python]

Just go with your heart I guess

[gray gazelle]

should i print this book or munkres topology?

i know nothing about topology and set theory

[thick python]

I'd personally recommend munkres

[gray gazelle]

awesome thanks

i like munkres cover more so munkres it is

oh also

should i get the second edition of it

does it even matter to start with

[thick python]

¯_(ツ)_/¯

[crystal lion]

this should always be the primary reason to choose a textbook

glad to see someone else with the same principles

[gray gazelle]

great minds think alike

Munkres is a munk

[inner sentinel]

Content comes third. First is the cover. Second is the cover as well.

[gray gazelle]

ayo i found a way to get books 10 times cheaper so now I can get 9 books instead of 1!

so

im looking for an introductory analysis book

and a calc 3 book

[inner sentinel]

I recommend not Stewart

Just anything else

Spivak Calc on manifolds

[gray gazelle]

Why not stewart tho

[inner sentinel]

Because that book has scarred me for life

Because the author is allergic to proofs

[gray gazelle]

oo

Isnt analysis

Proofs

[inner sentinel]

Calc III

Not analysis

[gray gazelle]

ohh

my bad

[inner sentinel]

Baby rudin is classic for analysis. If you want something less intense, Bilodeau has a real analysis book that’s pretty good and not as hard as rudin.

But rudin is the gold standard for it.

[gray gazelle]

I see

As long as its fun

[inner sentinel]

I think Tao has a real analysis book as well but could be wrong?

Haven’t done anything with it, but I think I remember hearing about it

[gray gazelle]

Ill keep it mind

also

how about

oh wait

i need linear álgebra for abstract algebra right

[inner sentinel]

Artin

Artin Artin and Artin

[gray gazelle]

?

oh

[inner sentinel]

Artin’s Algebra

Great text

[gray gazelle]

does it cover both topics

because if it does

[inner sentinel]

Starts from linear algebra and goes into group theory, ring theory etc.

I’m on chapter 13 rn

[gray gazelle]

DAMNN

[inner sentinel]

Great book

[gray gazelle]

ok im going to get it

[inner sentinel]

Absolutely amazing imo

[gray gazelle]

sounds awesome

ok so far

i have in my to buy list

munkres topology
spivak calc on manifolds
bilodeau or baby rudin

[crystal lion]

add gallian contemporary abstract algebra

[gray gazelle]

and artins algebra

[crystal lion]

and you're list is starting to come together

[gray gazelle]

alright

also

recommend me a math book thats not a textbook

like

idk sharing stories, biographies, etc.

and then my list will be complete

i was thinking of getting Erdos biography

but im not sure

[crystal lion]

gallian has a couple biographies inside of it

that's why it's the gold standard

[tranquil ocean]

@gray gazelle read the Weil conjectures by Olsson

[still jay]

I second this, it was a very interesting read

[ripe granite]

http://math.fau.edu/yiu/PSRM2015/yiu/RECREATIONAMATHEMATICS/Grothendieck.pdf

[crystal lion]

"Grothendieck’s father, whose name may have been Alexander Shapiro"

he's related to ben shapiro

how tragic

[past ice]

anyone know of an all-purpose gre math subject test review book that covers the usual fare of topics in a shallow but broad manner? i feel like i'm selling my soul asking for this, but dammit i want to go to grad school

basically I've taken a bunch of grad courses in algebra and analysis but i've never taken the standard computational ode and multivariable calc courses, and it's been several years since i've done computational lin alg or practiced basic integration by substitution etc. the subject test is in two months and for now i just want to quickly revise those subjects well enough to do well on the test and it would be convenient if the core stuff was all in one place

[vocal panther]

Maybe this one? I'm not to sure about the exact needs but I believe this covers most if not all of the GRE math subject test: https://www.amazon.com/Cracking-GRE-Mathematics-Subject-Test/dp/0375429727?asin=0375429727&revisionId=&format=4&depth=1

however I think there are people more qualified to help with this

[sage python]

This is good for revising the topics

Questions are a bit too easy

But you can just use this for material and easy practice and then try to find others later. Honestly idk if there are any good practice tests floating around

[past ice]

@vocal panther shit thank you so much that looks perfect. I wasn't looking at the standard gre prep books because a friend gave me the REA one and the review section was really bad and incomplete, and i kinda assumed they would all be similar

[vocal panther]

Yeah np!!! Idk much about this area but as long as it works that's good

[past ice]

@sage python noted. thanks for the heads-up

on the other hand, it seems like the one i already have has harder practice tests than the actual gre. so it works out great

[hearty steppe]

How does one prepare to score top 80%+ in Math GRE lol

[hasty turret]

Idk that doesn't seem hard tbh

Math gre sounds like an annoying PITA rather than a real difficult exam

[sage python]

The hard part about the mGRE is the speed

You have to do 66 questions in 170 minutes iirc

So basically 2 and a half minutes per question

But one was like

det(4x4 matrix with polynomial coefficients), take the derivative

[livid ermine]

[gray gazelle]

jee advanced

is hard for maths

[gray gazelle]

no I am studying for adv

its not hard

but the course/syllabus is huge

which can be a problem

the individual question themselves arent hard

oh...

i am in 9th grade

will start preparing

after 2yrs

yeah but i recommend to make your maths very strong it will help a lot and reduce stress in class 11

like try to study 10th maths in class 9th if u r serious and interested

and in 10th try to study class 11 math

[gray gazelle]

oh..thanks for the tips

[stray veldt]

<@&268886789983436800> this is probably scam

[gray gazelle]

Which Edition of Artin's Algebra should I get?

[sage kelp]

Just get the one you find

[gray gazelle]

alr

[crystal lion]

that’s a really cool bookstore you got there

[glossy grove]

[gray gazelle]

ok so far i have in my list:

-munkres topology
-spivak calc on manifolds
-artin's algebra
-naive set theory
-the weil conjectures
-gallian contemporary abstract algebra
-bilodeau / baby rudin

[quick hornet]

why are you taking 50 courses at once

[gray gazelle]

Uh no i mean

This will probably be the only time ill get to "buy" books so i might aswell get all of em at once

i aint gonna read em all at once

probably

in a year or so

[gusty smelt]

Don’t buy them at once.

Buy it just before@you study something so that you don’t have a change of heart and end up wasting money

[quick hornet]

ah i see whats going on

[gray gazelle]

I See

[quick hornet]

alright, fine then

[gray gazelle]

Ill keep that in mind

[quick hornet]

if you want to "buy" them now in preparation for the future

[gray gazelle]

my friend can get me each book for 3 bucks each

around 3-5 bucks

[quick hornet]

oh that isnt the direction i was expecting this to go

but i guess that works too

[gusty smelt]

Oh alright just buy em then kek

[quick hornet]

why not just buy a bunch of textbooks and flip them on amazon/ebay though lmao

[gusty smelt]

If that’s not too much money

[quick hornet]

seems like a great arbitrage opportunity

[gusty smelt]

I assume it’s cheap Indian print memes or smth

[quick hornet]

ah sure

[gray gazelle]

nah im not from india

[gray gazelle]

Wdym

Uhm either way

Did i pick good books

I plan to self teach myself linear algebra, abstract algebra, set theory, topology and analysis

oh i should probably add a proofs book?

[primal summit]

Do you have any experience with set theory?

[gusty smelt]

Gillian is not good book.

[gray gazelle]

just a little little bit

[gray gazelle]

why?

[gray gazelle]

i watched a few vids that sparked the interest on set theory

[stray veldt]

there is #book-recommendations message for proofs

[gray gazelle]

OH THAT ONE

I was forgetting it

Tytyty

[stray veldt]

i mean you can get a book but those are pretty long

[gray gazelle]

ye

sooo, i might get rid of gallians

an add a linear algebra one maybe

[tribal cedar]

currently studying from linear algebra by jim hefferon

https://www.google.com/url?sa=t&source=web&rct=j&url=https://joshua.smcvt.edu/linearalgebra/book.pdf&ved=2ahUKEwjgxKKP0avyAhWwSfEDHcofAEwQFnoECAcQAQ&sqi=2&usg=AOvVaw27Fr515b0-3lHH84QVq7L7

check it out, it's free

[primal summit]

Anyone know of a good source to learn basic theory of continued fractions?

[wispy peak]

I am planning on purchasing an analysis textbook, currently I am thinking about Abbot. I am a highschooler studying it for fun, so there is no pressure from school. I have heard that Abbot is generally easier to follow but still rigorous enough, and given the fact that I cannot dedicate all my study time to it because of school this option seems good. Is there any textbook that would be better or just anything I need to keep in mind?

[wispy peak]

not sure, although khan academy might have it

[primal summit]

I doubt it

They don't have much past hs level and introductory college stuff

And this is not a topic many people care about

[wispy peak]

if anyone has the answer, please ping me with the reply

o ok

sorry then, i havent studied this before so

[primal summit]

np

I appreciate the help anyways

[wispy peak]

no problem

[prisma snow]

I think abbot is good in your situation, yeah

[wispy peak]

o ok thanks

[solemn rover]

this is obvious but i find the wikipedia page on this topic to be very helpful

[primal summit]

I've read through that but there's a lot of statements with no proofs there

And every paper I can find is like 'obviously this theorem is true'

[sage kelp]

@wispy peak I have been reading Abbott and it is really accessible. It will fit really well for your needs

[wispy peak]

ok, thanks

ive heard well about it from others too

ill go for that mostly

[sage kelp]

Yeah, I mean if you want an introductory text, Abbott is fine. Then you can move to other books

[wispy peak]

ya, im thinking of using papa rudin a little later

[flint forge]

@primal summit kind of a weird approach but iirc there is material in Brin and Stuck about continued fractions from a dynamics perspective which is kinda cool

[primal summit]

i'll check it out thanks

[gray gazelle]

Should i get Abbott instead of Rudin or Bilodeau?

I think ill get Abbott, from what ive readed here

[analog lava]

abbot is easier and more gentle

rudin will change you

[gray gazelle]

for good or bad?

I assume the latter

[sage python]

For good

[analog lava]

hard books are good

struggling with the exercises and going back and forth between theorems etc

[gray gazelle]

wait

[analog lava]

is really good

[gray gazelle]

i see

like

it makes me think

[analog lava]

yea

even before the exercises

[gray gazelle]

ill take that into account

[analog lava]

u will have to do some effort to understand the slick proofs

making u better

[marble gulch]

"slick" as in "hand-wavy"?

[analog lava]

ummm

idk

haha like

not hand-wavy but

like does little effort to make sure u understand

or idk

[marble gulch]

That's basically most math books.

[analog lava]

abbot

tao

pugh

those are analysis books that prove things way different than rrudin

especially tao and abbot

way different not as in with technique but with explanation

[marble gulch]

I know Tao likes using asymptotic arguments a lot.

[analog lava]

i guess

but i meant like

these 3 books are way more gentle in their proofs

and are also slower

rudin is dense

im now in papa rudin

and its just dense aswell

not much prose

not much (if any) examples

fucking amazing exercises

and thats it

[marble gulch]

Royden is similar.

[analog lava]

nver read

[marble gulch]

There is not a single example in Royden.

[analog lava]

wow really

[marble gulch]

Yep.

[analog lava]

ig in the measure theory chapters in papa also the same

lmao

ig measure theory is abstract hehe jk

[marble gulch]

Constructing measure spaces in non-trivial.

[analog lava]

i guess

im still learning so idk

but ig i cant think of a measure other than 3 or 4 + lebesgue integral

so yea haha

[marble gulch]

Does papa rudin cover Daniel integrals?

I forgot.

[analog lava]

maybe

i am still in chap 2

so idk

[marble gulch]

I just checked. It doesn't.

[primal summit]

Asking for a lot of recs today but it seems like I need some holes in my education filled. I need to learn about convex geometry, a book would be fine but the best thing would be some paper that is not too long but comprehensive

[gray gazelle]

hey uh

thoughts on gallian contemporary abstract algebra?

or does anyone know an introductory Level abstract algebra book

YO how about

Steven Warner - Pure mathematics for beginners

Its 262 pages long

And claims to rigurously introduct the reader to topology, set theory, abstract algebra, number theory, real analysis, complex analysis and linear algebra

[cursive orbit]

well judging from the corresponding coursera course

it tries to do a lot but everything is at the bare minimum surface level

[willow pecan]

Induction is number theory?

[cursive orbit]

idk

it's weird

[willow pecan]

X for doubt

[cursive orbit]

but all I know is it can't compare to any dedicated abstract algebra book

[willow pecan]

This seems like too brief for any depth

How can you explain why groups are important in 40 minutes?

[cursive orbit]

seems like a borderline scam

it makes you think you're learning a lot when you're not

[past ice]

Warner seems to have built his brand off of "get 800 on SAT math" type stuff so I wouldn't bother with that book

[cursive orbit]

lmao

[willow pecan]

Yikes

[past ice]

uh wtf is a pre-beginner

[cursive orbit]

A “pre-beginner" is a math student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting.

[past ice]

sounds sus tbh

[cursive orbit]

yeah I definitely wouldn't buy that book

might as well buy like a discrete math book at that point

I just checked the book and the entire abstract algebra section is like 4 pages long

[past ice]

that's hilariously bad

[glossy grove]

Aren't we going to talk about how he sells the instructions to learn a single song for 20$

[quick hornet]

99% of online courses are not worth the money, and the remaining 1% are very expensive and basically just one-on-one tutoring

online courses not affiliated with an educational institution, that is

[gray gazelle]

The only online courses worth doing are probably the ones from fancy pants schools where you get a fancy pants degree at the end

[sage python]

And where you learn to play the fancy pants man game

[gray gazelle]

i love him

[sage python]

It was so much fun

I grew up on that, Shift, Bug on a Wire, Bloons Tower Defense, Angry Birds, Temple Run

[lament belfry]

i love those books

what abt fireboy and watergirl doe⁉️

[lapis sundial]

i miss fancy pants

[ionic wren]

You remember the temple run cheat?

[sharp latch]

I do lol

[sage python]

@ionic wren which?

[ionic wren]

The one where you went right a couple times a think

And you would just be able to run straight forever

And it would give you an achievement

[sage python]

Hmm, I don't remember it offhand

[gray gazelle]

love that game, especially during library times in middle school when we were suppose to be researching online for a book.

the best math course online is cool math games.

[gray gazelle]

oh shit

I just realized the book i got, in a legal way of course, has the "GET +800 ON SAT TEST!"

Crying rn

[frail lily]

hello loods

been trying to understand Markov models and chains a bit better, quite a bit of probability theory behind it

any fairly introductory prob textbooks that you really liked?

[gray gazelle]

I skimmed a book, I think by ross, it was okay

I think there were a few standard books on stochastic processes, I can't remember which ones were easier

[frail lily]

I'm around the level where I've only done math in terms of background for ML

Are the r/math book recs any good?

[gray gazelle]

I don't think I have ever looked at that

[frail lily]

I have access to a uni library and I just take random books and read them

but they're sometimes super introductory and sometimes super hard

[gray gazelle]

Ah, I think the other book I skimmed was karlin and Taylor

[misty wyvern]

I liked Grimmet and Stirzaker for (non-measure-theoretic) probability theory and stochastic processes. If I ever teach a class in prob theory I'll use that book.

Bremaud for pure Markov chain machinery is probably your next best bet.

[split pond]

does artin cover a good amount of linear algebra? or does it assume you have a prior knowledge in LA?

is it good as an introductory book for both LA and abstract algebra?

[eager stump]

It's ok enough for linear. I personally like to separate the two

[split pond]

alright

[misty wyvern]

yeah separate the two. there's a lot of depth to linear algebra that abstract algebra won't have time for, though you'll do the important general things for multilinear algebra

[split pond]

any recommendations for books on Linear algebra?

[hasty turret]

I guess friedberg looks good

[cursive orbit]

Axler

[gray gazelle]

axler is the hatcher of linear algebra

[sage python]

They're both controversial but for different reasons

Axler's writing seems smooth from what I've seen

But his philosophy on determinants is idiotic

Hatcher has a valid take on the material it presents

But I find that it's really a book for people who already have good visual intuition rather than a book to help you develop it

Also I remember the quality of exposition dips hard for Van Kampen and for cohomology

[split pond]

oh alright , will look into it

thanks!

[gray gazelle]

anyone know any good books on these topics?

looking for additional resources

[cinder turtle]

Hello guys! I am trying to learn about vector, I do have a bit of understanding like what are vectors? how do we find inner product of two vector, unit vector etc but I want to learn why we use these formulas to find these things, like the prove behind those formula like proper explanation for derivation of every formula, I am student of computer science and i am taking the course computer graphics it deeply revolves around vectors concept, and I was never taught the LA conceptually in school, all they did was made us force to remember the formula but i now really need to understand the concepts, any help would be greatly appreciated, currently my focus is to understand basis of vector, span of vector and orthonormal basis. I am sorry my English is bad but I hope I made sense of what I am trying to ask?

If anyone can recommend a book!

[velvet briar]

Check out 3b1b "essence of linear algebra" on YouTube for some quick videos on it

[cinder turtle]

Yes i did yesterday but still I was lost 😦

[velvet briar]

"Linear algebra done right" is a very strong book, but is proof-based. Maybe check it out, but be aware it might be a tough book.

[cinder turtle]

Thanks @velvet briar, I'll look into it!

[golden hull]

hi guys ! do u know a book with only integrals and their results ? (one and various variables)

the same for linear algebra and analytics geometry

[quick hornet]

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

has links to a bunch of other pages of lists

most of it is sourced from Abramowitz and Stegun btw

which now exists as https://dlmf.nist.gov/

its not JUST integrals but it has a lot of them (probably the most of any place anywhere)

im not exactly sure what you mean by "the same for linear algebra and analytic geometry" though

like, for linear algebra, would it just be a massive list of row reductions? lmao

linear algebra doesnt really have anything with the computational difficulty of integrals

its very "nice"

and analytic geometry... is very very broad

if you want a book series with a fuckton of integrals

Prudnikov-Brychkov-Marichev

theres 5 volumes

(though you probably only want volumes 1 and 2, maybe 3)

that said, this is like, super duper overkill for any modern uses

since now we have computers

but like... if you REALLY want a book specifically

and have a thousand dollars to burn

it exists.

[gentle wharf]

Can anyone recommend a book for trignometry for undergraduate level?

[lapis sundial]

(there is trigonometry at an undergraduate level?)

[prisma snow]

It's the easier trig where you prove everything using exponentials 🙃

[quick hornet]

unironically rudin

in the sense that the 2 or so pages rudin writes on formally defining the trig functions is the only thing undergrads know about trig that high schoolers don't

(at least as far as real numbers go)

obviously any other analysis textbook would serve this purpose as well.

[gentle wharf]

Do u know abt the JEE exam

[quick hornet]

...oh.

forget my advice then

you just want advanced high school trig

[gentle wharf]

Yeah

I mean here where I live your school grade really don't matter for the level of education

I be 14yr old and my friends (my age) even know abt complex numbers but I dont

[lilac storm]

Tell me about any Book or any video on number theory ......where I learn easily .........

[frosty girder]

i think thats eveywhere

but for your purpose, SL loneys book should be much much more than enough

[karmic thorn]

This is not something that should worry you. Take your time. Your progress doesn't depend on your friends' progress.

[radiant turret]

Higher algebra is good

[radiant turret]

Indeed

[lethal axle]

umm what board do you follow

[gentle wharf]

SSC

[lethal axle]

ok you know you can get ncert textbooks for free online

10th grade one has trig

[radiant turret]

Ncert is spoon feedin tbh

One should study frm diff books if he wants to devlope his problem solving starts

[lethal axle]

yeah if you want a good one you can get iit jee pearson foundation book

thats rlly good

[radiant turret]

[frosty girder]

[hasty turret]

tfw jee is just math gre but worse

[cursive orbit]

Tfw jee

[frosty girder]

gre?

[hasty turret]

Look up "math gre" on this server

[frosty girder]

what is this mess
jee math in the us or sth?

[hasty turret]

Yes

[quick hornet]

uh

the gre and jee are totally different exams

theyre not really comparable besides being calculus-heavy timed exams

theyre not even for the same career stage

[hasty turret]

I know

But,the questions are very similar

Like you could expect gre style questions to appear on Jee

[quick hornet]

the jee isn't entirely multiple choice

[frosty girder]

time to grind GRE i suppose

[quick hornet]

a lot of GRE questions are designed with the multiple choice-ness in mind

lots of integrals which would be super time consuming to compute by hand, but which you can play around with a bit and rule out all answers except 1 quickly

[frosty girder]

wait who gives GRE? HSers?

[quick hornet]

undergraduates take it to apply to graduate school

[frosty girder]

[quick hornet]

theres the "general GRE" which has trivial mathematical content

and then various "subject GREs"

[hasty turret]

Well,there are actually 2 JEE exams here. One is called "mains" and is entirely multiple choice

[quick hornet]

including a mathematics subject GRE

[hasty turret]

This same trick applies here too

[frosty girder]

it does have 5 numeric questions in each subject as well
but tbh they are the same format as the MCQs

[quick hornet]

and half the subject GRE is not calculus

like the calculus-ness of it is often exaggerated since thats typically the most time consuming part

lots of weird ass funky integrals and whatnot

but half of it is on basic probability, combinatorics, lin alg, a bit of intro group theory and topology

[frosty girder]

[quick hornet]

those do tend to be the easier questions if youre familiar with the subject though

[frosty girder]

so, if i got this right,
GRE math is an exam with a lot of calculus (not as much as people say but still) and a few other parts of maths, and is strictly timed?

[quick hornet]

the mathematics subject GRE, yes

[frosty girder]

that sounds like JEE math with extra steps

[quick hornet]

the general GRE has a mathematics component but its stupid easy

like its expected that a math applicant gets 100% on it

maybe one or two questions wrong because brain fart

[frosty girder]

ah,
so GRE is the SAT for UG students?

[quick hornet]

kindasorta

[frosty girder]

:i_see:

[quick hornet]

you can look at https://www.ets.org/s/gre/pdf/practice_book_math.pdf for some example problems that might appear on the GRE

i think its a bit dated though, the GRE has slowly gotten harder over time

(it uses percentile-based scoring rather than numerical scoring so this doesnt really matter much though)

again there ARE questions from math beyond calculus but theyre really really easy lmao

"do you know the definition of a group"

you might notice that even the calculus involved isnt really that hard

mostly just time consuming

like a typical IIT JEE integral is way harder than most GRE integrals

there are some genuinely hard questions though, this one only 22% of people got it right

which you might notice is only slightly better than random guessing

||this stat surprises me since my immediate guess would be the correct answer||

[gentle wharf]

Yeah I have got a lot to study in the years ahead then....

[quick hornet]

didnt you say youre 14?

i would not worry about the GRE lmao

[gentle wharf]

Yes

[quick hornet]

its taken by ~22 year olds

american ~22 year olds specifically

(or those applying to grad school in america)

[gentle wharf]

What do you people mean by grad school?

[quick hornet]

postgraduate education; Masters degrees and PhDs

you can do it after your undergraduate (bachelor's)

most students dont though, its reserved mostly for the particularly smart/motivated/academic-minded

[gentle wharf]

Then what is the degree education called

[quick hornet]

you mean for a bachelor's degree?

"undergrad"

[gentle wharf]

Oh

I have school for 10 standards general and then high school for 11th and 12th

[gray gazelle]

Bachelor's degree, master's degree, blank's degree, what is the word for blank here

?

[quick hornet]

doctoral

[gray gazelle]

Doctoral's degree?

[quick hornet]

doctoral degree

[gray gazelle]

Doctor's degree?

[quick hornet]

no one says that

but sure, technically

[gentle wharf]

Career eh big tough thing to figure out

[analog lava]

is it only once?

A?

[frosty girder]

yes

[analog lava]

lmao

cool

[night harbor]

hello everyone, I'm a student in undergrad coming from another major entering 3rd year in "General mathematics" (opposed to the "applied mathematics and statistics" major), as I understood my admission was a bit "atypical" so I aim at preparing and step my level up by 1. Getting a bit ahead of the program by reading the classes first and trying to have a basic grasp of the concepts and 2.improving my mathematical thinking and my problem solving ability
so I was thinking about buying one of these book (or another of this kind), is there any you would recommend more ?
https://www.pearson.com/us/higher-education/math---science/mathematics/advanced-math/advanced-math/transition-to-advanced-math---intro-to-proof.html
thank you by advance !

[willow pecan]

See the intro to proofs section of #books-old

[gray gazelle]

I'm still reading through this but so far it's great, for this one I suggest having a pen or paper or anything similar to jot down things in since it's really not enough to just read and think you'll just remember everything afterwards imo

https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0134746759

[night harbor]

Oh thank you I didn't check it out yet

[night harbor]

Oh yeah this one seems to be very popular, might be one I will definitely end up reading
Thanks !

[small garden]

I'm just gonna start reading any book that pops up here lol

[gray gazelle]

[primal summit]

Do u remember the correct answer here nami?

[quick hornet]

||A i believe||

[primal summit]

You could do this explicitly with like, multivariable chain rule for the first differentiation right?

[quick hornet]

yeah i just checkd, it was ||A indeed||

[primal summit]

[full linden]

Anyone has some lecture notes on probability theory? (Non measure)

[novel solar]

Is this book good for introductory combinatorics

[prisma snow]

I've heard great things. @karmic thorn is using it and highly recommends it

[willow pecan]

Manan also recommends Tao though

[golden hull]

Ty, I'm preparing to do a entry test and I need to overkill because the uni only have 15 spaces >-<

[misty wyvern]

the GRE is trivial, you only have to study for the math gre

to my eternal shame though i made more errors on the general gre

's math section than on the qualitative stuff

[quick hornet]

i mean, its just a list of integrals

it wont teach you to actually do integrals

unless your plan is to memorize thousands of integrals? lmao

[prisma snow]

Trueeee

I guess Bona is bad

[golden hull]

I didn't saw the Prudnikov-Brychkov-Marichev yet, and I have a good lvl of integrals (I already pass my uni exams) but Im looking some content to do (?

[still jay]

You could also try “Inside Interesting Integrals” by Paul Nahin

[golden hull]

Ty! It looks very useful

[gray gazelle]

Good books for probability theory?

[eager stump]

It's very nice

[mellow wren]

Wtf lmao 15 spaces
Damn

Although studying obscure integrals seems like kind of a waste of time
But I don't know what the university wants lol

[golden hull]

I think I'm gonna have a lot of time (8-9 months to re do 2 years of uni) and when I was doing the test of calculus I prepared them in 1 week max so... (Tbh I was looking integrals because I don't want to re do the same and ,improve my memory)

[karmic thorn]

[hearty steppe]

I need to check out Tao sometime. I see it mentioned too much

Still really stickin to rudin tho

I’m basic

[misty wyvern]

Looking for beeg books on topological group theory

I need a general reference and learning place

[radiant turret]

Do u mean books of micheal artin ?

Arent there any pdfs of his book in the net

[karmic thorn]

They need a physical copy

@sour briar As far as I recall, hardcovers are almost always standard editions. I'm not aware if there's a paperback standard edition out there.

[karmic thorn]

You could probably find a used copy in good condition for a reasonable price

[hasty turret]

You could download the ebook version and take print outs

It's not ideal,but it's probably cheaper than buying the book,I think

[stray veldt]

check abebooks

[gray gazelle]

good linear algebra book for someone that uses linear algebra extensively but haven't properly studied it.

[willow pecan]

Friedberg

[gray gazelle]

thx I look into it.

I found a pdf and I like the contents, starts up with vector spaces right away. Thanks.

[undone pine]

Does someone know any book on group theory treating generally concrete applications of it and introducing some notions to understand it? (Just to read something for general culture during holidays)

[analog lava]

contemprorary abstract algebra

[tulip blade]

wdym by concrete applications?

maybe Abstract Algebra: Theory and Applications by Judson

never used it but its used at some good schools i think so its probably fine. and it has applications in the title so it probably has those. Im not sure if abstract algebra has any applications to concrete though.

abstract-algebra for construction workers: concrete applications.

[gray gazelle]

Fraleigh

[undone pine]

Thank you

[nocturne wedge]

Hello ladies and gentlemen. I would like to ask you mathematicians and those interested in maths that, could you please recommend me some books on ancient greek mathematical philosophy and history of astronomy until the renaissance? Also if you add the history of engineering and medieval era robots to it, that would be great. Thanks in advance.

[gusty gorge]

For ancient greek work; Euclid's elements, the Almagest by Ptolomy, and Arithmetica by Dophantus are good sources

[bronze raven]

How much of math book recommendations come from marketting versus honest reviews. Is it the case that the most popular books got their reputation by simply being well written or is it more of a factor of certain teachers in universities saying its the best book theyve used and causing a chain reaction of others to pick it up. Is there an amount of books that will forever be overshadowed and not publicly know because of this?

[gusty gorge]

maths is a bit more objective tbh, that may the case for popular maths books, but for textbooks, there's only so much information that can be presented, like all of the calculus books are pretty much the same, presenting pretty much the same information, the only thing that'll probably change are the problems

[bronze raven]

So it probably doesnt become an issue until you deal with topics with less standardization

But then people dont write books at that level

So its probably a non issue

[gusty gorge]

Yeah, and when you get more and more specialized, it gets to a point where there are literally only 1 or 2 books on the subject, so it's even less of an issue of overshadowment

[sage python]

So the thing in math is

[foggy relic]

ex: spivak calc vs stewart

[sage python]

Most people just teach out of the book they know

[foggy relic]

same content, just diff problems

[sage python]

@foggy relic this is not a clear comparison

The audiences are different

[bronze raven]

yeah its not equal

I think Michael helped me understand perfectly

Who is the one in charge of deciding what a standard Analysis/Algebra/Number Theory curriculum for undergraduate?

ones*

[sage python]

Each school does its own thing but there's usually just some sensible choices that are made by profs and textbooks which just become standard

[primal summit]

How come so many people recommend hatcher then even tho it's bad

[bronze raven]

I am starting to hate it more and more honestly

[gusty gorge]

Haven't read Hatcher tbh, was thinking of reading Rotman when I get to it

[primal summit]

You should

Rotman is 👌

[bronze raven]

actually though?

[primal summit]

I'm enjoying it very much, there are some small parts where I wish.he would elaborate more but I've never been left confused for more than like 3 mins and some of those are my fault

[bronze raven]

[molten agate]

any idea where to look for all of spivak calculus exercise's answers? and free?

[sage python]

You want some dank complex analysis problems?

@marble solar

My friend wrote these two psets for the bootcamp he TAd in

[lapis sundial]

downloads for later

[crystal lion]

broke: coding bootcamp
woke: complex analysis bootcamp

[eager stump]

how is this a thing

and here i had lost all hope

[solemn rover]

rotman's supposed to be really good

[foggy relic]

whats a good book for an intro to mathematica, given i have 0 cs background

[bronze raven]

What are some resources on reading lists or curriculum that a statistics undergrad should know?

[foggy relic]

a statistics undergrad should know statistics

[willow pecan]

Your best bet is to look at the degree requirements for a statistics undergrad at some big highly ranked university and then see the descriptions of the corresponding courses and what textbooks they use

[misty wyvern]

nobody should know statistics

[bronze raven]

yeah im doing some research now qq

i was hoping for one of those meme book lists from a ***** website

[willow pecan]

[misty wyvern]

@bronze raven Go through Wasserman's books, they're basically the best stats references. Approximately MS-level but not PhD stuff.

If you want the PhD-level stuff, learn some measure theory and pick up Keener.

[bronze raven]

what is some

up to what topic ud say?

i only have maybe a first year stat knowledge sadly

[misty wyvern]

Know how Lebesgue integrals work, know some Hilbert space theory, then that's sufficient.

But it sounds like Wasserman is more useful for you, if you have a solid computational math background like linear algebra.

Since you have the advanced role you probably exceed the level Wasserman needs.

[bronze raven]

better safer than sorry

but is his All of Statistics good for everything you'd learn in undergrad?

because my goal is to only have undergrad level knowledge

im not sure how much that is either

[misty wyvern]

Yes, All of Stats and All of Nonpara Stats will cover all the stuff an undergrad + MS student learns.

[bronze raven]

Is it rude to say I find that hard to believe

Two books covering an entire 4 years?

[misty wyvern]

Not at all, you'll miss out on elective-type stuff like hiearchical modeling and machine learning, but they cover all thte core material.

Yes, believe it or not stats degrees are trivial.

[bronze raven]

[misty wyvern]

For a mathematician at least.

[bronze raven]

I hope thats a lie

[misty wyvern]

My man, I've interviewed stats undergrads before who could only do linear regressions.

[bronze raven]

I havent learned any proper stats theory in school

[misty wyvern]

You have no idea.

[bronze raven]

Thats probably the low end though

[misty wyvern]

No, these are the high end, out of Ivies.

[willow pecan]

[misty wyvern]

Anyways Wasserman will cover all the core material.

You'll miss out on some important stuff (IMO) like I mentioned but they're elective-type material.

[bronze raven]

Thank you I only want to collect these for future if I am feeling up for learning more stats

Im not really sure what hiearchical modeling is

or machine learning

Ive only heard of them as buzzwords

[misty wyvern]

Hierarchical modeling is a kind of structured approach to statistics more useful for practical problem solving than reading papers, it's something any mathematician can pick up in a few minutes with a good introduction once they know the core stat theory. So I wouldn't bother.

Machine learning is a lot more interesting but typically not that mathematically exciting. Nonetheless a pretty rich field right now. Loosely speaking it's a type of computational statistics. More formally it encompasses a range of recursive semiparametric statistical methods. Might be worth learning if you're interested in AI.

[bronze raven]

Thanks for the explanations might consider them in future but ill start with the basics

[misty wyvern]

I'm not going to totally shittalk ML, there's some ML theory out there that hangs with the hardest analysis in math.

But most ML is meme-tier math.

[bronze raven]

My main motivation for learning is just to be more literate

[willow pecan]

I think that statisticians and mathematicians have different motivations

[bronze raven]

Yeah for sure

[misty wyvern]

No, our motivations are the same. We want to get grant money and waste as much time as possible.

[willow pecan]

[bronze raven]

I want to be able to know if correct statistical methods were used for studies in the future

And then learn more arbitrary stuff beyond that

Because I feel like all the statistics you learn K-12 in NA is frequentist propaganda

[misty wyvern]

The frequentism-Bayesian debate was thought up by utterly deranged people.

Different tools for different situations.

Anyone who tells you there's a sharp distinction is a con artist.

[bronze raven]

Yeah I liked that when first learning stats

Everything I learned truly felt like a tool

So I am sort of interested in learning the theory behind it also

[golden stag]

Best book

[misty wyvern]

tell me why

what's a covering space

oh wait i remember now, some alg top stuff

I should go back to Tom Dieck and learn some alg top

[nocturne wedge]

Thanks for the suggestions @gusty gorge.

By the way, which one of these books should I buy?

[narrow talon]

There’s some areas of ML with some pretty heavy math though (I know you didn’t imply it was all meme tier, but I see it generally get glossed over). Geometric deep learning, neural tangent kernels, optimal transport, and a lot of unsupervised/self-supervised learning are pretty good areas to see a lot of math - usually analysis and geometry - beyond just standard optimization, algorithms, and probability

[misty wyvern]

Yeah, I mentioned later that a subset of ML deals with actual hardcore math.

I'm tangentially familiar with the transport and wavelets stuff.

Also worth noting in NN convergence results the probability also gets pretty hardcore.

[dark ocean]

Hello everyone,

Can you tell me please what level is needed in probability and geometry to better break through in optimization and variational calculus?
And what books do you recommend !?

Thank you!

[willow pecan]

Do you want to do like optimal transport stuff? If so you'll need a very good foundation in measure theoretic probability

[dark ocean]

I learn machine learning more precisely in optimization, statistics in large dimensions ... and there is a lot of probability and notions of geometry (polyhedron, convexity, etc.)

[willow pecan]

Oh

Ok

Do you do theoretical ML/statistical inference type stuff

Or more application focused

[dark ocean]

Little both.

But my master's thesis is more application focused.
I want to do a PhD so I want to learn the basics that I don't have and that I discovered in my master.

[marble solar]

Did you have the option of doing a Masters thesis or exams?

From what I've seen the masters thesis doesn't help that much

[gray gazelle]

id like to read a book on prime numbers

about their properties and such

Preferably not a very long book

around 500 pages or so if possible

[eager stump]

if it's not a prime number of pages then...

[willow pecan]

It sounds like you want a book on number theory

How much math background do you have

[quick hornet]

http://www.math.toronto.edu/~ila/Cox-Primes_of_the_form_x2+ny2.pdf

probably beyond what youre asking

but its the most significant text i know of JUST talking about primes

chances are you actually want an elementary number theory book

since those talk a lot about primes

[gray gazelle]

I took calc bc and i have to read Abbott analysis

and a brief introduction to proofs

i see isee

ill try to look for an elementary numbee theory book then

[tranquil ocean]

Yeah something about primes is pretty vague

Basically all of number theory is about properties of primes in some way

Take a look at Silverman's introduction to number theory maybe

[dark ocean]

Sorry but I don't understand you question !

[gray gazelle]

Alr alr

Ty

[sharp latch]

If you’re looking for a casual book over a textbook try Derbyshire’s “prime obsession” it’s a nice text to get people interested in math and primes and introduces some of the harder stuff in pretty simple terms

[sinful pewter]

collatz introduces some of the harder stuff in pretty simple terms

but I don't fall for it

[weak apex]

Any recommendations for an intro in to discrete maths? Please @ me for any suggestions

[gray gazelle]

I just finished reading a bit of it and ngl i really liked it. By any chance, do you know other books like it?

[remote ginkgo]

this book is great

[remote ginkgo]

logicomix was mildly amusing. also feynman's quantum electrodynamics was fun semi-popsci-ish stuff

but had actual computation in it

with some fun lil historical stuff

[icy skiff]

Does anyone know of a good book that covers harmonics, resonance and perhaps relations of them to the universe?

[willow pecan]

What is resonance

[icy skiff]

I suppose it’s the relation of frequencies, where they are “in tune” or they resonate with each other.

[quick hornet]

this sounds cranky

like that "432 hz tuning resonates with our bodies and brings spiritual enlightenment" crap

[lapis sundial]

lol

[quick hornet]

(no clue why the universe would pick an integer number of hz, given that seconds are not at all a fundamental unit...)

[gray gazelle]

isn't resonance a materials thing

like glass has some resonance frequency and if you scream loud enough in that frequency it breaks

[quick hornet]

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

theres a weird internet rabbit hole that says that our bodies or our eardrums resonate better or worse with certain frequencies, causing various health effects

this should immediately strike you as bullshit due to human bodies being composed of very different materials

as well as different humans having differently sized and proportioned bodies

but cranks gonna crank

[gray gazelle]

cargo cult science at its finest

[quick hornet]

also stuff about the "natural resonance of the universe" or something

(air has different natural frequencies depending on pressure FYI)

anyway, back to the question

harmonics and resonance is... very very broad

and a mathematician's understanding of those words is very different than a physicist's or a musician's

i mean, they talk about the same thing, but they'll study different things in relation to them

talk to a mathematician about "harmonic analysis" and they'll think of fourier series and topological groups; talk to a physicist and they'll think of waves and strings; talk to a musician and they'll think of chord progressions

so you'll need to clarify exactly what you're after

"relate them to the universe" is perhaps the most broad phrase ever spoken in human history.

[icy skiff]

Haha yeah that was a bit inaccurate. I’m not really looking for anything in particular, but not musician harmonics. I’m somewhat more interested in it from the physics side, but I just want to understand more about harmonics/resonance in general

[gray gazelle]

cool math books that arent textbooks?

[quick hornet]

https://www.books4school.com/spongebob-squarepants-1-2-3-under-the-sea-board-book-9780449814802-0449814807.html

[gray gazelle]

[brisk ice]

can you give an example?

like books about math that are not exactly a book on a specific subject maybe?

[gray gazelle]

too hard

and sure thing

prime obsession - bernhard riemman and the greatest unsolved problem in mathematics

and