book-recommendations

[gray gazelle]

I gave Pre-RMO in 2016

Was nice

[gray gazelle]

rmo is regional and the syllabus is same

The difficulty level of the examination increases from the Pre-Regional Mathematical Olympiad (PRMO) to International Mathematical Olympiad (IMO).

[shadow tusk]

thanks for your contributions @sturdy shore, the description's now been changed https://github.com/ossu/math

[hasty turret]

Why is Geometry and topology an advanced topic?

[shadow tusk]

I guess that's because topology isn't included in the three content areas that are specifically recommended as required for every mathematical sciences major program

which are Calculus, Linear Algebra, and Applied Statistics and Data Analysis

according to the 2015 CUPM curriculum guide

[narrow fiber]

well

I think the genuine reason

is that topology and geometry can get Really Hard

[foggy relic]

This list rivals the fast track

[sage python]

Looking up what this is I don't think people actually take that seriously

[shadow tusk]

is it bad?

[uncut zealot]

Of these the only two I plan to take are calculus and LA, which I've already taken years ago. Data analysis isn't even offered at my school.

Also, I was talking with a friend of mine who wanted to know more about fractals and I realized I literally only know the pop-math version of fractals. What are some recommendations for learning about fractals given a reasonably strong undergrad math background?

[fallow cypress]

Yes it's good, really gentle introduction; you might want a more advanced textbook if you have more experience, but other than that, no complaints

[shadow tusk]

went to reddit and heard good things about https://www.amazon.com/Fractal-Geometry-Mathematical-Foundations-Applications/dp/111994239X

[random spear]

looking for maybe grad level set theory? I'd like to get into ordinals, axiom of choice, etc

[sturdy shore]

grad level would assume you already know all those and would skim through them

I assume you are looking for something on the level of jech - introduction to set theory (baby jech)

[quiet shore]

anyone have any strong opinions on Stein & Shakarchi b4's treatment of probability? (the funcanal book, ch. 5 titled "Rudiments of Probability Theory") I liked good chunks of b1 and b3 and want to know whether the treatment is too sparse / too dense / etc. given that the topic is only given one chapter

[sullen spruce]

yeah, I need resources to learn a few topics which are not provided in NCERT and Aakash modules, for example number theory

[rigid trail]

Any recommendations for an introduction to PDEs?

[narrow fiber]

evans is the book I'm studying from

which is wonderful so far

[remote sparrow]

evans is a graduate book. for undergraduate, consider strauss or zachmanoglou

[daring lake]

Hi, sorry to interrupt. I am planning to take a course on real analysis this semester and though to get Royden and Fitzpatrick to supplement it. Would that be a good book?

[remote sparrow]

royden is graduate

[orchid mortar]

Define good

As said, Royden is graduate

[remote sparrow]

math sorcerer reviewed fitzpatrick favorably

he says it's the book he used

[rigid trail]

Thank you

[remote sparrow]

https://www.youtube.com/watch?v=-yksoVsb47s

[rigid trail]

I'll check them out

[remote sparrow]

this video could help too

i don't really know much else tbh

[random spear]

ah my bad---i'd still be interseting in hearing though. i prefer the slow pace through intro grad texts so long as they have enough content that i can parse through it eventually

[daring lake]

Oh, what would be suitable for UG?

[remote sparrow]

baby rudin, abbott, cummings, bartle and sherbert, etc.

there is a wide variety

[daring lake]

Okay, I will take a look

thank you

[remote sparrow]

baby rudin is likely to be the most difficult if you are studying it completely by yourself, but if you have a mentor or a dedicated study group, it could work

rudin also has the most supplementary resources available

francis su and winston ou have lectures following baby rudin

francis su goes from chapters 1-5

winston ou goes to chapter 7 i think

[sturdy shore]

kunen is the canonical intro grad text from what I've seen

focused on forcing and independence proofs

[random spear]

oo thank you

that's a big part of what i wanted to see

[sage python]

Idk about bad but departments do what they wanna do based on their internal ideas, resources, etc. Nobody cares about some self-proclaimed governing document

[daring lake]

Okay, I will look through them, tysm

[narrow fiber]

oh interesting to see asmar here lol

my physics prof will draw on parts of it I think

[cedar flume]

Hello, can anyone recommend book for differential geometry please

[young cloak]

Does there exist a "Bible" of Number Theory?
Just as Algebra has 'Algebra by Serge Lang'.

[frosty yarrow]

Anyone?

[hazy elk]

It's a fine book, the subject of cookbook/technique oriented ODEs is boring so can't really comment more. The "theory" is easy to understand and the problems are mostly routine applications of the techniques.

I don't know who needs to learn ODEs like this tho

Cus applied math ppl + scientists and engineers do comp stuff anyways for differential equations and whenever some analytical stuff shows up you can just look up the technique

Waste of time for everyone

But well if you need it for a course, not much you can do.

[gray gazelle]

you mean elementary number theory, analytic, or algebraic?

i'm assuming elementary

[grand thistle]

also if you use baby rudin there’s a good supplement that tells you what exercises are good to do and even has exercises not in the book

https://math.berkeley.edu/~gbergman/ug.hndts/m104_Rudin_exs.pdf

i used it for my first time learning analysis and although it was hard this helped a lot

[daring lake]

Thank you very much for sharing

[young cloak]

Yeah elementary maybe...
If that fulfills.
Though doesn't matter to me, because if any other subfields have prerequisites I'm planning to cover that up too.

[gray gazelle]

try Burton or Dudley

for ENT

[young cloak]

any difference between two?

[gray gazelle]

dunno, I've only done Burton - but I heard Dudley is good too.

[young cloak]

Because I already took Linear Algebra, Abstract Algebra and Analysis...

[gray gazelle]

none of that is needed for NT imo

but if you've done algebra i suppose it helps

how far into algebra are you?

[young cloak]

I was kinda looking for more advanced texts

[gray gazelle]

hold on, I think I might have what you want

[young cloak]

Just groups

[gray gazelle]

if you want something advanced, try "ireland/rosen's a classical introduction to modern number theory"

it's a graduate text

[young cloak]

ok it's more towards analytical ig?

[gray gazelle]

probably doesn't matter then

[gray gazelle]

it requires you to be familiar with some basic abstract algebra and builds from the ground up

[young cloak]

@gray gazelle
Thnx - my college math department has scarce pure Number Theorists

[gray gazelle]

no worries, enjoy

and good luck

[young cloak]

cool

[spring anchor]

Hey. Does anyone have solution manual for the problems in the book on Analysis by N. L. Carothers..

Can you please share the link?

[fluid hull]

Hello!
Does anyone have any book/lecture note recommendations on an elementary introduction to formal linguistics? Specially if it does specify connections and inspirations from formal logic?
A history of the subject would also be lovely.

[iron granite]

I want all books which will outline how to earn money from a math degree. Please write your recommendations in set builder form.

[real veldt]

Become a software developer 🙂

[gray gazelle]

Is Douglas B West's book good for graph theory?

[fluid hull]

We do use it for our graduate course on graph theory and have covered almost all the first 5 chapters.
It seems pretty standard and beginner-friendly.
Bondy & Murty is also a good book, so I've heard

[gray gazelle]

Bondy and murty is too expensive for me to buy physically

Douglas B West's book got an Indian subcontinent edition

So much cheaper

[fluid hull]

Oh, is having a physical copy something that is necessary?
There are resources for finding PDF files of books that are much too expensive.

[finite thorn]

I'm thinking about getting myself a kindle (specifically a kindle scribe whenever that comes out in my region) to read math books, does anyone else think this is a good idea? The tablet itself is expensive but you can write on pdfs so that could work well I suppose

[iron granite]

I was setting it up for someone to go {} but this is actual advice.

[gray gazelle]

I personally prefer physical books haha

Just a choice

[fluid hull]

Haha, of course. That's perfectly valid🌺
Well, I'm from a country that doesn't really provide the resources to buy any books that aren't translated unless you find one luckily in your university library, so getting PDFs and printing them is how I usually get "physical copies".
Maybe you can print it chapter by chapter as you read through the book; it'll also save money if you end up only needing parts of the book, rather than its totality

But West is good too, either way.

[crimson leaf]

West is a good intro

Diestel is good as well but more difficult and terse

[gray gazelle]

Hmm ok, thanks for the help

😄

[swift dome]

any recommendations on linear algebra that are thorough and at a beginner level

[crimson leaf]

Computational or proof based

[heady ember]

Look in pinned

[rigid barn]

Hoffman & Kunze if you want real linear algebra, not just matrices and column vectors

[mossy flume]

for something proof based I really liked FIS

[crimson leaf]

Yeah for proof based FIS is beginner friendly

[gray gazelle]

Serge Lang's Introduction to Linear Algebra

[gray gazelle]

beginner level LA is usually never proof-based

it's almost always computational

and saturated with determinants

[shadow tusk]

not a book but check this out https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/

[crimson leaf]

That depends on which country you're in and school you go to

[sage python]

Yeah the reason it's common in America to have this split isn't that it's good pedagogy, as much as many people cope themselves into thinking this

It's that a lot of departments aren't in a position where it makes sense to have a completely separate path through the first two years for future math majors. A lot of people don't come in thinking they'll major in math, and manpower is limited.

So you just put both future math majors and future science/engineering majors through the same first two years

[crimson leaf]

There also tends to be a lot more engineering+physics+comp sci students who will take LA than math students

[sage python]

And yeah the needs of science/engineering majors will be prioritized in that case because they're the bulk of the students (and thus of the funding)

Then after second year when you know who your math majors are

You do things right

But in some American universities where there is more manpower and demand, and in many countries (e.g. a good part of western Europe I think) where you apply directly to your major

You can teach linear algebra including the abstraction from the beginning

[mossy flume]

yea the benefit of going to a large school is that the only LA class I've had was proof based from the beginning

and the computational lin alg course is completely separate

and the university had enough profs to run both separately

but ofc not every university can do this

[mossy flume]

there tend to be a lot more of people in those majors than math lol

math is relatively unpopular compared to engineering and CS especially

[remote sparrow]

niven, zuckerman, and montgomery may be right for you, while remaining firmly undergraduate.

[remote sparrow]

#book-recommendations message

[hollow hedge]

Hi, I am taking a Calc 1000 course and I didn't do so well last time, I ended up dropping the course. Primarily I struggled because I've never done any highschool math/algebra before, to the extent that terms like "distribute x" or "isolate x" were foreign to me, so was the Trig used. I feel fairly confident in those things now, but I'd like to be better prepared this time. I'm looking for any book recommendations. Especially those with lots of examples and practice questions.

There is no textbook required for the course, they base it off this free source: https://openstax.org/books/calculus-volume-1/pages/1-1-review-of-functions

However, they do have an optional recommended textbook "Single Variable Calculus: Early Transcendentals by James Stewart" is that worth it? It's over $100 as most textbooks are, so I'm hesitant.

[cursive orbit]

no

if you really want a physical copy of a textbook, buy a used version of stewart

or earlier edition

those are often near-identical and are 10% of the price

[loud finch]

Any book recommendations for 17 year olds? I’m interested in pure maths and stats. I’m looking for a book which would be suitable for my age and doesn’t have any advanced graduate level mathematics🤞

[remote sparrow]

there is no book suitable to your age specifically (see an exceptional case in lyra), but rather to your background. what have you learned already?

[loud finch]

I’m from the UK (Ik a lot of people here are from America so they have different names for courses). But I’m studying a level maths and further maths. In general some of the topics I’ve done are differentiation, integration, linear algebra, proof by induction, complex numbers

[remote sparrow]

#book-recommendations message

some of the recommendations are not relevant. if you have already learned some linear algebra, you can look at the pins.

[loud finch]

Ok I’ll take a look at them, thank you

[real veldt]

Complex analysis recommendations?

[hollow peak]

stein shakarchi, marsden, ahlfors, and conway are all pretty good

[sage kelp]

Thomas’ Calculus looks really good to me so far! I’m about to finish Chapter 2

[karmic onyx]

algebra by serge lang is my least favorite algebra text

[cursive orbit]

@karmic onyx ping pong

Cunningham

now

[boreal vine]

Any calculus introduction book recommendation?

[karmic onyx]

i'm literally in livermore

[hazy elk]

If I were your age, I'd either read Abbott "Understanding analysis" or Axler "Linear Algebra done right" or Gallian "contemporary abstract algebra". I think all these books are approachable for ppl who haven't studied proofs (and also contain math you definitely need to know if you go into math), alternatively if you have specific interests like number theory you could read any elementary number theory book.

[hazy elk]

I'd advise against reading an "intro proofs book" unless you are unable to progress through sections despite having read them multiple times (over a week). Simply because there's more fun ways you can learn math

[devout hollow]

Hello. Can anyone recommend me a brief introduction to the basics of abstract algebra? To provide some information on my background in algebra, I finished "Introduction to Linear Algebra" by Serge Lang, and have also read up to page 184 of "Linear Algebra" by the same author.

[heady ember]

Schroder works too

(anal book)

[glacial crypt]

understanding anal is nice tho

the first chapter shows you how to prove things

[heady ember]

The last 2 pages of Enderton's Elements of Set Theory (logic appendix) is also nice for getting an idea of how the flow of trying to prove something goes imo

[gray gazelle]

does anyone know any good pre-university book?

[heady ember]

Be more specific, what topic do you want people to give you recs for

[gray gazelle]

trig and algebra and calculus

[heady ember]

In that case probably Khan Academy and Pauls' Online Math Notes are common recs, though they are not books but online resources

[frosty yarrow]

ah alright, thanks for the response. do you think getting advanced engineering mathematics by Kreyszig would be better instead, since it has quite a large portion on DEs already (instead of buying a separate book for DEs)?

[heady ember]

They're free too btw

[gray gazelle]

oke thank you

[heady ember]

np : )

[sage kelp]

Thomas’ Calculus

[frosty yarrow]

calc made easy, got me into calc in the first place

very simple explanations yet very real concepts

https://www.gutenberg.org/files/33283/33283-pdf.pdf its free aswell

[iron panther]

any recomendation for a book on advance calculus

[narrow fiber]

by advanced calculus do you mean analysis or just more rigorous / broader calc

[tepid prairie]

Advanced Calculus by David V. Widder. 🙂

[fading wave]

anyone have good book for real analysis?

I really want to have practice problems WITH solutions

[hazy elk]

Depends on why you wanna learn DE's, like I said it's probably pointless for scientists and engineers to learn a bunch of techniques (which they may or may not need) to solve DE's and instead just learn it when it shows up.

[frosty yarrow]

Thanks!

[cedar flume]

Any book that covers Functions of bounded variations & Cantor set

Royden ?

[karmic thorn]

Introductory textbook for hyperbolic geometry?

Ideally at an advanced undergrad/early grad level

That was a fast react

I'll take a look, thanks

It could cover the first bit of the course, so looks good

The stuff beyond is probably more GGT anyway

Geometric Group Theory

[sage kelp]

What about a book with more rigorous calculus? Something similar to Spivak or Apostol?

[sick vector]

Courant's Intro to Calculus and Analysis.

[foggy relic]

Loomis Sternberg

[alpine rover]

gallian's contemporary abstract algebra

if you want something easier (which i doubt), you can do saracino

if you want something harder, you can do artin, fraleigh, or d&f

i absolutely loved gallian though, thought it was the perfect level of instructiveness, readability, and enjoyability

[glacial crypt]

d&f can be quite terse

gallian is great

[iron panther]

thanks

[alpine rover]

agreed, very dry but good reference

[cold lodge]

hello peeps

[solemn rover]

We say that a set is of cardinality aleph null if it can be put into one-to-one correspondence with the natural numbers. So for example there is a bijection between Q and N, so Q is of cardinality aleph null. There is a bijection between the algebraic numbers and N, so the set of algebraic numbers is of cardinality aleph null. The set of finite binary strings is of cardinality aleph null.

We know that there are sets which are strictly larger than N in the sense that they cannot be put into one to one correspondence with N. So for example the real numbers are "too big" to be put into one to one correspondence with N.

aleph 1 refers to the smallest set which is strictly larger than N.

any set which is in one to one corresondence with it is said to be of cardinality aleph_1

We don't have any concrete, easy to understand examples of sets which are known to be of size aleph_1, other than "the union of all the countable ordinals"

[cold lodge]

ive been thinking of buying how to prove it by daniel velleman but the first edition seems to be much cheaper for me than the second or third edition. Are the differences in editing worth paying for?
third edition: £26
first edition: £3

[solemn rover]

The set of real numbers is strictly bigger than N, so the cardinality of the real numbers is at least aleph_one, but it could be larger - it could be much larger! we don't know.

[dapper root]

I don’t think “we don’t know” is the best way to describe it

It kind of suggests that there’s an answer and we could discover it

[solemn rover]

that's true but they said relatively simple terms. Hahaha.
I believe Woodin thinks the continuum hypothesis has an answer, but I don't know why he thinks that.

[sturdy shore]

for a platonist it would be normal right? like there exists a true model of set theory in a platonic realm and in it CH is ...

[solemn rover]

To elaborate, the commonly accepted axioms for set theory do not give us enough information to decide whether the reals are of cardinality exactly aleph_one, just as the axioms of group theory do not allow us to decide on their own whether an arbitrary group is Abelian.

[solemn rover]

I feel like there are platonists who believe in multiple equally valid models of set theory tho

[sturdy shore]

yeah of course, I just said it would be normal

[solemn rover]

yeah

[sturdy shore]

not the only platonist take, but one of them

[copper radish]

Follow-up: I got the Advanced Calc book based on recommendations here. Thanks

[dreamy fog]

Can anyone recommend me a book on advanced calc or YouTubers etc. Riemann integral/double integral/leibniz/laplace transforms. Preferably also loads of practice questions

[heady ember]

Pauls' Online Math Note probably works, although its not a book

[icy knot]

Understanding Analysis or the one by Bartle

[foggy relic]

which book?

[pliant falcon]

I recommend Spinors and Spacetime by Roger Penrose for anyone interested in advanced relativity!

[oblique dove]

DM if you are interested in reading https://venhance.github.io/napkin/Napkin.pdf (a insight to undergraduate math) with me.

[sterile harness]

just fyi i tried reading some of that (as a current high schooler)

i feel like it goes too quick and you need more background than he says you do

[oblique dove]

yeah, i suppose so. it assumes you have experience writing proofs

[sterile harness]

yeah but not only that

like he says you should do abstract algebra before linear algebra

but gives examples of stuff involving matrices for different kinds of groups

ik you could learn some of that stuff but still

like i went on to the chapter after that (measure theory i think) and it just got way too hard way too fast

[oblique dove]

matrices are taught in precalculus in the us

eh maybe he does go too fast

idk

[blissful pike]

I just finished math Math's uni recently and looking to deepen and boarden my background

I painfully realized there were things I could just not get to :'(

[oblique dove]

What do you mean?

[hazy elk]

I think napkin is a stupid book, there isn't much value in "getting a general exposure to a lot of different kind of surface level math"

Maybe as a recreational tool, but it shouldn't be a main source of study I feel

Just read a good pedagogical math book

[oblique dove]

well its def not for self study to actually learn the topics

its more for just getting an overview of what is taught

[mossy flume]

it's not meant to be a deep textbook

it's meant to be a surface overview

[jagged bloom]

any book that covers analytic geometry at more advanced level?

[sterile harness]

ik but its too hard to be like that imo

[ember slate]

hello, I am reading book of proof right now and i'm planning on reading a discrete math book afterwards, should i continue reading book of proof or skip directly to the discrete maths book? the discrete math books covers a lot of the same material, that's why i'm asking

[solemn rover]

I looked up the napkin and it looks like in the most recent draft he took out the part in the intro where he suggested that olympiad math chads need a special book because they can learn 6 times as fast as everyone else

Good stuff

[fervent bolt]

Foundation book for IIT JEE? (currently in high school class 10)

[solemn rover]

https://cdn.discordapp.com/attachments/716264872018706443/1011185954339422208/unknown.png

[minor knot]

I recommend Pearson's foundational series

[fervent bolt]

done.

also completed class 11th R.S. agarwal but left geometry cuz i will do it later

[solemn rover]

It's a 900 page book at this point. At some point past 600 pages, I think it begins to present itself as "an educational thing you learn from".

[coarse frost]

Oh come on

[coarse frost]

if you want you can try reading the 11th ncert books, they have good intuition sometimes

they are mostly awful tbh but eh

sometimes they can be fun, when they make sense

which is rare

[fervent bolt]

what about chemistry?
I havent started chemistry of the next classes so how and where should i start?

[coarse frost]

NCERT

[hasty turret]

You have Claydon, JD LEE and Atkins for theory

[coarse frost]

that is the book godsend

Especially for inorganic chemistry

[hasty turret]

I guess Solomon and Fryhl is strictly better from a JEE pov

[coarse frost]

There are a ton of other books but i havent really tried them so i cant say about them

[coarse frost]

The original edition

the arihant print is dogshit lol

[fervent bolt]

thanks

[coarse frost]

Shockshwat

reminds me of my name

eerily similar to shashwat

lol

[fervent bolt]

my original name is shashwat lmao

[coarse frost]

oh lol, well you are doing good

you have completed 11th maths yeah?

[fervent bolt]

yep and physics too

[coarse frost]

Nice

i wish i had done that in 11th

:penzene:

😭

[fervent bolt]

which class/college are you in rn

[coarse frost]

Im in no class

im a dropper

Yohan the poet in you scares me sometimes

[coarse frost]

me:

[fervent bolt]

JEE Mains is in 10 days

[coarse frost]

[fervent bolt]

you prepping for MAINs or cleared mains and prepping for adv?

[coarse frost]

i am aware

im preparing for whatever can get me into iisc

lol

[fervent bolt]

what is iisc

[coarse frost]

indian institute of science

[fervent bolt]

i see

i need nit or iit cuz CS

[coarse frost]

cs huh?

nit is a game of main rank, so shouldnt be too bad perhaps 🤷‍♂️

[fervent bolt]

hopefully

i need a rank under 8000 in jee adv

[coarse frost]

8000 is about 120-140 depending on the year

2025 if too far away to say anything really lol

[fervent bolt]

what is 120-140?

[coarse frost]

120-140 marks in advanced

[solemn estuary]

count me in-

[fervent bolt]

oh soka

Rare

[solemn estuary]

no i meant the jee part

😭

[fervent bolt]

soka

[coarse frost]

not as far as im aware

[coarse frost]

do you have to give it this year?

[solemn estuary]

next year

like

target2024

[fervent bolt]

वास्तव में

[coarse frost]

I see

[solemn estuary]

wbu?

[coarse frost]

my condolences

[fervent bolt]

10 days for him

[solemn estuary]

my condolences comrade

[fervent bolt]

715 days for me

[solemn estuary]

365-ish days for me

[fervent bolt]

hopefully 2025 isnt set by iit guhwati 😭

wait

2023 is set by guhwati

[solemn estuary]

mhm

[fervent bolt]

Toughest paper by iit was by guhwati

[solemn estuary]

unprobable for 2025 to be set by them too

what's ur strongest sub?

[fervent bolt]

Physics

[solemn estuary]

sameeee

my dad teaches physics

like

jee prep level

and he's given out decent ranks

[solemn estuary]

i see two consecutive iit delhis oof

yeah

[solemn estuary]

iit papers are generally considered one of the toughest

[fervent bolt]

2nd toughest entrance exam after GaoKao in china

[solemn estuary]

add to that the amount of people prepping to give it and the competition

pushed my mental health off a cliff but we dont talk about that

[fervent bolt]

Sometimes its even tougher than GaoKao

[solemn estuary]

^

our coaching is supposed to have a model A, model B and an n120

model B is sometimes tougher than model A 😭

[fervent bolt]

If you can solve this question your JEE Physics is completed

Toughest question ever in JEE

[solemn estuary]

rotational mechanics-

we've done that topic

[fervent bolt]

It was asked in 2016

Set by guhwati

[solemn estuary]

was rushed tho so not my strongest area

[fervent bolt]

try this question

[warm sparrow]

toughest exam in the world after the china one

[solemn estuary]

i have been okay in physics uptill wpe and picked myself up from electrostatics now

[warm sparrow]

china one is harder only bc of several subjects

[solemn estuary]

mhm

🤨

[fervent bolt]

Relatable

[solemn estuary]

this seems pretty easy-?

[coarse frost]

9 days

[warm sparrow]

shockshwat which class are you in? 12th?

[fervent bolt]

try to do it

[fervent bolt]

10th

[solemn estuary]

alr

[warm sparrow]

can you do it

[solemn estuary]

what coaching y'all go to (if ur comf sharing that is)

[fervent bolt]

ofcourse not 💀

[warm sparrow]

local coaching + unac

[fervent bolt]

Local coaching by iit graduate (pradeep agarwal )

[warm sparrow]

unac is pretty wasteful tho nirmaan batch physics teacher is dog

[solemn estuary]

narayana iit academy

[warm sparrow]

@fervent bolt r u prepping for ioqm or anything

[warm sparrow]

rich fuckk

[solemn estuary]

no my dad teaches here so faculty discount

[coarse frost]

i go to a local coaching

[fervent bolt]

PRMO kinda

i got rank 3 of state in NSO

[solemn estuary]

we've got this kid in our class

[solemn estuary]

what class

[warm sparrow]

nice

wait

[fervent bolt]

10th

[warm sparrow]

sof or actual

[fervent bolt]

sof

[warm sparrow]

lmfao

joke of a "olympiad"

[solemn estuary]

yeh that too 😭

[fervent bolt]

actual is out of my league

[fervent bolt]

exactly

chemistry and physics was easy but biology was NEET level 😭

[solemn estuary]

y'all know any good servers for phy?

[warm sparrow]

come to #serious-discussion

dont flood this one this is for books only

[solemn estuary]

oh yeah okay this is going offtopic

[fervent bolt]

invite link: Physics

[hasty turret]

That's the only reputation they have, yes

[fierce hedge]

This whole conversation gave me anxiety of the JEE paper I gave in 2015

Especially that Rotational mechanics question

[formal bronze]

Are you sure about that?

[hasty turret]

No

nvm IITs are actually good in terms of research

[paper ferry]

Working through the first 6-7 chapters of Axler's linear algebra (for context, up to inner product spaces), and it's all getting very abstract. Are there books that mainly cover applied linear algebra?

[karmic thorn]

Olver, Applied Linear Algebra

Also the more standard recommendations, Strang's Linear Algebra and its Applications and the book by Lay with the same title

[alpine rover]

I was going to say Strang but better (I think) is Elementary Linear Algebra (Applications Version) by Anton and Rorres

[fossil raft]

Can anyone suggest a beginner level book to know about 'Topology' which studies the patterns of closeness.

[hasty turret]

Munkres is pretty beginner friendly

[honest reef]

What are some great books for algebra 1, algebra 2 & Geometry?

[night prairie]

Would I need anything past chapter 5 (rings, modules, grassman ring, determinants) of Hoffman Kunze to go through all of Aluffi? I would finish the rest but I would prefer to get to Aluffi as soon as I cover everything from HK that would help with that.

[delicate hemlock]

Aluffi is essentially self contained, but yeah going through chapter 5 of Hoffman Kunze should be more than enough

[night prairie]

Yeah I would just like to see certain concepts appear in their most primitive forms or on their own like prime factorization of polynomials (chap 4), all the stuff about rings and modules in chapter 5. Chapters 6-8 cover stuff which mostly seems to apply to analysis but not algebra unless I am mistaken (very, very possible!)

[narrow fiber]

Chapter 5 from H&K is also generally good to have gone through

None of this is necessarily required for Aluffi bc as walter said the latter is p much self-contained but Aluffi offers a sort of second, more general perspective of what's going on in certain places

[misty geyser]

Anyone got recommendations for books that are 'continuations' of GCSE Maths/Further Maths? Thanks

[restive falcon]

a level textbooks maybe

[gray gazelle]

Serge lang's basic mathematics or just do khan academy

[gray gazelle]

I need your help, is Artin a good book for Linear & Abstract Algebra?

[foggy relic]

Yeah its good

[night prairie]

Yeah, I wanted to see the specific cases in HK first. I understand Aluffi is self contained and have had no issues at all going through some of the early sections but since I am self studying I prefer to "do it right" rather than rush. Also HK would help with having more confidence with anything with matrices in Aluffi. I did notice that there is some mention of canonical forms in Aluffi so I am wondering if I should go through chapter 7 of HK first or if I can just cover all of chapters 1-5 of HK and then stick to Aluffi.

[narrow fiber]

I did chapters 1-7 in H&K when studying it with certain parts omitted

[narrow fiber]

It's great for abstract algebra but I definitely don't think it's the best for learning linear algebra, especially the first time around

[fluid skiff]

Apart from book recommendations, is there a channel for reading groups here?

[night prairie]

yeah I'll be doing the same, just following some random syllabus I found online

[slender cargo]

This would be a cool implementation

If it was possible to have a channel dedicated to a textbook

[crimson leaf]

I don't think there's anything stopping you from doing a thread in the appropriate topic channel

[slender cargo]

I suppose. I think a neat idea though would be to have a books section, and a book opt-in command so that you can view the channel

[sturdy shore]

I guarantee you there is not enough demand for many individual books for that to be worth its own section

[night prairie]

I'm down for Aluffi if anyone else is :>

[honest reef]

Those are great but i wanna learn using books

[crimson leaf]

Lang's basic mathematics is a book..

[mossy flume]

yea but who is gonna run the reading group and keep it alive

and make sure people actually follow / don't drop off (super common issue)

[slender cargo]

oh I was more so thinking of just having a channel for a book existing in perpetuity

people can simply discuss their progress or ask questions whenever

[mossy flume]

so the normal topics channels but with artificially focus on some random text?

[slender cargo]

the downside imo would more so be that it separates help further. questions that could go into real-complex-analysis go into spivak's calculus channel

[slender cargo]

I guess it could be put that way. I personally thought it'd be fun to talk about progress on a text. It feels awkward to me to just pop into a topic channel and talk about how many pages I got through yesterday, but maybe that's more of a me issue

[molten mason]

Do you guys know that website by the author who has the realanal.pdf he wrote available for free

[sturdy shore]

do you mean knapp?

http://www.math.stonybrook.edu/~aknapp/books.html

[molten mason]

I just found it, Lebl, thanks for that link though I'll save that one too

[sterile harness]

Where can I learn how to solve non-homogoneous linear recurrneces?

[fluid skiff]

I am planning to start reading topology book from scratch

[lime sapphire]

this guy's books are nightmarish

teaches you an entire course worth of material before giving exercises that aren't even sorted 😭

[sturdy shore]

yeah I wish exercises were there after every subsection instead

the books are amazing tho imo, the parts I've read at least

[orchid mortar]

I wouldn't complain about free books

[light umbra]

What are the best resources(Books/Youtube channels/websites) to learn Cal2 and discrete mathematics?

[woven glacier]

what are some good online resources for a physics student?

[molten mason]

Calc II there's Professor Leonard on YouTube and Paul's Online Notes online

[bleak hornet]

You guys think that Rudin or Apostol is a great choice for a first course in Real Analysis?

[bleak hornet]

Paul's Online Notes are simply the best, not only in calculus, but in Diff. Eq as well. Love them!

[bleak hornet]

I'm not really sure, but I think Lovász might be a great deal

[sage kelp]

Totally depends on your background. Although not sure that Rudin and Apóstol are similar level texts

[light umbra]

Thank youuu Ill check it out

[gray gazelle]

Rudin is pretty shit for a first course

check out Tao or Abbott

or Elementary Analysis by Ross

[lilac bronze]

I'm going through Folland right now for my grad Real Analysis class

It's okay

Makes sense to me anyhow, generally, but real analysis isn't really my field so I'm not sure how much that's worth

[sage python]

@lilac bronze depending on what your field is, could still be useful to know

[lilac bronze]

I want to do graph theory

[sage python]

First off eyyy

[lilac bronze]

eyyy

I actually got Real Anal in about 10 minutes, and a graph theory course right after that

[sage python]

Second, some analysis ideas do kick in in graph theory depending on what you're doing

[lilac bronze]

Yeah, asymptotic stuff

probably some ramsey theory

[sage python]

That but also studying spectral theory of the Laplacian

[lilac bronze]

Definitely could come in handy, but generally prefer strict graph theory

[lilac bronze]

Never really been exposed to that, actually

[sage python]

In the k-regular case, equivalently of the adjacency matrix

There are some combinatorial properties of graphs that are controlled by spectra

For example, and this is near and dear to my heart

There's something called the Cheeger constant of a graph

Which measures connectivity. It's analogous to a similar constant (also named Cheeger) for surfaces

In both cases, the constant has bounds above and below in terms of the first non-zero eigenvalue of the Laplacian

[turbid mural]

what point-set topology books would you recommend

[crimson leaf]

graphons are pretty cool

[foggy relic]

Munkres, hatcher's notes

[bleak hornet]

I am currently having a course in general topology (which in fact requires just a little bit of real analysis), using Munkres. Thank you!

[bleak hornet]

funny thing the last teacher that lectured it used Rudin

but the man is so smart that he's bald

[bleak hornet]

Thank you!

I'm thinking of using Abbott's Understanding Analysis, seems very well written

[foggy relic]

Munkres dosent have any formal prerequisites

the first chapter is dedicated to naive set theory

[mystic orbit]

Hatcher's notes for suuure

It's quite compact and brief

It gives all that you need to get started with the stuff that need pointset

And in practice, you learn any extra pointset that you might need on the go anyhow

[mystic orbit]

Is folland graduate analysis?

[sage python]

It's measure theory, basic functional, some extra topics

Many undergrads will see it but it's common to not see until grad school

[final sorrel]

That is probably my favorite analysis text. I also am impartial to A Radical Approach to Real Analysis by Bressoud and Analysis by Tao

[bleak hornet]

I see, I only know one teacher that used Tao, other teachers rather using a book from a author that is from my country, called Elon Lages

maybe because it is not as big as others, has quite good exercises and is not that scary

[sudden kindle]

yes

[narrow relic]

I liked Methods of Real Analysis by Goldberg although I think some of the definitions are not clear or may be not general enough

[gray zephyr]

The first book of the OpenMathBooks series is now available in English. The books are free and you can edit them in whatever way you want. The books range from elementary level to precalculus level.
https://sindrsh.github.io/openmathbooks/

[crimson cipher]

Any recent (past 15 years or so) books covering content similar to Hörmander's The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis? Both at the introductory level and at the advanced level would be great.

[hazy elk]

Does anyone know a decent intro for p adic dynamics?

I found "P-adic Deterministic and Random Dynamics", Khrennikov

[solid wadi]

Hello! I am looking for an introduction to Abstract Topology with possibly more examples from Algebraic Geometry, or discrete spaces, or something else similarly exotic, and possibly more abstract nonsense. Is there anything like that out there? I want to understand the topology of algebraic curves (Zariski), various topologies on discrete spaces, simplicial complices, and look for applications to Computer Science.

[solid wadi]

What I mean is: the definition of topology is abstract and kind of order-theoretic, but the standard introductions hasten to introduce real, infinitesimal, metric, all that stuff. Zariski topology is the first example that comes to mind that breaks this pattern, but I recall seeing similar constructions in discrete spaces and in many other places where intersection and union of stuff can be shown — this stuff will then be called open sets even if it looks nothing like fuzzy balls of analysis. I am looking for more such «unusual» examples, presented in a systematic way. Surely there must be something!

[gray gazelle]

pointless topology?

[solid wadi]

Any specific book you have in mind?

I am thinking to read some Frames and Locales (seems to be «the» pointless topology book) and some Topology: A Categorical Approach (has a whole chapter of examples).

[brittle breach]

what's a good book on Fourier analysis

I have read the better part of SS Fourier analysis

[remote sparrow]

maybe tolstov's fourier series?

stein has also written some graduate treatments on fourier analysis and harmonic analysis

and there's a book by zygmund that everyone seems to regard as a good reference

old though

[sterile harness]

I'm not sure if this belongs here but does anyone know a website that offers online accredited math courses beyond Calc III and Linear Algebra? (preferably not a ton of money lol)

[split bluff]

Highly doubt

[slender cargo]

I think The Open University might work. Although I don’t think it’s cheap

[marble solar]

There's always Korner's Fourier Analysis book

but in general to go further, you'll have to learn the material of the other stein and shakarchi volumes

[sage kelp]

The Open University, but not sure it’s cheap either. If you find anything good please let me know as well, it would be interesting

[sterile harness]

I looked into it, I can’t really figure out how to take a single class it seems to be only in modules

[sage kelp]

Well, I’m sorry to say this but I guess there’s always self studying. That’s what I am doing

[gray gazelle]

No sorry, never read about it

I know one person though so maybe I'll ask them

[solid wadi]

Please ping me if anything comes up!

[gray gazelle]

check out Johnstone's "Stone Spaces"

[covert oxide]

Hey, are there any books that have/are on functional equations?

[gray gazelle]

openstax should have something (it's all free), otherwise any book from libgen is fine, I would take I peek at every book and take the one that I like most

[glacial crypt]

we cant mention that website here I think (discord tos)

[broken meadow]

Correct do not talk about using libgen here as it is against tos (i dont know exactly what is and isnt allowed regarding conversation but definitely telling someone to use it is not allowed)

The mathematics server does not endorse piracy because we kind of have to

[brittle breach]

I am looking for a graduate book

post Rudin RC

[pseudo forge]

place where you study+first book of old testament

ig that's vague enough

[karmic thorn]

Grafakos?

[forest sleet]

I like Grafakos and Duoandikoetxea

[marble solar]

I'm a big fan of Stein's Harmonic Analysis

[hearty steppe]

I strongly suggest this paper https://arxiv.org/pdf/2102.12086.pdf

here is the article i found it from, with two more papers https://morioh.com/p/6ddb372549bc?fbclid=IwAR3Tny3Vy2pflfBhyhKLwWEWej5SLDOCsG9PMKTTiV5rYWYTSRPl8dinAVI

[brittle breach]

thank you @karmic thorn @forest sleet @marble solar @hearty steppe , will be checking these out.
SS Fourier analysis got interested in this area

[exotic patio]

Hello, I found this book recommendation guide thing on the internet and I'd like to know if it's worth following

https://i.imgur.com/eA6ME3t.jpeg

I was mediocre at maths, I finished highschool basic exams, had some more stuff on 1st year universities, teachers always hated me because I kept asking why and why

so I was looking for something different

perhaps there are better "foundational" approaches out there? Or is this just silly

my dream is to do computer science and backend IT

[heady ember]

"Foundations first is active mental multilation"

You do not need a whole book on set theory to get into math

Also, that image is very unclear and blurry

[exotic patio]

Yes, you have to open it in browser because discord scales it down in the preview

[lean pagoda]

That chart makes no sense whatsoever

[dapper root]

These get posted every once in awhile and they’re always so dumb

“Do 12 books before you start algebra 2”

[heady ember]

Oh yeah sorry. But yeah I agree with neverbloom

[exotic patio]

I'm really bad at remembering things as they are, I need to understand why something works the way it works, I'm a bit crazy, perfectionist so to speak

[heady ember]

No reason to read Enderon unless you genuinely are interested in some set theoric stuff, for example

[karmic thorn]

The only natural list:

1. Algebraic Geometry, Hartshorne
2. Industrial Society and its Future, Kaczinsky

[exotic patio]

i've read the second position on that list

rip foundational approach

:(

[heady ember]

No don't do foundations first

[karmic thorn]

Chasing perfection and mastery is highly counterproductive, speaking from my experience

It can make you hate math very quickly

[hollow peak]

they post this crap on 4chan threads

do not waste your time with this

[exotic patio]

I don't care, I am in position in my life where my wellbeing does not depend on understanding it, I am in no rush

I just want something from the lowest denominator and work my way up

[lean pagoda]

I like how the chart ends at Spivak/Apostol but the 4th (apparently required) book is Landau lmfao

[karmic thorn]

All the more reason to enjoy it thoroughly

Don't think that doing set theory like a logician first is necessary or sufficient to pursue other math

[hollow peak]

there's a reason why mathematicians just use naive set theory before returning to it formally later

it's genuinely a pain in the ass to get stuck in the weeds and it shields you from much more interesting stuff

[exotic patio]

so what would be the best way for someone to start from the bottom and get an all around knowledge

[karmic thorn]

I was in the same spot as an early undergrad and it took me some time to give up on this bottom-up, foundations-first mentality

[hollow peak]

of course it's down to personal preference, but you could just do basic mathematics by lang, then book of proof by hammack, then apostol and you'd be golden

[karmic thorn]

It was a sheer waste of time in retrospect

[exotic patio]

I'm already halfway through with Laws of Truth and it's been a breeze, a few problems stemming from not being a native speaker but that's it

[heady ember]

Me doing Enderton right now:

[hollow peak]

i fucking hated smith

[heady ember]

But it's fun to me so

[hollow peak]

they used it for my logic class in freshman year

[karmic thorn]

It's fine I also had (have?) major issues with consistency and learning discipline so I couldn't make myself stick to anything

Including Enderton

[exotic patio]

alright so maybe to rephrase my original question, which books are an absolute soul crushers in this list

I recon Landau

[lean pagoda]

Read any introductory book on whatever topic you're interested in
If you feel like you lack the mathematical maturity to approach any of those books you can read any of the proof books in that chart (velleman, hammack, or that "a transition to advanced mathematics" book)

[hollow peak]

none of them are soul-crushing per se, but it's pointless doing books that are basically intro to proofs like 4 times

you could get away with reading a total of three books on this list and go on to do productive mathematics

probably less if you pick things up as you go

[heady ember]

Yeah might as well use smt like Schroder as your intro to proofs and get to learn real analysis simultaenously

[exotic patio]

I don't even know what are these things

[hollow peak]

this was essentially my path

[exotic patio]

I really would like to change jobs and start doing IT, CS, backend, low level, I find it fascinating

I have a massive amount of free time in my current job and nothing to do

so I figured hey let's try maths again

but I don't really have any specific goal in mind, on one hand gamedev is always fascinating, I was very passionate about video games my whole life, but on the other hand computers are no less exciting for me

I had some bad luck in elementary school, I was bullied xdd by my maths teacher

[hollow peak]

that's very admirable to come back to learn math for fun imo

[exotic patio]

which resulted in me not learning any maths for majority of my youth

[hollow peak]

i hope you enjoy what you end up reading, because I know that I at least have found a lot of myself through studying it

[exotic patio]

dude doing these IT, CS courses feels like I'm some monkey stacking blocks together hoping for something to happen and it's so frustrating and not fun

alright boys

thanks for thoughts

you didn't change my mind

I will follow this 4chan infographic

I will come back when I will bleed out

[hollow peak]

if it work it works

I really strongly recommend you feel comfortable with skimming or skipping through parts that you find incredibly tedious or boring and perhaps coming back later

[dapper root]

Imagine recommending you do a set theory book

[hollow peak]

chances are with that route it'll come back again at some point

[dapper root]

And then saying “okay here’s a book on proofs”

After

[heady ember]

[exotic patio]

my elementary maths teacher bullied me to hell

I was attending a private elementary, one of the best in country and I had poor background

[hollow peak]

also helps avoid burnout from overcommitting to being super thorough

[exotic patio]

she tried to make me stay 1 year more when I was 13, told everyone I was dumb as bricks

[crimson leaf]

This graphic makes no sense to me

[exotic patio]

she made me take a Wechsler Intelligence Scale measure test when I was 13 to prove it, I came back with 146

imagine

[heady ember]

uno reversed

[exotic patio]

but now when I think of it perhaps it was all a ploy

I certainly dont feel like 146

[dapper root]

I think #book-recommendations is not the best time to ponder your elementary school math teachers

[exotic patio]

yes

sorry

[polar elm]

Putting aside the fact that it's too many books with overlapping content, I actually think the infographic is solid if you're doing a foundations-first approach

[heady ember]

"if you're doing a foundations-first approach"

Why do foundations first

[polar elm]

Idk lol

[crimson leaf]

You're like doing a proof book then set theory then you're doing this foundations of analysis book only to go to basic math by Lang?? and then like another two proof books?? Then you're doing spivak/apostol at that point just read some analysis

[heady ember]

I am reading Enderton's Set Theory book right now

[hollow peak]

how else can you do analysis if you don't know the proof of cantor-schroeder-bernstein

[crimson leaf]

Also I disliked a transition to advanced mathematics

[polar elm]

😂

[narrow oyster]

steve brunton my beloved

[heady ember]

A h y e s

[crimson leaf]

they are correct that it's not a great first proofs book and is surpassed by things like book of proof but at that point I don't see the value in it

[exotic patio]

I don't mind re-reading stuff, I read a lot of literature

[polar elm]

@heady ember I mean, I agree with the general sentiment expressed that foundations-first approach probably isn't best for most people. But it's clear FRANCA has made his mind up on doing it. Chaigenvalue, bacono, etc. told him that they wouldn't recommend it but he said he's cool with foundations-first

[exotic patio]

so as long as I'm not crunching things in my head it's fast

[polar elm]

Oh okay

[heady ember]

The problem is that to read stuff like Enderton's introductory logic book, you already need to know some algebra I think? For the examples

[exotic patio]

You mean Elements of Set Theory?

[polar elm]

The better question is why don't you mind re-reading stuff? Isn't that kind of a waste of time? It's good to revise things But reading "entire books" can't seriously be called revision.

[hollow peak]

yeah foundations first is generally weird in the sense that the power of abstraction is heightened after you've seen math in context

otherwise it's kind of abstract for abstract sake

[heady ember]

I meant his logic book, if you're gonna legitimately do a deep dive into foundations (which most ppl here, including myself, won't recommend)`

[hollow peak]

it's like doing category theory before taking abstract algebra

[crimson leaf]

I would remove logic the laws of truth, elements of set theory, foundations of analysis, basic mathematics (unless you need it but if you need it I'd read that first,) and probably everything between that and spivak/apostol and really at that point you could probably just read something like Schroeder either after book of proof or off the bat and be good

[exotic patio]

I don't know what I want to accomplish, I have many points of interest that I always found fascinating, I want to get to know better the science behind them to make a choice, I am not studying maths at any university and if I am ever going to try again I want to know what I'm in for

[polar elm]

I think you could probably learn the necessary algebra in hammock and velleman, no?

[heady ember]

Idts?

I meant abstract algebra

[polar elm]

oh wtf

[hollow peak]

hammack doesn't have any algebra

[polar elm]

I didn't know you needed that for enderton

okay that's werid

[heady ember]

Pretty sure you need that to understand some examples

[exotic patio]

That's exactly what I am most afraid of down the road

[heady ember]

Even when doing Enderton's Set Theory book, the author has introduced the notion of groups, fields, commutative rings with identity, etc

[polar elm]

@exotic patio you have alot of time on your hands right? How about D&F before Enderton to get your algebra sorted /s

to clarify, don't actually do that

[exotic patio]

:D You have to give me the full title

[crimson leaf]

It's dummit and foote abstract algebra

but if you look up d&f math book it'll probably be the first thing that comes up

[heady ember]

Normally people read Enderton after a course in abstract alg anyways

Also, to be clear, abstract algebra is not highschool algebra

Its quite different I would say

[polar elm]

Well now that I found out that Enderton requires notions from algebra, I would move Enderton from the list. Or at least not recommend reading all of it.

[crimson leaf]

A lot of the early stuff is very familiar it's like looking at algebra you've done from a new formal perspective

[exotic patio]

Alright, anything more that is not that much foundational on this list?

[heady ember]

I was referring to his logic book btw. But unless he's seriously interested into set theory, yeah I wouldn't recommend doing his set theory book either (which requires no real prereqs).

[exotic patio]

There's a big "Start Here" above the Logic Laws of truth"

and then you go down and follow the yellow line

[polar elm]

Ohhhh

That changes everything then

[lean pagoda]

Because the chart is generally a complete meme

[exotic patio]

There's no logic book from Enderton on this list

[polar elm]

Yeah I was wondering why a book on introductory set theory requires notions of groups and commutative rings

[exotic patio]

Yeah I was suspecting it to be a complete meme but I picked up Laws of Truth and I really enjoyed it so far, I'm halfway through

[heady ember]

Enderton's Set Theory book does introduce groups, commutative rings with identity, etc in chapter 5. Its just that, in spite of that, you don't really need much prior knowledge for that chapter

[hollow peak]

most mathematics doesn't use set theory period

[heady ember]

Yeah you don't need much beyond naive set theory

[polar elm]

okay yeah

so the chart is good then?

in terms of pre-reqs

[heady ember]

That's a meme chart

[hollow peak]

i promise you that you are intelligent enough for cat theory

[heady ember]

Just go into #cats

There, cat theory

[polar elm]

Oh it's meme chart for sure lol

But I think what's interesting is that for @exotic patio it's actually a decent path to follow Assuming he wants to do a foundations-first approach (not commonly done) and doesn't mind re-reading content.

[lean pagoda]

Reading an elementary set theory text as your first mathematics book (possibly after some kind of transition book/proof book) like the chart suggests is like reading an introductory general topology book as your first book

I'm sure it technically works

[heady ember]

Honestly, you can probably just start on Spivak straight away

[lean pagoda]

But it's pedagogically just not very fruitful

[heady ember]

I'm doing it for fun so

[exotic patio]

I'm 1 month in 200th page of Logic Laws of Truth while working full-time x)

[hollow peak]

math mastery route: a course on arithmetic -> munkres -> abott understanding analysis -> how to prove it -> homotopy theory of (infinity, 1) categories

[exotic patio]

I'll write that down

[hollow peak]

no please do not

i was joking

[exotic patio]

oooooooooh

ayayay

see, this is the issue

this is why I came here

[polar elm]

Well, I'm happy that you're making good progress

[exotic patio]

was the man who did this graph joking or not

I understand that asking the question if it's reasonable or not is stupid if the whole idea behind it is stupid

[hollow peak]

it looks like a serious attempt to me but again, this is shit they post on 4chan

i've said my piece already

[heady ember]

Probably just avoid it

Why are you (seemingly) so adamant about following that particular chart anyways?

[exotic patio]

there's no alternative, either do this or do elementary to high school to undergrad math courses

[lean pagoda]

Whatever the motivation behind the chart was, just know that it makes no sense for the most part (and from seeing some other similar charts that seems to be a common theme)

[exotic patio]

I even searched for foundational approach before posting and didn't find any others

[narrow fiber]

LMFAO

[polar elm]

All jokes aside, it makes sense from his perspective though no?

i.e. explicitly wanting to do foundations-first

[heady ember]

Why do you want to do foundations so badly then? It doesn't seem to me that you have implied an exceptionally strong interest in foundations anyways

[exotic patio]

I'd like to be ready for whatever comes next and see if I can get comfortable with it

this is why I didn't really choose anything specific

[heady ember]

Unless you're gonna spec into foundations, its probably gonna be near useless to you

[hollow peak]

well what we're saying is that the chart is excessive for that purpose

[heady ember]

Doing something like linear alg would probably be more fruitful

[hollow peak]

^^^^^^^^

[exotic patio]

on one hand I'd love to change my jobs and do IT related stuff, backend seems mighty interesting, low level aswell, but then there's other stuff that's also very interesting

[hollow peak]

that a million times over

[lean pagoda]

There are like 2 foundation related books in that chart and two very elementary one at that so I don't think that chart is trying to depict a road to study foundations

[exotic patio]

electronics, mechatronics, microcontrollers

so to sum it up, if not this, then what

[polar elm]

Right it's not about studying foundations, just about starting from foundations

[hollow peak]

those topics can be rendered very mathy if you so please

microcontrollers are classic examples of control theory and electronics have differential equations to them behind the seams

[exotic patio]

I guess statistics, big data is something less interesting for me

[polar elm]

I don't even think the chart is good for foundations-first because there's way to much overlapping content. But he also said he doesn't mind re-reading content

[lean pagoda]

Well that's fine, but then the chart ends 3 books into it

[polar elm]

right

I still think that's fine though? Since the focus isn't foundations per-say

just knowing enough to move forward

[exotic patio]

I was talking with my friend who's C++ backend something and he tried to show me a bad IF statement that's unreadable, I optimized it and made it readable just from knowing half of that Laws of Truth books and told him about Morgan's Law, guy makes twice the money I do

i just really want to be good at what I do

it feels as if my problem comes from not knowing what I want to do

so from my understanding so far, there is no real foundational approach to a freshman year

I always imagined that the more you would know the faster you could work and the more elegant solutions you could come up with in CS and IT

from a point of view of a complete outsider

Thank you, I apperciate that a lot

Every time I tried to do those entry courses I'd hit the wall at some point, there was something I couldn't do because of my lack of understanding mathematics

and I tried so many

Yeah but now I am at the point in my life when i no longer need to, I am set, so to speak, so I figured

I see

I will write this down and I will go your way if this thing bleeds me to death

anything before precalc that's a requirement

?

Where I live all these jobs always come down to how well can you move your way with social techniques in the end

no matter what you do

unless you run your own thing

I picked a lot of skills up on the way so I'll be fine, did many things in life

[polar elm]

I thought FRANCA wasn't learning math for career progression, but just because he was curious wanted to explore the beauty math had to offer

[exotic patio]

I kind of do but I am probing the options here

[exotic patio]

I am in no hurry and I am not dead set on anything

[polar elm]

Hm that kind of contradicts what I see here: #book-recommendations message

It's probably a little bit of both

career progression and natural curiousity

[exotic patio]

I secured for myself a situation where my work is very passive, I'm a manager at a hotel and I take night shifts, I get things done in like 2 to 3 hours and then I spend the rest of the night on whatever, the pay is good, the job is fun because you get to talk with interesting people you wouldn't meet in any other way, so I picked up maths because I was always passionate about video games, my end-goal is to provide IT services for many people that I got to know while funding the game project I'd like to work on

[polar elm]

Btw you should probably move out of #book-recommendations. I think the book discussion part of this thread ended a while back

[exotic patio]

I just wanted to say that I appreciate everyone's input and time, I think I have a much better understanding now of what I'm doing and I have a back-up line to default to, thanks so much, you guys are the best <3

[polar elm]

Whatever path you choose to follow, I hope you enjoy it and find what you're looking for

[queen topaz]

I want a book to learn algebra basics to advanced. I want to start learning trigonometry. I am looking to strengthen my basics and learn something new. Please recommend a good book.

[covert oxide]

Thanks

[gray gazelle]

alright I 'll take note. although it's somewhat weird that libraries are legal, or I guess that's because at the end of the day they are all the same gov related ass* * * * who profit in one way or another over it

[mystic orbit]

hypocrite

[heady ember]

I do set theory for fun lol

I know it won't be that useful in the future

Unless I spec into foundations

[orchid mortar]

I'm 95% sure there are 0 logicians in your area

[heady ember]

Well, if I ever do a PhD in any field of math, I would not want to do it locally

[fiery steppe]

Hey everyone. A little back story about me: I am 15 years old from India, and I have a burning passion for math and hope to pursue it as a career one day. I feel like I have a good amount of mathematics knowledge for my age, but most of that comes from videos of channels like 3b1b and numerphile; I haven't really learned any complex topics formally. (Of course, I have done really well in school, but our school curriculum is much more basic than the level of math I am talking about here)
My question is what should I do right now to expand my mathematics knowledge more formally? What should I do before going to college that would help my CV and, more importantly, allow me to be fascinated by math further?
Maybe I am thinking about this in the wrong way, I am also seeking for some form of guidance. Any help would be appreciated!

[fallow cypress]

Have you tried Khanacademy?

That's usually the recommendation for stuff up to calculus

You can learn a lot on that website

[deep vale]

i have been using it and its really nice

[fallow cypress]

Paul's online notes are good for calculus-sequence classes

[remote sparrow]

i saw antonio montalban give praise to mileti's logic book, which is pretty nice

not related to above discussion

he made lectures from enderton's set theory and logic books

[fallow cypress]

Mileti's logic book is great!

I love it

[grand thistle]

any good books on information theory from a probabilistic perspective?

[inner token]

Functional analysis

[swift dome]

Linear algebra Recommendation - doing my undergrad

[remote sparrow]

#book-recommendations message

[hazy elk]

1. Don't worry about college for now, focus on enjoying math.
2. Read a book like "Burton, elementary number theory." Or "Book of proof, Hammock" to see how much you like proof based math.
3. If you really liked reading the above books, you should consider preparing for isi/cmi's exams/scb exams for iisers from 11th (while learning the math that you enjoy)
4. You can dm me (I'm also from India)

[fiery steppe]

Thanks! But isn't scb exam for banking?

I will check out the books that you recommended

thanks for the help

I have checked out a book of calculus, by michael spivak. I did the first two chapters, which were all about proof based math. It seemed fun, but a little elementary at first so maybe I should keep going with that book?

[hazy elk]

No it's the entrance test for iisers

[hazy elk]

Oh yes, then you should definitely continue spivak

[fiery steppe]

ahh mb

[fiery steppe]

okay

[fierce hedge]

Do they still ask both Biology and Maths in the exam?

[hazy elk]

Yes, I'm also hearing rumors that from next admissions cycle they might have subject cutoffs too (all the subjects)

Which kinda sucks

But they want to remedy too many ppl in certain majors or some shit, idk what's up with that

[fierce hedge]

That's gotta be some bs

Btw do you have an idea about the scholarship/stipend there? @hazy elk

[hazy elk]

Hopefully

[hazy elk]

You can get inspire if you do well in JEE adv/boards

[fierce hedge]

I studied in niser and the batch next to ours was the last where everyone got stipend

[hazy elk]

Then there's kvpy

[hazy elk]

They stopped inspire for everyone 2-3 years ago

That messed the gender ratio apparently

[fierce hedge]

bruh, that's just sad

[hazy elk]

Our iiser used to have gender parity, now the ratio is like 1:2 against women

[hazy elk]

Courtesy of the govt

[fierce hedge]

No surprises there

[junior isle]

How to prove It or book of proof?

[hasty turret]

Wasn't KVPY cancelled?

The KVPY scholarship is now merged with INSPIRE apparently

[hazy elk]

Yeah you're right, forgot about it for a sec

[split bluff]

@junior isle how to prove it is good, is the one i'm studying, i've never read the book of proof but i heard it's good

[broken cosmos]

Hey

[loud cradle]

A good intro text is the dover book "information theory" by Robert Ash. Most of the book uses only discrete probabilities, so elementary probability suffices (no measure theory). Primary use case considered is Shannon-style noisy channels

[turbid mural]

does anyone know a good english translation of Funkcje zespolone by Franciszek Leja

[remote sparrow]

https://sites.math.rutgers.edu/~greenfie/currentcourses/math503/math503_text.html

https://sites.math.rutgers.edu/~greenfie/mill_courses/math503a/instruct.html#text

https://www3.nd.edu/~jdiller/teaching/archive/fall09_60370/index.html

found some links with brief reviews for complex analysis books (mostly graduate)

[sage python]

This server's already got the best set of complex analysis reviews

In pins 😛

Though I guess some of these books aren't in mine lol

[mystic orbit]

sup dami

[sage python]

Ey how you doing?

[mystic orbit]

gud

[loud cradle]

that first link is from 1997, it predates stein and shakarchi, marshall, etc

[mystic orbit]

I just finished exams a couple of days ago so I'm finally free to do math

haven't seen you discussion in a while

are you only active in #book-recommendations anymore? lol

[sage python]

Nah I haven't been active much in general because of traveling but I talk around in places if you can find me

[mystic orbit]

traveling

sounds fun

[grand thistle]

ah thank you

[dull summit]

https://archive.org/details/gri_33125012922544/mode/2up

Found this recommended in a book about the 4th dimension

They probably summarize the book better than me

Its pretty interesting thinking about how different objects would look though

the more rapidly the gradient changes the more obviously discernible corners are at larger and larger angles

[remote sparrow]

https://www.cambridge.org/us/academic/subjects/mathematics/algebra/matrix-mathematics-second-course-linear-algebra-2nd-edition?format=HB&isbn=9781108837101

looks like garcia and horn's book has a second edition coming up

i have a copy of the first edition (not titled matrix mathematics, although it has a heavy focus on matrix theory)

[loud cradle]

that is the horn of horn and johnson?

[remote sparrow]

yup

[loud cradle]

nice

[remote sparrow]

https://www.maa.org/press/maa-reviews/a-second-course-in-linear-algebra-0

https://nhigham.com/2017/06/08/a-second-course-in-linear-algebra-by-garcia-and-horn-2017/

a couple of reviews of the first edition for those interested

[dense pumice]

Where can I learn about the mathematics of like, rhythm? Is that related to combinatorics somehow?

[sterile harness]

Might wanna check out this video: https://youtu.be/cyW5z-M2yzw

[dense pumice]

God bless

[verbal grove]

Hmm. Is there not a video recommendation channel?

[cursive orbit]

typically there doesn't exist a lot of videos on more advanced mathematics

at least compared to books

[remote sparrow]

what are some undergraduate-level category theory books

i know of riehl

leinster and awodey are common recommendations

is that about it?

brief reviews of books would be helpful

[remote sparrow]

and if you could buy just one, what would you choose

[lethal vine]

If any one is interested in Physics or is thinking of a career in an area of physics research I recommend reading this:

It touches a lot on pretty modern research, what we know and don't know, which I think is pretty important to know for the future of physics.

[remote sparrow]

can sipser's book on theory of computation be read by someone with relatively little CS background? just mainly math like myself

or theory of computation in general

ucla teaches an algorithms class in the math department that has no programming required

can clrs be read profitably with little CS background?

besides basic programming skills

[gray agate]

I might be naive, but theory of computation doesn't require much CS background necessarily, as long as you're well grounded in graph theory, discrete maths and etc...

This should be fine if you only have a good grounding on Concrete Mathematics (such as Knuth).

Though you can perhaps wait for someone more knowledgable to answer your question.

[formal bronze]

Yes, it is fairly accessible, I started with the book when I had very little background in CS(or even math for that matter).

[remote sparrow]

thanks

my school offers an algorithms class and a cs theory class, but they're locked behind a couple of boring programming classes. i get programming is a useful skill, but that stuff shouldn't really be a mandatory part of the cs curriculum. i can understand putting algorithms behind a programming wall, since while the content is more theoretical than programming, it's directly relevant for programming. but cs theory ehhh

and by programming i mean tries to teach skills relevant to software engineers, like object-oriented programming

[formal bronze]

At my university, math majors have two compulsory programming courses that are mainly theoretical.

[remote sparrow]

i have just one

it's just an intro to programming pretty much

software engineering classes shouldn't be a (required) part of CS degrees. idgaf about design patterns or disciplined methods of writing robust code. yes, it's good to learn how not to write spaghetti code. but i feel like this should be something you should teach yourself, or at least not require it.

[formal bronze]

Why do you think they shouldn't? Seems like a good thing to know. If you're arguing that this is something that can't really be taught well in a university setting, then that is something I am not knowledgeable enough to comment on.

[honest river]

Anyone knows some good books/pdfs on mathematics in automotive industry?

[stray veldt]

uh, that sounds very wide i doubt there is a book on that

great book!

i clicked download pdf and it downloaded a docx instead

[karmic thorn]

I've seen a few Springer series that seem to be devoted to very niche engineering applications of mathematics

[stray veldt]

i mean i know there is https://link.springer.com/book/10.1007/978-3-030-59897-6

which isnt precisely math but close enough?

but there are a ton of other aspects of automotive industry that use math

[silver herald]

More precisely, automotive is a wide net even in engineering. A better question to ask would be "What type of math should <X> topic in automotive eng. require?"

[sage kelp]

Any recommendations for Optimization books?

[silver herald]

What is your background and are you looking for an intro. optimization book or something more specialized like Convex Optimization, for instance

[heady ember]

Lol I have the whole set in my bookshelf from years ago

All the printed pages are now all stuck together because I have never opened them for so long tho

[gray gazelle]

What do you guys think of the further reading suggested

is there any reason to pick up more logic/proofs/settheory/numbertheory books after reading how to prove it?

[heady ember]

If you're interested in learning about them sure

But its not really necessary to go read something like either of Enderton's books otherwise

[gray agate]

What does Sternberg's Advanced Calculus do that I won't find in say Apostol or Rudin? I know he introduces Differential Geometry, but in terms of the Calculus (i.e the chapters on integrals, and differentiation) is there anything novel?

[swift dome]

PDE and ODE mostly

[honest river]

Yeah that makes sense. Im looking for some examples of math problems and application of math in automotive industry. Im interested in working in that area and wanna know what kind of math i would be dealing with.

[remote sparrow]

https://www.reddit.com/r/math/comments/10if1sy/most_well_written_textbooks_yall_have_ever_read/

@hollow shore this your thread?

[hollow shore]

no lmao

[remote sparrow]

okay lol

[hollow shore]

why would you think that's me?

[remote sparrow]

op is thomyorkestan1106

i'm sure thom yorke is some popular celebrity idk who he is

[distant spear]

Chitanda we like

[remote sparrow]

yes

[graceful dawn]

Tao's chapters are boring. Is it only for me?

[remote sparrow]

some people would agree

i don't, but a few would be inclined to feel the construction of the number systems may be unnecessary or long-winded

[gray gazelle]

I like how almost no one elaborate on their answers and just post their favorite books

[gray gazelle]

Would you recommend any of these books?

[sturdy shore]

they are just standard books on intro number theory, discrete math, logic and set theory

I recommend goldrei's books for a friendly intro to the latter 2 topics

[sage kelp]

I have taken real analysis, I would like an intro book just to get a hang of it but also, my focus will be on convex optimization

[crimson leaf]

intro to optimization by Chong and Zak seems good so far

[sturdy shore]

<@&268886789983436800>

[wispy pebble]

ty

[crimson leaf]

I didn't think this book was that bad

[analog lava]

atiyah mcdonald

[mystic orbit]

@gusty smelt lmfao

Owned.

[gusty smelt]

who owned me smh

[mystic orbit]

Cope.

[analog lava]

what did i do

[gray gazelle]

Best calculus book for self study?

[stone orbit]

Anyone got a recommendation for recreational mathematics?

[remote sparrow]

martin gardner has written a number of math puzzle books, several of which are published by dover

[remote sparrow]

proof-based or not?

[stone orbit]

thank you

[onyx wren]

anyone have a pdf of FGA explained?

[crimson leaf]

Against tos

[hollow shore]

Spivak.
Btw my fav tarkovsky is stalker :3

very closely followed by the mirror

[uncut zealot]

openstax is free: https://openstax.org/details/books/calculus-volume-1

[remote sparrow]

just got a bunch of money from lunar new year

time to burn all of it on math books

[orchid mortar]

The calc books are big - I'm not sure who's tried to use them

Sour are you a librarian

[grand thistle]

has anyone used alekseev's "Abel's theorem in problems and solutions"?

[glacial crypt]

have you tried first book of the bible library

[buoyant vessel]

does anyone have basic algebra by Jacobson pdf?

[devout silo]

Finding the value of an algebraic equation and is proving the value of an algebraic equation the same thing

[karmic thorn]

Any good sources to learn about integral equations?

Mostly looking at the basics and concerned with some simple linear versions (Fredholm, Volterra)

[sage kelp]

Thomas’ Calculus

[remote sparrow]

no, if you're asking if i work as one in a professional capacity

[sage kelp]

Why? What’s your background?

[crimson leaf]

My background is proof based linear algebra and graph theory I also know some combinatorics from my research. It has a great chapter 0 to go over what you need and it's what we're using for the optimization course I'm currently in

[onyx wren]

no it isnt?

pdf versions of books exist online because people are students