book-recommendations

[mellow rivet]

I don't do math anymore sadly

[weary hare]

Oh may i ask why?

[mellow rivet]

When lance lance changed my name to "a girl." they also said that I was lying, I'm keeping my eye on this user.

[molten gulch]

many are around

[mellow rivet]

Imaginary friend thingy occupying my mind currently, and in the past it was an inability to think

It's been a good 4-6 months I believe since I've been able

[molten gulch]

bunch of users named FBI have been trolling here recently

[mortal iris]

Huh?

[mellow rivet]

Yeah kids trying to troll, this is what modmail is for :3

Also pre uni and highschooler don't imply eachother

Pre uni is math level

[weary hare]

Oh i got a simmilar problem minor schizophrenia.

[mellow rivet]

Highschooler is based on you being in highschool

[mellow rivet]

It sucks being unable to do what I think I used to love, but eh, like goes on.

[weary hare]

Well you see around were i am from pre-uni is used to refer to near the end of high school classes so thats why.

[mellow rivet]

Yeah that makes sense

The pre uni role here is just a math level, so highschoolers can be undergrad if that is the level of math they are doing

[weary hare]

Good to know thanks but you do seem to be a high schooler no?

[mellow rivet]

I am indeed :3

[livid yew]

Appreciate it

[weary hare]

I think its exactly what you want . Also other text like "book of proof" might be helpful to learn to do proofs like to work with proofs. But for language and symbols that is definitely it

[weary hare]

Np

[livid yew]

Funny enough I find it similar to computer theory. In my class we wrote proofs like this, not as rigorous but similar

[weary hare]

They are indeed simmilar

[viral plume]

I'm in 8th grade and I am very passionate about this subject. if you can recommend me a book, good, if not it's ok (English is not my first language so if there is something wrong in this message, sorry )

[vale patrol]

What kind of book ?

[viral plume]

just to read how peoples think or how to think like a mathematician if you understand

or some books about math but for my age

[vale patrol]

There’s a book called chess, I guess. Let me check the name

[vale patrol]

No I am not sure but heard of it

[vale patrol]

I don’t know any books for that, but if you want to read books on how people think or in general psychology

You should consider The Laws of Human Nature by Robert Greene

[viral plume]

thank you very much 🫶

[west parrot]

Hii everyone. Is there any book(s) that cover these? I am mainly looking for practice questions. Thank youu!
Unrelated question, this is what I am doing in Mathematical Analysis II, I was wondering, is this standard?

[cunning stirrup]

Does anyone have any references on where to continue studying? I wanna self study algebraic number theory (I have a class, but the professor only sends pdfs once every week). The syllabus is the following:

Integers: divisibility and factorization.
Euclidean domains, principal ideal domains, and unique factorization domains.

2. RINGS OF ALGEBRAIC INTEGERS
Algebraic number fields and rings of algebraic integers.
Integral bases. Examples: quadratic fields and cyclotomic fields.
Existence of integral bases for the ideals of a ring of algebraic integers.

3. DEDEKIND DOMAINS
Factorization of ideals: existence and uniqueness of factorization into prime ideals.
Chinese Remainder Theorem: norm of an ideal.
Fundamental identity concerning the factorization of ideals generated by a prime number.
Dedekind’s Theorem and the Dedekind–Kummer Theorem.

4. FACTORIZATION IN QUADRATIC FIELDS AND IN CYCLOTOMIC FIELDS

5. THE IDEAL CLASS GROUP
Finiteness of the ideal class group.
Class number of an algebraic number field.
Characterization of rings of integers that are principal ideal domains.
Lattices and full lattices in a Euclidean space.

Minkowski’s bound.
6. UNITS IN RINGS OF ALGEBRAIC INTEGERS
Dirichlet’s Unit Theorem.
Kummer’s lemma on the non-existence of non-trivial integer solutions to Fermat’s equation for regular prime numbers.

Thus far I've finished chapter 2

[foggy quest]

"Introduction to Analysis in one Variable" and "Introduction to Analysis in Several Variables" here: https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/

[mortal iris]

Sequences and series is typically covered in Analysis 1. So is Riemann Integration. The subtopics seem to suggest a very applied Vector Calculus course rather than Analysis for the rest.

[molten gulch]

Does anyone have any good resources for learning Latin and/or ancient Greek? For context as to languages I know/are familiar with:
C2 in English (native speaker)
B1-B2 in Spanish
A2-B1 in Hindustani/Hindi/Urdu (heritage speaker)
Formerly B1 in Mandarin, haven't spoken it in a decade, barely remember any of it
A1 in Czech

So varying grammar systems, cases, etc.. are a mild pain in the arse for me but they're not scary to me.

My main goal here is to learn enough Latin to read something like Virgil's Aenid, Cicero's speeches, etc... or a similar level. I could just pop open a dictionary or read a translation but I do want to properly understand how texts like this were written in the past and also I just have an interest in latin and greek from a linguistics standpoint and feel that I have a large hole there I need to patch

<@&268886789983436800> asking for pirated resources

[sage cedar]

i was just asking where to get it vro

[astral meadow]

@sage cedar indeed, we can't allow people to ask for such resources; unless provided by the book's author themselves, it's still bound to copyrights, and therefore can be subject to copyright claims. We gotta be compliant with discord's ToS as an affiliate server!

[sage cedar]

oh mb

[plush stone]

are these all postgraduate math topics?

[molten gulch]

undergrad

[signal flax]

Guys hi im in the 10th grade I was wondering how I could learn more advanced math than I already learn ( I saw integrants and the complexity of it seemed very appealing) also I don't want to persue it as a job I just want to do it cause it seems something I could do in my free time ? Any suggestions on how I could learn more advanced mathematics maybe some books idk ? Also I'm stuck I found mit courseware but idk where to start ?

[plush stone]

i don't think so, they got a postgraduate role

[molten gulch]

https://www.jmilne.org/math/CourseNotes/ANT.pdf
https://link.springer.com/book/10.1007/978-3-662-03983-0

[signal flax]

Any recommendations will be useful

[molten gulch]

Yes but alg nt is in some places an undergrad topic, some places it's grad

[molten gulch]

thomas' calculus

[plush stone]

ok as you say

[plush stone]

search your math topics there you want to learn

or you can use khan academy, to get some idea

[signal flax]

Yeah but like how would I be able to learn if idk the things before like idk if you get what I mean wouldn't they be advanced?

[plush stone]

hmm i understand

[signal flax]

I mean the things that they teach before the things I wanna learn

[plush stone]

you can khan academy then

[signal flax]

Is it free ?

[plush stone]

it will teach you things you need to know before you start your adv mathematics journey

[plush stone]

yes

both khan academy and mitopencourseware are free

[signal flax]

Ok

[signal flax]

Thanks does it have like not homework but like some practice ? To test my knowledge

?

[plush stone]

if youare just doing this for hobby, i would suggest don't go for books right now, because those take a lot of time

[cunning stirrup]

what?

Postgrad

[plush stone]

khan academy has some practice problems and tests

[signal flax]

Ok but the website does it have any practice is there a website with some practice?

[plush stone]

I knew it

[signal flax]

Yeah some I want not many

[cunning stirrup]

chapter 1 is early undegrad though

[plush stone]

yeah but other chapters didn't seemed like undergrad topics, also you got a postgrad role

[cunning stirrup]

Where would you even have time to put this into an undegrad xd

I had pretty much algebraic courses every semester after my first year

[plush stone]

uhh you have to find that out, also in mitopencourseware you will find sheets and pdfs of problems in the course you will watch, you may try to solve those

[plush stone]

i know i know but @molten gulch told you are undergrad

[molten gulch]

I didn't

[plush stone]

i mean you did say those are undergrad math topics 😅

anyways

nevermind those

[cunning stirrup]

first chapter is undergrad

You could maybe fit a few of these topics in undergrad

[plush stone]

does the books recommended in the channel topic helps?

[cunning stirrup]

I'm reading Number Fields now

[plush stone]

https://mathematics.gg/books

[molten gulch]

This is somewhat out of date compared to the pin list

But it also has some recs not in the pin list

Hmmm

What if we merged both

[plush stone]

still it's good in my opinion

[molten gulch]

Agreed

Idea!

but I don't want to ping mods >.<

uhhh

[cunning stirrup]

also it's published under a series intended for masters+

[plush stone]

also your messages are hidden because you are a spammer? 😅

at least that's what showing it to me

[plush stone]

i see

very tricky situation

[plush stone]

hope those helps mate

[cunning stirrup]

yeah, I'm reading now

stuck in a proof

[plush stone]

i think most topics in your syllabus have lots of proofs right?

[cunning stirrup]

Yeah

[molten gulch]

This is the case in most pure maths courses

[cunning stirrup]

The book I was reading initally I was on page 220~

on Number fields it's now page like 50 lol

[plush stone]

how do you all even remember all those proofs? 😅

[molten gulch]

Practice and eventually some bits of intuition

[cunning stirrup]

You reason through them

motivate them

why it should be true

instead of just following it along

you become a better mathematician

[neon crater]

What about function fields

[plush stone]

i see

[neon crater]

Weils basic nt is a really great book

[cunning stirrup]

I don't care about them

[silk latch]

Hello! if any one here is aware of spivak calculus( I mean have used it). The book generally starts with what would be the end of most calculus books I.e limits(very in depth), upper bound, and a few hard theorems. It’s my intro to calculus. Could I tho like read until the limits chapter and then start on derivatives and integrals in the book( needing it for a computational based calc exam, don’t really wanna give up on the deep intro). Any opinion here would be very useful

[compact bough]

good news it's like one of the main books ppl here seem to recommend lol

idk what to say about the idea of reading until limits but i'm sure someone else can help!

[silk latch]

Well that is great

well who would guessed the book that is marketed as calculus for mathematician would be famous with mathematicians😭

[silk latch]

Thank you sir🫡

[compact bough]

not a sir but you're welcome ig

god can ppl not read profiles or even nicknames

[compact bough]

ikr lol

[silk latch]

Sir is gender neutral😭

[compact bough]

ppl glaze the fuck out of it but for a good reason

[silk latch]

I’m sorry ma’am

[compact bough]

it rlly isn't
and either way just don't call someone that if they tell you not to pls

i'm trying to help you in the long run

[silk latch]

Sadly tho it’s the only book that way

[compact bough]

all good just be careful pls

[silk latch]

I really do use it in a gender neutral way tho

Didn’t mean anything with it

[shut geode]

regardless of how you use it is a gendered term

[silk latch]

I’m explaining myself is all

[shut geode]

ok but if you misgender someone accidentally you dont need to explain why you did it just apologize and try not to next time

[compact bough]

idk if your first response to someone just asking you not to call them something it comes off as kinda defensive or rude if you try to explain yourself instead of just apologizing and saying you won't do it again

[silk latch]

Okay I’m fr sorry😭

[dawn shoal]

I'm looking for a textbook (or some other resources) that covers the following topics (perhaps partially). It's best if it contains problems and solutions to them, but if a textbook is good, I'll also be interested in it.

1. Wiener and Poisson Processes – Basic properties.
2. Markov Processes – Definition, equivalent conditions, and basic properties. Strong Markov property. Regularity of trajectories.
3. The Markov Property for Strong Solutions of stochastic equations with Lipschitz coefficients.
4. Markov Semigroups, infinitesimal operator, resolvent, and generator.
5. Continuous-Time Markov Chains.
6. Diffusion Processes.
7. Feynman-Kac Formula.
8. Connections with Partial Differential Equations (PDEs). Probabilistic solutions to the Dirichlet problem.

[compact bough]

it's all good just pls be a bit more considerate with these things lol

[silk latch]

Yeah I just felt bad that’s why I was explaining myself and again very sorry and sorry if I came off as rude after

[compact bough]

all good dawg i already accepted your apology

[silk latch]

Thank you

[odd cargo]

are popsci books even worth wasting time on?

especially those physics ones?

[vital bane]

It's not lol

[mortal iris]

There's only one I'd consider worth spending time on. Definitely not a waste.

[marble solar]

Leonard Susskin's Theoretical Minimum is good

Especially if you don't have time to work through a more serious physics book

The problem with the road to reality is that it's too hard

It'll take way too long to get through the mathematics in there

[mortal ore]

if it helps id make fun of u for calling me ts bc it sounds like reddit lingo

even tho im a guy

[compact bough]

thanks for the gold kind stranger

[odd cargo]

an area of which i am most confident.

[mortal ore]

beautiful prose there folknem!

[marble solar]

Ahuh, ok

Open up the table of contents, and see how far you know the math

For me, I end at about chapter 15-16

[quiet patio]

hi guys

any recs for books about counting?

combinatorics and such

[odd cargo]

at what level

[quiet patio]

undergraduate

[odd cargo]

i think that brother is trying to get me killed

[marble solar]

Lol. You don't wanna do 400+ pages of undergrad-to-2nd year grad math before you get to any physics?

[odd cargo]

like graph theory combinatorics?

[quiet patio]

well no I'm thinking stuff like questions about poker hands...

[odd cargo]

"Winning Ways for Your Mathematical Plays" J. Conway

[odd cargo]

1000 pages of shitting down your throat

[quiet patio]

thank you

[marble solar]

Ah, an area of which you are most confident!

Sarcasm aside, the theoretical minimum is a good place to start for pop-physics

[odd cargo]

That might as well be a textbook

[odd cargo]

nah i already gave up

ill stick to my higher mechanics texts

[marble solar]

Well somtimes it's nice to have everything in one book

[marble solar]

This lasted less than 30 minutes. Ah to be a young undergrad again

I remember when I thought I could do Algebra

Good times

[odd cargo]

A common point of contention among physicists

[woven wharf]

Read the book, "scythe"

[odd cargo]

This shit is so true

my brain has been at this constant state of purgatory since i learned how to do proper arithmetics

and mind you, been over 12 years since.

if you even look at my notes now, its literally me writing the same thing every 3 pages

[compact bough]

grue...
p

[compact bough]

real!!

[heavy idol]

”If G is a group and H is a subgroup of G…”

[somber cradle]

do you know the book Abstract algebra Textbook by Dan Saracino

[weary hare]

I don't encourage you read these "how to think like a mathematician" like books even though there are a lot of them. It makes you fixed at a certain view point so i encourage you to do more harder and interesting math and just go higher and higher and you will become a mathematician yourself.

[molten gulch]

yes what of it

[mortal iris]

The math is developed with a lot of heavy exposition, examples and aesthetically pleasing sketches. It's neither rigorous like a math text nor heavily computational like a physics text. It is pop physics with the math front and center because most of the physics cannot be done justice to without it.

[vital bane]

So is it like?

[molten gulch]

[thorn crow]

Logarithms and trigonometry haven't really been my strong suite right now and I'm trying to find book to self-teach myself about those concepts.

It's really hard to go further into calculus while having a weak grasp in those 2 fields. So I'm stuck in the power rule rn

does anyone have any good book recommendations on logs and trigs?

[onyx shore]

Can an recommend me books for logs, trigs like the guy above. I also need similar help. And also a book for linear algebra

[cunning elk]

literally any standard US algebra 2 textbook works

[fair bear]

whats a good textbook for alg 1? (linear algebra)

[cunning elk]

“algebra 1” in a precollege setting is not linear algebra.

introductory linear algebra deals with matrices, systems, linear maps, vector spaces, eigenvalues, etc

high school algebra 1 is usually one variable linear and quadratic equations, two variable linear systems, etc

[mortal iris]

Stitz and Zeager's Precalculus

[mortal iris]

This is a pop delulu text from a physics perspective.

[signal zenith]

Real mathematicians contributed tho

So I’m surprised it’s bad

[mortal iris]

It's not great but not bad either. Definitely for delulu physics tho.

[fallow aspen]

<@&268886789983436800>

[patent granite]

how to know ur good in maths or not

[odd cargo]

excellent suggestion, if i had a degree in physics.

[gray gazelle]

When you’ve taken your Real Analysis class or Discrete Mathematics class in college

[patent granite]

I mean I like to study it

I'm avg in it

All I lose is calc mistake

[patent granite]

Mostly

[gray gazelle]

I lowk thought you were asking “how to know if you’re into maths”

[patent granite]

Um it's kinda same doubt

;-;

[gray gazelle]

Maybe you have issues with your foundations?

[patent granite]

Yeahhhhhh

[gray gazelle]

Make some effort with studying the basics: Algebra, Pre-Calculus and Trigonometry

[patent granite]

1 have roughly 2 months for my next grade to start and i have to finalize that should I take maths or bio

I*

[gray gazelle]

next grade?

[patent granite]

Yeah

[gray gazelle]

you mean college?

[patent granite]

Nuh

School

[gray gazelle]

oh AP classes!

[patent granite]

11th going

[patent granite]

Huh

@gray gazelle so wht to

;-;

[gray gazelle]

i somehow cant edit

[patent granite]

Wht

Uhh

[gray gazelle]

i lost signal

[patent granite]

Oh

[gray gazelle]

Try to read Serge Lang’s Basic Mathematics

I’m pretty sure he had specified in the preface where to skip if you’re knowledgeable enough with arithmetic and how much it covers the high school maths.

[patent granite]

I will

Try

[trail void]

just make sure ur "prealg/alg1/alg2/collegealg + trig or precalc is on point

and ur set

try to do calculus afterwards

and if u dont really have that geometry in you, try covering it

alongside alg 2 ideally

[grim delta]

Hi, sorry for my question on this channel but: isn't there an offtopic channel in this discord?

[trail void]

#discussion #serious-discussion #chill

[trail void]

i believe this is best as reference tbh rather than trying to learn from it as a complete beginner

[gray gazelle]

He isn’t a complete beginner

And there’s no “better” books in high school maths

They’re all the same with different authors/publishers

I tend to advice my students when relearning the basics to avoid those with publishers

Example of them are Serge Lang’s Basic Mathematics and Kolmogorov’s Mathematics: Its Contents, Methods and Meaning

[trail void]

i think if you dont wish to spend several months on a textbook then books like "demystified" and "for idiots" or just shorter books are better (only till calc 1)

it doesnt really matter where you learn from until calculus/linear alg or proof based mathematics imo

[grim delta]

I don't have access to this channels, how do i get access?

[tender river]

id:customize

[tender river]

click on "id like to socialize option", that should remove the studying role

[grim delta]

Im actually like this

[trail void]

reclick

[grim delta]

it doesnt do nothing

[tender river]

type ",iamnotstudying" here

[hasty eagle]

No selfroles matching apotato.
See ,selfroles --list for the list of valid selfroles.

Mar 9, 2026, 7:49 PM

[strange wedge]

Not exactly a book rec but anyone know any good tools to generate problem sets?

Or maybe like a good free online resource that has decent quality problem sets

Gimme a ping so I can come back

[tender river]

https://github.com/jonathanrlove/makemeaqual

[wispy bison]

does anyone have any recommendations for learning about the arithmetical hierarchy?

[odd cargo]

you mean order of operation?

oh never mind

[dull ruin]

How to learn algebraic geometry

[molten gulch]

How much maths have you already done

[dull ruin]

Basic abstract algebra and category theory

And also some number theory/complex analysis

[molten gulch]

have you done any topology?

[dull ruin]

Kind of

Don't really understand it

but I've read a book

[signal zenith]

Learn commutative algebra first on the level of Atiyah Macdonald and learn a little bit of point set topology (tbh you don’t actually need that much since AG style topology involves stuff you don’t see too much outside of AG eg irreducible spaces, noetherian spaces…) then read some basic AG book eg fulton Algebraic curves or Gathmann’s AG notes. Later on you’ll learn scheme theoretic AG from Vakil or Hartshorne probably

[dull ruin]

Ok, thank you

[signal zenith]

You only need enough topology to understand gluing constructions and sheafs

[dull ruin]

tbh i've done most of the prerequisites to vakil, except for commutative algebra and topology

ok

I'll learn commutative algebra nexr

[signal zenith]

Yeah you gotta eat your veggies basically

I recommend learning dimension theory as well, on the level of the fundamental theorem of dimension theory in Atiyah Macdonald

[dull ruin]

Interesting

Honestly i'm more interested in Number theory, but also interested in AG

Ok

I'll learn atiyah-macdonald then dimensional theory

[grim delta]

,iamnotstudying

[hasty eagle]

Removed the studying! role from you.

[grim delta]

this worked lol, thank u very much

[molten gulch]

dimension theory should be in atiyah

[dull ruin]

so i only need to get atiyah then

ok that's what i'll learn next

[molten gulch]

there's another book https://dspace.mit.edu/handle/1721.1/116075.2 which has all the stuff in atiyah + all the exercises of atiyah + solutions and I think it covers the material a bit differently but is also free

[dull ruin]

i like free books!

thank you

[remote sparrow]

@frozen perch

[frozen perch]

Hmm, I picked everything up incidentally through unpublished computability theory notes or the Algorithmic Randomness book by Downey and Hirschfeldt. But what's good...

Cooper is very friendly and definitely covers it

That won't get into measure or topology too much from what I recall, so for stuff that's not just the computability theory perspective you'd need another resource

[gray gazelle]

you're still flagged as a spammer lol

[molten gulch]

1 year, 10 months, 30 days left

[compact bough]

@pseudo heart

• ted shifrin's multivariable mathematics (book), his lectures of his math 3500 and 3510 courses that follow the book (youtube playlist), and his work worked "differential geometry: a first course in curves and surfaces"
• lee's intro to smooth manifolds (book that i never read enough)
• robert davie's playlist on diffg, his playlist on manifolds, and his one on tensor calculus (videos)
• the entirety of morgan weiler's channel on youtube (videos giving notes on stuff like forms)
• some of eigenchris's videos on tensors/tensor calc (youtube playlists)
• all 4 playlists under the courses tab on whybmaths' channels
• a little bit of spivak's calculus obviously

imma send more

[compact bough]

mix of vids and books

[molten gulch]

lee is peak

[molten gulch]

also something something ISM is diff top and IRM is diff geo

[compact bough]

also for the specifically diff forms side of things i suggest

• bachman's geometric approach to forms (book)
• exterior calculus in graphics (lecture notes)
• the way that gregory bixler, dan piponi, and duarte maia present the visualization of forms is rlly good too (literally just search any of their names followed by "visualization" and "forms") (pdf blog post thingies)

[livid blade]

is there an equivalent of Apostol's Calculus for ODE? By this I mean an ODE textbook that

• doesn't assume a prior non-rigorous computational course
• doesn't explain things in tediously "American pedagogical" detail assuming the student is incapable of following an argument
• nevertheless, still covers the classical applied ODE material
• doesn't devote half its space to dynamical systems (this is intended to exclude Arnol'd, Teschl, and books like that)
• isn't full of errors (though I have not read the book myself, I have read that Birkhoff & Rota, used for MIT 18.034 for a long time, is notoriously buggy)

[compact bough]

^ @pseudo heart also an important note

[gray gazelle]

Boyce’s

[livid blade]

From what I have read of that book it fails my second criterion

[midnight gulch]

Simmons maybe, or Ince

i assume you have already looked at Tenenbaum right?

[livid blade]

Yes, and also Ince (which I am not sure can be read by post-1920 humans)

I have not seen Simmons, I will check that one out

[gray gazelle]

how about Zill’s?

[livid blade]

Also have not seen, will check out

[pseudo heart]

tysm!!

[compact bough]

ofccc!

[compact bough]

these are all some of my favs :3

[pseudo heart]

irm?

[livid blade]

Introduction to Riemannian Manifolds, also John Lee

he has four now

[pseudo heart]

ahhhh

[livid blade]

c2b7_97705, meowl, thank you! I will take a look at those two

[compact bough]

yee bc you need your manifold to be (pseudo)riemannian to get a metric on it

[livid blade]

mrs. coboundary, when did you get the fancy uncial font

[gray gazelle]

the classic 5th edition btw

[compact bough]

nitro

[livid blade]

one day John Lee will run out of manifolds to introduce people to

[compact bough]

atp he's gotta just be called John Manifold
inventor of the manifold

[livid blade]

except when he goes to France he's really confused because everyone calls him John Variety

[hollow peak]

Every smooth manifold admits a metric btw

[remote sparrow]

https://www.amazon.com/Introduction-Ordinary-Differential-Equations-Mathematics/dp/0486659429

maybe old-fashioned

it seems like people think of such treatments that fit the criteria you lay out as a bit outdated generally

[livid blade]

will check that one out also, thank you! This fits me since I am also a bit outdated

[craggy zealot]

"Can someone please tag the bot or send a link for the 'Bartle Real Analysis' solutions PDF? I can't find it in the search

[gray gazelle]

<@&268886789983436800>

wait idk if it's allowed to ask for PDFs of such

[mellow rivet]

If it's an actual legal pdf I see no issue

Our issues are mainly some stuff being against TOS

Like piracy

[gray jungle]

hey we can not support piracy, its against discord TOS to ask for illegal copies.

[mellow rivet]

Oh it seems it is copyrighted or whatever

Valid modping then

[craggy zealot]

How can I find permissible solutions if

I want to make sure

[gray gazelle]

If you have his intro to real analysis book, he doesn't have a solution one, but he does provide hints at the backend section

[craggy zealot]

Yes, I know, but I want model solutions because they are the only acceptable ones.

That's true, but there isn't time to solve a huge number of questions without being sure.

If anyone can help me, I would be very grateful.

[molten gulch]

it's not

[gray gazelle]

"use brain" and "go to office hours"

your prof would help you better than some discord user

[mellow rivet]

Sorry im dumb I should've guessed on them being unable to find it

[river rock]

any measure theory book?

[ember lark]

[rigid trail]

I am LADR hater but MIRA lover

[frozen perch]

Sensible take

[jolly dawn]

Introductory book on enumerative combinatorics? I have linear algebra in R^n and introductory group theory (product groups, quotient groups) under my belt, and some multivariable calculus, but I don't know any Ring theory or Probability Theory that is commonly required to learn advanced topics.

I would like a book that goes in depth into core topics in enumerative combinatorics but also includes some review, if anyone knows any 🙂

I was considering "A course in enumeration" by Aigner, but it seemed a little too advanced for me. I don't have much time and need to cover the core topics until summer

nvm I found it.

[signal zenith]

Maybe not very useful for diff geo aspect of forms but I would add that I recommend Bott Tu differential forms in algebraic topology

[pearl frigate]

Does anyone have recommendations for more informal/hobbyist maths? I'm trying to improve my repertoire and I feel some fun reads could be nice.

I wouldn't mind a more complex read though if anyone has ideas.

It's a ploy by big maths to make you buy more maths books. 😱

[trail void]

literally ur a mfin mathematician for fuckin ten + years mate write me a full fucking roadmap in appendix

TAKES 2 PAGES

i think they get discounts etc if i remember correctly

they also have like book fairs where they get free books and libraries full of basically any text you want

IRRC

yeah ironically its like one of those situations where yk rich ppl end up paying way less than the average folk LMFAOO

obv not but if ur rich its way more preferrable

yk being an international student is also somewhat of a humiliation ritual cuz ur restricted heavy

[ember lark]

[wispy bison]

Thanks!

[ruby forge]

you never heard of a library??

Oxford and cambridge are copyright libraries, so they have most books ever published

There's some online access to ebooks too, but I think ebooks were only recently included to copyright libraries' access rights

some colleges do book grants, some will buy a copy for the college library on request

[trail void]

yes mfers have access to all the elite books in the world

[ruby forge]

the 97% state school oxford college has £1000 higher rent than the richer colleges 😔

Used to be the poorest college before a £27,000,000 donation 2 years ago

[trail void]

hm i suppose for those who wish to enter university as soon as they graduate highschool this does indeed set an impossible goal, regardless of grades. A scholarship doesn't add money to your wallet, only relieves some you have to give out of your own pocket

[ruby forge]

oxford are quite good with bursaries tbf

they've got the money for it

[trail void]

again if it were upto me i'd take a gap year or two and do something on my own to fill the funds required for such an adventure

or again you can go somewhere else and proceed here later on

upto you :))

[ruby forge]

tbf the rent is £6100 which would be one of the cheapest for any other uk uni, so it's not really that bad

[trail void]

again, compare that to europe or anywhere else and third worlders

[ruby forge]

i don't have the money for travel and i fear employment

i already have my oxford offer to read mathematics starting in october, so I think I'll just enroll and use my college's enrichment travel grant to explore the world :)

[trail void]

youre starting bachelors ? 🙂

[ruby forge]

yessir

[trail void]

im very happy for you :)) soar high

[ruby forge]

you too, i hope the workload is bearable haha 😅

[hybrid sigil]

You can also get access to mathematical books via big public libraries like British Library or mathematical societies

Probably there is something like that in the US too, maybe in New York?

Mm, maybe not in the US, it seems like AMS membership doesn’t provide any library access

[shadow vector]

Not really since you can get em all free online.

[compact bough]

yeye that's a good one too

[odd cargo]

oxford wont let their students go homeless dawg, just get accepted in and dont worry about rent.

my only advice to you is not to bring any more than you need to your university dorm

[vital bane]

There's no way! What?! 6100 pounds a month??

[odd cargo]

no

lmao

probably 6100 over a period of 6 to 9 months

[vital bane]

Why does no one make such a donation to me?

[vital bane]

Oh that makes more sense

[vital bane]

I've been wanting to go through that book, how is it?

[shut patio]

[ruby forge]

No it's a flat rate for the year. Usually it's for 6 months and you have to vacate out of term times. But due to renovations, in 2nd and 3rd year, it'll be offsite accommodation but for 9 months, and only have to vacate over summer.

[silk latch]

Hello guys! What do you is the best sequence for combinatorics(from intro to like pretty advanced). Also, you can assume proof skills.

[glad raptor]

Guyss does anyone have textbooks or exams from oxford about discrete mathemfatics(specifically relations) if yes I will appreciate it

[silk latch]

Ik a great book that has a chapter about it

But a specific exam from Oxford

I think they have their exams online

[silk latch]

https://www.bodleian.ox.ac.uk/collections-and-resources/exam-paper-archive

This is the archive for them

[glad raptor]

Omg great

[silk latch]

Form 2000s

[silk latch]

I’m glad I found what you were looking for

Also in general most proof books would have great chapters on relations

Naive set theory and or book of proofs

Have very good exercises

I only used book of proofs tho

[glad raptor]

Dosnt matter i only need to estimate how the questions look so ik what to expect on my exam. My professor’s son finished there and she is using his tasks for almost everything lmao

I was replyong to the from 2000 message

[silk latch]

Well good luck😭

[glad raptor]

Not to your last

[silk latch]

Oh oh

Ic

Well I was gonna say the book basic mathematics has a weirdly good chapter on mappings

[glad raptor]

Yee im good with those but my prof is very fond of brain twisters that are not so naive hahahah

[silk latch]

Yeah book of proofs is pretty big fan of those too

😭

[glad raptor]

Ooo cool

[silk latch]

Well it’s good for you to be challanged

[glad raptor]

Yhh

[silk latch]

Genuinely great the exercises are insanely good

[glad raptor]

I actually like relations sm

Cuz its very useful

[silk latch]

Cuz I tried hammack before and he was meh

[glad raptor]

Especially in computer science

[silk latch]

Are you like into cs or complexity theory more?

[silk latch]

It’s pretty pretty useful

Relations are very cool

Functions are relations and they are pretty much most of math

😭

[glad raptor]

Yhh very true

[silk latch]

I want a graphing calculator that can graph relations

[molten gulch]

Does anyone have any nice resources for the history of algebraic geometry? The goal here is to introduce some of the basic intuition for why one should care about the notion of a variety or solution sets to polynomial equations in the first place?

This seems quite easy to do with linear algebra, as linear systems of equations are abound, and solutions to these equations have clear geometric significance, but I'm having trouble coming up with a good way to introduce why one should care about systems of polynomial equations and how grobner bases can make it easy(ier) to solve these equations. I'm familiar with how back in hellenistic times, the greeks studied intersections of planes with various conic sections, but what led them to consider these problems in the first place? Besides that, where did the notion of projective and affine spaces (specifically the modern language/definition to talk about them) come from?

[lean tinsel]

any books to learn single variable calculus from scarcth

i wanna start real analysis 1 by Terrence tao sir

[molten gulch]

Thomas or Stewart are fine

[molten gulch]

This is a good book for analysis

also Jen, I just downloaded Dieudonne's paper and started reading it

Looks very promising for what I was going for here

[lean tinsel]

thomas calculus you meant

[molten gulch]

yes

[lean tinsel]

oh ok

[fossil nest]

ive been slowly reading and rereading and rerereading https://www.jstor.org/stable/2317664 a quick overview by dieudonne of some of the MANY phases of the history of algebraic geometry id love to share my struggles in reading it

[idle sky]

Oh you mean discover of conics?

[molten gulch]

I'd very much appreciate that!

[molten gulch]

Conics are quite a general object, algebraic geometry can study conics yes, but that's not all that it's used for

[remote sparrow]

https://archive.org/details/historyofalgebra0000dieu/

i saw this

[fossil nest]

note its very sketchy in parts and i dont think its a very good place to look for intuition, but its maybe a good place to get a sense for some of the structure of the history, though note also this article is from the 70s iirc and the field’s moved very far since then

[remote sparrow]

https://math.stackexchange.com/questions/4785558/history-of-algebraic-geometry-morphisms-and-birational-geometry

https://dzackgarza.com/rawnotes/Class_Notes/2016 and Earlier/GeometryFinalVersion.pdf

[lean tinsel]

can. you also tell me is it ok if i side by side do book of proof

[idle sky]

For conics I have read the book by Pappus.... That's a great book to develop intuition regarding identification of graphs from equations and it also helps with some quadratics

[molten gulch]

Agreed, mainly what I'm looking for is the more concrete varieties side of things rather than schemes as the end product is going to be a short 3-5 page note on what algebraic geometry is and why one may come to care about it, so I think slightly older sources should be fine(?)

[molten gulch]

I'm familiar with the theory, I'm more looking into the history of their study, but this does give me another marker on the journey, which is to take a look into a bit of ancient greek mathematics, I appreciate it

[molten gulch]

should be fine alongside calc

[lean tinsel]

thanks

[halcyon rapids]

Book recommendation for a beginner

[midnight gulch]

dr seuss

[molten gulch]

What have you studied so far, based on that one can give you recommendations

[fallow aspen]

It would probably be a good idea to give some context. A beginner can mean anything from someone who is starting their undergrad to someone who does not know how to do basic addition of numbers

[idle sky]

Yeah that book has the history also I guess. I know you are talking about how Mathematicians think of this and how it proceeded. For example, I have read the history of bombelli before he discovered numbers( complex plane) , used the integration of 1/(1 + x²) dx which led to the discovery of euler's identity of e^(i θ) = cos θ + i sin θ... He first factored 1+x² as (1-xi) (1+xi) and then converting it into partial fractions.

[molten gulch]

ye

[idle sky]

So you can prefer hall and knight

And SL Loney for the geometry part

[molten gulch]

These are the very basic ideas of algebra and geometry, this is not algebraic geometry as I am referring to it

as an example of an affine variety

[idle sky]

I am sorry.... I am still in High School. So I think I can't help you further.

[molten gulch]

Yeah that's fine

[halcyon rapids]

I will check that out

[halcyon rapids]

None

[fallow aspen]

Do you know how to do 3 + 3?

[halcyon rapids]

Someone starting their undergrad but haven't studied math's in my high school either

[halcyon rapids]

8? Like if we mix them E3

[fallow aspen]

https://www.khanacademy.org/ You can learn everything there from the most basics, you can see yourself what level u are at currently

[red geyser]

can someone help me with trig

[red geyser]

#book-recommendations trignometry

#book-recommendations algebra

[molten gulch]

Why are you stating the name of the channel repeatedly

now

https://www.stitz-zeager.com/szprecalculus07042013.pdf This should have everything you need

There's also S.L. Loney's Plane Trigonometry and Hall and Knight's Higher Algebra

Also Lang's Basic Mathematics

[red geyser]

thanks

[runic breach]

Is michael spivaks calculus 3 a good book?

[molten gulch]

his book is just called "Calculus"

[runic breach]

Sorry, I meant third edition

[signal zenith]

Really really goated

Prob my fave math textbook

I feel like if you understand the content you get really good geometric intuition for cohomology

There is also many concrete computations where you just explicitly take an integral to find some characteristic numbers and stuff, so I also really like it for learning characteristic classes

It’s quite cool

I mean it’s just goated pretty much in everything it has in the book

[glad raptor]

I am doing a double major one in cs and the other in actuarial maths but i was in a math oriented highschool and now the actuarial maths course takes a more theoretical approach at the start so i guess both

Sry for the late reply i was afk

[vital bane]

Holy peak

[vital bane]

Alright I'll definitely need to go through this then

[full pike]

you guys recomend some self-taught english book?

I really need one, I suck in english

Idk if this is a good place to ask.

[velvet flax]

is there any number theory book that is comprehensive enough to serve as a general reference and has a somewhat modern viewpoint

i guess what im asking for is an analogue of lang but for number theory instead of algebra

[midnight gulch]

neukirch for algebraic number theory

[wicked fractal]

Neukirch my goat

[midnight gulch]

not sure for other areas of number theory, and i don't think any comprehensive "general reference" exists

[wicked fractal]

Also check Silverman for elliptic curves

D&S for modular curves/modular forms

These go hand in hand

[velvet flax]

ty!

[vital bane]

You mean for speaking? For that I think the best way is just to watch movies and shows with english subtitles and just practice speaking with other people

If you mean reading and writing then yeah just read whatever books you're interested in, fiction or non-fiction and practice writing

Oh yeah? name every number then

[full pike]

for i in R:
i = then

[median egret]

ℂ∪ℍ

Yall I need an epic book for complex analysis

Specifically tuned for electrodynamics stuff

Any recommendations?

[pulsar veldt]

Boa Anizio

[full pike]

caralho mano, até aqui 😭

tu é meu maior fã, não é possível

[pulsar veldt]

Só vim ler o chat q eu sempre fico

[full pike]

hmm, legal

estudando o que ultimamente?

acho que nunca puxei papo de verdade ctg

[pulsar veldt]

We better be speaking english

[full pike]

yeah

[pulsar veldt]

Physics, Calculus and Olympiad Mathematics

I used Moyses' physics book, but I got to the part where he uses vector calculus, and I haven't studied that yet

Im still learning integrals (through Thomas' Calculus book)

[full pike]

It is not necessary to speak english here, I think it. I saw some people speaking in French lately.

[pulsar veldt]

Huh

[full pike]

Damn, you look pretty advanced

[vital chasm]

We allow non English in the help channels only

[pulsar veldt]

Ok

[full pike]

do you want to take some Bachelor's on physics or math?

[vital chasm]

Its not like we don't like other languages, its just easier to moderate

[pulsar veldt]

By now I'd choose physics, I still have some time to choose tho

[full pike]

it is compreensive, thanks

[pulsar veldt]

Maybe, but I don't think It helps in competitive math, specifically for OBMEP (Brazilian mathematical olympiad for public schools)

[full pike]

Maybe in some maner, I believe it can be pretty productive actually.

And what do you think about OBF and OBFEP?

[pulsar veldt]

I know more math than physics, despite what I said

Specifically high school physics

Which is required for those olympiads

[full pike]

You can gain a scholarship on Farias Brito or Ari de Sá by earning a medal. Some of these guys called me after I earned only a silver medal xd

[pulsar veldt]

Are these schools?

Never heard of them

[full pike]

yeah, it is very famous on ITA/IME niche

[short coral]

Does anyone have book recommendations for learning mathematics at an advanced Secondasry School or 'high school' level?

Things to solve this with:

[pulsar veldt]

I got TME 1 (An Excursion Through Elementary Mathematics vol.1) in my desk

[full pike]

these sort of things are undergraduate level, if you want why this work

[pulsar veldt]

I guess it would be easier for me getting a medal in mathematical olympiads than physics olympiads

Because its lower in general content to learn from where I'm now

[short coral]

Oh, ok. Do you know about anything for an undergraduate level?

[full pike]

you can pick Terence Tao's analysis book, it's pretty good for anyone who hasn't had some contact with undergraduate material

[short coral]

Alright, thanks!

[full pike]

Its a very good book, I had the number theory one to do a seminar.

[full pike]

You are welcome

[pulsar veldt]

Have you heard of MONT? (Modern Olympiad Number Theory)

[full pike]

Maybe I saw in the IMPA's library

[pulsar veldt]

😯

[full pike]

You want to make OBM or just OBMEP?

[pulsar veldt]

I'd like to try OBM

Do you think I still got time? I have this and next year

only

[full pike]

good luck, I never succeeded to get in, but you look very prepared

[full pike]

make the Jacob Palis olympiad, It is very hard to get in OBM by OBMEP

and yes, maybe you can get a bronze medal in time

just work hard

[pulsar veldt]

I heard some people say they are making in-person exams by now

There were some guys using AI past year

[full pike]

:/

[pulsar veldt]

This makes it harder to me to get in OBM

[full pike]

But, still easiear to get in OBM by Jacob Palis

[full pike]

what state do you live?

[pulsar veldt]

Thick Bush

[full pike]

XD

In Cuiabá dont have any applications?

[pulsar veldt]

Gotta watch for it when there be applications

I live far away from Cuiabá tho

[full pike]

Bruh, this is sad

look for some olympiad classes at Farias Brito or Ari de Sá

maybe you can get a scholarship

[pulsar veldt]

OBMEP probably is gonna be my unique chance for getting an application to IMPATech

[full pike]

look for PETI - OBM too

[pulsar veldt]

I will try OBM, but I don't think I would succeed from it

[full pike]

just try, maybe you can get it. I can help you too if you want

[pulsar veldt]

fine

Do you know if I could sum my ENEM result with olympiad medal?

[full pike]

You cannot

[pulsar veldt]

Ok

I think thats all

Gn

[halcyon rapids]

Class 10th hai level mere

Thanku

[shut grotto]

I have the complete opposite opinion lmao

not a MIRA "hater" tho, I just didn't like it very much

[primal mica]

MIT’s main library has a worse physics section than my personal library.

But that’s all I looked at while I was there, I didn’t really explore other subjects

[surreal bay]

hi just coming in2 ask
what do you all think of vilenkin’s combinatorics?

& should i read it after bonás book?

[gloomy monolith]

Hey everyone! I’m a UK college student studying CS and maths. I’m mostly into pure maths, though stats is cool too. Anyone got any good book recommendations? I’m looking for something that starts simple and gradually gets more advanced, doesn’t need to assume a ton of prior knowledge at the start. Not looking for encyclopedias, just a solid, readable book. Open to anything in stats or pure maths NOT mechanics!

Thanks!

[signal sparrow]

Guys, would u say "Linear Algebra Done Right" by Sheldon Axler is a good book for lin alg?

[hybrid sigil]

it is

not only it's linear algebra, but it's also done right!

[shut vortex]

I prefer Gilbert Strang's books.

[hybrid sigil]

it doesn't make Axler's book bad though ;)

[vital bane]

Not for a first exposure imo

I think FIS or HK is better for a first course in LA

[hybrid sigil]

"Concrete Mathematics" by Knuth, Graham, Patashnik is interesting

[ember lark]

It's good for a first course if you supplement with some resources about determinants, rref, and matrix versions of stuff like spectral thm, diagonalization, etc

I recommend it though

[ember lark]

Also if you have already taken a first course that covered this then definitely read ladr

FIS is good too

[cunning elk]

strang just comes off as incoherent from what ive read

[hybrid sigil]

yeah, Strang has a particular, somewhat unusual style of presentation, it shows in his video lectures and books too. It's not bad and many people like it, but it's not for everyone

but shouldn't we invite/write some Discord bot to reply to those questions about Linear Algebra books? I bet this question has been asked, thoroughly discussed and answered approximately a million times

we can even provide a list of concrete users of this Discord recommending one book or another :) Normally if a user X recommends FIS, they will keep recommending it and so on

[trail void]

good idea

[rocky geode]

Hey
I am a computer science undergrad and have done a UG level combinatorics course. Other relevant coursework might include UG level graph theory, discrete math, statistics.
I am looking for some good books on combinatorics, I would prefer something which is less heavy on proofs and more focused on problem solving.

[signal zenith]

Is ur username based on the inheritance cycle books?

I love those books

[mortal iris]

Either Epp or Rosen's Discrete Mathematics should do the job. For stats, Wasserman's All of Statistics is a solid place to go to.

[rocky geode]

I am looking for books on combinatorics, also I have covered most of the topics from Rosen’s Discrete Math

[mortal iris]

Oh mb. I read your question wrong.

[mortal iris]

You can try Peter Cameron's Combinatorics. It's pretty algorithmic and not super heavy on structural proofs.

[signal sparrow]

yes omg i'm so happy that like quite a few people have noticed

[rocky geode]

Thanks

[arctic gull]

Hope you remember me lol

[arctic gull]

How should I do Hall and knights higher algebra? It's a little too advanced for me

Could you recommend some other books which are perfect to understand math properly, in depth ?

Want to study as many books as I can

[arctic gull]

I feel like Hall has the theory not in depth

[mortal iris]

Let me get this straight. It's a little too advanced but it's not covering things in depth? Make that make sense lol.

[odd cargo]

If its a little advanced for you then dont read it, look for an introduction to algebra book that has rigorous treatment.

[mortal iris]

What you seem want is a book that babysits you through everything. Such things are often not conducive to learning. If the text makes things deliberately hard to understand, then it's a different matter.

Hall and Knight's Higher Algebra is certainly not one of those texts but you might as well go one level lower to Algebra for Beginners instead if you find it difficult.

And you are free to seek help when you don't understand something.

[mortal iris]

I don't know what connotation of rigor you're using here but if elementary algebra feels difficult without it, then proper mathematical rigor might just make things worse if the student is not used to it already.

[odd cargo]

maybe i shouldnt have said rigorous but what i meant was a book that could bridge between arithmetical quantities that you could attach some concrete example to with algebra.

you also have books that do a good job demonstrating algebraic laws without getting into proofs and all that

ideally, you should be looking for a book that does both (though i doubt you would find a book that does either entirely separately) if you havent done maths properly

at least at the middle to high school level

[mortal iris]

Hall and Knight's Algebra for Beginners is great for that, which is why I recommended it now. However they did come in asking for something equivalent to Higher Algebra given the stage of the Indian curriculum they're facing atm.

[odd cargo]

never mind, i thought they were tlaking about higher algebra

[mortal iris]

They were. They found it too difficult. That's because their foundations are lacking. In which case going back to middle school level Algebra like in Algebra for Beginners is the best thing to do. Which is what I suggested above.

[vital bane]

Oh lol I thought you guy's were talking about Brian C. Hall's rep theory book

[abstract wren]

guys can you give me textbooks for self learning math?

[rich sun]

that depends a lot on what level of math you want to learn

[molten gulch]

What maths do you already know and what do you want to learn

[spark notch]

could anyone recommend me some maths books to work on my concepts (class 11 JEE aspirant btw)

[mortal iris]

Hall and Knight's Higher Algebra, Loney's Plane Trigonometry and Coordinate Geometry. Johnston's Intro to Linear and Matrix Algebra. Thomas and Finney's Calculus and Analytical Geometry. Blitzstein's Introduction to Probability (first half).

(Being an aspirant for an exam is quite stupid btw.)

[tidal lodge]

Calculus Made Easy is this a good starter book?

I need a book too thats covers all of integrale vektoren etc. im 16yo and it would be my first math book

Just a book covering all starter school math and maybe the start of studium

[molten gulch]

this covers differential and integral single variable calculus

you'd need something else for multivariable and vector stuff

[swift topaz]

Read stewart it covers vector and 3d calc

[dull ruin]

How should i learn automorphic forms and the langlands program? I’m decently familiar with abstafct algebra, great at complex analysis, i know basic analytic and elementary number theory

[oak mirage]

i love stewart

[spark notch]

aahaha thank you for the recommendationss

seems like you dont know much about the indian system thoo

[normal crystal]

https://tenor.com/view/tyler-joseph-twenty-one-pilots-tyler-joseph-before-after-tyler-before-after-gif-7614623452995519722

[mortal iris]

I know it very well. I've lived it.

[spark notch]

OH SHITT

okay i am sorryyy

my bad

[zinc remnant]

books for improving coordinate geometry(I am kinda beginner so...)

[blazing holly]

Have you checked out openstax? Pretty sure they have a geometry textbook

[hollow tundra]

Should I read the principia of Mathematica?

[hasty sand]

Newton's or Russell's ?
you know what, neither in fact

[signal zenith]

Don’t unless you’re interested in history of math

Contrary to popular belief it does not actually take 500 pages to prove 1+1=2 and modern exposition is much better

[hollow tundra]

How long does it take lol

[split osprey]

dhar mann book guys?

[wary atlas]

Well if you use your eyes it might be instantly

If I have an apple and another apple it’s gonna be two apples

[dull ruin]

wait so are there are any good books for this?

[hollow tundra]

What is two

[wary atlas]

To me it’s a representation of a thing

[signal zenith]

Like 80 max

[wary atlas]

Idk the real definition

[signal zenith]

You need to develop enough set theory to define induction the natural numbers and principle of recursive definitions

Then once you’ve defined everything it’s immediate

I think the axioms you actually need are axiom of pairing, axiom of union, comprehension, and power set (to define successor you must apply axiom of union to the set {x, {x}} so you somehow need to show that’s a set), axiom of infinity aka axiom of induction (to define N and addition)

[zinc remnant]

Nah

[signal zenith]

So that’s a decent bit but not 300 pages or whatever worth

[wary atlas]

I’m not versed in abstract math but is a physical two different than a marked two in a equation

[signal zenith]

Wdym by a “physical two”

If you mean like 2 apples the intuition is that the mathematical 2 is just a formal way to construct a model for something with 2 objects

In a way where we can actually prove things abt it

[surreal bay]

^
mb

[signal zenith]

I mean we have some axioms for what we think numbers should satisfy (Peano’s axioms) and then the set theory construction of the naturals is just a way to define mathematical objects (sets) that satisfy these axioms

But any other mathematical structure that satisfies those axioms deserves equally well to be called “the naturals”

Whether those axioms are the right ones to describe numbers is more of a philosophical than a mathematical question…

[outer carbon]

Anyone have any good differential topology recommendations? Heard that there are two approaches to the subject: differential and topological. I’d be more interested in a topological approach

[signal zenith]

This is not really a textbook but a good overview of outstanding problems in differential topology in dimensions >= 4 is “the wild world of 4 manifolds”

Assuming you aren’t just looking for an intro to smooth manifolds but an intro to some of the modern research question called differential topology that is

[outer carbon]

It can be over any dimension of manifold. However, the more abstract the better

More of foundations

[cursive orbit]

guillemin and pollack

[novel anvil]

For a project of mine i need to have a good grasp on octonions. Do you have recommendation on a book to learn everything about this, clifford algebra and potentially Jordan algebra. It's ok if it's part of a larger book on more than these concepts.

[signal zenith]

For foundations as someone else said Guilleman and Pollack is good, I’d also recommend Lee ITSM

[tidal lodge]

Wich book do you mean ian stewert or james stewert ?

So likee the title of the book

And maybe if you know if there is a german version of it

[fallow aspen]

James Stewart - Calculus

[tidal lodge]

Ok imma read it

[celest sluice]

hi everyone i am taking ODE's in the fall semester and im looking for some book reccomendations in advance

[swift topaz]

Hm

Nagle is what I read

Fundamentals of differential equations

Ch1-9

[odd cargo]

bruh, do yall schools not have a recommended reading list or something

[swift topaz]

Sometimes the list is trash

[odd cargo]

doubt it

cool

[swift topaz]

i mean yea u can learn from any textbook really

[signal zenith]

Qingkai Kong a short course in ordinary differential equations

[restive imp]

Completely out of context if you want to learn precalculus, calculus and calculus with more variables I reccomend the books of calculus of stewart where you will find a book for precalculus another for calculus and another one of calculus with many variables. And I think there isnt much difference between versions so Dont worry about that.

[heady nexus]

book recommendations for formal logic / FOL? I dont think there are any necessary prerequisites, and have heard Enderton come up a good bit on reddit.

[midnight gulch]

enderton is good, i like kunen's "the foundations of mathematics" as well

[heady nexus]

I've seen both actually and in fact have smith's notes bookmarked. I don't know how the exercises compare between all of them though. I'll probably use multiple books though so I suppose that isnt very important.

[heady nexus]

Kunen ive also seen floating around and being recommended, looks very clean from briefly skimming through it a couple of times

So there are solutions to almost all of the problems? Pretty good,

Is this like meant to be covered fully in a semester or is there only part of it you should read?

[fair bear]

guys book rec for pre algebra?

[heady nexus]

Not for a logic class, just for the love of the game. I do have experience with proofs and basic analysis at the level of (baby) rudin so I have a working understanding of the very basics. I see no reason to not finish the textbook though and would be my goal, as I am not in a particular time crunch.

[odd cargo]

elements of algebra. Euler

[molten gulch]

Euler's writing style may be difficult for someone in middle school

[molten gulch]

Openstax prealgebra is fine

[odd cargo]

its not bad man

[fallow cypress]

I will warn you that it might not make sense unless you have more experience playing around with abstract mathematical structures

Abstract algebra like group theory and so on is usually a good way to come into contact with those ideas

[heady nexus]

yeah it just piqued my interest after some reading on it, I have a vague idea on what it is about but I assumed that it would be more of an introduction to philosophy, specifically logic

im in no rush to learn these things though so I usually take a good deal of time to understand and develop an intuition

[fallow cypress]

It is very cool!

just don't be discouraged if things don't make sense the first time you see them

[brisk berry]

I'm new to IMO scene and preparing for IMO I have around 2 years for preparing for IMO. can u recommend me books to cover IMO syllabus and have unique and creative problems

[trail void]

max stirner giving math advice

[vestal moth]

Is anyone using math books named Basic maths by serge lang?

[remote palm]

Anyone know any good math books for like yr 9 level

[ember lark]

If you have good algebra knowlegde, learning intro level calc would open up a lot for you

[proper trout]

✋ I'm about to finish it

[vestal moth]

Is it worth it book?

[vital bane]

"The beginner should not be discouraged if they find they do not have the prerequisites for reading the prerequisites."

Me trying to learn Atiyah-Singer Index Theorem be like

[wicked fractal]

Lol good luck

[thorny nest]

something on linear algebra please
the yt videos cover everything including basic matrix floof that i have already done
i just want to study the geometrical aspect of linear transformations

@ me pls

thx

[primal mica]

I personally thought Strang was pretty fine for more pictorial approach to intro linear algebra

[sinful herald]

I've also worked through it and I think if it's the first time seeing the material then there are better options. If I recall correctly he explicitly mentions in the preface that he expects you to have already seen most of the material, just not quite as formally as he presents it. Other than that, I thought the intuitive geometry section was put together poorly. The rest of the book was fine.

[jolly tendon]

Elementary LA by anton

[vestal moth]

What’s a better alternative to that book?

[fallow aspen]

If you're trying to learn the material covered by Basic Mathematics and haven't seen it before then working through Khan Academy up to precalculus would probably be a good alternative

[proper trout]

honestly I've struggled particularly at that section

[thorny nest]

can i try it?

[mortal iris]

3B1B has some nice videos for intuition. There's also Georgia Tech's Interactive Linear Algebra textbook online.

[mortal iris]

You'd rather go to classics like Loney for the Geometry. Lang has a separate Geometry text too but idk how good that is.

[mortal iris]

Hall and Knight's Elementary Algebra for Schools. At some point after you're comfortable with algebra you can start with Loney's Plane Trigonometry.

[open thicket]

Im looking for a book with lots of examples regarding calculus( mainly integration ). Any suggestions ?

[runic breach]

Is S.L. Loneys Plane Trigonometry a good book for learning trig?

[runic breach]

From what I know Calculus by michael spivak is a good book for overall proof and examples of calculus.

[ember lark]

The answer to all of your questions is "Linear Algebra Done Right" by Sheldon Axler.

[ember lark]

This channel can now be archived and closed as all future questions are answerable by this

[midnight gulch]

no

[ember lark]

[fiery elbow]

WHat are some good algebrea books, like not linear but algebra 1

[molten gulch]

For plain old modern algebra 1 which usually covers groups (whereas linalg 1 is all vector space theory) artin's algebra should be fine

[cunning elk]

pre-university role

somehow I don’t think they’re talking about abstract alg

[molten gulch]

when someone says algebra but not linalg I assume they mean groups rings fields 😭

[cunning elk]

ive seen lots of precollege students confuse “one variable linear equations” with “linear algebra” so usually im a bit skeptical whenever someone mentions it

[void lintel]

From where you buy mathematics book? amazon is good?

[ember lark]

ebay sells for cheap for relatively g ood quality books

[gray gazelle]

https://www.abebooks.com

[fresh skiff]

Where is sour drop

[remote sparrow]

use bookfinder or a print-on-demand service

[odd cargo]

A classic

[vestal moth]

I’ve never tried trigonometry before

[dark wolf]

Really? That feels like a sin

(Someone please pity laugh)

[vestal moth]

Huh

[dark wolf]

Because in trig it’s a whole lot of sin cos and tan

[vestal moth]

Ooh, hhhaah

[dark wolf]

You get a tan cos of sin

[vestal moth]

I get it

[vestal moth]

Hahah

[dark wolf]

Thank you for laughing

It’s means the world to me even if it’s just pity

[dull forum]

thank u for clarifying the fact that ur not indian

[slim wave]

if u a non Indian i recommend you to do elementary algebra. hall and knight aint elementary lvl gng😭😭😭

wot

sarcasm gng, ts for any person indian or not

[vital chasm]

Sorry the whole conversation has been pretty interesting so far

[night heath]

Is rs aggarwal good for grade 9

[tranquil sage]

Any suggestions for a measure theory book. Goal is to learn it for probability theory, stochastic processes and ML sort of stuff but also just for fun. Am a second year financial math undergrad and my only previous exposure to pure math is reading abbots analysis rudins analysis and axlers LADR.
was thinking taos?
also open to an online course reccomendation

[remote sparrow]

https://measure.axler.net

i would also suggest looking at billingsley

[tranquil sage]

Thank you! I didnt know axler had a measure theory book, I enjoy the clear structure of his writing so will give this a look

[molten gulch]

https://measure.axler.net

[gray gazelle]

Currently studying Differential Equations for S.L. Ross, completed 3 chapters up to Orthogonal and Oblique Trajectories.

Can someone recommend a book for further practice containing difficult problems?

[edgy saffron]

????

that was fast

didnt even ping anyone

[modern umbra]

Any books that explain about vector fields? Been wondering a little

[tame tree]

loring tu intro to manifolds

[twilit pulsar]

Recently I got the book Introduction to Topology (by Gamelin & Greene). I took graduate differential geometry (from do Carmo's book) before this and was quite lost on the fundamentals of differentiable manifolds due to taking classes out of order. Does Introduction to Topology provide a sufficient exposition on manifolds to prepare one for a differential geometry class?

[twilit pulsar]

If not I second this question

Well I suppose I'll know soon enough just by working through it in full. It'll take some months though

[midnight gulch]

it looks like it covers very little about manifolds

[slow forge]

What's the best book for linear algebra?

[odd cargo]

who @'d me

[crude sage]

I'm looking for a book that has computational exercises on Galois theory and field theory: things like discussing irreducibility of polynomials, finding Galois groups, calculating degrees of extensions, using the Fund. Thm. of symmetric polynomials, etc

Our exam may be something of a speed competition involving mostly exercises of that sort, so I need to prepare

[molten gulch]

friedberg insel spence

[thorny nest]

id suggest a book called upadhyay and upadhyay

for 9th grade

[runic breach]

In Loneys Plane Trigonometry when it sais “Euc VL 33” is that like a citation to a paper?

[odd cargo]

possibly referring to euclids elements

[runic breach]

Is there anywhere I can access them?

[odd cargo]

tried google?

[warm roost]

hello, does anybody know about a good linear algebra book? consider i only know the basics

[dull ruin]

”Linear Algebra done right” is mentioned every time i swear

[warm roost]

i will look it up, thanks!

[dull ruin]

But really someone more knowledgable should answer

[trail void]

check pins

[heady nexus]

Usually I think that you would do more computational LA before getting into proof based LA, especially if you don't know how to write proofs. Anton is a good book and has a lot of exercises.

[warm roost]

are you referring to the elementary linear algebra book?

[trail void]

yes

its better for engineers/physicists/applied mathematics

[molten gulch]

<@&268886789983436800> requesting pirated resources

[remote knoll]

We can't help you with this, due to Discord TOS

[gray gazelle]

Oh, I see. I am sorry

I didnt know

[remote knoll]

No worries. Best of luck finding it.

Sorry we couldn't be of help.

[gray gazelle]

Its okay, I appreciate it.

[shy coral]

Has anyone here read Hrbacek & Jech's 'Introduction to Set Theory'? I'd like to know what you think of the book and if you would recommend it.

[midnight gulch]

its good, i would reccomend it

[shy coral]

okay thank you

[midnight gulch]

i also like Roitman's modern set theory, which covers much of the same content

[shy coral]

i'll check it out then thx

[primal mica]

Strang is great in my opinion. Linear Algebra Done Right is a gentle read for linear algebra with proofs, but for most it’s a second pass through the introduction of the subject (it even says so in the preface)

I’m sure there is a lot of info in the pinned, but as a biased physicist, I liked Strang, but I also was already very familiar with the subject before I used the book, which would also bias me.

[last cipher]

I can attest that Strang’s LA is amazing. You can accompany the book with his lectures from MiT as well

[frozen perch]

#book-recommendations message

Endorsed, basically

[midnight gulch]

except for axler?

[frozen perch]

If you have some proofs under your belt, the standard rec is FIS or Axler

If you have a whole course under your belt already, and understand the determinant, then Axler is acceptable

But the title makes claims the book does not back up!

[quiet berry]

if you mean the algebra taught in school, any book you can get your hands on or from a library is going to work. the website/app khan academy is also very nice

[jolly tendon]

i want to try the linear algebra done wrong

sounds interesting

[normal crystal]

https://tenor.com/view/head-gif-2485157009672650539

[leaden sand]

I keep on coming here to look for good fantasy book recommendations and then remember this is a maths server.

[ember lark]

?

[midnight gulch]

that statement is fair if they are taking a certain kind of computation-focused course

[ember lark]

so your linalg class doesnt cover vector spaces, subspaces, span, linear independence, bases, or linear maps.

[ember lark]

an intro linalg class that doesn't have any of [these](#book-recommendations message) is not a linalg class

ok well you must cover spans and vector spaces if you cover bases

and you will indirectly be exposed to linear maps (though ur class is weird and bad if it doesnt actually mention them) if you cover matrices

[midnight gulch]

some courses either barely cover or essentially ignore vector spaces and linear maps

[ember lark]

doesnt sound fair to name it linalg then lol

[midnight gulch]

often a course like that would be called something like "matrix theory"

[vital bane]

Re:Zero light novel/web novel

[leaden sand]

Thank you!

[little yew]

Yeah, true. I'd either just call it "Linear Algebra for Engineers" because of how abstracted first courses can be to where you don't really need to worry about rigor (depending on department) or just "Matrix Theory".

[mortal iris]

Read the Tolkien Legendarium if you haven't already. It's got so much that you'd probably spend a few years there. It is arguably THE fantasy template.

Need I mention A Song of Ice and Fire by George R. R. Martin. Hopefully he finishes the series before kicking the bucket but what's already there can take you a while to go through.

There's also Lev Grossman's Magicians trilogy which is a satirical fantasy with twisted interpretations of elements from both Narnia and Potterverse. There's also an awesome TV adaption of the same.

For mythological fantasy, you can also consider checking out Rick Riordan's Percy Jackson, Heroes of Olympus and Kane Chronicles. There's also Bibek Debroy's 10 Volume Mahabharata which is a historical mythological fantasy (but also a religious text of sorts).

If you're into manga, then there's Witch Hat Atelier and One Piece. If you're into anime then there's Hunter × Hunter (the manga is good but some of the exposition is tough to consume in that medium). There's also Frieren and Fullmetal Alchemist Brotherhood.

Among manhwa and LNs, Omniscient Reader's Viewpoint and The Beginning After The End are excellent reads. Tower of God used to be amazing as well but I've not caught up in some time. There's ofc the aforementioned Re:Zero and also Mushoku Tensei.

[remote sparrow]

mushoku tensei

https://tenor.com/view/crine-im-crine-son-im-crine-anthony-mackie-tiktok-gif-10273212848663596705

[vital chasm]

For a nice English web novel, check out Mother of Learning

[vague nimbus]

any recommendation for studying projective geometry ? (if anyone has taken a course on it i would like to ask him questions about the subject if possible)

[vital bane]

Not "years" but yeah at least 1 year to catch up with Arc 10

If you read 2 chapters a day

Maybe more during weekends

[lapis patio]

hi

[mortal ore]

@molten gulch you got a buddy it seems

[proud osprey]

I liked Kazuo Ishiguro's Buried Giant a lot. And Pratchett's Discworld books are a fun read!

[hybrid sigil]

Buried Giant is great!

[charred heath]

Anyone recommends resources for Pre-university physics?

Mention me

[junior kelp]

hi ! does anyone have good resources for PDEs ? Specifically heat and transport equations

[normal crystal]

https://www.amazon.com/Introduction-Continuum-Physics-Steven-Pride/dp/1108844618

https://youtu.be/NoF4WYV5DMs?si=O4AH52MpIX8k11ho

[charred heath]

I did NOT ask for this

I needed books

[mellow rivet]

You asked for proud physics

[charred heath]

What -

Wait

[normal crystal]

hey man, I didn't question your demands

[mellow rivet]

Proud->pride

[charred heath]

Pre-university not proud...

That damn autocorrection

[mellow rivet]

The term "proud physics" isn't commonly used

[charred heath]

My bad

[normal crystal]

Preuni

[mellow rivet]

Preuni->proud->pride omg im lgbtq!

[normal crystal]

Conceptual Physics - Hewitt

[charred heath]

Ah yes, I got that one
But it's very light in math

[normal crystal]

do you know calc

[charred heath]

Not yet

[mellow rivet]

Preuni also doesn't tell us much

We need to know what you know to help

[charred heath]

Collecting resources though, I do it at once and never again

[mellow rivet]

Preuni means vastly different things in different places

[charred heath]

Hold up,

[mellow rivet]

Like what math can you do and what physics can you do as of now is much more important than the label "preuni"

[charred heath]

Don't mind my current math level, I'm collecting resources early

For various reasons

[normal crystal]

The other algebra based books are similar ie Cutnell, Giancoli
you can look at a typical university textbook and ignore the the calc somewhat

[charred heath]

Here is the syllabus

Part 1: The Level

· Difficulty: Advanced High School
· Prerequisite: Calculus (differentiation, integration, vectors)

---

Part 2: Topic List

I. Mechanics

· Motion and Force
· Forces
· Work, Energy, and Conservation Laws
· Momentum and Collisions
· Circular Motion and Gravitation
· Oscillations

II. Thermodynamics

· Heat and Temperature
· Thermodynamics of Gases

III. Waves

· Wave Properties
· Sound
· Light

IV. Electromagnetism

· Electric Fields and Currents
· Magnetism
· Electromagnetic Induction and AC Circuits

V. Atomic Physics (Modern Physics)

· Electrons and Light
· Atomic Structure and Quantum Theory
· Semiconductors and Nuclear Physics

[mellow rivet]

Then we need to know how far you plan to go with physics I'd assume

[charred heath]

☝🏻 does that answer your question?

[mellow rivet]

Yes that'll definitely allow people to get you better resources than guesswork on what you are doing.

[normal crystal]

University Physics or Fundamentals of Physics are typical texts

[molten gulch]

😭

[charred heath]

I don't need to study both, right?
You recommend one?

[normal crystal]

just look and see which you like better
they have similar coverage

[charred heath]

That means look for the one with better pictures 👀
(Or that's what I'll do)

[molten gulch]

Young and Freedman's University Physics
Halliday, Resnick, and Walker's Fundamentals of Physic

Or just start by reading independent texts on the topic

Taylor's Classical Mechanics
Griffiths' Introduction to Electrodynamics
Shankar's Introduction to Quantum Mechanics

I have nothing really good for particles at this level

[molten gulch]

No, pick one

[normal crystal]

he's not ready for the upper level texts
TCC pls!

[molten gulch]

no go for the one that's more rigorous or has a style of writing you prefer, images can always be subtituted

[charred heath]

I see.
So: Conceptual physics as an intro
Then move to Young and Freedman's University physics OR Fundamentals of physics (based on writing style, and difficulty)
Good?

[fallow aspen]

You'd need to learn calculus in between

[normal crystal]

If you never had exposure to physics and don't know calc
Hewitt is a good book

[charred heath]

Yeah, I'm studying math too (on that in a min)

I'm preparing for a specific exam which requires me to study pre-university level Math, Chemistry, and Physics

I'm collecting resources rn

[normal crystal]

if it's for a specific exam, the answer is easier
use what they say to use

[fallow aspen]

If its a high school level physics the calculus-based physics text might be overkill depending on the exam

[charred heath]

See the syllabus above 🔝

[charred heath]

They just drop the past exams, give you the syllabus - and that's it. You gotta figure it out yourself

One sec

These are the topics for math

Would Aops suffice?

[fallow aspen]

that's just a normal high school syllabus

[proper trout]

I think its overkill imo tho im pre-uni

[fallow aspen]

so yes i think so

[molten gulch]

Oh- he said he'd done calculus and integration tho, or was that something he had to learn and then was gonna do phsics

[charred heath]

The later

[sullen gulch]

hellos

[charred heath]

Yes it is, that's what I meant by "pre uni"

[mellow rivet]

For casual conversation, head over to #discussion #serious-discussion or #chill

This channel has its own purpose, and it isnt for regular conversation.

[charred heath]

So, what are your recommendations?

Hellooo

[chrome mica]

Does anyone know any book that is about discovering mathematics, not just "consuming" it?

Like discovering number theory or something like that

[dapper root]

Oh there’s a combo book like this

It’s like Combinatorics through discovery

Let me find it

https://bogart.openmathbooks.org

[chrome mica]

Thank you!😊

[stone heart]

For jee class 11

[mortal iris]

Start by making yourself intuitively comfortable with the essentials of Calculus and Linear Algebra. At the Pre-Uni level, it's more than sufficient if you can follow 3B1B (LinAlg, Calc). Read from the Feynman Lectures in Physics. Solve problems from Irodov's Problems in General Physics. This is sufficient to bridge the gap between Pre-Uni and First Year Physics. You can add the three volumes of University Physics as a supplement for topics not explored as much in Feynman's Lectures such as Electrical Circuit Analysis.

[charred heath]

That's essentially useful, thank you.
These resources help me bridge the gap, as you say. Then I'll be able to learn from the resources provided here, in this order:

• Conceptual Physics
• University Physics (Freedman, Young)
• Fundamentals of Physics.
  Right? That's the plan I guess.

And for Calculus, I can use Stewart's.

[mortal iris]

Conceptual Physics is for a first introduction to physics. Assuming you've not even done Precalculus.

Also I'd recommend Halliday, Resnick and Krane's Physics over the Halliday, Resnick and Walker's Fundamentals of Physics. The latter is verbose and confusing at times.

The stuff I mentioned is a better to work with if you're learning independently. Allows you to gain better insight. Using the aforementioned texts to complement for your syllabus is better.