book-recommendations

[short fable]

Prestige is generally obnoxious and connected to each other

[mortal iris]

Show me the data.

[short fable]

The data being, all the top jobs having graduates from specific places

[odd cargo]

surely you could come to a satisfactory mathematical conclusion as to why the exam should be terminated, why is it still being championed?

[mortal iris]

IITs are not held in special regard for any jobs. I
Very few IITians actually have the skill to be desirable. Most of them are just excellent machines who can follow orders.

Private universities in India offer better placements and corporate ladders from what I've seen.

[mortal iris]

We are a country that champions drinking cow urine to cure cancer. Go figure.

Not too long ago I shared the national standard for math curricula here. Plenty of folks had a good laugh about it.

[sand urchin]

fermat's enigma by simon singh is perfect if you want that veritasium vibe

[mortal iris]

People here don't care for the education. They care for the tags regardless of the cost.

[short fable]

Oh are you well versed in the high level private unis in India? How do I gauge?

[mortal iris]

I am. I work with plenty of unis in my current position. And most of these unis in India are run by big time businessmen looking to funnel talent for themselves and their connections. Such places tend to bring better offers to the table and are more privy to being flexible in their curriculum to allow for students to secure more than their standard streams of jobs.

[short fable]

In any case in the India arm of my department, there is a huge concentration of IITians (a specific one no less). Considering that their skills are fine (i.e. not fantastic but not poor), being from IIT was indeed a factor

[mortal iris]

I'm not referring to the absolute number of jobs here. This is a relative comparison. Very few proper private unis in India as opposed to IITs.

[odd cargo]

thats still ridiculous man.

[short fable]

I'm guessing there's no easy way for me to figure it out apart from how big the alumni corner is in Wikipedia

[odd cargo]

if someone told me that the only way i could be accepted into a particular residency program is by enrolling on to a specific university id be pretty pissed

[short fable]

There are always going to be such snobbish places but overall there are relatively more meritocratic places

[mortal iris]

Weird considering all IITs are very different.

The older 5 have some clout

But the rest barely do

[short fable]

I'm going to assume there's some rivalry between B and D from what little I read

[mortal iris]

Bombay, Delhi, Kharagpur, Kanpur and Madras are the most well known ones.

All of them have some rivalry

But a vast majority of IITians are not from these places.

[odd cargo]

do they atleast offer scholarships for their graduates?

[mortal iris]

No. In fact some IITs saw a protest due to fee hikes recently.

[short fable]

Yes my company hired from the ones you mentioned (again, one in particular)

I'm happy to say at least the newer hires do not just come from IIT

[mortal iris]

Must be an idiotic company policy.

[short fable]

And indeed the private Us (with an alumni corner)

[short fable]

Think the company's new to hiring in India, and the prestige is still the easiest to work around

[mortal iris]

That tracks given the relative age of these private unis. They need to establish a track record first.

[short fable]

count of CEOs of S&P500 certainly works

Though it is sad in the sense we're just like any other money hungry company

[odd cargo]

IIT's strongest soldier right here.

[mortal iris]

One needs to standard the counts for the time period to make sense of that.

Not everyone is Sundar Pichai

And it's not like he's even doing what he studied in the IIT

He's just running the ship. Those qualities are hard to come by in IITs given the way the entrance works.

[mortal iris]

I honestly don't think IITs themselves are bad. They have room to improve but they solid. The issue is the process of getting there and the political mess that makes it so stupid.

[short fable]

My personal thought is that a uni should not matter, but of course it does.
There's a reason why Grothendieck can notice a difference between his time at Paris and elsewhere. But education's purpose is for people to learn but this nature of empowerment will always make it at odds with capitalists need to make education part of the conveyor belt for workers

[mortal iris]

Especially the old 5. Great institutions.

[mortal iris]

Well, during my time in Europe, it certainly did not seem like the uni matters. But I was in academia and had strong recs from a leader in the field I worked in. That matters more in our world imho. It just so happens that these pioneering folks tend to huddle in well-known places because they make fancy offers to them.

And honestly I found the vibe of some prestigious German unis to be far more depressing as opposed to where I studied and worked lmfao.

And mine was not the most well known institution for what I was working on for sure.

[short fable]

It does, but the more progressive the society, the less you can feel it, which is good.
There's always going to be Oxbridge, ENS Paris, HU Berlin, whereever

[odd cargo]

brother, you just told me that the university not only does not guarantee you a job, but also does not offer scholarships to their alumni, pretty fucking horrendous in my opinion.

[short fable]

That's sad. I would find them oppressive but not depressing

[mortal iris]

Afaik no universities anywhere generally guarantee jobs or alumni scholarships, but I may be wrong.

[short fable]

It's 2026, nowhere guarantees a job, but you're certainly ranked higher from a 'better' place

[odd cargo]

no a lot of russel group universities do guarantee a job with the condition that you graduate with a 2:1 or 1st

we're assuming your degree is that in STEM

different standards when you're a liberal arts student

[mortal iris]

Honestly, I've worked in a few prestigious unis in Bonn, Heidelberg and Munich (least depressing of the three) and none of them cared about these places. Same can be said about where I was enrolled as well. Ik Rhodes scholars in Oxford who only got it thanks to connections within the committee. HU Berlin is not even mentioned in the same vein as most MPIs in Germany. ENS is well known but so is ETH and EPFL but nobody really cares all that much if the person recommending you is solid and your work is solid.

[mortal iris]

Very interesting. This is news to me honestly.

[short fable]

Harvard to me is a prime example of prestige mattering though. I think it's 'okay' in terms of education/research quality but you just meet powerful people easily

[odd cargo]

i mean of course it'll take time for you to be employed fully after graduating if you havent been going to fairs when you're in university

but if you do go to these fairs and connect with folks

you're almost guarantee'd one, especially if you have a 1st class degree

in maths, physics or whatever from a prestigious university here in the uk

take cambridge or oxford for example

and if you do decide to do a post doc in that same university, you'll probably be offered a position within the university

[short fable]

Ah Oxbridge my favourite uni in terms of having to wear formal wear to exams

[odd cargo]

i feel like i shouldnt be saying "guarantee'd" cuz it almost always depends on the person

also, american universities have a fuckton of merit-based scholarships

[oblique hatch]

That’s only Oxford 😢

[short fable]

Oh damn Cambridge doesn't do it?

[oblique hatch]

Nope

[signal zenith]

This is crazy to me. I’ve met some of these kids and they’re definitely socially stunted yet despite literally destroying their lives for academics they haven’t struck me as all that much academically smarter than just someone who’s had a normal education

It’s pretty cooked

[desert oriole]

Were you at MPI in bonn?

[desert oriole]

could you elaborate?

[jade kernel]

is "excursion in mathematics" something something a good read?

[mortal iris]

Didn't work there but have been there.

[mortal iris]

Lack of social inclusion and very frenzied (due to exam load) students in general until they join a group to work with.

It gets better once you work with a group tho.

[desert oriole]

I am planning on doing my degree in Bonn

[mortal iris]

Math?

[desert oriole]

yes

module handbook looks interesting

[mortal iris]

Honestly the math programme there is worth it. Regardless of the city and general university vibe.

Good luck.

[desert oriole]

thank you

[desert oriole]

are the people nice?

I have heard that the atmosphere is eorse than at other unis

[mortal iris]

Mostly. But if you don't like them you'll find much nicer ppl in Köln one city over

Takes a short train ride

[desert oriole]

Only 20mins right?

[mortal iris]

Yep. So long as there are no delays

[desert oriole]

Do you perchance know whether one can take modules /seminars in köln and have them accredited

[mortal iris]

I have no idea. You'd have to ask the respective unis for that. I never worked in either math department.

[desert oriole]

Did you do physics in bonn?

[mortal iris]

I do know that they have a combined physics grad programme. And also economics iirc

[mortal iris]

I worked there for a bit, yes. Also in Köln.

[sand urchin]

yeah its actually a pretty solid classic for recreational math if that's what you're into

[olive grotto]

Any math textbook recs for pre-college algebra ?

[hushed spire]

what books do you guys reccomend in terms of category theory?

[mortal iris]

For the absolute beginner to the subject, Lawvere's Conceptual Mathematics.

[hushed spire]

i am going through cat theory for programmers, do you have any reccomendations for when i finish it so i can go deeper into the subject?

[mortal iris]

This book is more than good enough to go in depth without going into the algebraic topology-esque roots of the subject. But if you want that then you're gonna need a lot more before getting into categories.

[hushed spire]

i see

[mortal iris]

When I say roots, I mean historically. One really doesn't need alg top to talk about categories and understand how useful they are. CS is a perfectly fine playground to motivate categories.

Lawvere's book is one of those methodical deep dives that avoids the alg top stuff altogether while going across a bunch of basic undergraduate level math in the language of category theory and going deeper into those areas.

[hushed spire]

no the rest of the areas of math i want to tackle them for the love of the game

[mortal iris]

https://tenor.com/view/triple-h’s-entrance-triple-h-mr-mcmahon-spitting-water-grand-entrance-gif-3941416687926065570

[tiny gulch]

Category theory mentioned?

[hushed spire]

(anyways type theory and PL research departments of my university are corpses sooo....)

[mortal iris]

Type theory is cool stuff. Was learning it to study formal proof assistants a while back.

[sand urchin]

nice, were you using lean? heard it's getting super popular

[mortal iris]

Yep

[round verge]

Guys best algebra textbook?

[mighty tartan]

have you tried reading the earliest pin

[cunning elk]

pre-university role

no you don’t need a textbook for precollege math lmao

[gray sedge]

Dies anybody in know any good philosophy books or stuff by Aristotle like ex rhetoric by Aristotle

[warm ivy]

Hey all! Could I have a book recommendation for beginner discrete maths? It’s been a while since I’ve done any form of math so something that can get me in without making me feel like I have 0 clue what’s happening

[gray gazelle]

That doesn't stop them from studying with a textbook.

[winged ferry]

For precollege stuff just use khan academy or something

[normal crystal]

Epp or Rosen
or Math for CS free on MIT OCW
there are some other OER texts too

[warm ivy]

I’ll have a look into those

[normal crystal]

there are (multiple) lectures and assignments for the MIT MCS
but it's less beginner friendly

[warm ivy]

Are they all good for self study? I heard that math textbooks are better off in a classroom setting

[warm ivy]

Ah okay all good

I am in uni at the moment doing DM, but it’s quite hard for me as I don’t really have a maths background

So anything that could just kinda give me a step up, in my own time or if it’s just a case of making sure I’m doing everything the course gives me

[normal crystal]

what book does your course use

[warm ivy]

There’s no book it’s all lectures and online questions

Which of course makes it harder cause there’s no middle ground follow along but it is what it is

[normal crystal]

Rosen, Epp, MIT cover most of the same things
just take a look and compare to your course

[warm ivy]

Easy as, thanks for the suggestions 😁

[normal crystal]

why are you telling this to elrichardo
anyway, he always comments something like that

[gray gazelle]

OH

i replied the wrong one

[gray gazelle]

With your role assigned, I assume that you're still at HS, in a gap year, or smthn. Here are the textbooks I've encountered:
Lang's Basic Mathematics (covers all topics on high school maths)
Gelfland's Algebra

Oh yeah, you could check out Professor Leonard too!
https://www.youtube.com/watch?v=0EnklHkVKXI&list=PLC292123722B1B450

I read Wu's book when I was around 11-12, Understanding Numbers in Elementary School Mathematics, it was quite good and rigorous. I saw in his page that he did an Algebra one and you could look it out if you're into this approach. https://math.berkeley.edu/~wu/

However, if you're like those typical mathematicians who learned senior level maths as a child, here are some good abstract algebra textbooks:
Alluffi's Chapter 0
Artin's Algebra
Allenby's Rings, Fields and Groups

[gray gazelle]

thanks for the notice

[normal crystal]

he wants people asking for help to just stand outside and absorb the precollege math from the ether

[ember lark]

love professor leonard

[cunning elk]

I just find most precollege texts in wide circulation to be really poorly written lmao

[gray gazelle]

something that didn’t worked for you doesn’t mean it will not work for everyone 🤷‍♂️

face it or not those high school students still have maths textbooks in their curriculum

You won’t also get that much in depth foundation from Khan Academy and Professor Leonard alone (hell, even Prof Leonard recommends taking his lectures while having a textbook/reference book)

[cunning elk]

the textbook is usually there just to have boring ahh exercises the teacher can assign for homework

at least that’s how it was at my hs

[gray gazelle]

ig some schools have bad textbook choices

[wicked flicker]

does anyone know a good textbook for reviewing logarithmic equations and exponential equations

im just looking for practice problems

[urban helm]

,iam living

[hasty eagle]

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

Feb 19, 2026, 7:56 AM

[urban helm]

,selfroles

[hasty eagle]

Please select the desired selfroles! (Use ,iamnot to remove your current selfroles.)

1.   Helpers
2.   Not Very Ppl
3.   Talks
4.   Role that does nothing
5.   Archivist
6.   she/her
7.   they/them
8.   any pronouns
9.   ask pronouns
10.  she/he
11.  he/she
12.  she/they
13.  they/she
14.  he/they
15.  they/he```
Please type the numbers corresponding to your selection, separated by commas, or type `c` now to cancel. (E.g. `2, 3, 5, 7, 11`)

[urban helm]

,talks

[rich sun]

#bots

[urban helm]

,iam talk

[hasty eagle]

Gave you the Talks selfrole.

Selfrole selector timed out, your roles were not updated.

Feb 19, 2026, 7:58 AM

[mortal iris]

Stitz and Zeager's Precalculus is free and contains lots of exercises along these lines.

[wicked flicker]

sounds good

[mortal iris]

No clue

[wicked flicker]

thanks actually it has questions that im looking for

[mortal iris]

Probably a few months ago

[indigo blade]

im not sure if its the right place to ask but some textbooks are only available to buy as reflowable ebooks legally while being available as fixed layout in shadow libraries
how is it possible and is there a way to get the fixed layout version legally as a student?

[midnight gulch]

there's no way to convert between the two formats in general. whether you can find the fixed layout version legally depends on the specific book

if you have access to the epub file you might be able to convert it to another format and do it that way, though i'm not sure

but usually with the "legal" channels you don't have the file

[indigo blade]

the fixed layout available in shadow libraries is clearly not converted

[midnight gulch]

yes, it would usually be from another source besides the epub

[indigo blade]

i think you can still dedrm the file if you have bought it from vital source and other similar stores

[midnight gulch]

if you are willing to dedrm then why not use the shadow library

both are illegal

[indigo blade]

hmm...

[midnight gulch]

if you did get rid of the drm its possible you could convert it, but it would be an annoying process either way

like theres no built in way to do it, you would have to make it fixed in a weird way

i don't like epubs for that reason, they're just a terrible format

[leaden rapids]

Can anyone recommend a good textbooks on vector fields? I need to understand this topic in detail

[mortal iris]

Mathematical Analysis Vol. 2 Zorich.

[blazing holly]

Idk many books which are solely about vector fields
But there are plenty of books w/ sections on vector calculus and I know some books for those

Later chapters of Stewart’s, I believe there are some Dover books, and I think there are some physics texts which have dedicated vector calc sections

@leaden rapids

[leaden rapids]

Thanks Killuminati and KySquared

[vital bane]

You're welcome

[fluid chasm]

also any recommendations on cryptography?

[molten gulch]

We're using katz and lindell's introduction to modern cryptography in my class alongside boneh and shoup's course of graduate cryptography

first one you can find the second edition floating around, but obv I can't tell you how to find that, and for the second, it's available legally for free

[fluid chasm]

thanks:)

[rigid trail]

Hey I'm going through Katz and lindell as well in a grad crypto course!

Crypto is so peak

[molten gulch]

The notation is burning me alive, the material itself is fine but the notation HURTS ME

[rigid trail]

Mood

[molten gulch]

like my only problem here is remembering wtf PrivK LR-cpa A,Pi is

I really really dislike the notation, but otherwise the material is fine

[wicked fractal]

This is why I don't do cryptography

[wanton pollen]

got that forbidden munkres

[molten gulch]

lol

[hybrid sigil]

What's a good book to get me up to speed with LaTeX? I know the basics, but don't know how to do commutative diagrams, or numbering of formulas, and sometimes stumble on multiline formatting. The book has to be short and focused, but still systematic. I see that there is "Math into LaTeX" book by Graetzer, is it good?

[remote sparrow]

https://tobi.oetiker.ch/lshort/lshort.pdf

this was how i learned the basics of LaTeX

otherwise, i just used google as needed

https://q.uiver.app/

use this to make commutative diagrams

https://www.overleaf.com/learn

overleaf documentation is good

[hybrid sigil]

thanks! Yeah, I type everything on Overleaf now, don't even bother to install LaTeX locally

[umbral field]

you can get a long way just by reading the documentation of the packages you are using for a particular thing

e.g. if you want to do commutative diagrams, the best package for that is tikz-cd and you can get good enough to make basic ones just by looking at the examples in the introduction (provided you're already familiar with the matrix typesetting it's based on)

similarly you can go a long way in formula arrangement by reading the amsmath documentation, since that package provides most of the fancy alignment options

[signal zenith]

im ngl just google everything and use it a ton and you'll be good enough

you dont need to go out of ur way to read books on it

[humble sierra]

[warm plover]

best book for self studying precalculus in 3-6 months (i’ve been looking at axlers)

[full pike]

chud?

[normal crystal]

mathcordian

[trail hemlock]

good one unc

[normal crystal]

I appreciate all the positive feedback
especially since I know you look up to me

[trail hemlock]

saying allat at an astounding 4 foot 3

[mortal ore]

fetch me a blunt pledge

[desert oriole]

chud

[normal crystal]

I never knew you were that short
new factoid

[compact bough]

any book recs for geometric algebra?

(as opposed to algebraic geometry)

[rich sun]

I call upon you @fickle whale

[compact bough]

oh my god that banner

[next fox]

Can't they drop it here as a learning resource

[midnight gulch]

maybe these? #book-recommendations message

[compact bough]

ooo i'll look into those

i've heard of macdonald's books and briefly skimmed free chapters but never fully read them

[cerulean thicket]

@trail hemlock are you @worthy kindle by chance?

[fickle whale]

I still stand by those for the time being

[fickle whale]

the sauce for my banner? absolutely

However it's perhaps not the best place to learn GA, but a good resource once you're acquainted.

My banner is FIGURE 3 in Section 5.1, https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.9754

[fickle whale]

I see you got linked one of my other posts on the topic, I pretty much stand behind that list, though my list of "next place to go" is often under revision

[compact bough]

alright!

[fickle whale]

let me know if you have any questions, or want more esoteric resources @compact bough

[compact bough]

will do, tysm!

[remote sparrow]

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

[minor falcon]

What is the difference between Stewart's "Early Transcedentals" and "Concepts & Contexts"? Which book should I use if I'm getting started at Calculus?

[cerulean thicket]

@minor falcon
Welcome to Mathcord new nerd! :)

[daring wolf]

Serre's Linear Representations of Finite Groups is a good book

idk if these will cover what will be done in your courses but I mean the book is good

[vague heart]

Currently trying to chip away at Susanna S. Epp's Discrete Mathematics with Applications. Good book.

Does anybody recommend a book for proof writing and another for pre-calculus (more algebra and trigonometry)?

[short fable]

Pre calc IDK (just learn calc) but there's Hammack's Book of Proof

[crimson pasture]

what is a good reference text for linear algebra?

[main lodge]

this is off topic but dragonforce is a really good band

[short fable]

I'd like to know the answer to this too.
But for matrices there's a few standard ones

[earnest quartz]

idk but I'd like this too

[crimson pasture]

I wanna know about matrices

[tender river]

steve roman

[supple chasm]

Hi guys. Any good resources for studying Z transform?

[short fable]

https://www.cambridge.org/highereducation/books/matrix-analysis/FDA3627DC2B9F5C3DF2FD8C3CC136B48
Or similar
See also this comment https://math.stackexchange.com/questions/2006938/matrix-analysis-textbook-recommendation#comment4121041_2006938

[dim delta]

My real analysis class is extremely computational. It's not a tremendous amount of theorems and proofs. Rather, it's a lot of "prove that this sequence converges." The book that we use doesn't really focus on what's on the test, or the homework he assigns (he does not assign problems from the book). Can anyone recommend any good analysis books that focus more on the...computational...side of things? I'm basically looking for the opposite of Rudin.

Also, is there a channel that I can go to and vent about this shitty ass class?

[mortal iris]

Most Calculus books would cover things like that. Zorich has a solid mix of both calculation and proofs in case you wanna try that out.

[mortal iris]

I should add that Zorich is a pretty rigorous text despite it.

Spivak. Calculus. Thank me later.

You think that and that is exactly why you should go through Spivak

Also, Linear Algebra by Friedberg, Insel and Spence.

[dim delta]

This still requires epsilon N type proofs. It’s just that they are extremely…specific. Maybe spivak or Apostol.

[bold prairie]

I use Calculus by OpenStax. Are there reasons not to use it? I just want to make sure it's good enough and I didn't "choose wrong" so to speak.

[warm plover]

i wanna self study calc bc BUT to do that i need to self study precalc. I plan on doing selected units of AoPS Intermediate Algebra and the whole AoPS Precalc, not to just fully prepare, but to also rpep for stuff like AMC/AIME. Is this a good plan?

[molten gulch]

no it is fine

[normal crystal]

it's A LOT of pages
even for typical calc books
the Strang Calc book it's built on is also free (older edition) on MIT OCW, and like a third the size
but that's all irrelevant if you like the openstax enough and are fine working through it

[remote sparrow]

wdym by that

u did functional analysis right

or am i thinking of someone else

[crimson pasture]

I responded to someones message

I wanna know about matrices

reference text

[shut geode]

i like serre

denis serre

[bold prairie]

Interesting. The only thing I saw that was against using that book was the fact that it's not advanced enough. But I guess "a lot of pages" doesn't necessarily imply advanced.

[normal crystal]

I think it covers all the standard material for Calc BC/typical college frosh calc
it wouldn't be chosen for an honors calc or more in depth course
there are other free calc texts like APEX or Active Calc
or the popular paid books are Stewart or Thomas
if you're fine with Openstax, then it's fine

[remote sparrow]

https://www.amazon.com/Matrix-Analysis-Second-Roger-Horn/dp/0521548233

https://www.amazon.com/Second-Algebra-Cambridge-Mathematical-Textbooks/dp/1107103819

[midnight gulch]

basically linear algebra with a focus on matrices (rather than vector spaces in general) as well as the numerical/applied side of things

for undergrad textbooks though they are very similar

[rose notch]

you can read lang's basic mathematics and jump straight into apostol's calculus

thats what I did

[normal crystal]

are we finally getting that mobile game about chipping potatoes that the kidz have been clamoring for

[molten gulch]

this is for game engine dev but Gregory - Game Engine Architecture

[normal crystal]

new edition out now ish

for a class?
most of the intro books are based around a particular engine/lib

[molten gulch]

:o

where

ah

[normal crystal]

yea, split two volumes
as if book prices aren't already skyrocketing

[lilac hull]

What's the best reference for category theory if am a beginner?

[floral lantern]

Riehl and Leistner are standard references.

[lilac hull]

I see thx

[remote sparrow]

awodey is good too

[lilac hull]

Yeah that's what someone suggested too

[normal crystal]

CPE?
maybe look for a partner group and use what they use

ohhhhhhhh
computer engineering
the google results had me worried

no, I get ya now😂
is this a required hackathon?
or shits and giggles
if it's rn, I would just look for some easy tutorials after choosing what tech you want
or finding an intro book for unity or godot

[hybrid sigil]

I can share my list of resources related to gamedev

But it’s not books, mostly blogs, talks, YouTube videos, game dev communities

There are some books too, in particular this Game Engine Architecture that has been already recommended.

[junior isle]

I need to learn the basics of point set topology over the summer in preparation for an algebraic topology course in the fall. What books do you recommend? I know munkres is the standard but everyone I know hates that book so I'd like some alternatives

[hybrid sigil]

But I’d suggest just jumping in and figure it on demand while implementing a clone of some game that you find fun. Then publish it on itch.io, get some people play it

Then repeat for a more complex game, rinse and repeat

I can share some of my games too) and blog posts about them and the process :)

Giving up is also an option! No pressure then, just chill!

🧘‍♂️

[normal crystal]

oops

[hybrid sigil]

Viro et al. Maybe Lee “Intro to Topo Manifolds”. Maybe Armstrong. Then there is a nice book “Essential Topology”

That’s what I have and like

[junior isle]

I like Lee but I feel like it lacks point set topology theory since its not a point set topology.

I haven't heard of the other ones

I'll look into them

[hybrid sigil]

Why? It has like 100 pages about that

[tame tree]

munkres is a perfectly fine book

[tame tree]

you can check out IM james topological spaces and uniform spaces too for an alternative reference

or sutherland's introduction to metric and topological spaces

or willard

[hybrid sigil]

Yeah, was about to suggest this too

Sutherland

[tame tree]

pretty solid

[junior isle]

oh I was looking at an older edition

that does look like everything I need

[midnight gulch]

as @hybrid sigil mentioned, crossley's essential topology is good. the first half is point set and then it goes into algebraic topology, which could be helpful for you

[compact bough]

are there any good resources on vector valued differential forms or tensor valued differential forms?

[midnight gulch]

it doesnt go nearly as deep into general topology as munkres or similar books, but it gives you basically all of it you need for algebraic topology

[vital bane]

Woahhh this is a thing!?!? Sick!

[compact bough]

it is!

[vital bane]

https://en.wikipedia.org/wiki/Vector-valued_differential_form

Damnnn

Very cool

[compact bough]

indeed
i just wish it weren't so hard for me to find good resources on it

[molten gulch]

I recall seeing a bit of this in kobayahi nomizu, unsure how deep the coverage is

[compact bough]

the most i know about VVDFs is that $\omega(X\otimes\eta) = \omega(X)\eta$

[hasty eagle]

⋆ ˚｡⋆୨୧˚ ¡∫ĮŁVẼŘ!｡･:*✧

[compact bough]

hmm
i'll check it out

[cerulean thicket]

@compact bough
Welcome to Mathcord, new nerd

[cerulean thicket]

And hey Ryan

[compact bough]

thank you
nerd

[velvet flax]

i like john kelley's book

maybe engelking if you are the type of person who likes books like lang's algebra

[tender river]

hatchers notes

[plush marten]

guys I need book recommendations

i want to learn how the history of mathematics and how they proved the basic formulas

like e.g. complex numbers, how they got to the idea, how they used the unit circle and proved the basic rules
also are there free ones online if not ill go to libraries and ask for

[mortal iris]

This should be a good start.

[velvet flax]

is nagata's "local rings" any good

or are there similar more modern sources

[plush marten]

ty!

[remote sparrow]

https://www.rxddit.com/r/math/comments/1ra4kqw/whats_your_favorite_math_book/

[lament scaffold]

Axler's Linear Algebra done right or Intro to linear algebra by Gilbert strang which is more easy read and good for applied sciences

[midnight gulch]

latter

[rigid trail]

Latter

[errant bane]

Can someone please suggest a book to read about finitely generated groups in detail

[gray gazelle]

baby rudin and will always be

[remote sparrow]

recommend me anime/manga (or related non-japanese manga-inspired comics, e.g. manhwa or manhua)/light novels where cooking plays a prominent role in the story. things i've already consumed are food wars!, delicious in dungeon, peaceful camping life in another world, and the top dungeon farmer.

[balmy root]

Bambino!
https://en.wikipedia.org/wiki/Bambino!

Drifting Dragons might be good. https://en.wikipedia.org/wiki/Drifting_Dragons

[frozen perch]

Yakitate!! Japan is about baking bread

Has a lot of sendups of other media by the end, it’s pretty fun

[mortal iris]

Toriko if you wanna read something long

Also even if you don't read One Piece, the Baratie arc sets up one of the main characters and is quite philosophical about what makes a chef. It's very much readable as a stand-alone arc so long as you know the character motivations of the Straw Hat crew coming into the restaurant.

It also sets up the climactic arc of the East Blue saga in One Piece and many ppl get really into the series around this point or just a few chapters later. Tho, the earlier chapters are just as golden, this arc creates a genuine sense of purpose.

[errant bane]

I am studying about the actions of such groups on compact metric spaces. I want a text to deepen my understanding of finitely generated groups and provide me with some good examples

[urban sequoia]

Is cengage good?

[trail void]

regarding what

too vague

[urban sequoia]

For trigonometry and calculus

[tough talon]

Well the problems are fine

But theory is shit

For trigonometry u can refer complete trigonometry by webster wells or sl loney

And for calculus u can refer to thomas calculus

[trail void]

honestly conceptually no

it is designed for a course rather than like letting u enjoy it

im not sure which book exactly ur referring to so this is personal opinion

[sacred thicket]

cooking plays a role in dorohedoro from time to time

[normal crystal]

Oishinbo

[burnt scaffold]

does any1 have advice on where to find easy access to algebra problems in the first grade of high school ie factoring,matrices,absolute values,systems, discussions etc.. We just finished that part of algebra and while i do understand the concepts and can do simple problems i can't do more complicated problems and i'll need it in the future

moreso my problem isn't understnading its recognizing/practice

what books specifically what websites

i don't need explenations i just need a problem and an answer

[cunning stirrup]

Holomorphic functional analysis recommendations?

[bold prairie]

I will have linear algebra sometime in the next semester. Any book recommendations so I can take a look and learn a little in advance?

[cunning stirrup]

You should be good with linear algebra done wrong

[grim delta]

Hi, any good book about general topology? thanks in advance 🙂

[burnt scaffold]

any advice for me?

[cunning stirrup]

Just google a random textbook

[burnt scaffold]

what exctly

[cunning stirrup]

Its Hs math

Exact book isn't important

[molten gulch]

friedberg insel and spence

[burnt scaffold]

yeah but i can't find it

you're a "likely spammer"

@molten gulch

[cunning stirrup]

You can't find a general education math textbook...?

[burnt scaffold]

nope i suck at googling

[molten gulch]

yes I know

[cunning stirrup]

Go to your local library

They will have several options

You can take it home

[burnt scaffold]

tommorow is sunday lol and im motivated as fuck right now for some reason

so if anyoneh as reccomendatons i can download and do right now will helo

help*

i know this is like expecting stuff to be served on a silver platter but whatever i hope it works at least once

[cunning stirrup]

Are you american?

[molten gulch]

No, you will not be given material on a silver platter, please learn to search things for yourself

[burnt scaffold]

no

[cunning stirrup]

Which state?

[burnt scaffold]

why did you assume that

[cunning stirrup]

Whi h countdy then

[molten gulch]

but if you so badly want a book

here

[burnt scaffold]

bosnia and herzegovina

thats a gotcha lol

most people havent even heard of it

[molten gulch]

https://www.stitz-zeager.com/szprecalculus07042013.pdf

[molten gulch]

Many people have heard of it

[burnt scaffold]

ty4

[burnt scaffold]

most!=many

i wanted to bring up an american as an example but thats a bad idea

ask a french person or brit

or like a norwegian

russian

chinese

[cunning stirrup]

Of Bosnia?

[burnt scaffold]

well idk what the gaokao has on european geography

[cunning stirrup]

That's a default country

[burnt scaffold]

in my experience no

more people have heard of like Nauru for being fat than my country

[molten gulch]

I have no idea who nauru is

But I guess maybe I know more about the region due to having a passing interest in the history and evolution of slavic languages and related linguistics stuff

[cunning stirrup]

Can we stop the spam here?

[molten gulch]

(and having family there)

[burnt scaffold]

how is this spam

[burnt scaffold]

it's an oceanian country with funny city names and is the most obese country on earth

by average bodyfat%

[cunning stirrup]

Anyway yeah, general recommendations for holomorphic functional calculus would be appreciated

[burnt scaffold]

oh yeah it also doesen't have a capital

[grim delta]

Hi, any good book about general topology? thanks in advance 🙂

[molten gulch]

munkres

[grim delta]

thanks

[lost arch]

is there maybe a standard/widely recognized text on optimization?

[remote sparrow]

what kind of optimization

[molten gulch]

what type of optimization

[normal crystal]

the optimal kind

[dim delta]

Also Mendelson is good for beginners.

[normal crystal]

there is this
https://web.stanford.edu/~boyd/cvxbook/

[lost arch]

like introductory textbook. i dont know what specifically the curriculum will be for the optimization course in the uni, but considering its all put in the framework of financial technologies (fintech, hft, neobanking, hedge funds etc) id say something centered around methods used in finance

[slim maple]

What’s a great book that everybody should read, not one that has like 1000 pages or have incomprehensible words that you need a PHD to understand

[compact bough]

i'd argue shifrin's multivariable mathematics would be a good candidate, but i'm biased

[lost arch]

probably an alphabet but im biased

[slim maple]

Il try this out

[somber echo]

Anybody interested in bcov

[normal crystal]

sorry champ
I fell off on the Bovine Coronavirus news

[heavy idol]

how’s “counterexamples in topology” as lighter reading on the side while learning pointset?

[unique garden]

Between "Discrete Mathematics With Applications" by Susanna Epp, "How to Prove It" by Velleman and "Book of Proof" by Richard Hammack, which is the best for someone just getting into proving things on their own

[heavy idol]

ive read “how to prove it”

[unique garden]

is it good as an intro?

[heavy idol]

i liked it

i havent read the others tho

it has a good elementary explanations with truth tables n stuff

[unique garden]

alright

[vital chasm]

Its less of a light read and more of a reference

[heavy idol]

ah

will it provide context for theorems provided in a topology textbook

[river rock]

I'm trying to re learn calc 1 to fix my foundation on calculus and to proceed further as a quant also as a math major student. would you recommend me to read Michael Spivak Calculus or Apostol Calculus? i prefer rigours explanation

[shut geode]

its more just a compilation of counterexamples to some of the more common misconceptions people encounter. it aids in building your intuition about topology

[heavy idol]

ah alr

[molten gulch]

how to prove it and book of proof are fine, epp's discrete maths contains a smattering of topics (graph theory, elementary number theory, combi, discrete probability, and automata, (very basic) FOL and set theory)

[unique garden]

Is epps the “best” in your opinion?

[floral lantern]

I’ll be honest, the stuff in the book is really very technical

[heavy idol]

ok

[molten gulch]

I found it meh, had to use it for a class, and the big problem I have with it is that each covered topic could get 1 or more books on it

[floral lantern]

But it’s excellent to own!

Really a wonderfully in depth book

[heavy idol]

fair

[floral lantern]

With so many great examples

[unique garden]

So I should stick with one of the first two

[floral lantern]

A lot of them are super hard though 💀

[unique garden]

Ima go with the free one :3

[heavy idol]

i kind of want something that’s not just “introduction to this topic” beginning to end

so you can flip through and find interesting stuff

[molten gulch]

hammack is a good choice, for discrete maths there's also https://discrete.openmathbooks.org/dmoi4.html

[unique garden]

I’m just trying to learn how to prove things because I’ve like nearly done a thing in cgt, but need to formalize it 😭

[heavy idol]

i like how to prove it since it covers a range of topics (mainly focused on set theory)

so the constructions it uses are very often used in other contexts

so you also get a lot of practice working with things like posets and closures of relations

[cinder turtle]

best book covering all of amc and ioqm

[normal crystal]

If your only goal is to learn proofs, one of the latter
Book of Proof has more supplementary material

[short fable]

Boyd is intro.
If you want to join quant be prepared to read more than intro.

[lost arch]

thanks

[lilac needle]

guys has any1 solved math circles?

there are some questions in the induction part where i cant figure out how to do

[willow pecan]

#❓how-to-get-help

[wind carbon]

guys any website or resource where i can learn calculation tricks to speed up my calculations?

[cunning elk]

https://www.cut-the-knot.org/arithmetic/rapid/index.shtml

cut the knot also has a ton of other cool stuff to read about

[wind carbon]

alr thanks bro

[cunning elk]

np

[urban sequoia]

Advanced trigonometry and calculus. Does it have like minimal theory? We have volumes but they don’t mhave much concept

[river rock]

have anyone ever read "linear Algebra Done Right" by Axler? if yes, would you recommend me that book or you have a better recommendation?

[mortal iris]

Very nice book. Very anti-determinants tho lol. I also like Friedberg, Insel and Spence or alternatively Shilov. But Axler's approach feels a lot more structured as opposed to these two. It really depends on why you're learning Linear Algebra. If you wanna do math, Axler is good. If you wanna do physics, Shilov or FIS are better. If you wanna do something else like data science or computer science, something that focuses more on computations, matrix decomposition, etc. like Johnston's books would be better.

[rigid trail]

Personally I really don't like his anti-deterninants approach but to each their own

[river rock]

Ohh, say that im going for quant.. then i could go for johnston right? or still better to go for axler? I'm pretty sure i've seen one from stang too, "Linear Algebra learning with data"

[rigid trail]

Determinants make a lot of results both much more slick and more intuitive

[mortal iris]

Johnston is better if you want a slightly broader view of things. But if you intend to focus on data science then Strang's Linear Algebra and Learning from Data is a great choice as well. Axler is no good for ppl who don't wanna focus on rigorous math.

[river rock]

hmmm, im still wondering if quant needs to focus on rigorous math or basically just need linear algebra to be good at some part

because mainly they use stats and probability

with a little bit of calculus, same case for ML iirc

[somber echo]

Anti determinant is stupid and makes the task a lot harder in my opinion

Axler is a good read tho, i guess it would be wise to complement with some other books that treats determinants nicely

[river rock]

Then, would FIS be better then for rigorous math?

[lost arch]

same

both are good

[river rock]

ahh, alright then ill get fis instead

[mortal iris]

You don't need rigorous math for quant. You need to be able to model mathematical results well and draw interpretations from said models. While the underlying language is precise, you don't really need to write proofs and be held to the same standards a mathematician is held to. Unless of course your interest is in the mathematical side of data science as opposed to being a quant.

[river rock]

well you are right, but im going for quant research which basically need rigorous math, aswell as a math major..

[mortal iris]

Okay. If you're entering the academic arena then a rigorous text is definitely better. That said, I'd still recommend Johnston (it is fairly rigorous) as it's more aligned to quant (lot more on matrix decompositions and tensors) than an FIS. I'd add Strang's book to supplement.

[sand chasm]

Does anyone know any good books on combinatorics? Preferably not super outdated, something relatively advanced, grad level.

[molten gulch]

Bona's walk through combinatorics for intro, Stanley's enumerative combi 1 and 2 as well seem nice and modern (they got a new edition a few years ago)

[river rock]

ill keep that in mind

[river rock]

i use Blitzstein

[molten gulch]

Blitzstein is a probability text, not a combinatorics text

[river rock]

eh, its diff?

i thought its the same

well mb

[mortal iris]

Nope. Combinatorial probability is but a tiny part of what probability is all about.

[river rock]

ahh i see, i mistook it as probability.. well now i know, thanks

[lapis ledge]

Hi

You guys have books

For math of course Tojo

[half void]

?

[lapis ledge]

Is your name Tojo?

[atomic crystal]

join our apostol server if you are serious

[cunning stirrup]

Not really a book recommendation, but I'm interested in a reference for the proof of the prime number theorem using complex analysis and the Chebyshev function. For some reason I can't find one that's available for free / that I have access using my university

[lapis ledge]

Hi guys I want a book

[atomic crystal]

@river rock we have a study group

https://sheafification.com/the-fast-track/

[lapis ledge]

I SAID I WANT A BOOK SO YOU BETTER GIVE ME ONE OK

[atomic crystal]

you will want to look at this

[cunning stirrup]

please stop

[lapis ledge]

Why

Sorry

[cunning stirrup]

You're acting entitled

And it's annoying

[lapis ledge]

I’m bipolar

[cunning stirrup]

Okay? Sorry to hear that

[lapis ledge]

That’s literally me

[mortal iris]

Go get it then

[lapis ledge]

Oh I have one

[half void]

My name is not Tojo

[lapis ledge]

It was just a typo and I tried to go over it

[mortal iris]

Landau and Lifschitz is a bit dated on a few fronts tbf. Might consider updating the physics list.

[lapis ledge]

I know no one called Tojo

[half void]

Depends which one. Some of them are still very useful.

[atomic crystal]

in what way

[atomic crystal]

our apostol server is separate from this btw, im just posting the fast track here

@mortal iris i think really its only outdated wrt kolmogorov theory of turbulence

and even then there really is no better synthesis of physics than landau

[mortal iris]

Quantum theory and classical field theory is notationally dated. The latter barely touches anything related to topology or differential forms which is the modern way to approach the subject and the treatment of GR is abysmally inadequate imho. Also, the series is just generally very hard to read because of outdated conventions and limitations in print back in the day.

[mortal iris]

There in fact is. Florian Scheck has a relatively more modern series for the barebones of it all. And it's a little more sympathetic to mathematical rigor as well.

It is missing treatments of fluids and elasticity though but that doesn't seem to concern your list all that much.

Also, David Tong's lecture notes are a great place to start as well. He's got pretty much everything.

[mortal iris]

I agree

But perhaps better as a reference as there are better places to teach yourself from than L&L. Legendary texts nonetheless.

[atomic crystal]

the fast track list is essentially a speedrun to qft

https://theportal.wiki/wiki/Read

check this list out

the portal is a deeper look into the different branches

both the fast track and the portal lists are made by the same guy, the progression of texts on the portal would be more toward your liking

[atomic crystal]

good stat mech resource

[molten gulch]

I personally don't agree with the idea of speedrunning to QFT or rather speedrunning to any field of maths in general

It very quickly can lead to burnout, issues, and even wanting to quit mathematics in general

[atomic crystal]

thats fine, filter gonna filter

[odd cargo]

https://tenor.com/view/mao-gif-25413392

[half void]

Yeah, these lists have good books, but ultimately i wonder what portion of people who pick up one of these « tracks » finish it—that is, if they even finish the first book.

[molten gulch]

Agreed

[mortal iris]

Yep. It's often better to take time to be thorough with your fundamentals. Mathematical QFT needs quite a daunting bit of exposure to work through and riddled with open problems at every turn.

[mortal iris]

I have a lot to say about this but I'm too tired so I'll pick this back up tomorrow lol

[wicked fractal]

cs major ahh mindset

[cunning elk]

me when basic discrete math is supposed to be a cs major weeder at my school

[cerulean thicket]

Hello nerds

[cerulean thicket]

Victini pfp :o

[normal crystal]

elrichardo in the lecture hall getting up to scream
"you don't need a textbook for discrete math
you don't need these lectures!"
on his way outside to absorb more ether

[cunning elk]

it was all revealed to me in a dream

[cyan edge]

Can someone tell me where possibly i can find gn berman mathematical analysis book solutions

[cyan edge]

asking multiple times is not as good as i think, it is better to have a solution manual

[rocky geyser]

I’m planning to work on both calculus and linear algebra a ton over the next couple years. I’m hoping to come out with a fairly comprehensive understanding of both fields to the level of working in biomechanics (around diffeq+ linear at a college level). Does anyone specific recommendations on recourses for this?

[cyan edge]

Ok

Do you think GN Berman mathematical analysis book is a popular one.

[lapis ledge]

does anyone have the envision algebra I book

[cyan edge]

I am learning from Thomas book. Will I able to solve after learning from thomas

So what book do you recommend for university lvl calculus book.

Stewart ?

So just from lectures

[wicked fractal]

cs majors would bitch and moan about taking discrete math

[cyan edge]

So what problem books do you recommend for solving.

Ok

Thanks

[wicked fractal]

Tbh somewhat I don't blame them. The CS major version of discrete math is low quality

It's taught in a horrible way

[midnight gulch]

i took the cs version of discrete math and it was fine

like basic set theory, propositional logic, graph theory, stuff like that

[wicked fractal]

The concepts are what you'd except but the proofs are a different breed

Almost as if the prof is acting performative with the proofs

[midnight gulch]

wdym

[wicked fractal]

3 pages of proof just to prove that union is distributive

I'm going to take it next semester and I will buy the book too for future meme reference

[midnight gulch]

wtf is this

[wicked fractal]

guts

[lapis ledge]

no one responded 🙁

[midnight gulch]

yeah nobody has that

[lapis ledge]

Everyone in my class has it

[rich forum]

🥀

[midnight gulch]

is ts real

i thought berserk was good

[rich forum]

it is

[leaden hearth]

wtf

[oblique hatch]

What’s a good source on BN-pairs?
I’m reading Trees by Serre, and it assumes some knowledge now (chapter 2, section 1.7), but I don’t really have any

[cunning elk]

quantifiers moment

i remember the course as a whole was taught poorly ye

one time they decided it would be a good idea to prove the irrationality of \sqrt{2} by

INDUCTION???

[dapper root]

How the hell could you do that? Induct on the denominator and show it can’t have n as a denominator?

[signal zenith]

This is actually a modern approach to irrationality proofs iirc

Idk any of the details and idt it’s exactly induction

But it’s some argument that rules out larger and larger denominators

[wicked fractal]

There is a proof I forgot how it went but you use Łoś's theorem

[cunning elk]

surely there are better classical examples to introduce induction LMAO

like \sum^n_{i=1} i

[atomic crystal]

thx fo rec!

[atomic crystal]

cs majors do zero cs

[hallow oriole]

mathematical 'coffee table' books. like not popmath but books that a math undergrad could pick up and read. ex. mathematical constants 1/2 by finch, the integral books by valean, proofs from the book, the symmetries of things, excursions in nt, alg, and anal, mathematics made difficult(~), a short book on long sums, the cauchy-schwarz master class, fractal geometry of nature, etc

in particular, i specifically want mathematical books that deal with proofs. explicitly not popmath. pretty pictures and clean arguments preferred

#book-recommendations message link to previous time i asked q

[remote sparrow]

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

A coffee table book, also known as a cocktail table book[citation needed], is an oversized, usually hard-covered book whose purpose is for display on a table intended for use in an area in which one entertains guests and which can serve to inspire conversation or pass the time. Subject matter is predominantly non-fiction and pictorial (a photo-book). Pages consist mainly of photographs and illustrations, accompanied by captions and small blocks of text, as opposed to long prose. Since they are aimed at anyone who might pick up the book for a light read, the analysis inside is often more basic and with less jargon than other books on the subject.

aren't the books you mentioned not really casual reads?

[hallow oriole]

yes but its for a math department coffee table

i would describe them as casual reads tbh

[remote sparrow]

the knot book by colin adams

the foundations of computability theory by robic also has a lot of informal exposition

dale rolfsen's knots and links has a lot of interesting pictures that can be discussed even if the meat of the book is pretty sophisticated

visual group theory by carter could be interesting

https://www.ohmsha.co.jp/book/9784274066177/

https://www.ohmsha.co.jp/book/9784274067860/

if these undergrads could read japanese, they could check out these guides to fourier analysis and diffyqs

@hallow oriole

https://bookstore.ams.org/car-30/

[compact ore]

if someone had counterexamples in topology on their coffee table i would indeed be entertained by it for however long it took for them to complete their business

but i don't think it's what you want

[urban heron]

https://fixupx.com/Jonathan_Blow/status/2025342887253475565?s=20

Jonathan Blow (@Jonathan_Blow)

Reason: Everything up to page 50 is basic linear algebra, but with no attempt to communicate intuition or visualize anything. The idea of implementing everything as you go in code is interesting, but Scheme is an awful language for this, and they also never run the code, inspect it or reason about it. It is just there, and adds nothing to the conversation; almost any reader will skip the code.
︀︀
︀︀I just don’t see the point of

**💬 19 ❤️ 213 👁️ 26.2K **

FixupX · Feb 21, 2026, 10:52 PM

[remote sparrow]

livingston and murasugi are other knot theory references to consider

https://bookstore.ams.org/browse?simplesearch=dol

[normal crystal]

maybe mathematicians rather just have coffee on their coffee table

[remote sparrow]

dolciani mathematical expositions is a series you could look at

[hallow oriole]

oh this is a good idea

[hallow oriole]

this is one i thought of it's what i want yes

[hallow oriole]

oh ill look into these, these are neat

[normal crystal]

I think it might be Structure and Interpretation of Classical Mechanics
but since twitter is a disaster to look at, idk

[molten gulch]

I misread it, excuse me

[remote sparrow]

needham's books probably fit the bill

[molten gulch]

My brain is very good at bad autocomplete

[normal crystal]

np

[molten gulch]

It is not SICM either

[remote sparrow]

https://fixupx.com/jonathan_blow/status/2025341939344982118?s=46

Jonathan Blow (@Jonathan_Blow)

I am giving up on this book after 50 of 200 pages. What should I read instead?

**💬 54 🔁 26 ❤️ 849 👁️ 76.7K **

FixupX · Feb 21, 2026, 10:48 PM

use nitter or sotwe

if u don't wanna deal with twitter

[normal crystal]

oh yeah, they have that too
I really do hate that people still use Twitter and it's such an abomination to check
like thanks for putting rando tweets from 2023 and before at the top for no reason

[sly zodiac]

Hey guys I have a question I'm someone who knows Nothin in maths and i want to get started in probability and statistics as well as calculus are there any books I can read?

[mint pebble]

hm whats your main understanding

[sly zodiac]

See I'm preparing for a college entrance exam which is in like 10 months and for that I need to have a solid understanding in statistics and probability, linear algebra and calculus and I'm also a CS major trying to get into Machine Learning so if I had a solid understanding on these and a good foundation it would be helpful

[mortal iris]

One typically starts by learning how to add, multiply, etc. if they know nothing.

[mint pebble]

okay, do you struggle with proofs or understadning the concepts

[sly zodiac]

I mean- true i know those stuff when I said nothing I meant in those topics

[sly zodiac]

Both really

[mint pebble]

hm, okay I will send you a list in couple hours I have to check my libaray

[sly zodiac]

Currently I'm watching Stats 110 playlist by harvard but I also wanna use the time i have in college so looking for a textbook since I can't use my laptop or phone in class

[sly zodiac]

Yessss ofc take your time i don't mind and thank you

[remote sparrow]

those lectures have a book associated with them

https://stat110.net

[mint pebble]

that is true

[sly zodiac]

How do- oh thank youu

[river rock]

Which better for better concept understanding and proofs, Spivak Calculus, Stewart Calculus, or Apostol Calculus?

for rigorous math

[lilac hull]

Rudin's Real and Complex Analysis

[river rock]

is this calc?

[tender river]

No

[river rock]

oh its for analysis, not yet going for that tho

[tender river]

ull probably learn more about proof writing from spivak and apostol than from stewart

[river rock]

hmm, well that exactly answered my question. i haven't try apostol, maybe later once i finished learning calc from spivak

[remote sparrow]

either spivak or apostol

[river rock]

i found it spivak quite confusing but make sense at the same time

[remote sparrow]

there's an answer book

there are also some answers in the back

[river rock]

oh? i didnt know that, that super helpful

[sacred thicket]

i think there are translated versions

my teacher has similar book about thermodynamics in russian

[mortal iris]

Spivak has a good balance of both proofs and calculations but heavier on the proofs. Though, conceptually you're better off picking a Real Analysis book like Cummings' or if you wanna do a little extra then Zorich. Spivak's exposition borders on intuitive and rigorous but it's organisation can be off putting at times. All great books nonetheless. If you're already doing Spivak then best to stick to it. The problems are fantastic and most of the learning will come by working on those.

[remote sparrow]

yeah there are translations

currently there aren't english translations for the books i mentioned

[river rock]

hmm , im still writing "graph of function" section from spivak book, i still can go with real analysis i guess? now if i go with zorich, based on your opinion, where should i start taking notes? since spivak only teach about function and graph, them jump straight to limit rigorous definition, where epsilon-delta definition introduced. Sometimes im js quite confused what section should i learn to fit my trajectory as a quant researcher, i dont want to js apply models, but want to understand the concept behind it aswell so i can understand more, id be bluntly say want to be like jim simons lol. I also already start learning probability with blitzstein book, and going for valleman proof book aswell with either johnston or strang for linear algebra. Prolly will need discrete math aswell later, also going for DS/ML

[grim wyvern]

need a book on fuctorial approach for algebraic groups other than waterhouse

[signal zenith]

Another one to add: wild world of 4 manifolds

By Saveliev

[heavy pelican]

It's by Scorpan

[slow roost]

another one: A Panoramic View of Riemannian Geometry, by Berger

it is pretty high level stuff but super interesting

[vital chasm]

Counterexamples in Analysis is not bad too

[hushed spire]

what books do you guys reccomend on point set topology? my inventory so far is understanding analysis and LADR

no i am convinced by munkres, includes alg topology too for later very gemmy yes...

okay, i'll take it into account.

s

[zenith quarry]

hey any recommendations for an undergraduate who tryna get better insight on group theory?

ive studied it before but very surface level

[plush stone]

Hello, any book(s) recommendations for the math required in Data Science?

[zenith quarry]

i have very basic understanding of the subject since ive touched on it for fraction of the semester while studying discrete maths you think Lang's books you mentioned suitable for me to start with?

[sacred thicket]

Counterexamples in Topology
Topology - a Categorical Approach

also i dont recommend lee

[zenith quarry]

actually it was dummit and foote's 3rd edition of abstract algebra that i studied with but after semester ended i didnt follow through

i will check those too

ty yj

[vital chasm]

Paradifferential calculus is hard

Some harmonic analysis thing that lets you deal with bounding nonlinearities like products and function composition

Its quite useful for nonlinear pde apparently
So I am trying to pick it up

But Guy Metivier's writings are kinda hard to read

I barely know anything about them too

[plush stone]

Anyone?

Well I looked up and found that the topics required are

1. Algebra
2. Linear Algebra
3. Calculus (For optimization)
4. Probability
5. Statistics
6. Discrete mathematics
7. Optimization theory
8. Information theory
   At least that's what the internet and chatgpt is saying, so if you can give some recommendations or correct me here

I'm starting from scratch and I would like to go full deep on this

[hybrid sigil]

Just four years of study and you are ready!

[plush stone]

No problem

[mortal iris]

If you wanna learn the math properly then you'll have to learn to break down the formal definitions you're learning to suit your understanding. Essentially, take notes of everything until you're comfortable enough that you don't have break down formal definitions and theorems too much. You can't just pick and choose what to learn in basic analysis if you're going to learn it. You're simply gonna have to do all of it. Understanding things conceptually don't necessarily mean you'll have to do things rigorously though. You can work with intuitive pictures and still be fine so long as you're crystal clear about the pitfalls and exceptions. This is hard to do even with rigor but easier to spot while using precise language at the very least.

[plush stone]

I see

I will keep a note of it

Can you then suggest a good book for each of these math topics then?

Wait statistics aren't part of math?

[hybrid sigil]

Borcherds videos are fun and nice for additional insight and some applications or connections to other areas, but probably not sufficient as a single source. Also he doesn’t give exercises

[hybrid sigil]

Why you specifically don’t recommend Lee? I assume you mean his ITM book

[plush stone]

Thanks @balmy breach @flint prawn for the help, I'm keeping notes of all of your recommendations

Actually I know calculus but not formally

Okay

Oh i'm dead serious, since I don't have any job, might as well use this time for some learning

[river rock]

alright, i get it.. then ill start learnign from zorich while shifting between several hours with blitzstein

[plush stone]

Well data science isn't really my final goal but at least I want to upscale myself so that I won't be the only dumb person in the room if I ever have to opt for a data science/analyst job

How about I start with linear algebra and then I go into real analysis? Seems easier to me, right?

[river rock]

so eh, if i learn mathematical analysis and johnson linear algebra, will it be sufficient? and probability + stats

[plush stone]

Oh I'm going to declare myself dumb, so I start from scratch

Not that I'm saying I won't understand anything but if I'm going to dive into that, I should do it properly with all the prerequisites prepared and doing it consistently

Unfortunately I don't have that luxury, but I will keep that in mind

Btw, nobody knows a good source to learn statistics? I guess I have to look deeper in the internet

Even though it isn't part of mathematics...

[river rock]

stats110?

i learn through casella and berger "Statistical Inference"

[plush stone]

Thank you

Oh and also I know this isn't latex channel, but does anybody know a good tutorial to learn everything about Latex and TexStudio? I want to write some papers

Maybe an online source where I can read through

Does overleaf works same as TexStudio?

It's cloud and my internet sometimes is bad, so I would like the offline TexStudio

Okay okay

I will look into it

I use the normal notepad in Linux

Okay I will look into it

[sacred thicket]

imo lee is not a very good textbook if you want to learn topology on its own. it rushes through things needed for manifolds, so it may give reader an impression that pretty T2 spaces and manifolds are the only things one should care about.
though its very kind to beginners which is nice

[river rock]

i use latex workshop in vsc, connected to TeXLive

with wsl

[plush stone]

I think I'm going to stick with TexStudio😅, I read the post and seems like the author is really hardcore into customisations which I didn't even understood

Anyways, thanks for all of the help

[heady ember]

VSCode has integrated GUI for Git whch is a plus

GitHub Codespaces is nice if you need fast compilations

[remote sparrow]

pretty cool guide even tho i never tried this myself

sadly the author committed suicide

[blazing holly]

WHAT

[remote sparrow]

https://news.ycombinator.com/item?id=38352158

mike986

In case you are not aware of these awesome postshttps://castel.dev/post/lecture-notes-2/https://castel.dev/post/lecture-notes-1/

Hacker News · Nov 20, 2023, 6:29 PM

[hybrid sigil]

I also read about someone’s experience with Live TeXing here: https://journeyinmath.wordpress.com/2022/09/30/live-texing/

Just taken a look at that, it’s very impressive that people can produce such high quality lecture notes live!

[errant bane]

Can someone please suggest some references to study finitely generated groups in detail.. most of the books out there only cover finitely generated "abelian" groups (for eg. A First course in abstract algebra by Fraliegh). Thank you in advance

[oblique hatch]

What do you want to know about fg groups?
The reason most first courses will teach fg abelian groups is because there’s a nice and fairly elementary classification
But general finitely generated groups are way more complicated
If you wanna go that way, I’d suggest looking at geometric group theory (which will need some algtop)

[hybrid sigil]

“Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations” by Magnus et al. might be interesting for you

[hybrid sigil]

For geometric group theory I’ve recently found a book “Office Hours with a Geometric Group Theorist”, haven’t got a chance to read it much, but it looks fun!

[oblique hatch]

Yeah
I read Loh’s intro to ggt originally
And since then I’ve acquired no shortage of ggt books i like

[hybrid sigil]

They say that the book should be mostly accessible to undergraduates and mention other references in that area:

[oblique hatch]

Bridson and Haefliger is good but I’m not sure I’d recommend it as a second book unless you’re very metric geometry pilled
Idk anything about the others

(And it’s definitely not a first book)

[delicate hemlock]

de la Harpe is nice

[errant bane]

I am studying the actions of such groups on metric spaces. So i want to have a good bank of examples and their properties, as in how their subgroups look like, what are their homomorphism, what kind of structure do they have etc. All to help me work with them and understand them better

[compact bough]

are there any good resources on de rham cohomology or cohomology in general?

[molten gulch]

DR Coho is covered in most diff geo books AFAIK

[compact bough]

maybe i haven't looked hard or read enough of the ones i've got then

thank you!

[molten gulch]

Chapter 17 of Lee's smooth manifolds is a chapter on dR stuff

for example

[compact bough]

i rlly have to actually sit down and dive into Lee's smooth manifolds goddamn lol
ty i'll go look for it in there!

[molten gulch]

And for further introductions to just homology and cohomology I think most algebraic topology books have stuff on that

[compact bough]

alr

[molten gulch]

idk if you like hatcher but he has 2 chapters in his alg top book

for example

[compact bough]

holy shit
i'll def look into that

[molten gulch]

And ofcourse any text on homological algebra as well such as Weibel or Rotman (who also has an alg top book)

[compact bough]

got it

[signal zenith]

Differential forms in algebraic topology by Bott Tu

One of the greatest math books ever

The entire book is algebraic topology explored through de Rham cohomology and applications

It’s goated

[compact bough]

i'll look into it tysm

[odd cargo]

why aint nobody tell me rudin's book is closing in on 100 years

[languid harbor]

why should it matter?

[odd cargo]

fuck does this mean?

he's obviously goated status

even more now after the fact

[tame tree]

uh what

[molten gulch]

why does this matter? The book is still relevant as always because analysis as taught to first years hasn't exactly changed much

[tame tree]

it was 1953

we have

27 years

hopefully they do some 100 year anniversary edition that puts it back into print

[loud cradle]

wha? is PMA out of print?

dover opportunity

[oblique hatch]

I mean
The fact that now it’s generally considered an unforgiving book is probably a symptom of that

[cursive orbit]

it's unforgiving because calculus education has changed

but the exercises in the book are still gold

[tame tree]

i think it is outside of the international editions and “only authorized to be distributed in the indian subcontinent” editions

i believe theres some volunteer project where they texed it

[oblique hatch]

I mean
Yes, but isn’t that just the reason for what I said?

[molten gulch]

yes

[latent lotus]

I'm taking real analysis next semester but kinda shaky with proofs still any proof books i should read before then (I've read proofs by jay cummings)

[tame tree]

arguably its where youll learn to write actual proofs

[latent lotus]

my discrete math class was a lot of proofs

but i sucked lol

[mortal ore]

Everyone does at first honestly

[latent lotus]

its a very unique way that u have to think imo

[mortal ore]

Yeah

[tame tree]

im just saying that getting better at writing proofs entails writing proofs about real mathematics

[mortal ore]

Sadly you dont learn in school how to effectively justify your arguments

[tame tree]

these “proof” books are nice and all but they dont really prepare you

[mortal ore]

Let alone when these justifications can be undeniable

[latent lotus]

thats fair

[mortal ore]

Also once you do start writing proofs for higher mathematics itll honestly feel like ur getting worse

But youre highly likely getting better

[tame tree]

you can brush up on the “proof techniques” which are just general ways of proving if then statements

like contrapositive, contradiction, whatever

review induction at some point

[mortal ore]

Yeah induction is a nice tool to have in the back

U never know

[latent lotus]

yeah induction was a point i struggled with

[mortal ore]

Just think of it like dominos

[latent lotus]

but im starting to understand

[tame tree]

a tip is to prove the statement for n = 2

and then use that idea in the induction step

[mortal ore]

If u want to know that ur chain of dominos will fall, all u need to know is that each domino will knock the rest down and that the first one was knocked

[latent lotus]

i get the overall principle but sometimes actually doing it doesn't feel straightforward

[mortal ore]

Ah gotcha

Yeah usually u have to see a way to manipulate previous cases in

[rigid trail]

Proof of base case and proof that case => next case

or contrapositively, not next case => not current case

[mortal ore]

Btw @tame tree I really regret not taking algebraic topology this semester ngl

I psyched myself out bc I failed the top 1 final but even my profs were saying that my lecturer was bad so I really should've cut myself some slack in january

[tame tree]

i didnt take it either LEL

somewhat regret it too

[mortal ore]

Im just taking fucking history of math over ts

Like what am I doing

[tame tree]

id had saved time with regards to having to self study it on my own in the near future

[mortal ore]

Yeah

I can take top 2 next spring tho so its whatevs

Honestly might be better to since ill be doing AG and alg NT

[tame tree]

but idt it was even full on algebraic topology

it was like some stuff from the second half of munkres

[mortal ore]

Surely its more than that

[tame tree]

not rly

[mortal ore]

Odd

I dont recall homology being in munkres

[tame tree]

it ends at section 77 of munkres

i can lowkenuinely just study it over the summer probably

[mortal ore]

Real

I gotta do some rep theory studying soon

Since I decided to focus up on algebraic combinatorics for the time being

[tame tree]

rep theory sounds important to study at some point

but i think ill have to learn algebra properly

[mortal ore]

Fair enough

Algebra is the goat anyways so its worth

[tame tree]

[mortal ore]

Trust trust

Wait what area do u mainly work in rn

[tame tree]

im mainly interested in differential stuff

like analysis, diff geo, pdes, complex analysis ,

ive been liking topology as it appears with regards to these topics as well

[rigid trail]

algebra has not treated me well

[cursive orbit]

algebra is beautiful

[mortal ore]

Gotta hodge pill u now

[rigid trail]

i need to work on alg because i havent been trained sufficiently in it and i'm ass

group theory is fine but even simple ring theory sometimes fucks with me

rings are so fucky

[cursive orbit]

theres stuff out there applying nullstellensatz to Einstein constraint equations

[compact bough]

$\star$

[hasty eagle]

⋆ ˚｡⋆୨୧˚ ¡∫ĮŁVẼŘ!｡･:*✧

[mortal ore]

Real

But theyre so pretty

[tame tree]

i care when things are infinite and continuous

[rigid trail]

how to become goated at algebra? 🙏

[tame tree]

idrc about like no formula for quintics type of questions

[rigid trail]

i only took alg1 on groups rings fields and i'm scared to go further bc i didn't do allat well...

[tame tree]

but ill accept algebra if it comes up in things i do care about

like exterior algebra is fun

linear algebra is fun etc

[rigid trail]

i lowkey thought linalg was quite dry 😶‍🌫️ like on its own anyway. i started to appreciate it a bit more when i was applying to hilbert spaces but that's more so hilbert spaces being cool than linalg being cool

honestly algebra has felt quite dry to me in general 😭 probably because i dont grasp it strongly enough

feels like magic computations and no insightful intuition aside from some groups concepts

[tame tree]

maybe i should say that i dont like doing solely algebra

[bright umbra]

Hello everyone. Is there any good advanced calculus book (MIT level) that you guys can recommendate to me?

[normal crystal]

"MIT level"
they use their own notes, and according to OCW used to recommend Simmons

they don't use a real analysis book for those courses

so to feel like doing MIT level calculus
don't do what MIT does
got it🤡

sadly, I actually do

[cunning elk]

mit 18.01/18.02 is just vanilla computational calculus lmao

same as any other uni

[bright umbra]

Alr thx

[whole crystal]

Guys recommendation for books about learning math.

[molten gulch]

all important question is "at what level"

[compact bough]

what type/level of math are you aiming to learn?

[whole crystal]

Undergrad math uni

I need different perspective on how to learn math

[molten gulch]

start with real analysis and algebra

[whole crystal]

What do u mean?

[molten gulch]

if you want to learn undergraduate mathematics

[whole crystal]

No

[molten gulch]

start by learning real analysis and abstract algebra

[whole crystal]

That’s not what I mean

[normal crystal]

plot twist
he really wanted learning how to learn

[whole crystal]

Ive already finished this courses

Just see that there is space for improvement

In terms of acquiring math knowledge

[normal crystal]

the learning how to learn type books aren't really for people who already completed analysis and abstract algebra

[whole crystal]

Pass course is one thing

But get the gist of the topic

Thanks!

Did you read maybe Terence tao’s “solving math problems”?

Thanks a lot

[rapid solar]

hey guys i would love a book recommendation that isnt just some textbooks a calculus course would use

[fiery scarab]

im absolutely horrible

[rapid solar]

if anyone has anything do let me know

[trail void]

u mean a supplementary text which doesnt serve as a textbook?

[rapid solar]

exactly

[trail void]

Michael Range definitely

What is calculus?

[rapid solar]

i went to my universities library and all i could find was just textbooks that have example problems that dont go into much depth about books

[rapid solar]

like introduction to integrals and vectors

and derivatives

all that stuff

graph related math

oh

shit

sorry

thats the name of the book

im so stupid

im sorry

off to a great start

[trail void]

broo its ok 😭

its chill

[trail void]

yes i totally get it dw

There is also another book i like

but its more for analysis and its abt historical developments of it

the one i just recommended u briefly touches analysis

(quite alot but not as detailed)

Check this one out

[rapid solar]

i just want to get good at math you know

i love it so much

[atomic crystal]

you would want apostol imo

[rapid solar]

so much so i started minoring in it

and i join this server

everyones doing some crazy shit

i want to get to that level

[trail void]

where?

ive only met ppl online doing crazy shit w maths

others are just meh

[rapid solar]

i mean in this discord server

i mean im looking around

and its some pretty crazy shit going on

[trail void]

nahh trust me

you doing alright just work ur way up

[rapid solar]

alright let me look into what is calculus

and who gave you the epsilon

[vapid wagon]

i forgot what epsilon is for

damit

[stoic sundial]

Fermat’s last Theorem

Good book

[green swan]

Are there any good books to accompany an ODE course (that is frankly mostly computation based)? I want to have a more fundamental understanding of ODEs. I looked at V. Arnold's textbook but I was wondering if there is anything more modern

[proper trout]

same here lol

[grand cosmos]

i think the one that is cited a lot is the one in ams gtm series

gsm*

[mortal ore]

Same way u do anything else

Practice

[rigid trail]

What are some good resources to practice

any books with good problem sets?

i have dummit and foote i guess i should trudge through some of that...

:(

[mortal ore]

Dummit and foote

[rigid trail]

Okay then

thanks for the push in motivation