book-recommendations

[burnt juniper]

wait didn't Martin say he had to write and rewrite Winds of Winter multiple times because he wanted it to be a thousand-page tome and tie up some loose ends or something

[remote knoll]

I thought winds of winter wasn't going to be the last book

It was supposed to be the second to last? And then the last was supposed to be a time for wolves? Or was that random rumors that went around and I took as fact?

[leaden hearth]

i think the last is supposed to be "a dream of spring"

[remote knoll]

I honestly disengaged a long time ago because waiting actively for several years is unhealthy.

[leaden hearth]

lemme check

[burnt juniper]

it was Dream of Spring that will be the last but he did say there are some subplots he wanted to finish in WoW

[leaden hearth]

fr its been like forever

[burnt juniper]

iirc

this is going to become another Wheel of Time situation isn't it

author passes before finishing and project gets picked up by another author

[formal raven]

People

[burnt juniper]

yes

[leaden hearth]

i think Martin said he didnt want anyone else finishing the series

[formal raven]

How do u write this using a pen on paper

[burnt juniper]

oh well cliffhanger forever then

[leaden hearth]

yep

[slender yacht]

This is a very fancy p

[formal raven]

I looks like a bunch of squiggles if I write it

[slender yacht]

You start with the hook

And then draw the leaning stick

Is how i would do it

[formal raven]

Uh huh

Imma just write (very fancy curvery p) (A)

[slender yacht]

😭

I hate the R they use in relations

It's almost as fancy

But good luck my guy

I don't know what to respond

[formal raven]

Notations should be simplified if we must write it using a pen 😭

[slender yacht]

For real, we're no wordsmith

[formal raven]

Next they’ll expect me to write with a feather and ink directly

[slender yacht]

https://tenor.com/view/stickman-fire-writing-gif-2048052287611259724

[short osprey]

The Tell-Tale Heart by Edgar Allen Poe

[sudden kindle]

Their writing is this fire???

[mortal iris]

Flatland

There's of course Dune if you're okay with soft magic-esque things but not really magic.

Assassin's Creed has some books as well. And pretty much most genres in period fantasy kinda have little to no magic.

[cunning elk]

oh shi i remember reading that long ago

[nova canopy]

I love Assassin's Creed

[silk dew]

fire writing

[short osprey]

Yeah I love thw symbolism of the "eye of a vulture"

The*

[meager python]

What books u guys recommend rn reading infinite powers

[mortal iris]

Spivak's Calculus. Ditch pop math. Read the real deal.

[steel hornet]

what’s a good book on history

like napoleon

[mortal iris]

Napoleon is a book? I thought he was a person.

[steel hornet]

Real funny

[mortal iris]

What are you looking for exactly? Any specific area of interest?

[steel hornet]

I’d say Great War leaders

Like Napoleon.

Mehmet 2nd

I’m looking to Chinese the Romance of the Three kingdoms

[mortal iris]

The Kingdom DP is showing lol

[steel hornet]

I’ve read The count of mento Cristo like 3 times now

I have nothing else

[mortal iris]

Churchill has stuff written about himself and the wars he's been in. That said his racist colonial cruelties don't get a mention.

[steel hornet]

Right….anyone but Churchill??? No? Lol

Well I wouldn’t mind reading a fantasy novel

[solid zenith]

the romance of the 3 kingdoms is fiction

[mortal iris]

Ashoka The Great has a nice biography. It's called Ashoka: Portrait of a Philosopher King.

[solid zenith]

the records of the three kingdoms is the history book

[steel hornet]

This is what I live for

[mortal iris]

Consider the Viking Sagas for this. There's plenty of them that have been translated and most have been inspired by real historical events but have been narrated with a lot of whimsy and exaggeration lying on borderline untrue things as well.

[steel hornet]

Thanks I’ll look into it

who knows about Shackleton incredible voyage

Any thriller book that reads at good as that?

[trail void]

explored my grandpas library today

didnt know he knew peak

[plucky lantern]

Hi could anyone recommend a textbook for PDEs? I feel like I want some more practice questions to work with

[trail void]

The Dawn of Everything a New History of Humanity by David Graeber & David Wengrow.

[chrome mica]

Can someone tell me if the proofs in Book of Proof are sufficiently rigorous?

[trail void]

https://www.youtube.com/watch?v=bIwX4QuL90k

kurzgesagt has a history channel now

[steel hornet]

Have you read it?

[trail void]

long ago yes

[steel hornet]

This isn’t the one that ran away from Napoleon

?

[trail void]

napoleon wasnt born yet

[steel hornet]

Lol

I think there was a king Louis in napoleons reign

Maybe XVI

[steel hornet]

thank you local handsome bastaed

Bastion of ambition

[trail void]

youre familiar with sapiens by yuval harrari?

well the book i just recommended is much better at representing history without many fallacies than this

and also its more anarchic in nature

written by cultural anthropologists

700ish pages of pure fun

you can then go into any era i prefer 1500s-1800s europoe

[steel hornet]

I know about this book

But im just like

How much of it is actually real

We know like 0.00000001% of human history

[steel hornet]

The dawn of everything?

which author is the archeologist

[meager python]

Ok

[trail void]

pretty sure both

one of em passed away

[trail void]

yeah its just an overview sort of

brief

if u wanna go into it more than u neewd other books

[steel hornet]

tell this

Would the book cover the Ottoman Empire?

[trail void]

yes

not in detail

[steel hornet]

see you 700 pages later

Try not to get lost

[velvet flax]

does anybody have any interesting math books in german

preferably on algebra

or complex anal

[chrome mica]

"complex anal"😂

But no, I'm portuguese

[valid parrot]

Is sl loney coordinate geometry good book

Dose it has good problems

[remote sparrow]

https://www.youtube.com/watch?v=uCuy1DaQzWI
https://www.youtube.com/watch?v=0KQYNtPl7V4
https://www.youtube.com/watch?v=sH03uLuOtSY

given kurzgeshit is a german climatewasher and genocide denier, i doubt his history channel will be of any value

<@&268886789983436800>

[midnight gulch]

its pop-science and pop-history, it wouldn't be of any value regardless

for random topics it doesn't really matter, its no different to any other general source on the topic

[desert eagle]

ig hes tryna not offend anyone

[remote sparrow]

who's "anyone?" i guess people that know the history of colonialism and imperialism aren't part of that group? or people who know that the invisible hand of the market won't magically solve climate change?

[normal crystal]

is the hand invisible so it's easier to commit theft🤡

[past bolt]

Hi, I currently have a “extendable wings contraptions/jet pack” obsession going on thanks to an Artificer character I’m playing. Does anyone know any good under-grad to mid-college+ level engineering, design, and fabrication books and resources I can get ideas from and that are also good for studying up in that area?

[normal crystal]

are you really asking for engineering textbooks to make a jetpack with wings
like a videogame

[past bolt]

Aeronautical engineering for small craft. I had to get the words of my head to make better sense of them.

[normal crystal]

is that just a euphemism for what I said above though

well, maybe someone can help

[past bolt]

Anything from any angle helps. 🤷‍♂️

[normal crystal]

one year deadline so you can fly around like cupid next Valentine's

[past bolt]

What was once science fiction is now “modern” fact.

[past bolt]

Oh, clever for a test run.🤣

[normal crystal]

I remembered I actually have this book
https://www.amazon.com/Wheres-My-Jetpack-Amazing-Science/dp/1596911360/

[signal zenith]

I prefer funky anal

[velvet flax]

👅

[signal zenith]

BadEmpanada 💀

[vernal ore]

Yakub's greatest soldier

[vernal ore]

This dude's gone of the deep end recently

[signal zenith]

Dude has been off the deep end for a long time

Bro does not know how to log off it doesn’t matter who you are or what you disagree with him about he will send you death threats on twitter over literally anything lol

[vernal ore]

He should stick to history videos. He used to have a stronger understanding of societal issues a couple years ago, but he's lost that. Either way, his politics are not built on strong fundamentals so I don't really take anything he says seriously unless it's backed up by sources

[remote sparrow]

examples?

[remote sparrow]

examples?

[vernal ore]

Of what?

[nova canopy]

OMG STAR TREK

[remote sparrow]

give some examples of how he has a weaker understanding of "societal issues" than before

[vernal ore]

No

What's this politics channel?

[worthy kindle]

good one unc

[vernal ore]

I agreee with asking for examples for the death threats as that's a serious accusation, but I didn't claim that and I'm not gonna begin a full political debate with you

[signal zenith]

I mean look at his twitter for 5 minutes lol

Idk I haven’t been on twitter in years

That’s the way he was back then I have no doubt in my mind he hasn’t changed

But I have no desire to debate politics with people that online lol

Get your politics from people who aren’t permanently angry. There are plenty of leftists fitting that description. Anger isn’t a good basis for politics

[past bolt]

Yep, even religion.

[past bolt]

Thanks. I’ll check it out.

[remote sparrow]

not trying to dunk on you here, but saying, "yep, even" is supposed to set up for something less obviously political, but you ended your sentence with something obviously political

[past bolt]

Honestly, I pulled the sentence out of my ass, ||because I was thinking back to an argument I had with someone else that tried to say religion couldn’t be political and didn’t follow a similar MO at some levels.||

So, let’s not go there.

[outer gull]

looking for a starter book on linear algebra for a high schooler to go into deeper topics any suggestions?

[midnight gulch]

what specifically would you look for in "deeper topics"?

there are a couple of directions you could go in

[heavy pelican]

Artin Algebra

[cunning elk]

most lower division linear algebra courses are focused more on matrix computations than actually proving anything

[midnight gulch]

?

[heavy pelican]

Author, name of book

[cunning elk]

if you want a more rigorous approach you might look at FIS, hoffman/kunze, etc

[midnight gulch]

are you answering them? if so that is a terrible reccomendation

[heavy pelican]

It's not a terrible recommendation. I was a high schooler when I read it

I can attest its a very accessible and good book that will teach the kid what mathematics is if they wish to learn so

[midnight gulch]

nvm i was thinking of a different book with similar author and name, i guess that one works

yeah i was thinking of emil artin's geometric algebra, i think ive heard that book just referred to as algebra or something

it technically could have been an answer to their question, but would have been a bad one lol

[heavy pelican]

Oh lol

[heavy pelican]

Yeah, I should specify. "Algebra" by Mike Artin

The only thing I'd say is to not rush. Take it one step at a time, the abstraction slowly builds up chapter by chapter. They'd be able to stop any time and return to it later.

I remember being too eager and rushing, which is a double edge sword. Hence the warning.

[trail void]

no correlation btw

[spiral heath]

Book recommendations for linear algebra engineering undergrad?

[cunning elk]

what books do the linalg classes at your school use

[spiral heath]

Larson

[cunning elk]

op its contents seem a bit on the small side

[odd cargo]

https://tenor.com/view/baby-laugh-ai-baby-babyfryingme-baby-sob-folk-gif-18221933230434867320

[stone basalt]

https://textbooks.math.gatech.edu/ila/

Full free online interactive book

[cerulean thicket]

@stone basalt
Welcome to Mathcord, new nerd. Hope you enjoy your stay!

[stone basalt]

@cerulean thicket
Welcome to mathcord, nerd. Hope you enjoy your stay!

[cerulean thicket]

I've been here since June of 2025...

But thank you nonetheless

[stone basalt]

Not subject to reflection property huh

[sacred thicket]

illustrations in fomenko fuchs alg top are astonishing

[silk dew]

I like poe's poems more

sorry for late response

[tidal hare]

I need a non-fiction book reccomendation guys

I like Maths, Science, Comp. Science, History, Politics and just... more stuff ig

[vernal ore]

Anyone has book recomendations for the Elliptic functions/integrals? I'm reading Greenhill's textbook, it's pretty good but a bit convoluted at points

[short osprey]

like the poems in The "Raven"?

[past bolt]

Get back to me when you learn to speak like an adult because I can’t hear over the sound of your diaper being changed.

[violet burrow]

I can absolutely recommend "The ailing Empire" by Sebastian Haffner. It's about the history from the creation of the german empire till the fall of the Third Reich. Haffner really gets into details about alliances and why the world wars started and how the germany of Bismarck almost inevitably slid down the path of our favourite painter.

Or George Orwell's Animal Farm and 1984 (I mean it's kinda fiction, but more an allegory on reality.)

[lost arch]

im currently learning analysis with Browders Intro to Analysis. To those who're familiar with the book, do you think it can be called a comprehensive course of real analysis? i know there's always Amann & Escher's three volumes set that dont compare to Browder at all but still. How much real analysis would one know if he studied Browders book?

im asking because i wanna know how much of analysis ill have lacking when ive finished the book

[lost arch]

you say you're willing to study law in your bio, then go for Hobbs, Lock, Rousseau, Constant, Montesquieu. Anything of the mentioned authors will be of value

[tidal hare]

Thank you!

[tidal hare]

Thank you!

[mellow rivet]

<@&268886789983436800>

[static cairn]

What is the best book for number theory starts with peano axioms?

[tame tree]

fwiw, if you want to do peano axioms, terence tao's analysis 1 beginning is about that

and there's also the online natural numbers game, which has you do it in lean

hopefully someone chimes in with an actual number theory recommendation tho

[wicked fractal]

What's your motivation for learning number theory? Peano arithmetic can be learned on its own and you can find it in many standard books

[static cairn]

Start in Mathematical Olympiad

[wicked fractal]

[static cairn]

MONT

It doesn't mention Peano, so I'm looking for another book.

[static cairn]

Thats not good?

[wicked fractal]

I don't have any book recommendations geared towards math olympiad sorry

I can give you a list of number theory book recommendations though

[static cairn]

Okey thanks

I will definitely choose something for myself

[molten gulch]

Yes olympiads are blegh

[cerulean thicket]

@violet burrow
Welcome to Mathcord, new nerd

[fast harness]

does anyone know any good books for EDA? currently i'm reading an introduction to statistical learning but if any1 knows any better books let me know

[violet burrow]

Are you the official greeter of this server?

[umbral field]

no he's just like that

[cerulean thicket]

I'll take this as a compliment

[normal crystal]

if you were baffled by the SML book, that is gonna be rough book to choose instead

Harper has video lectures on YouTube from OPLSS you can look for

[remote sparrow]

@normal crystal any webtoons you've been reading lately

[normal crystal]

oops, I think you asked me in the other channel and I forgot to answer
recently I was reading
Echoes of a Reverse Planet
Glitch Utopia
The Magic Theory of the Regressed Sword Saint
Veteran of the Apocalypse
The Genius Girl Who Hides The Martial World's Public Enemy
Murim Psychopath
My Simulated Path To Immortality

Android or Gboard knows what you type

[odd cargo]

you can do better than murim psychopath man...

[normal crystal]

enjoy your furry daily vlogs on the homepage

[normal crystal]

@remote sparrow based on your previous recs, I think the ones of those you might possibly enjoy are
My Simulated Path To Immortality
Veteran of the Apocalypse

or none

idk, surprise me

[remote sparrow]

they both look like slop

i recently binged aza

https://www.webtoons.com/en/fantasy/aza/list?title_no=3994

[remote sparrow]

what are you reading

[obsidian otter]

Need a math book to binge

[odd cargo]

novels or just manhwa?

[remote sparrow]

manhwa
webtoons don't have to be of korean origin

i can't say i've been particularly gripped by any k-novel thus far

the ones i've seen seemed better off adapted in comic form; they practically read like scripts for an upcoming manhwa adaptation

dude i found you on google

[odd cargo]

honestly i havent really been reading much manhwa recently, except maybe bad born blood, but theyre lowkey dragging that one.

i havent read a novel since second coming of gluttony either lmao

but i do sometimes read the first few chapters of new manhwas just to scope and see whats going on

murim psychopath iirc was status window slop or some shit

[remote sparrow]

orv seems to be like

a korean one piece

ppl keep saying it has a slow start and it gets really good after like 100 episodes

as far as the manhwa anyway

difference is that orv's novel actually has an ending

so cool ig

i read like 40ish episodes of the orv manhwa and haven't gotten back to it

[odd cargo]

that author or artist has a sheet of solid manhwa too

other than orv

[remote sparrow]

https://www.mangaupdates.com/series/n50wl4o/omniscient-reader

which one

[odd cargo]

its tower slop

[remote sparrow]

tower of god was good for a while

it's literally just korean one piece now

[odd cargo]

was that what it was called?

[remote sparrow]

idk

[odd cargo]

nah thats not it

[remote sparrow]

aren't there at least several tower stories

tower of god is probably one of the OGs

[vital chasm]

My local time warden cannot be this cute

[odd cargo]

This might still be a good manhwa though, check it out if you have the time.

[remote sparrow]

isn't this the story kim dokja read

the protag of orv

[remote sparrow]

well she's a petplayer now

[odd cargo]

i have no clue

its called the world after the fall

[normal crystal]

waaaaaaay more than several

did you ever read Mage Again

[trail void]

the artist:

[rapid fjord]

can we stay on topic please

[mortal iris]

Nope. That would be Tower of God.

But it's gotten very weirdly off the rails imo since the Hell Train and Last Station arcs.

[mortal iris]

THE OG. Afaik it was planned to be an entire universe on its own. But idk what happened. The story keeps getting dragged into long and weird tangents.

I used to love it. But rn with the Lo Po Bia family and Po Bidau family at war, the story has diverted way too much from climbing the tower. It's possible to develop the lore while making progress with the main storyline. And ToG was doing that so well up until The Last Station arc.

Imho it's seriously fallen off.

It used to dominate the webtoon charts back in the day.

Yes. It's becoming your run of the mill power fantasy

He's hella interesting. Not as a character but as an irregular within the tower

[stoic oak]

I don't get the idea of loving maths and doing it unless you are forced to do it, I mean what's even fun in it, yeah it's kinda fun when ur getting problems but other than that it don't make sense to me. I still wanna get into maths thou but I just don't know how to 😭, I know the basic principles and formulas of 3d geometry, calculus and algebra. Which book shld I start with?

[fast harness]

Like every science, Math is an art

The idea of loving it comes from appreciating that

But it depends what kinda math do you want to learn

[stoic oak]

There are different types of maths?

[fast harness]

Yes

Theres statistics geometric calculus etc

If ur already familiar with those things I’d suggest learning linear algebra next

[midnight gulch]

well if you don't enjoy math, you most likely won't enjoy it from forcing yourself to do it

are there any related topics you find interesting?

[stoic oak]

Well I've liked doing algebra and geometry

[midnight gulch]

maybe you could try like a beginner friendly abstract algebra book?

[somber echo]

try dummit and foote

[midnight gulch]

no

really don't think that is the right kind of book in this case

there are better introductions, books like those exist for a reason

[desert oriole]

lang undergraduate algebra

[stoic oak]

oo alrr will do

[mortal iris]

If you don't find it fun, then no point forcing yourself to get into it. You'll regret trying to. Do what you like. There's more to the world than math but we just like to find it in all those things as well. You don't have to.

[stoic oak]

i just meant i never actually tried doing math by myself on my own interest, i was always forced to do it because of academics. I just wanna give it a try and see what it’s about.

its not like im forcing myself to get into maths rn

[mortal iris]

If you're not already interested then chances are you won't be. But there's no harm in exploring stuff. Just don't go in with unrealistic expectations of some sort of epiphany that will motivate you to pursue the subject.

[midnight gulch]

yeah, most people find interest in math (or anything for that matter) by independently stumbling upon it or someone like a teacher causing that spark

either way, its best to start with what you know you like and go from there

i would say an abstract algebra book is probably good because it revisits a lot of ideas you're probably familiar with but from a new perspective. whether or not that perspective would be interesting to you is hard to say

[mortal iris]

I would also view linear algebra and euclidean geometry in the same vein.

[stoic oak]

aight imma let you know bout my experience w it!

thanks for the recommendation thou

[midnight gulch]

fraleigh's abstract algebra i think is a good example, there's probably better ones but that's all I can think of right now

pinter's as well

thats the one i personally used for a first introduction

[normal crystal]

furries killed it

[shell maple]

which is not being taught in most schools...
science is the study of what you don't know

so if you already know all the forms and plugging in to do calculations idk what you're doing!!

[normal crystal]

did you not read that far
dog people
cat people

watch the creator do a spinoff webtoon from Rachel's perspective
just to antagonize the fans

[mortal iris]

Not that I like it but a valid defense is that the methods and curricula are designed to cater to the many as opposed to the few. The interested few tend to diverge in different ways. Some come to appreciate mathematics as an art form, some come to appreciate it's utility, some come to build things with the science they know and some come to the fascination of what they don't know. If the curriculum and instruction catered to finding things out and proving/solving beautiful problems then we would be left without engineers, doctors, philosophers and so much more.

General schooling aside what is really worrying is why aren't there enough schools to cater to exactly these things. If universities can provide instruction for a focused degree, why can't at least some schools also provide instructions in a manner that caters to audiences who want to do science or mathematics in the proper sense?

Engineers do not do or need math besides theory to identify problems and data to troubleshoot. At the end of the day, it's a craft. I'd argue that cs and physics folks use math the same way mathematicians do, just in different areas and often not rigorously (not that one cannot do it).

[mortal iris]

I wonder why. What do you do as an engineer and how does the math help

[urban rose]

Anyone using Hodder Boost for IB Math AI HL?

[mortal iris]

Well. That's more so mathematical modelling and experimental design tbf. I can understand engineers working along these lines requiring math but most do not?

Like what you're doing is not so far off from experimental physics either.

Like if I were working at a factory and some equipment went bust, what math do I need?

Or let's say the circuit I made doesn't do it's job correctly. Would I work out the math or troubleshoot by playing with the circuit?

Yeah. That's pretty much where I am getting at tbf. Engineering is usually very tinkering and troubleshooting heavy in the industry. And engineers predominantly find themselves in the industrial sector as opposed to academia.

For those who wanna or do work in an area that requires designing, modelling and testing things there is ofc a bit more math involved but the extent would likely depend on the specific case.

Yeah but like diagnostic stats is more so learning how to run them and interpret the data is it not? It's more so data analytics.

This academia or industry?

Very interesting. This is fascinating to know.

I was always under the impression that engineering students learning all sorts of complicated math is kinda pointless.

[vital bane]

Can I apply survival analysis on myself to see whether I live or die? (Get into a good PhD program or not)

[mortal iris]

I think there might be a fixed point theorem that tells you no rather easily xD

[shell maple]

What's your favorite book

[mortal iris]

That's random and also too broad a question. Give me a genre or smth to narrow it down and I can tell you my top 3.

[shell maple]

do you not believe that there's unity in all knowledge?

was only curious about your current interests but if you ask.. hm I won't say real analysis, I'm tempted to ask for linear algebra but I'll ask for abstract algebra or numerical analysis:)

[vital bane]

Favorite rational homotopy theory book

[shell maple]

Okay now I get why you wanna be narrow

[oblique hatch]

I’m sorry, if you’re applying to PhDs the answer is you die
If you don’t get in you get executed
If you get in, academia kills you

[remote sparrow]

a little bit

[shell maple]

Is academia worse than industry?

[mortal iris]

My current interests do not lie in pure mathematics. Never have tbf. That has nothing to do with favourites tho. Weird way to ask a question about interests (mine lie in quantum foundations and information theory) ngl.

If I were to recommend books for Abstract Algebra then I'd go with Judson for an introduction. It's got nice applications and also sagemath exercises so you'll grow in familiarity with computer algebra systems as well. For harder problems I'd look at Herstein's Topics in Algebra. For advanced material I'd use Gorodentsev. Always nice to check out Keith Conrad's blurbs on some of the topics as well.

For numerical analysis I'd just use FNC. It's a solid starting point. I don't see much of a point going further into it with FA and stuff. Much more interesting to look at HPC but at this point books imho are not that useful.

[mortal iris]

DNE. Never gone into it. Not interested either.

[shell maple]

information theory

Then you probably have read some percentage on Number theory I assume?

as both study structures in numbers... ig?

[mortal iris]

Not for or in the context of information theory but yes. The basics.

[shell maple]

Oh what would be a good start in your opinion then

[mortal iris]

That's like all of math more or less.

[vital bane]

If you get in, academia kills you

Only if I die

[shell maple]

I firmly believe there's unity in all knowledge anyway

[mortal iris]

To what?

[shell maple]

Number theory

[vital bane]

What about spectral theory?

[mortal iris]

Uh huh. Explain the unity of general relativity and quantum theory. I'll wait.

[vital bane]

favorite book

[mortal iris]

Burton's Elementary Number Theory is solid.

[wicked fractal]

What's your motivation? Are you looking for elliptic curves? Dry number theory? Analytic flavor?

[mortal iris]

Moretti's Spectral Theory and Quantum Mechanics.

I also like Einseidler and Ward's FA book for this. It's not necessarily geared to my interests but a very nice book nonetheless.

[wicked fractal]

I should write a book recommendation list for number theory and maybe someone can pin for future use

[indigo blade]

what is a nice book about mathematical logic that is both beginner friendly and rigorous?
i really want a good logic book to start my CS journey chat

[shell maple]

dude isn't that like an open problem in physics 😭 ??

unity is unknown...

[gleaming sparrow]

Guys, I want to get really really really good at mathematics

[tired linden]

I think a comprehensive list of different books for every main field with several books, based on why you want to study the field/current "skill" level, would be extremely beneficial, because I know especially for myself that navigating what books across different topics would be the best for me and what I want is extremely difficult to navigate, and it's not like I have the pockets to buy tons of books and see which works best

[wicked fractal]

Yes that's my goal. When I get home I'll write a summary of each number theory book I know and what can you get from it

[gleaming sparrow]

Could you guys suggest me some books for these topics:

1. Coordinate geometry
2. Number theory
3. Probability
4. Trigonometry
5. Calculus

[tired linden]

I'm currently reading Number Theory by George E. Andrews (published in the 1970s I think) and it's pretty yummy. It is pretty terse (that is, it often asserts things assuming the reader will be able to figure out why the previous implies the current, which in some cases can take a few minutes) but I quite enjoy it. As for 3 4 and 5, if you're studying them for school I think the best thing to do would be the check out whatever textbooks your school uses for them

[gleaming sparrow]

I need something that doesn't require much prerequisites

[tired linden]

The book I mentioned doesn't really have any, imo, except I suppose basic notation you might not see in high school like sum and divides and modularity

It's written to be digestible for both math students and humanities students so it's not incredibly technically dense

[gleaming sparrow]

Well, not everything will be Greek to me then. I will check it out, thanks!

[blazing holly]

What branch of CS do you wanna get into?

[gleaming sparrow]

Not exactly CS, I just want to study these topics to the best of my ability for an exam

[blazing holly]

That gives us a better frame of reference as not all branches require the math you mentioned

[gleaming sparrow]

Call it a penchant

[tired linden]

Mhm!

[gleaming sparrow]

It's for an exam, not any branch.

[tired linden]

When will you be taking the exam? That is, are you needing to learn these subjects for the first time, or just study them?

[blazing holly]

Ah okay

[tired linden]

In terms of studying I think past papers are the best way to study for specific exams

[gleaming sparrow]

Just study them.

[blazing holly]

Is it a math placement exam by any chance?

[tired linden]

Instead of vaguely studying the material and trying to guess what will be on the exam

[gleaming sparrow]

No. It also has sections for physics and chemistry

[tired linden]

Applied mention

Instant ban

[blazing holly]

Applied mention
Instant mod

[gleaming sparrow]

Hm, that's true. I just wanted to get a better idea of what I am gonna study for the next month.

[tired linden]

😨

[gleaming sparrow]

It'd be nice to have some material accompanying me

That's all

[blazing holly]

Im sorry Lana
I must defend my applied brethren’s

[tired linden]

I don't know the full situation but I think it's generally best to study one field at a time, because then your brain kinda molds itself into that field. Like if you're studying both number theory and graph theory, you have a math brain, but if you zero in specifically on number theory, now you have a number theory brain, and the connections feel much more natural. The same applies to other things like hobbies

[tired linden]

No one is perfect

[gleaming sparrow]

That's such a good observation! But I lack time, and I need to prepare these all at a time as the questions mix multiple concepts from the ones I mentioned.

[blazing holly]

Some of us like getting paid

[gleaming sparrow]

Glad to be in the minority then ig

[tired linden]

I have to stay in school as long as possible to postpone getting a JOB 😨

[gleaming sparrow]

No

The J word

My eyes

Please censor it the next time I'm around

[tired linden]

Will do

[blazing holly]

In terms of importance, I’d spend the bulk of your time studying calculus, as physics & chem are rooted in it

[gleaming sparrow]

Much appreciated!

[tired linden]

I agree

[blazing holly]

Stewart is an instant go to

[tired linden]

I agree with that also

[forest coyote]

Black book by Vikas Gupta

[gleaming sparrow]

Hm, true. I have studied these topics before, you could say I need some kind of a level up.

[forest coyote]

Questions only

[gleaming sparrow]

Hm

[tired linden]

Wait so what kind of exam exactly is it?

Is it some sort of placement or evaluative exam?

[gleaming sparrow]

An engineering entrance exam

[tired linden]

Ohhh

[gleaming sparrow]

Yes

A bit like the SAT

[forest coyote]

Which one

[tired linden]

I think probably building a general intuition would be better than trying to cram a ton of knowledge, given your time frame

[gleaming sparrow]

Hm

But how do I do that

[odd cargo]

study, a lot.

[gleaming sparrow]

Yeah, that seems to be the best possible way

[gleaming sparrow]

The JEE

[mortal iris]

https://tenor.com/view/assassins-creed-gif-3542437

[forest coyote]

Ya bro do black book

[odd cargo]

i doubt a pre-u student has anything better to do with their time

[gleaming sparrow]

Hm

[mortal iris]

Nothing like it. SAT is reasonable.

[gleaming sparrow]

I had to make sense of the situation, not the best at drawing analogies

[forest coyote]

Agree

[mortal iris]

Call it an Olympiad level entrance exam that relies on rote memory and formula vomit as opposed to real skills.

[blazing holly]

Agreed

[gleaming sparrow]

Hm, what do you suggest?

[mortal ore]

Are we talking about JEE

[gleaming sparrow]

Welcome to the table, hiido

[mortal iris]

Quit preparing for that shit and find alternate options. There's plenty. Do your due dilligence.

As far as generally studying stuff goes, I can recommend stuff

But not for that bullshit.

[gleaming sparrow]

Yes, but again, what do you suggest? Besides, I plan to learn these topics out of general interest anyway.

[mortal ore]

Might as well just go to a US school frankly

[gleaming sparrow]

Hm, what if I genuinely want to study this stuff? Then?

[mortal iris]

1. Pogorelov's Analytical Geometry,
2. Burton's Elementary Number Theory,
3. Blitzstein and Hwang's Introduction to Probability,
4. Gelfand's Trigonometry,
5. Spivak's Calculus.

[gleaming sparrow]

Do these build concepts from the ground-up or are they jargon-heavy?

[mortal ore]

Spivak as a first read is pretty ballsy

[mortal iris]

Potentially have Lang's Basic Mathematics and Geometry book for reinforcement at hand.

[gleaming sparrow]

Noted

[blazing holly]

Calc- stewart’s early transcendentals (it has sections on trig so you don’t need another text for that)
Probability - any stats book works, I have one by Wackerly

The others, i dont know much

[mortal iris]

It's doable. But not with the same standard of rigor you'd expect at the undergrad level.

[gleaming sparrow]

Thanks for the suggestions!

[blazing holly]

Imo spivak is ideal if you already know some calc OR are a maths student

[gleaming sparrow]

I have always wanted to learn mathematics the mathematics way, this exam stuff doesn't really suit me

[blazing holly]

Stewart is the standard for 99% of stem students

[mortal ore]

Stewart into spivak is pretty effective ive heard

[mortal iris]

You do require a solid background on Precalculus before picking up Spivak or even Blitzstein when he gets to continuous probability distributions. Lang's Basic Mathematics is good enough for that but for a more standard course you can also look at Axler's Precalculus.

[wet sentinel]

true, its more natural to immediately start with PMA or RCA instead

[gleaming sparrow]

Will take a look into these!

Anything for physics?

[blazing holly]

Openstax is also good

Free resources in a bunch of subjects

[mortal ore]

Fuck it just start with hartshorne

[gleaming sparrow]

Oh

[wet sentinel]

real

[blazing holly]

Is general physics or smth precise?

[wet sentinel]

but why would someone do that

[gleaming sparrow]

General physics

[wet sentinel]

I mean after stewart isnt it more reasonable to just go for some RA book instead of spivak?

like say rudin or abbott

[blazing holly]

I have one by Sears & Zemansky

[mortal iris]

Halliday, Resnick and Krane (5th Ed). Along with Feynman's Lectures and Irodov's Problems in General Physics.

[gleaming sparrow]

Is it good?

[mortal ore]

Probably

[blazing holly]

I disagree w/ Feynmann im ngl

[mortal ore]

Idrk much about calculus texts I was mathematically afk until abstract algebra

[gleaming sparrow]

Noted

[blazing holly]

I enjoyed it

[mortal iris]

Why?

[wicked fractal]

Go read D&S. I'm watching you

[wet sentinel]

fair

[mortal ore]

Dummit and Soote

[mortal iris]

https://tenor.com/view/harvey-specter-suits-suits-tv-suits-usa-aura-gif-2734246581103925492

[wicked fractal]

Life before and after D&S

[blazing holly]

I don’t see it much as a book to learn from, but more so to gain awareness

[wet sentinel]

life before and after NT/AG arcs

[gleaming sparrow]

The college physics one?

[wicked fractal]

Truly

[blazing holly]

University physics?
If so, yes

[mortal iris]

Exactly why I didn't mention it as a primary text. It's a solid set of lectures to couple with a standard text and a problem book for insight.

[gleaming sparrow]

Hm

[wicked fractal]

Life when you realize things can be thought of as Galois representations

tfw you spot reciprocity in nature

[gleaming sparrow]

I suck at chemistry

[wet sentinel]

btw does one need background in representation theory to study these or is it ok to see representation theory for the first time here

[wicked fractal]

Chemistry is cool if you look at quantum groups

[gleaming sparrow]

Yeah, this went over my head too

[mortal iris]

Near absolute zero

[wicked fractal]

Depends on what you want

You can absolutely get exposed to representations early one

I mean you already are

[wet sentinel]

i mean yea

[gleaming sparrow]

Do I get to represent myself using representation theory?

[wicked fractal]

Linear algebra

Maybe know things like induction, restriction etc

[mortal iris]

You need to study a lot more math or physics to make sense of that comment lol

[wicked fractal]

Tensor products as well

[gleaming sparrow]

True. And Thanks for the recommendations

[wet sentinel]

where to learn about galois representations

[wicked fractal]

But if you want to play with basic examples of Galois representations that's completely fine and accessible

[wicked fractal]

Yes

Have you gone through Dirichlet characters?

[wet sentinel]

tysm for the recommendation

[wet sentinel]

I know what a dirichlet character is, nothing more nothing less ig

[wicked fractal]

yeah these are Galois representations

[somber echo]

I can vouch this is the best recommendation

[wet sentinel]

yea ok but like where to read about galois representations in details. Like if one wants to study modular forms, one reads something like D&S.

[wicked fractal]

Yes you can go into many rabbitholes with this

[wet sentinel]

there is this recommendation, is there any other resource to supplement this one?

[wicked fractal]

I recommend learning Dirichlet characters really well

[indigo blade]

can i reask my question again if it wasnt answered or its potential spam?

[wicked fractal]

This can be learned while doing algebraic number theory

Also make sure you learn how to connect it to Kronecker Weber. Super important

[somber echo]

Did you do a course of ANT? 🐜

[wet sentinel]

no

[somber echo]

Also basic idea of p adic is required

[wicked fractal]

If you want representations coming elliptic curves then you will have to do some elliptic curves obviously

Then you can look at the Tate module

But anyways let's not get ahead of ourselves. Learn your Dirichlet characters

[wet sentinel]

something related to this?

[wet sentinel]

true

alright thanks deltoid and nHecke(G)

[vernal tinsel]

even in book recommendations...

This server is number theory pilled

[vital bane]

Deltoid's dms

[somber echo]

It's a good sign

[wet sentinel]

supposedly deltoid's channel should do the job but he almost never yaps about galois representations in that channel

[mellow wren]

diamond shurman

[wet sentinel]

ohhh ok nice, tysm

[mellow wren]

you should know elliptic curve stuff before learning about galois representations tho

a big class of galois reps come from elliptic curves so they're pretty important to the theory

later on if you keep learning about the the theory you'll learn about reps coming from abelian varieties but that's not as important when you're starting out

[dapper root]

the the the-ory

[wet sentinel]

how much should i know? Does D&S not cover the necessary stuff?

[dapper root]

2 doesn’t divide odd numbers

[wet sentinel]

if no then would something like silverman's rational points on elliptic curves do the job?

[wet sentinel]

bro still remembers this

[mellow wren]

not really

you'd need to know the basics from like silverman's arithmetic of elliptic curves

[dapper root]

My memeory is very good

[mellow wren]

like at the very least you'd need to know how elliptic curves over C work

idk if the silverman book you mentioned covers that

[wet sentinel]

I see, I will keep that in mind. I wanted to study elliptic curves sooner or later anyways

[mellow wren]

you need that because like

the most basic examples of galois reps come from elliptic curves

then you have more complicated examples coming from cusp forms

and it just goes on from there

you can argue that dirichlet characters are technically the simplest example because they're 1D reps but that's kinda cheating lol

[wicked fractal]

Cheating?

[shell maple]

i love your takes:)

[wet sentinel]

ohhh ok. I will keep everything you told me in mind and see what to do from there

[wicked fractal]

JEE?

[mellow wren]

1D reps don't exist lalalalalalalalalalalalala

[wet sentinel]

tysm irony

[mellow wren]

🫡

[wicked fractal]

Ah so class field theory is not real

[mellow wren]

🚬

my religion only believes in GL(n) for n>1

[hoary hinge]

What are the best resources to learn undergrad math topics covered in Putnam?

I only have AIME qualification and studied up to Calc 3.

[azure pelican]

Hello, can I get some book recommendations for analytic geometry?

[low thorn]

whats the best book for pre university math

[midnight gulch]

mainly just practice problems from previous years

there's also the book putnam and beyond

[blazing holly]

Openstax + youtube honestly

[normal crystal]

I recommend this book if I can find it🤡

[wicked fractal]

Basic Number Theory:

• "A Classical Introduction to Modern Number Theory" By Ireland and Rosen.
  Read chapters 1 to 5. You can technically do more but I recommend learning the later chapters in other books.
• "A Course in Arithmetic" by Serre.
  This book is short and touches both analytic and algebraic aspects briefly. It goes over quadratic forms if you are into that.

Algebraic number theory:
For this, I mainly used Neukirch as my go to book. It's the classical book. You can also look at Milne's notes. There is also "Number fields" by Marcus which I think is easier to read and it has a lot of exercises too but it does not go into depth.

Analytic Number theory:
The classic go to option here is Apostol's "Analytic Number Theory." It's beginnner friendly compared to what I'm going to recommend after and it focuses on proving the prime number theorem. It also goes over Dirichlet's theorem on arithmetic progression.
If you feel like you liked the log spam flavor of number theory, you can look more into books like Montgomery's "Multiplicative Number theory" or "The Distribution of Prime numbers" by Koukoulopoulos.

Elliptic Curves:
For a gentle introduction, you can look at "Rational Points on Elliptic Curves" by Silverman. If you want to dive into these things seriously then you can look at "The Arithmetic of Elliptic Curves" by Silverman and the sequel to this book.

Modular forms:
If you care about geometric aspects and Galois representations then I highly recommend starting with Diamond and Shurman. For an analytic approach you can look at the sequel to Apostol's book. It goes over Ford circles.

Class field theory:
Technically you can just go with Neukirch but there are other ways to go about this. If you don't know the deal with class field theory then read Cox's "Primes of the form x^2+ny^2." Then you can look at Childress. It's easier to read than many traditional sources. For serious things you can look at Milne's notes or Cassels & Frohlich.

@shell maple

yall mods can we pin this please?

@split portal

[dense blade]

any books good as a first introduction to topology?

[molten gulch]

munkres

[dense blade]

ive got mendelson's already, bit dense ngl

[dense blade]

mmmm ive heard mix things about it tho

like some ppl say they cant decipher the book

still thanks for the recommendation

[rigid trail]

I learned intuitionistic alongside classical

Neither are prerequisite to the other really

I took a course

Idk what good books there are for logic

What area of logic?

I mean like proof theory, model theory, etc

Intuitionistic and other systems are studied in several different contexts

[brisk ridge]

Hi, what book do you recommend for measurement theory?

[molten gulch]

https://measure.axler.net is free, there's also the books by folland, royden, rudin, schilling, etc...

[rigid trail]

Yeah the two main branches in logic are proof theory and model theory

"syntax" and "semantics"

[dense seal]

I would not say this lol

proof theory is basically dead and type theory is puppetting it's corpse

set theory and computability are also big fields of logic that are independent

[peak furnace]

idk if this has been mentioned before but the free download link for dummit and foote's abstract algebra is dead

actually it seems like a lot of the download links on https://mathematics.gg/books are dead or otherwise not working, although i wonder if that's a mobile/data thing?

probably doesnt help that my connection appears to be unstable

[peak furnace]

yeah pi.math.cornell.edu simply wont load for me

not really looking for a book rn just procrastinating ig

[shy pine]

book for general relativity, preferably lots of practice questions and maths-heavy

[fiery bay]

Thanks man i'll save this, That's useful

[somber echo]

Ask in physics server

[shy pine]

I already did

i just want books for the maths that you would use really

that's why i ask here

like, could you recommend some books on PDEs, and differential geometry?I know those are important for GR

[midnight gulch]

well any math book about those topics would go far deeper than what you use in the physics

[tender cobalt]

Lee Smooth Manifolds and Riemannian Manifolds for differential geometry

do you want to learn only for GR?

[shy pine]

not necessarily, i just need it for that atm

[mortal iris]

You can use Rustum Choksi's PDE and O'Neil's Semi-Riemannian Geometry.

Latter expects some background in Topology tho.

[tender cobalt]

I think any beginner GR books cover the necessary math

like schutz, caroll, also misner thorne wheeler goes through it too

[shy pine]

should i get a book tor topology too then 😭

imma have to carry back so many books atp

[shy pine]

okay cool

[mortal iris]

Do you wanna study GR rigorously?

[midnight gulch]

Tu's an introduction to manifolds is similar to lee's book and has an appendix covering the neccessary topology

[mortal iris]

Well. They tend make some casual errors every now and then.

[tender cobalt]

average physicist teaching math \j

[shy pine]

I just want to have enough understanding to where I can listen to someone talk about it and not be super confused

[mortal iris]

Then just get MTW

[shy pine]

okay an appendix is probably good so i can lookup what else to study

[mortal iris]

Don't bother with math texts

[tender cobalt]

is mtw dummit foote of gr

[shy pine]

wdym? i want to know the maths

[midnight gulch]

do you want to know the math for its own sake?

[tender cobalt]

MTW (Misner Thorne Wheeler) will teach you the math you need as you go on for GR

[shy pine]

idk if im making sense 😭

[mortal iris]

But not rigorously right? Cos there's two different games here.

[shy pine]

yes i want to know all of the maths

[tender cobalt]

i think he probably has no idea what hes getting into

[shy pine]

oh okay cool

[mortal iris]

Same

[shy pine]

yeah sorry i don't have any idea 😭

im just curious really

[mortal iris]

Do you know the difference between how mathematicians and physicists tend to approach math?

[shy pine]

idk dude i just want to learn the maths

[mortal iris]

How much physics or math do you even know? Let's start with that

[shy pine]

if there's pre requisite knowledge i can just study those beforehand

[mortal iris]

There's shit tons and it depends on how you wish to approach the subject my lad.

Math done the mathematician way and math done the physicist way can be very different.

Even if conveying the same thing. The methods vary vastly.

[tender cobalt]

||mathematician way: sin x defined from exponential ; physicist way: sin x = x ||

[mortal iris]

In physics you can get away by using empirically obvious arguments. In math, you need proofs for those things.

[shy pine]

what math would you say is required to know, I can tell you if i have/haven't done those rather than listing everything I've ever done?

[tender cobalt]

Just list the general topics you know

[shy pine]

okay then mathematics way

[tender cobalt]

like calculus, ODEs, classical mechanics etc whatever

[shy pine]

uh okay then maybe like ODEs, Linear algebra and Analysis ?? im not entirely sure how that helps as i don't know what's required in the first place and if these are relevant 😭

[mortal iris]

Real Analysis, Point-Set Topology, Linear Algebra, Group Theory, ODEs and PDEs. Finally Differential Geometry.

[shy pine]

thank you ❤️❤️

that's what i needed i think

[midnight gulch]

well you are saying "what math is required". that kind of implies your motivations for learning the math is specifically to be able to understand the physics

[shy pine]

i want to understand the maths to watch YouTube videos about GR physics

😭😭

[midnight gulch]

in that case it would be a waste of time to learn so much stuff, as much of it you wouldn't even use

[shy pine]

???

wtf

i like learning maths

fym waste of time

[midnight gulch]

it depends what your motivations are, like i said

[shy pine]

I don't understand

my motivation is that i enjoy it??

[mortal iris]

From what I can see it's hard to see you like it given how little you know about it.

[shy pine]

im only first year sorry 😭😭

[mortal iris]

Cos it's pretty common knowledge as to how physicists and mathematicians operate differently.

[shy pine]

uh okay

[mortal iris]

Aside from the arcane mathematical physicists such as myself but even we have our differences lol.

[tender cobalt]

...

To watch yt videos u just need to know calculus lmao

[mortal iris]

Not even that lol

[tender cobalt]

Yea XD

[midnight gulch]

yeah then that plan is good, just know that math and physics are two separate disciplines. they have quite a bit of overlap but the focuses of each are very much different

[mortal iris]

Suspension of belief and lack of critical thinking is all you need

[shy pine]

idc im curious about it now

[tender cobalt]

you havent answered what math and physics do you know currently

only then we can help you with a proper roadmap

[shy pine]

???

i already did tho

[tender cobalt]

oh mb didnt see

[mortal iris]

Majoring in math or physics?

[shy pine]

maths

[midnight gulch]

well yeah that clears things up a bit

lol

[mortal iris]

Okay. Then this is good

[tender cobalt]

if u know analysis and linear algebra then u can pick up Tu's intro to manifolds

and learn topology from the appendix as you go

Or you can even go for Lee's topological manifolds for the topology

[midnight gulch]

yeah thats how i learned (am learning) differential geometry, tu is good

[tender cobalt]

i touched tu after calculus 2 and still was able to follow through

LOL

(didnt finish)

[mortal iris]

For GR specifically O'Neil's book is great. You can probably pick it up after learning a bit of topology. Mainly what you need is an understanding of connectedness, compactness and separation axioms. Tbf a lot of this is implicitly taught if you did multivariable analysis properly. That's often good enough to start O'Neil.

[mortal iris]

Consider reviewing Analysis from Zorich for some physics context. Pretty sure you can do O'Neil right after since you already know Linear Algebra.

Although doing some Group Theory can be very helpful beforehand as well. Understanding isometries come very handy when you get to Killing vectors and stuff.

[shy pine]

okay so: Tu's intro to manifolds, O'Niels GR, Analysis from Zorich, Rustum Choksi's PDE and O'Neil's Semi-Riemannian Geometry, Lee Smooth Manifolds and Riemannian Manifolds for differential geometry

is that everything?

[tender cobalt]

if u finish these all u will become goated 🔥

[shy pine]

i did group theory, but it was mainly i think dihedral group and some general core concepts like subgroups isomorphisms and maybe other important stuff

[shy pine]

yes i understand it's a lot of information and will take a while but I like to have something to do

[mortal iris]

Well if you know how to identify symmetry groups in this context you are good to go. In GR we would deal with some Lie Groups is all.

[shy pine]

alright then

[mortal iris]

Which are essentially groups that are also smooth manifolds

[mortal iris]

You don't need to look at Riemannian Geometry to do GR. Doing Semi-Riemannian (for GR) alone is more than fine if you have some experience with Euclidean Geometry. Elements of Riemannian Geometry will pop up by themselves wherever necessary. You can check out prereqs to O'Neil and work through them alone.

[shy pine]

okay noted, I'll get the semi riemannian one

[tidal hare]

Anybody got recs for History, Psychology, Law, etc. Non-fiction books?

[short fable]

What do you want to learn

[sick river]

nature of existence by mctaggart

[tidal hare]

Anything ig, the book should be interesting and recreational but also informative. If the book regards law or history then it's optimal that the history refers to Europe or the law mentioned is regarding Britain.

[short fable]

Any interest in rich people?
https://press.princeton.edu/books/hardcover/9780691215730/as-gods-among-men

[tidal hare]

Ooh, that looks interesting

[odd cargo]

if you're in university, just sign up for classes relevant to physics

[shy pine]

I don't have very many physics modules though?

[odd cargo]

I dont mean fluid dynamics or stuff like that

i mean modules like diff geometry

[shy pine]

lemme see

[odd cargo]

functional analysis and topology, all relevant as well

tensor calculus is probably mandatory for you guys

[shy pine]

i don't think there's diff geometry module that i can see

[odd cargo]

Differential geometry?

[shy pine]

there's this one

[odd cargo]

Are you looking at first year modules only?

[shy pine]

that's 2nd yr lemme look at 3rd

oh wait that's the sams

idk

[odd cargo]

The title should literally be "Differential geometry" with an added curves and surfaces probably

[odd cargo]

this is differential geometry

[shy pine]

there's no title of that

😭

[shy pine]

hmm okay

idk if i want to do it as a module tho

I'd rather do a different module and just self-study diff geometry

[odd cargo]

Most of the math you need for physics you already take in first year tbf

like probability and physics, ODE's and what not

[odd cargo]

up to you

[shy pine]

first year of maths?

[odd cargo]

First year in university

if you're doing a course in maths

[shy pine]

oh okay just generally

i wanna do all the units but they don't let u 😭

[odd cargo]

a lot arent worth wasting time on tbh

differential geometry would be a module i would sign up for, regardless if i have an interest in physics or not

[shy pine]

huh? but they look interesting?

[odd cargo]

real interesting stuff there.

[shy pine]

i mean 80% looks interesting to me

[odd cargo]

Do the differential geometry module

or sign up for it

[shy pine]

I can't yet

it's 2nd yr

[odd cargo]

i know, just dont forget when the time comes

i lowkey should be doing maths rn

[shy pine]

hmm I'll make a list i suppose

[limber saffron]

Is there anyone studying Sigma injective modules ?

[runic rover]

Any books or free resources for basic physics

[mortal iris]

How basic?

[covert vector]

free resources : openstax university physics is decent

[short fable]

There is https://lightandmatter.com/books.html
Can't speak about the quality though

[lost arch]

hey guys, a couple of questions:

1. what are the prereqs for differential geometry?
2. are manifolds regarded as something that needs special, separate study from diffgeo? are they supposed to be learned before or after diffgeo? what the relation between them in general?
3. is riemannian geometry a subset of differential geometry? or is it just ''advanced'' diff geo (ive seen people say that somewhere)?

[long laurel]

ive really gotten into philosophy lately and ive always loved math. usually philosophy courses offer math courses with the two go hand in hand. does anyone have a good recommendation of a book that does this?

[lost arch]

into philosophy of which kind?

[long laurel]

i guess in this context it doesnt really matter. i just want to see how both the subjects are presented together as an argument

[lost arch]

it matters to understand the nature of the interplay between them that you were presumably seeking, but if you just want a book with ''philosophy'' and ''mathematics'' put together in the title, there's a nice book by Linnebo,''Philosophy of Mathematics''

again, idk what exactly you are looking for. a remark: Linnebo's book is about intuitionism, empiricism, nominalism and other ways to think about math foundations (also usually called ''philosophy of mathematics'')

i guess it would be hard to find a book that connects whats usually understood by philosophy (Heidegger, Plato, Nietzsche, Bergson and whatnot) and mathematics

[radiant ingot]

Moby dick?

[lost arch]

dick, exactly

[long laurel]

but obviously the nature of the philosophy would be argued using two perspectives: mathematics and philosophy

that would explain it

thanks!! ill check these out

[lost arch]

<@&268886789983436800>

yeah nvm

[long laurel]

what was rhat

[lost arch]

scam attempt

[long laurel]

are we allowed to talk here

i was going to ask about your ug math degree

[lost arch]

just dont pay attention to this kind of messages

[lost arch]

i dont have one

[long laurel]

will do

[long laurel]

you have the role

oh sorry i guess you dont have the degree yet

[lost arch]

yes, im studying math at the undergraduate level

[long laurel]

oops

how is that going

[lost arch]

not that good since im not a math major, i study various liberal arts (formally), besides people would be angry we're talking in the channel meant for talking about books

[long laurel]

thats why i asked this

[lost arch]

btw if anyone would be so kind to reply id be very grateful

[tender cobalt]

1. Multivariable analysis (analysis in R^n) and linear algebra if you want to learn diff geo of curves and surfaces, also you need some pointset topology if you do manifolds
2. You can learn elementary diff geo of curves and surfaces in R^3 or R^n, and then there's diff geo of manifolds which work with different spaces than R^n. Both are part of diff geo as a whole, not separate. Usually people learn diff geo of curves and surfaces, and then move on to manifolds.
3. Riemannian geometry is differential geometry on smooth manifolds, and yes it is much more advanced than your differential geometry of curves and surfaces

[lost arch]

thanks!!

[tender cobalt]

the general roadmap is diff geo of curves and surfaces -> some topology and smooth manifolds theory -> riemmanian geometry

[molten gulch]

I mean you can kinda skip the C&S stuff and just do topo -> snooth manifold theory

[tender cobalt]

True

Also yeah you can skip curves and surfaces diff geo entirely and start with topology and manifolds

[indigo blade]

so i found this for recommendations for mathematical logic
https://www.logicmatters.net/tyl/

[wicked fractal]

No problem. Happy to help

[gray gazelle]

Ya it’s quite nice

btw

Peter Smith was convicted of downloading cp 😭

It’s a good book regardless

[odd cargo]

how do you know this information

never mind just read a reddit post on him

cambridge is on some bullshit

[leaden hearth]

bruh

damn it

[somber echo]

Read about the author kindly

.

Somebody recommended priest's intro into logic instead cuz it's cool

[signal zenith]

To clarify it isn’t Priest who is in that article

But Smith

[somber shore]

Chat I want to learn poly-dimensional geometry, what's a good book? I've studied physics-based mathematics up to some basic functional analysis and measure theory (primarily for QM)

[mortal iris]

1. Real Analysis, Point Set Topology, Analysis on Manifolds and Linear Algebra are the pre-requisites. Group Theory is a useful addition.

2. One usually can (and some do) study Topological Manifolds before getting into Differential Geometry which mostly deals with Topological Manifolds with Differentiable Structure. The former isn't entirely necessary to do as a prereq tho.

3. Riemannian Geometry is essentially the study of Smooth Manifolds with a Riemannian metric (a generalisation of the notion of distance). It's pretty much where one gets all the usual ideas about curves, surfaces, areas and volumes in physical space.

Typically Riemannian Geometry is a lot easier to motivate than general Differential Geometry (which also includes things like Semi-Riemannian Geometry and other weird things) which in turn is easier to motivate than a general study of Topological Manifolds. That said, elements of both are used implicitly when one gets introduced to Riemannian Geometry.

[lost arch]

thanks for such a detailed answer, comrade

[somber shore]

Privet comrade 🇷🇺

[mortal iris]

Nws. Imho, if I were to study geometry from scratch, I'd go, Euclidean Geometry -> Riemannian Geometry -> Topological Manifolds -> Semi-Riemannian Geometry -> Algebraic Geometry.

[lost arch]

zdravstvuy

[lost arch]

semi-riemannian geometry being a necessary step??

tbh im hearing about it for the first time now

btw, do you know any good books on euclidean geometry? ive seen a couple but they seem incomplete and are mostly about affine spaces

[mortal iris]

Not really a necessity. But it is rather well developed thanks to GR and shows you how one can play around with the metric a little to get drastically different results. Consider it more of a very useful physics-inspired detour.

[mortal iris]

Lee's Axiomatic Geometry is solid.

[molten gulch]

Loney's plane trig is fine

[ivory swift]

ngl im afraid of old books

I'll check it tho, thank you

[molten gulch]

you can't copyright a proof

[normal crystal]

Math Sorcerer ai'ed a Guide To Proofs, huh

[proud osprey]

What if the proof uses an illegal number

As in here: https://en.wikipedia.org/wiki/Illegal_number

[desert wraith]

Any good introduction to linear algebra and analitic geometry books? They can be seperate books but still a bit beginer friendly

[rigid trail]

That's common

[molten gulch]

friedberg insel and spence

[cerulean thicket]

@rigid trail
One, nice Bocchi pfp
Two, welcome to Mathcord :D

[rigid trail]

Hi, thanks!

I'm not that new to this server but I recently rejoined

[cerulean thicket]

In that case, welcome back :D

[rigid trail]

[mighty tartan]

qiu back again

how many returns is that now

at least half a dozen

[rigid trail]

Probably around that

[fickle dock]

cheap books to ask for for my birthday? i'm thinking a book on a topic that i'd otherwise never see in my education that is still accessible at my level. or something that goes deeper into a topic i already know in some interesting way. rn i know all of hs math (although my knowledge is kinda rusty and it was not taught rigorously) and calc 1/2 but also not in a rigorous way more just computational. i have some understanding of formal logic and mathematical structures but not proofs yet

so like idk maybe something on math history or recreational mathematics? need ideas

[rigid trail]

are you interested in math history? interested in higher math?

[midnight gulch]

a book like fearless symmetry comes to mind

or those author's other book "elliptic tales"

it doesn't require much if any mathematical experience but those introduce some interesting concepts in number theory and algebra

another book i read somewhat recently was sabbagh's the riemann hypothesis

[ember lark]

Watch zundamons theorem for Free

[dense blade]

https://youtu.be/UjurXfCNikc?si=tNe871sSmQtoomo_

[daring relic]

I chose (c) 1968 George B. Thomas' Calculus to tutor calculus online. I am not a fan of modern publishers pushing overly chatty asides in math textbooks.

[remote sparrow]

what about one or two expensive books?

for example, spivak's calculus would work quite well

[deep berry]

A lot of advanced mathematics books you can get way cheaper by just looking for used previous editions.

[remote sparrow]

yeah sure

[vital bane]

Understanding Analysis by Stephen Abbott

Or Algebraic Geometry by Robin Hartshorne

either would work (jk 2nd one wouldn't)

[fickle dock]

i was looking into those. do you have any reccomendations from them there's so many idk what to choose lmao

[midnight gulch]

what topics would you find interesting

[fickle dock]

i'm not sure i only recently got interested in math so ig jus anything

[vital chasm]

Counterexamples in Analysis and Counterexamples in Topology is an interesting read

Though in some sense more like a reference

[gray gazelle]

mind u

he also had sss intercourse with prostitutes

[cerulean thicket]

Hello

[gray gazelle]

https://www.dailymail.co.uk/columnists/article-259746/Return-dirty-don-.html

mathematicians/philosophers trying not to do something creepy/weird

yeah compared to philosophers 😂

especially those ones in the 19th century

[midnight gulch]

i also realized just today that the guy who wrote this book was convicted of a similar thing as well

that case was even worse it seems

[pearl copper]

Atomic habits

[gray gazelle]

nah spinoza’s ethics is clearly better

ts frying me 🫩

[wicked fractal]

https://bookstore.ams.org/view?ProductCode=GSM/79

This should fit the requirements that you stated. It's computational and it's something very interesting which is never taught in high school

[daring wolf]

https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/pubtexts.php

https://cdn.discordapp.com/emojis/1438162508908331089.webp?size=48&animated=true&name=pinkNODDERS&lossless=true

great historical work on algebraic geometry in 1950-1960s

don't buy it, or try to read it

[mortal iris]

Plofker's Mathematics in India is a good math history text that you'd otherwise not hear of.

[tender cobalt]

@mortal iris what is prob stats about and why should we care?

[remote sparrow]

🎰

gambling games of chance are a pretty obvious way to motivate probability and statistics

also, the idea of quantifying the likelihood of future events is another compelling reason to care

[tender cobalt]

ooo

what does statistics help us in

idk any application other than machine learning

[remote sparrow]

...like clinical trials?

or google biostats

quality assurance at factories depends on some knowledge of stats, since you can't feasibly test all products, but only a sample

[odd cargo]

practically every aspect of biomedical research is hypothesis testing.

[short fable]

I think his question is how basic statistics is useful

Advanced statistics is indeed used in machine learning and econometrics

I think a big point to make here is that something that is mathematically advanced does not make it immediately more useful

And basic statistics on treatment, etc. are still being relied on

[odd cargo]

figuring out the p-value of two given means is not "advanced statistics"

[short fable]

Machine learning is not p-value.

[short fable]

The asker clearly doesn't place a lot of value in this basic stuff too

[odd cargo]

its all fucking statistics, isnt it?

i hate people who say stupid ass shit

[sand urchin]

anyway for recreational stats maybe check out the lady tasting tea

[mortal iris]

Why ping me here for this lol. The entire world runs on stats. That's enough to care.

[odd cargo]

i despise statistics man, i really do.

[mortal iris]

Why? It's beautiful

[odd cargo]

im just being reactionary

if you grew up calculating alot of statistics by hand, you'll hate it, and if you dont, you're probably a masochist

[mortal iris]

Thermodynamics. Economics. Psychology. Information theory, both classical and quantum. Quantum physics. Diagnostic medicine. Image recognition. Computer vision. So many things.

Not all of them require machine learning but all of these do benefit from it regardless.

Heck even education and politics.

Percentiles and polls and what not

Stats are everywhere. Sports ofc.

[mortal iris]

If you calculate a lot of statistics by hand then you have too many fingers

[odd cargo]

did your school not teach you how to calculate the mean, standard error of the mean, or standard deviations?

and also, being someone who does biomedical research, a rigorous definition for a lot of the statistical tests we are expected to do will hardly be found.

we dont get classes in statistics, unless i actively try and sign up for one

[olive grotto]

Hello guys, if you don't mind I would appreciate books recommendations for STEM subjects, mostly physics, math, bio and chem. I have poor knowledge so maybe something beginner-friendly

[plush marten]

Hi, I'm here to ask for book recommendations, kinda like Veratisium's videos, where they talk about the story of how they proved different formulas or explain the purpose of using a specific area of fields. I'd like to learn math with stories or historic backgrounds, if possible.

[mortal iris]

Yes and I never did them by hand. Refused to even for an exam. I know how to if needed but that need comes only in the event of an apocalypse lol.

[mortal iris]

Hi, I'm here to ask for book recommendations, kinda like Veratisium's videos,

So you want to be bullshat while making things sound cool as opposed to correct?

[short fable]

calc the mean is by .mean

[wicked fractal]

You can check out Keith Conrad's expository papers or John Baez.

[mortal iris]

I'm not sure they'd understand them if they're watching Veritasium without being alarmed by some of the casual errors made by that channel.

[wicked fractal]

Yes that's the point. I want them to get into these things properly and stop watching Veritasium for math content

I think it was an alright channel till they uploaded their p adic video and I was pissed

[mortal iris]

This one is valid

[mortal iris]

This is a book you can try out

[wicked fractal]

Something I found frustrating about TAing Indian students is they worship JEE way too much and I think it's damaging their mathematical reasoning abilities

I yet have to see something good coming out of JEE

[short fable]

With international exposure I think that worship fades

Or at least, that's the best possible way

If that worship doesn't fade after internationalisation, it's difficult to say

[mortal iris]

You won't. Imagine being given Olympiad level problems to solve with a minute for each. There's no way to be good at this without being mechanical and devoid of reasoning.

[odd cargo]

every time i see that exam brought up, its always in a negative light

how bad is that exam

[mortal iris]

And some of the problems regardless of level are just in poor taste.

[short fable]

They're not really that hard

[mortal iris]

Very. There are some cool problems occasionally but overall it's poorly designed and intended to do everything but support education or test genuine skills.

[wicked fractal]

From my experience it doesn't fade away. There's some god awful toxic mentality around that exam. Apparently you get "humbled" or if you did good then you're gifted or something and I'm just like ????????

If anything there are better ways to get yourself humbled

[odd cargo]

is it an entrance exam into university-level engineering sciences or just some bullshit

[mortal iris]

Just take an analysis course in high school. Most of these shits who think they can do Calculus well because they do unreasonable integrals will be left in dread.

[mortal iris]

Both

Gaokao, yes. JEE is not a cultural thing. It's a money thing.

The exam was not as bad as it is today as opposed to like 30 years ago.

[odd cargo]

ill be honest, one exam dictating your future prospects in maths, engineering or physics sounds a little too crazy

[mortal iris]

Privatising education and outsourcing training to coaching centers who make a fortune by strategising the exam while killing the subject.

[wicked fractal]

And the worst thing it's an Olympiad type of exam

[mortal iris]

And in India it's bad considering they are the sole entry point into the elite universities by name, the so called IITs.

They're just as trashy as your average university here for the most part.

With the exception of a handful of IITs

[odd cargo]

shouldnt be too difficult then, no?

[mortal iris]

But one could honestly get in with full scholarships to far better institutions if they had the agency to look.

[odd cargo]

still stupid though

[mortal iris]

One minute per problem on average

[odd cargo]

hell nah

[mortal iris]

Including both physics and math, let alone the chemistry stuff

[fickle brook]

Yes

[odd cargo]

@mortal iris did you do the exam?

[mortal iris]

It's not like that in India. It's just that under social and peer pressure due to the big name carried by these IITs (think Ivy League level of fame but worse both in quality and due to high demand), the students don't have a chance to even explore their options. The teachers here also don't know any better. They're arguably stupider than the students.

[mortal iris]

I was preparing for it for a while but then I quit. Did give the first part of the exams which are relatively reasonable. Despite qualifying for the advanced exam I decided to not appear.

[wicked fractal]

Based

[odd cargo]

Do these IIT's guarantee jobs?

cuz if so then im not shocked

[mortal iris]

Hell no. But very high suicide rates are guaranteed.

[odd cargo]

interesting how this is a classical symptom of a lot of modern day prestigious univeristies

cambridge as well, though a lot of reforms were introduced

[plush marten]

like I want to learn the story of how they got there & proved it (learning advanced maths throughout too)

[mortal iris]

Tbf for IITs at the very least, a big part of the suicide rate is the stunted social development of the kids who work their nuts off to get in. They don't know how to deal with anything but the adversity of studying for exams.

[tired drum]

Hey , guys any good book for Combinatorics?

[odd cargo]

Combinatorics (A Problem Based Approach) by P. Mladenovic, nice book.

[mortal iris]

Some kids are put in coaching institutes as early as 4th grade.

[short fable]

No, but they are also the only way in to prestigious jobs (apart from international top unis)

[mortal iris]

Not true.

[odd cargo]

the fuck...

[tired drum]

thanks

[short fable]

Not entirely true, but very true in a high statistical sense

[mortal iris]

There's also a city in India called Kota in Rajasthan which is literally a coaching center on its own.