book-recommendations

[molten gulch]

if you want rigour, try spivak, apostol, or abbott's understanding analysis

[remote sparrow]

grimmett and stirzaker has a solutions manual

[past dust]

After spivak then abbott what would be the next step?

[molten gulch]

folland or axler or royden or whatever for measure theory

[sharp goblet]

hi, what are good resources for counterexamples?

[pine tundra]

I don't think there are 😅

[normal crystal]

there are books on counterexamples for specific topics

[sharp goblet]

I just found mainly on analysis, I'm not sure about other topics

[full cairn]

Counterexamples in topology: https://link.springer.com/book/10.1007/978-1-4612-6290-9

[normal crystal]

you can just search Amazon or whatever

[sharp goblet]

thanks

[ivory tundra]

WOAHH

[full cairn]

I'm still looking for the elusive book on counterexamples in finite dimensional linear algebra

[normal crystal]

<@&268886789983436800>

[past dust]

Never heard of measure theory what’s that ? Shouldn’t after abbott be a real analysis book like pugh?

[molten gulch]

no, because they cover basically the same core material for single variable analysis

measure theory is integration

[molten gulch]

Do such even exist?

[gusty star]

🧐can directly start real analysis if i know Limits , continuity and Differentiation, Application of derivatives ,integration, Application of integration, Differntial equations

[molten gulch]

yes

[past dust]

So should i do something like this ?
Thomas calculus -> Spivak Calculus -> Abott’s understand analysis -> Measure theory

I’m not a math major but would like to do it as a hobby

Topology stuff seems cool

[molten gulch]

Thomas Calculus OR Spivak -> Abbott -> MT

[gusty star]

Which thomas calculus you going to use ?

[molten gulch]

early or late transcendentals it's fine

[past dust]

Early transcendental

[gusty star]

Picture one ?

I feel it useless

I like non picture one

[molten gulch]

there is no "non picture" thomas calculus text

unless you want to go dig some ultra old edition, even then it probably has pictures

[past dust]

Why thomas or spivak ? Spivak is rigorous while thomas application based so wouldn’t they complement each other ?

[molten gulch]

most undergrad maths books have pictures

[molten gulch]

because they both cover the same material

[gusty star]

If someone already study thomas why to study spivak again why not jump on analysis

[past dust]

Alright is there a roadmap of what to do study for non math majors interested? Like what to do after measure theory and all that

[full cairn]

yes, fin dim vector spaces are very poorly behaved, so such a book could be 1000s of pages

[molten gulch]

You could do functional analysis, you can also do complex analysis after real analysis, you can do algebra and linear algebra, etc... bunch of directions you can do, some you can start much ealier than others. You can also do topology after RA and get into diff geo, etc...

lots of ways to go

There's no such thing as a mathematics roadmap beyond like "you should know some analysis and algebra"

and "do measure theory after real, do commutative alg only after you've solidfied some other bits of algebra etc..."

[tender river]

spivak to abbott would be pointless, spivak to spivak Calculus on Manifolds (or a likewise multivar book) or rudin (or a likewise book) before folland would be a better choice

[valid spire]

Any good book recommendations for a first year maths student?

[humble kiln]

hi i recently got done with a probability and statistics course, and i did learn a lot and got a decent grade (B) but i feel like i would benefit from a deeper and more thorough understanding since near the end of the course i survived off of just method memorizing, what are the gold standard textbooks for probability and statistics, the course didn't have a textbook which is why I'm asking here

[tender river]

what courses do you take in the first year

[remote sparrow]

you can read measure theory or you could do multivariable analysis, complex analysis, fourier analysis with the riemann integral, or really any topic that assumes only a basic real analysis background. it could be nice to read carothers and rudin after spivak.

[past dust]

Would abbott understanding analysis be enough for real analysis ?

[molten gulch]

yes

[past dust]

How long would abbott take for 2 hrs everyday ? It’s 300 pages would it take much?

[past dust]

The amount of options is astonishing lol

[molten gulch]

no it's not

[past dust]

I mean it’s ok compared to what i was doing before pretty strict

This and then this nothing else

[vagrant oak]

Yeah and the one thousand exercise book. I think I'll definitely be using it

[remote sparrow]

the one thousand exercise book is the solutions manual

[vagrant oak]

Oh... I thought that was a separate thing but that makes way more sense lol

[cursive rivet]

it will probably take a bit longer than that, but when I did a similar thing years ago to learn RA, I got through it in 1 summer of every night, rereading the section I read the night before, doing some exercises from that section, then reading the next section, and repeating.

[vital bane]

How are fin dim VS poorly behaved? they're one of the nicest objects

[vital bane]

#1059828221887135774

[vital bane]

How did you find a picture of me!??!

[fresh skiff]

The legendary arc

[past dust]

Are you done with your arc now ?

[outer helm]

do u have any references for representation theory other than Serre's book?

[remote sparrow]

i heard fulton-harris and lorenz are good

[outer helm]

alright thanks

[past dust]

Where should i put graph theory in my studies ? Would it be after single var calc or what
And what books ? I’ve heard west graph theory is good

[remote sparrow]

this is also a dover book btw

you'd be saving money

[grim ore]

Im lost at what you are asking for?

I feel like you should finish the calculus sequence before touching proof based maths regardless

[past dust]

I’m asking after which course would it be natural to do graph theory

[grim ore]

Is it proof based?

[past dust]

Yes

[grim ore]

After calculus i-iii sequence, linear algebra definitely, and an intro to proofs class

That would be reasonable after that point

[true sail]

Could anyone recommend me a free "data structures" book? There's a wikibook on data structures, which I already saw, I would like another another, freely available book

[full cairn]

https://opendatastructures.org/ and https://donsheehy.github.io/datastructures/ are free. Haven't read them myself, but they're listed as recommended background on https://jeffe.cs.illinois.edu/teaching/algorithms/

[limpid fern]

Book recommendations for someone trying to learn precalc/calc? My last math class was precalc in HS. I can barely remember the Unit circle and the quadratic equation

[true sail]

Thank you!

[bronze crater]

any book recomendation for graphic programming?

also, https://www.realtimerendering.com/ this what i want to read

an idk if i really capable right now to read it

[glacial leaf]

I really liked "calculus I for dummies"

it's not a rigorous treatment, but its good enough for self-studying

[rain nova]

I took a class with Jeff Erickson and definitely would recommend his book. It explains concepts really nicely

[remote sparrow]

nielsen and chuang?

[normal crystal]

challenge accepted🤡

[past dust]

What book is good for proof writing ? I’ve heard book of proof by richard hammack is a good one

[errant adder]

yall, i need a book to learn about transformers like jacobians and stuff. any recommendations?

[remote sparrow]

that book is fine

[remote sparrow]

transformers?

https://tenor.com/view/optimus-prime-griddy-fortnite-fortnite-dance-gif-10671681376985389771

[past dust]

I should do it before analysis right ? I also heard j cumming one too

[vital chasm]

Instead of a book, 3blue1brown's series probably gives you a better understanding of jacobians, i doubt you can find a book on just jacobians

[remote sparrow]

try mimicking some proofs in your analysis book first to see if you can do without it, but i did a proof-writing course before so no sweat

[mortal ore]

That's what discrete is at most colleges

I think they call it discrete bc u learn about countable sets as well

[past dust]

How is the combination of linear algebra done right and strang linear algebra and it’s applications

[pulsar palm]

I like “Who Moved my Cheese”

[brazen oyster]

calculus so ez

integration

[marsh ingot]

Try Real Analysis then

[thorn hinge]

Has anyone studied climate models via lyapunov functions? I will have to do a seminar on the topic for a course and I'm searching for references

[brave pebble]

hows algebra notes from the underground by aluffi

[pale geode]

I like the who shat on my head book

[analog blade]

Yoo

What's a good linear algebra book

[sturdy shore]

haven't used the book but I'm a fan of how he orders topics and his writing is quite lucid

also didn't realize he has some exercise solutions at the back until now, another plus

[rose lotus]

have an idea of where i should start as a sophomore who just got out of algebra 1 looking to learn the needed material for like calculus or linear algebra? rn the most i got is limited knowledge on reduced row euchulan form and how to do polar coordinates i know like quadratics and all that already?

[plush rain]

make sure you understand the curriculum for pre-calculus and algebra ii, you can refer to khan academy for a list of topics

[rose lotus]

alright thanks

is calculus itself hard ? i understand the idea of integrating from a to b but not indefinite integrals. i also understand that polar coordinates are used to make it easier to integrate for some shapes i forgot

derivates are the rate of change at a given point and integrating is the area under a given curve? i’ve never seen someone integrate a function in the negative y values (quadrant 3 and 4)

i read that when i was trying to understand what analysis was lol. i guess calculus lets you understand things in lower levels of math like deriving the area of a circle, and i’m assuming analysis lets you understand and maybe derive calculus formulas i really don’t know though

ohh

i never really thought about why i just like thought its logic to be able to use infinitely small rectangles and an infinite amount

like it just makes sense to be able to do that yk i never really understood that there’s a whole topic about the why

i understand that

you’re in college i’m assuming lol. i really like math and like the whole understanding and just all of it. except geometry

[dim pendant]

Dos anyone have any significant critiques of Apostol's book on analytic number theory? I'm looking to give math one more try before I quit for good and start getting rid of my collection.

[slender wasp]

I'm doing it currently (finished Chap 4) and I love it. I tried Stopple before (did half and quit) and Apostol is so much better. Although, I'm partial to Apostol's writing style (I liked his two Calc books and half of Analysis book as well). I was stuck in Chap 2 for a bit, then realized I just needed to go a bit slower than I was expecting, and I'm really liking it now.

[dim pendant]

Appreciate the review in progress

[remote sparrow]

quit math now so i can purchase all your books

[wicked fractal]

Apostol was my first number theory book. I read all chapters.
The author is an excellent writer. His writing is clear and concise. The book starts from ground zero starting from divisibility. Ideally you want to have a basic understanding of concepts in complex analysis. It covers:

1. Divisibility
2. Modular arithmetic
3. Primitive characters
4. Quadratic reciprocity
5. Arithmetic functions such as Mobius, Euler totient, Mangoldt etc
6. Dirichlet convolution
7. Dirichlet characters and Gauss sums
8. Dirichlet's theorem on primes in arithmetic progression
9. Dirichlet series, L-functions and the Gamma function.
10. The prime number theorem
11. Partitions (Jacobi triple product)
    Compared to other books like Montgomery & Vaughan, it's fairly lenient. You can read the next book to read more about the partition theory. It goes over modular forms.
    Overall, definitely would recommend it to anyone starting NT

[dim pendant]

Appreciated, mate. Glad you enjoyed it! Although I'm not surprised :P

[static vortex]

Anyone have any books that are non math related they would recommend?

Maybe something you can learn from or philsophical/futurist sort of ideas

[vernal tinsel]

Maybe pin?

[timid lion]

testo junkie

[eternal canopy]

hi guys I’m a high school student with a lot of free time, so I decided I’ll study a lot of math. I wanted to start off w the basics, how do you guys recommend something like Discrete Mathematics with Applications by Susanna Epp?

[solemn rover]

sounds fine to me

i recommend looking at the introduction to see how the author assesses the prerequisites

[steel cloud]

i want to learn category, which textbook will be good ?

[vital chasm]

Basic Category Theory by Leinster is very approachable

[daring wolf]

mac lane
emily riehl

[steel cloud]

okay

[steel cloud]

okay

[tiny gulch]

:D

I would recommend Leinster

Also Bartosz Milewski’s series

[steel cloud]

okay i will look at it

[ember slate]

Did anyone use tao's LA notes over just the book by insel?

He seems to use the book for exercises

I don't know if i should just read the book or just use his notes

[fast warren]

Yoh

Any recommendations for calculus books for engineering

[outer helm]

Récoltes et Semailles from Grothendieck but idk if there is an english version

[vital chasm]

fiction wise, Unsong is an interesting and funny read

web novel

chapter 1 is literally called "Dark Satanic Mills"

its hilarious

[tardy geyser]

Hi, I'm a freshman in high school and I'd like to start studying for the Mathematical Olympiad in my country. I'd like to start studying with algebra and number theory. Can you recommend any books I could use, as well as others in general, e.g., combinatorics, because for geometry I already have Euclidean Geometry?

[indigo thistle]

Friends, are there any YouTube playlists, books or lessons on the concept of trigonometric limits? If there is, please share it with me 🙏

[molten gulch]

organic chemistry tutor's algebra and precalculus playlists

[indigo thistle]

thank you very muchhh

[violet shuttle]

baby rudin

[jovial tree]

watch it on 1.5x cuz he is a slow talker😭

[distant moon]

a baby this?

https://static.wikia.nocookie.net/deltarune/images/c/c7/Rudinn_battle.gif/revision/latest/scale-to-width/360?cb=20201231213259

[eternal canopy]

Sure, thanks

[tiny gulch]

yessssss

[dark hull]

Hey I’m soon to start UG maths at imperial, any tips for books or yt videos I can engage with to get ahead of my course? (Preferably stuff that I’ll be able to understand with A level maths and FM knowledge)

Thanksss

I can tell u the first one is called intro to uni maths

I don’t remember the order of the others

[tiny gulch]

congrats for imperial! heard good things about it

[dark hull]

If they do I haven’t been able to find it

I’m on my phone rn I’ll have another look later

Okay thanksss

[dark hull]

Yeah I’m looking forward to it

Heard they have a year programme at MIT for one lucky student

Bet I’ll have a look

[tiny gulch]

-# not sure i'd call that "lucky" in this political climate

[dark hull]

Ha maybe not

Watch me get deported if I get it

[tiny gulch]

[tribal crow]

@dark hull welcome to the mathcord, and congrats on getting into Imperial!

[dark hull]

Thank youu

[sly jolt]

if you fared well at A level FM, the only totally new thing in first year imperial is analysis and algebra

if you're a pretty good mathematician then after FM rudin's principles of mathematical analysis shouldn't be that far out of your grasp

[dark hull]

Yeah I did well, I did FP1 and FM1 edexcel tho so I could be missing out on some useful prerequisite knowledge in other modules

[dark hull]

I’ll be sure to check it out

[sly jolt]

remind me how the system works in england, does this mean you did no further stats?

it's different in wales and even that was years ago lol

[dark hull]

Further pure and mechanics

[sly jolt]

maybe take a look at further stats then

probability and stats is a first year module at imperial if i remember rightly

[dark hull]

We have FP, FM, FS and D which each have 1 and 2

[dark hull]

Obvs u can’t do 2 if u didn’t also do 1

[dark hull]

(Further pure, mech, stats, decision/discreet)

U pick 2 on top of core pure modules

[dark hull]

Stats 🥀

[sly jolt]

I hated stats too until i started doing AI

it all made sense then

[dark hull]

The stats in regular maths never made any real sense to me

It just feels like a little bit of a pseudoscience

Made up if ygm

[sly jolt]

because it is

before rigorous stats, it's all just 'confidence intervals are at 95% because uhh umm well uhhh they are' and so on

uni level stats is slightly more interesting though but still just feels a bit hand wavy unless you go quite far with it (a stats focused degree)

[dark hull]

Yeah but I suppose I’d better get used to stats bc if I want to go into big money jobs it’ll be a big part of that

[sly jolt]

tbh the stats for most jobs is actually fairly easy

[dark hull]

Pure is my baby but I think some stats modules will probs set me up nicely if I wanna be a quant or smth

[sly jolt]

yeah if you're good at pure you'll be fine. even the stats modules in your degree will attack it from a pure maths perspective with justification for most things (as much as is possible)

[dark hull]

Okay that’s reassuring

[sly jolt]

i remember in first year stats we hadn't yet covered enough calculus to prove everything so there were some components that was like "this is true because it is just dont worry about it"

but not much

i didn't go imperial but a similar quality uni

[dark hull]

Can I guess

[dark hull]

Also what calculus is it worth learning before so that stuff like this will make more sense to me

[sly jolt]

just have a good grasp of integration

[dark hull]

I’ve done some reduction formulae and feynmans technique but other than that I haven’t gone beyond what I learned at A level

[sly jolt]

general advice for the first year or 2 of your degree, spam integrals as much as you can with as many methods as you can

because they'll be everywhere

[dark hull]

Not a problem, integration is my fav

[sly jolt]

linear algebra will be your only module that doesn't have integration haha

[dark hull]

Yeah might need to top up on my linear algebra tbh

Is it worth learning eigenshit before I start my course?

[sly jolt]

i found linear algebra very easy, some people find it very hard

[dark hull]

I’ll be honest it was one of my least fav bits of FM

[sly jolt]

it's more abstract than calculus in so far as you'll get vector spaces and general algebraic concepts for the first time

which throws off quite a few people

[dapper root]

Memes that 1 person relates to

[short cobalt]

Has anyone here read shadow slave

[tough shadow]

that sounds familiar

[violet hound]

hello I need help I finally decided to do something with my life and now im starting college in 2weeks but I forgot most of the math i learned in Hs. Ive been trying to relearn using Paul's online notes and the occasional khanacademy lesson but ngl ive been struggling anybody good books or resources I can use i start in like 2 weeks in ive already resigned myself to playing catch up for my first semester or so any advice for a local idiot

[analog blade]

Hi

Who's the idiot?

Focus on Algebra during those two weeks

and pick up on the basics of trig

I have a book somewhere

https://www.govst.edu/uploadedFiles/Academics/Colleges_and_Programs/CAS/Trigonometry_Short_Course_Tutorial_Lauren_Johnson.pdf

[ionic arch]

hii

[coarse condor]

Im a indian kid going to college to study engineering . BUT I WANA STUDY

Algebric typology

Book recc

Plej

[frozen perch]

Hatcher is free!

And also one of the standard texts

[ember slate]

Is there a proof based mit ocw linear algebra course?

[cunning elk]

https://ocw.mit.edu/courses/18-700-linear-algebra-fall-2013/

this literally took 5 seconds to find on the website...

[molten gulch]

Hatcher, assuming you know some point set topo

[novel shoal]

did this course https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/ with a lot of exercices from simmon's calculus book, should i go into calculus spivak or understand analysis Stephen Abbott?

thx 🙂

[upper estuary]

Abbott is amazing!!!! But it may be a good idea to pick up both books and switch back and forth between them when you get stuck

(which is what i do and it's been working out pretty well)

[novel shoal]

so maybe i should read and use them both in the same time ?

[vast jackal]

do elementary algebra by hall and knight and higher and then some trig, you can do the calculus by khan academy

[verbal phoenix]

has anyone read stillwell's geometry of surfaces? what sort of level was it, im aiming to be reading like year 1/year 2 undergrad so i dont want to be reading stuff that actually requires a bunch of prerequisites from later in a maths degree

[grave lintel]

if you know single variable calculus already, you could probably go into understanding analysis, although some things will feel slightly less motivated without knowing multivariable calc

[topaz breach]

Hello, I would like to ask for a topology problem book recommendation, the closest thing I came across that was somewhat reliable is Big List - MAT327, I am asking if there are actual books with good problems.

[remote sparrow]

https://www.ams.org/bookstore-getitem/item=mbk-54

https://www.amazon.com/General-Topology-Dover-Books-Mathematics/dp/0486434796

https://www.amazon.com/Introduction-Topology-Second-Dover-Mathematics/dp/0486406806

[topaz breach]

Thank you very much, I will check them out

[rose lotus]

Are there any good algebra II books covering lots of algebra 2? like all of it and NOT at a super high level like MIT's OCW classes

[cunning elk]

precollege curriculum is so oversaturated online that you’re bound to find smth workable

[covert ibex]

is there a book on a more abstract view of a random variable? or if there's another way to look at risk and statistics in a more abstract way?

[molten gulch]

their website is still down

The site was down the last 3 days for me

[forest roost]

Hello ! I have graduated my hs this year and took a gap year to prepare for uni entrance. I want to improve my math from basics and upto Olympiad lvl if I can. I want to learn the usual hs stuff but a bit more in depth like the algebra,trig,geometry,calc, probability,stat etc. I am not sure about which course I should follow.

Thank you

[vital chasm]

For calculus i can suggest opening a copy of Demidovich's Problems in Mathematical Analysis (its just a calculus text) and do as many of the 3000+ exercises as you can

Theres answers at the back of the book so its good for self study

[normal crystal]

idk about "up to Olympiad lvl" but otherwise that's pretty much an exact description of the Art of Problem Solving series for each subject

[forest roost]

Would that be enough to start ug ?

[remote sparrow]

you don't need to know pre-university math at an olympiad level to start ug

[normal crystal]

you can just look and see🙃
but yes, they have through calculus

[normal crystal]

frankly, that was an unrealistic not happening goal to me
but they can still use Aops

[forest roost]

Yes but I just want to learn it for pure sake of my interest

[forest roost]

Ohk thanks

[remote sparrow]

how about try looking at some early university-level books

[forest roost]

I am still not good with basics I want to start from there

[normal crystal]

I feel like I my repeated claims Chipper reads on a flip phone have now evolved

[shut grotto]

Any resources I can use to learn more about the axiom of choice and its consequences? I'm looking for anything ranging from an simple overview to mathematically rigorous texts

[pale geode]

T. Jech - Axiom of Choice is a 248 page book specifically talking about it.

[dim widget]

Does anyone have any reccomendations on diff geo/diff top books

[shut grotto]

Ty!

[foggy quest]

Pair Introduction to Analysis in Several Variables from https://mtaylor.web.unc.edu/notes/math-521-522-basic-undergraduate-analysis-advanced-calculus/ with https://mtaylor.web.unc.edu/notes/linear-algebra-notes/ and https://link.springer.com/book/10.1007/978-1-4419-9982-5

[open trench]

Are there any short introduction books to catergory theory?

[outer helm]

Leinster book is my favorite

but a short one idk

[dim widget]

ironically already using Lee's book but I'll take a look at the other stuff. Though this is in context of a grad course

[wet sentinel]

do people perceive D&F as a hard abstract algebra textbook?

[wicked fractal]

No

Very lengthy

There might be a couple of hard questions

[wet sentinel]

i wouldve find it a bit strange otherwise because it seems friendly

[wet sentinel]

ah yea, thats the reason why i didnt continue with it

[wicked fractal]

Many such cases

[wet sentinel]

I mean 200+ pages for intro group theory is a bit too lengthy lmao

meanwhile langs undergrad algebra covers group theory in about 60 pages

[wicked fractal]

Lang is just better

Especially his complex analysis book

[wet sentinel]

yea i like his style tbh

he gets straight up to the point and explains where necessary

although it is harder to read than other textbooks since some steps in proofs are skipped/omitted but that can be dealt with (unless you are doing something like reading his algebra book as a first course in algebra )

[dim widget]

D&F? Oh um that one I mean it's alright? I personally prefer Hierstein's book and Rotmann's one big book

[modest glade]

any recs for algebraic geometry? no particular subject, just a general introductory work, if it exists

[pliant wadi]

I am kind of looking into the intersection between quantum information and model theory, any recommendations?

[north summit]

Is there a real difference between ahlfors complex analysis 2nd ed and the 3rd ed?

[pliant wadi]

Classically, I'd say that fischer's book is considered a good beginner intro, provided you have the basic algebra background. There's also a more computational approach with lesser pre-reqs, Ideals, Varieties and algorithms.

[wet sentinel]

yea D&F is fine, its just a bit long. I dont know about hierestein but i will make sure to check it, also by rotman's one big book are you referring to his GTM book 2nd edition?

[modest glade]

alright i’ll check those out, thank you!

[pliant wadi]

Bumping this up

🥺

[pliant wadi]

Also check fulton's book

That's a typical early reference

[modest glade]

sounds good 👍

[modest glade]

also i’m sorry that nobody’s answering your question 😭

[pliant wadi]

It's okay, life is hard

😭

[dim widget]

Yeah, he has a decent treatment of Galois in there at least. Definitely better than his Galois book. Though Herstien* (I mispelled it) might not be as good for you if you're looking for a graduate text but it is a very solid introduction to group and ring theory imo

[fathom forum]

Hey guys, i'm an undergraduate student of physics, wondering to change while mastering to math, i'm into differential geometry, what books you guys would suggest me to start at this topic and learn how mathematicians would talk about.

My english is rusty btw

[twilit pulsar]

Manfredo do Carmo's Riemannian Geometry

@fathom forum

[violet shuttle]

that is a great image for a cover

[outer helm]

woaa

[violet shuttle]

i see why you'd use it as a pfp

[outer helm]

beautiful

[twilit pulsar]

Could u tell I like it

[violet shuttle]

though of course it is in principle possible to get away with just two charts

[twilit pulsar]

nuh

[violet shuttle]

i agree it'd make the picture worse

[twilit pulsar]

gotta cover all the boundaries to make sure it's smooth

[violet shuttle]

...what are you talking about

just use a slightly extended upper and lower

oh, i guess this has the nicety that you don't need to extend anything

[twilit pulsar]

ohh u meant that

[violet shuttle]

i agree it's prettier in that sense too

[twilit pulsar]

yeah the math is way nicer if u just use 6 coverings

you only need to solve the problem on one of them anyway

[violet shuttle]

i indeed remember some examples in Lee using the coordinates on a sphere explicitly

[twilit pulsar]

and just say "likewise" for the other 5

[north summit]

Look at this prices

[remote sparrow]

when textbooks didn't cost 1/5th of your rent

[sage python]

For Buck that's $9.95 too much

Garbage book

[molten gulch]

How bad

[sage python]

Contender for the worst math book I've read

[molten gulch]

I mean, what specifically about it

[willow merlin]

which book explains qoutient sets, partitions, equivalence classes and symmetric difference properties

[vital chasm]

Tamara Lakins, the tools of mathematical reasoning chapters 4 for set theory and 7 for equivalence relations and quotients

Symmetric difference shows up as a long exercise tho

Its still a good read to start math anyway

[opaque urchin]

Can anyone recommend me a book to read out of boredom and curiosity
I'm very into linear algebra and topology so something similar to those subjects?
It doesn't have to be those themes, just the vibe yknow

[wicked fractal]

Idk what you mean by this

I don't know what you consider vibing

[opaque urchin]

Well I'm just okay with anything that kind of has the same vibe as those subjects but idk how to explain it well

[wicked fractal]

I do have a couple in mind that use linear algebra

One of them happens to have a lot of exercises too

[opaque urchin]

Oooo okay

Can you list them so that I can check them out myself :)

[wicked fractal]

I'm using you like pure things

The ones I have in mind right now are "Naive lie theory" by J Stillwell and "Number fields" by Marcus

[opaque urchin]

Okayy I will check them out, thank you both

[wicked fractal]

The first one is probably more suited for your liking

It's very lenient and it's a nice thing to read when you're bored

The latter one is also nice too and it uses linear algebra

It has a lot of exercises so you won't get bored

[opaque urchin]

Oooo that's greatt, I will definitely read them 🫡

Thank you very muchh 🫶

[wicked fractal]

No worries. If you like any of them (or both) and want to learn more I can give more resources

[slim compass]

i want a really like fast way to learn fourier transform and also inversion and some things like that so that i can apply in combinatorics and number theory any book reccomendation for that

it can be non rigorous , i just want to use it as a tool for now

[final sail]

Does this have to be maths books?

[slim compass]

would be better if it was a maths book, but physics is fine unless is uses examples from physics (i dont know any physics beyond mechanics)

[frozen perch]

I desperately need to know what this means for fantasy fiction

[heady ember]

:notthis: slurp would disagree

number of people who relate => 2 > 1

[feral hound]

I'm in class 11th and i want to build my basics strong, I'm preparing for jee, can anyone recommend some good books? Like my basics is really not that good

[fluid violet]

HELL YEAH

[hollow berry]

group theory book any suggetions?

[molten gulch]

Artin's Algebra

[meager mural]

For trying to learn quaternions for first time what is the best source for it

[molten gulch]

@fickle whale

[fickle whale]

Are you looking for a book specifically or would videos and articles be fine

And what is your goal, I assume it has to do with graphics programming?

[meager mural]

Yes it is

And anything just a good source I can learn from it

[fickle whale]

I'd start with

https://youtu.be/htYh-Tq7ZBI?si=hbPPSQxja6IbgrKQ

https://enkimute.github.io/LookMaNoMatrices/

https://youtube.com/playlist?list=PLsSPBzvBkYjxrsTOr0KLDilkZaw7UE2Vc&si=Y1thW40lwXgHbIBE

Freya Holmer has a nice video on the subject in an elucidating (GA) manner

[meager mural]

Thanks 😊

[fickle whale]

Start there

[pale mica]

freya holmer to sudgylacmoe pipeline is real, don't let anyone tell you otherwise

[fickle whale]

You know I discovered sudgy first and I've like never intentionally watched a freya video, her shit just shows up from time to time

Then she popped up in the bivector server one time yapping and sharing her new video

[pale mica]

the cat snail is amazing marketing

[molten gulch]

same

[sleek sparrow]

audiobook was better (updated) and is on youtube but i still recommend reading this

[meager mural]

If pga is easier than normal math why didn't it replace normal math throw years

[fickle whale]

It's new, and many standard things have found ways around it that more or less work, and so they don't see the reason to adapt. You can consider it a historical accident

Although the work of Clifford and Grassman predates that of Gibbs and heaviside, PGA comes into its own through the work of Gunn, Selig, and to some extent Lengyel (though I would be wary of the work of Lengyel, he is very opinionated and crankish, the lengths he goes through sometimes are absolutely psychotic. But he does also document some things that I haven't seen others speak much on)

[meager mural]

I have a werid question I asked about quanternions and u give me the first link about it but the other 2 is about pga is that a way to say it better than this complicated thing (quaternions)

[fickle whale]

Quaternions are a special case that don't make quite as much sense unless you have the background of GA or PGA

In my opinion

If you look at GA in 3 dimensions, or PGA where everything passes through some origin, then the quaternions do your rotations there, the same thing as even numbers of reflections or even multivectors

It's hard, but possible, to justify quaternions, their multiplication, and how it works geometrically to do 3D rotations without this link, but it's much more difficult

And by spelling it out to this degree, it also becomes obvious how to do more exotic things than regular quaternion as well

Like dual quaternions, which incorporate translations, and are often used in things like skinning or mesh posing

Or CGA which is used in some robotic control and image processing, which I won't explain but just mention

[vital bane]

This is true, William Rowan Hamilton had an extensive background in GA and PGA before he invented quaternions

[gray gazelle]

Hello, is there any specific recommendation on Markov chains, Brownian motion and stochastic calculus?

[remote sparrow]

https://www.amazon.com/Probability-Measure-Patrick-Billingsley/dp/0471007102

https://sites.math.duke.edu/~rtd/PTE/PTE5_011119.pdf

https://pages.uoregon.edu/dlevin/MARKOV/markovmixing.pdf

https://link.springer.com/book/10.1007/978-3-031-14205-5

https://link.springer.com/book/10.1007/978-3-319-31089-3

https://link.springer.com/book/10.1007/978-1-4612-0949-2

[gray gazelle]

Thank you!

[digital dust]

Can someone recommend me ODE book with strong historical motivation plz 🥺 (I like it when the author introduces why is it this way)

[cunning elk]

try Simmons?

[digital dust]

thx I'll go check it out :3

[foggy quest]

http://mtaylor.web.unc.edu/wp-content/uploads/sites/16915/2020/10/diffeq.pdf

[digital dust]

Thank u :3

[wanton pollen]

do i choose de carmo or lee for diff geo?

[vital chasm]

Do Carmo does 3d diff geom

Classic stuff like Gauss's Theorema Egregium

But i actually dislike do carmo cause his writing style is quite

Err

Not to my liking

Ted Shifrin has notes covering a similar set of material

https://math.franklin.uga.edu/sites/default/files/inline-files/ShifrinDiffGeo.pdf

[remote sparrow]

do carmo has written more than one book

[vital chasm]

Ah

I assume she meant Differential Geometry of Curves and Surfaces for some reason, my bad

[desert gate]

Has anyone read Navigating the Math Major: Charting Your Course? It's very new, and seems potentially useful (am junior in undergrad), but I'm a little suspicious of how useful / correct advice this would be to follow vs speaking to an advisor. Also it's $65.

[gray gazelle]

I'm just starting out mathematics (I'm talking little to 0 math skills),
Was hoping someone could recommend a well guiding math book (something that'll cover Algebra, Probability, Sets, and precalculus)

Starting out uni with little math knowledge I'd take anything fr

[white laurel]

Need to decide on a master's thesis, but got no clue what half of the topics I can choose from actually are. Could somebody offer me some standard reading material on stochastic volatility models?

[orchid vortex]

Are Jean-François Le Gall book's actually good for self-study ?

[past dust]

what do yall recommend or lin alg ? there is lin alg done right and wrong

[tiny gulch]

linalg done wrong

[past dust]

and are they a first course book ? some people say they are a second course book

[tiny gulch]

that i'm not too sure about

[past dust]

how is lin alg and it's application by strang

[tiny gulch]

Have heard good things about strang

[molten gulch]

decent but very computational

I like linear algebra done wrong by treil and friedberg insel and spence

[white laurel]

Gonna use this https://link.springer.com/book/10.1007/978-3-642-35401-4

in case anyone else is curious

[past dust]

what are the differences between linalg right and wrong

[tiny gulch]

LADR has a chip on its shoulder

[molten gulch]

read a bit of both and see which you like more

[molten gulch]

what does this phrase mean? /genq

We've heard it our whole lives yet never understood it

[tiny gulch]

It’s like

It has something to prove

Very “my way or the highway”

Holding a grudge

[molten gulch]

ahhhh

[violet shuttle]

it only means the holding a grudge thing

it's like if someone chipped your shoulder

you'd be pretty upset!

[molten gulch]

ohh okay

[violet shuttle]

insta ignore for pinging me

[viral knoll]

Why'd bro ping someone for this question and why'd bro ask this in book recommendation 😭

[steel cloud]

What are the reviews of Bartle's Lebesgue measure theory book?

And rotman algebraic topology, how is this, is that good for beginners?

[daring wolf]

see pinged messages for this

this one

[steel cloud]

thank you

[autumn whale]

Best book for understanding discrete mathematics (other then Kenneth H rosen) for beginner and I'm currently having difficulty in understanding recurrence relation if there is any resource or book that are better in theory part that I can refer to?

[tiny gulch]

it's been good so far!

[steel cloud]

okay

[tribal crow]

@autumn whale welcome to the mathcord!

[wintry quartz]

Anyone know any good books for lie theory?

I mainly want to learn about the exponential map and (co) adjoint representations

This is cuz I am getting gate kept by this knowledge when I am trying to learn symplectic geomerty

[steel cloud]

Is there no topology's book review pins?

[vast star]

https://mathematics.gg/books/point-set-topology

And I believe somebody told you about algebraic topology already

[steel cloud]

Yes

[steel cloud]

Thank you

[remote sparrow]

well, they're good for their intended audience (graduate students who have the background to read them)

[misty shell]

just got matt parker’s books, didn’t know he was a writer

[willow peak]

Best calculus 2 textbooks?

[pale mica]

He is a writer, a mathematician, and creator of the parker square

[autumn whale]

Thank you higher!

[cunning elk]

Stewart, Thomas, etc are all pretty common and decent(?) for a computationally focused calculus class

[willow peak]

alright thank you so much Ill check em out

[loud cradle]

this one flies under the radar a bit.. i think it's pretty good although it is short, so it doesn't cover everything you would typically see in a first course
bartle is a good author though

[steel cloud]

okay

[brittle orbit]

sup

[gray gazelle]

Is there any books, which teach me maths practically not just random formulas??

[rotund eagle]

what do you mean by "practically"?

[gray gazelle]

You know it should teach me visually, like for example:- i dont want to read quadraric equation formula and midpoint formula, it should teach me where we can see the quadtatic equation in real life

[marsh ingot]

Thats applied math

[rotund eagle]

if you are talking about the school level math, then can not help, do not know the appropriate resourses in English

for the uni level Linear Algebra, for example, can recommend David Lay "linear algebra and its applications"

[gray gazelle]

I mean maths itself is application right??

[rotund eagle]

applications is only a small fraction of modern math

[marsh ingot]

Yeah, applicated to itself and other branches as Physics or Biology

[gray gazelle]

But my school taught me just numbers, and formulas and how ro solve, it didnt teach me how to think maths in real

[gray gazelle]

Yessss, iam having problem with physics, i can solve equations but i am not understanding why it used

[rotund eagle]

which grade are you in?

[gray gazelle]

There is a book of elementary algebra serge lang, it is practical somewhat, but it is not in order

[gray gazelle]

Iam working as a bank employee, but im interered in learn maths, I like to learn coding and stuff so, im learning maths as my hobby

[marsh ingot]

Any background or starting from zero?

[gray gazelle]

Yaaa i have background, im know upto some calculus..like i said, i can solve problems, but i want to learn the reason why it is working??

And i download maths books from zlibrary, but i dont know which book should i read

[marsh ingot]

You need some foundations and that mean some theory to understand whats going on in every step. Linear algebra and caculus are good options to start

[gray gazelle]

Ok, where can i learn any sources?? And how can i learn to apply it in real life

[rotund eagle]

oh, well, then I can recommend "Gödel, Escher, Bach". At least the beginning is pretty accessible for an adult even without the deep knowledge in math. It reveals some deep connection between the logic (which is the part of math) and some real life problems.
But it is only the portion of math, and by no means is a comprehensive textbook. So yes, I would suggest the LA book I've recommended earlier.
For physics you can look Faynman's Lectures or Orear Physics

[rotund eagle]

Most of advanced math (like calculus and LA) you can not apply in everyday real life. These are special instruments designed to solve the special tasks. So specify, which tasks you want to solve?

[gray gazelle]

Ok, thanks i look into it... ❤️❤️

[normal crystal]

ixnay on the pie rah say
here

[gray gazelle]

Is there any website which make me apply maths

[gray gazelle]

But learning without applying, do u think it is good?

[gray gazelle]

I didnt understand

[marsh ingot]

Learning is always good

Even if you not apply it everyday

[gray gazelle]

I have this guilty feeling, that if u cant apply, then it is waste to learn, may be i should change my perspective🫠

[normal crystal]

don't discuss piracy on this server

[gray gazelle]

Hmmm ok

[sinful barn]

Guys I;m doing the year 10 syllabus in Australia but I don't really understand much

Like to the longest extent

mb wrong place

[rotund eagle]

In order to learn in such way you need to set a goal first. To decide the final project you learn math for. For example, at the end you want to be able to code the relaistic simmulation of fluid behaviour. Or planet motion. Or some cryptograpy staff. An then search for the resources to learn keeping your ultimate goal in mind.
Just "teach me some math" is a quite vague request

[gray gazelle]

Ohhhhh thanks for the feedback!!!!Yaaa i want to learn physics simulation,Yaaa i take your words, and start my preparation

[rotund eagle]

Good luck!

[gray gazelle]

Thanks❤️

[marsh ingot]

I dont apply the math Ive learned everyday in real life applications but for researching and I dont think its a waste of time in anyway

[gray gazelle]

Ohhhh ok, i will change my maths application OCD, and try learning maths

[kind minnow]

I'm full on pure maths, applied gets weird for me

[timid lion]

pure mathematicians are truly the most oppressed class

[sly thistle]

Hi, does anyone have any good book recommendations for stochastic calculus?

[slender wasp]

If you are interested in maths for physics, you can try flipping thru a book like mathematical methods in the physical sciences by mary boas, or mathematical methods for physicists by arfken/webber.

[gray gazelle]

Is the book good for basics???

[slender wasp]

I guess. One person's basics are another person's advanced. if you know just Calc and wanna get a sense for what applied maths involves before you go deeper, then it is good.

[gray gazelle]

Ok, thanks buddy

[violet shuttle]

...a mathematical methods book for physics is not at all what i think of as basic

You can try learning some basic physics first, coding as you go. Start with mechanics stuff, then learn some electromagnetism and analytical mechanics, then quantum mechanics.

I don't have good reccs for the basics. But I think Taylor's Classical Mechanics book is good for the analytic mechanics, and Griffiths for electromagnetism. But you should first get a basic understanding from e.g. wikipedia and, i guess, AP physics problem worksheets (someone can probably think of a better rec for these).

for quantum mechanics i reccomend Shankar's Principles of Quantum Mechanics. It'll teach you the linear algebra in the first chapter, which is the hardest.

[slender wasp]

OP said they know calculus Boas' preface:

[violet shuttle]

when I hear "mathematical methods" I'm thinking the book will include, say, the classical orthogonal polynomials and uses, fourier and laplace transforms, Sturm Liouville theory, Green's functions, series methods for ODES, maybe some complex analysis, maybe the gamma function.

I remember Arfken. It was pretty advanced, though I skipped around. It sounds like it happens to cover the introductory material early but... well... I somehow doubt that you'll do better than a book that actually focuses on linear algebra, and one on differential equations.

Boas, idk

[slender wasp]

Fair enough. OP, Arfken is probably a lot more than Boas initially (as mentioned above). I'd say you can flip thru Boas to see what all stuff you may be interested in. But, as someone else suggested above and then later, it may be useful to just figure out what project/physics you are interested and pick up stuff accordingly, for which you can get specific recommendations.

[gray gazelle]

For electronics, i bought breadboard and other electric stuff from amazon.. It really helps me learning electricity.., Where can i find miniature mechanical equipment, do u know where to find those mechanical stuff??

[gray gazelle]

Yaa i definitely give it a try

[violet shuttle]

i mean, you can typically empirically basic mechanics with stuff in any house

get a pulley and some rope, or make jury-rigged equivalents out of a toilet paper roll and the thingy the roll goes on

do you own or know someone with a bike?

classic demonstration is to spin a wheel and try to turn it

you can get any assymetric object and throw it in the air to demonstrate the tennis racket theorem (e.g. a phone). Or a literal tennis racket

[gray gazelle]

Yaaa i have a bike

[gray gazelle]

Ok i will try, basically my aim is to understand mathematics, and want to apply that maths in physics, i know maths, but i want to find the logic,behind it, so yaaa iam learning maths again

[violet shuttle]

classic problem is to determine the height at which an unrolling roll of e.g. toilet paper (pinning the paper to the wall) will hit the ground at the same time as one that just falls.

for electromagnetism, getting enough to actually measure things is probably best done by buying stuff

for optical stuff, you can confirm a couple qualitative features of the Fresnel equations pretty easily, and another if you buy some polarizing film (or if you really want, you can try making a polarizer yourself, but that might be kinda difficult and finnicky) (also try looking at screens, the sky, a rainbow, transparent plastic objects, other polarizers)

and with those aviation burning lens you can make a (bad) "telescope" and "microscope" and see things like virtual images

(and you'll also see that spherical abberation is a bitch)

and, of course, a strand of hair for diffraction

Perhaps a calcite crystal for birefringence

[gray gazelle]

Wowww😲are u a physicist???

[violet shuttle]

Other things: you can make a cloud chamber with dry ice and alcohol.

[violet shuttle]

merely a physicist in training, though don't be so impressed, these are pretty well known

you can calculate drag coefficients for, say, falling coffee filters

i don't know how you can easily confirm quantum mechanics without getting some kind of light source with spectral lines you could compute. sodium lights aren't really common anymore. there are those small devices to ionize gas in tubes for demonstration, but that would require getting one.

[gray gazelle]

Yaaaa i will definitely try, iam taking maths as my hobby thats it!!but i definitely try these

[violet shuttle]

I don't think you can easily see the Fraunhofer lines with just a cheap diffraction grating

Oh, you could try burning some salts and seeing lines

Though a bunsen burner is kinda needed to prevent crowding the signal with the spectrum of the heat source's flame

In principle you can measure hbar (and confirm the quantum statistical mechanics leading to the result) by measuring the entropy of an ideal gas but I don't think that's very easy to do yourself

If you have a higherr budget: Onte I saw a listing on amazon claiming to sell a chunk of YBCO (a high temperature superconductor) for a couple hundred bucks. If you then buy some liquid nitrogen you can then measure voltage-current curves. And maybe get some levitation? Not sure how strong of magnets you need for that.

[blazing prairie]

I need a book

hey

any one here

[broken totem]

!da2a

[hybrid sparrow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[broken totem]

just let people know what book or topic you would like recommendations in

[blazing prairie]

geometry

[narrow girder]

if it's geometry, Jacobs' Geometry: Seeing, Doing, Understanding is not bad imo

[blazing prairie]

uh! just i wana say that i am in high school not give too advance book

Jacobs' Geometry: Seeing, Doing, Understanding it's look old book can any one recommend some other new book

[broken totem]

it's old but good

it goes through most of the basic geometry you'd reasonably expect in a high school syllabus

[blazing prairie]

oh! ok i think there are only 4 chap(if i am not wrong)

[narrow girder]

i don't have a newer recommendation, sorry

and no, there are at least 10 chapters in Jacobs

[blazing prairie]

ok

i think i got the wrong pdf from google

my bad

[narrow girder]

there are 17 chapters total

spread over 600+ pages

[blazing prairie]

yeah i got

i am downloading it

[narrow girder]

i can't recommend my other geometry books to you as a high schooler though, so this is my only recommendation

[blazing prairie]

thanks for this book recomendation i saw the book now i am downloading it

btw are you people are of universities or olypiad people

[old elk]

Has anyone used this book?

[blazing prairie]

no

[broken totem]

i'm sec 3

[narrow girder]

a dropout

[blazing prairie]

oh!

[old elk]

[blazing prairie]

tried for imo

[vast jackal]

Just do aops geometry

that's the most comprehensive and easiest book I've seen

tho the challenging problems are kinda hard, I tell you you would be 1 level higher

[half robin]

Does anyone know of a good introduction to and or some expository work on arithmetic statistics?

[wicked fractal]

You can look at analytic number theory

Good books on this: Davenport, Montgomery

[rare crescent]

Hi I wanted to deep more on exercises and feel that i know more of mathematics and physics than what i learned at highschool, any academics level recommendation?

[sand path]

Can anyone recommend good books on geometry aimed at early undergraduates ? Maybe something slightly less dense then coxeter Introduction to Geometry

Thanks, I’ll check them out.

[cinder crane]

So hey just wanna get started with real analysis is terence tao good

[lyric fulcrum]

Hey Guys I got International Rank 603 in IMO Is That Good?

[twilit pulsar]

IMO is not a book

[trail hemlock]

yes

[vestal plover]

wow, that looks great!

[fresh skiff]

True words

[tiny gulch]

So true

[sage kelp]

Can anyone recommend a fairly rigorous textbook on calculus of several variables? I was skimming Shimamoto, but it feels not that rigorous. I tried Hubbard and Hubbard but their writing style I felt it was too leisurely. I am mainly interested in differentiation in preparation for optimization.

[remote sparrow]

shifrin

or edwards, jr.

https://www.amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/0486683362

[sage kelp]

I guess I can try Shifrin first

Any recommendation as to how many exercises solve?

[vital bane]

As much as you can in a reasonable amount of time

[slate condor]

can anyone recommend me a puzzle/problem book that includes such problems that I can solve mentally, without pen and paper, but needs quite a bit effort?

[fierce mountain]

Easy

Except perfect squares

Every other will be closed

Cuz perfect squares have odd no. Of factors

[cunning elk]

yea this is nowhere near "quite a bit of effort"

knowing basic NT breaks this wide open in seconds

[vital bane]

I don't know about a book but here is a fun little puzzle for you

"Show that every even natural number greater than 2 is the sum of two prime numbers."

[cunning elk]

uh but for fun little toy puzzles Martin Gardner’s books are pretty good

I have an old Chinese copy of his “aha insight”

fond memories of reading it when I was like 9

[jagged dagger]

Hii

[obtuse walrus]

guys should i go through calculus spivak or apostol before going to the principle of math analysis

[lunar topaz]

I want book recommendations to get op at maths in 3 months vacation

[obtuse walrus]

what kind of maths

[vapid nest]

anyone have any recomms in general for books related to quant fin at a relatively basic level

[obtuse walrus]

do u have prob and stats

and u know know stuff like calc , diff equation so on

[vapid nest]

yeah i have stats but im still in high school so a slightly lesser advanced book

would be good

[vapid nest]

uhh sure i guess

[obtuse walrus]

ok check out first course in prob

[obtuse walrus]

check calc spivak

[vapid nest]

you got links to those books?

[obtuse walrus]

after this real analysis

[vapid nest]

like ebooks?

[obtuse walrus]

k wait

can i dm u

[vapid nest]

sure

[heady lance]

Hi, what are your thoughts on Lang's algebra?

[molten gulch]

Difficult unless you already know some algebra at the UG level and even then, difficult

[hasty linden]

Hey can anyone tell me which book i should get as a 10th class students in India
Btw I am weak in maths

[heady lance]

My background is aluffi's chapter 0, but I didn't read the last two chapter's. Mostly I just heard that some chapters were recommended for me (galois and homological ) over the ones in Allufi but I am not really sure if its is worth it

[molten gulch]

What are you learning specifically

[hasty linden]

Class 10 all chapter like i know formulas but need questions for practice

[molten gulch]

That means nothing to me, specifically, are you studying algebra, analysis, geometry, what

[hasty linden]

AP ,geometry and trigonometry and circles

[molten gulch]

https://www.stitz-zeager.com/Precalculus4.pdf

[hasty linden]

You are elder brother

I m in school level rn

[molten gulch]

I'm not your "brother" /srs

[hasty linden]

Sorry if you are sister

My mistake

[molten gulch]

you're fine

[carmine gate]

bro's preparing for quant interviews

[old elk]

I thought someone from the channel had already used the book.

[split pendant]

Man I'm bored with MIT

The lectures are boring as hell

[carmine gate]

☠️

[torn blade]

who wanna bet this guy is not in MIT

[obtuse walrus]

jus go throu the ncert brother'
u would be fine try rd sharma

[celest patrol]

I am looking to learn category theory out of interest, are there any introductory books you recommend?

[tiny gulch]

Leinster’s “basic category theory” is good

For very basic you could check out Cheng’s “the joy of abstraction”

Bartosz Milewski’s YouTube series is also good

[celest patrol]

Thank you!

[tiny gulch]

[obtuse walrus]

dont memorize the formula understand and prove them

[tiny gulch]

glad to see more people wanting to learn category theory :)

[obtuse walrus]

not to be a bummer whats category theroy

[normal crystal]

it's this thing HS students study when they decide they like math

[limber night]

Any recommendations for a book on number theory which also has a decent amount of exercises besides an introduction to the necessary theoretical knowledge?

[tiny gulch]

Spicy graph theory

I’d say the 3 pillars of category theory are equality, composition and perspective

[heady lance]

theres an problmes in algebraic number theory

[tiny gulch]

It has interesting things to say on when you should consider two things “the same” and when you shouldn’t

It also gives a general theory of composition, which is about combining a bunch of small solutions to a big solution

[heady lance]

I think most chapters are acessible, but Ireland and Rosen are a gentler intro if you want one

[tiny gulch]

And it also gives a general theory of translations in perspective, in terms of interconverting between different areas or types of math, so that hard problems in one become easy problems in another

A category itself is just a particular kind of network - one where it makes sense to chain or compose any path of edges together to get a single edge

E.g. something like a friend network wouldn’t be a category - if A is friends with B and B is friends with C, that doesn’t mean A is friends with C

But something like a road map might be, if you view the vertices as intersections/destinations, and the arrows/edges as paths between these, since you can chain paths together

[violet shuttle]

huh, i would've thought "universal diagrams"

[tiny gulch]

For me that comes under is-does duality, which is part of “perspective”

[violet shuttle]

That sounds profound but I don't know what it means.

[tiny gulch]

The rough idea is that there tend to be 2 types of perspectives one can take on something

What it “is”, and what it “does”

This isn’t even something fundamentally mathematical

[violet shuttle]

Like objects vs morphinms

Or do you mean like, constructions vs axiomatic definitions

[tiny gulch]

The “is” of a word is like its definition, and the “does” of a word is like its usage

I don’t know all the details of what a bus “is”, in terms of how the engine works, how the chassis is made, how the seats are manufactured

But I can focus on what it “does” for me, which is provide convenient transport

“Is” tends to be more about internal, essential properties of something

Whereas “does” is more about external, observable properties, how it interacts with other things, what you can use it for, the purpose it serves

In physics, what the electron “is” changes from model to model

It could be a particle, or a wave, or a wavefunction, or an excitation of a quantum field, or…

But what the electron “does” stays more consistent - it repels other electrons, it conducts electricity, it forms chemical bonds

Does that make sense?

[tiny gulch]

<@&268886789983436800>

[hasty linden]

What happened?

[tawny ledge]

what r u asking

too many topics at once, is it incompleteness or logic

[tawny ledge]

this is aesthetics logic

within immanuel kant

[tiny gulch]

Oh this isn’t a question I’m trying to explain some examples of is-does duality

[tawny ledge]

its a projection of thought and basis of argument

yea

[tiny gulch]

Wdym by aesthetics logic

[tawny ledge]

cite page 1 of critique of pure reason

aesthetics logic is what you've said

[tiny gulch]

(for reference I know basically 0 philosophy)

[tawny ledge]

yea so you argue that "does" imply its utility, while "is" defines characteristics within an hierarchical layer of thought

like you said, "what a bus is" you may refer to an engine, door, chassis, hood

thats hierarchical and layer of thought and perception

[tiny gulch]

I see

[tawny ledge]

rlly basic stuff

u shld learn abt metaphysics and metalogics

it'll help

[tiny gulch]

So your saying I should read this critique of pure reason thing or smth

[tawny ledge]

and pay off

[tiny gulch]

uhhhhh

[tawny ledge]

not exactly that, but, its more so metaphysics and metalogic

[tiny gulch]

I generally don’t like philosophy 😅

[tawny ledge]

yea but Philosophy is universal isnt it?

a lot of math is derived from philosophy

[tiny gulch]

idk about that

huh

[tawny ledge]

like ZF+C logic systems

godel incompleteness

[tiny gulch]

ah im more in the applied math world

primarily a physicist!

[vital bane]

Applying category theory to other category theory

[tiny gulch]

As I keep bringing up, category theory is actually relevant to condensed matter physics

Physicists care about it

[vital bane]

I remember bubs talking about some 2-categories in his AdS/CFT research or something and I remember cond mat people use the AdS/CFT duality right?

or is it different?

[tiny gulch]

Idk anything about what bubs does

AdS/CFT does come up but there’s many ways cat theory manifests in condensed matter

[tawny ledge]

do you know abt knot theory

[tiny gulch]

Not too much

I do know about knot invariants via TQFTs

[tawny ledge]

oh

yea

i dont know much abt it

there

[wicked fractal]

I do

[topaz river]

Is this just Cat theory?

Do all category theorists become philosophers at some point in their career?

[tiny gulch]

no, is-does duality is something that happens all the time

it's not fundamentally categorical

it's not even fundamentally mathematicsl

[tiny gulch]

and, no

[dim oyster]

Recommend me any book for Maths for High Performance Computing
and Quantum Computing beginners to expert level. thanks

[daring wolf]

||hartshorne /j||

[hollow berry]

any books or websites where i can find imc preparation exercices

[idle mortar]

Ai talk here nice

[gentle jasper]

I’m looking for a workbook or just more interesting problems than are found in a Calculus book.

Sort of actually applying the basics of calculus. E.g., problem sets where I need to use the squeeze theorem, Mean Value Theorem, FTC, etc.

[marble solar]

Spivak's Calculus

Has plenty of difficult exercises

[vital bane]

Can you teach me TQFTs? 🙏

[modest marsh]

i better not have more incentive to gamble after reading this

thats a dangerous game

[cunning elk]

life is gambling 🤓

[modest marsh]

lmao great reference

[cunning elk]

odamn

[modest marsh]

i really never thought about it that in depth before

but i can see how it is relevant. thats interesting

[tiny gulch]

I don’t think I know enough about them to

[modest marsh]

ok ngl this is actually a really cool topic @silent roost thinking about it even more is insane because even tiny things like blinking could have a negative consequence. like if you blinked at the wrong moment and missed something being thrown at you

even if its not likely to happen it still shows the uncertainty of every day life which is pretty fascinating

its kinda fun assessing the risk to something that at first glance wouldnt have much of an effect on you

[gray gazelle]

I want a book that will tell me what is wrong with me.

[normal crystal]

https://www.amazon.com/Chainmail-101-Learn-Beginners-Steps/dp/B09PHBSTKW/

[gray gazelle]

Fitting.

[frozen perch]

I hope it fits, or you’ll have to remake it

[deep moat]

Recommendations for Number Theory books? I have decided to move on from stats and algebra and want to try number theory instead. I've been reading the ||pirated version|| NT of AOps

Any good introductory book is fine

[molten gulch]

Rosen's elementary number theory

If you know some complex analysis you could try aposotol's number theory

Also heard good things about ireland and rosen but AFAIK that one is a good but more difficult

[deep moat]

I'll take a look at this :)
Thanks for the recommendation! I'll be on open to anyone's other recommendations

[ember slate]

Would you guys recommend a course/lecture notes or a book to study a certain subject?

[vital chasm]

It depends on the subject because it depends on what resources are available

[deep moat]

Honestly, I prefer both!
It really depends on how well you wanna understand something and have a grasp on it fulltime!

But on all cases, books are more preferable since it has more information

[ember slate]

I thought the same

Thank you

[topaz river]

"The knight in rusty armor"

[turbid arrow]

,iam !

[hasty eagle]

You already have the selfroles studying!, do you want to remove them? (y(es)/n(o))
(Tip: use ,iamnot to remove roles without this prompt.)

[turbid arrow]

,iamnot

[hasty eagle]

Removed the studying! role from you.

Session timed out waiting for user response.

Aug 24, 2025, 1:44 PM

[full cairn]

Has anyone read Differential Forms by Guillemin and Haine? I need to learn differential forms and I'm torn between that and Lee's ISM and Tu

[potent thorn]

I am in Standard 8th(13 years old) and I need a book to build mathematical foundation.....(to prepare FOR JEE Advance)

[floral lantern]

if you know abstract algebra just read ireland and rosen

[twilit pulsar]

have you read any religious texts perchance

there's the classic—the Bible's New Testament—then other texts including the Torah, the Book of Mormon, the Apocrypha and other pseudepigraphical texts, and so on

these texts have strong themes of repentance throughout, which is closely tied to self-improvement

[twilit pulsar]

why am i getting sus react, lots of people see religion as a good thing for self-improvement

[foggy quest]

I agree with the self improvement aspect. If you rid yourself of the seven sins, pride, envy, gluttony, greed, lust, sloth, and wrath, you become much more healthy and productive in work

[pale mica]

There's many ways to improve one'self, religious texts are quite a mixed bag. Some parts can be helpful, maybe. But a lot of parts are harmful.

There doesn't necessarily exist a single convenient book or source that will tell you what's wrong with you anyway. It's an assumption that would be very reassuring, but I find it to be false in practice. I've found that I needed to go through various different places to find bits here and there that matched up with myself.

as for books, I would first start with asking your doctor, and see what they say, or a friend or 2

[full cairn]

In my religion, being healthy and productive is a sin

[acoustic dew]

Which book do you recommend to start Building True Mathematical Thinking?

[gray gazelle]

I'm an atheist and I have, and I did not like them.

[acoustic dew]

The second one seems really interesting, I'll check it out.

Thanks you Sabrina!

Sorry for answering late, I was taking a walk...

a big one...

[worthy kindle]

a big one...

[acoustic dew]

Yeah, that's why I took like 4 hours to answer...

I even forgot I asked for the book 😅

[remote sparrow]

#book-recommendations message

[summer badger]

Anyone got book recommendation for pre calc?

[leaden yacht]

Does anyone have any book recommendations for convex optimization at roughly the early grad level? I am looking to fill some holes in my background and I am ideally looking for a text which situates optimization problems in computational complexity.

[scenic delta]

Does anyone have any good book recommendations for partial differential equations?

[leaden yacht]

if ur ok with a bit of measure theory and functional then evans is the canonical choice

[sand path]

Anyone used Basic Probability Theory by Robert Ash? Was deciding between that and Blitzstein

[marble solar]

For undergraduate books Walter Strauss' text is very good

For graduate book the standard introduction is Evans book

[remote sparrow]

https://bookstore.ams.org/amstext-54/

this book by rustum choksi

[remote sparrow]

blitzstein way better for first-time learners

[paper trail]

So you don't believe in them because you don't like them or perhaps because you'd have to change your lifestyle, not because you don't think they are true :))

[fluid violet]

who are you to decide other people's beliefs?

Though this is off-topic for this channel, take it elsewhere

[paper trail]

Bro is having a meltdown, lol. Nobody decided what he should believe in, but something didn't make sense in his statement, because it isn't about liking, but about finding it useful and beneficial.

[queen zenith]

Heyyy!!

Can anyone please (please, please) recommend me a good book on statistics that take from a beginner (discrete stats) and build up to advance concepts (like ML algos)?

Anyone who helps me, I will wish you "conquer the world and dominate the universe".

[sage python]

People speak loosely, and the context is such that it doesn't make sense to interpret the word "like" hedonistically in that sentence

[paper trail]

It may be the case

[sage python]

"Yeah idk if I like that argument" is another way of saying that you're not convinced by it

[fluid violet]

no-one is having a meltdown, learn to have respectful discourse online

[paper trail]

yes, but it's unfortunate not to put in some effort to express your thought if you deem it worthy of sharing.

[sage python]

This isn't a lack of effort, I would say that particular wording is fairly common colloquially

[paper trail]

If you don't think it's worth the effort, maybe it would be better not said

[sage python]

If this were a formal argumentative work, sure that wording is a bit loose. But this isn't that, it's a casual conversation, and I would say...

Okay there we go (for the late onlookers: a message was deleted before this)

First off that's nonsense, people were always vague

It's about the environment

But second

[marble solar]

What a way to exist at the wee hours of the morning

[paper trail]

It's a about the way you conduct yourself.

[sage python]

You using this term pejoratively tells me enough about you, and retroactively means you were likely engaging in bad faith, and is against server rules, so goodbye

[marble solar]

What a fun crashout this is

[sage python]

Oh wait he got automodded

LMFAO

Lol see you Chipper

[sage python]

Yeah I thoroughly enjoyed this

[solemn rover]

he trolled in #theoretical-cs as well

[thick prawn]

Best book for multivariate analysis?

[gray gazelle]

It is a book at the end of the day. I didn't like reading it. I didn't like the contents of the book. End of story. Also, there was no mention of my lifestyle nor what I think to be true. You made assumptions for no reason.

[gray gazelle]

I used Serge Lang when I was learning. But, some people don't really like that one.

https://amzn.eu/d/bnWsdPO

[acoustic dew]

I see

Thanks!

[umbral pollen]

suggest a best book for discrete mathemtics . I am a computer sceince student and want to know begineer level book that helps me in logical programming

[vital chasm]

Tamara Lakins, The Tools of Mathematical Reasoning was the text used in my university

[zinc badger]

I have every Math book that you may or may not use in your entire life

It is a pdf
Does anyone of you want it?

[coarse condor]

To get started with k theory

[zinc badger]

Anything

[normal crystal]

no piracy on server

[pure rock]

yes please

[zinc badger]

Only names
No pdf

[zinc badger]

Yup

[normal crystal]

server policy, you're advertising piracy

[zinc badger]

It is a list of many

[normal crystal]

<@&268886789983436800> you can debate the nuance

[pure rock]

can you dm me the names

[zinc badger]

Ohk

[zinc badger]

Yes

[zinc badger]

But how?
If you can't suggest books
How will the channel work?

[normal crystal]

this is a recommend books channel
not a request to pirate channel
anyway, you already understand

[zinc badger]

<@&268886789983436800>
Is it allowed to send a pdf of list of books?

[zinc badger]

Oh
I see

Not send tons of them
Only recommend best ones

I want to ask for a handount on
Polynomials

[remote knoll]

@zinc badger you can suggest books, you just can't pirate them. It's Discord TOS.

If you have a list of books, that's ok, but pdfs are a sus format because of security vulnerabilities.

Why not a text document?

[zinc badger]

Ok sure

[zinc badger]

Do you have POLYNOMIAL and BOUNDING handout?

[remote knoll]

like, a handout for grade school algebra?

[zinc badger]

Competitive math

[remote knoll]

I would start here: https://artofproblemsolving.com/wiki/index.php/Resources_for_mathematics_competitions

[zinc badger]

Oh nice thanks

[slate condor]

lol. Actually, I got interested from Cal Newport's Productive meditation. So picked math as my walking partner. You can try that too. It's fun!

[safe pebble]

Hello everyone
I want to ask does anyone here know a good integrals book for advanced techniques something that contains content similar to the book of marvelous integrals by miguel santiago (I couldn't get it 🥲)

[marble solar]

Almost impossible integrals, sums and series by Valean

[wintry quartz]

anyone have a good book on lie groups?

I wanna learn about adjoint and coadjoint representations mainly

[foggy quest]

I would check here: https://mtaylor.web.unc.edu/notes/lie-groups-and-representation-theory/

[vital bane]

Michael Taylor's biggest fan

[remote sparrow]

try lorenz's book, it looks good

https://old.maa.org/press/maa-reviews/a-tour-of-representation-theory

[rich sun]

The text is, yeah

[timid lion]

what is bro reading on

i actually much prefer light mode for reading

[hidden crow]

fr

dark mode if not for gaming makes me sleep

[static bane]

anyone know any good geometry/trig books

[vital bane]

his phone

He has a laptop btw but doesn't use it for reading stuff

[pine tundra]

Because you're reading it in dark mode and you're on a phone

[deep moat]

Aops for geom (if you want to prep for competition maths)

Schaum's Geom and Trig are good

is this gdocs?

[potent raft]

Hi guys, I have this math books collection on 11 volumes called fundaments of elementary math.
It's pretty decent and complete. It is high school/college level.
Do you guys know another similar collection on sqme level?
I'd like to know.

[rain nova]

Anyone have thoughts on Tao's measure theory book? My course uses it as the main textbook but I've heard it's not the best since it leaves a lot of fundamental proofs as exercises and doesn't stress the importance of specific results

<@&268886789983436800>

[zealous coyote]

For a second it seemed like you were asking for moderators' opinions on Tao's book haha

[chilly relic]

Friends, do you know any English books I can order from Amazon that cover both algebra and geometry, mainly focusing on the theoretical part but also including exercises? I’d like it to be up to the 12th grade level, suitable for university preparation.

I'm in 11th grade btw

[rain nova]

I did not but I wouldn't mind that too

[chilly relic]

Anybody?

Yes but i live in Georgia where we study in our langiage

Oh is that a book?

Yes I already do. I just enroll in university where study is in English so that's why i want English books

Well okay then i buy aops

Wow what a price

😄

[worthy viper]

SQL for dummies has a secret chapter on non ecludian geometry

and its really good

[austere knoll]

I can concur!

It's a really enjoyable book!

[cyan furnace]

Any books on algebra 2?

[austere knoll]

well I'm from east europe right

and there was this writer

in englihs

called isabella holowatch

her book on "introduction to the algebra mind"

[clear agate]

hello, do you guys know any good linear algebra books for computer science applications?

[remote sparrow]

#book-recommendations message

[snow ether]

What would be a good textbook to self-learn differential equations from basically zero? (apart from prerequisite calculus knowledge)

[austere steppe]

try "an introduction to oordinary differential equations" by Earl Coddington

my first one, cleared it up well

[jaunty parcel]

AoPS would cover geometry (including trigonometry) pretty well with the touch of problem solving.

[tacit torrent]

Any books that teach linear algebra constructively?

[austere steppe]

uh... no?

I mean not that I know of

linear algebra is all about abstraction

not really any way to "derive" it constructively

you can only "define" things

like tensors, tensor multiplication, and all of that lovely stuff

[halcyon plank]

Should i use balck book?

For probelms

[vapid nest]

any books which could potentially be understandable for a grade 12 student basics of college level applied math

[molten gulch]

Is anyone familiar with texts related to results and theory of Probabilistic Automata? I'm not looking for anything specific, I'd just like a collection of results I can look into, similar to how it seems many introductory theory of computation texts have collections of results related to classical deterministic and nondeterministic (finite) automata

[molten gulch]

Stewart's Calculus

Strang Linear Algebra

[vapid nest]

got links to any of em?

[molten gulch]

Not free ones, no.

https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/1733146679/

https://www.amazon.com/Thomas-Calculus-Transcendentals-Single-Variable/dp/0134439414/

[tacit torrent]

I don't understand what you mean. All of mathematics can be "derived" constructively from what i know

[austere steppe]

yes

but

Linear Algebra is all about stuff thats already defined

because its convinient to define it that way

[tacit torrent]

There are plenty of theorems there though

I don't understand where you're getting at

[tacit torrent]

I mean, that's all of mathematics

Things are defined some way because they make sense that way

[austere steppe]

ok thats true

BUT

I dont myself know how to constructively teach Linear Algebra

like could you do it?

[tacit torrent]

Well, that's ok

I'm sure you could do it, may be impractical for undergrads though

I'm more interested in a source to know how you would do it

[austere steppe]

Idk lol

[tacit torrent]

I know there are books that create analysis constructively

[austere steppe]

I would just make em memorize it all?

[austere steppe]

ofcourse

[tacit torrent]

What you mean?

There are theorems and proofs just like in normal courses

Definitions and stuff

It's just a different flavor of mathematics

[austere steppe]

yeah that I would show them

like I wouldnt start

well

"constructively"

I would more say this is how it is, so this is how it is

not "why"

[tacit torrent]

?

[austere steppe]

ok nvmd ig Im making no sense to u

[tacit torrent]

Well, yeah. If the mathematics can be built in a constructive way then you have the math

Teaching is just a matter of how you would approach it as a teacher