book-recommendations

[mortal iris]

Stewart has got more examples to babysit you

[weary remnant]

Yea it really takes too long

Doing Stewarts

[mortal iris]

Then why bother asking? Go get your classics.

[weary remnant]

Just want some opinion especially comparing the two era’s..

[mortal iris]

What eras?

You wanna study Precalc from Descartes, Euclid, Lagrange, Bernoulli, etc?

[weary remnant]

1900’s and the 2000’s which are the contemporary now

[mortal iris]

Anything post 1950s on Precalc is essentially the same.

[tender cobalt]

imo there is no use trying to learn precalculus in all that fashion lol, you never use most of it later even in calculus anyway , only a few things are needed

if you wanna do hard things in that level, try out some indian class 12th math textbook

or A level further maths works too

[mortal iris]

Please. No. They all collectively suck.

[tender cobalt]

ye they do suck i know

Im well aware of that

And if youre a masochist looking for crazy precalc level problems, then check out some jee math book

[mortal iris]

Today I saw one of the books "prove" that the equation of a straight line through the intersection of two lines on a plane is a linear combination of the two lines that passes through the point of intersection by arriving at 0 = 0.

[tender cobalt]

😂

theres also stuffs like showing a point lies on a circle by arriving at 0 = 0

[mortal iris]

I'm aware. Stupid textbooks.

[tender cobalt]

if they introduce some formula Ax + By for example

Then the exercises are literally like

"Calculate when A = 1"

it doesnt even tell you what to calculate

It just tells you and assumes you know what A means from the chapter

😂

[hybrid sigil]

Is it normal to go into university math studies while "hating proofs"? I'd say that proofs are essential and I wouldn't really go into something if I hate an essential part of it...

[tender cobalt]

if ur doing A levels

just pick up a calculus book like Thomas Calculus for now

[weary remnant]

Then Can you review this book by richard brown? Advanced mathematics: precalculus with discrete mathematics

[odd cargo]

bro just choose a book

[merry reef]

I don't wanna do maths just a maths based subject although I hate to admit it but I get what U mean I should have a better outlook on it

[weary remnant]

Can’t im no expert in choosing

[hybrid sigil]

fair enough, probably for engineering or something, it's possible to focus more on calculational/applied aspects of math

[odd cargo]

no idea why you were negotiating then lmao

[hybrid sigil]

there is always a coin flip if all variants look equally good!

[merry reef]

I wanna do computer science but Ur right I have a bad habit of focusing on the parts of math I like which isn't good in the long run

[hybrid sigil]

not clear if this habit is bad or not, I think it's debatable. I.e. it's like two different schools: some say that one should have a well-rounded skillset, i.e. be a jack of all trades and should work on their weakest sides. The other school says that you should work on your stronger sides instead because you really enjoy those and can get deeper and use it as a competitive advantage

[obtuse hemlock]

whats everyones opinion on How to solve it by Pólya

[hybrid sigil]

but on the other hand, proofs in mathematics are really essential and you won't be able to progress through a normal math curriculum without them (even for engineering or CS degree)

[hybrid sigil]

many people like it, but I didn't, it felt that I didn't learn anything new, maybe I read it too late. For me it was just a compendium of relatively straightforwad methods: look at small examples, generalise, abstract, solve a simpler version of the problem, "divide and conquer".

[mortal iris]

You'd say that but I've seen some Indian math programmes where the students don't do a single proof

Just saying, bad curriculum exists

Indian undergrad math overall is a pathological example. You can cherry pick the decent programmes here.

[mortal iris]

Good for kids getting into math

[hybrid sigil]

yeah, that's why I defensively used "normal curriculum" there :)

[mortal iris]

The thing is, that's considered normal here lol.

[hybrid sigil]

like Ecole Normale Superieure, you know :D

[hybrid sigil]

I'd recommend Zeitz "Art and Craft of Problem Solving" instead, that's a cool book, with interesting problems to solve

[mortal iris]

I would love to see what opinions ppl have of this curriculum that is considered standard in India.

[mortal iris]

Keep in mind that quadratics, analytical geometry and single variable calculus including linear first order ODEs are part of the high school curriculum.

[split portal]

The link seems to be down for me

[mortal iris]

Sus

[hybrid sigil]

this seems to have proofs in there, no? And uses some reasonable books like FIS, Artin or Kostrikin

and even has my Andrews book in there somehow :D

(an Elementary Number Theory book with combinatorial flavour that somehow ended up being recommended for Algebra readings)

[mortal iris]

Okay. Hidden detail. Those books are listed but never really used.

[hybrid sigil]

too many Discorders got intrigued by mysteries of Indian education!

[mortal iris]

Here you go

[mortal iris]

They have a small course on logic pretty late into the programme. Look at the real analysis course. It's pathetic.

I should also add that Calculus based physics is the norm in high schools here. That mechanics course is also completely redundant. We also do a lot of vector and matrix algebra in schools. So it's possible to jump into Linear Algebra directly.

[steel plank]

hey, im interested in learning graphics programming and i have a lot of free time on my hands so i want to first strengthen my skills and knowledge on the relevant math topics needed before learning c++ itself . i have completed a-level maths pure 1, 2 ,3 and 4 and mechanics..im looking for a great book that covers everything i need to know, would love something that can take you from a beginner-intermediate to an advanced level . ty

[mortal iris]

Linear Programming is also covered in the high school curriculum

[hybrid sigil]

it's somewhat short, do they just stop at sequences? But anyway, I am not an expert on math education by any means, so I will withdraw my opinions!

[mortal iris]

Like there's so much redundancy that it doesn't make sense. Almost half the curriculum is high school math.

[mortal iris]

From what little I've spoken to ppl in colleges that use this curriculum, real analysis isn't even offered in most cases. And yes it is just properties of reals and real sequences and series.

[molten gulch]

only...sequences? No differentiation or (riemannian) integration?

[mortal iris]

In separate Calculus courses. Most of which is at the high school level.

[molten gulch]

Huh..wtf???? I thought that analysis courses generally covered at-least differentiation (with proofs)

[mortal iris]

They do, in most reasonable curricula.

[hybrid sigil]

maybe check out this: https://www.gamemath.com/book/intro.html

"3D Math Primer for Graphics and Game Development. "

[steel plank]

nicee tysm

[mortal iris]

It's funny that even the monotone convergence theorem is done without proof lol.

I should also add that most math profs in such institutions have come through the same system and haven't done a lick of research in any field, not even like a masters thesis.

[molten gulch]

That is absurd, even at the uni we go to, which doesn't have a too strong maths department, we do up to riemann integration in the analysis course, and everything is done with proofs

[molten gulch]

I find that...somewhat surprising to hear that people who haven't even completed a master's degree are allowed to teach material like this

[mortal iris]

Oh no. They have a degree

They've never done any research

Because a masters dissertation is optional

And even those who do end up doing a reading project of sorts to be done with it.

[molten gulch]

Ooooh okay

I see

[mortal iris]

And their undergrad was basically this. If I showed you what they do for grad programmes it's even more laughable

Physics is just as funny.

[molten gulch]

I would like to see this, I need a few laughs in my day today

[mortal iris]

Well I can't find the overarching rec. But this one is from a supposedly reputed uni.

It's honestly not the worst

But it's not good either

[molten gulch]

....we have Galois theory in undergrad wtf is this 😭

[mortal iris]

We have PSTop also in undergrad. Also they do Functional Analysis WITHOUT Measure Theory in GRAD SCHOOL

[molten gulch]

mhm, here we have a FA course without measure and another with, and topo in undergrad too

[mortal iris]

FA without measures in undergrad is understandable

[molten gulch]

Ye

I agree

[mortal iris]

Oh yeah. Notice that the programme has no research module at all.

Let alone things like differential geometry. Introducing measure theory in like the third semester of a grad program is preposterous.

[molten gulch]

Also this is absurd, they're recommending students learn PDE from Evans when the course prereq is....calculus

Are they trying to set up students to fail?

And for multivar analysis they recommend....baby rudin????

Isn't baby rudin's multivar section known to be quite poorly written?

[mortal iris]

The whole book is tbf but it's like the last 70 odd pages or so that covers multivariable and not well.

[mortal iris]

They rarely use the books they recommend anyways

They have some random Indian author from this system who wrote a book for this system and still poorly.

[molten gulch]

this smells a lot like how in the US you generally have unis using specific textbooks even if they are absolute trash due to publisher deals

[mortal iris]

Nah. It's different here. Incompetent profs and even worse students combine to NEED material for PASSING exams. Almost nobody in these unis actually gives a shit about math.

And this is the vast majority of the country.

[molten gulch]

Why is it all about exams even after one gets into uni, I just don't understand the constant competition and why go into a degree if you aren't even interested in it, then deal with professors who don't know what they're doing, etc...it feels like some horrific cycle

[mortal iris]

It's basically like they want formula vomit and all proofs worked out in excruciating but not rigorously detailed.

[molten gulch]

Of what I've heard, and please correct me if I'm wrong, many don't even want proofs, they just want formulas

[mortal iris]

It very much is. In India one needs to qualify for undergrad, grad and even PhD programmes via exams. Even some jobs have exams lol. In the case of these jobs they don't even qualify you for the job but rather training.

[molten gulch]

Oh what the actual fuck

[mortal iris]

You would be entirely correct. It's an attitude that exists thanks to this wonderful JEE exam lol. Ofc incompetent math educators in the school level play a role too.

[molten gulch]

I wonder how different it was when my parents were in uni then, they said they have quite fond memories of their studies, but that was 30+ years ago

[mortal iris]

I forgot to add eligibility to be a lecturer or prof at a uni. Which is why you have so many postgrads with zero research experience teaching here lol.

[mortal iris]

Well it depends a bit on where they studied

IITs are not so bad if you get in. It's the getting in that's bad.

Calcutta University back in the 80s was pretty hot and had good quality for its time.

[molten gulch]

The mere existence of the JEE as it is irks me, I wonder how the situation is in China, Korea, Japan, etc...as I've heard they all also have their own very difficult enterance exams. I also wonder how difficult it would be to break people out of this mindset, as I've seen my own fair share of the "just give me formulas who cares abour derivations or proofs" mindset here in the US too

[mortal iris]

So did Madras University

[mortal iris]

China's Gaokao is a different kind of beast from what I gather. It's kinda all encompassing in some way and not just for STEM majors.

[molten gulch]

I see

Good to know

Also, do you mind if I sent you a friend request?

[mortal iris]

Sure

Korea and Japan idk really. The ones who are interested in stuff seem to be able to break out eventually. The upside is that they have institutions that are far better placed in terms of quality.

In India the interest itself seems misguided and the institutions prey on that.

The sheer number of theoretical physics wannabes who go to grad school and then cannot comprehend anything is laughable.

Looks like the CSAT is also similar to Gaokao in scope.

[remote sparrow]

https://link.springer.com/book/10.1007/978-1-4612-0691-0

https://www.taylorfrancis.com/books/mono/10.1201/9780203710920/knot-theory-vassily-olegovich-manturov

https://a.co/d/8hsHQEC

rolfsen predates the knot polynomials and is rather poorly typeset, but is still useful

[shy wadi]

how to get into commutative algebra? :p

[shy wadi]

also what pre-requisites would i need

[molten gulch]

a course in algebra which has covered modules, and probably being familiar with some galois theory

[shy wadi]

are there some good (non course) resources for those?

[molten gulch]

atiyah and mcdonald is standard I think for commalg, look at the prereqs listed in there

[shy wadi]

It is designed to be read by students who have had a first elementary course in general algebra.

thanks!

[molten gulch]

Keep in mind that "first algebra course" in the 70s is very different than first algebra course of today

[shy wadi]

[hybrid sigil]

What is the principal difference between this and just the study of commutative rings?

Haha, probably none, at least the very first sentence of Atiyah McDonald is telling me: “Commutative algebra is essentially the study of commutative rings.”

[daring wolf]

yeah there is no difference

[hybrid sigil]

I find it somewhat odd that instead of calling it “Ring Theory” then, which makes more sense, people call it “Commutative Algebra”

[daring wolf]

Well ring theory is like more general lol

because not necessarily commutative

and there are good stuffs happening in commutative case different from it, hence people put "commutative"

[hybrid sigil]

Well, call it Commutative Ring Theory then

[daring wolf]

afaik there is a book named commutative ring theory lol

by matsumura i think

[hybrid sigil]

That’s my guy

[daring wolf]

i think this is also somewhat because of algebraic geometry, or other algebraic methods applied to commutative rings

so it makes more sense to call it commutative algebra than just commutative ring theory

[hybrid sigil]

Well there are plenty of algebraic methods applied to groups

And no one calls study of abelian groups "Abelian Algebra"

(I hope)

[daring wolf]

that's not my whole point haha 💀

[hybrid sigil]

I’d expect that Commutative Algebra should study commutative algebraic structures, be they groups, rings or whatever, just a too generic name

[daring wolf]

well these should include modules over commutative rings, algebras, vector spaces etc

and you deal with them

obv

sometimes group theory appear yes

[hybrid sigil]

Ok, that’s reassuring!

[molten gulch]

yes I also prefer this name heavily anyway, and also I feel like the underlying theme there is ring theory anyway and we just use modules over these rings or whatever to study...rings

[hybrid sigil]

we should start a campaign

make ring theory great again and all of that

[drifting anchor]

Check out OpenStax online textbooks on high school and some undergrad university math.

They're free, in depth, and are awesome

[normal crystal]

make chipper potato again

[heady ember]

How much of Jacobson's Basic Algebra I should one read to get a good foundation in algebra, that is sufficient for further inquiries into math?

I just want to know this to set expectations for how long it'll take me ig. Kinda like mentally preparing myself for the ride ig

If a topic is niche without being interesting enough on its own to compensate for it, I might want to skip it.

Also, how does the chapters on modules and galois theory compare to books specialised on those topics? And would it be recommended/discouraged to skip those chapters in favour for said specialised books?

[obtuse hemlock]

indian education is a joke to be honest, even in high school (i attend an A levels school) the whole syllabus is total memorization, there is no concept behind anything, and they just rely on memorizing strategies - partly why cambridge and all really want indian students to take APs, and they underperform badly because we dont get ANY INTRODUCTION to graphs until undergrad (which is also weak). Like there is no graphs for any calculus chapter or log or anything. As for the IITs or IISC the top premier institutions around 2 million teens may give it a go every year, and there are two rounds, JEE Mains and JEE Advanced, if you clear JEE advanced with a national rank of below 200, you have a very good chance at attending a great US university (like MIT) or I've seen a few people at Cambridge. JEE Advanced top 10's are usally able to get full scholarships to MIT. JEE will actually teach you the maths and graphs of much higher level (alongside physics and chemistry), i've given A level further maths papers to JEE students and they've aced them, but the regualar CBSE student wouldn't even get 15-20 in it. The curriculum is definitely hard due to how confusing they can make the questions, and the indian olympiads, IOQM --> RMO --> INMO are STUPENDOUSLY hard. It's a whole different realm, and most people are happy with 10 on 100. That's why theres a huge amount of tuition centers and more here. There are a few great places to study, but its almost impossible to attend them.

What i've noticed is, in neighbouring countries, lots of people want to leave the country and almost everyone attends international schools. In India thats not the case and it's still a huge minority, but it is certainly growing as competition rises. Best part is, the reason all these JEE adv crazy students go abroad instead is because they want research facilities, I mean if a student has that amount of knowledge at high school level, they love the subjects, and they leave just because of the research. The whole country knows about it, but is never ready to fix it.

[mortal iris]

Not true at all of our neighbours. Attending such schools is very much the case for only privileged ppl there.

[mortal iris]

You're wrong about the graphs bit. It exists (I can confidently say so for CBSE and ISC) , it is also taught if the teacher is competent. It's just rarely a part of the evaluation.

[obtuse hemlock]

To be honest that’s quite shocking to me, my school teachers are ex CBSE and they claim that that graphs are practically ignored, and my brother studied at CBSE and he said it does not even compare with AP graphs, sure the content is strong but it’s nothing graphically compared to international standards

[mortal iris]

JEE doesn't teach you shit. The main technique to ace that exam, especially advanced is to build a large solved problem database in your head by copious amounts of problem solving. As a result, most competent students by JEE standards have solved enough problems that they can answer questions like muscle memory as opposed to thoughtful application. Ask them to write proofs and you'll see.

[obtuse hemlock]

That makes quite a bit of sense to me, I gave someone I know srudying JEE a STEP paper and they did horrible in it

[mortal iris]

It is very much comparable. It's just not taught well or completely because of the examination focus and the examinations don't care about them. So all the standard textbooks overlook them. But it's very much a part of the curriculum. I've taught a lot of shit to my 11th grade students that's otherwise overlooked in their books and consistently asked graphical problems. Graphs in the sense of data analysis is a major miss tho.

[obtuse hemlock]

That could definitely be the case, there’s a huge tutor culture here, and I mean there’s one tutor who teaches around 3-5 subjects at once. All they do is ask people to memorise the textbooks and give them lots of practice questions, and they get crazy good results, hence why everyone ends up there

Most tutors are like this, they come to your house open the textbook and recite it to you, they even teach history sometimes

[mortal iris]

Yep and also, the system has been in more of a decline lately than progressive lol. Boards are competing for pass rates rather than quality education. As a result the material has become tamer and problems that would invoke critical thinking have practically disappeared to pander to weaker students. The bigger problem is that these supposedly weaker students never wanted to take mathematics but were forced to.

You'll see a marked difference from papers in the 80s and 90s as opposed to the 2020s.

[obtuse hemlock]

There has been a recent introduction where students can take Foundation Maths in 10th grade, and dropping it in 11th was already possible. The pass rate point is totally true, I myself was studying a bit for the Indian Olympiad’s IOQM and the people say that clearly you need to cover the curriculum from the past 10 years that has been removed in specific, because every year it’s being made easier and easier in order to increase pass rates

[mortal iris]

Also, if you pick out potential projects for the students in their curriculum it's laughable. I saw a project suggesting a Venn diagrammatic proof for the distributive properties of unions and intersections in sets. How tf is that a project?

Like what type of shit are they on?

[molten gulch]

Prefacing what I'm about to say with "most of the information I am about to share or questions I'll ask are based on 2 things, my parents who wrote the JEE and advanced, IIT, and civil service exams (and passed all of them) in that era (1980-1990s), my dad went on to study physics (and got a phd in it) and my mum went on to study mech E and did her master's in signal processing stuff I think. My cousins who are in India right now are in their late teens and wrote the JEE recently, so I also have a tiny bit of data from them; and also I'm not from India, I was born in the US and have lived here my whole life, so am used to a very different education system, so I apologize if any of my questions come off poorly or wrong"

Okay so

a few questions

[mortal iris]

It's funny because while the book doesn't care for the proof, I've made my students do them algebraically and visually in classes already.

[obtuse hemlock]

We don’t learn anything besides the strategy we have to memorise to solve a problem, the curriculum is utter shit. I am personally aiming to study abroad, and the reason I joined an A levels school was because of my brothers experience with CBSE and how he had to learn so much new stuff in university in the US. It’s foreign to us

[molten gulch]

To this, I wanted to know that alongside the reduction of difficulty of problems, has the "culture to pass" you described above also led to easy but very poorly worded convoluted problems becoming the norm led to the rise of the coaching institutes directly? Like, it seems like everyone in India goes to school, then coaching, then maybe further tutoring after that every single day

[molten gulch]

Also here, I know you probably wouldn't have a full answer to this due to the nature of the question but I might as well ask, what are the main reasons the boards are competing for pass rates? Even if they whisk more and more people through the gauntlet year over year, would this not lead to many people who are inexperienced or not ready for uni getting placed for uni and then the uni having to clean that mess up? Or is that what is happening right now?

[molten gulch]

How the hell is that a project? I had that as first week homework problem at uni 😭

It takes literally 5 minutes to solve

[mortal iris]

The convoluted problems that are poorly worded are more of a JEE things (and NEET if you count physics). Although some easy but poorly worded problems still exist in your regular texts.

And yeah more or less all students are stuck in that

[molten gulch]

That is disappointing

[mortal iris]

Money. Better pass rates = More schools operating with your board for unsubstantiated Prestige = Greater fraction of students going to said schools = Greater administrative payments to the board from them.

[molten gulch]

Oooh I see

Breaking such a cycle seems very difficult

I've probably made it clear before (in other channels) that I am no fan of the current Indian government, but, if they actually wanted to fix this madness, what could be done about it?

[mortal iris]

It's a very carefully crafted system lol

[mortal iris]

Very difficult really. If they went for truly holistic and balanced education then the execution would require a lot of skilled grassroots level educators which are lacking even in low population countries that have been historically doing better in this regard overall.

But one could fix that by giving potential teachers access and exposure to learn and grow in a healthy international environment with funding. But very few take it up anyways.

But the catch is that a shift like this would naturally lead to more fluctuations in grades and this would require schools to be even more accountable to overbearing parents.

Clearly they don't really care for it. They will put out policies that sound good on paper. Execution still depends on how much you're paying whom.

Under the table of course.

[wicked fractal]

this sounds depressing

[remote sparrow]

the ones that succeed enough usually go to other countries, which is a net loss

google brain drain

[mortal iris]

Numbers don't always make up quality. The best engineers by far don't even do engineering. They want to set up their own business or climb corporate ladders. Our biggest exports are Tech company CEOs in the USA for instance. Your average engineer here has subpar practical skills and no industry exposure. In the topmost institutes, they get the latter to some degree. Yet, companies often require written tests and mandatory training phases with small stipends before handing out an appointment letter. This is both because companies are cheapskates and also for quality control.

As far as doctors go, I'd argue the situation is better but on the ground level, all they do is spam you with antibiotics thoughtlessly. At private hospitals they will tell you to perform invasive surgeries without a thought because it makes them money. Idk much about medicine really. The first aid, critical care and crowd management is obviously something they're good at. Plus cheaper services overall.

But testing and diagnosis is well...

I mean I've just been talking about STEM. Social Sciences are a different kind of joke lol.

[cunning elk]

to be a social sciences academic rn

[molten gulch]

That's sadly what they are, stereotypes. Maybe 30 years ago when my parents got their degrees and moved to the US things were a bit different, but things have changed a LOT. These days it's all about getting a degree, starting your own business (and flooding an already overfull market because many times the business ideas aren't even unique), and overall it's just disappointing. Basically, what Killuminati (and sour drop) said

[normal crystal]

who tf do they think managers work for🤡

oh, so they're just deluded
understood

being a manager and being a small business owner aren't even the same thing

your pops has Robert Kiyosaki books, doesn't he
I already know

AND I BROUGHT IT BACK TO #book-recommendations RELEVANCE
LIKE A CHAMP 🏆

ok, hear me out
take your predicament and make it a win
self-publish a new (similar) book series
Chipper Dad, Potato Dad
yw

"chipper dad supported my desire to be an engineer,
potato dad wanted me to be a fantasy of management"

ok, now you owe me 10% of revenue

[zinc fiber]

Yea but it’s hard to become a business owner

You have to be very experienced at something

[twilit pulsar]

you just have to have a certain amount of executive function

[proper trout]

Generally, which one should I start with first? sorry for bump

[normal crystal]

Chipper Dad, Potato Dad

[river jetty]

Depressive? Like what?

https://tenor.com/view/theofalso-dog-fan-temperature-gif-14129060235766298709

Nvm abt that, i just came here to see books recommendations

What the sigma

Ohhh i get it

Nvm abt my question, anyways, can someone recommend me a book to start studying pre calculus?

https://tenor.com/view/meowl-cat-owl-gif-16304756704527773823

I need to improve in algebra and trigonometry

Consider that i dont know functions in R

[normal crystal]

call me Killuminati Jr
https://stitz-zeager.com
or openstax

[blazing holly]

Openstax is also goated

[chilly willow]

I mean, everyone works for someone else to certain degree. But engineers can have their own company, at least in my country its not uncommon

[blazing holly]

https://openstax.org/books/precalculus-2e/pages/preface

https://openstax.org/books/algebra-and-trigonometry-2e/pages/preface

[river jetty]

And you dont need a degree to have a big company, kinda strange but true

[chilly willow]

I was not thinking about big companies, just companies. Its true that you don't need a degree, but most ppl are going to be much better with the degree than without

[river jetty]

Yep, those years suffering an doing the best to have a degree will be rewarded in one way or another

[chilly willow]

yes, I think this too

[river jetty]

This is for everyone. If you have the opportunity to study, take advantage of it. Almost 90% of my relatives were working hard in the field, because that was the only way to survive, they didn't had knowledge, they only knew to work hard

Fortunately they are now living in the city, with their respective families

[midnight wedge]

Anyone knows a good book for high school geometry? I suck at identifying patterns on questions and I need to train

[mortal iris]

Serge Lang has a great book for this. A slightly more challenging book would be Kiselev.

[mortal iris]

Depends on what you're looking for.

For logic alone Epstein is a fine pick. For a foundations course in math, Cummings is the better choice.

[tender cobalt]

Epstein? XD

[hybrid sigil]

Yeah, engineers can earn quite a lot actually, especially if you go in finance or big tech. Starting your own business is not for everyone, and it’s also risky and far from guaranteed to bring a lot of money

[gray gazelle]

Introductio In Analysin Infinitorum by Euler, unironically

Book 1

Synopsis of results in elementary mathematics by Carr is good too

book 1 again, these might be controversial recommendations but there isnt a lot to learn in precalc, these books go over a lot of stuff and Carr's book is just a list of theorems so you have to do the work, its much more active in my opinion

[river jetty]

Tysm for the book recommendation bros, i will check them later

[twin parrot]

This book has reputation for producing one of the greatest mathematicians, first time actually seeing someone recommending this

[vital bane]

@remote vortex

[tender cobalt]

Isnt that the book Rammanujan learnt from

[static bane]

Any pre-calc books?

[gray gazelle]

When I was in highschool (which was a few months ago) I wasted a lot of my time finding a "proper" precalc book, I used those old english ones Hall and Knight, Bernard and Child, looking back at it I think it was a huge waste, though Bernard and Child goes over a LOT of stuff, I forgot most of it, I spent some time with Carr and it seems to make you cover the essential stuff, it even has a proof of irrationality of π, I think it was a very good book overall and highly recommend.

There's not a lot to learn in "precalc", just be done with it and move on to real math

If thats your thing, if you arent into math then just read your school math book

[gray gazelle]

Yes

[blazing holly]

I sent one to another person a few hrs back, scroll up a bit and you’ll find it

[odd cargo]

As good as supplementary reading could get, definitely not primary though.

ffs its a synopsis

[gray gazelle]

I used it as primary for a while

served me well

Just ask other people for help if you get stuck

[hybrid sigil]

It’s like those people who recommend learning C++ by reading the 2000-pages formal language spec, because it worked for them

There are many ways to learn, but why choose to learn from a source that was not even designed for that?

Ramanujan probably didn’t have a choice, and likely is very different to all of us anyway

[odd cargo]

you had hall and knight, as well as bernard and child, and still chose to use a synopsis as primary reading material?

[hybrid sigil]

And recommending Euler’s (!) book in Latin for pre-calc (!) in 21st century is even more suspicious

I wonder why no one is even commenting on that, where is Killuminati? :D

[odd cargo]

i mean, there're english translations of that book available online, so im not tripping over it

nice little intuitive approach in there but using that book as primary reading material is also bad.

definitely use a more modern book though

[gray gazelle]

Yeah, I found it faster

And more hands on

[gray gazelle]

Well yeah, I guess not everyone will like it

[odd cargo]

i dont know about that man...

[gray gazelle]

No, I didn't recommend the Latin version 😭

But it is a very good book in my opinion

In my and André Weil's opinion

[odd cargo]

that stitz and zeager pre calculus book is really good, and its free

[hybrid sigil]

Not sure if André Weil can really remember and relate to learning pre-calculus, he was far too advanced

[vague scaffold]

ı need a book for euclidian geometry

[gray gazelle]

Coxeter

Geometry Revisited

I hope no one has problems with that recommendation lol

If you want to learn a lot of geo its good

[gray gazelle]

Well idk

[hybrid sigil]

I have :) It’s “revisited”, which suggests that it’s good for the second course, not the first

And likely the person is asking for a first course. Or at least it is worth asking them

[gray gazelle]

Cem Tezer or someone has lectures on yt

better as a first course

[gray gazelle]

Fair

Someone suggested Lang's Basic Mathematics above, it has geo, should do well for a first course

[twin parrot]

Carr is a book of essential results, the reader is assumed to supply the proofs themselves or find it from somewhere else. But this wasn't a problem for Ramanujan because he would see the proofs in his dreams anyways:D

[gray gazelle]

https://youtu.be/JZcRwrhCTiA?si=LkeXE9CEOLwywg8c
Here's how you can do that too!

[novel anvil]

Book recommendation for octonion algebra and symmetry groups. 👏

[molten gulch]

Sorry >_<

[mortal iris]

And De Methodis Serierum et Fluxionum by Newton for Calculus, I assume?

[gray gazelle]

Certainly not, Euler's book is actually worthwhile

[mortal iris]

It's a good book to have. Not a good book to use as primary learning material.

[gray gazelle]

Fair enough

If I could go back to 9th grade I'd prefer to read it over anything else I read

[mortal iris]

The thing with historically relevant sources is that you recover a lot of the original motivations to do certain things or insights that are lost to time. But going through them formally by modern standards is a waste of time.

[mortal iris]

Perhaps you can do us all a favour and when you have the time, write a book in the modern context inspired from the same with the benefit of hindsight.

Because I'm not denying the source's value. It's just hard to contextualise. Unless someone adapted it for modern treatises like some ppl have with say, Euclid's Elements.

[gray gazelle]

I suppose, I'd have thought it worthwhile regardless

[gray gazelle]

Euclid and Beyond?

[mortal iris]

Lee, Axiomatic Geometry. If you're beyond the high school level.

[mortal iris]

Nah. There are a few others like the one above.

[gray gazelle]

I have thought of doing so to be honest

I decided in highschool that I'd write a book after I graduate, like an introduction to higher mathematics

Fair enough, I'll try after my entrance exams

If I pass

[mortal iris]

Good luck. As someone writing a book for the last five years I can tell you it's no easy task.

Though my work is a bit too ambitious

Although I might be able to write a joke math textbook a lot sooner than this half a decade long and continuing project of mine lol

[gray gazelle]

"Mathematics Made Difficult"

It was funny

[gray gazelle]

Thanks

[gray gazelle]

whats it about?

[mortal iris]

Quantum Theory. Mathematically Rigorous with Physical context written for Physics students. I want it to be more comprehensive than Cohen-Tannoudji's 3 volume text.

[gray gazelle]

I see

I'd be happier if it was smth like what I intend

Sucks

[mortal iris]

I'd leave writing long form math to math writers. I am a physicist in the end. But I do like to have rigorous texts for the purpose of doing the physics as opposed to play around with mathematical structures for fun.

I've not found one for quantum theory that fits the bill that way for me. There are multiple if you put them together but very different styles and almost all are missing the empirical context aside from Cohen-Tannoudji (not exactly rigorous) but even there I feel like there can be improvements.

And foundations is pretty much overlooked.

[gray gazelle]

i see i see

[tender cobalt]

I was planning on writing a theroetical minimum book series on math and physics

starting with linear algebra and analysis then some analysis R^n and then doing some physics with those

lmao

[tiny crescent]

I need a detailed book about Computer Architecture

Talk about computer hardware especially

[hybrid sigil]

I think this one is popular, does it cover what you need? You can google it

[tiny crescent]

Have you read it?

[hybrid sigil]

Nope, only sampled

They also have another one: “Computer Organization and Design”, which is a lighter read

I read the bits of that that were relevant to topics that I found interesting at the time. But that’s only a small fraction of the book

[mortal iris]

Wouldn't that just be Newtonian Mechanics?

[mortal iris]

Great goals to have but I'd worry about finishing what's on my plate first lol.

[hard dove]

is bartle and sherbert good book for prerequisites for real analysis?

[mortal iris]

Prerequisites? It is an analysis book?

[molten gulch]

Is is an analysis book

[tender cobalt]

electrodynamics too

And then some QM

[tender cobalt]

yeah lmao

well it was an idea to learn things myself

to learn and explain by writing

[mortal iris]

No. R^n is Euclidean. We'd need more than the standard topology (metric) on that to get to Pseudo-Euclidean which is correct the playground for classical electromagnetism without gravity.

[tender cobalt]

well i had big ambitions for it lmao

[tender cobalt]

oooo

[mortal iris]

None whatsoever with just linear algebra and multivariable analysis. You need functional analysis bare minimum if you wanna be rigorous and work with Dirac's postulates.

[tender cobalt]

I seee

[mortal iris]

The physics pretend quantum mechanics will be fine tho.

[grave lintel]

its much easier and more fun to say what youre going to do in the future than to actually do it

[tender cobalt]

well i planned all this a year ago when i was just getting started with math lmao

[tender cobalt]

yup lol

[mortal iris]

Or maybe quantum information theory which just works with 2 level systems.

[mortal iris]

With 5 years and counting I couldn't agree more.

[mortal iris]

The best way to do that is doing that everyday as you work. It takes a while until you can get used to this tho. I have several physics courses that I've done through which I always go back and make as rigorous as I can on a weekly basis and type them out. This was in grad school tho.

The one blemish in there would be my QFT courses.

[odd cargo]

funny story: i remember trying to write a book and wasted so much time on it that i almost failed my first year in university

[tender cobalt]

damn

how long do you think it takes to finish learning say linear algebra from something like Shilov@mortal iris

[mortal iris]

Yeah. Prioritize what's in front of you. You'll get the opportunity, eventually.

[mortal iris]

Very subjective.

I'd say at least a month if you have nothing else to do.

[tender cobalt]

ohh

[odd cargo]

learned that the hard way

[mortal iris]

Book writing obviously. Only after writing a book can you learn what the university is teaching you to graduate right? So you should be the authority on the subject and write about it so that the university can give you your degree.

[gray gazelle]

lol

[signal basin]

hey im 16 in the uk , college student studying a level math and further math, i have finished there content in self study and have this book called calculus by howard anton , is this a good book for self study? and if notwhere should i go from here , thanks in advance

[ripe lance]

What calculus book should i refer to as someone in between highschool and stem ug if i wanna learn for my own sake and for my syllabus in the future: apostol vs spivak vs stewart vs thomas?

[old elk]

name of book?

[verbal phoenix]

what are like the goto books for the mathematics of poker?

[thick gyro]

could someone please recommend me a computational linear algebra book? i need a concise book (unlike "intro to LA" by Strang) and that doesn't give a zillion examples (unlike LA and app. Lay's).

something on par with James Stewart's Calculus book but for Linear Algebra.

[loud cradle]

isn't stewart's calculus sort of the opposite of concise?

anyway maybe try lang's "intro to linear algebra"

[thick gyro]

i thought so too, but i tried it and it was a good book. Doesn't go in too deep and give me lots of examples (just one or three is fine).

[loud cradle]

yea fair, but then what does concise mean here

[thick gyro]

atleast for the Calculus I part

[loud cradle]

stewart is like 1500 pages long iirc

the lang book i suggested above is less than 300 btw

[thick gyro]

in this context, a book that explains a topic without going all over the place.

This is such a big problem with Strang's Intro to LA.

even in the first 2 chapters

[loud cradle]

yea, strang is almost synonymous with "all over the place" if that book is anything like his earlier "linear algebra and its applications"

[thick gyro]

i tried that book too, and it felt off from the VERY beginning

[thick gyro]

i'm looking at Lang's book right now, doesn't he write proof-based books?

[loud cradle]

generally speaking yes, but he has written several more introductory books that are mostly pretty good and i think might be in line with what you want

"intro to linear algebra" is one of them

his two calculus books are also pretty good

none of those are proof-oriented

although he does give you reasonable explanations for why things are true

note: he also has another book called "linear algebra" (not "intro to...") which is more theoretical

[thick gyro]

yeah i was confused about that at first, thanks

[thick gyro]

which ones would you recommend?

it could be about any math subject

[loud cradle]

well i wouldn't recommend most of his books tbh, but the introductory ones on linear algebra, calculus and few others are pretty good and more "to the point" than the huge colorful tomes that are often used for those subjects

[thick gyro]

would you recommend the calculus books over Stewart's calculus?

[loud cradle]

if you're looking for computational books (not ones that are proof based) and which are more focused and less full of clutter than stewart, then i think they are pretty solid choices

i can't claim to have read all that many calculus books for comparison though

[thick gyro]

would you recommend any proof-based books? i'm familiar with basic proofs.

ok, i see that his calculus book looks quite nice

[loud cradle]

for calculus? spivak is generally what i would recommend

best calculus book in existence

(it doesn't cover multivariable calculus though)

[thick gyro]

ok, i might try spivak after Lang's book.

[loud cradle]

you could try reading it now if you already know basic proofs

it's proof based but also does computations

has interesting and often fairly challenging exercises too

[thick gyro]

oh, i thought it was solely proofs

[loud cradle]

nope, it proves everything but it has computational examples too, and the exercises are a mix of proofs and computations

[hybrid sigil]

Then it won’t be “calculus”, it’s in the name! Calculus calculates ;)

Calculus without calculations is “real analysis”

[ripe lance]

What calculus book should i refer to as someone in between highschool and stem ug if i wanna learn for my own sake and for my syllabus in the future: apostol vs spivak vs stewart vs thomas?

[humble spire]

Aops

[hard dove]

My bad, for kind of measure thoery amd thing. Thaat comes in real analysis 2 or something.

[velvet flax]

spivak

then dieudonne

or either papa or baby rudin if u dont like the frenchness

[hard dove]

isnt it analysis book? Real and complex?

[velvet flax]

he has 3 analysis books

[loud cradle]

looks like its coverage of topology is pretty limited, you might need to supplement a bit

[velvet flax]

baby rudin is "principles of mathematical analysis"

papa rudin is "real and complex analysis"

grandpa rudin is "functional analysis"

[loud cradle]

unc rudin is "fourier analysis on groups"

[cunning elk]

zapped them before i could finish the mod ping nice

[elder veldt]

Hey guys, can anyone recommend a book specifically for invariants, I don't want something putnam level but a decent book would be greater. Thanks

[hard dove]

yeah, i see. But just wanted to do little practice that I forgot before to start for my measure theory (I'm having backlogs). Topology is not much needed for measure theory.

[loud cradle]

as long as you know enough to understand borel sets etc it should be fine at least to get started

[hard dove]

heine borel sets?

i don't remember them at all. Just know heading.

[loud cradle]

no, borel sets are a measure theory thing, the sigma algebra generated by the collection of open sets in a topological space

[hard dove]

still have to dig that myself. Thank you.

[velvet flax]

is there any way to cover similar ground to kobayashi+nomizu in a clearer idiom

i like it but its a bit painful

[cursive rivet]

basically all of it is covered somewhere else in other books these days, but it's really the only place that covers all of it in one place in that generality

for the Riemannian geometry, the most similar perspective is Salamon's Riemannian Geometry and Holonomy Groups imo, but I think it's best as a second source

for the complex geometry, a combination of Moroianu's book on Kaehler geometry, Joyce's chapters on complex geometry in his book Riemannian Holonomy Groups and Calibrated Geometry, and Salamon should cover similar ground. For the characteristic classes, Bott-Tu is pretty good, and somewhat covered by Tu's differential geometry book

Also, Kobayashi-Nomizu was written before the explosion of gauge theory, which is at a similar level of difficulty but super relevant to all of this. I like Haydys's notes (though tbh there's no book on the stuff I love), which also supplement all of this well, especially the characteristic classes and principal bundles

I can't emphasize enough that you should learn the non-holonomy Riemannian geometry from literally anywhere else as a first source, if you have not seen it before

[mortal iris]

STEM is very broad. I'd argue medicine and bio students don't really need to learn calculus beyond meanings of rates and applications in probability almost entirely heuristically. Engineering and chem students generally don't need beyond calculations with the basics and physics students can go one of two ways, applied where you can do what an engineer does for calc or theoretical where you want rigor. Math students should go through a rigorous course.

[mortal iris]

Never really learned about context huh.

[mortal iris]

You can work it out yourself. Fairly simple combinatorics and game theory.

[ripe lance]

I am considering math/physics/computer science, thats why I was asking so specifically. Using STEM as a broad category was misleading, apologies

[mortal iris]

It's still very broad lol. Computer science engineering and theoretical computer science are vastly different lol. If you have no inkling for what you'd be doing then you can consider Thomas's Calculus. Spivak or Apostol would be better only if you were going into math or theoretical physics/cs.

Thomas is easier for a high schooler to pick up as well.

[mortal iris]

Consider doing numerical linear algebra with a mix of theory and calculations involving computers (because nobody does useful calculations by hand anymore)? A good section of FNC is dedicated to this.

You can couple that up with this book for more theoretical details but still focused on computing stuff.

[tender cobalt]

Also Treil's Linear Algebra Done Wrong is a nice idea too

Not bloated with examples

and concise

@mortal iris Yo do you have any advice for learning chemistry

[proper trout]

Can someone provide rigorous books for highschool mathematics?

[blazing fiber]

Lang - basic mathematics

[mortal iris]

Nope

[tender cobalt]

@mortal iris have you seen this book

looks pretty good

[mortal iris]

No

[mortal iris]

Why?

Cover aside.

[tender cobalt]

Basically book like Taylor but has a geometric pov

Also covers noethers theorem and symmetry, which taylor only mentions

These chapters caught my eye XD

[mossy mauve]

Hi! I hope this is the right section to ask this question. Do you have any recommendation for books focused on exercises of differential geometry? I have an exam coming up and I'd like to practice. The course followed Abate-Tovena's "Differential Geometry". Thank you in advance!

[pseudo heart]

does anyone have any recommendations for a linear algebra book that goes a bit more in-depth into the topics besides "Linear Algebra Done Right"?

[thick gyro]

omg thanks, my goal was to learn NLA after normal LA.

[tender cobalt]

Linear Algebra Done Wrong by Treil

[jade yew]

I'm trying to get into Number Theory(from the little bit I have checked about the subject I find it extremely interesting)

Is there a book which could help me get into this subject(Ie an Introduction to the subject?)

[mortal iris]

Pick up Module Theory by TS Blythe. I believe it's open access. Or Linear Algebra via Exterior Products by Sergei Winitzki. They'll take you deeper in different ways.

[tiny crescent]

I took a look and it showed me that this book is difficult to read

[normal crystal]

the same authors have another book you can read first, Comp Org

[tiny crescent]

I mean

Reading the index alone makes me confused

[normal crystal]

but also, maybe you don't want you actually asked for then

[mortal iris]

Pretty sure an index is meant to be confusing because it doesn't explain anything and just tells you which page you can find what terms

[tiny crescent]

I mean i just want to learn memory

[tiny crescent]

Yes, I didn't understand anything

I just know sram dram cache and some stuffs

When i read the index i said wtf

Suppose i read all of this?

[normal crystal]

why would you look at the index first
instead of the ToC

[mortal iris]

Because the index starts at 0

[normal crystal]

THIS IS SO CRAZY
JUST PAGES OF WORDS AND NUMBERS

[tiny crescent]

Even toc make me confused

[normal crystal]

anyway, Comp Org by them is simpler

[tiny crescent]

Have you read it?

[normal crystal]

parts, yea
but both are well known textbooks

[tiny crescent]

I need someone to tell me
What are the differences between the two books

[normal crystal]

are you ok

[tiny crescent]

?

[mortal iris]

Use hands. Open book. Use eyes. Read. Process. Compute. Return differences.

Which part you having trouble with

If you opened the index again then ig there's nothing more to say.

[tiny crescent]

I mean, the first one is more analytical than designing

And why you guys laugh at everything

[humble spire]

No one is laughing gng

Js go n read

[mortal iris]

I'm not laughing. But if you can tell this much then you can see more by skimming through the books and then you can make a decision.

If you asked something along the lines of "why do you think this book is a better fit for me" then we could give you an argument. Asking for the differences is like asking us to do your due diligence.

[mortal iris]

I skimmed the book a little. Doesn't seem like there's any proper coverage of geometry. Just uses notation that is conventional in geometry.

Why you getting offended? Also you said "I need someone... " so maybe choose your words wisely.

[normal crystal]

I told you one was simpler than the other, by the same authors
and then you immediately said you need someone to tell you the difference

[mortal iris]

Good for you then. It's been mentioned twice by two ppl and now a third time.

Then why ask

Since you supposedly know what ppl have read and not

[normal crystal]

I could have heard of the books this minute and still figure it out
you're not even trying

anyway, gl

[mortal iris]

Oh mb. You were asking for "someone" lol

Not anyone else's problem if you can't read for yourself. And with that I'm out.

Begin at the index. Maybe you'll find out the differences xD.

Wait. Did I throw you?

[hybrid sigil]

Burton “Elementary Number Theory” is nice, I am reading it. Has mostly gentle exercises. A somewhat more difficult book is Niven Zuckerman. It has cooler problems sometimes. And there is also Friendly Intro to NT by Silverman, it’s less of a textbook and more to show what NT is about, I read a couple of chapters for fun, it was entertaining

[mortal iris]

Burton is super nice. I can share a set of lecture notes based on it as well from an undergrad course I did if you want smth concise.

[hybrid sigil]

Wow, so international, we can send this to the stars now, like Voyager

[normal crystal]

hope he appreciates the alien replies more than ours

if you 🤡
you're gonna get 🤡 'ed

[vague scaffold]

ı think you may start with olympiad nt books.

i think adreescu titu is great

[normal crystal]

no piracy

can you delete so we don't need a modping

[tender cobalt]

didnt @normal crystal already tell you

[tender cobalt]

.

??

[mortal iris]

Add Hindi, Mandarin, Bangla, Tamil, Kannada and Telugu as well. After all, most techies around the world speak these as opposed to German or French.

[tender cobalt]

LOL

[mortal iris]

Maybe ask in binary. Your computer might be able to help

Then why you still here

[tender cobalt]

Since u already asked gpt

why are you still here

[tender cobalt]

exactly

GPT should "know" everything right??

Bro cant u just read both books

if you knew what you were trying to learn you would've picked one by now

But what are you trying to learn? whats your goal

Its not a novel bro

[mortal iris]

I think he never looked at this thing called the dictionary and understood the word skim.

[tender cobalt]

Can you just skim through first few chapters

Both books will teach you more or less same thing

[mortal iris]

Another way to do that would be to learn solid state physics and semiconductor electronics.

[tender cobalt]

Yeah that as well

Bro both books teach you how computers work 🙂

Mf did you try reading the fucking preface?

[mortal iris]

Aren't you doing exactly that?

[tender cobalt]

The preface of a book tells whats it about

Read the preface of both books

Then judge for yourself

What did you understand?

Which one does what?

What could go wrong if you end up finishing one book? You'll still learn how computers work and how tf ur asking through this screen thorugh the internet how the io of ur keyboard is typing into discord?

Yeah the preface is intended for the person who never read the book

[mortal iris]

It's not even difficult to find reviews or both books online if you know how to use a search engine.

[tender cobalt]

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

🤣

[mortal iris]

Telugu boi. See. I told you to try Telugu lol.

[tender cobalt]

LOL

We already told you the Organization book is simpler

[normal crystal]

one is their ug textbook
the other is their grad textbook
it's not more complicated than that

[mortal iris]

For recommendations. Maybe try using a dictionary.

[tender cobalt]

Isnt that clear?

If u wanna learn computers

u will need to see indian stuff

all day

[mortal iris]

Racist

[tender cobalt]

you cant fiond shit about computers by americans in youtube

because microsoft google etc are ran by chinese and indian

which

organization?

[mortal iris]

Well not entirely but largely

[normal crystal]

this is going a weird direction
we should move on

[tender cobalt]

Architecture book will be difficult for you if you have no idea what is a computer

Btw both books assume you know programming

so i would recommend you start with something like C Programming language

before diving in to learn how computers work

[mortal iris]

Buddy stop. He has the video. Let the racist watch it and be humbled.

[tender cobalt]

I skimmed it

[tender cobalt]

Yeah right

racist ass squirrel

because i have experience with computers?

@mortal iris This guy is ragebaiting 🤣

Whoever 🙂

[mortal iris]

Ever since he said he read the index, I knew.

[normal crystal]

imagine ending up getting banned because you refuse to read two prefaces
or even the product pages
so it goes

[mortal iris]

Does it matter? You're eventually gonna work for one or remain unemployed.

Statistically at least (with some large errors lol)

Yes. That's why they run the biggest tech companies in the world.

[tame tree]

well thats a sweeping generalization and a half

[mortal iris]

I would agree if you said theoretical computer science given the state of research in our country.

[normal crystal]

<@&268886789983436800>
it's been enough of this

[mortal iris]

Then good luck

Like you even know what I'm referring to.

To agree with that

[zealous coyote]

Don't be racist.

[zinc sundial]

meanwhile I was trying to figure out whether he knew what superficial meant

[real marsh]

I mean play stupid games win stupid prizes is a thing

[mortal iris]

I have half an inkling this guy himself is Indian considering how we tend to be extra racist to ourselves lol

Either way, back to book recs please

[normal crystal]

I do wish there was a way to YouTube search by region
if I missed how, feel free to tell me

[real marsh]

We're also not asking users to send in proof of their race to decide if they're being racist or not 💀

[mortal iris]

Lol dw. Just a passing remark.

[mortal iris]

Use a VPN?

[normal crystal]

I don't think that will influence search much

well, depending

[mortal iris]

It does. The ranks afaik are region dependent and there's also a bunch of paid stuff and features which are region dependent.

But if you wanna filter your videos by source region then tough luck.

[normal crystal]

ok, so I know it will in the large
but for specific things it won't help
yea

[jade yew]

Alright, thankyou!

[jade yew]

I would love that, thankyou!

[normal crystal]

it doesn't help that search in general has gotten worse

[jade yew]

Are they easy to get into?

[hybrid sigil]

I personally don’t think so, I started reading one NT book by Andreescu, and well it’s as you would expect: it starts throwing Olympiad-level problems at you from the very first pages. The proofs are short and somewhat cryptic. It started relying on some properties of binomial coefficients right from the start too (in more usual books they spend a small chapter on binomial coefficients). I think it might be good for prepping people for Olympiads, but not necessarily good for studying NT

I even deleted that book, so can’t quickly give you an example of what I mean, but I hope it’s clear

[jade yew]

Ah alright.

And would you say NT would be that difficult for a person who would be in A level?
-# My self esteem isn't the highest lol

[hybrid sigil]

Shouldn’t be too difficult. You can start with that “Friendly Intro to NT” book by Silverman, see how it goes, and check out Burton too

There are some proofs in those books though, not sure if you are comfortable with that.

[proper trout]

After Lang's basic mathematics what should I use? afaik Spivak's calculus would be too ambitious

Just tryna map out my journey in advance

[mortal iris]

Here you go. And for anyone else that this might help out.

[jade yew]

I find them interesting so I dount that'd be much of an issue.

[jade yew]

Alright thankyou!

[mortal iris]

I'd recommend doing Proofs by Cummings with Real Analysis by Cummings. You could start Proofs alongside Lang's Basic Mathematics.

Real Analysis by Cummings is on the easier side to work through than Spivak' Calculus when it comes to the problems but still gives you a solid background. Iirc it covers a smidge more than Spivak being a proper Analysis book, but it's more gently paced and Ig there's like associated videos online too. I would say, keep Spivak handy though. You could try the harder problems in there later. You should also consider using Pete Clark's Honors Calculus Notes.

Alongside this, take up Linear Algebra Done Right by Axler. This is typically what a first semester undergrad schedule looks like. You could also throw in a deeper dive onto high school material such as Euclidean Geometry to add to this. Or maybe intro to programming.

[tender cobalt]

Any combinatorics books?

[tender cobalt]

He could actually start with Zorich too.

[mortal iris]

Not the best idea if you've not done a course on proofs. He clearly assumes you know how induction, contradiction, contrapositives, construction, etc. works.

He does briefly go over the basics of logic and proofs but it isn't sufficient imho. One of the weaker points of the book.

[tender cobalt]

Maybe he could do a book on proofs and set theory then go on with zorich

[tender cobalt]

But spivak is also a great idea actually

[mortal iris]

And then when he throws ZFC at you for completeness you'd be confused AF.

[tender cobalt]

yea i actually got lost where tf he brought in zfc from 🙂

[mortal iris]

You really don't need much set theory to study mathematics. Naive set theory works perfectly fine and the level of introduction in Cummings or any other standard Proofs text is sufficient.

[tender cobalt]

I mean

Set theory is a good idea to learn proofs with

naive set theory, that is

thats what i mean

thats how i learnt to write proofs, from some naive set theory

[mortal iris]

It is, but you don't need to go through the whole charade. The key elements are enough to motivate different kinds of proofs. And this is covered in nearly every Proofs text.

[tender cobalt]

yeah im not talking about whole

something as much as munkres chapter 1 is enough for most set theory in math lol

[mortal iris]

Consider watching the first two lectures of this course for some context. Or maybe read from these notes.

[tender cobalt]

oh wow i was actually going to ask you about this playlist

😭

I was going to ask how can I supplement it with exercises

[mortal iris]

It is fantastic but I'd recommend this only if you have the mathematical maturity of at least Analysis 1.

[tender cobalt]

Ye i have that much maturity i can say that

the only immaturity i have is laziness and inconsistency 🤣

[mortal iris]

So you've worked through a full course on Real Analysis?

[tender cobalt]

anyways how can i supplement it with exercises

[tender cobalt]

not really full

i havent done series and riemann integration

[mortal iris]

First get that done with. This course more or less demands it of you.

[tender cobalt]

other than that, i covered metric spaces, sequences, limits differentiability etc

[tender cobalt]

alright

[tender cobalt]

But arent u not fond of "X of Physics" "X For physics" stuffs

[mortal iris]

There are exceptions. He does it the way I like it.

[tender cobalt]

ooo wow

okay now tell me how can i supplement it with exercises

[mortal iris]

I'd be remiss in saying that his courses are probably what informed my taste as well lol

[tender cobalt]

Oo

[mortal iris]

Although I started with his lectures on GR of which this is essentially an expanded version.

That one has some problem sheets you can try out. Much would be relevant.

[feral maple]

Hi everyone, I'm looking for a differential calculus book. Some recommendations? (I'm studying electrical engineering)

[remote knoll]

Like a bog standard introduction to calculus book aimed at first year engineering students?

Stewart

[mortal iris]

Thomas's Calculus.

[mortal iris]

Or that if you want broader material.

Paul's Online Notes are also an excellent resource.

[remote knoll]

Khan academy has a course as well

Lots of options

[feral maple]

Thanks!

[feral maple]

I have this one

[obtuse thistle]

Hey guys starting sem 2 of 2nd year now. Upcoming modules are real analysis and also complex analysis. I’ve heard good things about understanding analysis by abbot so I have that on my buy list, what do you reccomend for complex.

[odd cargo]

use whatever ur uni recommends

theyre usually good books

[vital bane]

Peakkkk

Abbott is peak

[obtuse thistle]

Yeah I think I’ll buy it for real

Strangely I’ve heard real is harder than complex but my module is only 10cred vs 20 on complex

[vital bane]

Yeah if you learn Real anal properly, complex anal will be easy

[obtuse thistle]

Ah ok

I’ve got them at true same time lol

[mortal iris]

Stein and Shakarchi

[mortal iris]

It very much is. The reason your module works like that is likely because Complex Analysis has many areas of applications that are coverable in a standard course such as some connections to number theory, special functions which are common in applied math and sciences, among other things.

Whereas with real analysis, the real fun begins when you branch out to analysis on manifolds or measure and integration which in themselves are so vast that it cannot occupy the same place as a standard real analysis course. Not to mention there are interesting things like Fourier Analysis, Differential equations, etc. So Real Analysis courses often tend to be minimal.

[mortal iris]

It's quite anal to call them anal

[obtuse thistle]

Ok Ive bought Abbot, unfortunatley my uni only releases its reading list next week, so im unable to view lecture notes and suggested books until then.

[queen hedge]

Has someone read any recent exciting math/research paper they'd recommend ?

[static idol]

Hustlers academy: the rise

[blazing holly]

It depends on what areas of math you’re into

[mortal iris]

Plenty of good stuff on vixra

[violet portal]

Does anyone have a book recommendation that covers topics of graph theory

[molten gulch]

Diestel

Bollobas

Bondy and Murty

[slow roost]

I used Agnarsson & Greenlaw in undergrad and it was one of my favorite classes. Never checked out another graph theory book though

[velvet sandal]

diestel the goat

[odd cargo]

that dude the other day genuinely gave me motivation to read through those old euler books and thats what i've been doing these past couple days

eulers got it for sure.

[slow roost]

which have you been reading?

he was pretty good

[odd cargo]

foundations of integral calculus

it kind of feels like reading through notes

[bright epoch]

Bollobas extremal graph theory

Excellent book

[sick hemlock]

guys what math books do you reccomend

idk

math

oh

but i want math

just general math

like in math in general

im currently studying math

dude, i gave you context just math in general

like just math

what more could you possibly ask

MATH

like addition and math and stuff

numbers

[obtuse thistle]

https://tenor.com/gB6d3hBjctE.gif

[sick hemlock]

wdym huh

im just doing math

dude i expected this server to be smarter

is algebra the same thing as math

is that a yes or no

[obtuse thistle]

https://farside.ph.utexas.edu/Books/Euclid/Elements.pdf

@sick hemlock

[sick hemlock]

the link doesnt work for me

is geometry a type of math

what does that e thing mean

this is so confusing

kindaergarden-ahh bro

[obtuse thistle]

hes clearly ragebaiting the guys got primus top 1

[sick hemlock]

dude are you serious

[obtuse thistle]

Mid list

[sick hemlock]

WHAT

[obtuse thistle]

Honestly all mid takes

[sick hemlock]

no primus is goated

[sick hemlock]

wait are you rage baiting me

im confused

i unironically love primus

this is my server

[viscid remnant]

let's stop this conversation and stick to this channel for book recs only

also please do not post server links

[sick hemlock]

[sick hemlock]

mb

do u even know who primus is

[viscid remnant]

<@&268886789983436800> user is clearly ragebaiting and posting server links and ing when being asked to redirect a conversation.

[edgy ermine]

yeah primus is pretty good

[sick hemlock]

do u even know fugazi or operation ivy?

[rapid fjord]

stop posting your server link

[sick hemlock]

YES

[obtuse thistle]

not top one cmon

[sick hemlock]

ok ok

[rapid fjord]

and this conversation is really off topic for the channel, please redirect to #chill or #discussion

[sick hemlock]

k thx

[sick hemlock]

but they are good arent they?

whos UR favorite band?

wait go to chill

[edgy ermine]

i recommend the very hungry caterpillar as a book

[obtuse thistle]

idk dawg im just looking for book recs

[viscid remnant]

do you understand redirect. This is the third time you're being asked

[sick hemlock]

me 2

its so peak

[sick hemlock]

the very hungry catipillat

[molten gulch]

For what field?

[velvet flax]

inverse semigroups, the theory of partial symmetries by mark lawson

[steel peak]

Someone pls give me an book recommendation

[velvet flax]

sheaves in geometry and logics: an introduction to topos theory

[obtuse thistle]

Bros on a roll

[steel peak]

Alr

Thx

[velvet flax]

i have a mental library of books to ragebait with

[steel peak]

Wait

But it’s 50 dollars off Amazon?

Have any other apps to use

?

[molten gulch]

for what

like what field of maths

[steel peak]

The boo costs 50 bucks

Have anything cheaper?

[molten gulch]

https://linear.axler.net

here's a free book

ig

[steel peak]

Alr alr

So uhm 59 bucks again off Amazon…

[molten gulch]

yes it's free for the pdf

[steel peak]

Oh thx

[obtuse thistle]

Do u have a uni library?

[steel peak]

@obtuse thistle @molten gulch thx

[obtuse thistle]

Most of the time u can just borrow it and most unis will have the book u need

[molten gulch]

I mean, what do you want books on

what subfield of maths

if you're not specific people will recommend damn near anything

[obtuse thistle]

like sheaves in geometry and logics: an introduction to topos theory

[velvet flax]

sketches of an elephant

[obtuse thistle]

thank you femboyl0ver9 🙏

[velvet flax]

also maybe differential forms in alg top

but thats a somewhat different flavor

[obtuse thistle]

just keep it coming

[velvet flax]

kobayashi+nomizu

[obtuse thistle]

https://tenor.com/wtGq.gif

[velvet flax]

may's a concise course in alg top

dieudonne's treatise on analysis

also engelking's gen top bc its useful as a ref

[molten gulch]

🔥

I like lee or munkres for basic topo

[daring wolf]

munkres is awful

cant read that shit yapping

[molten gulch]

Munkres definitions feel weird to me, not because they're improper definitions, but he just says so much in the definition

[daring wolf]

yeah

[molten gulch]

like

one seems far easier to understand for me than the other

[vital chasm]

The perspectives are different
The former is what you would exactly do if element chasing

[molten gulch]

Ahh okay

[mortal iris]

No Longer Human by Ozamu Dazai

Undefined notation to a reader is the most non mathematical thing. It may be common for us but not for everyone.

[violet portal]

Anyone have a good book suggestion on The Langlands Program aka the "Grand Unified Theory of Mathematics"

[chilly willow]

I'm finishing precalc, starting calculus soon. I realized that it might be a good idea to have better geometry foundations. Any recommendations?

[remote sparrow]

start calculus

[violet portal]

You should probably work on trig fundamentals over geometry and I would recommend college trigonometry by Carl Stitz but if you really want to do geometry then geometry by Harold R. Jacobs is a good option

[chilly willow]

why its a good idea to avoid geometry now and go directly to Calculus?

[chilly willow]

I might do trig alongside calculus

[violet portal]

Fair point

Thanks

Thanks

[remote sparrow]

because you're finishing precalc? why delay calc?

[remote sparrow]

precalc has trig no?

[chilly willow]

yes, the book I'm using teaches algebra, then very little calc and lastly trig

but I didnt feel very comfortable doing trig

[remote sparrow]

try a diagnostic test from stewart's calc book

https://tenor.com/view/dbz-discord-gif-24306382

@green aurora

[chilly willow]

good idea, thanks

[stuck delta]

does anyone know any sources to find pdfs of iwritemath books? I do have a physical version with me but it is already written and i want to study blank pages for a math final

[tender cobalt]

same

[cedar crypt]

This is from Munkres right

[remote sparrow]

the passage from the left is

[cedar crypt]

Yes yes.
I heard that the book is amazing but I didn't find it that helpful ngl

[tender cobalt]

Helpful for?

It's a book just focused on topology by itself

[tender cobalt]

Thats actually a great benchmark to see if ur able to start calculus or not

I finished most of precalc from his appendix 🤣

I did all 80+ trig proofs

[cedar crypt]

Self study 😞💔

[tender cobalt]

it is

actually pretty nice for self study

cuz its easy

[cedar crypt]

Maybe I am just too dumb

[cedar crypt]

Not everyone is smart bro

[tender cobalt]

It doesnt require smartness dude

Have you done chapter 1 properly?

[cedar crypt]

Sure

[midnight gulch]

"too dumb" = not enough preparation

[tender cobalt]

If you can do all exercises from chapter 1, then topological proofs become really easy

[tender cobalt]

This.

@cedar crypt What are you trying to learn in topology?

[tender cobalt]

i cant find, do you have

[mortal iris]

Here. It's among the top 3 pages if yk what to search for 😑

[tender cobalt]

Thanks

[tender cobalt]

Wow with video solutions

[hybrid sigil]

Ah, those famous video lectures! I think I even watched 3-4 of them myself

It was quite inspiring

As a motivation for different areas of mathematics

[frosty pond]

Don’t mind this guy he’s ragebaiting

[split trench]

Hello

[tender cobalt]

Love how Schuller clearly speaks and has proper articulation in every single word he says.

[mortal iris]

Aye. He's very well articulated despite English not being his first language. We invited him over for a conference as well at my prev uni. Brilliant man.

[tender cobalt]

Coool

[shrewd wyvern]

Hi guys. Can someone recommend good introductory real analysis books? Thanks in advance.

[twin parrot]

Abbott

[molten gulch]

Read the list in pins

[tender cobalt]

Any good NT books?

[chrome wasp]

Schroder

[tender cobalt]

☠️

[wet sentinel]

what NT tho? elementary, algebraic or analytic?

[tender cobalt]

anything 🙃

[wet sentinel]

apostol's introduction to analytic number theory

[odd cargo]

whats a good book on proof theory

[remote sparrow]

https://www.amazon.com/Theory-Cambridge-Theoretical-Computer-Science/dp/0521779111

#book-recommendations message

[obtuse thistle]

I got a question

when u guys go thru maths books do u guys write everything down and prove it.

Or do you just read, try to understand then just do examples

[bright epoch]

it depends on the book and my familiarity and what I want out of it

[ashen galleon]

Personally ,I survey the concepts to grasp their structure, trace the proofs to internalize the underlying logic, and then work on examples to solidify my understanding

[violet portal]

Anyone have a good book suggestion on The Langlands Program aka the "Grand Unified Theory of Mathematics"

[molten gulch]

Generally it takes a lot of work to start reading about langlands, and a lot of the work is still in the form of papers, not full compendium sized books yet. Start by learning some algebraic number theory and then class field theory (I think)

CCing @wicked fractal bcz I think they know a bit more about number theory than us

[violet portal]

i have already read and did number theory and class field theory

[dapper bobcat]

Hey guys I’m just average at math. I come from a family that isn’t all that strong academically so I’m doing decent with where I’m at. I’m taking AP CALC AB. I love thinking about math and if I was a math super genius and I wish I knew more math and could use it to help others. But in school I sometimes get confused. Are there any books I can read to help me improve my math skills, become faster at generic math skills, and books that will help me understand more advanced topics.

[mortal iris]

Well for starters speed isn't really relevant to doing or thinking about math. That's useful only for competition and grades. So take your time.

[tender cobalt]

Check out Thomas Calculus

[violet portal]

He said he was in calc ab and wanted to work on the fundamentals not calc 1 2 and 3

[violet portal]

Any of the basic math books by the for dummies publisher will do I would do the algebra 2 one and also geometry and maybe that one about a refresher for adults

[midnight gulch]

beautiful

[tender cobalt]

he said he wants to improve his math skills and understand more advanced topics

and asked for a book suggestion

so i said thomas calculus

if he does first 5 chapters that pretty much covers him for calc ab too

[tender cobalt]

or a precalculus book

[tender cobalt]

Apostol vs ireland rosen

NT

[junior palm]

has anyone read advanced modern algebra by joseph by joseph j rotman? how is it

[remote sparrow]

just cover a subset of the book?

[tender cobalt]

exactly

[tender cobalt]

the latest edition is two parts

Its a pretty nice book tbh

i read some parts

but would probably not be a good idea for first time learning algebra

[velvet flax]

it seems nice from what ive read of it

rotman's writing style is generally very lucid

however, my principal recommendation for an algebra book will always be lang

[velvet flax]

lang feels more comprehensible than dummit and foote for some reason

[velvet flax]

i think his presentation of the topics is just seductive

it tastes like boiled chicken with no spices

[velvet flax]

simon's course of analysis

and to a lesser extent kobayashi and nomizu

bc i was reading a book on mechanics

and the stuff in k+n contextualizes it nicely

[remote sparrow]

https://www.math.harvard.edu/in-memory-of-professor-emeritus-benedict-gross/

[tidal coyote]

https://math.stackexchange.com/questions/3781324/prove-int-02-fracdx-sqrt1x3-frac-gamma-left-frac16-right-ga?noredirect=1

where can i go to learn stuff like the top answer here

elliptic curves

[fresh skiff]

oh God the professor passed away 😭

[lament scaffold]

Just a side note, what's everyone's most enjoyable book about science

Not looking for anything to learn but just a good read for entertainment

[tender cobalt]

Any good algebra lecture series following something like Jacobson Basic Algebra

[tender cobalt]

OH NO BRO 😭

JUST AS I WAS ASKING FOR AN ALGEBRA LECTURE SERIES

OMG

💔 😭 💔 😭 💔 😭 💔 😭 💔 😭 💔 😭

[heady ember]

Richard Borcheds

[gleaming mango]

Does anyone have a math book recommendation which i can buy to improve?

[normal crystal]

you're gonna have to be more specific or nobody will answer

[gleaming mango]

I am a highschool student on the 2nd year and i want to improve my math. I want to have a solid base and still get further trough the equations. If someone could recommend me two books, being one, to have a great solid base, and two, to improve and get further into equations.

Thx

[mortal iris]

Bruh

[odd cargo]

rotman is 👍

[desert wraith]

Any good recommendations for elementary number theory? Gonna study it on my own

[mortal iris]

Burton is a great place to start

I also sent in some notes here earlier that you could use. They're based on Burton and more concise.

[molten gulch]

WHA-

This is...news to me

[desert wraith]

Thank you very much

[polar goblet]

What are some good books to learn proofs

[molten gulch]

hammack

[polar goblet]

Thanks

[mortal iris]

Cummings

And that's a lot of different scripts in your uname

[polar goblet]

:3

[polar goblet]

I’ll give it a shot

[tender cobalt]

Difference between Apostol and Ireland Rosen for NT?

[mortal iris]

How many books are you working through lol

[tender cobalt]

none

😭

Yo guys I can't find Legendre's Formula in Niven's NT book. If anyone knows if the book has it or not, please let me know

[molten gulch]

Bro don't end up like ASR just start a book 😭

[tender cobalt]

😭

2-3 probably

[mortal iris]

I don't even properly read books anymore. I just take what I need and move on. It's been a few years since I needed to work through a book. Back when I used to it was typically around 3-4 shuffling them around until I was done. Higher the number, more independent the books were.

[slow roost]

yeah I couldn't even tell you how many books I'm "reading" at the moment. I just pull different ones from my collection and dip in for a few pages / problems

there are a few more main ones

I'm preparing to take the math GRE subject test again, so I'm reviewing basically all undergrad material

[mortal iris]

Aren't these like predominantly MCQs?

Granted they can be interesting ones

But do they actually test for any skills in writing proofs?

[slow roost]

yeah it's all multiple choice. Roughly 50% calculus, 25% algebra, and the rest is a mix of pretty much everything. Some analysis, topology, graph theory, number theory, even stats

it doesn't really test proof writing skill, but definitely being able to apply major theorems

[mortal iris]

Weird imho. Considering that's what UG math is meant to train. This looks more like UG physics/applied math of sorts.

Ig there's not enough manpower to check proofs and even if there were, there can be a bias because even career mathematicians can write mildly shaky proofs and they all have eccentric tastes.

[slow roost]

yeah, there are a lot of strong undergrad math majors who struggle with this test because they haven't practiced integration for years

[mortal iris]

Oh no. It's the find the magic trick type of problems eh.

[slow roost]

eh, maybe a few, I think it's mostly fairly straightforward. But the time factor is killer

2 hours 50 minutes for 66 problems

I totally bombed it the first time I took it

[tender cobalt]

same LOL

[twin parrot]

What do you mean "don't end up like ASR". He's already kinda inconsistent like me lmao. The difference between he and me is he knows the chapter 1 of every math topic

😭

+He knows how to code

[mortal iris]

That's the entire purpose of choosing to do things that are largely independent or can reinforce what im learning. I had one year which I just spent on QM (Physics version), Functional Analysis, Quantum Foundations and Convex Optimization.