study-discussion

[lament heath]

<@&268886789983436800>

[odd imp]

Hi everyone, I have just joined this server and did not know where to share this (hopefully this channel is appropriate. If not, lmk and I can delete it). So I graduated 3 years ago and took some math courses during my undergrad program (there weren't that many options but I took the courses that I could get).

Anyways, after graduating from uni I registered for a online self-paced calc 1 course from ASU but found it hard to commit to it. Learning math in general was hard for me for some reason. I guess it has to do with transitioning from a structured classroom environment to independent learning? I am not sure.

I have recently decided to give math another shot by taking that online calc 1 course again. But I have noticed that I am experiencing the same motivation and concentration issues. I don't know if this is a sign that I am am finding it hard to do math beyond pre-calc? I have also tried various study techniques (pomodoro, to-do lists, independent deadlines, etc) but none of them seem to be working. I am not sure if anyone has been through something similar? If so, how did you figure out your ideal way of studying?

[abstract radish]

alright guys best study tips?

[floral musk]

adderall

[abstract radish]

?

pls i need this its finals

[floral musk]

what specifically are you studying

[abstract radish]

trig, slope(linear+non linear eqn), factoring, geometry, power rules

ib grade 9

[floral musk]

oh then just do a shit ton of problems

but what do you mean by power rules

like in the sense of calculus

[abstract radish]

exponent laws

[floral musk]

oh

[uncut saffron]

After having studied through James Stewart essential calculus 2nd ed, esp nearly all of the problems except for going through maybe 2/3 of the vector calc chapter;

If I finish up the vector calc chapter of that book, do you think I will be fine moving onto Differential Geometry of Curves and Surfaces by Do Carmo?

I'm looking at this book because I've had a lot of interest in sampling points on surfaces and playing around with parameterizations of surfaces, and I'd looked into what book might be related to that and I landed on the Do Carmo book :)

Thank you

[scenic shuttle]

<@&268886789983436800>

[viral osprey]

Bot is slow :/

[silent tangle]

legendary thorn sighting

[viral osprey]

Typo

[scenic shuttle]

he was giving us free money 🥀

[red rapids]

Typically no. Stewart doesn't prepare you for a course that requires you to prove things rigorously. You at least need a course on proofs to consider starting elementary differential geometry. Preferably a course in real analysis.

Also O'Neil's Elementary Differential Geometry is a better alternative to Do Carmo and might just be accessible without a course on Analysis.

[uncut saffron]

Oh thank you, this is good information, I'll definitely start some study on real analysis and look into proofs more :)
I really appreciate the recommendations, and thank you for recommending a specific text.

If I am just applying the mathematics for ex in deriving sampling distributions for programming, how can proofs improve my ability to apply that math or think about how to apply it? I don't have a lot of experience with proofs, but I am definitely open to giving them more of my time.

[red rapids]

Won't really help much practically unless you have rather specialised knowledge about relevant algorithms and proofs associated to their analysis and optimization. But as a skill, It does make your logical application razor sharp though and makes it easier to identify bugs.

A much more applied introduction would be Kreyzig's Differential Geometry. He does write for an audience without the mathematical training to do rigorous proofs. But I suggest giving O'Neil a try. It's objectively the better book to read from.

[uncut saffron]

Ooh interesting. Perhaps after studying more with proofs I'll work through that text :)
Thanks! You've given me a lot to think about :D

[forest atlas]

is this splitted formula considered like an error or smth graders would take away points in general?

i could center it with white space but that would mess up plots again

[lost drum]

Hello ,

in task management ,brian tracy and other experts in time management advice to start by the MIT:most important task in order to priorise the to do lists of tasks from most important to less important , but What's the importance property of tasks and goals ?
Because when we try to apply that method on everything ,judjing that thing to be very important and big and conciderable and significatif
what it means generaly and exactly ?

[floral musk]

when reading a book with no exercises (e.g. kobayashi+nomizu) how do you make sure the material crystallizes in your brain

ig proving all the theorems works, but then you run into the issue of time management

[normal sleet]

I'm here because I want answers to this too
So far I'm just going through the theorems one by one in Stein's singular integrals but its taking a lot of time

[modern crescent]

Anyone here understands modular multiplicative inverse?

[compact fjord]

if i am correct you add mod to the multiplicative inverse. Eg -7 will be 1/7

[normal sleet]

Suppose that y and m are coprime, that is, gcd(y, m) = 1

By Bezout's lemma, there exists two numbers a and b such that
am + by = 1

Now if I hit this equation with mod m, I get
(a mod m)(m mod m) + (b mod m)(y mod m) = 1 mod m

But m mod m is 0, so we get
(b mod m)(y mod m) = 1 mod m

Therefore you see that mod m, multiplying by b somehow undoes multiplying by y (because b*y=1 mod m), so we call b here the multiplicative modular inverse

[normal sleet]

You are not correct

[raw tinsel]

-7 * 7 === -49 !== 1 (mod 3)

[modern crescent]

I do get that.

I was using Euler's method to calculate the modular multiplicative inverse and they somehow converted 27 to 7. I'm trying to understand how they got 7 from the 27.

[normal sleet]

Mod what

[raw tinsel]

oh god, is that AI

anyways 27 is in the same equivalence class as 7 modulo 10

because 7 differs from 27 by a multiple of 10 (by 20 = 2 * 10, to be exact)

[normal sleet]

mod 10 is just taking the last digit, and 27 and 7 both end with 7...

[modern crescent]

I just asked it to list the ways to calculate modular multiplicative inverse.

[raw tinsel]

for something as simple as that u would probably not use / need that method though

i mean you could just brute force it

"what multiplied by 3 is 1 modulo 10"

(and one may observe 3 * 7 === 21 === 1 mod 10)

[modern crescent]

I can't when I'm using it for RSA encryption

The number is gonna be extremely large

I can't brute force it for such a big number

[raw tinsel]

well you aren't going to be calculating it by hand either

[modern crescent]

That's why I wrote a python program

And it's giving out errors ;-;

[torn olive]

If you're writing a program, finding the coefficients for Bezout's Lemma in your situation is the best way to go about this. There are plenty of online resources on how to compute these coefficients. The term to search is the "Extended Euclidean Algorithm" @modern crescent

and also test on very small cases that you can verify by hand (good general debugging advice)

[torn olive]

and then in particular for RSA it is very easy to also compute the euler totient. More specifically if p, q are your primes, the phi(pq) = (p - 1)(q - 1)

so then given your public exponent e, it is very easy to find the modular inverse of e mod phi(pq) via the Extended Euclidean Algorithm

[modern crescent]

Yea I'm using that.

[modern crescent]

def modinv(a, m):
    if gcd(a, m) == 1:
        result = a^(etf(m) - 1)
        return int(result)

My code for the inverse.

Euler totient is just (p-1)(q-1)

[torn olive]

ok so big issue number one

all these computations are supposed to be done modulo some number

you shoudl be doing that, not just computing the power

computing large powers is very hard
computing large powers modulo N is very easy

[modern crescent]

ahhh

No wonder I'm getting the wrong values

I'm guessing I didn't get the math well enough

That's why my program is malfunctioning

[modern crescent]

If I were to calculate it on paper for smaller numbers, how would it go?

[torn olive]

I mean essentially you take mod as you go

and choose small primes to work with

like if you want to compute 5^3 mod 7, well 5 * 5 = 25 = 4 mod 7

and then 5^3 = 4 * 5 = 20 = 6 mod 7

rather then doing 5^3 = 125 and then doing mod 7

for doing this in Python, the pow function takes an optional modulus argument

you can look up the docs

[dusky glade]

Hm, I'm no longer burnt out 😳😳

[edgy sierra]

i'm completely burnt

roasted

cooked

[lost drum]

Hi ,

Tell me Goals to fix in mathematical learning ?

Goals to fix when we read textbook and the goals to fix when we do exercices ?

[normal sleet]

Most importantly have fun

[lost drum]

Yeah , but a study goal ?

[normal sleet]

It completely depends on you surely
If you want to then do the exercises but it completely depends on book
Some books don't have good exercises
Some books don't even have exercises

[lost drum]

What goals should one set when studying mathematics?

What goals do high-performing and very expert people set for themselves when studying mathematics?

Like tell me the goals you set when in a book there is no exercices .

[scenic shuttle]

reading papers online or finding another book

[normal sleet]

Again this depends on the book
If I just need to know it somewhat ill get the main ideas and move on
If its crucial to my work I'll go through everything in detail

[foggy horizon]

Do you personally move on from an exercise set once you feel like you have a solid grasp of what the section/chapters exercises are trying to make you apply?

I feel I have a good grasp of proofs with quantifiers but don’t know if I should continue the rest of the proof with quantifiers sections exercises,or move to the next and do them later

[normal sleet]

you dont have to do them all

at least read them all

even trying to understand wha all the exercises are saying is reinforcing the concepts

[foggy horizon]

I always take a picture of the entire exercise part and then pick out the ones that look fun

[normal sleet]

nice

also you're not obligated to stick to the book, if you think you wanna move on feel free

[final goblet]

can somebody explains me groups rings and fields?

[lost drum]

Yes , my problem is that I dont know what to want ?

, what is the goal to set ?

Here is a list of some :

Mémorise important formulas and why they work

Applying concepts to reinforce our training and being powerful and speed in solving biger problems and challenges with easyness .

Solving our gaps and difficulties and our ignorance , having a lot of techniques to solve a question but as a good directive goal it may be a hard exam to solve in time limits , understanding reasonings.

And there are other goal's to set .

Tell me a list of important goal's ?

[viral osprey]

Nobody has a single list of definitive goals you can/should follow. The reasons why any person would study a thing will differ from person to person. People can give you general goals that apply to most people. But usually those are pretty obvious.

For the practice of learning a given thing in math it's going to be different for everybody also.

There's a spectrum between staring at the cover of a book and never looking at it or thinking about it again and reworking every detail of the book multiple times in depth.

A lot of what you ought to do is determined by context. Do you have the next couple years to work on this one book? If not, the latter end of the spectrum is not appropriate (and for most people this is the case).

Do you care to learn the contents of this book/topic? If yes, the former end of the spectrum is not appropriate.

For actually studying a particular book, usually the things you can do are also kinda obvious. Can you do every exercise? Can you reprove every theorem? Have you memorized every definition and result? Have you rewritten everything? Could you lecture every detail in a class format? Have you tried? etc

Should you do all of these exhaustively? Probably not. That would be incredibly time consuming and very hard.

Which should you do? It depends on what you think works for you, how much time you have, how much you care about this particular book, blah blah.

I had a prof once tell me the way she studied was by lecturing the material to their teddy bears.

I had another prof once tell me the way you should study is by sitting down by yourself and thinking real hard about the material.

Both are sorta silly in their own way lmao

[lost drum]

Yes, but a mathematician who is powerful

[viral osprey]

Who cares whether you think they are powerful?

[lost drum]

Or someone who is the best student of his country , have a goal that I dont know .

[viral osprey]

If what they do doesn't work for you their approach is irrelevant to what you ought to do.

[lost drum]

Yes but maybe they have some goal's like : making theories well logicaly constructed

By formalising them .

[viral osprey]

This falls under what I said earlier

The general goals most people share tend to be fairly obvious. The rest tend to be contextual and specific.

The goals of somebody doing number theory and of somebody doing set theory don't always agree.

For example

[lost drum]

Yes ,

But sometimes we can fix really bad goal's

Or the one that doesn't matter

And following the worst path .

[viral osprey]

I think it would be silly to assume you can fix peoples goals in cases where they study fields that you know nothing about.

[lost drum]

Yes, that's why I need an expert of a field

His knowledj to have a good guidance .

because I may follow goal's witch are just time loosing

[viral osprey]

If you're talking about for your own personal benefit, then I think you waste a lot of time trying to metagame and over philosophize rather than ... actually just doing math...

[viral osprey]

The list of things you can/should do/try are kinda obvious if we are talking about learning math.

You basically just have to try stuff and figure out what you feel works best for you.

Oh yeah, worth mentioning, Lara Alcock has some general books related to this that you might like.

"How to think about analysis" is one of them iirc

How to solve it by polya is also roughly relevant. But that book is a little dry imo.

[lost drum]

Yes

Me I have a rule is if we dont have the right goal's we will have not significant one's

When knowledj and consciousness are expended

The best goal's will be known

And their plans will be known .

It's like a child Goal is to by a chocolat but a mature one is different .

As a begginer in maths like undergraduate is to solve an olympiade

[viral osprey]

Goals and plans differ from person to person. It would be kind of silly to claim that there are "best goals" in general or even in math.

[lost drum]

Yes, but the imagine the biggest ambition of high school student is to solve an olympiade problem or obtain bacaleaureat with 20/20 mark

Or else

But an advanced mathematician

Is to unifie all domains of mathematics

[viral osprey]

Have you ever actually talked to a mathematician?

[lost drum]

But the high school will not fix thouse goal's because of the limits of his consciousness scope .

[lost drum]

The professors of my département

And I read also Poincaré, Dieudonné, Hilbert ..tao

[viral osprey]

You've walked away from those interactions making conclusions that are pretty silly.

[lost drum]

Like imagine you try to explain for a boy the sexual pleasure

He will not understand it

He will associate it to his prefered chocolat ..

And a simple adult also will not have Elon Musk goal's

To colonise multiplanets spaces and colonise mars ..

[viral osprey]

Do you know what a faulty generalization fallacy is?

[lost drum]

Because he has not knowledj .

[viral osprey]

Follow up question: Do you see why this is an example of one?

[lost drum]

Yes , because

They wanted to sum up and synthetise all works

Between 1700-1900

and gived unique axiomatic systems and order all domains

With geometric topology and diff geo ..

[viral osprey]

You have no clue what you are talking about

Some people wanted X to do X, does not imply all people want to do X.

[lost drum]

Search architecture of mathematics Nicolas Bourbaki

[viral osprey]

No, use common sense.

Mathematicians are not homogeneous

Not all mathematicians have the same goals

They don't all study the same way or do the same things.

[lost drum]

Yes

[winter nebula]

Guys

What if

I work through examples

And read a math book actively

But not do a single exercise/problems/proofs

And finish the book

What's the outcome

Do you think there's anything to gain at all

@green terrace what do you think TCC

[lost drum]

And then it's not simple, because some are working on real world problems ,some are very creative ... like the World champions knows what are the goals that matters and thouse to attack in the math oceant :

Euler ,kolmogorov,tao..

But you will find a professor of 75 years old that didn't accomplished anything

Interesting .

[winter nebula]

What's accomplishment lmao

[green terrace]

No, you need to do the exercises for the ideas to really stick, a small amount may, but you won't be able to use them unless you have experience working through the arguments yourself

[winter nebula]

Doing something "groundbreaking"?

do you know most areas of math and sciences like physics chemistry whatever

is built upon works of one another

no matter how trivial

[green terrace]

What one person might find interesting, another may not find as interesting

Like, I personally am not very deeply invested in number theory myself, similarly, a combinatorialist may not be directly interested in the geometry stuff I'm interested in, for example

[winter nebula]

Even one of the most "groundbreaking" theorems are not "accomplishment" of a single person but thousands of professors who contributed to subsubsubsub cases

[winter nebula]

Yeah

[green terrace]

Now, I know there's deep connections between all of these fields (namely I think Langlands connects rep theory (which has some combi in it) to alg geo and number theory, so-)

[winter nebula]

Yeah

But it's still not like a "grand unification"

[lost drum]

You know because why, you will find yourself inside the mathematical oceant with a library of 199 millions books and you fix random goal's with random tasks and then there's no meaning it's very confusing .

[winter nebula]

the domain still differs

[green terrace]

Yeah, people in those intersections will have to know of (and probably enjoy using) most of the tools that they need to bring between sides

[winter nebula]

That's because you can never learn everything?

What's a random goal lmao

[normal sleet]

I think 99.9% of us aren't going to be Gauss or Kolmogorov or Tao and there's nothing wrong with that
The big figureheads are too busy directing the field, the small fry like the rest of us can clean up the details and develop their ideas further

[winter nebula]

And even Tao doesn't know everything

He doesn't even know epsilon % of entire world's math

No one does

[normal sleet]

Both are equally important
Math is built on piles and piles of trivialities
Any work you do is a contribution however small

Just have fun so that you're happy and willing and able to contribute in your own way

[winter nebula]

Everything matters

Every single math area matters for the future of human race

you never know where you may end up using something

[green terrace]

Also, personally, I see maths as an end in itself, not really as a means to an end, so I'm just content learning whatever tf interests me

[winter nebula]

When Gauss and Riemann developed differential geometry they didn't know it would be used in modern theoretical physics and even machine learning and data analysis to solve real problems after 200 years

[normal sleet]

Yeah real life applications don't exist here, no one cares whether my solutions lie in what sobolev spaces

[winter nebula]

When the quadratic guy solved shits by making this complex number thing up out of the blue

who knew that it'd actually prove usefulness to real world?

I mean even negative numbers and irrational were thought to be absurd back in the days

but if these guys did not persue any of these thinking "its not an accomplishment im not really doing anything meaningful"

Would we have come this far?

[winter nebula]

Yeah

Just find curiousity and chase it

That's literally all it takes

And you don't have to solve Millenium problems to contribute big

[green terrace]

Also as a system, it turns out that each of us have very varying interests in mathematics

[winter nebula]

James is goated

[green terrace]

Like, I personally like geometry quite a lot, James likes theory of computation, computability, and complexity theory, logic, type theory, numerics and symbolic algebra on computers, etc..., Astrid likes c*mbinatorics and g*aph th*ory, etc....

[winter nebula]

Bro is a polymath of ultimate form

[green terrace]

Yeah it's goated as hell

[winter nebula]

Firstly I get 20 friends for free from you

who wishes me on my birthday

And then these 20 friends know different areas of maths

wild

yall the ultimate friends, TCC

fire

[lost drum]

But it imagine you published a book few read it.or it will be forgotten in the deepen Heart of libraries .

[winter nebula]

so?

The guy who needs that result

Will find it

from the deep depths

[green terrace]

Who the hell cares, I'd be happy to get published and that at-least someone finds my results useful

[winter nebula]

Bro cmon

[green terrace]

I'd be content with my life

[lost drum]

Among 100 millions of books ?

[winter nebula]

are u a 15yo indian kid who saw ramanujan story in YT and those motivational lion videos about "no ones gonna remember you"

go back to studies

[winter nebula]

Bro

[green terrace]

yes because usually maths research is niche enough there's a small number of authors in your subfield

[winter nebula]

🙏

categorising exists

searching a book by title and topic exists

[green terrace]

There are literally some fields where you can count the number of people working in the field on your paws

[winter nebula]

No one fucking enters a million book library of english literature searching for a quantum field theory book

[winter nebula]

exactly

[winter nebula]

.

There are books I've found

that NO ONE bought from Amazon or springer

[green terrace]

Also math overflow and math stack exchange

[winter nebula]

But regardless i found it because i needed it

[green terrace]

Some that aren't even on amazon and you have to buy directly from the author/publisher

who will have a custom print made for you

[winter nebula]

yeah

[green terrace]

because it's niche enough they can do that

[winter nebula]

yeah

exactly

[green terrace]

And small or self published titles are nice IMO

but finding the good ones takes time and practice

[winter nebula]

Yup

But eventually if it exists

it's found

[green terrace]

Like Hubbard and Hubbard is good

Cummings' analysis and proof books are good

etc etc

[winter nebula]

Yup

@lost drum now now

don't run away from convo after u realise we're not agreeing to you

[normal sleet]

My professor doing regularity of elliptic free boundary problems says there's like six people doing what he is doing

[winter nebula]

that's gonna leave us wasted here

[green terrace]

Case in point

[winter nebula]

(maybe hes trying to prove the point by discord messages, no ones gonna find urs in millions 😹)

[winter nebula]

Let's do Algebraic Extraterrestrial Modular Arithmetic Interdimensional Octopology Theory of Fields

[green terrace]

New vixra article incoming

slender about to become the most well known vixra article publisher

[winter nebula]

LOL

[normal sleet]

You joke about this but someone recently tried to prove P=NP with homological algebra
The paper was clearly AI generated and halfway through the guy was talking about the finiteness of the universe among other hot garbage

[green terrace]

LMFAOOOOOOOOOOO

[winter nebula]

LMAOOOO

LMAOOOOOO

[winter nebula]

Bro definitely proved Problem = No Problem tho

[dire marlin]

@tropic root the problem is, idk which one to go next

i dont know the name of the subject

as well as the requisites of it

(context i was asking about a general path of mathematic so that i can go through almost all field from basic like calculus, linear alg, etc to group and field theory, abstract linear algebra, optimizations, etc)

[normal sleet]

You can pick a uni and go through their curriculum if you want a general layout

This can usually be found on their website

[dire marlin]

im currently in an uni ( again but not for mathematic ), it was IT

maybe i misunderstand your sentences

[normal sleet]

Just in case I wasn't clear I'm not saying to enroll in a uni, I'm saying to just open a uni math dept's website and see their curriculum structure for inspiration

[dire marlin]

do you have any suggestion, my country university teaches alot of things, and they dont publish anything like that on the website

[normal sleet]

I think ETH publishes this for eg

I'm not from ETH though

My uni's grad requirements suck so I wouldn't recommend it

[normal sleet]

https://math.ethz.ch/de/studium/bachelor/bachelor-mathematik/details.html

It is in german but I trust you can translate with your browser

[lost drum]

The proove of what we said is that goal's it's knowing what is wanted, a désirable idea of the futur so goals are combinaison of the will and knowledj.

So if you wanted without knowing what you want and having no idea of it, you're will has no meaning

So the biggest is you're knowledj the larger is the set of goal's that you can think of.

So you can choose the one that has biggest quality and you select with you're own subjective criteria to define that quality .

Therefor the plans for them can be known and efforts are directed in a plan that has causal relationship impact with the goal's can be known .

So with that knowledj all what remains is to combine it with it's application .by concretising what is virtual

So the best goal's are acheived.

But me I asked for a goal lists to set in order to not choose some random meaningless goal's in mathematics

[lost drum]

?

[dire marlin]

im looking through it, but master mathematic doesnt have any specify on what to learn ?

do master one behave different than bachelor ?

[winter nebula]

???

if you dont know what you want

[viral osprey]

Sorry had to go do some stuff.

I think you are just saying a bunch of stuff you think sounds really deep in order to try and justify conclusions you've already made that don't actually make that much sense.

[winter nebula]

Then dont bother going into anything

not everyone has to want anything or have any dreams , wills, passion or whatever

you can still go over your life the same way and you're not any less than other people

Quite often I see so many people being confused about what to want or what to set as goals, but honestly if you dont know what youwill do, then don't bother

Eventually you might end up just finding something along the way

It can't be forced

I can hand you a roadmap of math right now but you won't find interest in it

[viral osprey]

If your goal is to do math I don't see how doing bad philosophy here helps ngl.

[winter nebula]

I can hand you lists of 1000 books but you already would have if you wanted to

[winter nebula]

Maybe just try doing a progression of textbooks?

Maybe try searching on youtube about math videos and find what interests you and try learning that?

Honestly just do whatever, if you find everything in math "meaningless", then dont even touch math lol

right now youre just suffering from dunning kruger

[viral osprey]

All the essays in the world on the deep nature of mathematics, learning and goals ain't gonna make you better at math.

Eventually you actually have to DO math.

[lost drum]

No, but imagine if someone lived 40 years in new York he knew it from A to Z .

[viral osprey]

Does me/you imagining this make either of us better at math?

[lost drum]

And you are knew to visit it's actually better to follow that expert hé will show you everything .

[viral osprey]

If you ask your profs or literally any other mathematician about how to improve at math

Most will also tell you that you need to actually do math to improve

[lost drum]

Yes, like having an honest mathematician like jean Dieudonné as a mentor and you follow his math vision, his books with courses and exercices

With his goal's and way of conceptualising mathematics

You will reach a greatest level .

[viral osprey]

Maybe old dead mathematicians who live in entirely different contexts from you or I aren't the greatest role models?

Do you think all advice from the pope is also relevant to you?

[lost drum]

Yes but also with their pedagogical knowledj they studied math éducation from very long time

[viral osprey]

Not all mathematicians are credible sources on pedagogy

[lost drum]

: the book of anciens and new how they teach and how they train their students ..

[viral osprey]

Pedagogy research is not the same as mathematics research

[lost drum]

Over centuries

[viral osprey]

Usually mathematicians teach, that does not imply all mathematicians are competent or knowledgable at teaching or on pedagogy.

[viral osprey]

A book being old and important does not imply it is a good source to learn from currently.

Swap book for pedagogical method in that sentence and you can get a roughly similar implication that I would argue is also true.

A lot of things we know/do now are things we realized were improvements on things ppl knew/did in the past.

[lost drum]

Yes

[viral osprey]

Fwiw I am not saying old books and statements from old famous mathematicians aren't helpful, valuable or sometimes relevant.

What I am saying is that they should be taken with a grain of salt.

[lost drum]

jean Dieudonné books of analysis

Are richer then thouse i studied in class.

And then pedagogical experts have goal's about a student

[viral osprey]

Newton stuck needles in his eyes and galois died in a duel. Are you also going to do the same?

[lost drum]

And know what is mostly benificiel for him .

[viral osprey]

"For him"

Are you dieudonne?

What if things they say do not apply to you or do not work for you?

[lost drum]

No

[viral osprey]

You see the issue right?

I'm not saying "don't listen to these people"

[lost drum]

Galois dead for his girl freind .

[viral osprey]

I'm saying take what they said and did with a grain of salt. They were just as capable of doing stupid things as anybody else.

[viral osprey]

I think some of the reasons for this are debated still. He was very active politically as well.

Either the ams or maa have collections of history of math papers in some books. One of those books has a paper on it.

It's either in "sherlock holmes in babylon" or "who gave you the epsilon".

Some math historian folks have claimed there were some political motivations involved in his death I think.

[lost drum]

Yes and with a mathematician

Like jean Dieudonné who mastered set theory, analysis and worked on Russell , von Neumann.. of logics

And studied algebric geometry ..

He studied also very hard history of a lot of mathematicians..

But following advices and conception of mathematics David Hilbert , Bourbaki, Terence tao ,

Curry,

[viral osprey]

No I think this is also not fully known. See for ex here:

https://hsm.stackexchange.com/questions/9/why-was-Évariste-galois-killed

[lost drum]

And the logician of Stanford ..

You have big knowledj of methodological studying and you have good goal's

[viral osprey]

Saying the names of famous mathematicians won't make you better at math.

[lost drum]

With a certain conception of mathematics .

[viral osprey]

We get it. You read about these people. Cool. That won't make you better at math. You have to actually do math to get better at it.

Fwiw since you bring up curry

There's a whole talk by soare about why turing gets so much priority on some of his work despite kleene, curry, church etc doing certain things before him that he later also proved

And part of soare's point was that the work they did was of lower quality in the sense of being unintuitive and hard to work with

Like, to the point of actively damaging the field (sorta paraphrasing soare here)

Later people did a whole lot of work on making old methods and ideas in computability readable, intuitive and easy to work with.

This is not just limited to turing btw

Folks like Hartley Rogers and Alistair Lachlan also did a lot of work trying to put early computability in a more workable form afaik (though several decades later and for different reasons afaik).

Point being old dead famous mathematicians may have done a lot of neat stuff and had a lot of cool insight, but they weren't perfect.

You shouldn't treat them like they are.

[lost drum]

Hilbert says in his articles of mathematics axiomatics affirms : mathematics is a game of meaningless symbols with rules in paper . And Wittgenstein in his linguistics book says : in math it's all all about algorithmes and not meaning .and von Neumann advice to his student : in mathematics you dont understand you learn how to use it

And with Terence tao blog and masterclass and books

And advices to his own students and conferences ..

[viral osprey]

I heard gerhard gentzen was a nazi. Should I listen to everything gerhard gentzen had to say too? He was also a famous and talented mathematician.

Have you read much about kronecker?

[lost drum]

Here it's an overgeneralisation of what I said .

Me I'm telling of having the truthful knowledj of mathematicians .

Not the false ideas .

I have no relation with his political views or whatever .

[viral osprey]

"The truthful knowledge of mathematicians" should be taken with a grain of salt, because mathematicians are often wrong about things.

[lost drum]

They can be wrong. But look

If 2 players are going to play chess .

[viral osprey]

If you haven't, you should read about the history between kronecker and cantor.

[lost drum]

1 random player starts with his poor goal's and his expérience ..vs an other player learned from Kasparov

, Karpov,

Coached by Carlsen..

[viral osprey]

Homie, can you make a coherent point without name dropping?

[lost drum]

And a lot of greatest chess players he took their advices and followed them .

[lost drum]

Yes

[viral osprey]

Do you know what an appeal to an authority is?

[lost drum]

,he tried to remove him from uni

And it's natural to do so

[viral osprey]

I feel like it went a lot further than that.

[steady cosmos]

wtf is maths bruh

It is a waste of time

[lost drum]

Because imagine trying to change 2000 years tradition of mathematics activity .

[steady cosmos]

Lol

[viral osprey]

Apparently we just cargo cult about dead famous people.

[steady cosmos]

Ai can do everything

[viral osprey]

Seems irrelevant to the discussion here ngl

[steady cosmos]

Idk

Fuck

[viral osprey]

No need to spam

[lost drum]

Kronecker when he was opposed to cantor it's probably

[lost drum]

What most people will do but not as kronecker because how 2000 years of mathematics was done and someone camed to change the tradition

it's not easy to accept

[viral osprey]

People argue about the value of certain axioms now.

The issue isn't arguing about that

Sometimes famous smart people do dumb shit

Kronecker was just wrong about the value of cantor's work

[lost drum]

Yes and he is lonely at that time

Except his freind dedekind and Hilbert

Who is open mind to his works .

[viral osprey]

I really doubt he was an isolated incident

There were also many people who had beef with early analytic ideas

Again, my point is raising these people up on a pedestal is stupid.

They were just some people who were smart and did some cool things. They were just as capable of doing very stupid and shitty things as well.

Surely if archimedes wrote a book on how to study math, some of the advice would be bad and some (possibly a lot) would not apply well to you.

(Obv some would be good/fine too ofc)

[lost drum]

Yes, and the player trained and tooken advices from Kasparov , karpov .. and a community of chess players behind him has advantages from the one who hasnt help .

[viral osprey]

Okay, so let's say you spend multiple hours everyday talking about chess compared to somebody who spends 10% of the same amount of time talking about chess and 90% of the remaining time actually playing chess. Who is going to be better at chess? You or the other person?

[lost drum]

Also when you study physics and tooken advices and knowledj from you're teachers, physists, mathematicians ...

[lost drum]

The person who studied their books of chess and took advices of experts and trained hé will have the expériences of 2000 years chess gaming

[viral osprey]

Not what I asked

[lost drum]

In 14 hours.

[viral osprey]

It would be cool if you actually answered the question I asked and not some other thing.

[lost drum]

But the person who is simply playing but never took advices

[viral osprey]

Not what I said

[lost drum]

From experts of chess

[viral osprey]

But also, by what I said they are clearly talking to people about chess as well.

They just also play chess.

The scenarios are the same. But you talk more about chess and the other person plays more actual chess.

[lost drum]

Yes that's evident

Me I was talking of someone who learns

[viral osprey]

Okay, if it's evident idk why you are answering a totally different q from the one I asked?

[lost drum]

And practice the knowledj of experts

[viral osprey]

The other person in my q would also be doing that.

[lost drum]

Not someone who was just listening .

[viral osprey]

The difference is in proportion.

[lost drum]

That's how also my freind

If you have with you tao , Hilbert, Dieudonné .. and a community of crazy

Mathematicians

[viral osprey]

Not what I asked

Keep throwing those names around though

[lost drum]

Who advices you and make for you plans and goal's

[viral osprey]

Protip for getting good at math: Say dieudonne a lot until the math gods bless you with skill.

Good idea.

[lost drum]

Dieudonné has books :

Honor of spirit mind,

[viral osprey]

Cool, do those help you if you don't actually read them and don't do any actual math though?

[lost drum]

Of course not .

[viral osprey]

Okay cool

So, then would you say that a reasonable strategy is to read what the experts have to say, take it with a grain of salt and also do a fuckton of math?

[lost drum]

I'm saying that we take a lot of knowledj and their advices .. then from them build a plan and a methodology of working mathematics

Then applying hard it's own methodology

[viral osprey]

That doesn't answer my question?

[lost drum]

Hardly .

[viral osprey]

Can you answer my question?

[viral osprey]

Does it sound like a reasonable strategy to you?

[lost drum]

Yes , but we take it grain of salt if it's truth and we find that he has a proove that his advice works

and we denie it and falsifie it

[viral osprey]

Yeah I'd agree then

[lost drum]

If it's innefictive .

[viral osprey]

Also wanna point out, that strategy in no way contradicts what you said here.

[lost drum]

It's how also in mathematics, physics ..

[viral osprey]

Pretty much all topics that I can think of yeah

[lost drum]

When you take knowledj of a community of experts and working with their light

You are well .

Like me I wanted to do mma , I will learn from john jones and a lot of champions and coaches ..

That's what I did in a time

When I went to work in an office in my holidays

a manager gived me a plan

[viral osprey]

Yeah I'm not saying don't listen to experts

[lost drum]

And I worked all my days

With The same plan .

I asked old man's there from motocycling

Work , I distribute packages

With simply doing as him

All my days works except one day were very excellent .

Also in analysis I had complet marks

And very good marks in matlab ..

I simply studied how other correctors solve exercices

And I immitated the process.

@viral osprey

What did you think ?

[viral osprey]

I think some of my suggestions earlier are worth considering.

Lemme find it

[viral osprey]

@lost drum these ones

Those were genuine suggestions.

Like, you probably shouldn't do all of them all the time. But depending on what you are going for and what you have time to do you can often do more than just reading+working exercises.

[fast osprey]

hi, anyone know any good planners/etc for time management?

[green terrace]

I do this all the fucking time

It does actually help me find mistakes (sometimes)

[viral osprey]

Yeah the general practice of lecturing through things is helpful

[wraith bison]

use anki it peak

[winter nebula]

Bro

Literally I can watch 10000 hikaru or naroditsky tutorial videos

or gothamchess ivdeos

that doesnt mean im automatically gonna get better at chess?

Just because i took "advice" ?

if thats how things worked

we would have more grandmasters

[winter nebula]

hes circling around for no reason

not even listening to what youre saying

[winter nebula]

same

[winter nebula]

Yeah listen to experts

LOL

[vernal sky]

rfk jr wants to see you in person

[winter nebula]

ronaldo fortnite kennedy junior?

[lost drum]

You are right

[dire marlin]

is it enough for me to learn

can someone rearrange this so that i can have a path

[winter nebula]

Group theory should fall in Abstract Algebra itself

[winter nebula]

add Calculus -> Analysis -> Topology

And Linear Algbera -> Abstract Algebra (Group theory and symmetry will be here)

[dire marlin]

Analysis is not calculus ? or you mean numerical analysis ( do it also contained in number theory )

[edgy sierra]

real analysis is different from calculus

though they intersect

also number theory is distinct

[wraith bison]

im unironically on something i thought that said cat theory

[tropic void]

Hi

[rotund zodiac]

here is how i would map it out

i added some courses in purple - if you are doing a university degree you will probably take these courses anyways

and i would say you can't get by without them

i've also boxed some courses in blue if they are typically one university course, i.e. symmetry is not usually explored on its own, its part of group theory, and perhaps linear algebra

[rotund zodiac]

oh and the grey arrows are recommended paths to take, sorry about that

[rotund zodiac]

numerical analysis is not in number theory I. it might be a little bit in number theory II
real and complex analysis are calculus over more abstract surfaces, and/or with way more rigor (for example, real analysis formally constructs the real numbers, instead of taking them for granted). this course is very central to a math degree, and is often lumped in with topology

also also, reading through what slender said, i would also recommend linear algebra before group theory

yap over

[dire marlin]

Tks alot

[lost drum]

No

[lost drum]

Watch less videos

But read books

I'm sure if you read 14 grandmasters books and you studied a lot of strategies

Of material wining, openings, middle and end game and some secrets,pawn structure ...

And you analysed ancient playings a lot.

You will end up having a big military of knowledj

That if you played you will beat easely .

And Im sure also that if you summed the knowledj of grandmaster to you're own knowledj you will beat a lot ofgrandmasters .

a with community of 100 books of grandmasters inside you're intellect you're very hard to beat.

And know that there are many people who were superior then you a lot and in the World rank we are maybe the last ones. But the way to be in the highest rang

Is only by having biggest truthful knowledj summed up with the most important work.

And with an immense humility to learn from people that you can be immensly superior and higher because the student can beat all his masters at the end of learning .

Yes, and in every decision you take there are probably in 9 billions of people in the World history of million years someone took it before you

And results were made so to repeat the best history it's only by asking what

Did others did ?

Search or ask others you will know.

[winter nebula]

Not really

Thats a very linear way to think it

[winter nebula]

Reading 100books doesnt make grandmasters live inside you

And it doesnt grant you the intellect automatically

Not until you apply every one of them and absorb and practice a lot

[winter nebula]

no

Having Knowledge != Intellect

in that case i could just keep reading 100000 math books and become the most intellectual mathematician alive

win 10 fields medal

The human brain is not a machine to do that

If you read 1 book

you need at least a few weeks to absorb all the material inside it and apply them

Then 100 books is literally years

Before you even become a "grandmaster"

And in that case, all those chess nerds who read lots lots of books already wouldve become grandmasters

[winter nebula]

😭 🙏

what are you saying bro 😭😭😭😭😭

I understand what youre saying and where youre coming from

If you actually read and master 100 books on something, its obvious youre gonna get good at it

But doing the thing fr is harder than just reading the books

[lament heath]

TIL that if i read 100 books on combat i will be very good at fighting people irl

[edgy sierra]

what if i just bring a gun

:/

[scenic shuttle]

[lament heath]

only if you read books on loading and shooting a gun 👍
username checks out 🤔

[lament heath]

also humans have existed for much less than 1M years

[spark topaz]

modern humans*

humans in general have a couple million years of history

[heavy needle]

Homo habilis for real

[lament heath]

"world history" seems to imply a much shorter timeframe than even modern humans but sure
took it to mean the same "people" since the invention of writing

[sturdy tundra]

Has anyone here tried Khanmigo AI (or something similar) for studying? I’m trying to relearn calculus and trigonometry, but it’s been difficult.

[lost drum]

Yes it's truth , For me the red diamond rule

to have a complet knowledj before working is much better to just working very hard but randomely .

[lost drum]

Sometimes Me I had that experience in my home ,I play with bots of cs 1.6

and I beat experts bots and played with freind and I won most of them

but when I went to a public server I was in the lasts of the list

they didn't let me to breath , most of the team with variety of skills went like fast devils

It's because it's easy to beleive that we are the best in the world about something but a truthful verification we find that it's not often the case .also in a high school of 20000 students it's also hard to be 1 rst rank .

Also I was bycicling for some weeks like all the days with some freinds until we saw some professionals on bycicling who were far then us .

Also in mathematics until you find some phd of the MIT ..

They were more skillful then us because they have biggest knowledj then us from witch they did the best work and learning also is a kind of work but an it's intellectual work .

[lost drum]

Ys .

But some knowledj in order to have it it's maybe what's very difficult

because you will do mistakes and you will fail and you have to think a lot ...

like messy said “I start early and I stay late, day after day, year after year, it took me 17 years and 114 days to become an overnight success."

[lost drum]

and a question like why is a 15years old of this century in math is better then the ancient old man egyptian mathematician ?

It's because the 15years old download math skills that intstructors and organisation of education in the world download in him

By choosing what the communities of the mathematicians on all countries made as creative skills and interesting things So indirectly he had a community inside of him .

And why doesnt a street fighter who had fighted for 50years will not beat a mixed martial arts championship like john jones ? it's same .

@winter nebula

[scenic shuttle]

no ai is garbage

you're making things complicated and confusing if you're relying on ai responses

[floral musk]

ai is bad for ur brain at the undergrad level

it makes u dependent

there is no replacement for bashing ur head against the wall until u get it

[winter nebula]

There's no comparison in math lol

Its not a chess competition

[winter nebula]

Yea

As i said

[raw tinsel]

There's no comparison in chess lol

Its not a math competition

[winter nebula]

Contribution of many people throughout the years, significant or trivial

[winter nebula]

You can quantify chess skills

U cant quantify math skjlls

Bcz It's subjective

[raw tinsel]

its also subjective but haha.

i joke

[winter nebula]

xd

[cinder terrace]

Hi so basically i was just wondering abt something. I am currently going into y11 this year and its just that whenever i study or try to study i would just at the start feel a sudden wave of sleepiness for like the first 20+ minutes and sometimes it be like me feeling sleepy then i dont then i go back to feeling sleepy and it goes continuously for like lets say 2 hours.

This only happens when im studying and it doesnt matter on like where i study or like what i study like i could still be feeling this when im in the library studying or in my backyard. Theres never been a time where i havent had this and it also doesnt matter what time i study. Today i tried studying at 8am and it still happens where i just feel so sleepy and also i do have good like 7-8h of sleep everyday.

This has been affecting my study time and im just wasting lots of time that i could be using to actually study. Is there any way to somehow fix this?

[cosmic pike]

Guys does anyone know how to build intuition for vector dot and cross products

[normal sleet]

Watch 3b1b

He has a nice video on dot products and stuff

[winter nebula]

Do physics with it

best way

[lost drum]

Speed to solve ,

Rigourousity ,beauty of theorems,their practability in other sectors .

[winter nebula]

Huh

Computation speed?

How does that contrast with chess

[lost drum]

like creativity how much it's original .

[winter nebula]

How do you measure and quantify that 🙂

Chess also in the end isnt "creative" and "original" anymore when chess engines learn it

It eventually becomes yet another mathematical system to solve

[lost drum]

Number of new propositions created .

[winter nebula]

lol what

i can create

infinite number of propositions in math

proposition: 1 + 1 = 2

proposition: 2 + 2 = 4

and so on

[lost drum]

but sum symbol , product symbol ,integral ,

[winter nebula]

Bro

Symbols dont mean anything

[lost drum]

a banash space

[winter nebula]

Banach space?

bro

math is not about symbols

its about the ideas and structure

You cant quantify math like chess competitions

you can measure how good someone is by ELO in chess

you cant meaure how good someone is in math

because math is not a game

you cant compare

everyone has different ideas

And its not even a competition

what are you trying to say lol

[lost drum]

yes

[lost drum]

an example lets compare beetween leonard euler with dirichlet : euler is : " e^it=cos(t)+i*sin(t) " dirichlete f:R to R , x to f(x) =1 if x in Q , 0 if x in R/Q

[winter nebula]

How the fuck do you compare that?

Both are different functions?

For different purposes?

😭

[lost drum]

how much it has applicability ?

[winter nebula]

And why does that matter?

[lost drum]

The first :students of physics,engineering and biology .. were using it

[winter nebula]

The first also concerns students of pure mathematics

Complex analysis, complex geometry relies on that stuff

Both of these two ocncerns pure mathematics

You wanna tell me the second is useless?

But lebesgue integration was created to solve functions like that?

Which is why it worked well as a "problem" ?

And you do realise lebesgue integration is used in so many places

in physics, statistics, machine learning

What are you gonna say lol

[lost drum]

I dont understand how it's useful

a function of rationals 1 then irrationals 0 and so on

[winter nebula]

Because functions like that gave birth to lebesgue integration?

[lost drum]

and what if you compare in beauty to mendelbrot fractals and

equations on the mysteries of nature or the ones that helped to create virtual gamings .

and you compare that with some bourbakisme theorems .

Like generalised distributivity

Product of sums =sum of products of course we dont know it's futur .

some theorems had big importance to build a method of attack on diverse problems and other had less .

there's also rigourousity and laconism and other criterias

to mesure the quality .

[dusky glade]

If nothing else works I suggest finding a study partner, though it won't be that useful if that sleepiness persists. Meeting with a study partner is only realistically possible once a month or smth

[cinder terrace]

For ur way on overcoming it do u still sometimes get it or like has it stopped?

I’m not too sure how does mine fully stop cuz it varies like crazy from like 20minutes to onetime almost 2h until I just gave up on trying to study

With the short bursts right my sleepiness starts at the start so like I’m 2min in studying and it happens

[lost drum]

I will say ,

I had an experience like you of absolute and +infinity confusion the solution is :

1-write 10 goals and choose the most important to the less

Then make a list of tasks write down all what you can think then plan from the first to the end then and that list is specefic to you're goal .

and then follow that way . it helps to reduce all complexity and a lot of things and multiple things to do not interesting things and law value tasks and lot of ideas that you want to apply by elimination of them and letting only what's most important that makes you're life very simple and it was said :"Action without planification is the source of all failures" , so always have a plan .Source :brian tracy .

and secondly go to a doctor .

[unborn flame]

Anybody wanna study math with me? Iam going to study proof writing and calculus, and a lot of other stuff before starting real analysis. Anybody interested?

[unborn flame]

Study actively instead of passively, make notes, speak,think, write and summarize yourself, do test papers etc... You can use study techniques, example the feynman technique

[lament heath]

personally i decide im not allowed to sleep or eat until things are done but that isnt a long term solution :c

[round glade]

is there any roadmap for beginners?

[bitter axle]

Does anyone have good review material like vids or notes for linear algebra, I need to do a deep ahh review for one of my CS electives

[scenic shuttle]

https://www.3blue1brown.com/topics/linear-algebra

[edgy sierra]

sheldon axler or gilbert strang

[winter nebula]

Both are so different bro..

[edgy sierra]

yes but it's la anyways

former emphasizes rigor

if that's what you want go for it

cue evil vs. good path

[rotund zodiac]

consider getting a bright light (or color-changing lightbulbs) for your study space. turn the light on only when it's time to study, and keep it off otherwise.
it didn't take very long for my brain to decide that "bright light = study time", probably because the lights at school are so very bright compared to my room but now if i need help focusing, i will turn on the bright lights and instantly lock in. other examples of environment control:

• dedicated study playlist that you only listen to when studying
• changing your desk setup (e.g. removing distractions) for study time
• locking your chair so you can't lean back on it (this really helps me idk why)
• slightly opening an outside window so the cold slaps you awake
• standing while working, or working on a whiteboard/blackboard

the tldr is, control your environment to be uncomfortable/more like school

[lusty tree]

what the fuck is the point of this if i cant check to see which answers i got wrong so i can go back and study them to get them right

so dumb

[scenic shuttle]

try contacting them on person

[jade furnace]

I finally completed Integrated Math 3, and I'm now ready to move onto Trigonometry.

Trigonometry is surprisingly short on Khan Academy, though.

[heavy rock]

here's a decent looking online trig book
https://yoshiwarabooks.org/trig/frontmatter.html

[worldly oyster]

Yo that's so great, I think I'm going to restart my khan academy again tonight. I got so frustrated with converstion and their wild way to explain it.

[jade furnace]

Thank you! I'll look at this soon!

[jade furnace]

That's a good idea.

Have fun doing Khan Academy!

It's a struggle sometimes, but I have noticed the benefits before, and it always feels good to finally get something.

[worldly oyster]

Sighs

[heavy needle]

Well if you have unlimited attempts you can just use a process of elimination

Maybe not the best way but you can do it

[fallen jasper]

Does anyone have any experience using AI for looking up definitions / explaining proofs of theorems while learning new maths?

(The context is that I just finished my first year of undergrad and am trying to read a paper (?) that a professor has sent me (and I lack a lot of the foundations!))

I guess I can also look at maths stackexchange and wikipedia and all sorts of wonderful sources on the internet, but it is terribly \easy\ to just babble to chatgpt and get a reasonable response. More precisely, I guess my question is "how reasonable are the responses, usually?"

( inb4 some remark about undergrads and reading - this is not alg geo, though it could be above my paygrade all the same :P )

[spark topaz]

that depends greatly on the subject

If a lot of (educational) material on the subject has been published, it should be pretty good

on spin bordism torsion functions it's gonna suck

[fallen jasper]

I dunno any of those words, lmao

It's about double affine hecke algebras

I'm not sure how much material is published or how to judge that

[spark topaz]

So it's generally useful for undergraduate classes but not very useful for research

[fallen jasper]

Yeah, ok. I suppose (and hope) a grad student in the right field would be able to parse this stuff with no issue. I'm just stuck on how to evaluate what "a lot of material" means in this context

Affine Permutations and Rational Slope Parking Functions (Gorsky, Mazin, Vazirani)
and I'm trying to read some seminar papers (MIT-Northeastern Spring 2017 DAHAEHA) to know what daha is

yeah

ok I shall do that too

thanks

[worldly oyster]

Oh hey, the issue with that is AI tends to pull from any source (Reddit being a famous option) , correct or incorrect, and can and will make things up as it has within the past.

You might spend more time correcting it than it getting far.

[small salmon]

At this point, I'm of the opinion that you should never use AI for anything that you don't already know, and can't already correct. In other words, the legitimate use cases are pretty slim still.

[barren remnant]

Khan academy?

[worldly oyster]

The moment I tried to log in, they had log in issues.

[lost drum]

"what should he do to learn mathematics from scratch
for passing AQA GCSE mathematics foundation,what are the programs and what are the books of courses and exercices and how much time it takes to finish them
Can you give us a list of ordered tasks for him ?
Because me I dont know the united kingdom program and ressources

[lost drum]

can you share us the tests and previous paper exams ?

[pulsar saddle]

i can give you some tricky exercises as supplementary material if you want

[jade furnace]

Sure thing! Feel free to give me some resources.

[lean egret]

Taking calc 1 and realized that my algebra knowledge may be lagging behind, what resources are there that can help me review?

Ill check it out! Ty

[dull horizon]

going to start calc 2 next week, it's almost been a year since i took calc 1, what topics should i revise?

[scenic shuttle]

revise differentiation rules (especially chain rule), basic integrals and u-substitution, algebra skills like factoring and simplifying, trig identities and unit circle values, and basic limits

[ruby basalt]

how do i study for calculus linear algebra and probability all at the same time

im in hs

Its way too much

Its my final exam and its basically like 3-4 topics

No the high school system is different here

I cant do that

Sooooo much

yea the thing is

We have done all of the topics

in the last 2 years

Now its just like

A final exam with all the topics in it

in may

yeah but i got 5 other subjects to study for

This isnt humane

damn

wtf

like just the basics or literally alot of it

[compact seal]

Guys I need some advice. I've been studying and doing my math hw, sometimes even the math contest portion of the textbook questions which my teacher doesn't assign.

I THINK I understand everything. Yet when I go to a test almost always there's questions which get me.

We learned logarithmic functions as an example and the power law

4^3 = 3log4

Yet when I was shown questions like:

8^(x-2) = 3^(x+4)

I couldn't solve it. Even though its the exact same logic...

In quizzes which test more on process (a lot like textbook quesfions) i usually get low 90s. But every unit test i still have remained at 70s.

I really want to be good at math, and im not sure if my issues are my weak fundementals or what (i never focused on math since 7th grade) and now that im in 12th grade I don't really know what to focus on for improvement.

I get this is kinda hard to give advice on, but I appreciate any advice in general.

Also I do well i all my other courses except for math including English, business, economics, computer science, etc... it's really just math which messes me up.

Im starting calculus next week snd im really trying to end the course with a 90%+

This math course i got around mid 70s on (my previous grade 11 mark was around low 60s so an improvement tbh but not enough)

[winter nebula]

Fear not soldier

Have you tried solving all questions from your textbook?

Also may I ask you what's your math syllabus

[lament heath]

4^3 = 3log4
i don't think you understand log identities...

[winter nebula]

i think it's a typo

[tiny jolt]

i'm studying complex analysis , there should be lim(z -> znot) before Δ in second last line , right ?

[normal sleet]

We need to see what that statement is equivalent to
But i dont think there should be a limit

[red rapids]

No. What they're doing here is defining the complex derivative at a point as the error term (slope) of the linear approximation at that point. Since the error term must be continuous at that point it can be expressed as a limit as well.

[red rapids]

Equivalent to the existence of the limit:
$$\lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0}.$$

[mossy shadow]

Killuminati

[tiny jolt]

from the second line Δ = [f(z)-f(z not)]/[z - z not] , there needs to be lim(z -> z not) in front of it

[river delta]

I don't think so. $\lim_{z \to z_0} \frac{f(z) - f(z_0)}{z-z_0} = \lim_{z \to z_0}\Delta(z) = \Delta(z_0)$, where the last equality follows from continuity of $\Delta$

[mossy shadow]

Moorts

[tiny jolt]

ohhhhh

but are you allowed to pass exact z not in Δ as it will cause the denominator to be zero

[river delta]

Delta is not actually defined as this fraction. Delta is just a continuous function on U and is equal to this fraction only where the fraction is well-defined

[tiny jolt]

i don't understand, it is defined as this fraction for all z in U , in the second line

[river delta]

no it isn't because you're not allowed to divide by zero

i.e. you can only divide by $(z - z_0)$ if $z \neq z_0$

[tiny jolt]

but the second line

[mossy shadow]

Moorts

[river delta]

the second line is true for $z = z_0$, because then it just says $f(z_0) = f(z_0)$

[mossy shadow]

Moorts

[river delta]

like $a = b = b + 0*c$ does not imply $c = \frac{a-b}{0}$

[mossy shadow]

Moorts

[tiny jolt]

so Δ is not defined for z = z not ?

[river delta]

yes it is, it's defined as a continuous function that satisfies the equation in line 2

there is nothing problematic with this even if $\Delta$ is defined for $z = z_0$

[mossy shadow]

Moorts

[river delta]

you have that for every $z$, $f(z) - f(z_0) = (z - z_0)\Delta(z)$

[mossy shadow]

Moorts

[river delta]

but you can only divide this equation by $z - z_0$ if $z \neq z_0$, so the fraction is only well-defined for $z \neq z_0$, but this does not mean (in any way) that $f(z_0) - f(z_0) \neq (z_0 - z_0)\Delta(z_0)$

[mossy shadow]

Moorts

[river delta]

in fact this last equation is trivially true, because both sides are 0

[tiny jolt]

okay so Δ is defined for z = z not but it is not equal to that fraction at z = z not?

[river delta]

the fraction is just not well-defined for $z = z_0$

[mossy shadow]

Moorts

[river delta]

so its not even a number

[tiny jolt]

so Δ at z = z not is equals to the limit of that fraction and this was defined at the third line when they said that Δ is a continuous function , am i right?

[river delta]

I think yes. The point is that if a sequence $(z_n)$ converges to some $(z_0)$ and $f$ is any continuous function, then $(f(z_n))$ converges to $f(z_0)$

[mossy shadow]

Moorts

[tiny jolt]

okay, now it makes sense

thanks dude , complex analysis is pretty difficult

[red rapids]

No. There does not and I literally said why.

[red rapids]

It's much easier than real analysis. It's likely you have to review your background then.

[tiny jolt]

oh, sorry i didn't get it

[red rapids]

Also, this definition is a bit problematic

[red rapids]

I mean, I explained what the equation meant as well. You should've asked as opposed to explain what you already said lol.

[tiny jolt]

funnily enough, my stupid college did not teach us real analysis

for some reason they thought it would be good idea to start from complex analysis 🙂

[red rapids]

The definition assumes that the error term is always continuous without proof. A typical necessary and sufficient condition for complex differentiability is that the function should satisfy the Cauchy-Riemann equations. From there, one should first show that if the derivative exists at any point, then it must be continuous at that point.

[tiny jolt]

i don't know what error term you are talking about neither have i studied cauchy riemann

i'm literally three videos in

[red rapids]

Seriously? When the guy in the video tells you about a linear approximation then what part do you think coressponds to the error term?

[tiny jolt]

that's the point , i don't know 😁 😆

[green terrace]

Maybe you should go review linear approximations from calculus

[tiny jolt]

i guess i'll just figure it out while studying complex analysis

[green terrace]

No.

[red rapids]

From what it looks like, if you don't review the basics, then all you're gonna be doing is looking at symbols and feigning understanding.

[tiny jolt]

😭 🙏

i'll ask you guys if i don't get something

[green terrace]

I will also say, I never realized that the tangent line approximation is just the first 2 terms of the taylor expansion + an error term

but wow

that's quite cool

[green terrace]

Why are you so hellbent on doing something that will only harm you

[green terrace]

Also no-one will be willing to help those who cannot help themselves at-least a bit

so

if you aren't willing to re-enforce your foundations to improve your understanding before asking a question

at MOST people will tell you to fix your shit

[tiny jolt]

i have studied calculus earlier and my text never really mentioned something like error term or the first 2 terms of taylor expansion you are talking about

[green terrace]

else they'll just ignore you

[green terrace]

Most calculus texts introduce the concept of taylor series

[tiny jolt]

don't get angry , im not doing maths major , i can't too much time on the subject which i won't be studying next semester , i know taylor and maclaurin series but the stuff you are talking about was not taught to me

[green terrace]

This is stuff that's taught in any half decent calculus course

aka something every STEM major has to learn and should know

[green terrace]

If you won't be studying or using complex analysis, why learn it, if you're so unwilling to review your fundamentals?

[red rapids]

Let me be a little more precise and say it's the linear correction term to the constant approximation.

[red rapids]

What text did you use?

[tiny jolt]

i was just asking for a little confusion i had and i don't have time to go back and study calculus again so i decided i will just figure stuff as i would study complex analysis

[red rapids]

I mean the confusion mostly stemmed from the fact that you didn't understand how they exploited the continuity of the derivative. That's enough of a reason to go back to the basics for a short review.

[tiny jolt]

maybe i have studied the stuff you guys are talking about , but english is not my first language and maybe my teacher already taught me the stuff yall are talking about but just didn't used the term you all are using

[green terrace]

You shouldn't need to review the entire book unless your foundations are truly that weak, you should only need to review a small number of concepts

[red rapids]

It's possible, but couldn't hurt to take a short review of calculus before going into complex analysis, especially considering you never did real analysis.

[green terrace]

In that case, maybe dumping what we are saying into something like https://deepl.com or similar may be called for

[tiny jolt]

okay i'll search and study the stuff ya'll are talking about and then continue with complex analysis

[red rapids]

The vids you're using does Cauchy-Riemann in the 6th lecture.

But it's best to study linear approximations, taylor expansions and a bit of multivariable calc before jumping into complex analysis.

[olive geode]

if you insert a lim(z -> z0) before the Δ then f(z) would have to be linear, since you get f(z) = C + (z - z0) * D for constants C and D. So that clearly can't be correct

Also, this is not really the right channel, this is for questions about studying itself. I think you want #real-complex-analysis or #calculus

[red rapids]

The Taylor theorem is essentially telling you exactly that if you have a many times differentiable function.

[compact seal]

Practically, any question which was assigned on homework and sometimes extra. I'm in grade 12 doing precalculus

[compact seal]

Just did that quickly mb I was hella tired yesterday

Better example:

3^(x-1) = 4^(x+2)
(x-1)log3 = (x+2)log4

log is log10 btw

[polar crest]

@elfin oasis hello

@elfin oasis let's chat about math I know u from before

[wide agate]

@elfin oasis im sorry about all the people pinging you

[elfin oasis]

you glow in the dark. you glow in the dark. you glow in the dark.

[foggy horizon]

@elfin oasis I think wise man wants to chat about math

He might even know you from before

[lone silo]

Hey I’m going into year 11 with the subjects Math method, Chemistry, Physics, business, systems engineering and English after being a low-mid tier performing student in general math in year 10. I was wondering if anyone could give me some tips or help me on my journey.

[sand violet]

copypasting this message from the regular discussion channel - i was wondering how would I pick up pure math study as a hobby? as I am not sure what my math level stands at as i don't know how to translate my country's math curriculum to american standard

[sand violet]

i don't know where to start

[rocky terrace]

Khan academy

Do everything upto calculus (or even upto multivariable calculus)

Then you can jump into real analysis (I'd recommend the book Understanding Analysis by Stephen Abbott) and linear algebra (Linear Algebra by Friedberg Insel and Spence)

or Hoffman and Kunze is good too

They are also good places to start

[winter nebula]

Number theory is a pretty nice place to start and then shift to linear and abstract algebra from there

[manic zenith]

hello

guys

i have 2 hrs to study vectors, measurement of angles and limit

and suggestions

[sand violet]

get to it

[manic zenith]

im doin it

[scenic shuttle]

do you mean you have a test/midterm in 2 hours??

[stray notch]

Is this reading list considered good?

I found it online

[green terrace]

No this is frankly out of order and not very good

what you read should be based on what you eventually want to study or do

[stray notch]

Oh

Well do you have a list similar to this one in the correct order maybe?

[green terrace]

No and I would not waste my time trying to construct one, just start by reading an analysis textbook like abbott or zorich (or even rudin but beware you will suffer) and an algebra book (jacobson vol 1 but it's very very hard, for something easier use artin or if you need something even easier, judson or gallian or such) then go from there, after analysis you can learn point set topology, complex analysis, measure theory (not necessarily in that order), for more algebra you can read jacobson 2 or lang or rotman or something, etc....

for diff eq you should've already done that alongside calculus

if you need a text there's arnol'd's book, there's one by boyce and diprima, there's one by deavney, one by strogatz, etc...find one you like

for linear algebra, axler or friedberg insel and spence are good, both are accessible and you should've done them alongside calculus, maybe right after

[stray notch]

Ahh but many of these names that you’ve mentioned are also mentioned in the list if I’m not mistaken

It might just be the order that’s bad

But thanks a lot for the recommendations

I will definitely look into it

[opal granite]

Also you dont need to read three abstract algebra books consecutively

[green terrace]

yes

[stray notch]

are the first 5 categories alright though? seems standard to me

[green terrace]

you don't need 5 school algebra books, nor 3 proof books

etc...

just throw the list out altogether

[stray notch]

not the books per se but the categories themselves

[green terrace]

they're meh

[stray notch]

damn alright

[green terrace]

at best

[stray notch]

reddit let me down

[stray notch]

https://github.com/TalalAlrawajfeh/mathematics-roadmap?tab=readme-ov-file

is this better

[green terrace]

that's just a dependency tree, and a bad one at that, mathematics is a lot...blurrier than this

[stray notch]

sorry about all these questions

[green terrace]

just don't follow any of these

don't try to overplan your way into mathematics

[stray notch]

alright

[green terrace]

pick up a proper analysis book and an algebra book and get to grinding

[stray notch]

analysis before algebra?

[green terrace]

you can do both in parallel, stop thinking about this like a line

[tight cipher]

hello, what math field that makes rich ?

[green terrace]

quant uses a lot of statistics and probability and if you're good enough and get in you can make a lot of money

[tight cipher]

I didn't choosed probability,statistics .

[versed void]

wouldn't finish all these books in a lifetime

like what.. bet you can skip a couple of those in between

[stray notch]

Which ones would you recommend skipping

[versed void]

just follow this guy

there is an unlimited supply of mathematics out there you can read... don't waste your time trying to fit all of it, just focus on one single "goal topic" or something you want to accomplish

just mindlessly reading out a bunch of topics without any goal, sounds like a waste of time to me

tried it before. you can't ever catch up to all of it at least set up a goal or something to build upon man

[uneven jackal]

TYSM for this, I'll save this in notes !

[glacial raven]

How do you guys study math generally?

What I do is just do practice questions until I think I am ready for it

Is that really it?

[scenic shuttle]

yes as long you're practicing it correctly

[glacial raven]

okay thanks

and also, what about the topics like I don't know even a bit?

Such as trigonometry or geometry

do I just brute-force it or what?

[uneven jackal]

I think read the concept or theory then do problem starting from easy problems then slowly increasing difficulty

[glacial raven]

mhm

But for me the problem with something like trigonometry is that there are so many possibilities to answer one question

And I am pretty bad at knowing what to apply

unless its brute-forced obviously

[vagrant hemlock]

if someone who recently came from canada to a completely new education system such as pakistan how can they catch up if they dont know anything basically

[glacial raven]

I guess you'll probably just have to adapt

Slowly incorporate the new theories into your study routine

[vagrant hemlock]

i did my december mocks and got a 90 out of 200 and if i dont get a 60% in the feb mocks

i cant move on

[glacial raven]

That's one situation to be in

[uneven jackal]

Yep so you have to train your thinking I guess, that's why start with easier questions

[vagrant hemlock]

ive never really been the type to study that much since i could always move onto the next classes since i was in canada

[glacial raven]

uh huh

[vagrant hemlock]

and i dont particullary have a proper study routine

[glacial raven]

So the small problem is I've got board in ~68 days

So I'll just make to patiently and slowly grind through, don't I?

[glacial raven]

Please structure your study using something like a time table and Google Calendar

[uneven jackal]

Just start with easy questions in a book

[glacial raven]

It's soo useful

[glacial raven]

The easy questions are... too hard for me

But yeah, I'll go over with what you said, thanks 👍

[vagrant hemlock]

i struggle w chemistry and comp sci more so ive made a schedule for those two as of rn

[glacial raven]

good

You should also do spaced repetition and active recall for me

Ive found that spacing it +3-6 days and Anki was the best for me

[vagrant hemlock]

whats spaced repetition?

[glacial raven]

So you basically learn a topic today