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1:50 PM
@Buraian Well, because the prerequisite of vector calculus is multivariable calculus, do you know of a textbook where I can learn it from?
2:09 PM
You can check out Khan Academy
Also any standard calculus textbook
How are you anyways @Prithubiswasleftmse
@Buraian what about pauls notes?
It's good
But, I felt that is for a person who learnt it and wants a second review
In my personal opinion, one should see the concepts and the connections together like one single story
Seeing something too technical like pauls notes feels like I lose the message if that makes any sense
@Buraian Personally, I prefer a strong grasp on both the computation and intuition. For example, my physics textbook introduced div,grad and curl, but didn't give any intuition for it (just some computation). So I watched a 3b1b video about it.
which book are you using O_o?
there is only one pure way to do this, and the correct way is to learn Differential forms
The (true) fundamental theorem of calculus
There is one good book I can recommend if you want only intuitive level, that is called Purcell's Electrodynamics, it is one of the best. issue is it explains magnetism with relativity
@Buraian Well, I am not from india, so I am not sure if you will recognize the textbook in our country.
2:16 PM
Bruhh!!
Plot twist of the century!
Wo kommt ihr her?
Where are you from
Du n dunnnn
plot twist of the century
I really thought you were Indian
2:17 PM
This
yes
My advice would be that you learn MV, and then you start reading Tristan Needham's Visual Differential Geometry. If you finish the book then you can do General relativity, tensor calculus, pure fluid mechanics etc
Also complex analysis is made some what easy using differential forms (need to check on this...)
Well I don't really have wishes to learn diff forms. because the formalism required is kind of insane.
It depends where you learn it from
The VDG book is not too technical like in terms of axiom - lemma-proof form
I will probably learn it after finishing real analysis.
Real Analysis as it is vs Differential forms presentesd as in Tristan's book is like an ocean apart
2:20 PM
I really think that differential forms is enligthenment
but, if you want to go the pleb route, then tao's part 2 does MV
@Buraian It is a nice generalization, but I don't agree with aleph0 that "it is a misconception that derivative and integrals are opposite".
Why?
Oh hold up buddy, wait till you learn fractioncal calculus
@Buraian I am learning basic real analysis from spivak.
In that, this idea takes in full effect and the integration -differentiation operators are replaced with the combined integrodiffernetiator something
@Buraian never heard of it.
2:23 PM
In it makes sense to take 1/2 derivative
instead of first derivative for eg
@Buraian vcubingx?
yews
@Buraian how far have you gone with tao?
I read through the chapter of chapter of sequences and got the definition of real number
I need to do exercises from the chapter on set theory. I got deviated into studying Abstract algebra
@Buraian I guess then your next video will be "my encounters with abstract algebra".
2:26 PM
LOL
🤣🤣🤣
You know me too well
I want to do a video on Galosis theory one day
@Buraian WOW you have gone that far? cool!
Sir no
I am still learning Ring theory, field theory
Pro tip: learn group theory before this, because most of the axiom for ring and fields can be written as them being a group
@Buraian Which textbook are you learning from? I guess gallian?
Yea Gallian only
it hast linear algebra in end too
I think this guy is quite good explainer as well
and , I found this guy as well when I was seeing some topology
this was a nice video
@Buraian Colourful chalks =)
2:32 PM
yes!
I stumbled upon him in "what comes after calculus".
Haven't seen that one
may check it out some time
@Buraian How are the proofs in real analysis like?
hm
well I mean, I've only done the chapter till set theory but ( in terms of exercises)
I imagine they are quite easy for you.
2:34 PM
I can say that it is way less technical than what you write through logic symbols in the basic math chatroom
@Buraian But you do have wayyy better math background and intuition.
Coz I have no friends and no life
Well I did have a life at some point but yes
I suppose it is easier due to my experience
@Buraian I also don't have much of a life, I think academia might have ruined my childhood.
but, I'd say as per as actual writing complexity/ thinking complexity, I'd say easier than logic chatroom, but, maybe that because I didn't study enough logic
@Prithubiswasleftmse sed
You know what's interesting
like what's really sticking to my mind these days
How closure of arthimetic operations on the rationals breaks when we take infinite sequences
42
Q: Give a concrete sequence of rationals which converges to an irrational number and vice versa.

DavidGive a concrete sequence of rationals which converges to an irrational number and vice versa.... My work I could give a sequence of irrationals which converges to a rational number... Let $r\in \mathbb Q,$ $$a_n=\frac {\sqrt 2} n+r$$ But I couldn't give a sequence of rationals which converges ...

the e definition for example
how's it that when we do the same thing infinitely many times closure is broken ? O_o
It turns out this is exactly how all irrational numbers are defined, you say it as limit of the many different sequence which gives them in end (technical jargon omitted)
Gonna be off then, back to german bashing
:weary:
@Buraian Sure. See you next time.

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