/sci/ - Science & Math

Yes.

>>10356303
Yep

>>10356307
>>10356305
Great but how exactly? What topics should I accent on?
I'm studying electrical engineering and embedded programming.

>>10356303
No.

>>10356303

>>10356316
Algebra has no notable use cases in modern life.

>>10356317
you have no notable use cases in modern life

>>10356317
Until you understand that everything is described by diff equations and the operation of differentiation is actually algebraic at its core.

>>10356324
>algebraic
Yeah right, I can totally see it - groups and rings of diffs.

>>10356326
Well, it can be naturally defined as a hom functor.

>>10356312
>electrical engineer
Applying the residue theorem.
>>10356326
https://en.wikipedia.org/wiki/Derivation_(abstract_algebra)

>>10356303
yeah, once I was pulled over by a cop and they thought I was drunk driving cuz the breathalyzer test came opt positive, I solved a complex analysis problem and showed em and they lemme go

>>10356324
>brainlet still doesn't understand that math is only as complex as you choose to make it
I'm not going to do some abstract shit to find some unknowns in a linear equation.

>>10356534
>linear equation
>unknowns
those are both algebraic concepts buddy boy

>>10356303
Yes, but just some simple parts of it, and in a non-rigorous way.

>>10356312
You see complex analysis when looking at signals and circuits.

>>10356541
Kek.

>>10356312
You have to take integrals, don't you? Learn some complex anal and some of those integrals will become solvable.

>>10357146
Dunno what you mean by 'take integrals'. I've passed calc 1, 2, and ODEs.
Currently at a dilemma between PDEs and CA.

>>10357156
PDEs are mundane as fuck, spice up your life with some CA.

>>10357286
o-okay

>>10356303
My understanding of complex numbers is "if you keep multiplying by i, you'll arrive back at 1, and that's kindof how circles work." I guess that kinda makes sense for projecting onto an xy plane, but was it ever really proven that "i" was anything more than a projective tool, and didn't constitute a loss in information?
For example, when lim(x->0) f(x) = g(x)/x, which is technically undefined, gets solved as 1 (or any other defined solution), this implies either a leap in logic or a loss of information. Are there any proofs that exempt complex numbers from these sorts of errors?

>>10356317
What? I use it and im not even stem

>>10356305
Source on pic?

>>10356326
The exterior derivative is a linear operator! Indeed the base of modern analysis and differential geometry is heavily rooted in algebra, though it's more linear algebra than groups and rings: vector spaces and algebras over fields, not modules and algebras over rings.

>>10358842
What do you mean by loss in information?
There's no leap in logic anywhere.

>>10358931
Second paragraph was an example of how information is lost when working with zero, but I can't think of any for complex numbers. Is proof by lack of counter-evidence really enough though?
What I mean is, was it ever directly proven, without arbitrary assumptions, that complex numbers were perfect representations of circles and circular motion?

>>10358947
There is no information loss there, I don't understand why you think there is.

You can represent circles perfectly well with real numbers alone, although using complex numbers makes some things neater.

>>10356317
>not using algebra to parameterize cooking rice so can get different textures just by cooking different amounts of rice without worrying about how much water to put
You're given all this math in school and you never think to use it?

>>10356326
d is a natural transformation

>>10358978
I'm a programmer, so I strictly follow the algorithm. Else, it's undefined behaviour - anything can happen, including being bitten by a raptor.

>>10358842
>For example, when lim(x->0) f(x) = g(x)/x, which is technically undefined, gets solved as 1 (or any other defined solution), this implies either a leap in logic or a loss of information.
nigga what are you talking about

>>10359018
>algorithms
Modern complexity theory and analysis of algorithms is lots of Fourier / harmonic analysis and abstract algebra. Yes, it actually has uses. Yes, it’s also pure theory