KF Math Thread - Discuss Math

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Tsar Nicky said:
Appreciate it, fren, but it gets me a fatal error and I CBA to troubleshoot it right now. I'll keep a note of it, though, so I'll get it figured out at some point or other.
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Might be because the font is missing. If you upload the LaTeX source file and errors to Pastebin or some other such service I could look into the matter.
NvII iS 8ulLt f0R 88C said:
You can use Overleaf as training wheels. Or normal wheels for that matter, I don't believe anyone uses LaTeX without a graphical interface.
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I use Vim
 
NvII iS 8ulLt f0R 88C said:
You can use Overleaf as training wheels. Or normal wheels for that matter, I don't believe anyone uses LaTeX without a graphical interface.
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I'm using it on desktop (MikTeX) and consulting a tutorial on Overleaf. I'm fine without an interface because I've used Lilypond before which is the same concept but for music so no worries
 
Tsar Nicky said:
I'm using it on desktop (MikTeX) and consulting a tutorial on Overleaf. I'm fine without an interface because I've used Lilypond before which is the same concept but for music so no worries
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It compiles and previews the changes you made automatically, so it is really handy if you write something and are not sure if it looks good or not.
Tsar Nicky said:
Appreciate it, fren, but it gets me a fatal error and I CBA to troubleshoot it right now. I'll keep a note of it, though, so I'll get it figured out at some point or other.
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I might be retarded for asking but did you do the begin document / end document commands? Also try porting it to Overleaf it also helps you with errors.
 
NvII iS 8ulLt f0R 88C said:
It compiles and previews the changes you made automatically, so it is really handy if you write something and are not sure if it looks good or not.

I might be retarded for asking but did you do the begin document / end document commands? Also try porting it to Overleaf it also helps you with errors.
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Yeah, I did. I'll try and check it in Overleaf later but for now I'm just trying to get shit written down
 
revenge of rebecca said:
Also please present a proof that 1 > 0
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It falls out pretty easily from the Peano axioms and some reasonable definition of "greater/less", if that's how you want to model arithmetic: https://en.wikipedia.org/wiki/Peano_axioms
0 is given to exist. The successor of 0, S(0) we name "1".
By the axioms, 0 itself is not the successor of anything, so 0 != S(0), or in other words 0 != 1.
1 is S(0) so 0 < 1.
Since 0 < 1 and the inequality is strict, we can say 1 > 0.
 
revenge of rebecca said:
OP, please explain to me what a lagrangian is. I do not understand it.

Also please present a proof that 1 > 0. Please help me understand what the hell "delta is greater than epsilon" means, prove the fundamental theorem of calculus, and walk me through the definitions of derivatives and integrals.

ty
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I'm not sure if you're joking about the calculus ones but if not I recommend this playlist. Especially if you're looking for an intuition rather than a fully rigorous proof.
 
This may or may not be a hot take here but I think one of the best ways to learn any mathematic concepts is to learn the concepts well enough and then try and use it for something practical. This could mean a programming project or an engineering project or whatever. It could mean something silly and stupid but still practical and in the real world. Mathematics as a skill has similar traits to crafts in that if you do it a lot you get really good at it, and the real world nature of whatever you are doing helps you understand.

I was recently programming something that had combinations, complex 3D relationships, and Linear Algebra and I got way better at understanding all of those concepts as a result. I took Linear Algebra in college for example but using it to do something useful has made understand what is going on in a much more fundamental way.

TyrasGuard said:
Love numbers, hate algebra. I cannot recall a single instance where I've used it.
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I think this is false and you just don't know it.

It takes you fifteen minutes to drive somewhere how long will it take you to drive there and back is an algebra question.
 
Napoleon III said:
This may or may not be a hot take here but I think one of the best ways to learn any mathematic concepts is to learn the concepts well enough and then try and use it for something practical. This could mean a programming project or an engineering project or whatever. It could mean something silly and stupid but still practical and in the real world. Mathematics as a skill has similar traits to crafts in that if you do it a lot you get really good at it, and the real world nature of whatever you are doing helps you understand.

I was recently programming something that had combinations, complex 3D relationships, and Linear Algebra and I got way better at understanding all of those concepts as a result. I took Linear Algebra in college for example but using it to do something useful has made understand what is going on in a much more fundamental way.


I think this is false and you just don't know it.

It takes you fifteen minutes to drive somewhere how long will it take you to drive there and back is an algebra question.
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Biggest driver of me learning new math is randomly trying to model games or shit I observe IRL. Often I just end up with unanswered questions, and then months or years later I learn something and it’s a real lightbulb moment.
I once basically invented the concept of permutation groups to try and understand something in a video game, got stuck, and dropped it. A year and a half later I actually learned about them and it made the knowledge so much more tangible
 
Hello, could any mathfags help with a predicament I am having? It's about racism and how to be the most racist you can logically be. If you want to maximize racism, you of course first think of the obvious answer: Be maximum racist to every race. But that doesn't work because you are now treating every race equal (because you are infinently racist to all of them) and thus no longer racist. For the sake of clarity, let's divide the races into compressible chunks (Indians, Blacks, MENAs, Whites, Indians, Chinks; so on) and give them the value of x. How do we maximize the difference of racism between races, while also giving the maximum racism per race? I tried to illustrate my problems with a graph. I hope I wasn't not that autistic while trying to articulate my problem.
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I wonder if it would be better to try to make every race mutually racist towards eachother, or if you would achieve more overall racism by having some underclass minority that is objectively trash and therefore accruing high levels of racism from a large majority
 
geckogoy said:
I wonder if it would be better to try to make every race mutually racist towards eachother, or if you would achieve more overall racism by having some underclass minority that is objectively trash and therefore accruing high levels of racism from a large majority
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I'm in favor of just dumping it all on niggers
 
The Ugly One said:
PDEs & numerical analysis (the latter of which depends heavily on linear algebra) for physics & engineering.
Algebra (including algebraic number theory & all things combinatorics-related) for computer science.

They're kind of all coupled to physics in the end. I mean you also need statistics & probability theory for physics, too. And engineering. And just like...stuff.

So I guess the answer is, "all of them except topology," because topology's just gay, who cares about shapes.
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Topology crops up more than one would think. At an elementary level, the intermediate and extreme value theorems in calculus are just special cases of the fact that continuous maps preserve connectedness and compactness. Functional analysis, which is the theoretical underpinning for PDEs, employs multiple topologies (e.g. norm, weak, weak*) to address the different flavors of limit and convergence.

However, when people use the term "topology" colloquially, I think they're probably referring to deforming one shape into another (e.g. saying that a coffee cup and a donut are somehow equivalent). This branch, which could be broadly described as algebraic topology or homotopy theory, is quite far removed from any kind of "applicable" mathematics. Even so, you can see shades of it when you're doing vector calculus. For example, since the curl of the gradient is zero, you know that conservative 3d vector fields necessarily have zero curl. The question of whether a zero curl vector field is conservative is a much more subtle issue that depends on the topology of the nonsingular locus of the vector field.

For example, if a vector field is infinitely differentiable on the whole of real three space, then it will be conservative if and only its curl is zero. This is because real three space can be deformed to a single point, which is homotopically trivial.

On the other hand, consider F(x,y,z) = [-y/(x^2+y^2), x/(x^2+y^2), 0]. If you mechanically compute its curl, you can verify that it is indeed zero. On the other hand, if you integrate F along one counterclockwise turn of the unit circle in the xy-plane, you'll get 2*pi, so F is not conservative. The nonsingular locus of F is all of 3-space with the z-axis removed, which is homotopic to the unit circle. This space has a nontrivial first cohomology group, which can be thought of as an "obstruction" to F being conservative.
 
Watched this last night, quite lovely. I'd really love to see some kind of expression of the "boundary" you can kind of make out in this animation
 
Here is a fascinating documentary that I can share that there is finally a math thread. (NOTE: I CAN'T EMBED IT BECAUSE THE EMBEDDING FEATURE FOR VIMEO WORKS LIKE A NIGGER.)

I always liked geometry because it was always a good basis for understanding some of the fundamentals behind some of the more complex concepts in mathematics.
I like the whole notion @Tsar Nicky of writing a definitive guide to early mathematical conceptualizations that are lost later in adulthood. I think that implementing geometrical examples and concepts would greatly benefit the content in Math For Retards. I'd find it to be hilarious of there can be a geometric representation of a puzzle piece and the mathematical definition in solving maybe certain variables would be a pretty funny representation of what a math for retards textbook could constitute.

I am personally glad there is a math thread on here finally and I am just going to pin this thread to see how it is progressively updated. I guess to also share one of my favourite math textbooks that actually helped me understand the application of math in engineering better is this textbook in particular Basic Technical Mathematics with Calculus, SI Version, Ninth Edition, 9th Edition . It's a bit of an older math book and I am sure that there can probably be some torrents that exist of it out there currently. This book doesn't get too crazy in depth in some of the more involved elements of calculus, or multivariable, but is a pretty good summarization. Along with a good start before delving into some of the more in depth books/material out there. I didn't like that Leibenz notation was extensively used before Larange notation, because to be honest. Larange notation is far more readable and just quantifies things and saves space a lot better. Personal preference in respect to feedback regarding that autistic little nuisance on my end.

I am almost tempted to begin getting back into math again, but just in a practical way now that I am a little more fluent in programming and to be honest I would rather have a practical approach with some of these concepts. Writing little programs in R probably might be my best bet, considering that I am currently in-between opportunities. So that might kill some time while I am job hunting at the moment.

The funny thing is that I have never heard of LaTeX until you guys brought it up in the thread and looks like that is something really useful to learn for me. Also it looks like it uses pretty good markup conventions which resemble just a brief glance something I would see in an XML or HTML format. I always learn something new from this site, which probably is the reason why the clear net wants to get rid of this site so bad.
 
The laplace transform is so fucking based... It's saving my ass
 
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