/sci/ - Science & Math

>>9652968

most good mathematicians use shortened notations already

at least good ones in their own lectures

not gonna watch your retarded vide o


and lmao at your picture, this looks absolutely retarded

>>9652968
Brianlets are always blaming random shit like notation for not being able to understand math
The fact is that if we fixed all the notation they still wouldn't get it
Don't fuck around pretending like revolutionizing notation is a thing that's going to happen

>>9653043
This. The video tries to explain why so many more people would pursue mathematics if the notation were changed, but the truth is that if you're too stupid to not understand notation how it is now, you'll never become remotely successful in whatever math-related field

>>9653043
>The fact is that if we fixed all the notation they still wouldn't get it
Maybe so, but there's also the possibility that it would be much easier to parse an expression

> if you're too stupid to not understand notation how it is now, you'll never become remotely successful in whatever math-related field
That's an extremely reductive viewpoint that doesn't help anyone.
Anybody can learn math. Sure, people learn at different rates, but that's no reason to simply throw out a blanket statement that "people can't learn math". Not everyone's as smart as you.

>The fact is that if we fixed all the notation they still wouldn't get it
I'm no educator, but I really do think that changing the notation can help people a great deal. It's not immediately clear why the sigma should represent a summation, and why a Pi should represent multiplication. We already have symbols that represent multiplication and addition, so why not use those? Using Pi and Sigma only adds to the things someone has to memorize when working with math.
What's wrong with trying new things and seeing if people improve their intuitive understanding of math? Math isn't static.
But that's just my view on things.

>>9652968

In group theory my textbook uses the absolute value notation to denote the order of an element. I got used to it so in number theory when dealing with order mod p for example I just use the absolute value notation but with a subscript "p" at the bottom right. I should really learn to latex fuck.

>>9653072
Let's rename "tangent" to "shplargle" and "sin" to "dick"

Is that a good syntax? Yes or no? Obviously no. So why not? Because it makes less sense than syntax that actually describes what it's doing

You're making a fallacious appeal to tradition. There's no good argument about more intuitive syntax, that's the ENTIRE PURPOSE of written language and symbolic representations of abstract concepts, I'm sorry you're too much of a brainlet to comprehend that

Diagrams are used to explain abstract concepts then we map them to the syntax used to represent those mathematical concepts. It makes more sense to use syntax that is ITSELF the diagram used to explain it, so it makes sense without having to think about it, that's the entire point of writing things down

That guy is a great youtuber, I am basically learning basic algebra and I still binge watch his videos like some ant with acess to alien libraries he cant ever understand yet are still mind stimulating

who cares about notation if it just represents an idea? I can't see any type of problem there

>>9652968
why not simply [math] y_{tt}[/math] ?

>>9652968
The triangle notation in the vid is horrible, It obscures the meaning of the original notation.

Also, repeated multiplication suddenly becomes a triangle?
I find this absolutely disgusting as the triangle is reserved for symmetric difference which is addition in sigma algebra's.
Verry confusing if you start writing repeated multiplication with these triangles.

Also, how would you write repeated logarithms?
those occur quite frequently in number theory.
you get a big fat stack of triangles?
[math]_2\triangle_{_2\triangle_{_2\triangle_8}}[/math]
absolutely disgusting.

>>9653572
with logarithms you might add an exponent behind the function. where composition of functions is multiplication and the exponent is the number of compositions
[math]\underbrace{f \circ \dots \circ f}_\text{n times} = f^n[/math]

When you do that with the triangle notation, you can not add the exponent to indicate the amount of times you itterate the function because its obviously ambiguous.
The upper part of the triangle is reserved for a different meaning.
[math]\underbrace{_2\triangle \circ \dots \circ_2\triangle} _\text{n times} = _2\triangle^n [/math]

I am at a loss of words to fully describe how disgusting this notation is.
my hate for it burns with the intensity of more than a thousand suns and the inventor should be completely destructed off the face of this earth

As we in the we write from left to right, (x)f for f(x) would be a good start, so that when you change the thing, you add stuff/transformation. But it's far too late for that.
I don't find the sum and product thing too helpful. I read sigma as s for sum and p as p for product. It's clear enough. Representing diffentials as faction does have its perks, I'd not change that. I don't like having multiple notations for inversion, however. 1/x for the inverse of x is odd. Even if all those things seem natural due to being used to them. Please don't respond angrily to this post before you sat down a bit and tried imagining not having been taught this and that notation from the start.

>>9653083
learn it, its reaaally simple.

>>9653572
implying it is repeated multiplication

>>9653635
>implying thats an exotic assumtion

>>9653043
It's perfectly fine and not brainlety at all to invent notations, not for the sake of making math look like kindergarten fingerpainting, but to make more visual stuff that should be and to get rid of unrigorous, handwavy garbage like Leibniz notations.

>>9652968
>Have you come up with any notation yourselves?
When defining the Riemann integral, if [math]\left( \sigma_i \right)_{i\,\in\,\left[\!\left[ 1,\,n \right]\!\right]}[/math] is a subdivision of [math]\left[ a,\,b \right][/math] that catches all discontinuities of [math]f[/math], then
[eqn]\underline\int_{\left( \sigma_i \right)_{i\,\in\,\left[\!\left[ 1,\, n\right]\!\right]} } f\ \leqslant \int_a^b f\left(x\right)\,\mathrm dx\ \leqslant\ \overline\int_{\left( \sigma_i \right)_{i\,\in\,\left[\!\left[ 1,\, n\right]\!\right]} } f.[/eqn]
I've seen upper and lower integrals being used for Riemann's integral, but not this way at all.

>>9653563
This is misleading since [math]y[/math] could be a vector function with coordinate functions or something similar. I'd use [math]\partial_{t,\, t} y[/math] instead.

>>9653083
>In group theory my textbook uses the absolute value notation to denote the order of an element.
[math]\mathrm{ord}_\left(G,\, \cdot\right)\, x[/math] is what you need. Or you can use [math]o\left(x\right)[/math] if you love ambiguity.