Tensor

burgers actually think that

>Lol, we have the best universities in the world.
Debatable but the majority and the average are glorified highschools, the only ones that don't suck are for the über rich.
>Lol, we have the most advanced space programs in the world.
Russian space program is resupplying ISS
>Lol, we have the strongest military in the world.
Implying killing lots of people makes Americans intelligent and not barbaric.
>Lol, we have the best businessmen in the world.
Holy shit businessmen are poison! Why would you ever be proud of that?
>Lol, we're one of the wealthiest countries in the world.
Being 13th on the list makes you technically correct I suppose
>Lol, we have a large amount of the leading tech in the world.
Yes but all of the engineers are leaving so that's changing .
>Oh, boy user. You sure showed us. LOL AMERICANS
Lol insecure Americans...

What do you want to be able to do? I use tensors a bit but I'm an engineer so my tensors are probably rather un-sophisticated compared to fancy pure mathematics constructs.

AG masterrace rep in. Dunno w tensor calc is, but I work with things that physicists would maybe call tensors on a daily basis. So if you should be worried, I should be. But I feel pretty comfy, so I guess it's ok.

>Lol, we have the best universities in the world.

You have lists of the best universities in the world made by Americans and English folks.
You're just like pro-Berlusconi Italians and pro-Erdogan Turks.

Having a degree from Oxford is good because it says "Oxford" and that's known. Do you honestly believe students from there are in any way better than students from some German universities like Göttingen?

You're not a true mathfag if you don't know basics of differential geometry.

HAHAHAHA

Tensors are sections of products of the tangent and cotangent bundle of some manifold. Tensor calculus just means picking a local orthonormal frame and working out the composite map in terms of the coefficients. Fidget about for 10 minutes with the whole index notation thingy and you're done.

We never mentioned tensors in differential geometry :(

So you didn't treat metrics and curvatures?

Its not a problem of learning about tensors. I just don't feel motivated to study them, and it seems imo a bit boring

Yes, I did.

differential geometry is fucking beautiful, understanding diff geo should be your motivation

These posts are becoming Reddit "pls give me an upboat"-tier.

This: And this: youtube.com/watch?v=KlC6mUnN6uM

tensors are just multilinear maps.

if you know what a determinant is, you already know a type of tensor, an alternating n-fold tensor (where n=dim V)

scalar product is just a bilinear map, so it's basically a two-fold tensor.

the idea behind tensors is to reduce multilinear maps to linear maps. also it's the most generic way to define multiplication between arbitrary things.
with multiplication, "multilinearity" is usually called "distributivity" and looks simply like this

(aU+bV)*(cX+dY) = acU*X + bcV*X + adU*Y + bdV*Y

>Debatable but the majority and the average are glorified highschools, the only ones that don't suck are for the über rich.
>Having a degree from Oxford is good because it says "Oxford" and that's known. Do you honestly believe students from there are in any way better than students from some German universities like Göttingen?

I don't think anyone means in terms of undergrad education, but research output. I'm a grad student, and my program has brilliant people from all parts of the world here.

actually scalar products are SYMMETRIC two-fold tensors

Rank two tensor~ [math]N \times N[/math] matrix.

If you got a tensor and a coordinate system of [math]mathbb{R}^N[/math] you can make matrix and take a vector of [math]mathbb{R}^N[/math] and just matrix multiplicate.

Fellow engineer here. One of the most useful things in maths for an engineer are indeed tensors. (Especially if you major in mechanics)

>13th
you went by the mean GDP per capita by PPP. here is the correct information by MEDIAN GDP per capita by PPP.

Note that the Scandinavian countries total population is ~8% of the united state's population, and while the data is convincing that Scandinavians are doing something right, we cannot be sure if such numbers would continue into higher populations.

So that is to say, America is the richest on average for nations with sufficient population sizes.

Further america has the 4th largest disposable income in the world, but the 3 nations ahead of it are small tax havens.

To address the other points; outside of the military much of that is due to public opinion and what people want.

NASA is no longer being funded as heavily because we don't care that much anymore and Americans are in a belief that "if we did it once, then we can do it now" and don't realize funding is needed to keep it up.

You claim that our average Colleges are glorified highschools, but I believe you are mistaken and are thinking of our community college program.

The idea that business men are poison is a bit baity, while they serve their own interest, they do not actively attempt to harm the country, only further their own interests

I haven't seen any statistics on our engineers leaving so if you can provide me with some material on that i'd be interested. But rest assured that the number of students that are wanting to be engineers is growing in america.

Americans as a whole don't understand that our pride as a nation and a people doesn't come from objective empirical facts, it comes from the pride and humility that we must have for the great men that came before us, who have struggled for the ideals that as a modern people we hold as true, and that we must identify their character and emulate them in hopes of furthering the american cause for Freedom and Liberty. We haven't been very good about it in recent years, but it takes a consciousness in our people to realize it.

weirdly enough I never really "got" the intuition behind the "matrix" version that physicists would show me, but once I just saw it this way (as sections of a bundle) it became totally clear and not computational magic

No.

>yes, but all the engineers are leaving
You had me baited until this part. Being an engineer is basically the next meme here in the US, I just graduated from a public high school in Texas so I know. They lie to us for years about how there's such a demand for engineers even though stats show otherwise. I'm still going to UT for engineering anyways though

>pic related