The key to teaching division to young students who have only been introduced recently to more complicated mathematics forms is to make the student feel involved with the process, while finding it pleasant at the same time.
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Ok, it's time for a #FUNctionalAnalysis thread! Let's talk about Hilbert spaces. (I hope you like linear algebra, because that's what we're
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
— syzygay (@syzygay1) August 9, 2020
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
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1/OK, data mystery time.
This New York Times feature shows China with a Gini Index of less than 30, which would make it more equal than Canada, France, or the Netherlands. https://t.co/g3Sv6DZTDE
That's weird. Income inequality in China is legendary.
Let's check this number.
2/The New York Times cites the World Bank's recent report, "Fair Progress? Economic Mobility across Generations Around the World".
The report is available here:
3/The World Bank report has a graph in which it appears to show the same value for China's Gini - under 0.3.
The graph cites the World Development Indicators as its source for the income inequality data.
4/The World Development Indicators are available at the World Bank's website.
Here's the Gini index: https://t.co/MvylQzpX6A
It looks as if the latest estimate for China's Gini is 42.2.
That estimate is from 2012.
5/A Gini of 42.2 would put China in the same neighborhood as the U.S., whose Gini was estimated at 41 in 2013.
I can't find the <30 number anywhere. The only other estimate in the tables for China is from 2008, when it was estimated at 42.8.
This New York Times feature shows China with a Gini Index of less than 30, which would make it more equal than Canada, France, or the Netherlands. https://t.co/g3Sv6DZTDE
That's weird. Income inequality in China is legendary.
Let's check this number.
2/The New York Times cites the World Bank's recent report, "Fair Progress? Economic Mobility across Generations Around the World".
The report is available here:
3/The World Bank report has a graph in which it appears to show the same value for China's Gini - under 0.3.
The graph cites the World Development Indicators as its source for the income inequality data.
4/The World Development Indicators are available at the World Bank's website.
Here's the Gini index: https://t.co/MvylQzpX6A
It looks as if the latest estimate for China's Gini is 42.2.
That estimate is from 2012.
5/A Gini of 42.2 would put China in the same neighborhood as the U.S., whose Gini was estimated at 41 in 2013.
I can't find the <30 number anywhere. The only other estimate in the tables for China is from 2008, when it was estimated at 42.8.
