Math action like drill and practice help a kid increasing great mental number aptitudes. In addition, if the training is done regularly through playing around, youngsters effectively get acquainted with numbers.

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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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Joshua Hawley, Missouri's Junior Senator, is an autocrat in waiting.
His arrogance and ambition prohibit any allegiance to morality or character.
Thus far, his plan to seize the presidency has fallen into place.
An explanation in photographs.
🧵
Joshua grew up in the next town over from mine, in Lexington, Missouri. A a teenager he wrote a column for the local paper, where he perfected his political condescension.
2/
By the time he reached high-school, however, he attended an elite private high-school 60 miles away in Kansas City.
This is a piece of his history he works to erase as he builds up his counterfeit image as a rural farm boy from a small town who grew up farming.
3/
After graduating from Rockhurst High School, he attended Stanford University where he wrote for the Stanford Review--a libertarian publication founded by Peter Thiel..
4/
(Full Link: https://t.co/zixs1HazLk)
Hawley's writing during his early 20s reveals that he wished for the curriculum at Stanford and other "liberal institutions" to change and to incorporate more conservative moral values.
This led him to create the "Freedom Forum."
5/
His arrogance and ambition prohibit any allegiance to morality or character.
Thus far, his plan to seize the presidency has fallen into place.
An explanation in photographs.
🧵
Joshua grew up in the next town over from mine, in Lexington, Missouri. A a teenager he wrote a column for the local paper, where he perfected his political condescension.
2/

By the time he reached high-school, however, he attended an elite private high-school 60 miles away in Kansas City.
This is a piece of his history he works to erase as he builds up his counterfeit image as a rural farm boy from a small town who grew up farming.
3/

After graduating from Rockhurst High School, he attended Stanford University where he wrote for the Stanford Review--a libertarian publication founded by Peter Thiel..
4/
(Full Link: https://t.co/zixs1HazLk)

Hawley's writing during his early 20s reveals that he wished for the curriculum at Stanford and other "liberal institutions" to change and to incorporate more conservative moral values.
This led him to create the "Freedom Forum."
5/

“We don’t negotiate salaries” is a negotiation tactic.
Always. No, your company is not an exception.
A tactic I don’t appreciate at all because of how unfairly it penalizes low-leverage, junior employees, and those loyal enough not to question it, but that’s negotiation for you after all. Weaponized information asymmetry.
Listen to Aditya
And by the way, you should never be worried that an offer would be withdrawn if you politely negotiate.
I have seen this happen *extremely* rarely, mostly to women, and anyway is a giant red flag. It suggests you probably didn’t want to work there.
You wish there was no negotiating so it would all be more fair? I feel you, but it’s not happening.
Instead, negotiate hard, use your privilege, and then go and share numbers with your underrepresented and underpaid colleagues. […]
Always. No, your company is not an exception.
A tactic I don’t appreciate at all because of how unfairly it penalizes low-leverage, junior employees, and those loyal enough not to question it, but that’s negotiation for you after all. Weaponized information asymmetry.
Listen to Aditya
"we don't negotiate salaries" really means "we'd prefer to negotiate massive signing bonuses and equity grants, but we'll negotiate salary if you REALLY insist" https://t.co/80k7nWAMoK
— Aditya Mukerjee, the Otterrific \U0001f3f3\ufe0f\u200d\U0001f308 (@chimeracoder) December 4, 2018
And by the way, you should never be worried that an offer would be withdrawn if you politely negotiate.
I have seen this happen *extremely* rarely, mostly to women, and anyway is a giant red flag. It suggests you probably didn’t want to work there.
You wish there was no negotiating so it would all be more fair? I feel you, but it’s not happening.
Instead, negotiate hard, use your privilege, and then go and share numbers with your underrepresented and underpaid colleagues. […]