The resolution of mathematics problems is easier when you have the right resources. But what are the right resources? The answer depends on who you are, what you are trying to achieve, and why.
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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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“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. […]
