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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And here they are...
THE WINNERS OF THE 24 HOUR STARTUP CHALLENGE
Remember, this money is just fun. If you launched a product (or even attempted a launch) - you did something worth MUCH more than $1,000.
#24hrstartup
The winners 👇
#10
Lattes For Change - Skip a latte and save a life.
https://t.co/M75RAirZzs
@frantzfries built a platform where you can see how skipping your morning latte could do for the world.
A great product for a great cause.
Congrats Chris on winning $250!
#9
Instaland - Create amazing landing pages for your followers.
https://t.co/5KkveJTAsy
A team project! @bpmct and @BaileyPumfleet built a tool for social media influencers to create simple "swipe up" landing pages for followers.
Really impressive for 24 hours. Congrats!
#8
SayHenlo - Chat without distractions
https://t.co/og0B7gmkW6
Built by @DaltonEdwards, it's a platform for combatting conversation overload. This product was also coded exclusively from an iPad 😲
Dalton is a beast. I'm so excited he placed in the top 10.
#7
CoderStory - Learn to code from developers across the globe!
https://t.co/86Ay6nF4AY
Built by @jesswallaceuk, the project is focused on highlighting the experience of developers and people learning to code.
I wish this existed when I learned to code! Congrats on $250!!
THE WINNERS OF THE 24 HOUR STARTUP CHALLENGE
Remember, this money is just fun. If you launched a product (or even attempted a launch) - you did something worth MUCH more than $1,000.
#24hrstartup
The winners 👇
#10
Lattes For Change - Skip a latte and save a life.
https://t.co/M75RAirZzs
@frantzfries built a platform where you can see how skipping your morning latte could do for the world.
A great product for a great cause.
Congrats Chris on winning $250!
#9
Instaland - Create amazing landing pages for your followers.
https://t.co/5KkveJTAsy
A team project! @bpmct and @BaileyPumfleet built a tool for social media influencers to create simple "swipe up" landing pages for followers.
Really impressive for 24 hours. Congrats!
#8
SayHenlo - Chat without distractions
https://t.co/og0B7gmkW6
Built by @DaltonEdwards, it's a platform for combatting conversation overload. This product was also coded exclusively from an iPad 😲
Dalton is a beast. I'm so excited he placed in the top 10.
#7
CoderStory - Learn to code from developers across the globe!
https://t.co/86Ay6nF4AY
Built by @jesswallaceuk, the project is focused on highlighting the experience of developers and people learning to code.
I wish this existed when I learned to code! Congrats on $250!!