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) UCAS School of physical sciences Professor
https://t.co/9X8OheIvRw
2) UCAS School of mathematical sciences Professor
3) UCAS School of nuclear sciences and technology
https://t.co/nQH8JnewcJ
4) UCAS School of astronomy and space sciences
https://t.co/7Ikc6CuKHZ
5) UCAS School of engineering
6) Geotechnical Engineering Teaching and Research Office
https://t.co/jBCJW7UKlQ
7) Multi-scale Mechanics Teaching and Research Section
https://t.co/eqfQnX1LEQ
😎 Microgravity Science Teaching and Research
9) High temperature gas dynamics teaching and research section
https://t.co/tVIdKgTPl3
10) Department of Biomechanics and Medical Engineering
https://t.co/ubW4xhZY2R
11) Ocean Engineering Teaching and Research
12) Department of Dynamics and Advanced Manufacturing
https://t.co/42BKXEugGv
13) Refrigeration and Cryogenic Engineering Teaching and Research Office
https://t.co/pZdUXFTvw3
14) Power Machinery and Engineering Teaching and Research