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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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I just finished Eric Adler's The Battle of the Classics, and wanted to say something about Joel Christiansen's review linked below. I am not sure what motivates the review (I speculate a bit below), but it gives a very misleading impression of the book. 1/x
The meat of the criticism is that the history Adler gives is insufficiently critical. Adler describes a few figures who had a great influence on how the modern US university was formed. It's certainly critical: it focuses on the social Darwinism of these figures. 2/x
Other insinuations and suggestions in the review seem wildly off the mark, distorted, or inappropriate-- for example, that the book is clickbaity (it is scholarly) or conservative (hardly) or connected to the events at the Capitol (give me a break). 3/x
The core question: in what sense is classics inherently racist? Classics is old. On Adler's account, it begins in ancient Rome and is revived in the Renaissance. Slavery (Christiansen's primary concern) is also very old. Let's say classics is an education for slaveowners. 4/x
It's worth remembering that literacy itself is elite throughout most of this history. Literacy is, then, also the education of slaveowners. We can honor oral and musical traditions without denying that literacy is, generally, good. 5/x
As someone\u2019s who\u2019s read the book, this review strikes me as tremendously unfair. It mostly faults Adler for not writing the book the reviewer wishes he had! https://t.co/pqpt5Ziivj
— Teresa M. Bejan (@tmbejan) January 12, 2021
The meat of the criticism is that the history Adler gives is insufficiently critical. Adler describes a few figures who had a great influence on how the modern US university was formed. It's certainly critical: it focuses on the social Darwinism of these figures. 2/x
Other insinuations and suggestions in the review seem wildly off the mark, distorted, or inappropriate-- for example, that the book is clickbaity (it is scholarly) or conservative (hardly) or connected to the events at the Capitol (give me a break). 3/x
The core question: in what sense is classics inherently racist? Classics is old. On Adler's account, it begins in ancient Rome and is revived in the Renaissance. Slavery (Christiansen's primary concern) is also very old. Let's say classics is an education for slaveowners. 4/x
It's worth remembering that literacy itself is elite throughout most of this history. Literacy is, then, also the education of slaveowners. We can honor oral and musical traditions without denying that literacy is, generally, good. 5/x