How to mentally compute the cube root of the cube of a two digit number.

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Common Core math was the pinnacle of their evil genius, and low-point of our complacency... It disrupted the minds of an entire generation on how even the most basic things work.

Readin', Writin', & Rithmatic

How far did they get? Let's see.

1895 8th Grade Final Exam, Kansas:

1st grade mathematics work sheets and my mother's mathematics teaching style. Mathematics will not be so terrible, since it seems that parents are interested in preparing their little ones for mathematics before school age.

I grew up without understanding how people talk about mathematics as difficult as they do, it was my best topic at school.

@DesmondSwayne Sir Desmond is right. SAGE makes mathematical predictions based on flawed models.
I chose to stick my neck out almost 4mo ago here:
https://t.co/b0rT5Lq9HI
I experienced much anxiety doing this, aware that, if I was badly wrong here, I would be destroyed as a contributor.

That said, I thought the immunology so clear that I made three, specific & testable predictions which should apply if I was right.
Please examine them, on the right, under the pie chart:

In particular, I predicted that the epidemic would not reignite in London. Obviously, we have many “cases” but I urge people to disregard these & instead to look at excess deaths, on the principle that a severe (occasionally lethal) respiratory virus would show itself this way.

Here is a chart showing the trend of deaths in London alone over recent years. A prominent peak of deaths is evident as the virus swept through in spring. Also visible the August heatwave. But there are no excess deaths now.
I submit this is a striking example of herd immunity.

I’m still waiting for SAGE or indeed anyone to provide an alternative explanation for the sharp nature of the spring excess deaths peak which doesn’t involve herd immunity or otherwise removing from the pool those vulnerable to lethal outcomes (same result). Given this sharp...

When I was starting out as a grad student, I remember being frustrated with analysis problems where it didn't use DIRECTLY the things we spent so much time proving in class.

As an example, let's look at a standard real analysis problem:

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The problem looks like it can be done using the dominated convergence theorem.

This is an important theorem and is used in a lot of places outside a grad real analysis class. A student would go through a lot of buildup leading to this theorem.

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Now, let's see whether the conditions for DCT are satisfied.

First, for fixed 00 as n->infinity.

So we have a.e. convergence of the integrand in [0,1].

To the student, this builds a stronger case to use DCT to solve the problem.

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Finding an integrable dominating function is where the problem starts.

It would seem NATURAL (at least for me) to bound it with:

p.s. it feels "natural" to me because it is reminiscent of squeeze theorem problems, math students encounter in calculus.

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However, 1/x^n is not integrable in (0,1) and hence cannot be (further) dominated by an integrable function.

So, what I would do is since I know it converges a.e. to 1, maybe it converges uniformly to 1?

This leads me into a BAD detour.

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