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### Reference for a nice proof of “undetermined coefficients”

I'm teaching an honors differential equations class and have been using linear algebra heavily. I thought it would be interesting to include a proof of the method of undetermined coefficients along ...
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### Proof without words for surface area of a sphere [closed]

I love the book Proofs Without Words by Roger B. Nelsen. One of the proofs I liked the most was this: Area under one arch of a cycloid is 3 times the area of the wheel that traces it. You break the ...
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### Smoothness of $f(\sqrt x)$

I found that I need to use the following facts in a paper that I am writing. Let $f\in C^\infty(\mathbb R)$, then If $f(0)=0$, then $f(x)=x g(x)$ for some $g\in C^\infty(\mathbb R)$. If $f$ is even,...
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### Slick verification of the model category axioms for Spaces and SSets with the q-model structure?

We choose our category of spaces to be compactly generated weak Hausdorff spaces for convenience, denoted $CGWH$. Questions: 1.) Is there any sort of slick argument to verify that CGWH with the ...
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### Slick proof related to choosing points from an interval in order

Choose a point anywhere in the unit interval $[0, 1]$. Now choose a second point from the same interval so that there is one point in each half, $[0, \frac12]$ and $[\frac12, 1]$. Now choose a third ...
On one of my exams last year, we were given a problem (we chose five or six out of eight problems) on an exam, the goal of which was to prove the Bruhat decomposition for $GL_n(k)$. I was one of the ...