One suggestion would be to take an approach similar to that used for describing the $52!\approx 8.063*10^{67}$ ways to arrange a standard deck of playing cards as outlined in Scott Czepiel's Blog and ...

As @Adam noted, a function is Riemann integrable if and only if it is almost everywhere continuous. Giving a proof in terms of the Darboux integral (upper and lower sums) would also be rigorous. ...

First, an even easier estimate: $$V = \frac{1}{3} \pi r^2 h \approx \frac{1}{3} \frac{22}{7} \left( \frac{7}{2} \right)^2 9 = \frac{2 * 11 * 7^2 * 3^2}{3 * 7 * 2^2} = \frac{1}{2}*11*7*3=115.5.$$ Never ...

I know that this is a difficult issue that many of us struggle with. By the time a typical student reaches college, they have had over a decade of math classes and teachers. As such, most of your ...

"In the remaining sections of this paper we briefly discuss various occurrences of the stability and pinching phenomena in differential geometry. The results we present are, for the most part, ...

Here's my stab at a self-answer: I think we would all agree on the need for precise written notation is important within mathematics. Unless the context is specifically reverse polish notation, a ...

Late to the party to answer, but hopefully this will be helpful. I would say that the best source of incorrect proofs can be your students themselves! My undergraduate real analysis professor ...

You mentioned 3Blue1Brown's videos. If you're interested in making similar animations, Grant (the man behind 3B1B) actually released the entire python library he wrote for creating them: manim on ...

Let $y=a d x^2+ bd x + cd$ with $a,b,c,d \in \mathbb{Z}$ with $a,d \neq 0$, i.e., suppose the coefficients of the quadratic share a common factor of $d$. Then \begin{align*} x &= \frac{ - bd \pm \...

Personally, I've found that writing a rubric a priori to be a nightmare once answers move into the realm of proofs and such--there always seems to be an incorrect answer that ticks off parts of the ...