erfink
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Communicating to students the meaning of extremely large numbers
6 votes

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 ...

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(Riemann integrability) How do you explain this to a high school student?
5 votes

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. ...

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Is 'estimating' still considered a valuable skill?
5 votes

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 ...

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How to catch students from different subjects' interest to math?
5 votes

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 ...

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Quote to show students don't have to fear making mistakes
4 votes

"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, ...

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Grating mathematical phrases---How to correct?
3 votes

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 ...

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Resource request: incorrect "proofs" for undergrads to correct/critique
3 votes

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 ...

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How to make a mathematical dynamic graph?
2 votes

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 ...

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What can we learn as we reduce the fraction at the end of the quadratic formula process?
2 votes

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 \...

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Rubric for grading an undergraduate real analysis course
2 votes

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 ...

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As a TA, how to reduce imprecise notations/statements in students' exams
1 votes

In my own lectures, there are a couple things that I have found to be useful for addressing notation issues in math (especially calculus). Personally, I do a minimum of "correcting" while grading ...

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Is there a toy example of an axiomatically defined system/ structure?
1 votes

In the vein of other answers that would prefer a "real" axiomatic system, my suggestion would be...point-set topology. I know, crazy. Hear me out though... Only three axioms to give! -- arbitrary ...

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