Category: Other mathematics

The other day, I came across this problem on Twitter: How many distinct ways are there to color the vertices of a cube, such that exactly four are one color and...

I’m currently reading “Sweller’s Cognitive Load Theory in Action” by Oliver Lovell, specifically the section on reducing extraneous load...

The other day, I saw a tweet joking that while calculus teachers insist that \(\frac{dy}{dx}\) is not a fraction, the LaTeX is \frac{dy}{dx}. That reminded me o...

One thing I realized while writing and editing the previous article is the depth of the mismatch between notation for addition and multiplication (on the one ha...

By the time most students graduate from high school in the United States, they have seen the following operators*: Addition, subtraction, negation, multiplicati...

Conceptually, subtraction and addition of negatives are two very different processes. Subtraction involves an undoing of addition: It is an inverse function. Ad...

How notation gets in the way of understanding The other day I tweeted this: Objectively, I realize that \(\sqrt2\), \(\log6\), and \(\frac57\) are all specific ...

In this item, I will show how the basic logarithmic rules, including the Change of Base formula, follow from this equivalency: \[\log_b m = n \Leftrightarrow b^...

There are two basic forms of “memorization”: (a) Rote, through the repetition of the specifically, often decontextualized, data and (b) Habituation,...

This is another stab for me at what continues to prove to be a complicated topic: How our mess of mathematical notation obfuscates key patterns. This is also a ...