Dear writers of elementary math problems: If you ask children to “predict how many heads and tails you will get if you flip a coin 10 times,” there is no single correct answer since even a prediction of 10 consecutive heads is valid (if not the best). Please use some other verb besides “predict.” Thank you.
Something we’ve lost
A quote from George Will, from the extended commentary of Ken Burns’ excellent series on the Civil War.
How the common men and women of [the Civil War era] used the English language at that time is worth pondering. I think the normally literate 19th century American had as his entertainment popular novels: Balzac, Dickens, George Eliot. They didn’t turn on the television; they weren’t in that passive receiving mode. They were in the active mode, which reading is, and popular entertainment then was popular novels. Dickens: not bad. Also, they didn’t pick up the phone when they wanted to communicate. They wrote letters. They had the discipline of expressing themselves in complete sentences and rounded paragraphs. And that’s something we’ve lost.
Binary magic trick
I found this magic trick in a set of Christmas crackers a couple years ago which is completely based on binary arithmetic. The link above does a good job of explaining why the trick works — and how a new trick can be generated using base-3 arithmetic.
Infinite number of monkeys
From Wikipedia:
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.
This can be formally proven using the second Borel-Cantelli Lemma, a topic which requires measure-theoretic probability. Thus leading me to one of the driest observations that I’ve ever read in a graduate-level textbook, following the proofs of the Borel-Cantelli Lemmas:
The record of a prolonged coin-tossing game is bound to contain every conceivable book in the Morse code [using heads for dot and tails for dash], from Hamlet to eight-place logarithmic tables. It has been suggested that an army of monkeys might be trained to pound typewriters at random in the hope that ultimately great works of literature would be produced. Using a coin for the same purpose may save feeding and training expenses and free the monkeys for other monkey business.
W. Feller, An Introduction to Probability Theory and Its Applications, Volume 1 (Chapter 8.3), page 202.
25 divided by 5 is 14
A good clean joke
Q: How do you tell the difference between an introverted math professor and an extroverted math professor?
A: The extroverted math professor will look at your shoes when talking to you.
Finite simple group of order 2
I like showing this to my students around Valentine’s Day. The singers were math grad students at Northwestern.
Design of scientific trials
For years, I’ve used the following clip in my Applied Statistics class when introducing randomized controlled experiments and observational studies. It was a big hit every single time.
STEM promotional video
A few years ago, the folks at Change the Equation asked various corporations to make 3-minute videos that could inspire children to take their studies of math and science more seriously. Here is one of the most impressive entries.
Pendulum waves
Courtesy of the physicists at Harvard: pendulum waves. Click here for more information.
Mean Green Math 