When I was very young, one of my teachers gave me the tongue-in-cheek article “The Complexity of Songs,” by legendary computer scientist Donald Knuth, and I thought it was absolutely hilarious. I was recently reminded of this article when preparing some recent lecture notes, and I’m happy to share this article here.
Unlike yesterday’s post, this headline was made unintentionally.
I stumbled across the following engaging and readable Q&A with Dr. Jonathan Pillow, a professor at Princeton who’s studying how the brain works using mathematics and statistics. I thought that this might be appropriate way of engaging students who think that the study of mathematics is utterly unimportant.
One of the standard topics in an undergraduate statistics course is the principle that two things that are highly correlated do not necessarily have a cause-and-effect relationship. Here is a hilarious example of this fallacy.
And, in case you’re wondering, here’s the rest of the story:
I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on various lessons I’ve learned while trying to answer the questions posed by gifted elementary school students. (This is updated from my previous index.)
Part 1: A surprising pattern in some consecutive perfect squares.
Part 2: Calculating 2 to a very large exponent.
Part 3a: Calculating 2 to an even larger exponent.
Part 3b: An analysis of just how large this number actually is.
Part 4a: The chance of winning at BINGO in only four turns.
Part 4b: Pedagogical thoughts on one step of the calculation.
Part 4c: A complicated follow-up question.
Part 5a: Exponentiation is multiplication as multiplication is to addition. So, multiplication is to addition as addition is to what? (I offered the answer of incrementation, but it was rejected: addition requires two inputs, while incrementation only requires one.)
Part 5b: Why there is no binary operation that completes the above analogy.
Part 5c: Knuth’s up-arrow notation for writing very big numbers.
Part 5d: Graham’s number, reputed to be the largest number ever to appear in a mathematical proof.
Textbooks have included the occasional awful problem ever since Pebbles Flintstone and Bamm-Bamm Rubble chiseled their homework on slate tablets while attending Bedrock Elementary. But even with the understanding that there have been children have been doing awful homework problems since the dawn of time (and long before the advent of the Common Core), this one is a doozy.
There’s no sense having a debate about standards for elementary mathematics if textbook publishers can’t construct sentences that can be understood by elementary students.
I recently came across an excellent article promoting internships from math majors who would like to use their quantitative skills in an industrial setting (as opposed to an academic setting). The concluding paragraph:
Faculty will continue to train students for academic careers. Some will pursue tenure-track positions in the institutions of their choice, but an increasing number of our students will take positions very different from our own. Let’s learn about those options and share them with our students. Then, when a student takes a good job and enjoys a successful career, let’s call that a win.
Here’s the full article: http://www.americanscientist.org/blog/pub/internships-connect-math-students-to-new-career-paths
I really enjoyed this, courtesy of BuzzFeed: