concrete mathematics

In the spring of 2019, I took a class in high school called “Concrete Mathematics.” Given that high school was years and years ago, why does this matter at all?

I credit this class as the first experience where I came to regard combinatorics and discrete math as something fun to study and not just a “category of competition math question.” As such, this class kind of has a special place in my heart, especially as now I’m doing research in combinatorics! This class was fairly unique as it was decidedly off the standard calculus track, and arguably it didn’t fully cater towards the “math competitions” end of high school math either. I also just really enjoyed/still enjoy learning about this area of mathematics and I think high school students should have the opportunity to learn about combinatorics, without necessarily having to get exposure to the subject through competitions.

The sad thing is that this class no longer exists anymore – at least not in practice, since no teacher at TJHSST now has the schedule space to teach it and students haven’t been able to drum up enough support for it. But if the students can bring back other classes (e.g. the quantum lab) from the brink of extinction they can surely revive a cool math class too… hopefully?

For now, this will live as a public repository of somewhat unpolished notes that are available for anyone to look at. The notes cover basic enumerative techniques, special sequences of numbers (Stirling numbers, Catalan numbers), generating functions, and enough group theory to understand Burnside’s lemma, among other things. I’ve chosen to leave these notes in a rough state because I wanted to preserve the integrity of the work that our class generated, so likely this contains formatting issues, vague or confusing language, among other things. Feedback, corrections, and pull requests are welcome, but may not be accepted if they alter too much of the original structure/work.

Here’s the pdf of notes and corresponding Github repository: