I did a thing! On Saturdays, we here at UC Davis run an event called Davis Math Circle. There are many wonderful subjects in math which are never taught below a collegiate level–at Math Circle, graduate students and professors choose such topics and teach some of the basics to middle/high schoolers in and around Davis. It’s highly interactive, and we try to construct interesting “group work” problems that are doable with no more than 6th grade algebra.
I presented error control coding, a field in the intersection of mathematics and electrical engineering concerned with clever ways of sending messages in a noise-resistant manner. Attached to this page is my powerpoint and my problems. I spent a fair bit of time constructing explanations, examples, and problems that will give you a taste of coding theory (and really, some of the core ideas of linear algebra). While I can’t present it to you (and help with math notation), I encourage you to try some problems–I think they’re quite fun, and so did at least a few of the students who came to my Math Circle this June. Please let me know if you find any typos, or if you have a question about any of my problems–I hope you enjoy!
Shoutouts to the wonderful Tai-Danae Bradley, a PhD student at CUNY who runs one of my favorite blogs, math3ma, for the idea of replacing matrices with graphs for our final computations, and Wencin Poh, a PhD student at Davis who organizes Math Circle (and about a million other things).
Note: I have a very rapid introduction to binary arithmetic in there. Don’t be intimidated by the fancy words–they’re just there so you know the “rules” of arithmetic. It’s best learned by simply trying to calculate some expressions, and then checking on Wolfram or something.