Thread: What topic or area in math is most interesting to you?

My math teacher has given us an assignment to choose any topic within or related to math, to learn about it, and to present it in pretty much any way (write a paper, sing a song, make a model, ect). I'm having trouble choosing something that really interests me, and that I'm at a level that I can understand.

What I find most interesting is game theory, but I've gotten to the point in my understanding where to go any farther would involve a whole lot of math that I am not even remotely close to understanding.
What are some other cool areas in math that would be good for this project? I like things that relate to people, their interactions, and behavior.

TIA

AP stat

I'd say probability and statistics. Most of the stuff has very interesting intuitive interpretation. And the area yields plenty of tools which are really useful in practice in engineering, econometrics, psychology, sociology...

For instance, there's a theorem in probability called the Central Limit Theorem, which states (non-rigorously) that a random quantity, being the sum of many random quantities, will follow a Gaussian distribution (the bell-curve). You'll observe that this is often approximately true with, say, population heights, SAT scores, etc. The height of a person from a population is random, and has got to do with many random factors, like genes and regimen. So is the score of a student drawn randomly from a huge group.

Another example. When we take the average of a number of raw measurements to obtain a more "precise" measurement, we are actually assuming that the raw measurements follow the Gaussian distribution. Theory says that the simple averaging operation is not the best one if the measurements being averaged are not Gaussian. There are myriad other methods other than averaging. For instance, the median, which is the best when measurements follow double-exponential distribution.