goalsetter11111

a really heavy math related research topic
for my senior project

I am trying to think of something really creative that I can self-teach myself the basics of

I maybe wanted to do something with Chaos Theory but I don't know where to teach myself that or its practical applications

any ideas to get me started?

Thanks.

nontraditional

Game theory?

If you're in high school, I've heard good things about the Dixit and Skeath text for undergraduates; if you're in college a book aimed at grad students might be a better choice.

In general, when I am looking for decent textbooks on a subject I put terms relating to the subject and then also "syllabus site:.edu" (no quotation marks) into a Google search. Then I look for syllabi that seem to directly address things that interest to me, and see what books those profs are using. I also look at MIT's Open Course Ware site and other sites like that.

goalsetter11111

I am in high school.

Possibly game theory. But even if I taught myself that, how could I do a research project on it?

nontraditional

You could use the theory to describe a situation that interested you as a game. For instance, have you seen the movie "21"? You could explain blackjack as a game and discuss the dealers' strategy, and why it results in the house winning (not every hand, but over time more money comes in to the house than goes out). Then you could explain a strategy based on card counting, and why it results in card beating the house. And if you needed a section where you went to the library and looked up facts and discussed them, you could discuss the ways that casinos crack down on that sort of thing.

Or you could discuss the history of chess computers. Because chess is such a complicated game, nobody has worked out a complete strategy. But chess computers are getting better all the time.

If they'll let you use human subjects, you could see to what extent people are rational (which means that they choose good strategies that maximize their outcomes). People aren't especially rational. You could demonstrate that by asking people to play a Prisoner's Dilemma game, and then attempt to explain the choices that people actually made. (Other people have already tried that, so that could be pretty straightforward research of the kind that high schools often assign.)

Another thing you could do -- this is leaving game theory behind -- is to discuss a logical paradox and the attempts to solve it using philosophical logic. For example, when Bertrand Russell was asked whether the set of all sets that are not members of themselves is a member of itself, how did he adjust his logical theory? What do you think of his way of dealing with it? Or, how did philosophers using logic to understand language deal with sentences like "The present king of France is bald," given that there is no present king of France, or the sentence "I am false"? (These are all quite old examples. I'm sure you could find something much more contemporary.)