Final Project

Choose one of the following options. All text must be typed in LaTeX. All images have to be computer-generated (using either the tikz package or another computer software). This project may be done individually or in small groups (no more than 4 people). You are encouraged to share your ideas/draft with your instructor as early as possible and get feedback. This is not a test but a project, so getting feedback and making any possible improvements before submitting your final version is highly recommended.

Option I.
Propose a new game and some variations of it for the Math Field Day Game Tournament (see rules here).

• Learn the current games. The list of current games is here, some of their possible variations are here.
• General Requirements for a Math Field Day Game:
  • Materials must be easy to get and inexpensive. We need to run the tournament for up to 150 participants and our budget is limited to a few hundred dollars. For example, counters, dice, boards printed on paper, etc. are OK, while something like full chess sets would be too expensive.
  • The rules must be simple enough so that they can be explained in a few minutes. The list of current games will give you an idea. Again, something like chess is way too complicated.
  • Each round must take no more than 3 minutes.
  • The game must allow different minor variations such as the initial sizes of piles, initial posititions of the counters, etc.
  • There must be some mathematics behind the game. One goal is that the participants learn some math while playing, looking for a strategy, and practicing.
• Describe the rules for the main ("first") game.
• Find a winning strategy for one of the players for the "first" game. This must be a full winning strategy, not just partial ideas. Provide a proof. Be detailed.
• Propose at least three variations (check out the current games for ideas.) Try to find a winning strategy for one of the players for at least one of the proposed variations. Partial ideas or partial lists of good and bad moves are welcome too here.

Option II.
Propose an idea for a high school Science Fair project.

• A Science Fair project is an ivestigation carried out by a student (or a small team of students) over a few months. It is basically a research project. (It is NOT just a "hard homework problem" that can be done in a couple of hours.) An example will be described in class. Here is one example of a board made for the Fresno County Science Fair by a student, and here is another one. This is just to give you an idea of what the final result may look like. You do not have to make a board, you are merely proposing an idea for such a project (see below).
• The project should be beyond the standard high school math curriculum. Feel free to use concepts and ideas you learned in college. However, the topic should be accessible to a high school student. Suggest some initial reading on the topic (at least 2 sources).
• Clearly state one or more questions that a high school student (or a small team of students) could investigate.
• Carry out the investigation to some extent or for some of the questions. Provide proofs. (Do not complete the whole project. See what you can do in a few hours, just to get a feeling for what it would take to do the whole project, and to make sure it seems feasible for a high school student.)
• Comment on the mathematics involved. What would a student learn (or master) by doing this project?
• More info on Science Fair: Fresno County Science Fair web site, California Science and Engineering Fair