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 for LaTeX or any other 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.
• Describe the rules for the main ("first") game.
• Find a winning strategy for one of the players for the "first" game. 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/strategies or partial lists of good and bad moves are welcome too.

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

• A Science Fair project is an ivestigation carried out by a student over a few months. It is basically a research project. (It is NOT just a a "hard homework problem" that can be done in a couple of hours.) A couple of examples will be described in class. Here is one example of a board made for the Fresno County Science Fair by a student. 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?