Theory of Games This project involves studying a general game in which two competing players choose separate strategies to reach opposing objectives. Using matrix techniques, the optimal strategy of each player is found for a few special cases. The plan for the project is that you will be given a brief summary of the subject, a list of key words for you to learn, and some problems to work on. You will be responsible for finding references yourself and learning about the subject. The problems will involve a two player zero sum game and calculating expected payoffs, optimal strategies and the value of the game. Each of you will be responsible for submitting your own individual report of the results in the end. Guidelines of the what the report should contain and the grading scheme will be given as the semester progresses.

Genetics This project involves understanding the growth in time of a female population divided into age classes using a matrix model. The limiting age distribution and the growth rate of the population will also be studied. The plan for the project is that you will be given a brief summary of the subject, a list of key words for you to learn, and some problems to work on. You will be responsible for finding references yourself and learning about the subject. The problems will involve playing with a given set of (assumed) mechanics that the population is following. Finding out survival chances and other properties. Each of you will be responsible for submitting your own individual report of the results in the end. Guidelines of the what the report should contain and the grading scheme will be given as the semester progresses.

Simulations This project involves down-loading a simulator from the web. Installing it at a computer where you can work. Then the project will involve (a) understanding properties of an existing model in the spatial stochastic simulator. The plan for the project is first to install the simulator in a working environment familiar to you. You will be given a brief summary of the subject, a list of key words for you to learn, and some problems to work on. The problems will involve understanding a particular particle system and running simulations to get an idea of what the particle system is doing. This may require tweaking the simulation engine code, which is written in C. Each of you will be responsible for submitting your own individual report of the results in the end. Guidelines of the what the report should contain and the grading scheme will be given as the semester progresses.

Real Data This project involves an investigation. Differs from the others in format. It will involve studying questions along the following lines. (a) Weather predictions: What does the weather report mean by "there is forty percent chance of rain today ?" It will be interesting to call local weather predictors or weather office to find out what they think about this and related weather predictions. (b) Earthquake Prediction: How are earthquakes predicted and how reliable have the predictions been ? (c) Ethics: What are the ethical problems involved in the data bases for DNA finger printing ? What are the ethical issues in the Human Genome project ? What are the legal issues in using DNA fingerprinting in courts ? how are they used ? (d) Finance: is the stock market really random ? Why choose a portfolio of stocks instead of a single stock ? What is the role of chance in an investment ? The plan for the project is : (1) Identifying a question you want to work with. You may choose one of the above or come up with your own question. If it is the latter you should talk to me soon. (2) Come up with a list of public ally available sources (Eg.: web-sites, magazine articles, books, news paper..) from which you plan to get access to the data. (3) Set up a plan on how you plan to analyse the data obtained. (4) Write up a report describing sources and inferences from the data. A detailed time-table for each of the above steps and the what the report should contain and the grading scheme will be given as the semester progresses.

http://www.math.ubc.ca/~athreya/302/projects/proj.html
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