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2010 Senior Projects

Abstracts

Abstract: The project began by contemplating isometries, or symmetries, in three dimensions. Apart from the usual isometries such as reflection, rotation, translation, and glide reflection, I found that three dimensions allowed for two new isometries: the improper rotation and the glide rotation. From here I explored chemical point groups using character tables provided in the appendix of advanced chemistry texts and attempted to prove which mathematical group they were associated with. A chemical point group is a description of the symmetries that particular molecules have. I also explored the construction of character tables.

Abstract: My project consisted of programming the classic board game of Risk and creating an adaptive artificial intelligence agent in the programming language of Java. The motivation behind the project was to create a better artificial intelligence agent than free games currently available online. Three artificial intelligence agents were created, two to provide baseline testing data at either end of the aggression spectrum, and the third, the adaptive one, using a well know learning algorithm called QLearning. Numerous tests were performed with the adaptive agent, the baseline agents, and a wide range of people with different computer gaming experience.

Abstract: The dimension of a geometrical set can be defined in several ways. I begin by discussing the every day notion of dimension and then introduce fractal dimensions, which are not restricted to positive integer values. An explicit construction of a fractal with a dimension of any given positive real number is developed as the main result, and I also present Mathematica code for generating pictures of these constructions.

Abstract: I focused on how to best approach the problem of robot to robot avoidance using Lego Mindstorm NXT robots. These robots needed to avoid in the context of a task to clear an area of debris while avoiding each other. Two methods were devised. One method involves using a robots sonar sensor to try and detect other sonar sensors. The other makes use of a robots ability to produce loud beeps and detect volume with a microphone. These methods were tested against each other with a control group of robots without a means of avoidance acting as a baseline.

Abstract: Pedestrian Evacuation Simulations are a crucial tool for building design as they ensure that people can exit a building safely and efficiently. The goal of this project was to build a simple pedestrian evacuation simulator, using agent based modeling, where each individual finds an exit by following clues like walls and other pedestrians. The results were then compared to other simulators to ensure accuracy.

Abstract: My project is an exploration of elliptic curves and the structure of the rational points on such curves. The points on an elliptic curve form a mathematical structure called a group, and they form this group under an additive operation that allows for adding two points on the curve to obtain a third point on the curve. Moreover, some curves have what is called complex multiplication, which is a specific mapping of points on the curve. I determined that this complex multiplication is a homomorphism, a mapping that acts on groups and preserves operations. I also examined a few examples of curves in finite groups to see what effect complex multiplication had on their points.

Abstract: In my project, I will introduce the famous conjecture in Number Theory known as the Riemann Hypothesis. Then I will discuss a different number system from real numbers, which is also built from the set of rational numbers . Finally I will talk about how we can define the Riemann Zeta function, which plays the central role in the Riemann Hypothesis, on the set of p-adic numbers.

Abstract: Course scheduling involves a significant amount of time and effort on the part of faculty members of ºÚÁϲ»´òìÈ college. To lessen this problem, I created a program that generates a schedule for ºÚÁϲ»´òìÈ with minimal human intervention. This program uses a genetic algorithm as a method of creating flawed schedules, which are then combined and changed to produce better schedules.