Abstract of Projects
“Moving Out: Modeling Population Migration Using Linear Algebra”
Abstract: A population migration model using linear algebra and Markov chains was examined. The model assumes that the total population of the system remains fixed, the migration rate for any two states is constant, and the eigenvectors of the population matrices are linearly independent. Changes were made to the model to incorporate relaxed assumptions. Limitations of the models were determined using proofs and an analysis of United States-Mexico population migration data.
“There’s Still Time to Change the Road You’re On”
Abstract: This is a
statistical investigation of students changing their majors at
“Of Mice and Mean: A Statistical Analysis of Ephedrine’s Effect on Mouse Respiration”
Abstract: The diet
“It’s Goal Time: Fitting NCAA Division I Women’s Soccer Data”
Abstract: In this
study, the goals and goal times of championship games in the 2003 Division I
women’s soccer tournament are fit to both the Poisson and Exponential
Distributions. This study is modeled
after Professor Chu-Chun-Ling of the
“Elliptic Curve Cryptography: Why are we making the switch?”
Abstract: In my
research, I have attempted to discover why the National Security Agency (NSA)
has decided to endorse Elliptic Curve Cryptography (
“Linear Programming and Game Theory”
Abstract: I am going to show how linear programming can be used to solve game theory problems. I am going to demonstrate this using a common game called Rock, Paper, Scissors and also by using two variations of this game. I am also going to extend this information in order to determine home linear programming can be used to solve the game theory problem called Undercut.
“The Dimension of the Coast of
Abstract: Fractal dimensions of objects, which are
non-integer dimensions, differ from the standard Euclidean whole number
dimensions. The fractal dimensions can be found in many different ways: The Hausdorff method, compass setting method, and others. So,
what kind of a fractal dimension does
Higby, Alan “Measuring the Difficulty of a Maze”
Currently no metric exists (at least publicly) that measures the difficulty of a maze. To meet this need, a metric was developed. A maze generation program was used to compile statistics on mazes to aid in designing this metric. The metric developed depends on the number of branches off of a maze’s solution path, the number of turns in the solution path, and the percentage of time that a greedy algorithm is successful while traversing the maze. The metric’s validity was defended logically and through a small set of test mazes.
Klink, Heather “SET and All Its Glory”
By altering the original deck of cards for the game SET®, an investigation into the mathematics of the new deck evolves. The cards in the new deck still have four attributes, but now the attributes vary in number of values. The investigation includes the number of cards in the deck, the number of sets given a premise at different times and the cap for the game. The game can be played by finding sets of three cards or sets of four cards. Since the new deck has attributes that vary in number, different combinations for each set must also be considered.
Medjesky, Chris Markov Chains and the SORRY! Board Game
Investigations into board games using Markov Chains have been used in the past to provide information and strategies on how to win. Here the game SORRY! was the subject of investigation, this time focusing on the expected number of moves needed to be taken in order to move from the START position to HOME. Due to the restrictions of the game, a “one-player” scenario was created to allow Markov Chains to be properly applied to the situation. Each card was analyzed to determine the probability of movement from one space to another and these probabilities were placed into a 60X60 matrix. With all other probabilities of movement fixed, the probability of movement using the 10 card was varied in order to determine the minimal number of turns needed to complete the “one” player game.
Pazul, Andy “An Investigation of the Perpetual Calendar Algorithm”
The purpose of my paper was to work with the perpetual calendar algorithm and find out where all of the key numbers came from, and find a handful of different numbers that may work. The majority of my paper does in fact explain and show 10 different sets of numbers, each being their own separate algorithm, that work to give us the day of the week for a specific date in time; past, present, future. I determined the different key numbers by noticing a pattern in the month numbers. From there I worked through the algorithm to determine the century numbers. I found out that the what ever the new month key values differ from the original set of key numbers, that is how many the century numbers differ by, keeping the rules of addition mod7 in mind.
Potocnak, Nikki “The 8 -iamonds: What are they and where do they come from?”
This research centers on the idea of polyiamonds. One must first look at the studies of polyominos and the idea of how to correctly and easily construct a polyomino. This research furthers those studies to cover the topic of polyiamonds and, following closely to the polyomino, the methods one can use to create polyiamonds. The sixty-six 8-iamonds are discovered and analyzed with the method of tiling. Of the sixty-six possible, only five of the 8-iamonds did not tile. Finally, all of the –iamond configurations were taken, from the 4-iamonds to the 8-iamonds, and put in a recursion scheme. The goal of this scheme was to find a pattern that could be followed in order to complete future research of the 9-iamonds and beyond.
Smith, Jessalyn “Investigations of Wavelets with an Application in Heart Rate Analysis”
Wavelets are used to numerically analyze signals that vary in both space and frequency. Wavelets are more versatile than other numerical methods because there are several different bases to choose from. Any desired base may be used to fit any application. All calculations computed are done so in a time efficient manner. This paper investigates two of the more popular wavelet bases, Haar and Daubechies. It also makes connections between wavelet methods and Fourier methods. Concluding the investigation is a practical application, which demonstrates the use of the Daubechies wavelet in heart rate analysis.
Zielinski, Danielle “Cryptography”
This paper examines the uses of
cryptology. Different types of
encryption methods that have been considered, including the Julius Caesar
cipher, the simple substitution cipher, the Vigenère
cipher, the jigsaw cipher, and the two-letter cipher. In addition, the public key cryptography
Caplinger, Joshua, “Activity Networks” Presented at the
Culp, Kevin, “Strategy for NCAA College Football
Presented at the
Deah, Emily, “Cutting Polyominos” Presented at
Klipa, Daniel, “Game Theory” This project was a study of introductory game theory, including von Neumann’s Minimax Theorem and Nash’s Theorem. Two zero-sum games were examined using von Neumann’s theorem, both modeling poker strategy in order to show the profitability of bluffing. It was predicted to be shown that bluffing is indeed a good mixed strategy, which one of the results did show, but the result of the other game was inconclusive. An application of Nash’s Theorem to a theoretical study of the Cuban Missile Crises is also explained.
Plimpton, Sarah, “Getting to the Core of
Packing” Presented at the
Brian, “An Ising Model of a Ferromagnet”
Presented at the
Abstract of Projects 2001
Clohessy, Erin. "A Variation on the Game of Hex." Presented to the mathematics and computer science faculty at the end of the semester meeting. Hex is a two-player game played on a N x N rhombus shaped board. This paper examines the four player game played on an octagonal shaped board. Strategies for winning are examined. The winner of the 4-player Hex type game is determined in the first few moves of the game.
Kanaan, Simon. "Dots
and Boxes." Presented at the undergraduate
research symposium held at
McCaskey, Meredith. Presented at the
Orr, Gabrielle. "Class Scheduling in the
Mathematics Department at
Quallich, Nicole. Presented
at the undergraduate research symposium held at
Stamp, Aaron. "Dots-and-Hexagons." Presented to the mathematics and computer science faculty at the end of the semester meeting. The child's game, dots and boxes is converted to play on a hexagonal grid. The known strategies for winning on the rectangular board are examined on the hexagonal board. A new strategy for winning on the hexagonal board is developed.
Stefanis, Lee. "Cuisenaire Rods and Partitions." Presented to the mathematics and computer science faculty at the end of the semester meeting. Ordered and unordered partitions of an integer are examined. The recursive relationship for unordered partitions is demonstrated using Cuisenaire Rods.
Vaccari, Amy. "Routing
of School Buses by Computer." Presented at