Undergraduate Math Research
St. Norbert College
The Summer Undergraduate Research Program in Mathematics at SNC consists of eight weeks of full time work open to St. Norbert College students with a declared mathematics major or minor. On the application form, students provide a list of their mathematics and other relevant course work, their research interests, and how a research experience would contribute to their professional goals. Students do not need to propose a project. Faculty members may already have projects in mind. The Mathematics Discipline reviews all applications and chooses which applicants will be awarded the summer positions. The research students (Poss-Wroble Fellows) are required to present their work at the national MathFest meeting in August and at the Pi Mu Epsilon Regional Undergraduate Math Conference on the SNC campus in November. Interested students are encouraged to speak with a member of the Mathematics Discipline, either before or after completing an application. Faculty members can offer insight into past projects along with the research projects proposed for the upcoming summer program.
Survey Labyrinth Probabilities
Nathan Leroy with mentor Lindsey Bosko-Dunbar
Labyrinth is a board game that was manufactured by Ravensburger in 1986. It is for 2-4 players with an age range of 7-99. The goal of the game is to slide the moveable columns and rows with an extra piece to maneuver your character to the treasure icons scattered about the board. We will be exploring mathematical elements such as graph theory, game theory, and probability in relation to the configurations of the standard 7×7 board for this game. We will be starting our research investigating a 3×3 board with similar ratios of pieces to the actual board. From this, we hope to scale up our findings to the larger board and perhaps even generalize to a board of arbitrary size. Once configuration numbers can be confirmed, we can break up or research with my direction being more probability and graph theory-based. I will explore a connection to the google maps path optimization algorithms that can help choose the best moves to get anywhere on the board in a game.
An Analysis of Strategic Thinking in Ravensburger Labyrinth
Lydia Mader with mentor Lindsey Bosko-Dunbar
Labyrinth is a board game for two to four players by Ravensburger in 1986. The object of the game is to collect all of your treasures and return to your starting corner before your opponents. Turns are sequential and consist of two parts–1) shift the board by inserting an extra game tile into a moveable row or column to change the configuration of the current board and 2) take the option of either moving your playing token along an open path made by connecting the game tiles or staying at the current coordinate on the board. Turns are completed in sequential order by players in a clockwise direction until one player obtains all their respective treasures and returns to their starting corner. The board consists of three basic types of game pieces: T, L, and I. The standard gameboard is a 7×7 square, with even rows and columns movable. We explore several factors that would optimize success during gameplay. Some of these factors considered are the configuration of the board, the location of the intended target, and the least amount of moves to a target. The analysis builds from a 3×3 reduced version to a 5×5 reduced version to analyze possible strategies for the full 7×7 board.