2003

Heather
Klink

"SET and All Its
Glory"

Advisor: Carolyn
Cuff (ccuff@westminster.edu)

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.

Chris
Madjesky

"Markov Chains
and the SORRY! Board Game"

Advisor: Carolyn
Cuff (ccuff@westminster.edu)

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.

Joshua Caplinger

"Activity Networks"

Advisor: Carolyn
Cuff (ccuff@westminster.edu)

Activity networks are directed graphs used to
coordinate a set of activities in some type of project. A
path is defined to be a group of activities that establish a connection between
the start and finish nodes. The critical path of an activity
network is the most important path because a delay in any one of these
activities will cause a delay in the overall project. In this study, each
activity in a constructed activity network was given is the form of a triangular
distribution. The expected values and the variances of each
activity were calculated in order to determine which of the paths was the critical path. It was observed,
using Tchebysheff’s theorem, that each path could
possibly be a critical path. Presented
at the MAA regional Conference in

Kevin Culp

"Strategy for NCAA College Football Overtime Games"

Advisor: Carolyn Cuff (ccuff@westminster.edu)

Results from past NCAA division IA seasons are analyzed and hypothesis testing and regression analysis techniques are used to determine which independent variables are most important to success and which factors of overtime games contribute most to a team’s success. A strategy is determined and tested using other overtime games from past years in NCAA division IAA. Presented at the MAA regional Conference in

2001

Merideth McCaskey

"Seeding Teams in the Men's 2001 NCAA Basketball Tournament"

Advisor: Carolyn Cuff (ccuff@westminster.edu)

Two seeding methods for the NCAA tournament were examined, traditional, in which the best team faces the worst in in first round play and cohort randomized method in which several teams are grouped and then randomly assigned to play against each other. The mathematics behind the seeding methods were examined. Application of both methods were applied in a simulation of the tournament using

Amy Vaccari

"Routing of School Buses by Computer"

Advisor: Carolyn Cuff (ccuff@westminster.edu)

Data of current school bus stops was obtained from a local school district. The three-opt branch exchange procedure was implemented and a traveling salesman tour was found. The tour was divided into a set of routes feasible with respect ot the capacity of the bus and travel time of the students. Sensitivity analysis of the bus capacity and fleet size was examined. Presented at the MAA regional conference in

(Click here for links to other mathematics abstracts at Westminster)