Mathematics Commons^™

Visualizing Sorting Algorithms, Brian Faria

Honors Projects

This paper discusses a study performed on animating sorting algorithms as a learning aid for classroom instruction. A web-based animation tool was created to visualize four common sorting algorithms: Selection Sort, Bubble Sort, Insertion Sort, and Merge Sort. The animation tool would represent data as a bar-graph and after selecting a data-ordering and algorithm, the user can run an automated animation or step through it at their own pace. Afterwards, a study was conducted with a voluntary student population at Rhode Island College who were in the process of learning algorithms in their Computer Science curriculum. The study consisted of …

The Mathematics Of The Card Game Set, Paola Y. Reyes

Honors Projects

SET is a card game of visual perception. The goal is to be the first to see a SET from the 12 cards laid face up on the table. Each card has four attributes, which can vary as follows: 1. Shape: oval, squiggle, or diamond 2. Color: red, green, or blue 3. Number: the number of copies of each symbol can be 1, 2, or 3 4. Filling: solid, unfilled, stripped Each card has a unique combination, for a total of 34 = 81 different cards in a deck. A SET consist of three cards for which each of the …

Graph-Ene, James E. Torres

Honors Projects

GRAPH-ENE is a rich internet application for building and manipulating undirected, simple graphs. It is intended for use as a classroom teaching aid, plus as a tool for students to interactively manipulate graphs for assignments. Being web based, it is portable—it can run anywhere a browser is available. Since it is interactive, it provides problem-solving capabilities that are not available using pencil and paper.

Geodesic Circulant Graphs Embedded On The Flat Torus, Cameron Richer

Honors Projects

In this paper, we will investigate graphs that arise from the intersections of geodesics embedded on the at torus. For any size collection of geodesics, the number of unique intersections is countable via their slopes. As well, any embedding of two geodesics gives rise to a circulant graph for which its chromatic number can be calculated from their respective slopes. Furthermore, the previously described circulant graphs embedded on the at torus are self-dual. This provides an effective face coloring of any graph arising from the embedding of two slopes on the torus.

Generalized Ordered Whist Tournaments For 6n+1 Players, Elyssa Cipriano

Honors Projects

In this project, we worked to see if it would be possible to extend the idea of an ordered whist tournament to a generalized whist tournament on 6n or 6n + 1 players. We focused on tournaments where the players are divided into n games of size 6 each consisting of two teams of size 3. We aimed to balance the 3 occasions where the players meet as opponents.

(4,8) Ordered Generalized Whist Designs - Existence Results, Nicholas Leveilee

Honors Projects

Ordered Generalized Whist tournaments are a new design. In this

study, we establish that ordered generalized whist tournaments exist for

tournaments with 8n + 1 players, n odd, with 4 players per team.

Teaching Statistics To Elementary Children: Using A Problem-Solving Approach To Enhance Learning, Kayla Lee Botelho

Honors Projects

When teaching statistics (or data analysis) to elementary children, it is beneficial to use a problem-solving approach that incorporates meaningful tasks to enhance the students' learning. This was determined through a careful review of literature, observations of elementary teachers, and the creation and instruction of data analysis unit. The unit required the students to collect data on heights, organize the data in charts, and display the data in line plots. In addition, the students analyzed the data to recalculate the average and other measures of central tendency and to answer questions that arose through the implementation of the lessons. In …

Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks, John Douglas Butler

Master's Theses, Dissertations, Graduate Research and Major Papers Overview

Describes students' attempts to solve nonroutine math problems and explores possible correlates of their performance, focusing on inattended (i.e., intentionally avoided) dimensions underrepresented in the literature, including attitudes, interests, values, aesthetics, metacognition, and representation. Analyzes objective and subjective data gathered from a sample of 9th-grade students at a high school in Rhode Island. Finds strong evidence of students' math-aesthetics in problem solving.

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Faculty Publications

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson

Faculty Publications

The study of ordinary differential equations has long been a staple in mathematics at both the undergraduate and graduate levels. Recently, instruction in the study of difference equations has widened, primarily due to the expanded role of the digital computer in mathematics. The two topics are inextricably linked at all levels, from elementary techniques through current research questions. Pursuing the analogies between these fields of study can only deepen the understanding of each. In particular, the study of many elementary topics in difference equations, requiring not even the use of calculus, can serve as a founda- tion for intuition and …