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Full-Text Articles in Mathematics
We’Re Here To Get You There: A Statistical Analysis Of Bridgewater State University’S Transit System, Abigail Adams
We’Re Here To Get You There: A Statistical Analysis Of Bridgewater State University’S Transit System, Abigail Adams
Honors Program Theses and Projects
Bridgewater State University first established its on-campus transportation service in January of 1984. While it began only running as an on-campus service for students throughout the day, the service grew to expand by offering an off-campus connection to the neighboring city of Brockton and absorbed the night service system from the campus safety team. As BSU Transit continues to grow, the organization is seeking ways to improve their overall service and better prepare their fleet and driver pool to accommodate this growth. The purpose of this research is to analyze trends among the data collected by BSU Transit and assist …
An Exploration Of Manipulatives In Math Education, Jade Monte
An Exploration Of Manipulatives In Math Education, Jade Monte
Honors Program Theses and Projects
Pre-existing literature has shown that the education system needs to re-evaluate mathematical teaching practices in a manner that can boost students’ confidence in mathematics. Thus, the research is to investigate the use of manipulatives in reducing students’ anxiety by increasing their learning experience and engagement in mathematics. Furthermore, the purpose of this thesis is to explain the interconnectedness of math manipulatives, student engagement, and problem-solving. An in-depth literature review is conducted, which contains definitions, important benefits and methodologies of manipulatives, as well as the teacher’s role regarding these three terms. When manipulatives, student engagement, and problem-solving are in harmony, students …
Factors Impacting Students’ Perceptions Of Mathematics, Amber Souza
Factors Impacting Students’ Perceptions Of Mathematics, Amber Souza
Honors Program Theses and Projects
I want to be able to present math in a positive light to all of my future students, regardless of race, gender, and math background. However, for teachers as a whole to be able to take this important step, they must first develop a deeper understanding of why math is a sore spot for many students.
Theory Of Linear Models For Estimating Regression Parameters With Applications To Two-Factor Studies With Unequal Sample Sizes, Zenan Sun
Honors Program Theses and Projects
In this thesis we explored some topics in regression analysis. In particular, we studied what linear regression is from a matrix theory perspective, and applied analysis of variance in a setting with two factors and unbalanced sample sizes. In addition, we applied Box-Cox variable transformation as a solution when the regression model violated the normality and equal variance (also called homoscedasticity) assumption. Our main goal is to use these theories to construct models and investigate questions related to lifetime earnings of people living in America by using real data. In doing so, we used the statistical software R to perform …
Finite Field Dynamics: Exploring Isomorphic Graphs And Cycles Of Length P, Catlain Mccarthy
Finite Field Dynamics: Exploring Isomorphic Graphs And Cycles Of Length P, Catlain Mccarthy
Honors Program Theses and Projects
For this project, we explore nite eld dynamics and the various patterns of cycles of elements that emerge from the manipulation of a function and eld. Given a function f : Fp ! Fp, we can create a directed graph with an edge from c to f(c) for all c 2 Fp. We especially consider polynomials of the form f(x) = xd + c and investigate how varying the values of d and c affect the cycles in a given nite eld, Fp. We analyze data to look for graphs that result in cycles of length p. We also identify …
Bounding The Rates Of Convergence Towards The Extreme Value Distributions, James Palmer
Bounding The Rates Of Convergence Towards The Extreme Value Distributions, James Palmer
Honors Program Theses and Projects
Extreme value theory is a branch of probability which examines the extreme outliers of probability distributions. Three extreme value distributions arise as the limits of the maxima of sequences of random variables with certain properties. In this paper, we will first give information about these three distributions and prove that they are the only limit distributions of maxima. After that, we switch to a discussion about Stein's method. Stein's method is commonly used to prove central limit theorems. Stein's method also develops bounds on the distance between probability distributions with regards to a probability metric. There are three essential steps …
Modified Ramsey Numbers, Meaghan Mahoney
Modified Ramsey Numbers, Meaghan Mahoney
Honors Program Theses and Projects
Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems in Ramsey theory look for structure amid a collection of unstructured objects and are often solved using techniques of Graph Theory. For a typical question in Ramsey theory, we use two colors, say red and blue, to color the edges of a complete graph, and then look for either a complete subgraph of order n whose edges are all red or a complete subgraph of order m whose edges are all blue. The minimum number of vertices needed to guarantee one of these …
Firefighter Problem Played On Infinite Graphs, Sarah Days-Merrill
Firefighter Problem Played On Infinite Graphs, Sarah Days-Merrill
Honors Program Theses and Projects
The Firefighter Problem was introduced over 30 years ago and continues to be studied by researchers today. The problem consists of a graph of interest where a fire breaks out at time t = 0 on any given vertex of thegraph G. The player, then, gets to place a firefighter to “protect” a vertex from the fire. Each consecutive turn,the fire spreads to adjacent vertices. These vertices are then referred to as “burned”. The firefighter also gets tomove to protect an additional, unburned vertex, completing the first round. Each vertex that the firefighter “defends” stays protected for the remainder …