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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 …
Time Series Forecasting Of Covid-19 Deaths In Massachusetts, Andrew Disher
Time Series Forecasting Of Covid-19 Deaths In Massachusetts, Andrew Disher
Honors Program Theses and Projects
The aim of this study was to use data provided by the Department of Public Health in the state of Massachusetts on its online dashboard to produce a time series model to accurately forecast the number of new confirmed deaths that have resulted from the spread of CoViD-19. Multiple different time series models were created, which can be classified as either an Auto-Regressive Integrated Moving Average (ARIMA) model or a Regression Model with ARIMA Errors. Two ARIMA models were created to provide a baseline forecasting performance for comparison with the Regression Model with ARIMA Errors, which used the number of …
Mathematical Models Of Covid-19, Kate Faria
Mathematical Models Of Covid-19, Kate Faria
Honors Program Theses and Projects
For more than a year, the COVID-19 pandemic has been a major public health issue, affecting the lives of most people around the world. With both people’s health and the economy at great risks, governments rushed to control the spread of the virus. Containment measures were heavily enforced worldwide until a vaccine was developed and distributed. Although researchers today know more about the characteristics of the virus, a lot of work still needs to be done in order to completely remove the disease from the population. However, this is true for most of the infectious diseases in existence, including Influenza, …
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.
Modeling The Global Plastic Pollution In Our Oceans, Anna Fateiger
Modeling The Global Plastic Pollution In Our Oceans, Anna Fateiger
Honors Program Theses and Projects
Plastic is everywhere—from our plastic bottles and straws to the inside of our phones and the clothes we wear every day. Its widespread use has left a legacy of trash, with large amounts of plastic spilling from landfills into oceans. The accumulation of plastic debris in our oceans has severely affected marine life and has even entered into the human food chain. In this project, we created a mathematical model to estimate global plastic waste-generation and ocean runoff using existing data from 1980 to 2015. Using a dynamic system, we calculated the amount of plastic that ends up in landfills …
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 …
On The Toughness Of Some Johnson Solids, Sean Koval
On The Toughness Of Some Johnson Solids, Sean Koval
Honors Program Theses and Projects
The Johnson solids are the 92 three-dimensional, convex solids (other than the Platonic and Archimedean solids) that can be formed with regular polygons. The purpose of this honor’s thesis work is to determine the toughness of some of the Johnson Solids and similar graphs. The Johnson solids can be broken up into classes of solids with certain characteristics. While there are only 92 Johnson solids in three dimensions, we can generate infinite classes of graphs in two dimensions with similar characteristics. We have identified some of these classes, studied the toughness of individual graphs and begun to analyze a few …
Exploring The Proportion Of Prime Numbers In Quadratic Extensions Of The Integers, Jamie Nelson
Exploring The Proportion Of Prime Numbers In Quadratic Extensions Of The Integers, Jamie Nelson
Honors Program Theses and Projects
No abstract provided.
Exploring The Use Of Predictive Analytics In Banking And Finance Decision-Making, Melanie Tummino
Exploring The Use Of Predictive Analytics In Banking And Finance Decision-Making, Melanie Tummino
Honors Program Theses and Projects
Predictive analytics is a branch of advanced analytics that is composed of various statistical techniques where each contributes in making predictions about future scenarios and outcomes. Some of these techniques include machine learning, artificial intelligence, data mining, predictive modeling, logistic regression, etc., and the patterns found in the results can be used to identify risks and opportunity. Predictive analytics is often associated with meteorology and weather forecasting due to the fact there are many attributes to contribute to a response, but generally, it has many applications in existing growing or established businesses, especially when it comes to decision-making about revenue, …
Exploring Dynamical Systems: Number Of Cycle And Cycle Lengths, Christine Marcotte
Exploring Dynamical Systems: Number Of Cycle And Cycle Lengths, Christine Marcotte
Honors Program Theses and Projects
No abstract provided.
Rubik’S Cube: The Invisible Solve, Allen Charest
Rubik’S Cube: The Invisible Solve, Allen Charest
Honors Program Theses and Projects
The Rubik’s Cube is one of the most popular and recognizable puzzles ever made. In this research, we use group theory to identify and analyze the different solutions for the Rubik’s Cube and its variations. Since they cannot be seen on a standard Rubik’s Cube, these different solutions are called invisible solves. But by putting specialized labels on each of the center pieces of a Rubik’s Cube, we are able to track each of the invisible solves and see how they are different from one another. Dependent on the size of the Rubik’s Cube, the number of distinct invisible solves …
Reconstructing Results From Voting Theory Using Linear Algebra, Brian Camara
Reconstructing Results From Voting Theory Using Linear Algebra, Brian Camara
Honors Program Theses and Projects
For many undergraduate students, achieving an understanding of upper-level mathematics can be extremely challenging. For us, it helps to connect these new concepts with material we are familiar with. This will be the central theme of this thesis. We will introduce some basic components of algebraic voting theory, along with briey discussing how (Daugherty, Eustis, Minton, & Orrison, 2009) used representation theory to achieve their results. We will then provide an alternative proof to the main result of the (Daugherty et al., 2009) article using linear algebra, which should be much more familiar to my peers. We will carry out …
Extremal Graph Theory: Turán’S Theorem, Vincent Vascimini
Extremal Graph Theory: Turán’S Theorem, Vincent Vascimini
Honors Program Theses and Projects
No abstract provided.
Symmetric Full Spark Frames, Brian Sheehan
Symmetric Full Spark Frames, Brian Sheehan
Honors Program Theses and Projects
A full-spark frame of an n-dimensional vector space is a finite collection of m vectors (m ≥ n) with the following property: every subset of cardinality n of the given collection is a basis for the vector space. In this thesis, we realize the symmetric group Sn as a matrix group of invertible matrices with n2 entries for n > 2: This representation induces a natural linear action on the vector space ℂn and we prove that Sn admits an orbit which is a full-spark frame if and only if n ≤ 3:
Creating The Perfect Nba Team: A Look At Per And How It Affects Wins, Gregory Hamalian
Creating The Perfect Nba Team: A Look At Per And How It Affects Wins, Gregory Hamalian
Honors Program Theses and Projects
Ever since Oakland Athletics’ general manager Billy Beane began applying analytical tools to compose a baseball team, professional sports teams have used advanced metrics to build competitive rosters. We use an exploratory data analysis strategy to find what statistics best predict team wins. Finding that the Player Efficiency Rating (PER) statistic best correlate with wins, we investigate the statistic to find its strengths and weaknesses. We look for ways to improve the statistic and adjust it to better evaluate player effectiveness. We also look for methods to best predict how the PER will change from one season to the next …
Characterizations Of Four Interval Wavelet Sets And Algorithms, Christopher Mcdonald
Characterizations Of Four Interval Wavelet Sets And Algorithms, Christopher Mcdonald
Honors Program Theses and Projects
Wavelets are mathematical tools used to represent signals such as audio files, pictures, videos, and various other types of data. The theory of wavelets has recently attracted attention in Mathematics because of potential in applications. At this point, the field of wavelet theory is fairly mature, and the literature contains a body of techniques which are exploited to design wavelets. One of these techniques relies on the construction of wavelet sets. A wavelet set is a set whose successive translations and dilations partition a line. In practice, wavelet sets are tricky to construct. In fact, there is no known classification …
(Knight)3: A Graphical Perspective Of The Knight's Tour On A Multi-Layered Chess Board, Frederick Scott Neilan
(Knight)3: A Graphical Perspective Of The Knight's Tour On A Multi-Layered Chess Board, Frederick Scott Neilan
Honors Program Theses and Projects
The Knight’s Tour is an interesting question related to the game of chess. In chess, the Knight must move two squares in one direction (forward, backward, left, right) followed by one square in a perpendicular direction. The question of the Knight’s Tour follows: Does there exist a tour for the Knight that encompasses every single square on the chess board without revisiting any squares? The existence of Knight’s Tours has been proven for the standard 8x8 chess board. Furthermore, the Knight’s Tour can also exist on boards with different sizes and shapes. There has been a lot of research into …
Modeling Consequences Of Reduced Vaccination Levels On The Spread Of Measles, Guillermo Ortiz
Modeling Consequences Of Reduced Vaccination Levels On The Spread Of Measles, Guillermo Ortiz
Honors Program Theses and Projects
Introduction: In this thesis we propose a mathematical model for the spread of measles in a closed population. In section 1 we offer a motivation for the project, describe the measles virus as well as its history in the U.S., and provide a brief summary of three epidemiological models from the literature. In section 2.1 we introduce some probabilistic tools used in our model. Section 2.2.1 outlines our stochastic model used for the spread of measles in a population, which is refined in section 2.2.2 to include health interventions from the CDC. We conclude the thesis by presenting in section …
Optimizing A Game Of Chinese Checkers, Nicholas Fonseca
Optimizing A Game Of Chinese Checkers, Nicholas Fonseca
Honors Program Theses and Projects
Chinese Checkers is a multi-player strategy game in which game play can become surprising complex as the game progresses. In spite of this game's complexity, questions involving games with multiple players have received little research attention. This paper considers the three player case and discusses how to describe short games. By utilizing these tendencies for short games, a heuristic function can be defined which associates a player's possible move with a heuristic value. These heuristic values guide a search algorithm which searches through all the possible moves made in a game. To guide this discussion for three player games, the …
A Critical Analysis Of Random Response Techniques, Emanuel Zanzerkia
A Critical Analysis Of Random Response Techniques, Emanuel Zanzerkia
Honors Program Theses and Projects
In order to understand and make informed decision on sensitive topics such as domestic violence and drug use, interviews have been used to collect data. However it is difficult to assess how truthful respondents are since they may not feel at ease revealing the truth to an interviewer. Surveyors of sensitive issues face the problem that respondents may be reluctant to answer truthfully since the respondent may feel pressured socially or may fear the repercussions of their truthful answer. Processes known as random response techniques have been introduced to allow interviewers the ability to extract information they need for a …
A Mathematical Foundation Of The Quantum-Classical Correspondence, Nina Culver
A Mathematical Foundation Of The Quantum-Classical Correspondence, Nina Culver
Honors Program Theses and Projects
In this thesis we explore the mathematical foundations that unite physics at a quantum scale, quantum mechanics, with a macroscopic scale, classical mechanics. We seek to understand the mathematical motivation behind the quantum-classical correspondence and how it unites two seemingly different theories of the physical world. We show how this correspondence binds the Hamiltonian theory of classical physics to the Hilbert space theory in quantum mechanics, and establish a way to translate between classical observables and quantum operators, using the Fourier transform. These approaches to “quantizing” a physical state can be applied generally to a wide variety of observable quantities …
Exploring Residents’ Attitudes Toward Solar Photovoltaic System Adoption In China, Yaqin Sun
Exploring Residents’ Attitudes Toward Solar Photovoltaic System Adoption In China, Yaqin Sun
Honors Program Theses and Projects
As the largest energy consuming country, China is facing environmental deterioration, which results from the overuse of non-renewable conventional energy such as coal. Solar photovoltaic (PV) energy, an unlimited and clean energy with minimal impacts on the environment, is considered to be a good alternative to alleviate this severe issue. A survey was designed and conducted among residents in some major cities. Based on the first hand data, basic statistical methods were utilized to examine Chinese residents’ knowledge of, concerns, and attitudes towards PV adoption. The research aims to identify the drivers and dynamics that most encourage customers to install …
An Analysis Of Numerical Methods On Traffic Flow Models, Terry Mullen
An Analysis Of Numerical Methods On Traffic Flow Models, Terry Mullen
Honors Program Theses and Projects
In this thesis, we implement Euler's method and the Runge-Kutta method to solve initial value problems. A goal of the project is to compare the two methods on preliminary problems illustrating limitations and advantages. We also apply the Runge-Kutta method to a mathematical model of traffic flow. This thesis sheds light on how the fourth-order Runge-Kutta method is implemented to solve the Optimal Velocity Model (Kurata & Nagatani, 2003). We identify initial conditions and base cases to run simulations of the model. We consider one-car and two-car systems to validate the application of the fourth-order Runge-Kutta method and the Optimal …
Life On The Floodplain: An Analysis Of Falmouth, Massachusetts And Osaka, Japan, Shellie Johnson
Life On The Floodplain: An Analysis Of Falmouth, Massachusetts And Osaka, Japan, Shellie Johnson
Honors Program Theses and Projects
After Hurricane Katrina in 2005, the awareness of flooding threats to coastal areas increased. For Massachusetts in particular, Cape Cod is still at high risk of flooding with any storm that comes and goes. However, all of these recent devastating floods and natural disasters have caused insurance prices to skyrocket. With my research, I specifically looked at Falmouth, Massachusetts and the possibilities to lessen the risks and which of these options would be the most financially sound for a homeowner. The possibilities include elevating a house in a high flood risk zone, selling a current house to move in to …
Exploring The Calkin-Wilf Tree: Subtrees And The Births Of Numbers, Kayla Javier
Exploring The Calkin-Wilf Tree: Subtrees And The Births Of Numbers, Kayla Javier
Honors Program Theses and Projects
No abstract provided.