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Full-Text Articles in Mathematics

Guide To The Dr. L.S. Dederick Papers, 1908-1956, Undated, Orson Kingsley, Patrick Koetsch Jan 2022

Guide To The Dr. L.S. Dederick Papers, 1908-1956, Undated, Orson Kingsley, Patrick Koetsch

Archives & Special Collections Finding Aids

Louis Serle (L.S.) Dederick was born in Chicago in 1883. He received his Ph.D. in Mathematics from Harvard University in 1909. From 1909 – 1917 he was a professor at Princeton University. From 1917 – 1924 he was professor at the U.S. Naval Academy in Annapolis, Maryland. In 1926 Dederick began working for the U.S. Army, Ordnance. During his time there he was the Associate Director of the Ballistic Research Laboratory at the Aberdeen Proving Grounds in Aberdeen, Maryland where he focused on ballistics research.

While Dederick worked as a mathematician at the Aberdeen Proving Grounds, he was involved with …


We’Re Here To Get You There: A Statistical Analysis Of Bridgewater State University’S Transit System, Abigail Adams May 2021

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 May 2021

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 May 2021

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 May 2021

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 Dec 2020

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 May 2020

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 …


Towards Enhanced Chlorine Control: Mathematical Modeling For Free Chlorine Kinetics During Fresh-Cut Carrot, Cabbage And Lettuce Washing, Parthasarathy Srinivasan, Mohammadreza Dehghan Abnavi, Anthony Sulak, Chandrasekhar R. Kothapalli, Daniel Munther Mar 2020

Towards Enhanced Chlorine Control: Mathematical Modeling For Free Chlorine Kinetics During Fresh-Cut Carrot, Cabbage And Lettuce Washing, Parthasarathy Srinivasan, Mohammadreza Dehghan Abnavi, Anthony Sulak, Chandrasekhar R. Kothapalli, Daniel Munther

Mathematics Faculty Publications

In this study, we developed a novel produce-specific mechanistic model to predict free chlorine (FC) dynamics during washing of disk-cut carrots, cut cabbage, and cut iceberg lettuce, in 3 L and 50–100 L tanks, and of shredded iceberg lettuce in 3200 L pilot-plant trials. Ranges for two key parameters: β (L mg−1 min−1) the apparent reaction rate constant of FC with produce constituents, and γ, the fraction of the increase of chemical oxygen demand (COD) contributing to the reaction, were determined at the 3 L scale. For disk carrots β∈[0.05,0.09] and γ∈[0.054,0.078], for cut cabbage β∈[0.05,0.10] and γ∈[0.09,0.12], and for …


Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor May 2019

Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor

ACMS Conference Proceedings 2019

Charles Babbage is widely known as the father of the computer, but he is lesser known for his contributions to natural theology and apologetics. In 1837 Babbage wrote the Ninth Bridgewater Treatise in response to a series of writings concerning faith and science that had been commissioned by the Royal Society. Among the remarkable features of the Ninth Bridgewater are mathematical analogies concerning the miraculous. We will explore these ideas, which range from the difference engine to a family of fourth degree curves, illustrating that for Babbage, miracles are not exceptions to natural law, but rather instances of a larger …


Paper Abstracts (2019), Association Of Christians In The Mathematical Sciences May 2019

Paper Abstracts (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.


Theory Of Linear Models For Estimating Regression Parameters With Applications To Two-Factor Studies With Unequal Sample Sizes, Zenan Sun May 2019

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 May 2019

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 May 2019

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 May 2019

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 May 2019

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 …


Σ-Ary, Minnesota State University Moorhead, Mathematics Department Oct 2018

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.


On The Toughness Of Some Johnson Solids, Sean Koval May 2018

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 May 2018

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 May 2018

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 May 2018

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 May 2018

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 Dec 2017

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 …


Symmetric Full Spark Frames, Brian Sheehan May 2017

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 Dec 2016

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 …


(Knight)3: A Graphical Perspective Of The Knight's Tour On A Multi-Layered Chess Board, Frederick Scott Neilan May 2016

(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 May 2016

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 …


Bytes Of Π, Spring 2016, Department Of Mathematics, Bridgewater State University Apr 2016

Bytes Of Π, Spring 2016, Department Of Mathematics, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.


Sampling And Interpolation On Some Nilpotent Lie Groups, Vignon Oussa Jan 2016

Sampling And Interpolation On Some Nilpotent Lie Groups, Vignon Oussa

Mathematics Faculty Publications

No abstract provided.


Identifying An M-Ary Partition Identity Through An M-Ary Tree, Timothy B. Flower, Shannon R. Lockard Jan 2016

Identifying An M-Ary Partition Identity Through An M-Ary Tree, Timothy B. Flower, Shannon R. Lockard

Mathematics Faculty Publications

The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h2(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, hm(n). We then use properties of the m-ary tree to prove an identity relating values of h2 to values of hm, showing that one sequence is a subsequence of the other. Finally, …


The Mystery Of The Non-Transitive Grime Dice, Nicholas Pasciuto Jan 2016

The Mystery Of The Non-Transitive Grime Dice, Nicholas Pasciuto

Undergraduate Review

No abstract provided.