Digital Commons Network^™

Imperfect Immunity And The Stability Of A Modified Kermack-Mckendrick Model, Kaylee Sims

Honors Theses

The classic Kermack-McKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified Kermack-McKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with real-world case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …

An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors

Honors Theses

We investigate the use of Google’s PageRank algorithm to rank sports teams. The PageRank algorithm is used in web searches to return a list of the websites that are of most interest to the user. The structure of the NCAA FBS football schedule is used to construct a network with a similar structure to the world wide web. Parallels are drawn between pages that are linked in the world wide web with the results of a contest between two sports teams. The teams under consideration here are the members of the 2021 Football Bowl Subdivision. We achieve a total ordering …

Length Bias Estimation Of Small Businesses Lifetime, Simeng Li

Honors Theses

Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …

Finding The Common Denominator: Understanding The Shared Experiences Of Female Math Majors, Abigail R. Rosenbaum

Honors Theses

Despite efforts to increase gender diversity in STEM fields, women remain underrepresented in mathematics, especially in advanced academic and research positions. This study aimed to explore the experiences of female math majors as they attempt to navigate this male-dominated space. Through qualitative interviews with seven female math majors, two female math professors, and a focus group with education majors at Woodbridge College, small liberal arts college in the United States, several common themes were identified that define the experiences of female math majors. The findings suggest that math is held at an elevated status in society and that there is …

The Efficacy Of The Covid-19 Vaccine In Mississippi, Ilyse Miriam Levy

Honors Theses

The Efficacy of The COVID-19 Vaccine in Mississippi

(Under the direction of Dr. Xin Dang)

By tracking and analyzing fifty-three weeks of COVID-19 data, this thesis analyzes the efficacy of the COVID-19 vaccine within the State of Mississippi. Over the course of these fifty-three weeks, I have also been able to calculate the confidence intervals for vaccination efficacy and the risk reduction due to vaccination by using data regarding the correlations between deaths and vaccination status, provided to me by the Mississippi Office of Epidemiology. My analysis demonstrates that the COVID-19 vaccine is effective not only in Mississippi but also …

An Analysis Of Educational Strategies Suited For Students With Asd, Quinn Ryan

Honors Theses

This paper will analyze several reasons why traditional educational practices are not well suited for students with ASD, and will explore multiple promising areas of research on mathematical education for these students. The project has several goals, which will be described in more detail throughout the rest of this paper. One such goal is to create a web resource for teachers that is designed to be suited towards students with ASD. The website will contain an overview of my research and analysis, as well as access to sample lesson plans. The purpose of the website is to bridge a gap …

Mindset Matters: Using Research-Based Strategies To Enhance Middle-School Math Instruction, Catherine Harvey

Honors Theses

No abstract provided.

The Relationship Between Teachers’ Beliefs Concerning Mathematical Problem-Solving And The Strategies Used For Teaching Third - Through Fifth - Grade Students, Jasmine L. Thomas

Honors Theses

Everyone uses problem-solving on a daily basis: paying bills, managing time, and making decisions. It is important to be able to solve problems effectively, especially in mathematics. In 2007, the Mississippi Department of Education produced a set of mathematical objectives for third - through fifth - grade students. These objectives use the phrase problem-solving, without defining its use in the mathematics classroom. To discover what mathematics teachers were actually executing in the classroom, this study used a valid online survey administrated through Qualtrics. The survey focused on determining third - through fifth - grade teachers’ definition of a problem, their …

La Vie De Blaise Pascal Et Son Heritage Mathématique Et Philosophique, Katherine Weeks

Honors Theses

This paper will discuss the life of Blaise Pascal, his philosophy and mathematics. We will first study the life of Pascal, by looking at his family, the success of his family, and how he was educated. We will then move onto study the history of the arithmetic triangle, which eventually becomes known as Pascal’s Triangle. Finally we will look at Pascal’s Pensées. Finally we will conclude that Pascal is not only known for Pascal’s Triangle but also his legacy in the Philosophic world. It becomes clear that Pascal would not have been the mathematician he was without the philosophy, and …

The Relationship Between Attitudes And Achievement In Mathematics Among Fifth Grade Students, Madeleine P. Michelli

Honors Theses

There have been a number of studies investigating how attitudes such as confidence and motivation affect students and their academic achievement. This study was conducted to identify specifically how fifth grade students’ attitudes affect their achievement in mathematics. Gender was studied to determine its effect on attitude and achievement. Furthermore, various types of personality traits were studied including extroversion, conscientiousness, self-control, and intellectual efficiency to determine their effects on achievement. To gather the data a questionnaire including a Likert scale survey and a math test was administered. The results indicated that there is a significant relationship between attitudes toward and …

The Calculus Of Variations, Erin Whitney

Honors Theses

The Calculus of Variations is a highly applicable and advancing field. My thesis has only scraped the top of the applications and theoretical work that is possible within this branch of mathematics. To summarize, we began by exploring a general problem common to this field, finding the geodesic be-tween two given points. We then went on to define and explore terms and concepts needed to further delve into the subject matter. In Chapter 2, we examined a special set of smooth functions, inspired by the Calabi extremal metric, and used some general theory of convex functions in order to de-termine …

A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson

Honors Theses

This research analyzed students final exam scores in a college mathematics class with geometric components and their van Hiele levels upon entering the class. After the class was completed, each student’s final exam grade was calculated. The researcher used a Spearman correlation to compare the two; the result was a correlation coefficient of 0.742. The researcher then reported that the results of the van Hiele test are a major component in predicting a student’s success in such a class.

A General Look At Posets Rings And Lattices, Courtney A. Phillips

Honors Theses

A lattice is a type of structure that aims to organize certain relationships that exist between members of a set. This thesis seeks to define lattices, and demonstrate the different types. It will give examples of lattices, as well as various ways to describe and classify them.

Equitent Problems, Payton E. Lindsay, Katelynn Kochalski, Gary R. Lawlor Phd

Honors Theses

No abstract provided.