Mathematics Commons^™

Applications Of Financial Mathematics: An Analysis Of Consumer Financial Decision Making, Alyssa Betterton

Honors Theses

Students always ask, “How can this be applied to the real world?” Mortgages, car loans, and credit card bills are things that almost everyone will have to make decisions about at some point in their lives. This research discusses the many different financial choices that consumers have to make. Consumers can use this information to understand how interest rates, the length of the loan, and the initial amount being borrowed affects the amount that is paid back to the companies. The intent of this thesis is to present the mathematical theory of interest. A web-based application has been built based …

Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson

Honors Theses

The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.

A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …

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 …

A View Into Secondary Education Mathematics, Thomas Krieger Jr.

Honors Theses

Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …

Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith

Honors Theses

The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Theses

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

Application Of Linear Algebra Within The High School Curriculum: Designing Activities To Stimulate An Interest In Upper-Level Math, Shelby Castle

Honors Theses

This senior project outlines potential lecture activities for a guest speaker or teacher in a high school classroom to present interesting applications of linear algebra. These applications are meant to be pertinent to things students at this age level are already learning or are interested in. The activities are designed such that the ideas of upper-level math are introduced in a very guided and non-intense way. The intent of the activities is mostly applications and interesting results rather than mathematical lecturing or instruction.

The high school level courses explored in this project are chemistry, economics, and health/physical education. For these …

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Theses

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

Tablet Usage In Secondary Mathematics Education And Recommendations For Improving Its Effectiveness In The Classroom, Meghan T. Dwyer

Honors Theses

As part of my honor's thesis project at Assumption College, I have been researching the ways that teachers are currently using tablets in their secondary mathematics classrooms. My thesis compares the benefits and drawbacks of having tablets in classrooms, tablets for every student, or no tablets at all. In the spring, I collected survey feedback from mathematics teachers in four different local school districts. I analyzed the data in order to determine the ways tablets are being used in classrooms, the reasons preventing teachers from fully integrating tablets into their instruction, the impacts training has had on tablet use, and …

The Effects Of Prompted Tutoring On An Emporium Model Math Course, Juliette Michelle Young

Honors Theses

My research goal is to investigate how specific prompting of students would affect their involvement and progress in an emporium developmental math course. With the aim of increasing the students’ involvement and progress I tested a method that was in tended to increase students’ perceived connectedness with the classroom and promote the use of the available tutors and teachers. I monitored consenting students’ progress in the Spring 2015 courses and sent emails to students who met any one of three different criterion: (1) If the students time investment was below a threshold. (2) If the student’s mastery pace was less …

Une Histoire De La Formation Mathématique En France: Les Réformes Et Les Philosophies De L’Enseignement Primaire Et Secondaire De 1420 Jusqu'À Aujourd’Hui, Rebecca Robinson

Honors Theses

France has produced many illustrious mathematicians who have profoundly impacted mathematics as they are today. While Descartes, Cauchy, and Borel (among others) viewed math as a lifelong pursuit, they began their education in an elementary school classroom with everybody else. In this study, I explore mathematical reforms and governmental documents throughout history to show how the education system has grown to emphasize a strong mathematical curriculum for all students and have consulted many philosophical articles on both the importance of math in a student’s education as well as different views on the manner in which mathematics should be taught to …

Change Bell Ringing And Mathematics: A High School Student Excursion Into Graph Theory And Group Theory, Kristi Carlson

Honors Theses

This unit was created as a way to introduce higher level mathematics concepts to advanced high school students. All five of the National Council of Teachers of Mathematics Process Standards are found in this unit. For most of the unit, students work within small groups

The Regular Polyhedra: A Study In Visual Aids For Teaching Geometry, Sammye Halbert

Honors Theses

Traditionally, mathematics, past simple addition, subtraction, multiplication, and division, has been taught of as being so boring, irrelevant, and in short, one of the unavoidable evils of school. An advertisement in The Mathematics Teacher expressed the general attitude of many students when it said, "mathematics was invented by an old magician in the desert who, with the help of his talking monkey, bakes equations and cupcakes in the hot sun." It seems that many students think mathematics is just one problem after another that has some mystical answer floating around in the air somewhere. The object is to get that …

Mathematics On An International Basis, Sandra Lee Sawyer

Honors Theses

Is the math of the United States inferior? In 1967 there was an international study of mathematics comparing twelve different countries: United States, Japan, Australia, Belgium, England, Finland, France, Germany, Israel, The Netherlands, Scotland, and Sweden. Funded in part by the United States Office of Education and five years in the making, the report was based on a test given to 133,000 students in different countries at the age of thirteen and at the end of high school.