Physical Sciences and Mathematics Commons^™

Trigonometry: A Brief Conversation, Carolyn D. King Phd, Tam Evelyn, Fei Ye Phd, Beata Ewa Carvajal

Open Educational Resources

These five units are specifically tailored to foster the mastery of a few selected trigonometry topics that comprise the one credit MA-121 Elementary Trigonometry course. Each unit introduces the topic, provides space for practice, but more importantly, provides opportunities for students to reflect on the work in order to deepen their conceptual understanding.

These units have also been assigned to students of other courses such as pre-calculus and calculus as a review of trigonometric basics essential to those courses. This is the second edition of the materials. Units 4 and 5 have been edited to reflect suggestions from instructors who …

Curving Towards Bézout: An Examination Of Plane Curves And Their Intersection, Camron Alexander Robey Cohen

Honors Papers

One area of interest in studying plane curves is intersection. Namely, given two plane curves, we are interested in understanding how they intersect. In this paper, we will build the machinery necessary to describe this intersection. Our discussion will include developing algebraic tools, describing how two curves intersect at a given point, and accounting for points at infinity by way of projective space. With all these tools, we will prove Bézout’s theorem, a robust description of the intersection between two curves relating the degrees of the defining polynomials to the number of points in the intersection.

Math 3100 - Mathematical Thinking: Communication And Proof - Week 1 Outline, Laura J. Wallace, Cory Johnson, Shawn Mcmurran, Min-Lin Lo

Q2S Enhancing Pedagogy

As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …

Math 3100: Communication And Proof - Assessment, Shawn Mcmurran, Min-Lin Lo, Corrine Johnson, Laura Wallace

Q2S Enhancing Pedagogy

As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …

Using A Faculty Learning Community To Promote Interdisciplinary Course Reform, Rhonda Bishop, Victor Piercey, Mischelle Stone

Journal of Mathematics and Science: Collaborative Explorations

As part of a multi-institution, National Science Foundation (NSF) grant-funded project, Ferris State University (FSU) joins a national effort to reform mathematics curricula. Researchers from FSU developed and facilitated a faculty learning community (FLC) as one strategy to redesign the traditional approach to the quantitative reasoning skill development of students in the departments of mathematics, nursing, social work, and the College of Business. Over the course of one academic year, the FLC provided an interdisciplinary faculty connection to develop pedagogical approaches that integrated cross-curricular concepts and context from each discipline. The FLC not only produced uniquely designed, learning-centered approaches to …

Curricular Change In Institutional Context: A Profile Of The Summit-P Institutions, Mary D.R. Beisiegel, Suzanne I. Dorée

Journal of Mathematics and Science: Collaborative Explorations

There is a national call to improve the mathematics curricula in the first two undergraduate years to improve student success and engagement. But curricular change happens in an institutional context: Who are the students, and what do they need to succeed? What is the climate for change? Does the department regularly revise its courses and curriculum? Is it common for different departments to collaborate on curricular change? What supports or obstacles does the department, college, or university have for changing the curriculum? Who are the institutional stakeholders, and what practices build their buy-in? In the SUMMIT-P project, nine different institutions …

Full Issue

Journal of Mathematics and Science: Collaborative Explorations

No abstract provided.

Math Department 2019-2020 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. This was an unusual year for our department as the coronavirus cut short our time on campus this year. Hence we were unable to have our usual events such as the Annual Mathematics Lecture, the Pi Mu Epsilon Induction and Awards Night, and there was no in-person commencement ceremony. But despite that, many great things happened in our department.

Communicating In Crisis Situations, Rick Gorvett, Chris Morse, Julie Volkman

Communication Faculty Journal Articles

Communicating technical information, especially in a crisis situation and particularly when the audience does not share the technical background, is a challenge that actuaries frequently face. This essay describes the dynamics and issues involved in crisis communications and provides some recommendations for actuaries confronting such a situation.

Good Teachers Borrow, Great Teachers Steal: A Case Study In Borrowing For A Teaching Project, Mike May, Rebecca Segal, Victor Piercey, Tao Chen

Journal of Mathematics and Science: Collaborative Explorations

Very few great ideas in teaching are without ancestors or descendants. This paper presents a case study in how one particular pedagogical project, the work at Saint Louis University as part of the National Science Foundation supported SUMMIT-P consortium, borrowed from other sources. The particular project was an interdisciplinary collaboration to make mathematics education more effective for business students. The various borrowings are treated in roughly chronological order from initial inspiration through planned adoption and adaptation of the work of others to the addition of features that only became available mid-project. The kinds of sources include a particular business calculus …

The Ubiquity Of Phi In Human Culture & The Natural World, Jennifer Bressler

Masters Essays

No abstract provided.

Math Across The Curriculum, Kelsey Mason

Masters Essays

No abstract provided.

Use Of Calculators In High School Mathematics, Alex Mcdaniel

Williams Honors College, Honors Research Projects

For many collegiate level mathematics courses at universities across the country, students are not allowed to use calculators. This is often a huge adjustment for students who have spent their entire high school career using calculators. Whether it is graphing or simple arithmetic, students relied on calculators in high school, but for college, the tool of a calculator may not be available for them. This leads to a multitude of questions: Should calculators be used in high school? Do calculators help students learn or are they simply a tool to get answers? Are calculators beneficial in some courses, but not …

A Cool Brisk Walk Through Discrete Mathematics, Stephen Davies

Computer Science Articles

A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!

Geometry Of Linear Subspace Arrangements With Connections To Matroid Theory, William Trok

Theses and Dissertations--Mathematics

This dissertation is devoted to the study of the geometric properties of subspace configurations, with an emphasis on configurations of points. One distinguishing feature is the widespread use of techniques from Matroid Theory and Combinatorial Optimization. In part we generalize a theorem of Edmond's about partitions of matroids in independent subsets. We then apply this to establish a conjectured bound on the Castelnuovo-Mumford regularity of a set of fat points.

We then study how the dimension of an ideal of point changes when intersected with a generic fat subspace. In particular we introduce the concept of a ``very unexpected hypersurface'' …

Cheat Detection Using Machine Learning Within Counter-Strike: Global Offensive, Harry Dunham

Senior Independent Study Theses

Deep learning is becoming a steadfast means of solving complex problems that do not have a single concrete or simple solution. One complex problem that fits this description and that has also begun to appear at the forefront of society is cheating, specifically within video games. Therefore, this paper presents a means of developing a deep learning framework that successfully identifies cheaters within the video game CounterStrike: Global Offensive. This approach yields predictive accuracy metrics that range between 80-90% depending on the exact neural network architecture that is employed. This approach is easily scalable and applicable to all types of …

Modeling Community Resource Management: An Agent-Based Approach, Maya M. Lapp

Senior Independent Study Theses

As the human population continues increasing rapidly and climate change accelerates, resource depletion is becoming an international problem. Community-based natural resource management (CBNRM) has been suggested as a method to conserve resources while simultaneously empowering traditionally marginalized communities. Because classical equation-based modeling methods fail to capture the complexity of CBNRM, Agent-Based Modeling (ABM) has emerged as a primary method of modeling these systems. In this investigation, we conduct a sensitivity analysis and thorough evaluation of an existing ABM of community forest management. We then modify the original model by providing a new enforcement mechanism that improves the validity of both …

Middle-School Mathematics Teachers' Use Of Formative Assessment Data, Shawana T. Green

Walden Dissertations and Doctoral Studies

A school district located in the southeastern United States uses benchmark tests as formative assessment to provide teachers with data to differentiate their instruction to meet the individual needs of students in their classrooms. Despite this effort, student achievement in mathematics in this school district has not improved. The purpose of this study was to gain an understanding of how middle-grade mathematics teachers used the benchmark results as formative data to guide instruction and meet student needs. The conceptual framework that grounded this study was the model of formative assessment developed by Black and Wiliam. For this basic qualitative study, …

Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol

Educational Leadership & Workforce Development Faculty Publications

Social influences on classroom learning have a long research tradition and are critical components of self-regulated learning theories. More recently, researchers have explored the social influences of self-regulated learning in cooperative learning contexts. In these settings, co-regulation of learning and socially-shared regulation of learning strategies have been aligned with self-regulated learning theory. However, without specific training or structure, teachers are not likely to explicitly integrate SRL strategies into their teaching. We use case studies to better understand how Zimmerman's theory of self-regulated learning (2008) and Hadwin's conceptual framework of socially-shared regulation of learning (2018) emerge from teachers' support of student-centered …

Intersections Of Deleted Digits Cantor Sets With Gaussian Integer Bases, Vincent T. Shaw

Browse all Theses and Dissertations

In this paper, the intersections of deleted digits Cantor sets and their fractal dimensions were analyzed. Previously, it had been shown that for any dimension between 0 and the dimension of the given deleted digits Cantor set of the real number line, a translate of the set could be constructed such that the intersection of the set with the translate would have this dimension. Here, we consider deleted digits Cantor sets of the complex plane with Gaussian integer bases and show that the result still holds.

A Mathematical Analysis Of The Game Of Santorini, Carson Clyde Geissler

Senior Independent Study Theses

Santorini is a two player combinatorial board game. Santorini bears resemblance to the graph theory game of Geography, a game of moving and deleting vertices on a graph. We explore Santorini with game theory, complexity theory, and artificial intelligence. We present David Lichtenstein’s proof that Geography is PSPACE-hard and adapt the proof for generalized forms of Santorini. Last, we discuss the development of an AI built for a software implementation of Santorini and present a number of improvements to that AI.

Discrepancy Inequalities In Graphs And Their Applications, Adam Purcilly

Electronic Theses and Dissertations

Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy inequality, which bounds the edge distribution between two sets based on the spectral gap. More specifically, it states that a small spectral gap of a graph implies that the edge distribution is close to random. This dissertation uses this tool to study two problems in extremal graph theory, then produces similar discrepancy inequalities based …

Predicting Stag And Hare Hunting Behaviors Using Hidden Markov Model, Rex Bringula, Ma. Mercedes T. Rodrigo

Department of Information Systems & Computer Science Faculty Publications

In this paper, we used Hidden Markov Model (HMM) to describe the gaming behaviors of students and whether they will exhibit “stag” or “hare” hunting behavior in a mobile game for mathematics learning. We found that there is a 99% probability that the students will stay either as stag or hare hunters. Our results also suggest that they would choose arithmetic problems involving addition. These game behaviors are not beneficial to learning because they are only exhibiting mathematical skills they already know. The results of the study show that stag and hare hunters have unique traits that separate the one …

The Knapsack Subproblem Of The Algorithm To Compute The Erdos-Selfridge Function, Brianna Sorenson

Undergraduate Honors Thesis Collection

This thesis summarizes the methodology of a new algorithm to compute the Erdos-Selfridge function which uses a wheel sieve, shows that a knapsack algorithm can be used to minimize the work needed to compute these values by selecting a subset of rings for use in the wheel, and compares the results of several different knapsack algorithms in this particular scenario.

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

Enabling And Threatening Factors Affecting Persistence. A Qualitative And Quantitative Study On Rural First-Generation Stem Students’ And Stem Faculty's Perspectives., Travis A. Miller

Graduate Theses, Dissertations, and Problem Reports

This study focuses on the factors that enable and threaten rural first-generation STEM students’ persistence. Limited empirical studies are available that focus on rural first-generation STEM majors’ persistence. Quantitative analysis was conducted using Kruskal Wallis H and Mann-Whitney U tests to determine any significant differences with the survey results. Content and thematic analysis was conducted on the student and faculty interviews to determine themes of enabling and threatening factors affecting persistence.

Enabling factors affecting persistence were found to be: Drive or Motivation, Experiences and skills, and Support. These were both faculty and student interview themes whereas a …

Isolated Point Theorems For Uniform Algebras On Smooth Manifolds, Swarup Ghosh

Faculty Articles & Research

In 1957, Andrew Gleason conjectured that if A is a uniform algebra on its maximal ideal space X and every point of X is a one-point Gleason part for A, then A must contain all continuous functions on X. Gleason’s conjecture was disproved by Brian Cole in 1968. In this paper, we establish a strengthened form of Gleason’s conjecture for uniform algebras generated by real-analytic functions on compact subsets of real-analytic three-dimensional manifolds-with-boundary.

Reflection On Use Of The "Reacting To The Past" Pedagogy In A History Of Mathematics Course, Davida Fischman

Q2S Enhancing Pedagogy

This brief report provides a reflection on the use of the "Reacting to the Past" (RTTP) pedagogy in a History of Mathematics classroom. The conclusion is drawn that the RTTP pedagogy is very successful in engaging students in active learning, and appropriate games may be utilized to help students learn about the role of mathematics in historical developments as well as in society today.

Student Perceptions Of Learning Introductory Mathematics In An Online Environment In Higher Education, Jamie Lynn Brooks

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the essence of student perception of learning introductory mathematics courses in an online environment at the college level. The central research question was, “What are the lived experiences of students who have completed introductory college mathematics courses in the online learning environment?” The phenomenon described was that of the beliefs and attitudes of the students who participated in introductory mathematics courses on the college level. The ideas explored were if students believe they learn effectively in this environment and how they believe they can best learn. Student beliefs and attitudes …

Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen

Zhi-Hong Chen

No abstract provided.