Physical Sciences and Mathematics Commons^™

Math Department 2022-2023 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. We had an exciting year with many activities and accomplishments. Our students have received awards, attended conferences, conducted research, and have really contributed to the life of the department. Our faculty have had many accomplishments in teaching and scholarship. We conducted several events such as Alumni Night, hosted a guest speaker for the university community, had our Pi Mu Epsilon induction and awards ceremony, and much more. We have heard from several alumni and are happy to report what they are doing. Our Math Club has been becoming more active. On the curriculum …

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 …

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Program: Senior Projects (Public)

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

Spectral Sequences And Khovanov Homology, Zachary J. Winkeler

Dartmouth College Ph.D Dissertations

In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the Asaeda-Pryzytycki-Sikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^n-filtration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi

Undergraduate Research Posters

We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.

Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans

UNF Graduate Theses and Dissertations

Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …

How The Perceived Value Of Education, Parental Influences, And Students' Perceived Success Affect Post-Graduate Decisions, Valerie Blanchard

Honors Projects in Mathematics

While technical education has been enhanced in many ways over the past few decades, college is still the preferred post-graduate path for many students and is the societal norm. This study will analyze the value that students view in their career path that leads them to make their post-graduate decisions. The goal of this research is to better understand why students pursue college and how these decisions come to be with specific attention paid to the impact of gender, interests, and self-efficacy. This understanding can educate others about the gravity of social norms and can start conversations about how to …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

A Comparison Of Logistic, Ridge, And Lasso Regression With Heart Failure Risk Data: Effects Of Sample Size, Predictor Correlation, And Predictor Weight On Outcome Accuracy, Mahmoud M. Aljuhani

Electronic Theses and Dissertations

Logistic Regression (LR), LASSO regression, and RIDGE regression are standard classification techniques for predicting a dichotomous output. Since these methods are applied for similar purposes and have different features, it is crucial to evaluate the performance of these methods under different controlled conditions. With this information, researchers can apply the optimal method for specific conditions.

Following previous research, which reported the effects of conditions such as sample size and multicollinearity on the performance of the classification methods, this research focused on the effects of when sample size, level of predictor collinearity, and predictor variable weight are controlled on the performance …

Developing Awareness Around Language Practices In The Elementary Bilingual Mathematics Classroom, Gladys Krause, Melissa Adams Corral, Luz A. Maldonado Rodríguez

Teaching and Learning Faculty Publications

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-on-one interview and of the circulating portion of a mathematics class from a second grade classroom. We use these examples to foreground instructional practices, for researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal …

Integrating Computing Into Preservice Teacher Preparation Programs Across The Core: Language, Mathematics, And Science, Lauren E. Margulieux, Patrick Enderle, Pier Junor Clarke, Natalie King, Caroline Sullivan, Michelle Zoss, Joyce Many

Journal of Computer Science Integration

This paper describes the beginning of a design-based research project for integrating computing activities in preservice teacher programs throughout a middle and secondary education department. Computing integration activities use computing tools, like programming, to support learning in non-computing disciplines. The paper begins with the motivation for integrating computing that encouraged widespread buy-in, design goals, and design parameters. The primary motivating factor for this work was preparing teachers to use technology to support learning in their classrooms. Involving computing education faculty in the preparation enabled the activities to include computer science and spread computational literacy. The paper also describes the process …

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Variety And Variation, Christopher Goff, Erik R. Tou

Euleriana

Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.

Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available.

This set of lecture notes is meant to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

Introduction to Mathematical Analysis II contains lecture notes that complement this book, with sections on integration, numerical series, series of functions, and selected advanced topics. Together, both volumes support a one semester or two-quarter course on introductory …

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

In Mathematics, As In Art, Andrew Granville

Journal of Humanistic Mathematics

The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?

Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield

Journal of Humanistic Mathematics

Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …

Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler

Journal of Humanistic Mathematics

Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …

Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel

Journal of Humanistic Mathematics

Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.

Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.

Faculty Submissions

Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …

Reconstructing Historical Earthquake-Induced Tsunamis: Case Study Of 1820 Event Near South Sulawesi, Indonesia, Taylor Jole Paskett

Theses and Dissertations

We build on the method introduced by Ringer, et al., applying it to an 1820 event that happened near South Sulawesi, Indonesia. We utilize other statistical models to aid our Metropolis-Hastings sampler, including a Gaussian process which informs the prior. We apply the method to multiple possible fault zones to determine which fault is the most likely source of the earthquake and tsunami. After collecting nearly 80,000 samples, we find that between the two most likely fault zones, the Walanae fault zone matches the anecdotal accounts much better than Flores. However, to support the anecdotal data, both samplers tend toward …

Temporal Sentiment Mapping System For Time-Synchronized Data, Jiachen Ma

Dissertations (1934 -)

Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a large-scale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online Time-Sync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …

Understanding College Students' Use Of Written Feedback In Mathematics, Erin Loraine Carroll

Theses and Dissertations

Many teachers want to help their students develop a growth mindset about their ability to do mathematics. Research has shown, however, that teachers simply do not know how to promote growth mindsets in their classrooms. Existing research suggests that one way teachers can support students' development of a growth mindset is through the written feedback they provide students. This study combines the research done on students' mindsets and written feedback to examine the interaction between student mindset and written feedback by analyzing written feedback provided to students in a College Algebra class and how students used that feedback based on …

The Impact Of Virtual Learning Modalities On The Academic Success Of Students In One Arkansas School District, Diane F. Richards

ATU Theses and Dissertations 2021 - Present

The COVID-19 pandemic changed the way Arkansas public schools’ offered students an education. While moving through this pandemic, many Arkansas schools implemented optional methods of delivery for their students. Some schools tried to maintain face-to-face classes, while others offered completely online classes. Still, others offered a hybrid format where students attended some face-to-face classes and online classes. One Arkansas school district offered all three options. School districts need guidance as to which teaching methods worked well. The long-term effects of the educational impact of COVID-19 are not known at this time. Schools could benefit from a guide with useful strategies …

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 …

Stop And Smell The Fractals: An Exploration Into Math, Poetry, And Everything In Between, Caroline Jennings

English Undergraduate Honors Theses

Stop and Smell The Fractals is a collection of poetry written during my time at The University of Arkansas. These poems highlight the connections between mathematics and poetry, focusing particularly on their emergence in everyday life.

Causalmodels: An R Library For Estimating Causal Effects, Joshua Wolff Anderson

Computational and Data Sciences (MS) Theses

Free and open source software for statistical modeling and machine learning have advanced productivity in data science significantly. Packages such as SciPy in Python and caret in R provide fundamental tools for statistical modeling and machine learning in the two most popular programming languages used by data scientists. Unfortunately, robust tools similar to these are limited in terms of causal inference. The tools in R that exist lack consistent and standardized methodologies and inputs. R lacks a comprehensive package that offers traditional causal inference methods such as standardization, IP weighting, G-estimation, outcome regression, and propensity matching in one common package. …

The Executive’S Guide To Getting Ai Wrong, Jerrold Soh

Asian Management Insights

This article explores how we see AI and argues that we mostly get it wrong. In the process, it explains the reasons backed by social science research on why we tend to get AI wrong and illustrates the dangers of doing so from a managerial and law-making perspective. Some readers may also find the article useful as a guide on how and when to manipulate portrayals of AI in your favour.

Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …

The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All …