Physical Sciences and Mathematics Commons^™

Avatars Runnin' On Dunkin, Keelin Robbins '26

Mathematics & Computer Science Student Scholarship

Keelin Robbins ’26, Computer Science major, Finance minor
Faculty Mentor: Dr. Martin Helwig, Mathematics and Computer Science

Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Alexander Navarro

Honors Theses

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

Doubly Almost Bipartite Leonard Pairs, Shuichi Masuda

Dissertations and Theses

In Linear algebra, the concept of Leonard pair (LP) was motivated by the theory of Q-polynomial distance-regular graphs. In this dissertation, we will first give a brief introduction to LPs and to two closely-related classes of objects: (i) bipartite Leonard pairs (BLPs) and (ii) almost bipartite Leonard pairs (ABLPs). Taking these as departure points, we will introduce a new class of object - doubly almost bipartite Leonard pairs (DABLPs). The primary aim of our work is to fully classify (up to isomorphism) this new family. In addition, since there is known to be a natural correspondence between Leonard pairs …

Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison

Seaver College Research And Scholarly Achievement Symposium

The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.

To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …

Traveling Wave Fronts Of Reaction Diffusion Differential Equations With Diffusive Delay In Biological And Chemical Models, William Barker

Theses and Dissertations

Functional differential equations (FDE) incorporate past states and or rates in the modeling of physical phenomena. Unlike ordinary and even some partial differential equations there is no method to find solutions of general FDE explicitly. Therefore, in order to study solutions of FDE, iterative techniques are often employed. Reaction diffusion equations are a specific type of partial differential equations that model diffusive spread, the rate of spread of due to a reaction term of some quantity. These equations arise naturally in fields such as biology, ecology and chemistry. In terms of studying dynamics of populations, previous states and even rates …

Stack For Computational Science, Mathematics And Engineering E-Learners, Idrissa S. Amour

Tanzania Journal of Engineering and Technology (TJET)

Petroleum economic evaluation involves estimating revenues from forecasted production profiles and field costs including capital expenditures (CAPEX), drilling expenses (DRILLEX), and operating expenses (OPEX). The existing cost-estimating tool requires several inputs making it time-intensive and difficult to use with few data during the early stages of projects. Majority of the previously developed time saving cost estimations proxy models rely on unrealistic assumptions that include uniform operational costs for different fields with a different number of wells, casings, and drilled depths. This work focused at developing proxy models that consider the variability of the development costs with different parameters. The developed …

Quik Church, Route 3.141592, Sarah Voss

Journal of Humanistic Mathematics

The following set of poems are from one of ten sections in a collection of poetry called Quik Church: Short Poems that Travel Far. Each section illustrates one of many “streets” which individuals often take on their spiritual journey through life, e.g., the Old Gods Path, Nature Trail, Memory Skyway, Mystic Avenue, Pastoral Lane, and so on. This one, Route 3.141592, is the route of mathematics and the science that depends on mathematics.

Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter

Graduate Research Showcase

“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …

A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong

Milne Open Textbooks

This updated text covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …

College Algebra, Leslie Bain

ATU Faculty OER Book Reviews

Review of OER College Algebra textbook by Carl Stitz, available at https://open.umn.edu/opentextbooks/textbooks/college-algebra

Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron

Honors College Theses

The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.

Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar

Honors College Theses

Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …

Proof Of The Kresch-Tamvakis Conjecture, John Caughman, Taiyo S. Terada

Mathematics and Statistics Faculty Publications and Presentations

In this paper we resolve a conjecture of Kresch and Tamvakis.

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

Ermakov Equations Can Be Derived From Zel’Dovich Pancake, And They Are Cold And Nonlocal Through Using Neutrosophic Venn Diagram, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

As we argue in a previous article, the labyrinthine worlds of Jorge Luis Borges are more than captivating narratives; they are portals to a deeper understanding of existence. By weaving elements of science-fiction fantasy with philosophical and ethical inquiries, Borges's short stories bridge the seemingly disparate realms of physics and the humanities, offering fertile ground for contemporary physics research. The present-day universe consists of galaxies, galaxy clusters, one-dimensional filaments and two-dimensional sheets or pancakes, all of which combine to form the cosmic web. The so called ”Zeldovich pancakes”, are very difficult to observe, because their overdensity is only slightly greater …

Recreational Mathematics: Where Is The Error?, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This short note is a funny problem for the trigonometry students!.

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

Seven Properties Of Highly Effective Problems, Thomas Ales, Kevin Peterson, Constantine Roussos

Journal of Mathematics and Science: Collaborative Explorations

In an effort to provide more critical thinking opportunities in their courses, instructors are embracing the power of problem- and project-based learning (PBL). In this paper we address the importance of problem quality when utilizing PBL. We list seven important properties that a high-quality problem should have. We conclude with an example of a problem that possesses all seven properties.

Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ₀ norm. Specifically, the ℓ₀ model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ₀ norm regularization term. Such an ℓ₀ model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this …

Preface, Mohamed Mahdi Tekitek, Manfred Krafczyk, Li-Shi Luo

Mathematics & Statistics Faculty Publications

[Introduction] Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications, a macroscopic or continuum description has usually been sufficient due to the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic …

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses (Archived)

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

The Negative Stigma Surrounding Mathematics, Marissa A. Greisen

PSU McNair Scholars Online Journal

There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well …

Benford’S Law And Its Applications To Accounting, Lucy Wilson

Mathematics Student Projects

In this paper, we introduce the concept of Benford’s Law, which is the mathematical observation that in many naturally occurring numerical datasets, the leading digits are not evenly distributed. We actually find that smaller leading digits appear more often than larger ones. We will explore when and why this phenomenon occurs and how we can use statistical tests to determine how well a dataset conforms to Benford’s Law. We will also see how Benford’s Law can be used by auditors in the accounting field to catch potential fraud.

The Traveling Salesman Problem At Taylor University, Jonathan Jinoo Pawley

Mathematics Student Projects

What is the shortest route to walk to every residence hall on campus, beginning and ending with the same hall? This question can be considered by applying the Traveling Salesman Problem, an easy to understand yet hard to solve problem in the realm of discrete combinatorial optimization. The Traveling Salesman Problem is useful as an introduction to optimization problems, and it also has immensely practical applications. This paper will serve as an introduction to the computational difficulty of the Traveling Salesman Problem and will also explore various approximation algorithms. We will subsequently apply our new understanding of the theory to …

Assessing Controls On Ice Dynamics At Crane Glacier, Antarctic Peninsula, Using A Numerical Ice Flow Model, Rainey Aberle, Ellyn M. Enderlin, Hans-Peter Marshall, Michal Kopera, Tate G. Meehan

Geosciences Faculty Publications and Presentations

The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial post-collapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly re-advancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of long-term dynamic adjustment. The glacier's long-term geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable …

Near Peer Pedagogies For Culturally Sustaining Computer Science And Mathematics, Cliff Freeman, Eli Tucker-Raymond, Juan Gutierrez

Journal of Computer Science Integration

In this study, College STEM Literacy Workers act as co-teachers in 9th and 10th grade classrooms alongside mathematics teachers as they both learn to integrate a 30-hour integrated computer science/mathematics curriculum. As part of the curriculum for educator learning, we adapted the Algebra Project’s “Model of Excellence” for culturally relevant-sustaining pedagogies. We used the framework to explore how teachers understand College STEM Literacy Workers’ contributions in the model as well as College STEM Literacy Workers’ own experiences in the classroom. We found that while teachers and College STEM Literacy Workers did not individually instantiate the model of excellence, they were …

Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers

Milne Open Textbooks

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …

Parents' Perceptions Of The Importance Of Teaching Mathematics: A Q-Study, Ashlynn M. Holley

Theses and Dissertations

Mathematics education has gone through multiple reform efforts over the last century and continues to be the target of improvement efforts. Past changes in curriculum and goals have sometimes led to heated debates between various stakeholders. Knowing the views of different stakeholders can help determine what common ground there is between these different groups and where areas of disagreement might arise. Parents are especially important to understand because they have been influential in past reform efforts. Despite the importance of parents' opinions, little research has been conducted concerning their perspectives on the importance of mathematics teaching. Using Q-methodology, I was …

Examining The Effectiveness Of Using Point-Of-View Video Modeling On Mathematics Improvement In Students With Learning Disabilities In Saudi Arabia, Tirad Alsaluli

Electronic Theses and Dissertations

Video Modeling (VM) is one of the most widely used approaches by researchers to improve many skills, such as academic skills in students with Learning Disabilities (LD; Boon et al., 2020). As the incidence rate of individuals with LD in Saudi Arabia increase (Almedlij & Rubinstein-Ávila, 2018), the need for evidence-based math interventions focused on the math development of individuals with LD also increases. Although VM is recognized as an Evidence-based Practice (EBPs), a limited number of studies have implemented VM as an intervention to improve mathematic skills. Implementing VM as a math intervention strategy would explore its effects on …

Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani

Journal of Humanistic Mathematics

Mathematics plays an important role in the linguistic structure of artificial in- telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al- gorithms, through AI, interfere with the thought of those who interact with …