Mathematics Commons^™

Murmurations And Root Numbers, Alexey Pozdnyakov

University Scholar Projects

We report on a machine learning investigation of large datasets of elliptic curves and L-functions. This leads to the discovery of murmurations, an unexpected correlation between the root numbers and Dirichlet coefficients of L-functions. We provide a formal definition of murmurations, describe the connection with 1-level density, and provide three examples for which the murmuration phenomenon has been rigorously proven. Using our understanding of murmurations, we then build new machine learning models in search of a polynomial time algorithm for predicting root numbers. Based on our models and several heuristic arguments, we conclude that it is unlikely for …

How Can We Explain Empirical Formulas For Shrinkage Cracking Of Cement-Stabilized Pavement Layers, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

In pavement construction, one of the frequent defects is shrinkage cracking of the cement-stabilized pavement layer. To minimize this defect, it is important to be able to predict how this cracking depends on the quantities describing the pavement layer and the corresponding environment. Cracking is usually described by two parameters: the average width of the crack and the crack spacing. Empirical analysis shows that the dependence of the width on all related quantities is described by a power law. Power laws are ubiquitous in physics, they describe a frequent case when the dependence is scale-invariant -- i.e., does not change …

Understanding Perspectives Of Power In A College Mathematics Classroom, Laura Seeberger

Honors College Theses

Power is embedded in teacher and student actions within mathematics classrooms, whether that power is known or not. Incorporating equity and inclusiveness requires a deeper understanding of this power behind actions. In this study, we developed and administered a three part survey questioning college faculty and college students how they perceive power related to common actions within a college mathematics classroom. For example, participants were asked whether a college math teacher assigning homework increased, decreased, or did both to the teacher’s power; then whether this action increased, decreased, or did both to a student’s power. Analysis of 16 faculty and …

Geometric Principles In Architecture Aesthetics, Vincent Gemmiti

Architecture Undergraduate Honors Theses

This study focuses on geometric formalism in three major monuments across different architectural eras in time. The use of three distinct geometric principles to outline the use of pure or manufactured shapes and figures helps to discover and isolate an aesthetic component of architecture within which it is contained. A collection of studies are implemented and are focused on orthographic drawings from each monument in horizontality and verticality, consisting of a dual set of overlay and interpretative drawings for each type of orthographic representation for each monument. A discussion follows and highlights the changes or similarities over time the role …

The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill

Master's Theses

We numerically investigate the effects that Environmental, Social, and Governance (ESG) scores have on portfolio optimization with Modern Portfolio Theory assumptions and how ESG scores correlate with the market returns of a rated company's stock. Additionally, we review and analyze a research paper published in the Journal of Financial Economics regarding ESG investing titled “Responsible investing: The ESG-efficient frontier” by Pedersen, Fitzgibbons, and Lukasz. Our overall goal is provide insight for socially responsible inclined investors, to help them understand what ESG scores tell us and how those scores may effect their overall investment returns."

Multicolor Bipartite Ramsey Numbers Of Balanced Double Stars, Ella Oren-Dahan

Theses, Dissertations and Culminating Projects

Given an integer n ≥ 1, the balanced double star Sn,n is a tree consisting of two vertex disjoint stars with n leaves each, connected at their central vertices by an edge. Given r ≥ 2, we consider the problem of finding the smallest integer N such that every r-colored complete bipartite graph KN,N contains a monochromatic copy of the balanced double star Sn,n. This question is an instance of a problem within Ramsey theory. In this thesis, we cover the history of Ramsey theory and our problem in general, provide an alternative approach to prove the two colored case, …

On The Number Of Strong Dominating Sets In A Graph, Frankie Mennicucci

Theses, Dissertations and Culminating Projects

This thesis investigates various problems related to the number of strong dominating sets in a graph. Given a graph G, a set of vertices D is said to be dominating if every vertex outside of D has a neighbor in D. Bród and Skupién proved that the number of dominating sets in a tree T on n vertices is at most 2ⁿ⁻¹ + 1. A set S of vertices in a graph G is a strong dominating set if every vertex x outside of S has a neighbor y ∈ S with d(y) ≥ d(x). We investigate the number of …

Formalization Of A Security Framework Design For A Health Prescription Assistant In An Internet Of Things System, Thomas Rolando Mellema

Electronic Theses and Dissertations

Security system design flaws will create greater risks and repercussions as the systems being secured further integrate into our daily life. One such application example is incorporating the powerful potential of the concept of the Internet of Things (IoT) into software services engineered for improving the practices of monitoring and prescribing effective healthcare to patients. A study was performed in this application area in order to specify a security system design for a Health Prescription Assistant (HPA) that operated with medical IoT (mIoT) devices in a healthcare environment. Although the efficiency of this system was measured, little was presented to …

A Central Limit Theorem For The Number Of Excursion Set Components Of Gaussian Fields, Dmitry Beliaev, Michael Mcauley, Stephen Muirhead

Articles

For a smooth stationary Gaussian field f on R^d and level ℓ ∈ R, we consider the number of connected components of the excursion set {f ≥ ℓ} (or level set {f = ℓ}) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g. the Bargmann-Fock field), a central limit theorem holds with volume-order scaling. Previously such a result had only been established for ‘additive’ geometric functionals of the excursion/level sets (e.g. the volume or …

A Statistical Look Into How Common Soccer Metrics Influence Expected Goal Measures In The Professional Game, Tristan George Rumsey

Undergraduate Honors Thesis Collection

The advent of sports analytics has ignited a fervor across all sporting disciplines, particularly soccer, where clubs are sprinting to harness vast data reserves to elevate team performance, spearhead effective marketing endeavors, and bolster financial gains crucial for club expansion. Much like Billy Beane's transformative "Moneyball" approach, soccer clubs are in pursuit of innovative strategies to transcend financial limitations and achieve triumph. In soccer, where goals are scarce commodities, heightened offensive efficacy becomes imperative. Presently, one metric stands out as pivotal in gauging a team's goal-scoring success: expected goals (xG). This metric quantifies the likelihood of a given shot or …

New Algorithms For The Multiplication Table Problem, Evan Blom

Undergraduate Honors Thesis Collection

In 1955, Paul Erdős initiated the study of a function that counts the number of distinct integers in an (n × n) multiplication table. That is, he studied M(n) = |{i · j, 1 ≤ i, j ≤ n}|. Much research has been done in regards to both asymptotic and exact approximations of M(n) for increasingly large values of n. Recently, Brent et. al. investigated the algorithmic cost in computing this function. Instead of computing M(n) directly, their approach was to compute it incrementally. That is, given M(n−1), they could quickly compute M(n) using another function δ(n) to count the …

Elasticity Of Orders In Quadratic Rings Of Integers, Jared Kettinger

All Theses

This project explores elasticity in quadratic rings of integers, specifically, those of the form Z[pω] where p is a rational prime which remains prime in Z[w]. For these rings, we establish an upper bound on the elasticity which is attained in many cases. We also prove that this upper bound is an equality in the case when the ring of integers is a unique factorization domain. During this process, we also prove theorems about the class group of quadratic rings of integers and develop a useful method for calculating a constant similar to the Davenport constant.

Asteroidal Sets And Dominating Targets In Graphs, Oleksiy Al-Saadi

School of Computing: Dissertations, Theses, and Student Research

The focus of this PhD thesis is on various distance and domination properties in graphs. In particular, we prove strong results about the interactions between asteroidal sets and dominating targets. Our results add to or extend a plethora of results on these properties within the literature. We define the class of strict dominating pair graphs and show structural and algorithmic properties of this class. Notably, we prove that such graphs have diameter 3, 4, or contain an asteroidal quadruple. Then, we design an algorithm to to efficiently recognize chordal hereditary dominating pair graphs. We provide new results that describe the …

Influence Of Parsimony And Work-Related Psychological Constructs In Predicting Turnover Intention When Using Machine Learning Vs Regression, Diego Figueiras

Theses, Dissertations and Culminating Projects

This dissertation explores the ongoing debate between traditional statistical regression models and machine learning (ML) algorithms in predictive modeling, focusing on the impact of sample size and the number of variables. Study 1 investigates the relationship between sample size and predictive accuracy, proposing hypotheses regarding the advantages of ML over regression as sample size increases. Additionally, the study examines the influence of the number of variables on predictive accuracy, emphasizing the trade-off between ML and regression models. Using data from the Federal Employee Viewpoint Survey, the research aims to contribute insights into the conditions favoring each modeling approach. Study 2 …

The Nature Of Undergraduate Calculus I Students' Participation In The Parallel Spaces Of Coursework And Peer-Led, Cooperative, Inquiry-Oriented Complementary Instruction, Karmen T. Yu

Theses, Dissertations and Culminating Projects

Calculus has long been known as a “gateway course” to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional approach called Complex Instruction (CI) and two other peer-led, cooperative learning models, Peer-Led Team Learning (PLTL) and Supplemental Instruction (SI). While the literature on peer-led models of cooperative learning confirms their effectiveness on undergraduate students’ academic outcomes in mathematics, this multiple-case study set out to address the following: What is the nature …

Spatiotemporal Negative Inventory Outlier Decomposition For Supply Chain Applications In Consumer-Packaged Goods (Cpg), Hayden Mcdonald

Data Science Undergraduate Honors Theses

Coca-Cola is a popular soft drink brand with sales occurring in every Walmart store across the world, which generates large quantities of data and requires a robust supply chain system. However, the company does not currently have a sophisticated, automated, and/or prescriptive system for detecting where, when, and why inventory outages occur and applying preventative measures to avoid loss of revenue from the absence of inventory on store shelves. This thesis proposes and applies a novel, prescriptive system for this purpose. An inventory outage can be seen as a ‘negative’ statistical outlier in a time series of inventory for an …

Mathematics Majors In Medical School Admissions: A Comparative Evaluation Of Mcat And Gpa Performance, Morgan Baker

Theses/Capstones/Creative Projects

Choosing a major as an incoming undergraduate student can be very stressful. This study investigates the differences in success that come with choice of undergraduate major, particularly focusing on the performance of mathematics majors. A large majority of medical school applicants come from a biological sciences background. Despite this preference, there is evidence that students from nontraditional majors produce higher Medical College Admission Test (MCAT) scores and superior grade point averages (GPAs). Utilizing data visualization and analysis through R programming, this research examines public data from the Association of American Medical Colleges (AAMC) to understand the benefits of pursuing a …

An Analysis Of Instructor Feedback, Olga Hawranick

Boise State University Theses and Dissertations

Carless & Boud (2018) capture the definition of feedback best as “a process through which learners make sense of information… use it to enhance their work or learning strategies (p.1).” This definition goes beyond feedback solely being the role of instructors and highlights the student component in making sense of the feedback which we reference in this study as “actionable feedback.” Are instructors providing meaningful feedback to their students to encourage revision? Past studies offer inconsistent results on most features of feedback and little is known about how some of these factors benefit students’ interactions with feedback.

This study aims …

Modeling Prices In Limit Order Book Using Univariate Hawkes Point Process, Wenqing Jiang

LSU New Orleans Theses and Dissertations

This thesis presents a time-changed geometric Brownian price model with the univariate Hawkes processes to trace the price changes in a limit order book. Limit order books are the core mechanism for trading in modern financial markets, continuously collecting outstanding buy and sell orders from market participants. The arrival of orders causes fluctuations in prices over time. A Hawkes process is a type of point process that exhibits self-exciting behavior, where the occurrence of one event increases the probability of other events happening in the near future. This makes Hawkes processes well-suited for capturing the clustered arrival patterns of orders …

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …