Mathematics Commons^™

A Comparison Of Assessment Experiences Between Standards-Based Practices And Traditional Practices Within Secondary Mathematics Classrooms, Emily Mayes

Honors Theses

The purpose of this research was to compare assessment experiences and find ways to improve those experiences for students in two mathematics classrooms: one classroom that employs Standards-Based Grading and one classroom that uses traditional grading practices. The research examines students’ perceptions regarding their level of preparation, their anxiety levels surrounding assessment, the validity of assessments, and using assessments and grading practices to give accurate indications of student progress in their learning, given the students’ perceptions. Students in both settings voluntarily and anonymously participated in completing pre- and post-assessment free-response surveys which asked questions about students’ assessment experiences. This research …

Complete Pick Spaces And Operator Inequalities, Georgios Tsikalas

Arts & Sciences Graduate Student Theses and Dissertations

This thesis is concerned with the treatment of three different research topics, all lying at the interface of complex analysis and operator theory. The first chapter is based on two distinct research projects, both revolving around complete Pick spaces. These are reproducing kernel Hilbert spaces that host an analogue of the Pick interpolation theorem for multipliers. First, we study a generalized inner-outer factorization in the setting of a particular complete Pick space over the annulus. The second project deals with the characterization of interpolating sequences for multipliers between certain pairs of function spaces that enjoy an analogue of the complete …

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

Determination Of Output Composition In Reaction-Advection-Diffusion Systems And Improving Language Model Performance With Re-Tuning, Eric Joseph Pasewark

Arts & Sciences Graduate Student Theses and Dissertations

There are 2 main subjects studied in this thesis. The first is on modeling chemical reactions. We formulate the problem of determining how much product is formed from a reactor and model this problem using metric graphs. We develop an efficient method to explicitly solve the problem on metric graphs. We work through examples by hand and with code to solve the problem. The second subject is a novel method to improve language model performance on compositional tasks. Our method teaches a language model to break a given problem into different subproblems, create prompts for these, and then solve the …

Hodge Classes In The Cohomology Of Local Systems, Xiaojiang Cheng

Arts & Sciences Graduate Student Theses and Dissertations

Let $S$ be an arithmetic quotient of a Hermitian symmetric domain and $X/S$ be a family of varieties over $S$. One interesting problem is to find the Hodge classes of $X$, and if possible, to prove the Hodge conjecture for $X$. Using techniques from automorphic forms, we studied the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and the Siegel domain of degree two. As a byproduct, we derived formulas for Hodge numbers in terms of automorphic forms.

Using Multi-Scale Spatial Models Of Dendritic Ecosystems To Infer Abundance Of A Stream Salmonid, Xinyi Lu, Yoichiro Kanno, George P. Valentine, Jacob M. Rash, Mevin B. Hooten

Mathematics and Statistics Faculty Publications

1. Understanding patterns of species abundance is essential for planning landscape-level conservation. The complex hierarchies of dendritic ecosystems result in different levels of heterogeneity at distinct geographic scales. Species responses to dynamic environmental drivers may also vary spatially depending on their interactions with landscape features. Monitoring abundance by explicitly quantifying their spatial and temporal variation is important for strategic management.

2. We analysed brook trout (Salvelinus fontinalis) count data collected from 173 sites in western North Carolina between 1989 and 2015. We developed a Bayesian hierarchical model that used single- and multi-pass electro-fishing data and characterized their respective …

Studying Hilbert’S 10th Problem Via Explicit Elliptic Curves, Debanjana Kundu, Antonio Lei, Florian Sprung

School of Mathematical & Statistical Sciences Faculty Publications

N. García-Fritz and H. Pasten showed that Hilbert’s 10th problem is unsolvable in the ring of integers of number fields of the form Q(p–√3,−q−−−√) for positive proportions of primes p and q. We improve their proportions and extend their results to the case of number fields of the form Q(p–√3,Dq−−−√) , where D belongs to an explicit family of positive square-free integers. We achieve this by using multiple elliptic curves, and replace their Iwasawa theory arguments by a more direct method.

Ua12/2/1 College Heights Herald: Ways Of The Future, Wku Student Affairs

WKU Administration Documents

Magazine edition of the College Heights Herald for the period April 8 - May 5, 2024.

• Anderson, Alexandria. Letter from the Editor – Science, Technology & Business
• Anderson, Alexandria. Women in STEM Make Advances
• Novoselia, Mariia. Turnover on Fountain Square: Local Businesses Share Concerns & Success Stories
• SOKY Rentals Offers New Apartments
• Walk2Campus: Where Home Meets Community
• Bush, Camden. Can a Baseball Team Reduce Their Goals to a Math Problem?
• Hawkins, Kaylee. Student Business Owners Share Experiences – Gatara Townsend, Andrew Garrett, Brittiny Sadler
• Ivory, Larkin. Bikewalk BG, WKU CHHS Offer Chances for Healthy Lifestyle – Health & Human Services

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Boolean Group Structure In Class Groups Of Positive Definite Quadratic Forms Of Primitive Discriminant, Christopher Albert Hudert Jr.

Departmental Honors & Graduate Capstone Projects

It is possible to completely describe the representation of any integer by binary quadratic forms of a given discriminant when the discriminant’s class group is a Boolean group (also known as an elementary abelian 2-group). For other discriminants, we can partially describe the representation using the structure of the class group. The goal of the present project is to find whether any class group with 32 elements and a primitive positive definite discriminant is a Boolean group. We find that no such class group is Boolean.

A Mceliece Cryptosystem, Using Permutation Error-Correcting Codes, Fiona Smith

CSB and SJU Distinguished Thesis

Using existing methods of cryptography, we can encrypt messages through the internet. However, these methods are vulnerable to attacks done by a quantum computer, which are a rising threat to security. In this thesis I discuss a possible method of encryption, secure against quantum attacks, using permutation groups and coding theory.

Representations Of Gender In Math-Related Films, Jacob Gathje

CSB and SJU Distinguished Thesis

This project analyzes how four popular math-related films - Hidden Figures, Mean Girls, Good Will Hunting, and A Beautiful Mind - either follow, resist, or reconfigure gender stereotypes in mathematics. It includes close readings of specific scenes in each of the films, along with broader analysis of the effects of how women and men are represented differently. It concludes forward-looking focus, providing suggestions for how future math-related movies can depict a more realistic and inclusive version of the field of mathematics. Ideally, this will help improve one part of the larger issue of gender disparities in math.

An Alternate Proof For The Top-Heavy Conjecture On Partition Lattices Using Shellability, Brian Macdonald, Josh Hallam

Honors Thesis

A partially ordered set, or poset, is governed by an ordering that may or may not relate any pair of objects in the set. Both the bonds of a graph and the partitions of a set are partially ordered, and their poset structure can be depicted visually in a Hasse diagram. The partitions of {1, 2, ..., n} form a particularly important poset known as the partition lattice Πn. It is isomorphic to the bond lattice of the complete graph Kn, making it a special case of the family of bond lattices. Dowling and Wilson’s 1975 Top-Heavy Conjecture states that …

Study Of Nanofluid Flow In A Stationary Cone–Disk System With Temperature-Dependent Viscosity And Thermal Conductivity, Anagha Susan John, Mahanthesh Basavarajappa, Igor V. Shevchuk

School of Mathematical & Statistical Sciences Faculty Publications

The substantial temperature gradient experienced by systems operating at relatively high temperatures significantly impacts the transport characteristics of fluids. Hence, considering temperature-dependent fluid properties is critical for obtaining realistic prediction of fluid behavior and optimizing system performance. The current study focuses on the flow of nanofluids in a stationary cone–disk system (SCDS), taking into account temperature-dependent thermal conductivity and viscosity. The influence of Brownian motion, thermophoresis, and Rosseland radiative flux on the heat transport features are also examined. The Reynolds model for viscosity and Chiam's model for thermal conductivity are employed. The Navier–Stokes equation, the energy equation, the incompressibility condition, …

Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata

Theory & Applications of Graphs

A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$.

We define the …

Representations Of Solutions Of Time-Fractional Multi-Order Systems Of Differential-Operator Equations, Sabir Umarov

Mathematics Faculty Publications

This paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is known through the matrix-valued Mittag-Leffler function. Multi-order (incommensurate) systems with rational components can be reduced to single-order systems, and, hence, representation formulas are also known. However, for arbitrary fractional multi-order (not necessarily with rational components) systems of differential equations, the representation formulas are still unknown, even in the case of fractional-order ordinary differential equations. In this paper, we obtain representation formulas for the solutions of arbitrary fractional multi-order …

Topics In The Study Of The Pragmatic Functions Of Phonetic Reduction In Dialog, Nigel G. Ward, Carlos A. Ortega

Departmental Technical Reports (CS)

Reduced articulatory precision is common in speech, but for dialog its acoustic properties and pragmatic functions have been little studied. We here try to remedy this gap. This technical report contains content that was omitted from the journal article (Ward et. al, submitted). Specifically, we here report 1) lessons learned about annotating for perceived reduction, 2) the finding that, unlike in read speech, the correlates of reduction in dialog include high pitch, wide pitch range, and intensity, and 3) a baseline model for predicting reduction in dialog, using simple acoustic/prosodic features, that achieves correlations with human perceptions of 0.24 for …

How To Make A Neural Network Learn From A Small Number Of Examples -- And Learn Fast: An Idea, Chitta Baral, Vladik Kreinovich

Departmental Technical Reports (CS)

Current deep learning techniques have led to spectacular results, but they still have limitations. One of them is that, in contrast to humans who can learn from a few examples and learn fast, modern deep learning techniques require a large amount of data to learn, and they take a long time to train. In this paper, we show that neural networks do have a potential to learn from a small number of examples -- and learn fast. We speculate that the corresponding idea may already be implicitly implemented in Large Language Models -- which may partially explain their (somewhat mysterious) …

Counting Hamming-Graceful Labelings Of Paths, Ashka Dalal

Mathematical Sciences Technical Reports (MSTR)

Let Γ be a graph of m edges and n vertices. A Hamming-graceful labeling of Γ labels vertices with binary strings of length m and the edge labels are induced by the Hamming distance between vertex labels. It is known that all paths have Hamming-graceful labelings, thus the question arises, how many possible labelings exist for a path of a given size. We develop an algebraic way to generate labelings, conjecture a method for counting, prove this for small examples, and verify larger examples using a Python program.

Statistical Modeling Of Right-Censored Spatial Data Using Gaussian Random Fields, Fathima Z. Sainul Abdeen, Akim Adekpedjou, Sophie Dabo Niang

Mathematics and Statistics Faculty Research & Creative Works

Consider a Fixed Number of Clustered Areas Identified by their Geographical Coordinates that Are Monitored for the Occurrences of an Event Such as a Pandemic, Epidemic, or Migration. Data Collected on Units at All Areas Include Covariates and Environmental Factors. We Apply a Probit Transformation to the Time to Event and Embed an Isotropic Spatial Correlation Function into Our Models for Better Modeling as Compared to Existing Methodologies that Use Frailty or Copula. Composite Likelihood Technique is Employed for the Construction of a Multivariate Gaussian Random Field that Preserves the Spatial Correlation Function. the Data Are Analyzed using Counting Process …

Key Benefits Of Small Group Instruction For Diverse Learners, Lydia Mcevoy

Master's Theses

Utilizing a mixed method approach this research study investigated the effects of small group instruction on the learning of diverse learners. Informed by a preliminary literature review that supports the use of small-group instruction, the researcher conducted a small-scale action research project to focus on three diverse learners in a 1st-grade classroom over four weeks. One of the findings of this project shows that small group instruction helps promote social and emotional skills as students feel more comfortable interacting with peers in a small group rather than in a whole group. Another finding indicates that students feel more encouraged by …

Fundamental 2-Quandles Of The M(1/2, 1/3, 1/3; K) Montesino Knots, Alex Abrams

Mathematics Theses

Every oriented knot has an associated fundamental quandle. Except in two simple cases, these quandles have infinite order. For every integer n>1, there is a quotient of the fundamental quandle called the n-quandle of the knot. In some cases, these n-quandles may be finite. In the case of the M(1/2,1/3,1/3; k) Montesino knot family, the 2-quandle is finite. In this paper, we investigate the structure of the 2-quandle and prove its size.

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 …

On Distortion Of Surface Groups In Right-Angled Artin Groups, Lucas Bridges

Mathematical Sciences Undergraduate Honors Theses

Surfaces have long been a topic of interest for scholars inside and outside of mathe- matics. In a topological sense, surfaces are spaces which appear flat on a local scale. Surfaces in this sense have a restricted set of properties, including the behavior of loops around a surface, codified in the fundamental group.

All but 3 surface groups have been shown to embed into a class of groups called right-angled Artin groups. The method through which these embeddings are created places large restrictions on all homomorphisms from surface groups to right-angled Artin groups.

One such restriction on these homomorphisms is …

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 …

On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

All Graduate Theses and Dissertations, Fall 2023 to Present

A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields …

Vectors And Vector Borne Disease: Models For The Spread Of Curly Top Disease And Culex Mosquito Abundance, Rachel M. (Frantz) Georges

All Graduate Theses and Dissertations, Fall 2023 to Present

Mathematical models are useful tools in managing infectious disease. When designed appropriately, these models can provide insight into disease incidence patterns and transmission rates. In this work, we present several models that provide information that is useful in monitoring diseases spread by insects.

In the first part of this dissertation, we present two models that predict disease incidence patterns for Curly Top disease (CT) in tomato crops. CT affects a wide variety of plants and is spread through the bite of the Beet Leafhopper. This disease is particularly devastating to tomato crops. When infected, tomato plants present with stunted growth …

Strategy-Proof Social Choice Functions On Condorcet Domains., Flannery Marie Musk Wells

Electronic Theses and Dissertations

A social choice function is said to be strategy-proof if no voter has any motivation to lie about their true preference. Strategy-proofness is a desirable property of social choice functions so we consider here functions that always satisfy this property. We add to this property the additional desirable conditions of anonymity and neutrality and present domains on which we can get a characterization of majority rule as the only social choice function that satisfies these three properties. Furthermore, we consider what functions look like when we drop the condition of anonymity.