Mathematics Commons^™

Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

What is mathematical modeling and how can inservice and pre-service teachers develop the skills and competencies necessary to increase confidence and interest in teaching relevant mathematical modeling lessons? Mathematical modeling is “the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CSSM, 2010, p. 72). By providing students with an opportunity to engage in relevant mathematical modeling prompts, we provide them with transferable skills and knowledge. The aim of this paper will be to provide insight into the relevance of teaching mathematical modeling, provide resources for integrating modeling …

Defining Areas Of Interest Using Voronoi And Modified Voronoi Tesselations To Analyze Eye-Tracking Data, Joanna D. Coltrin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a technology used to track where someone is looking. Eye-tracking technology is often used to study what people focus on when looking at a photo of another person. The eye-tracking technology records points on a photo that a person is looking at. When the photo being looked at shows a person, the points can be categorized by body part such as head, right hand, left hand, and torso. This thesis presents the use of partially circular areas to define the body parts of the person in the photo and therefore categorize the points collected by the eye-tracker. …

Extensions To The Syrjala Test With Eye-Tracking Data Analysis Applications In R, Eric D. Mckinney

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a process for measuring the movement of an individual’s eye(s) when that individual is looking at something. Many eye-tracking technologies exist to aid in calculating and recording data associated with what a person focuses their visual attention on. For example, eye-tracking technology can record points on an image that a person is looking at. Often the question arises as to whether two people, or groups of people, are looking at the same thing(s). This dissertation presents a new way (or test) to quantify those differences while taking into consideration the randomness associated with such data. Hence, the …

Joint Invariants Of Primitive Homogenous Spaces, Illia Hayes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Joint invariants are motivated by the study of congruence problems in Euclidean geometry, where they provide necessary and sufficient conditions for congruence. More recently joint invariants have been used in computer image recognition problems. This thesis develops new methods to compute joint invariants by developing a reduction technique, and applies the reduction to a number of important examples.

Using The Reshetikhin-Turaev Link Invariant Approach With Non-Semisimple Categories, Adam Robertson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Invariants of knots and links are useful because they give rise to invariants of 3-manifolds. In particular, combinatorial link invariants give rise to combinatorial invariants of 3-manifolds, which are hard to come by using traditional methods from classical topology. The Reshetikhin–Turaev approach, which is based in quantum topology, develops link invariants using semisimple ribbon categories. However, a large class of algebraically interesting ribbon categories are non-semisimple and so give trivial link invariants via the Reshetikhin–Turaev method. We modify the Reshetikhin–Turaev method to make it suitable for non-semisimple ribbon categories. We discuss explicitly the following three examples: semisimple modules for the …

Contributions To Random Forest Variable Importance With Applications In R, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major focus in statistics is building and improving computational algorithms that can use data to predict a response. Two fundamental camps of research arise from such a goal. The first camp is researching ways to get more accurate predictions. Many sophisticated methods, collectively known as machine learning methods, have been developed for this very purpose. One such method that is widely used across industry and many other areas of investigation is called Random Forests.

The second camp of research is that of improving the interpretability of machine learning methods. This is worthy of attention when analysts desire to optimize …

Introduction To Classical Field Theory, Charles G. Torre

All Complete Monographs

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

Visions Of Science: An Art Historical Exploration Of Medieval Scientific Manuscripts, Olivia Brock

Undergraduate Honors Capstone Projects

The late 16th century saw a new movement in the world of science to push scientific ideas and practice out of academia and into the hands of the layman. No longer were scholars the sole proprietors of science –everyday laborers, craftsman, and artists now had practical scientific principles at their fingertips that they could incorporate into their professions. This new spread of science was facilitated in several ways, including the publication of books incorporating detailed, explanatory images, new utilitarian instruments, and public lectures. Though science was disseminated through a variety of means, I have been particularly interested in the ways …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Dynamical Systems Analysis In Adaptive And Metapopulation Ecology With Applications To Conservation Management, Guenchik Grosklos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The ability for a species to persist largely relies on how well they adapt to the environment and their interactions with local and global communities. Specifically, if adaptation occurs quickly enough or nearby communities sufficiently promote growth rates, populations at risk of extinction may persist. In this dissertation, we first develop a method that estimates and compares rates of change in time series data of population densities and measurable traits (phenotypes). Additionally, we compare between genetic (evolutionary) and non-genetic (plastic) trait change to determine whether phenotypes change faster when driven by evolutionary or plastic change. We then focus on metapopulation …

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 …

Modeling The Extended Low And Sudden High Periods Of Activity In Infectious Diseases, Dana Strong

Student Research Symposium

This research explores how the aggregation of individuals during disease spread may, in conjunction with noise, explain how some diseases’ trajectories spend some time at low numbers after which there is a sudden outbreak.

Modeling The Spread Of Curly Top Disease In Tomato Crops, Rachel Frantz

Student Research Symposium

Curly Top disease (CT), caused by a family of curtoviruses, infects a wide variety of agricultural crops. Historically, CT has caused extensive damage in tomato crops resulting in substantial economic loss for the tomato industry. Control methods for CT are scarce, and methods for predicting and assessing the scope of CT outbreaks are limited. In this paper, we formulate two theoretical models, a deterministic model and a stochastic model, for the spread of CT in a heterogeneous environment consisting of beets (preferred host) and tomatoes. The models are composed of two susceptible classes and two infected classes (infectious beets and …

Manifold Alignment With Inter-Domain Diffusion, Andres Duque

Student Research Symposium

The integration of multimodal data presents a challenge in cases when the study of a given phenomena by different instruments or conditions generates distinct but related domains. In this paper, we propose Diffusion Transport Alignment (DTA) a semi-supervised manifold alignment method that exploits prior correspondence knowledge between distinct data views. DTA finds a bijection between two domains, which by assumption, share a similar geometrical structure coming from the same underlying data generating process. We empirically demonstrate the effectiveness of our method to integrate multimodal data, as well as how it can improve the performance of machine learning tasks, otherwise less …

The Outdoor Fashion Industry Is Not Sustainable, Joshua Hillam

Student Research Symposium

Outdoor fashion companies are responsible for a large amount of waste and pollution worldwide. I believe they are ethically bound to make changes in their manufacturing process to decrease their footprint because their products are used in outdoor environments that are impacted negatively by waste and pollution. The fashion industry as a whole is responsible for 10% of the carbon emissions worldwide. Research was conducted by first understanding what being sustainable means from the EPA, from individuals who work in the fashion industry, and from companies that advocate for more sustainable clothing. I then investigated what materials are the most …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

Student Research Symposium

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Finding Higher Order Interactions Using Local Corex, Thomas Kerby

Student Research Symposium

In applications such as financial markets, social networks, and gene expression data, the variables often interact in complex ways. Yet accurately characterizing pairwise variable interactions can be a difficult task, let alone efficiently characterizing complex higher-order interactions, which is an unsolved problem. This difficulty is exacerbated when variable interactions change across the data. For example, gene interactions in single-cell RNA-sequencing (scRNA-seq) data will typically differ from one cell type to another. To solve these problems, we propose a new method called Local Correlation Explanation (CorEx). Local CorEx captures higher-order variable interactions at a local scale by first clustering data points …

Ensemble Kernel Density Estimation, Ethan Ancell

Student Research Symposium

The problem of estimating a probability density function from data has many applications in machine learning and data science. Nonparametric estimators are useful in this context as they require relatively few assumptions on the densities. Unfortunately, standard nonparametric methods such as kernel density estimationtend to converge slowly to the true value in high dimensions as a function of the data sample size. Recent work has shown that optimally weighted ensembles of nonparametric estimators can be used to achieve a fast convergence rate when estimating information theoretic functionals such as information divergence. We explore the extension of this theory to density …

Development Of Particle Image Velocimetry Learning Tool: Learnpiv.Org, Kevin Roberts

Student Research Symposium

Particle Image Velocimetry (PIV) is an experimental measurement technique used for quantitative and visual analysis of the velocity distribution in a flow field. Researchers conduct PIV by using lasers to illuminate particles in a flow field of interest, digital cameras to record images of these illuminated particles, and PIV software to analyze the recorded images, producing a velocity vector field. Applying proper techniques to gather useful images and identifying PIV processing algorithm parameters to the collected images is a challenging task for novice PIV users who are unaware of the inner workings of PIV algorithms. Recognizing this problem, we created …

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Charles G. Torre

Research Vignettes

No abstract provided.

What's New In Differentialgeometry Release Dg2022, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This Maple worksheet demonstrates the salient new features and functionalities of the 2022 release of the DifferentialGeometry software package.

A New Non-Inheriting Homogeneous Solution Of The Einstein-Maxwell Equations With Cosmological Term, Ian M. Anderson, Charles G. Torre

Publications

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame.

When Is A Linear Connection A Metric Connection?, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet we use the DG software to answer the following question: When is there a metric tensor on M whose Christoffel symbols coincide with the components of a given linear connection?

The De Rham Decomposition Theorem, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet we show how the DG software provides for a local implementation of the de Rham decomposition theorem for Riemannian manifolds.

Explicit Synchronized Solitary Waves For Some Models For The Interaction Of Long And Short Waves In Dispersive Media., Bruce Brewer

Fall Student Research Symposium 2021

Four systems have recently been proposed for the study of the interaction of long and short waves in dispersive media. This poster establishes the synchronized solitary wave solutions for one of these systems.

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

On The Geometry Of The Moduli Space Of Certain Lattice Polarized K3 Surfaces And Their Picard-Fuchs Operators, Michael T. Schultz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

K3 surfaces have a long and rich study in mathematics, and more recently in physics via string theory. Often, K3 surfaces come in multiparameter families - the parameters describing these surfaces fit together to form their own geometric space, a so-called moduli space. In particular, the moduli spaces of K3 surfaces equipped with a lattice polarization can sometimes be constructed explicitly, which subsequently reveals important information about the original K3 surface.

In this work, we construct such families explicitly from certain rational elliptic surfaces via the so-called mixed-twist construction of Doran & Malmendier, which in turn produces the moduli …

Transformation Groups And The Method Of Darboux, Brandon P. Ashley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In the study of partial differential equations (PDE), one is often concerned as to whether or not explicit solutions can be obtained via various integration techniques. One such technique, known as the method of Darboux, has had particular success in solving nonlinear problems as demonstrated by the classical works of Goursat. Recently, Anderson, Fels, and Vassiliou provided a far-reaching generalization of Vessiot’s group-theoretic interpretation of the method of Darboux. This generalization allows for the characterization of Darboux integrable systems in terms of fundamental geometric invariants as well as the construction of Darboux integrable systems in general.

In this work, we …

Tractor Connections For Killing Tensors And Their Generalizations, Benjamin D. Shaw

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We create new symbolic software tools for the analysis of Killing tensors. Central to our work is the construction of the tractor connection defined on the tractor bundle, which allows one to obtain information about the space of Killing tensors without solving the Killing equations–an approach termed the tractor approach. We give a new application of the tractor approach which allows one to more easily check explicitly for linear independence of a given set of Killing tensors. We develop software to implement such methods in the case of rank 2 Killing tensors; similarly, we develop software to implement analogous methods …