Physical Sciences and Mathematics Commons^™

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

Correlations Between Soil Redness And Soil Properties That Affect Non-Native Annual Plant Distribution In Chaparral And California Sage Scrub, Madeline Blua

Electronic Theses, Projects, and Dissertations

Non-native annual plant species have degraded California Sage Scrub and chaparral and present obstacles to shrubland restoration. Red soil patches in chaparral and California Sage Scrub of San Bernardino and Riverside counties appear to support fewer non-native annual plants than non-red soils. The purpose of this study was to confirm differences in vegetation cover between red and non-red soils in shrublands and to use soil analyses to determine possible causes. During vegetation surveys conducted in April of 2018, it was confirmed that red soil sites had lower cover of non-native plants and higher cover of native plant species than the …

Tile Based Self-Assembly Of The Rook's Graph, Ernesto Gonzalez

Electronic Theses, Projects, and Dissertations

The properties of DNA make it a useful tool for designing self-assembling nanostructures. Branched junction molecules provide the molecular building blocks for creating target complexes. We model the underlying structure of a DNA complex with a graph and we use tools from linear algebra to optimize the self-assembling process. Some standard classes of graphs have been studied in the context of DNA self-assembly, but there are many open questions about other families of graphs. In this work, we study the rook's graph and its related design strategies.

Analysis On Suicidal Ideation Among Adolescents (12-17 Years) In The Usa, Himani Raturi

Electronic Theses, Projects, and Dissertations

Suicide is one of the leading health concerns in United States among adolescents and the presence of suicidal ideation (SI) is quite high, with ~20-30% of adolescents reporting it at some point. Though we have seen growth and development in the prevention of suicide, there is limited research on the ability to identify the adolescents which might be at risk for SI. The objective behind the project is to identify adolescents with SI using machine learning.

The project shows statistics from different articles on adolescents in the U.S. For this study, adolescent data was taken from NSDUH 2018. Moreover, detailed …

Email Data Breach Analysis And Prevention Using Hook And Eye System, Shubhankar Jayant Jathar

Electronic Theses, Projects, and Dissertations

Due to the recent COVID-19 outbreak, there were a lot of data leaks from the health sector. This project is about the increase in data breach incidents that are taking place. In this project, There is an analysis of different types of breaches that are found online and are practiced to steal valuable information. Talking about different aspects that lead to data breaches and which are the main sector or main epicenter for data leaks. The analysis tells that most of the data breaches are done using emails and to overcome this limitation a system has been designed that will …

Geospatial Applications To Mitigate Concentrated Animal Feeding Operations From Impacting Surface Water Resources, Elias Rex

Electronic Theses, Projects, and Dissertations

Concentrated Animal Feeding Operations (CAFOs) offer the ability to meet the rising demands of population growth by housing large amounts of livestock on relatively small areas of land, using medication to accelerate their maturation, and reusing waste products as fertilizers. However, there is a growing abundance of literature related to land use configurations and their effects on water resources, many of which highlight agriculture as a primary contributor of nutrients and fecal bacteria found in surrounding water resources. The purpose of this study is to advance the current knowledge surrounding CAFO land-use and its effect on tributaries within the Cape …

Bubble-In Digital Testing System, Chaz Hampton

Electronic Theses, Projects, and Dissertations

Bubble-In is a cloud-based test-taking system build for students and teachers. The Bubble-In system is a test-taking application that interfaces with a cloud server. The mobile applications have been built for Android and Apple devices and the webserver is hosted on Digital Ocean VPS run with Nginx. The Bubble-In application is equipped with anti-cheating mechanisms such as question-answer key scrambling, not allowing screenshots, screen recording, or leaving the application. The tests students take are sent to the webserver to be graded and have statistics calculated and displayed in easy to use format for the test creator. Instructors can use the …

Exploring Matroid Minors, Jonathan Lara Tejeda

Electronic Theses, Projects, and Dissertations

Matroids are discrete mathematical objects that generalize important concepts of independence arising in other areas of mathematics. There are many different important classes of matroids and a frequent problem in matroid theory is to determine whether or not a given matroid belongs to a certain class of matroids. For special classes of matroids that are minor-closed, this question is commonly answered by determining a complete list of matroids that are not in the class but have the property that each of their proper minors is in the class; that is, minor-minimal matroids that are not in the minor-closed class. These …

Permutation And Monomial Progenitors, Crystal Diaz

Electronic Theses, Projects, and Dissertations

We searched monomial and permutation progenitors for symmetric presentations of important images, nonabelian simple groups, their automorphism groups, or groups that have these as their factor groups. In this thesis, we described our search for the homomorphic images through the permutation progenitor 2^*15:(D₅ X 3) and construction of a monomial representation through the group 2³:3.

We constructed PGL(2,7) over 2³:3 on 6 letters and L₂(11) over 2²:3 on 8 letters. We also give our construction of S₅ X 2 and L₂(25) as homomorphic images of the …

Low Impact Development Best Management Practices Comprehensive Overview And Case Study, Graciela Rivera

Electronic Theses, Projects, and Dissertations

This project paper is an overview of the different types of best management practices (BMPs) that can be applied within a Low Impact Development framework. Low Impact Development (LID) is a type of stormwater management implementation that is growing in popularity. It allows developments to manage stormwater by working within established ecosystems to lessen environmental impacts. The cost and effectiveness of these practices are examined. In the first chapter, a comprehensive summary to LIDs and BMPs is presented.

The costs and effectiveness of bioretention, biofiltraion and infiltration basins, as well as permeable pavements, were studied and compared. The facility case …

Dna Complexes Of One Bond-Edge Type, Andrew Tyler Lavengood-Ryan

Electronic Theses, Projects, and Dissertations

DNA self-assembly is an important tool used in the building of nanostructures and targeted virotherapies. We use tools from graph theory and number theory to encode the biological process of DNA self-assembly. The principal component of this process is to examine collections of branched junction molecules, called pots, and study the types of structures that such pots can realize. In this thesis, we restrict our attention to pots which contain identical cohesive-ends, or a single bond-edge type, and we demonstrate the types and sizes of structures that can be built based on a single characteristic of the pot that is …

Minimal Surfaces And The Weierstrass-Enneper Representation, Evan Snyder

Electronic Theses, Projects, and Dissertations

The field of minimal surfaces is an intriguing study, not only because of the exotic structures that these surfaces admit, but also for the deep connections among various mathematical disciplines. Minimal surfaces have zero mean curvature, and their parametrizations are usually quite complicated and nontrivial. It was shown however, that these exotic surfaces can easily be constructed from a careful choice of complex-valued functions, using what is called the Weierstrass-Enneper Representation.

In this paper, we develop the necessary tools to study minimal surfaces. We will prove some classical theorems and solve an interesting problem that involves ruled surfaces. We will …

Excluded Minors For Nearly-Paving Matroids, Vanessa Natalie Vega

Electronic Theses, Projects, and Dissertations

Matroids capture an abstract notion of independence that generalizes linear independence in linear algebra, edge independence in graph theory, as well as algebraic independence. Given a particular property of matroids, all the matroids possessing that property form a matroid class. A common research theme in matroid theory is to characterize matroid classes so that, given a matroid M, it is possible to determine whether or not M belongs to a given class. An excluded minor of a minor-closed class is a matroid N that is, in a sense, minimal with respect to not being in the minor-closed class. An attractive …

Research In Short Term Actuarial Modeling, Elijah Howells

Electronic Theses, Projects, and Dissertations

This paper covers mathematical methods used to conduct actuarial analysis in the short term, such as policy deductible analysis, maximum covered loss analysis, and mixtures of distributions. Assessment of a loss variable's distribution under the effect of a policy deductible, as well as one with an implemented maximum covered loss, and under both a policy deductible and maximum covered loss will also be covered. The derivation, meaning, and use of cost per loss and cost per payment will be discussed, as will those of an aggregate sum distribution, stop loss policy, and maximum likelihood estimation. For each topic, special cases …

Hyperbolic Triangle Groups, Sergey Katykhin

Electronic Theses, Projects, and Dissertations

This paper will be on hyperbolic reflections and triangle groups. We will compare hyperbolic reflection groups to Euclidean reflection groups. The goal of this project is to give a clear exposition of the geometric, algebraic, and number theoretic properties of Euclidean and hyperbolic reflection groups.

Assessing Student Understanding While Solving Linear Equations Using Flowcharts And Algebraic Methods, Edima Umanah

Electronic Theses, Projects, and Dissertations

Solving linear equations has often been taught procedurally by performing inverse operations until the variable in question is isolated. Students do not remember which operation to undo first because they often memorize operations with no understanding of the underlying meanings. The study was designed to help assess how well students are able to solve linear equations. Furthermore, the lesson is designed to help students identify solving linear equations in more than one-way. The following research questions were addressed in this study: Does the introduction of multiple ways to think about linear equations lead students to flexibly incorporate appropriate representations/strategies in …

Modeling The Spread Of Measles, Alexandria Le Beau

Electronic Theses, Projects, and Dissertations

The measles virus has been around since the 9th century. Throughout the years measles have become less problematic in certain areas of the world due to research and the creation of vaccinations. Sadly, not all countries are fortunate enough to have adequate access to the vaccination, which leads to yearly outbreaks.

The goal of this project is to experiment with different mathematical growth models and examine their suitability for modeling outbreaks of measles. We will compare and contrast the exponential model, the logistic model, the SIR model, and the SEIR model. In addition, we will show how the epidemiological models …

Symmetric Presentations And Related Topics, Mayra Mcgrath

Electronic Theses, Projects, and Dissertations

In this thesis, we have investigated several permutation and monomialprogenitors for finite images. We have found original symmetric presen-tations for several important non-abelian simple groups, including lineargroups, unitary groups, alternating groups, and sporadic simple groups.We have found a number of finite images, including : L(2,41), PSL(2,11)×2, L(2,8), and L(2,19), as homomorphic images of the permutation progenitors. We have also found PGL(2,16) : 2 =Aut(PSL(2,16)) and PSL(2,16) as homomorphic images of monomial progenitors. We have performed manual double coset enumeration of finte images. In addition, we have given the isomorphism class of each image that we have discovered. Presentation for all …