Physical Sciences and Mathematics Commons^™

A Combinatorial Proof Of Supercranks For Partitions With A Fixed Number Of Parts, Jacob J. Gutierrez

Theses and Dissertations

In a previous paper by Eichhorn and Kronholm, a selection of supercranks for p(n,m) was established by generating functions. In this paper we will reprove this result with combinatorial witnesses for the selection of supercranks via integer lattice points.

Attitudes Towards Mathematics Of Developmental Mathematics Students In A Community College, Benjamin Ortiz

Theses and Dissertations

Reformations to developmental mathematics aim to remove barriers for students entering higher education. Challenges like costly multi-course sequences and high failure rates prohibit students’ access to college-level math courses and prevent degree or certification completion. Understanding factors that foster student success is critical to increase student success. This study focuses on students’ attitudes towards mathematics, utilizing the novice-expert continuum through Code et al.’s Mathematical Attitude and Perceptions Survey (MAPS) instrument. Student expertise scores, including all MAPS dimensions and specific dimension scores, were assigned. Kruskal-Wallis Rank-Sum tests identified differences in student populations by course and attitude dimension. …

How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa

Theses and Dissertations

There are many aspects a teacher can notice inside the mathematics classroom, and the more a teacher notices, the more difficult it is to teach. In this study, I particularly focus on noticing for equity, which describes the role of the teacher in attending to students’ mathematical thinking through an equity lens that can allow the instructor to notice the aspects of classroom mathematical activity that can make students feel less or more empowered in their mathematical practices (van Es et al., 2017). There exists few research about how students perceive their instructor’s effort to promote equity and …

An Automatic Solver For Optimal Control Problems, Marcel Efren Benitez

Theses and Dissertations

Optimal control theory is a study that is used to find a control for a dynamical system over a period of time such that a objection function is optimized. In this study we will be looking at optimal control problems for ordinary differential equations or ODEs and see that we can use an automatic solver using the forward-backward sweep using Matlab to solve for them from an 1 dimension to bounded cases and to nth dimension cases.

Case Studies Of Algebra 1 Teachers Selection And Implementation Of Mathematics Tasks Toward Situated Learning, Luis Román Sauceda

Theses and Dissertations

Mathematical tasks are vital in active learning, especially in situated learning. Adequate selection and appropriate implementation of tasks are steps toward success in engaging students for active learning. This study explored how a professional development (PD) workshop influences teacher participants’ capabilities in selecting, redesigning, implementing, and reflecting on mathematical tasks to promote situated and active learning. The teacher participants were Algebra 1 teachers from a South Texas secondary school. During the workshop, participants developed and implemented activities after being shown situated learning strategies to promote student-centered learning. They were required to design hypothetical dialogues to simulate their class practice before …

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …

Quasipolynomials And The Unimodality Of Gaussian Polynomials, Paul Marsh

Theses and Dissertations

We illustrate a method to prove the unimodality of Gaussian polynomials ${N+m \brack m}$ for $m = 5$ and $6$, building upon Dr. Brandt Kronholm's work, which proved unimodality for $m = 2,3,$ and $4$. Our approach involves viewing coefficients $p(n,m,N)$ of Gaussian polynomials $N+m \brack m$ based on how far away $n$ is from the central coefficient $p(\lfloor\frac{mN}{2}\rfloor,m,N)$ and then creating generating functions for those coefficients. We then take the difference of neighboring generating functions and change those generating functions into quasipolynomials to verify that their coefficients are non-negative. While the generalization of these generating functions for the coefficients …

Matrix Completion Problems For The Positiveness And Contraction Through Graphs, Louis C. Christopher

Theses and Dissertations

In this work, we study contractive and positive real matrix completion problems which are motivated in part by studies on sparce (or dense) matrices for weighted sparse recovery problems and rating matrices with rating density in recommender systems. Matrix completions problems also have many applications in probability and statistics, chemistry, numerical analysis (e.g. optimization), electrical engineering, and geophysics. In this paper we seek to connect the contractive and positive completion property to a graph theoretic property. We then answer whether the graphs of real symmetric matrices having loops at every vertex have the contractive completion property if and only if …

Data Science For Hospital Antibiotic Stewardship, Saikou Jawla

Theses and Dissertations

Antibiotics are widely used to treat bacterial infections, but their misuse leads to antibiotic resistance. Antibiotic resistance is one of the biggest threats to global health, food security, and development today. Antibiotic resistance leads to higher medical costs, prolonged hospital stays, and increased mortality. Antimicrobial stewardship is an approach to measure and improve the appropriate use of antibiotics in healthcare settings. Data science has the potential to support these programs by providing insights into antibiotic prescribing patterns, identifying areas for improvement, and predicting patient outcomes. We explored the role of data science in hospital antibiotic stewardship programs, including statistical methods …

An Investigation Into Optimal Descent Trajectories For Multipurpose Long Range Space Vehicles Under Advanced Conditions, John M. Levis

Theses and Dissertations

In this work, we investigate the problem of fuel-optimal control of space vehicle descent trajectories. The main tool we use to establish optimality is Pontryagin’s Maximum Principle. We present a variety of scenarios with increasing complexities, including drag, wind, and moving landing platforms in the context of differing atmospheric and gravitational conditions. Throughout the paper, we use a balance of analytical and numerical techniques. Finally, observations and conclusions drawn from the investigation form the basis for suggestions into additional areas of analysis.

An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers

Theses and Dissertations

This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms These modular forms can be represented in terms of Klein forms and the Dedekind eta function. The main focus of this thesis is to introduce the necessary theory to characterize these specific Ramanujan type congruences and prove their antichimerality.

Evaluation Of Black Holes In An Evolving Universe, John P. Naan

Theses and Dissertations

There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …

Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako

Theses and Dissertations

Missing data are common in real-life studies and missing observations within the univariate time series cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in the analysis of every incomplete univariate time series data. The reviewed literature has shown that the focus of existing studies is on comparing the distribution of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series data affect the fit and prediction performance of time series models. In this work, we evaluated the predictive performance of autoregressive integrated moving average …

Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo

Theses and Dissertations

In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code.

An Investigative Study Of Potential Factors That Contribute To High Under-Five Mortality Rate In Africa, David Banahene

Theses and Dissertations

Under-Five Mortality remains a significant challenge in developing countries, especially in Africa. The United Nations has implemented various measures, such as the Millennium Development Goals (MDGs) and Sustainable Development Goals (SDGs), to combat this issue. However, the success of these initiatives is uncertain. Our study investigates the social, economic, and environmental factors contributing to high Under-Five Mortality rates in African countries, using data from 1985 to 2020.We analyzed 53 African countries, partitioning them into training (45 countries) and testing data (8 countries). We conducted Multiple Linear Regression analysis and assessed the model performance using R-squared values and Root-Mean-Squared-Error (RMSE) values. …

Creation Of A College Math Club For High School Students, Lilian N. Chavez

Theses and Dissertations

This study aimed to investigate the variables that contribute to high school students' desire to join a math club, specifically the FMiM VIP Club, which is an extension of UTRGV's Follow Me into Math research project. The research utilized multiple questionnaire s to examine the combination of factors that contribute to the students' attitudes toward the math club. The participants were high school Algebra 2 students from two different schools, and the study was conducted in two stages. The first stage was conducted in the Spring of 2022, focusing on girls' math identity and their interactions with the FMiM VIP …

Quantization For A Nonuniform Triadic Cantor Distribution, Asha Barua

Theses and Dissertations

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. Let P be a Borel probability measure on R such that P := 1/4 P◦ S1−1 + 1\2 P◦ S2−1 + 1/4 P◦ S3−1, where S1, S2 and S3 are three contractive similarity mappings such that Sj(x) = 1/5x+2(j−1)/5, for all x ∈ R. For this probability measure, in this thesis, we determine the optimal sets of n-means and the nth quantization errors for …

Mathematics Teachers’ Working With Cooperative Learning, Jaime Gomez

Theses and Dissertations

Teaching styles vary greatly amongst educators. One being extensively researched and highly discussed is the method of cooperative learning. Although many studies have shown the benefits of incorporating cooperative learning into classrooms, it has not been a widely used method of teaching in high school mathematics classrooms. This study explores some of the efforts that teachers, who utilize cooperative learning in their classrooms, make to implement cooperative learning lessons successfully. Furthermore, this study also explores the challenges these teachers have encountered when using cooperative learning. Data was collected qualitatively by interviews and surveys from six in-service high …

Thermal Convection In A Cylindrical Annulus Filled With Porous Material, Anirban Ray

Theses and Dissertations

Here a study on thermal convection in a porous vertical cylindrical annulus which is heated from below is carried out. The walls are considered to be impermeable that is the velocity is 0 at the boundary walls. The cylindrical annulus is radially insulated. The governing system consists of the continuity equation, Darcy-Boussinesq equation, heat equation and the equation of state. Employing weakly non-linear approach, the basic state system and the perturbed system are derived. After obtaining the solutions to the basic state system, the pressure term in perturbed system is eliminated by taking double curl, and then eliminating the velocity, …

Traveling Wave Solutions For The Negative Order Hierarchy Of The D-Akns Equations, Brayton Isaac Wario

Theses and Dissertations

In the thesis work, based on the D-AKNS spectral problem, we study the negative-order D-AKNS (ND-AKNS) hierarchy. In particular, the first ND-AKNS equation is derived from the negative-order D-AKNS hierarchy, which is proved integrable in the sense of Lax pair. Furthermore, we discuss the traveling wave solutions to the ND-AKNS Equation, including possible soliton solutions.

Adjacency And Connectivity Matrices To Airline Connections Among Airports, Alejandra Munoz

Theses and Dissertations

We study how powers of adjacency and connectivity matrices can be used to investigate airline connections among airports. For this study, only matrices with all diagonal elements of “0” are considered (i.e., an airport is not connected to itself) and each matrix must contain at least one entry of “1” in each row and column (i.e., each airport contains at least one inbound and one outbound route). Sets of 3, 4, and 5 airports are discussed in this study, comparing cases with up to 3, 4, and 5 round routes, respectively, in an effort to find the amount of paths …

Modeling Functions Into An Angular Displacement Of An Elastic Pendulum, Brenda Lee Garcia

Theses and Dissertations

In this thesis we study the relation between analytic signals and a variety of pendulum systems. The representation of a signal as a pair of time varying amplitude and phase has been well studied and often related to linear mass spring systems. The differential equations describing pendulum systems are nonlinear and we provide analytical and numerical results regarding interpretation about the amplitude and the phase of signals in different pendulum settings. We report an explicit solution of the Elastic Pendulum problem in the case of linear phase. We develop an experimental procedure to piece-wise approximate bounded functions on a partition …

A Decomposition Formula For The Multi-Soliton Solutions To The 'Good' Boussinesq Equation, Aldo Gonzalez

Theses and Dissertations

In this thesis, we relate multi-soliton waves generated by the 'good' Boussinesq equation to the distribution functions in the classical linear Schrödinger equation. The linear Schrödinger equation describes the distribution of a particle or particles in a particular environment. The Schrödinger equation is linear, the superposition principle of the solutions, especially the eigenfunctions is nonlinear and we will show that we may observe similar behavior in the solutions of the Boussinesq equations for soliton waves. The work extends the study of two-soliton solutions to the Boussinesq equation to the case of three-soliton solutions. …

Pentagonal Tilings Of The Plane, Ariana T. Hinojosa

Theses and Dissertations

Tilings are mathematical objects that allow us to use geometry to visualize interaction between objects as well as to create artistic realization of mathematical objects in the plane and in the space.

We will focus on tilings of the plane that use only one type of convex pentagonal tile each, the pentagonal tilings. There are fifteen types of pentagonal tiles, with each containing their own set of restrictions. The main result of this thesis is an interactive realization of all fifteen types of pentagonal tiles using GeoGebra.

A Gpu Accelerated Genetic Algorithm For The Construction Of Hadamard Matrices, Raven I. Ruiz

Theses and Dissertations

Hadamard matrices are square matrices with +1 and -1 entries and with columns that are mutually orthogonal. The applications include signal processing and quantum computing. There are several methods for constructing Hadamard matrices of order 2k for every positive integer k. The Hadamard conjecture proposes that there are also Hadamard matrices of order 4k for every positive integer k. We use a genetic algorithm to construct (search for) Hadamard Matrices. The initial population of random matrices is generated to have a balanced number of +1 and -1 entries in each column. Several fitness functions are implemented exploiting …

An Application Of Matrices To The Spread Of The Covid 19, Selena Suarez

Theses and Dissertations

We represented a restaurant seating arrangement using matrices by using 0 entry for someone without covid and 1 entry for someone with covid. Using the matrices we found the best seating arrangements to lessen the spread of covid. We also investigated if there was a factor needed to create a formula that could calculate the matrix that shows who would be affected with covid with each seating arrangement. However, there did not seem to be a clear pattern within the factors. Aside from covid applications, we also investigated the symmetries in seating arrangements and the possible combinations with these arrangements …

Iterated Rascal Triangles, Jena M. Gregory

Theses and Dissertations

We introduce a sequence of number triangles, {Ri} i=0 infty , such that the entries of each share a common generalized recurrence relation. R1 is the Rascal triangle and as i grows large, Ri becomes Pascal's triangle. For all i, we provide a combinatorial interpretation and find closed-term formulas for the entries of Ri . Our proofs rely on generating functions and other combinatorial arguments.

On Approximating Solitary Wave Solutions For The Classical Euler Equations, Julio C. Paez

Theses and Dissertations

In this paper, we use a method based on Hirota substitution or the Wronskian method to find approximate solitary wave solutions to the classical Euler equations. This method uses a small parameter lambda as the basis of approximation, a parameter derived from the form of prospective solutions we consider, rather than the standard small parameters alpha and beta. The L-infinity norm and asymptotic notation are used to measure the accuracy of the approximation rather than finding the error explicitly.

Boundary Feedback Control Of The 3d Navier-Stokes Equations, Camille Renee Vasquez

Theses and Dissertations

We present a boundary feedback stabilization of the parabolic steady state profile of the incompressible Navier-Stokes Equations in a three-dimensional channel flow. The decentralized, static boundary feedback control laws are derived using Lyapunov technique. While the theoretical results are limited to stability enhancement for small Reynolds numbers, extensive numerical simulations and visualizations demonstrate the effectiveness of the proposed feedback law even in cases when the uncontrolled flow is turbulent.

A Statistical Comparison Of Covid-19 In The United States Across Political Affiliations And Census Regions, Margarito Torres

Theses and Dissertations

In mid-January 2020, the United States reported their first cases of the coronavirus disease (COVID-19) from a passenger returning from Wuhan, China. Initially, the situation wasn’t very alarming as in China and European countries, but the situation began to worsen in March 2020 when the number of cases began to multiply. Then, in a matter of a few months, the United States became the number one country in terms of total cases and total deaths from COVID-19. We have been closely observing the United States and the world since July 2020. Our study aims to compare the political affiliations and …