Mathematics and Statistics Electronic Theses and Dissertations (UMKC)The items in this collection are the scholarly output of UMKC graduate students.https://hdl.handle.net/10355/99022024-03-29T08:36:02Z2024-03-29T08:36:02ZA Cubic Spline Projection Method for Computing Stationary Density Functions of Frobenius-Perron OperatorAlshekhi, Azzah Ahmedhttps://hdl.handle.net/10355/913092022-08-30T18:02:44Z2022-01-01T00:00:00ZA Cubic Spline Projection Method for Computing Stationary Density Functions of Frobenius-Perron Operator
Alshekhi, Azzah Ahmed
Stationary density functions of Frobenius-Perron operators have critical applications in many fields of science and engineering. Accordingly, approximating stationary density functions f* is important and the focus of this dissertation. Among the computational methods of approximating the smooth f*, the linear spline and quadratic spline projection methods have been proven effective. However, we intend to improve the convergence rate of the previous methods. We will fulfill this goal by using cubic spline functions since cubic spline functions are twice continuously differentiable on the whole domain. Theoretically, we prove the existence of a nonzero sequence of cubic spline functions {fₙ} that converges to the stationary density function f* of the Frobenius-Perron operator in L¹-norm. The numerical experimental results assure that the cubic spline projection method gives the fastest convergence rate so far. In addition, when the stationary density function f* lies in the cubic spline space, the cubic spline projection method computes f* exactly no matter what n may be.
Title from PDF of title page, viewed August 22, 2022; Dissertation (Ph.D)--Department of Mathematics and Statistics, Department of Physics and Astronomy. University of Missouri--Kansas City, 2022; Includes bibliographical references (pages 143-150)
2022-01-01T00:00:00ZA Longitudinal study of modeling-based college algebra and its effect on student achievementChappell, Timothy Paulhttps://hdl.handle.net/10355/739992020-09-08T15:00:19Z2020-01-01T00:00:00ZA Longitudinal study of modeling-based college algebra and its effect on student achievement
Chappell, Timothy Paul
Low success rates and high withdrawal rates in gateway courses like College Algebra have deterred some students from attaining their educational goals. The university of study developed a Modeling-Based College Algebra course with the purpose of creating a better course for terminal students and yet still preparing nonterminal students for the next mathematics course. In this quantitative study, the difference between the two College Algebra courses in terms of average final grade, the D/F percentage, the withdrawal percentage, and the average final grade in a subsequent mathematics course was examined. The difference in median final grade, D/F percentage, and withdrawal percentage was statistically significant. The difference in average final grade in the subsequent math course was not statistically significant. The difference in median final grade, D/F percentage, and withdrawal percentage was statistically significant for female, male, and traditional students.
Title from PDF of title page viewed June 11, 2020; Dissertation advisor: Rita Barger; Thesis (Ph.D.)--School of Education and Department of Mathematics and Statistics. University of Missouri--Kansas City, 2020; Vita; Includes bibliographical references (pages 127-137)
2020-01-01T00:00:00ZA Mathematical Modelling Approach to Analyze the Dynamics of Math AnxietySoysal, Dilekhttps://hdl.handle.net/10355/913202022-12-13T20:04:46Z2022-01-01T00:00:00ZA Mathematical Modelling Approach to Analyze the Dynamics of Math Anxiety
Soysal, Dilek
The main objective of this study is to develop a mathematical modeling framework for a deeper understanding of dynamics of math anxiety as a contagious process. Borrowing from theories of the spread of infectious disease, we develop two classes of mathematical models representing the spread of math anxiety in math gateway classes. The first mathematical model does not entirely fit with our collected data of math anxiety (n=53, Calculus II & III summer of 2020). However, the second mathematical model, which is a generalization of the first model, can exhibit periodic solutions as observed in the collected data. In addition to the mathematical modeling framework, we have applied a variety of statistical methods and models to analyze the survey data. This includes descriptive analysis of the data, correlation and hypothesis testing, and a machine learning approach, which utilizes the classification and regression tree models to identify key factors associated with math anxiety. These regression tree models include factors such as gender, academic level, number of hours studied, motivation, and confidence. In conclusion, the present work lays the foundation for applying mathematical models to measure the spread of math anxiety in gateway STEM courses.
Title from PDF of title page, viewed August 23, 2022; Dissertation advisor: Majid Bani Yaghoub; Vita; includes bibliographical references (pages 148-161); Dissertation (Ph.D)--Department of Mathematics & Statistics, Division of Teacher Education and Curriculum Studies. University of Missouri--Kansas City, 2022
2022-01-01T00:00:00ZA modeling framework for spatial transmission of Covid-19 in local communitiesAlQadi, Hadeel Hassanhttps://hdl.handle.net/10355/903222022-06-02T16:04:11Z2022-01-01T00:00:00ZA modeling framework for spatial transmission of Covid-19 in local communities
AlQadi, Hadeel Hassan
COVID-19 is the recent infectious disease caused by the severe acute respiratory syndrome novel coronavirus (SARS-CoV-2). Because the transmissibility of the virus is relatively high and the outbreaks remained undetected for several days, COVID-19 turned into a global pandemic. Almost all countries in the world have been exposed to the virus. Just in the United States, the COVID-19 cases are over 75 million, with more than 886K deaths as of February 2022.
The pandemic duration and the enormous impacts on societies, economies, and public health have substantially affected the importance of conducting mathematical and statistical tools to analyze and predict the spatial transmission dynamics of COVID-19, which could provide invaluable benefits to global public health to reduce the chances of emerging new waves and control the epidemic. The current mathematical and statistical models have proved insufficient due to the lack of human behavioral and social processes, which have appeared to be vital to understanding the course of the pandemic.
This dissertation proposes incorporating human behavioral, demographical, and beliefs processes to improve the accuracy of the current mathematical and statistical models. These processes include structural characteristics associated with race, ethnicity, and gender, as well as the mobility of individuals within and between local communities and beliefs about accepting or rejecting vaccinations.
We focused on two modeling approaches to evaluate their capabilities and usefulness in predicting and analyzing the spatial dynamics of the disease associated with the processes mentioned earlier.
The first approach is statistical modeling, implemented with SaTScan. It enabled us to identify periodic spatial-temporal COVID-19 clusters and the location of their probability of occurrence and assess the spatial clusters with respect to demographic factors of gender, race, and ethnicity.
The second approach is mathematical modeling with Ordinary Differential Equations (ODE). We developed a mathematical model to describe the spatial spread of COVID-19 within and between clusters and investigated the global impacts of population movements from and to the local clusters on the spatial spread of COVID-19. Moreover, we utilized the method of Hopf bifurcation to test whether the oscillations in the COVID-19 cases are due to the natural characteristics of host-pathogen interactions.
Title from PDF of title page viewed June 2, 2022; Dissertation advisor: Majid Bani Yaghoub,; Vita; Includes bibliographical references (pages 167-190); Thesis (Ph.D.)--Department of Mathematics and Statistics, Department of Physics and Astronomy. University of Missouri--Kansas City, 2022
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