Mathematics
Permanent URI for this collectionhttps://hdl.handle.net/11274/15813
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Item Affect and achievement: creating an optimal learning experience in mathematics(7/14/2020) Skousen, Elizabeth; Navarra-Madsen, JunalynThis paper is an analysis of cross-curricular studies about motivation, affect, and engagement in a classroom setting. We further determine appropriate tools for measuring student engagement and affect. Student self-efficacy is a determining factor in motivation and engagement in the classroom. Three instructional methods are of particular interest in increasing student engagement and motivation: problem-based learning, mastery learning, and student self-assessment. We consider each of these instructional methods in turn as ways to enhance student self-efficacy and positive affect and conduct a statistical analysis on the correlations between these measures. Problem-based learning, mastery learning, and student self-assessment are positively correlated with student affect, motivation, and engagement, which contribute to student achievement and future learning of mathematics.Item An investigation of systems of population models(9/29/2017) Fritz, Kathryn S.; Marshall, David, Ph. D.; Machuca, Alicia; Edwards, Don E.The purpose of this thesis is to possibly help nontraditional, first-generation math students in their attempt at learning ordinary differential equations systems of population models with positive coefficients. I hope to accomplish this by building a guide containing some of the prerequisite mathematical concepts, demonstrating the procedures used while investigating the previously mentioned types of systems. The definitions of the vocabulary that is used to fully understand this process, the use of parameter population system to demonstrate the graphing program PPLANES, the explanation of the graphs created while using this program, and the use of Maple (Version 10) to find eigenvectors of the equilibrium points four case scenarios.Item Analysis of factors contributing to student’s academic performance in college’s STEM program(1/18/2022) Ayeni, Abimbola A; Falley, BrandiThe purpose of this study is to analyze different variables in understanding how they affect the academic performance of students taking STEM courses at a mid-sized college in the southern United States. These factors are classified into pre-college variables and college variables. The pre-college variables are ACT/SAT scores, gender, ethnicity, and first-generation student or not. The college variables are college GPA, Pell grant recipient, the student’s continuance with the degree major in sophomore year. Implementing regression analysis and using backward regression to remove variables that are not correlated to the response variable (CGPA), we were able to arrive at the best model using the three variables: ACT mathematics, ACT English, and gender. The resulting variables selected show us how the value of R^2 has helped us in making sense of the model selected by 14.2%.Item Analyzing the relationship between attendance in hybrid supplemental instruction and tutoring sessions and success in courses with traditionally high failure rates(8/30/2016) Kelley, Allyssa; Edwards, Don E.; Falley, Brandi; Marshall, DavidAcademic assistance programs have been around in some form or another since the mid-1600s, and they have grown and developed just as the demographics of students in tertiary institutions have. The supplemental instruction model is an assistance program that was built as a response to the needs of the shifting student body, and Texas Woman’s University is one of many institutions that have adopted a hybrid supplemental instruction model in an effort to increase student performance in their classes. The purpose of this research was to determine which, if any, factors impact the success of a student in the TWU Supplemental Instruction and Tutoring program using logistic regression analysis to build prediction models for success. The models that were created showed that, contrary to the hypothesis of this study that the number of SIT sessions attended would provide the largest impact, whether a student was determined to be at risk by the standards set by the TWU SIT program and whether the student attended the minimum number of required SIT sessions were the variables most influential on success.Item Analyzing trends in baseball Hall of Fame voting, through the use of Multidimensional Scaling(1/1/2014) Porter, Kalli Cherie; Marshall, David; Falley, Brandi; Edwards, Don E.The purpose of this study was to see if any trends exist within voting on the baseball Hall of Fame ballot. For this particular study I used the mathematical concept called Multidimensional Scaling. This approach allowed me to visually see the difference between players in relation to the number of votes received. The majority of the data obtained for this study was through the Baseball Writers' Association of America website and the National Baseball Hall of Fame and Museum website. Through the use of Multidimensional Scaling and R programming, I was able to construct two dimensions within the voting on the ballot. It was decided that characteristics pertaining to certain players make an impact on the number of votes received.Item Bayesian learning on dependent features(12/30/2011) Bengfort, Eric; Navarra-Madsen, Junalyn; Hamner, Mark S.; Demuynck, Marie-Anne; Edwards, Don E.Bayesian Learning is a robust machine learning algorithm. In addition to working well with limited sample sizes, Bayesian Learning also provides a probabilistic categorization. The caveat of performing a Bayesian Analysis is that the features of Training Instances are typically assumed to be independent of each other. As a result, Bayesian Learning will "struggle" to properly classify Training Instances with dependent features. This paper proposes an extension to the Bayesian Learning Algorithm which is capable of overcoming this weakness. This newly proposed algorithm will create new candidates for Bayesian Classification by performing permutations upon the Original Training Data. It is hoped that this upstart algorithm will be applied to biological data sets to find the solution to an unsolved medical problem.Item Benford's law and humanly generated prices in auction houses and buyout systems of virtual worlds(1/1/2014) Endress, Megan Brooke; Marshall, David; Falley, Brandi; Wheeler, AnnThe purpose of this study was to analyze the buyout, or "buy now," prices in auction houses of virtual environments, such as World of Warcraft and Guild Wars 2. Human players interact with an auction house user interface in order to buy or sell in-game items, purchasable with in-game currency. Players wishing to sell items can post their items on the auction house for set lengths of time, as well as set a starting bid amount and/or an amount in which other players can instantly buy the item. Since the establishment of Benford's Law, it has been supported that data generated by humans typically does not follow Benford's Law, proving to be a beneficial tool in detecting fraudulent accounting data. However, this study shows that the leading significant digits of these buyout prices in virtual environments created by humans follow Benford's Law by utilizing Kuiper's goodness of fit V_n test, a modified Kolmogorov-Smirnov test.Item Challenges the airline industry faces at present(1/31/2019) Tran, Y Thi Thuy; Falley, BrandiThe competition among businesses operating in the airline industry has become highly intense. This has resulted in creating different types of obstacles for those organizations. For instance, companies are now required to invest large amounts of resources in marketing and promotion activities to attract more and more customers. The main aim of conducting the present study is to identify various issues faced by the airline industry. For the present study, the research has adopted an inductive approach focusing on general assumptions then comes to the specific and applies to the industry, the research has emphasis on selecting exploratory research design technique. The sample size for the present study is 101 respondents from more than 10 different airline companies at Dallas-Fort Worth airport in Dallas, Texas includes American Airlines, JetBlue Airways, Spirit Airlines, Delta Airlines, Frontier Airlines, United Airlines, Alaska Airlines, Sun Country Airlines, Korean Airlines, and Qatar Airlines. From the study carried out, it can be concluded that there are large number of issues and challenges that are being faced by the companies operating in the airline industry. At present, conducting smooth flow of all operations and activities is no longer an easy task for companies. Companies are not able to determine suitable strategies that can support in attracting new customers and retaining the old ones in every possible manner. It is recommended to the airline companies to carry out external analysis on a continuous basis through PESTLE (Political environment, Economic factors, Sociocultural factors, Technological changes, Legal issues, Environmental aspects) as through this it is possible for them to know the external challenges that affect business operations.Item Comparing discriminant analysis and linear regression analysis to predict the alcohol consumption by high school students(5/30/2017) Hamal, Tamanna; Marshall, David; Falley, Brandi; Edwards, Don E.The purpose of the study is to compare the Discriminant Analysis and Linear Regression Analysis to predict the correlation between alcohol consumption by high school students and their social attributes and grades. Discriminant Analysis, developed by R. A. Fisher in 1936, is a statistical technique used to determine which variables discriminate between two or more mutually exclusive naturally occurring groups. Linear Regression Analysis is the most widely used statistical technique where straight lines are fitted to patterns of data. In this model, the dependent variable, the variable of interest, is predicted from independent variables using a linear equation. Even though the earliest form of linear regression was the Method of Least Squares, which was published by Legendre in 1805, and by Gauss in 1809, the term regression was pioneered by Sir Francis Galton. Regression analysis is the process of finding out the relationship between one or more dependent variables and the independent variables.Item Curves: the history and development of solutions and applications of higher order polynominals(26/11/2014) Blackburn, Dana; Navarra-Madsen, Junalyn; Edwards, Don; Marshall, DavidThe purpose of this thesis is to explore algebraic curves, from definition and origination to development and technological / scientific application. A broad and oft-underappreciated topic, I will begin by exploring algebraic curves based on their degrees. Each chapter of my paper will be dedicated to an algebraic degree, beginning with 1st degree and concluding with 5th degree polynomials. In each chapter, we will look at the history and timeline of mathematical methods associated with that particular degree, along with a biography of major players in its discovery and subsequent achievements. The treatment of each degree will finalize with a look at technological and scientific achievements that can be, at least in part, attributed to the mathematics behind it. We will even observe that the rate of change of our technological growth almost seems to model the numeric growth of our topic; i.e., what began as a slow, almost constant rate of change (degree 1) with ancient societies has accelerated through the centuries (and indeed, millennia) to an exponential rate (degree 3). My work will conclude with a look at what potentially lies before us if our technology continues to grow at this rate.Item Data mining EPA's Green Vehicle Guide: Profiling and prediction using k-means clustering and neural networks(8/30/2012) Smith, Tera Daun; Demuynck, Marie-Anne; Edwards, Don E.; Marshall, David, Ph. D.This thesis is designed to study data mining techniques and explore the predictive value of data from the EPA's Green Vehicle Guide which supplies pertinent information regarding environmental performance for each vehicle sold in the United States from 2000 to 2010. Using IBM® SPSS® Modeler to discover patterns most advantageous to statistical analysis of the data set, each vehicle's various variables and scores in relation to emission and air quality and Smart Way status are modeled using two techniques, k-means clustering and the artificial neural networks. Predictions based on analysis of this data set are as expected with all models claiming greenhouse gas scores to be the greatest predictor variable for Smart Way status. Therefore, engineers' and companies' focus on better technology to improve greenhouse gas scores will be essential if Smart Way status and environmental consciousness is a goal.Item Dealing with missing data in the work environment at King Khalid University(9/8/2020) Asiri, Zahra; Falley, Brandi; Hamner, Mark S.; E. Edwards, Don; Demuynck, MarieThis study is about missing data mechanisms developed by Rubin (1976), including missing data completely at random, missing data at random, and missing data not at random. This study utilizes a scenario at King Khaled University where potential employees complete a Post-Graduate General Aptitude Test (PGGA) to represent techniques for handling missing data. There are both traditional methods of handling missing data and modern methods that are more sophisticated for subsequent analyses and offer specific advantages. This study will go through the process of imputing data to understand how to deal with missing data depending on the missing data mechanism. This study concludes by providing recommendations for handling missing data primarily through regression imputation and multiple imputation, which are exemplified through the researcher’s simulated data related to the PGGA and job performance. Strengths and limitations of different techniques are discussed.Item Dealing with missing data in the work environment at King Khalid University(9/8/2020) Asiri, Zahra; Falley, Brandi; Hamner, Mark S.; Edwards, Don E.; Demuynck, MarieThis study is about missing data mechanisms developed by Rubin (1976), including missing data completely at random, missing data at random, and missing data not at random. This study utilizes a scenario at King Khaled University where potential employees complete a Post-Graduate General Aptitude Test (PGGA) to represent techniques for handling missing data. There are both traditional methods of handling missing data and modern methods that are more sophisticated for subsequent analyses and offer specific advantages. This study will go through the process of imputing data to understand how to deal with missing data depending on the missing data mechanism. This study concludes by providing recommendations for handling missing data primarily through regression imputation and multiple imputation, which are exemplified through the researcher’s simulated data related to the PGGA and job performance. Strengths and limitations of different techniques are discussed.Item Differences in Google Analytics between Web 1.0 and Web 2.0: A case study(2009-08) Sun, Jui-Hao; Demuynck, Marie-Anne; Edwards, Don E.; Hamner, Mark S.This thesis is designed to study the field of Google Analytics and apply it to real-world projects—the official website of Texas Woman's University and MatrixZK. The science of Google Analytics includes storing and analyzing users' information for a specific web site. Google Analytics works completely with the official website of TWU (Web 1.0). For studying Web 2.0, the author designed and programmed MatrixZK; however, the contents category did not observe useful data. After several testing, the author added functions of Google Analytics API to MatrixZK in order to monitor visitors' actions in the Web 2.0 website.Item The discriminant — From a quadratic equation to dynamic nonlinear systems(2011-08) Triplett, Ann; Grigorieva, Ellina; Hamner, Mark S.Most mathematics students don't understand the potential of the discriminant. Usually discussed while learning the Quadratic Formula to solve quadratic equations, students learn its use for the classification of type and number of solutions for each equation being solved. Most students memorize the formula, identify the correct values for each variable, and successfully solve to find solutions for the equation, but few of them ever understand or appreciate the power of that piece of the formula called the discriminant. There are many additional applications for the discriminant, and I will explore these. In particular, I discuss the role of the discriminant in: · The Quadratic Formula · Solution of quadratic equations with parameters · Solving linear differential equations with constant coefficients · Investigating types of solutions for linear differential equations with variable coefficients · Applications in Number Theory to Diophantine equations · Classifying conic sections · Dynamic nonlinear systems.Item Dynamic and control of autoimmune disorder under radiation(6/6/2018) Mirsaleh Kohan, Leila; Grigorieva, Ellina; Navarra-Madsen, Junalyn; Edwards, Don E.Autoimmune diseases can be developed by exposure to radiation. Ionizing radiation modifies the immune system and diminishing its normal ability to fight diseases. The extents of the modifications depend on the dose rate and duration of radiation exposure. This work employs mathematical simulations of autoimmune process dynamics under chronic irradiation. We have constructed a mathematical model consisting of four non-linear differential equations. The variables used in the modeling are the concentration of target cells of the tissue, concentration of cytotoxic T-lymphocytes against given cells, the concentration of tissue-specific antigen formed during the destruction of the target cells, and the concentration of T-suppressor cortical thymus. Utilizing the MAPLE program, we will illustrate that autoimmune processes could be accelerated by low dose rate in long chronic irradiation.Item Elliptic curves and cryptography(12/30/2015) Win, Khing Zar; Navarra-Madsen, Junalyn; Zhang, Jian; Edward, Don E.Item Euler's Rotation Theorem: Rotating objects in 3-space(2014-08) Taylor, Kasie; Navarra-Madsen, Junalyn; Marshall, David; Edwards, Don E.The purpose of this thesis is to explore Euler's Rotation Theorem as it applies to the rotation of objects along various paths. Matrices can be used to represent these rotations along with the equation for a specific sphere. After these matrices are selected Maple programming will be used to calculate and further animate the rotation of a sphere (the earth) along an elliptical path, while another sphere (the moon) is rotating in a circular path around the first sphere. The computations in this paper were performed by using Maple TM. Maple is a trademark of Waterloo Maple Inc. These rotations and the matrices that are yielded are known as orthogonal matrices. Even more specifically they can be thought of as special orthogonal matrices. This thesis investigates the various properties of these rotational matrices along with the relationship between orthogonal matrices and special orthogonal matrices.Item Examining the properties of the standard comprehensive examination through the use of factor analysis and multidimensional scaling(5/30/2016) Almalaq, AmjadThe purpose of this study was to examine the properties of a departmental comprehensive examination in the course of Elementary Statistics-I (MATH 1703) as used by the Department of Mathematics & Computer Science in Texas Woman's University during the semesters Fall 2012 through Spring 2015. Item performance was assessed with standard discrimination and difficulty indices. Factor analysis and multidimensional scaling were used to assess construct validity from unique perspectives. Internal consistency reliability was defined with Cronbach’s alpha coefficient. The data and findings support use of the examination, while studies of predictive and concurrent validities remain to be done.Item An exploration of mathematical proofs(8/31/2016) Beimesch, JamesThe purpose of this thesis is to teach methods of proving statements in mathematics. We will be dissecting proven statements and examining the individual steps to gain a greater understanding on how to prove statements. Mathematical literature such as books, textbooks, and lecture notes will be used as our major sources of information.