Mathematics & Computer Sciences
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Ray tracing in 3D graphics
(200012)The purpose of the study is to analyze the properties and functions of ray tracing, and to describe realistic 3D graphics applications. Ray tracing can be described as a global illumination based rendering method. Rays of ... 
Modeling autoimmune disease with differential equations
(20181003)In this project, I will build a mathematical model of a developed autoimmune process considering cell autoimmunity that plays the main role in any autoimmune disorder using a system of three nonlinear differential equations. ... 
The inverse problem to the Voronoi diagram
(200705)The primary purpose of this thesis is to address the problem of solving the Inverse Problem for the Voronoi Diagram where the Inverse Problem is: Given a diagram that is in fact a Voronoi Diagram find the set of points X ... 
Making the grade: A study of academic success
(201312)Freshmen account for more than fifty percent of students who drop out before completing their degree, which means that increasing the success rates for freshmen is a critical challenge for many colleges and universities. ... 
Euler's Rotation Theorem: Rotating objects in 3space
(201408)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. ... 
Challenges the airline industry faces at present
(20190131)The 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 ... 
A polychotomous, multivariate regression model predicting performance level in a core mathematics course
(200812)Enrolling students in a mathematics course commensurate with their performance ability is of great importance to mathematics departments at all institutions of higher learning. This research will utilize preexisting ... 
Mathematics behind Google's PageRank algorithm
(20180828)Google has become a name synonymous with web searching, to the point where Merriam Webster defines google as “verb: to use the Google search engine to obtain information about (someone or something) on the World Wide Web.” ... 
Statistical package utilizing the general linear model for R
(20180628)The purpose of this thesis is to formulate a statistical package for the program R. This package will utilize matrices for ease of calculation to make use of the general linear model to provide meaningful data. With this ... 
Using a statistical model to predict student success in Texas Woman's University mathematics program
(20180723)Admission applications from high school students are received yearly by colleges but majority of the students that are being admitted eventually do not graduate. Colleges need to base their admission requirements on some ... 
Inverting a positive definite matrix: A comparative study of two algorithms
(199912)The purpose of the paper is to investigate the efficiency of two matrixinverting algorithms that are restricted to positive definite matrices. The selected algorithms are a GuassJordan method and a gradient projection ... 
Differences in Google Analytics between Web 1.0 and Web 2.0: A case study
(200908)This thesis is designed to study the field of Google Analytics and apply it to realworld projects—the official website of Texas Woman's University and MatrixZK. The science of Google Analytics includes storing and analyzing ... 
Using data mining techniques to identify “the best” operational patterns for enrollment modeling
(200908)For any Educational Institution it is very important to know the number of new students and the number of returning students. Based on these numbers, there could be conducted predictions of the budget that the institution ... 
The discriminant — From a quadratic equation to dynamic nonlinear systems
(201108)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 ... 
A theoretical relationship between mathematics and mechanics
(201305)Classical mathematics began during the Egyptian and Babylonian time and solved problems analytically with no proof of theories being performed. In the late eighteenth century, theoretical problems began emerging into ... 
A longitudinal analysis using auxiliary information to model retention in undergraduate students
(200812)Attrition is an issue for colleges and universities, and attempts to retain students are becoming more and more difficult. This study focuses on predicting student attrition of first time incoming (FTIC) students over a ... 
Modeling symbiosis by a LotkaVolterratype system of differential equations
(201305)Biological symbiosis is necessary for life on earth. However, population based models of symbiosis are rare in literature. One problem is defining symbiosis, and whether is includes mutualism, commensalism and parasitism, ... 
Finite inductive sequence: Factoring technique
(199712)This thesis considers finite sequences of symbols extracted from an alphabet set. In this case, the alphabet set is the positive integers. The underlying hypotheses is that such finite sequence is finitely inductive (FI). ... 
A propositional calculus: Based on the Łukasiewicz's system
(200612)In Symbolic Logic, 5th Ed., by Irving M. Copi (Copi, 1979), there is a problem asking for the proof of the independence of each axiom from a set of axioms for a propositional calculus. This problem reads: 4. The Łukasiewicz's ... 
Optimal control of a biological wastewater treatment plant
(200905)In this paper a mathematical model of a biological waste cleaning plant is created and investigated. The model is described by a nonlinear system of two differential equations with one bounded control. An optimal control ...