Mathematics Commons^™

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 …

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.

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 …

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, …

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 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 …

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. …

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.

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.

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.

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.

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 …