## ASU Electronic Theses and Dissertations

Contributor
Subject
Date Range
2010 2017

This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between graph C*-algebras and fractal geometry. In this work, this theorem is extended from ordinary directed graphs to higher-rank graphs. Second, a characterization is given of the Cuntz-Pimsner algebra associated to a tensor product of C*-correspondences. This is a generalization of a result by Kumjian about graphs algebras. This second result is applied to several important special cases of Cuntz-Pimsner algebras including topological graph algebras, crossed products by the integers and crossed products by completely positive maps. The result has ...

Contributors
Morgan, Adam, Kaliszewski, Steven, Quigg, John, et al.
Created Date
2016

The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children. The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem ...

Contributors
Cavanagh, Mary C., Greenes, Carole E, Buss, Ray, et al.
Created Date
2016

A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet ...

Contributors
Merrill, Brandon Earl, Peet, Yulia, Herrmann, Marcus, et al.
Created Date
2016

The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem. This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a ...

Contributors
Treat, Kevin, Fishel, Susanna, Czygrinow, Andrzej, et al.
Created Date
2016

In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$-eigenspace component of the $p$-Sylow subgroup of the class group of the field at the $m$-th level in a $\mathbb{Z}_p$-extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}-1,f(T,\omega^{1-i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us ...

Contributors
Elledge, Shawn Michael, Childress, Nancy, Bremner, Andrew, et al.
Created Date
2013

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using ...

Contributors
Johnson, Jeffrey Ivan, Middleton, James A, Marsh, Josephine P, et al.
Created Date
2016

This study is a narrative inquiry into teachers' and instructional coaches' experiences of new curriculum policy implementation at the classroom and district levels. This study took place during the initial year of implementation of the third grade Common Core State Standards in Mathematics (CCSSM). Interviews were conducted with individuals directly involved in policy implementation at the classroom level, including several teachers and the school's instructional coach. Observations of the teachers' instruction and professional practice were also conducted. As an embedded researcher, I used this data to create a series of fictionalized narratives of the initial policy implementation experience. My analysis ...

Contributors
Frankiewicz, Megan, Powers, Jeanne, Fischman, Gustavo, et al.
Created Date
2015

Reprising the work of Kolpakov and Martelli, a manifold is constructed by face pairings of a four dimensional polytope, the 24-cell. The resulting geometry is a single cusped hyperbolic 4-manifold of finite volume. A short discussion of its geometry and underlying topology is included. Dissertation/Thesis

Contributors
Abram, Christopher Robert, Paupert, Julien, Kawski, Mattias, et al.
Created Date
2014

This thesis focuses on sequencing questions in a way that provides students with manageable steps to understand some of the fundamental concepts in discrete mathematics. The questions are aimed at younger students (middle and high school aged) with the goal of helping young students, who have likely never seen discrete mathematics, to learn through guided discovery. Chapter 2 is the bulk of this thesis as it provides questions, hints, solutions, as well as a brief discussion of each question. In the discussions following the questions, I have attempted to illustrate some relationships between the current question and previous questions, explain ...

Contributors
Bell, Stephanie, Fishel, Susana, Hurlbert, Glenn, et al.
Created Date
2014

Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. ...

Contributors
Jones, Kimberly, Tang, Wenbo, Kang, Yun, et al.
Created Date
2015

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries.