Physical Sciences and Mathematics Commons^™

Student Help-Seeking Behaviors And Teacher Instructional Practices: Examining Their Relationship With U.S. Student Mathematics Achievement, Michael C. Osborne

Theses and Dissertations--Curriculum and Instruction

Even though the United States (U.S.) spends, on average, more money per student than most Organisation for Economic Co-operation and Development (OECD) countries, it continues to lag behind its international peers in mathematics achievement. This study, which responded to the call for educational reforms that improve the mathematics achievement of U.S. students, aimed to examine the issue of student help-seeking behaviors and teacher instructional practices as they interact to affect student mathematics achievement. The Programme for International Student Assessment (PISA) defines student help-seeking behaviors as the ways in which students have a propensity to depend on the knowledge and intellect …

The Use Of 3-D Highway Differential Geometry In Crash Prediction Modeling, Kiriakos Amiridis

Theses and Dissertations--Civil Engineering

The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representation of the roadway surface have also been explored in the past aiming to …

Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments, Karthik Chandrasekhar

Theses and Dissertations--Mathematics

A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the ( …

Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle

Theses and Dissertations--Mathematics

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable.

To regularize the reconstruction, Astala et al. employ a high frequency …

An Inverse Eigenvalue Problem For The Schrödinger Equation On The Unit Ball Of R3, Maryam Ali Al Ghafli

Theses and Dissertations--Mathematics

The inverse eigenvalue problem for a given operator is to determine the coefficients by using knowledge of its eigenfunctions and eigenvalues. These are determined by the behavior of the solutions on the domain boundaries. In our problem, the Schrödinger operator acting on functions defined on the unit ball of $\mathbb{R}^3$ has a radial potential taken from $L^2_{\mathbb{R}}[0,1].$ Hence the set of the eigenvalues of this problem is the union of the eigenvalues of infinitely many Sturm-Liouville operators on $[0,1]$ with the Dirichlet boundary conditions. Each Sturm-Liouville operator corresponds to an angular momentum $l =0,1,2....$. In this research we focus on …

Undergraduate Mathematics Students’ Connections Between Their Group Homomorphism And Linear Transformation Concept Images, Jeffrey Slye

Theses and Dissertations--Mathematics

It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or …

Ε-Superposition And Truncation Dimensions In Average And Probabilistic Settings For ∞-Variate Linear Problems, Jonathan M. Dingess

Theses and Dissertations--Computer Science

This thesis is a representation of my contribution to the paper of the same name I co-author with Dr. Wasilkowski. It deals with linear problems defined on γ-weighted normed spaces of functions with infinitely many variables. In particular, I describe methods and discuss results for ε-truncation and ε-superposition methods. I show through these results that the ε-truncation and ε-superposition dimensions are small under modest error demand ε. These positive results are derived for product weights and the so-called anchored decomposition.

Equivalence Of Classical And Quantum Codes, Tefjol Pllaha

Theses and Dissertations--Mathematics

In classical and quantum information theory there are different types of error-correcting codes being used. We study the equivalence of codes via a classification of their isometries. The isometries of various codes over Frobenius alphabets endowed with various weights typically have a rich and predictable structure. On the other hand, when the alphabet is not Frobenius the isometry group behaves unpredictably. We use character theory to develop a duality theory of partitions over Frobenius bimodules, which is then used to study the equivalence of codes. We also consider instances of codes over non-Frobenius alphabets and establish their isometry groups. Secondly, …

The State Of Lexicodes And Ferrers Diagram Rank-Metric Codes, Jared E. Antrobus

Theses and Dissertations--Mathematics

In coding theory we wish to find as many codewords as possible, while simultaneously maintaining high distance between codewords to ease the detection and correction of errors. For linear codes, this translates to finding high-dimensional subspaces of a given metric space, where the induced distance between vectors stays above a specified minimum. In this work I describe the recent advances of this problem in the contexts of lexicodes and Ferrers diagram rank-metric codes.

In the first chapter, we study lexicodes. For a ring R, we describe a lexicographic ordering of the left R-module Rⁿ. With this …

Lattice Simplices: Sufficiently Complicated, Brian Davis

Theses and Dissertations--Mathematics

Simplices are the "simplest" examples of polytopes, and yet they exhibit much of the rich and subtle combinatorics and commutative algebra of their more general cousins. In this way they are sufficiently complicated --- insights gained from their study can inform broader research in Ehrhart theory and associated fields.

In this dissertation we consider two previously unstudied properties of lattice simplices; one algebraic and one combinatorial. The first is the Poincar\'e series of the associated semigroup algebra, which is substantially more complicated than the Hilbert series of that same algebra. The second is the partial ordering of the elements of …

Boundary Layers In Periodic Homogenization, Jinping Zhuge

Theses and Dissertations--Mathematics

The boundary layer problems in periodic homogenization arise naturally from the quantitative analysis of convergence rates. Formally they are second-order linear elliptic systems with periodically oscillating coefficient matrix, subject to periodically oscillating Dirichelt or Neumann boundary data. In this dissertation, for either Dirichlet problem or Neumann problem, we establish the homogenization results and obtain the nearly sharp convergence rates, provided the domain is strictly convex. Also, we show that the homogenized boundary data is in W^1,p for any p ∈ (1,∞), which implies the C^α-Hölder continuity for any α ∈ (0,1).