Mathematics Commons^™

Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway

Theses, Dissertations and Culminating Projects

This study focuses on a teaching experiment with 33 six-graders in a Kearny public school in Hudson County, New Jersey, during the 2017-2018 academic year. More specifically, this study explored a) the types of tasks and tools that can be used to develop students’ covariational and correspondence reasoning in learning about shadows and b) the nature of students’ reasoning about covariation and correspondence relationships as students engage in the use of tools and tasks. The results showed that the simulation and the tasks I designed had the students engaged in the learning process. Students were able to reason about the …

Dedekind Sums: Properties And Applications To Number Theory And Lattice Point Enumeration, Oliver Meldrum

Honors Papers

In this paper, we will explore the origins, applications, and properties of these sums and one of their generalizations. We seek to explain what these sums represent and how they behave by exploring some of their arithmetic properties. In addition, we hope to show the reader why one should care about these sums. We do this by presenting two important areas in which these sums appear: number theory and the study of enumerating lattice points inside of polytopes.

Graded Quivers And B-Branes At Calabi-Yau Singularities, Cyril Closset, Sebastían Franco, Jirui Guo, Azeem Hasan

Publications and Research

A graded quiver with superpotential is a quiver whose arrows are assigned degrees c ∈ {0, 1, · · · , m}, for some integer m ≥ 0, with relations generated by a superpotential of degree m − 1. Ordinary quivers (m = 1) often describe the open string sector of D-brane systems; in particular, they capture the physics of D3-branes at local Calabi-Yau (CY) 3-fold singularities in type IIB string theory, in the guise of 4d N = 1 supersymmetric quiver gauge theories. It was pointed out recently that graded quivers with m = 2 and m …

Gallai-Ramsey Number For Classes Of Brooms, Benjamin J. Hamlin

College of Graduate Studies: Theses & Dissertations

Given a graph $G$, we consider the problem of finding the minimum number $n$ such that any $k$ edge colored complete graph on $n$ vertices contains either a rainbow colored triangle or a monochromatic copy of the graph $G$, denoted $gr_k(K_{3}:G)$. More precisely we consider $G=B_{m,\ell}$ where $B_{m,\ell}$ is a broom graph with $m$ representing the number of vertices on the handle and $\ell$ representing the number of bristle vertices. We develop a technique to reduce the difficulty of finding $gr_{k}(K_{3}:B_{m,\ell})$, and use the technique to prove a few cases with a fixed handle length, but arbitrarily many bristles. Further, …

Conflict Free Connectivity And The Conflict-Free-Connection Number Of Graphs, Travis D. Wehmeier

College of Graduate Studies: Theses & Dissertations

We explore a relatively new concept in edge-colored graphs called conflict-free connectivity. A conflict-free path is a (edge-) colored path that has an edge with a color that appears only once. Conflict-free connectivity is the maximal number of internally disjoint conflict-free paths between all pairs of vertices in a graph. We also define the c-conflict-free-connection of a graph G. This is the maximum conflict-free connectivity of G over all c-colorings of the edges of G. In this paper we will briefly survey the works related to conflict-free connectivity. In addition, we will use the probabilistic method to achieve a bound …

Inverse Problems Related To The Wiener And Steiner-Wiener Indices, Matthew Gentry

College of Graduate Studies: Theses & Dissertations

In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of $k$ vertices and take the sum, it is called the Steiner $k$-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value?

Preparing Pre-Service Teachers To Present At A State Conference, Heidi Eisenreich

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

As mathematics teacher educators, we have a responsibility to prepare as many people as we can, to teach mathematics in ways that foster a deeper understanding of the content. We do this by teaching current and future teachers in college programs and providing professional development to in-service teachers. A less explored way is to prepare these “students” to present ideas they have learned to colleagues at their school, other schools in their district, and conferences. In this paper, I share my experience of helping students go through the process of preparing to present over the last two years at our …

Positivity Among P-Partition Generating Functions Of Partially Ordered Sets, Nate Lesnevich

Honors Theses

We find necessary and separate sufficient conditions for the difference between two labeled partially ordered set's (poset) partition generating functions to be positive in the fundamental basis. We define the notion of a jump sequence for a poset and show how different conditions on the jump sequences of two posets are necessary for those posets to have an order relation in the fundamental basis. Our sufficient conditions are of two types. First, we show how manipulating a poset's Hasse diagram produces a poset that is greater according to the fundamental basis. Secondly, we also provide tools to explain posets that …

Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.

Perturbed Obstacle Problems In Lipschitz Domains: Linear Stability And Nondegeneracy In Measure, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rⁿ. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L¹-norm of perturbations in the data.

Utilizing Multi-Level Classification Techniques To Predict Adverse Drug Effects And Reactions, Victoria Puhl

Undergraduate Honors Thesis Collection

Multi-class classification models are used to predict categorical response variables with more than two possible outcomes. A collection of multi-class classification techniques such as Multinomial Logistic Regression, Na\"{i}ve Bayes, and Support Vector Machine is used in predicting patients’ drug reactions and adverse drug effects based on patients’ demographic and drug administration. The newly released 2018 data on drug reactions and adverse drug effects from U.S. Food and Drug Administration are tested with the models. The applicability of model evaluation measures such as sensitivity, specificity and prediction accuracy in multi-class settings, are also discussed.

Case–Control Research Study Of Auto-Brewery Syndrome, Barbara Jean Cordell, Anup Kanodia, Gregory K. Miller

Faculty Publications

Background: Auto-brewery syndrome (ABS), also known as Gut Fermentation Syndrome and Endogenous Ethanol Fermentation, is afflicting people worldwide, but little is known about ABS patients’ demographics, health history, lifestyle factors, and diet.

Method: We conducted a broad-based case–control survey study on 52 patients known to have a diagnosis of ABS and their household members. The research compares the symptomatic group (N ¼ 28) to the asymptomatic group (N ¼ 18) regarding lifestyle and health, diet, and medical history.

Results: With a response rate of 88% and using rank-sum tests, the data demonstrate that patients with ABS have …

A Limiting Process To Invert The Gauss-Radon Transform, Jeremy Becnel

Faculty Publications

In this work we extend the finite dimensional Radon transform [23] to the Gaussian measure. We develop an inversion formula for this GaussRadon transform by way of Fourier inversion formula. We then proceed to extend these results to the infinite dimensional setting.

Recovering A Random Variable From Conditional Expectations Using Reconstruction Algorithms For The Gauss Radon Transform, Jeremy Becnel, Daniel Riser-Espinoza

Faculty Publications

The Radon transform maps a function on n-dimensional Euclidean space onto its integral over a hyperplane. The fields of modern computerized tomography and medical imaging are fundamentally based on the Radon transform and the computer implementation of the inversion, or reconstruction, techniques of the Radon transform. In this work we use the Radon transform with a Gaussian measure to recover random variables from their conditional expectations. We derive reconstruction algorithms for random variables of unbounded support from samples of conditional expectations and discuss the error inherent in each algorithm.

Solving System Of Linear Integro-Differential Equations By Finite Integration Method With Shifted Chebyshev Polynomials, Matinee Juytai

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the finite integration method by using the shifted Chebyshev polynomial (FIM-SCP). The major tool of our FIM-SCP is the shifted Chebyshev integration matrix. It is constructed in order to be a matrix representation for integrating over interpolated points which are generated by the zeros of shifted Chebyshev polynomial of a certain degree. The efficiently numerical algorithms are then created by the modified FIM-SCP for seeking approximate solutions of a system of stiff linear ordinary differential equations, a system of linear Volterra integro-differential equations, and a system of linear Fredholm integro-differential equations under some given boundary …

Sub-Cloning, Expression, And Purification Of The Wild Type And Mutated Sigma-1 Receptor, Christopher Koch

Undergraduate Honors Thesis Collection

The Sigma-1 receptor (S1R) is an important pharmaceutical target that has been linked to several neurological diseases and drug addiction. It has been proposed that multimerization of S1R is important for attenuating its interactions with the dopamine transporter (DAT) and that S1R agonists promote dissociation to a monomeric form necessary for DAT interaction. This project aims to assess the role of the N-terminal transmembrane domain in oligomerization and binding activity of the mammalian Sigma-1 receptor (S1R). N-terminal truncations lacking the transmembrane domain and the E102Q variant, which displays altered activity and cellular localization, were expressed, purified in order to determine …

On A Generalization Of Lucas Numbers, Skylyn Olyvia Irby

Honors Theses

In this paper, we consider a generalization of Lucas numbers. Recall that Lucas numbers are the sequence of integers defined by the recurrence relation: L_n = L_{n−1} + L_{n−2} with the initial conditions L_1 = 1 and L_2 = 3(or L_0 = 1 and L_1 = 3 if the first subscript is zero). That is, the classical Lucas number sequence is 1, 3, 4, 7, 11, 18, .... The goal of the present paper is to study properties of certain generalizations of the Lucas sequence. In particular, we consider the following generalizations of the sequence: l_n = al_{n−1} + l_{n−2} …

6th-12th Grade Math Teachers And Their Experiences With The Mississippi College- And Career-Readiness Standards, Dorothy Reid

Honors Theses

This thesis identifies and describes 6th-12th grade math teachers and their experiences with the Mississippi College- and Career- Readiness Standards. There are two parts to this thesis: 1) a survey distributed to public school math teachers across the state and 2) the written thesis. In my thesis, I craft teacher narratives from the quantitative and qualitative results of the survey. Listening to the teachers’ narratives provides beneficial insights to the implementation of the MCCRS at the classroom level. Teachers have many different experiences. My thesis offers policy recommendations, based on the teacher narratives, to three levels of education: teachers, schools …

Cubic Rank Transmuted Modified Burr Iii Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. …

Characterizations Of Marshall-Olkin Discrete Reduced Modified Weibull Distribution, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Characterizing a distribution is an important problem in applied sciences, where an investigator is vitally interested to know if their model follows the right distribution. To this end, the investigator relies on conditions under which their model would follow specifically chosen distribution. Certain characterizations of the Marshall-Olkin discrete reduced modified Weibull distribution are presented to complete, in some way, their work.