Mathematics Commons^™

Preservice Mathematics Teachers' Conceptions And Enactments Of Modeling Standards, Hyunyi Jung, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics [CCSSM] included Model with Mathematics as one of the Standards for Mathematical Practices [SMP] and a modeling strand in the high school standards. This common aspect of standards across most states in the U.S. intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers [PSTs] who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their …

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iv, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.

A Logistic Regression Analysis Of First-Time College Students’ Completion Rates At The University Of Southern Mississippi, Jesse Homer Robinson

Honors Theses

The demand for employees with a college degree is steadily on the rise in a plethora of competitive job markets throughout the United States. This increase in demand has aided in the increasing college enrollment rates throughout the country. However, unlike enrollment trends, the rate of college completion has not had the same fortunate rise.

The goal of this study is to research and compare differences among those first-time college students who completed college within four years, six years, or did not complete. The primary source for data in this study was the Office of Institutional Research at USM. Both …

Statistical Analysis Of Short-Time Option Prices Based On A Levy Model, Weiliang Wang

Arts & Sciences Graduate Student Theses and Dissertations

The Black-Scholes model has been widely used to find the prices of option, while several generalizations have been made due to its limitation. In this thesis, we consider one of the generalizations---the exponential Levy model with a mixture of CGMY process and Brownian motion. We state the main results of the first-, second- and third-order expansions for close-to-the-money call option prices under this model. Using importance sampling based on Monte Carlo method, a dataset of call option prices can be simulated. Comparing the simulated true prices with the three different order approximations, we find that the higher-order approximation is more …

Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch

Electronic Theses and Dissertations

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work …

Creating A More Efficient Course Schedule At Uno Department O Economics And Finance Using Linear Optimization, Tien Dinh

Senior Honors Theses

In 2012, Wormald R. & Guimond C. developed a mathematical model utilizing integer linear programming and network flow to help Worchester Polytechnic Institute (WPI) create a more efficient course schedule. Course scheduling was a major problem at WPI in 2012, as the manual process at that time often resulted in courses being assigned to inappropriate (too large or too small) classrooms. The University of New Orleans (UNO) is facing a similar challenge, as the current scheduling system at UNO does not always produce efficient course schedules. The goal of this thesis, therefore, is to improve upon the 2012 model by …

Resolutions Of Finite Length Modules Over Complete Intersections, Seth Lindokken

Department of Mathematics: Dissertations, Theses, and Student Research

The structure of free resolutions of finite length modules over regular local rings has long been a topic of interest in commutative algebra. Conjectures by Buchsbaum-Eisenbud-Horrocks and Avramov-Buchweitz predict that in this setting the minimal free resolution of the residue field should give, in some sense, the smallest possible free resolution of a finite length module. Results of Tate and Shamash describing the minimal free resolution of the residue field over a local hypersurface ring, together with the theory of matrix factorizations developed by Eisenbud and Eisenbud-Peeva, suggest analogous lower bounds for the size of free resolutions of finite length …

Properties And Convergence Of State-Based Laplacians, Kelsey Wells

Department of Mathematics: Dissertations, Theses, and Student Research

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different …

Black Students White Teachers: An Autoethnographic Analysis, Julie Harnett

Renée Crown University Honors Thesis Projects - All

This paper explores the many factors at play in a classroom and how they impact students of non-white identities. Embedded with thought experiments for you to analyze your schooling experience, the paper calls to recognition the imbalanced treatment of students based upon individual demographic profiles. This paper calls particular attention to how teachers perceive students and how this manifests itself in disciplinary practices and tracking. This relates to an analyzes the school-to-prison pipeline and links to other forms of school segregation. The paper also calls into consideration the educational experiences of the author and how they were shaped by the …

Discrete Time Risk Models With Random Premiums, Llewellyn Hillyer Smith

Mathematics Dissertations - Archive

Over the past century insurance companies relied to a large extent on the continuous time Mathematical Risk Model proposed by Lundberg, known for its ability to estimate the probability of ruin(capital reserve falling below zero), given the initial capital, linear premium rate and cumulative random size claims occurring at random times. In this Dissertation we introduce a discrete time risk model that allows random premiums, and derive the estimates of the ruin probabilities on both finite and infinite time horizons. Tools applied are drawn from modern probability and include,Martingales, Invariance Principle for Brownian motions, and Large Deviation Principle for the …

Affine And Projective Planes, Abraham Pascoe

Graduate Theses/Dissertations

In this thesis, we investigate affine and projective geometries. An affine geometry is an incidence geometry where for every line and every point not incident to it, there is a unique line parallel to the given line. Affine geometry is a generalization of the Euclidean geometry studied in high school. A projective geometry is an incidence geometry where every pair of lines meet. We study basic properties of affine and projective planes and a number of methods of constructing them. We end by prov- ing the Bruck-Ryser Theorem on the non-existence of projective planes of certain orders.

The Average Measure Of A K-Dimensional Simplex In An N-Cube, John A. Carter

Graduate Theses/Dissertations

Within an n-dimensional unit cube, a number of k-dimensional simplices can be formed whose vertices are the vertices of the n-cube. In this thesis, we analyze the average measure of a k-simplex in the n-cube. We develop exact equations for the average measure when k = 1, 2, and 3. Then we generate data for these cases and conjecture that their averages appear to approach n^k/2 times some constant. Using the convergence of Bernstein polynomials and a k-simplex Bernstein generalization, we prove the conjecture is true for the 1-simplex and 2-simplex cases. We then develop a generalized formula for …

Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon

Mathematics, Physics, and Computer Science Faculty Articles and Research

The class of nonassociative right hoops, or narhoops for short, is defined as a subclass of right-residuated magmas, and is shown to be a variety. These algebras generalize both right quasigroups and right hoops, and we characterize the subvarieties in which the operation x ^^ y = (x/y)y is associative and/or commutative. Narhoops with a left unit are proved to be integral if and only if ^ is commutative, and their congruences are determined by the equivalence class of the left unit. We also prove that the four identities defining narhoops are independent.

Secure Multiparty Protocol For Differentially-Private Data Release, Anthony Harris

Boise State University Theses and Dissertations

In the era where big data is the new norm, a higher emphasis has been placed on models which guarantees the release and exchange of data. The need for privacy-preserving data arose as more sophisticated data-mining techniques led to breaches of sensitive information. In this thesis, we present a secure multiparty protocol for the purpose of integrating multiple datasets simultaneously such that the contents of each dataset is not revealed to any of the data owners, and the contents of the integrated data do not compromise individual’s privacy. We utilize privacy by simulation to prove that the protocol is privacy-preserving, …

Particular Solutions Of Products Of Helmholtz-Type Equations Using The Matern Function, Xiao-Yan Liu, Ching-Shyang Chen, Wen Li, Ming Li

Faculty Publications

We derive closed-form particular solutions for Helmholtz-type partial differential equations. These are derived explicitly using the Matern basis functions. The derivation of such particular solutions is further extended to the cases of products of Helmholtz-type operators in two and three dimensions. The main idea of the paper is to link the derivation of the particular solutions to the known fundamental solutions of certain differential operators. The newly derived particular solutions are used, in the context of the method of particular solutions, to solve boundary value problems governed by a certain class of products of Helmholtz-type equations. The leave-one-out cross validation …

An Explicit Formula For Dirichlet's L-Function, Shannon Michele Hyder

Honors Theses

The Riemann zeta function has a deep connection to the distribution of primes. In 1911 Landau proved that, an explicit formula where ρ = β + iγ denotes a complex zero of the zeta function and Λ(x) is an extension of the usual von Mangoldt function, so that Λ(x) = log p if x is a positive integral power of a prime p and Λ(x) = 0 for all other real values of x. Landau’s remarkable explicit formula lacks uniformity in x and therefore has limited applications to the theory of the zeta function. In 1993 Gonek proved a version …

Magic Squares Of Cubes Modulo A Prime Number, Yevgeniy Sokolovskiy

Theses, Dissertations and Culminating Projects

This work is dedicated to the properties of the 3 × 3 magic squares of cubes modulo a prime number. Its central concept is the number of distinct entries of these squares and the properties associated with this number. We call this number the degree of a magic square. The necessary conditions for the magic square of cubes with degrees 3, 5, 7, and 9 are examined. It was established that there are infinitely many primes for which magic squares of cubes with degrees 3, 5, 7, and 9 exist. I apply n-tuples of consecutive cubic residues to prove that …

The Kumaraswamy Marshall-Olkin Log-Logistic Distribution With Application, Selen Cakmakyapan, Gamze Ozel, Yehia Mousa Hussein El Gebaly, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such as the Marshall-Olkin log-logistic, log-logistic, lomax, Pareto type II and Burr XII distributions. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary moments, skewness, kurtosis are derived. The maximum likelihood estimators of the unknown parameters are obtained. The importance and flexibility of the new model is proved empirically …

High Cognitive Demand Examples In Precalculus: Examining The Work And Knowledge Entailed In Enactment, Erica R. Miller

Department of Mathematics: Dissertations, Theses, and Student Research

Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a three-part study. To answer my research questions, I conducted classroom observations as well as pre- and post-observation interviews with seven graduate student instructors at a large public R1 university in the …

Graphs With Few Spanning Substructures, Jessica De Silva

Department of Mathematics: Dissertations, Theses, and Student Research

In this thesis, we investigate a number of problems related to spanning substructures of graphs. The first few chapters consider extremal problems related to the number of forest-like structures of a graph. We prove that one can find a threshold graph which contains the minimum number of spanning pseudoforests, as well as rooted spanning forests, amongst all graphs on n vertices and e edges. This has left the open question of exactly which threshold graphs have the minimum number of these spanning substructures. We make progress towards this question in particular cases of spanning pseudoforests.

The final chapter takes on …