Mathematics Commons^™

The Influence Of Dynamic Visualization On Undergraduate Calculus Learning, Julie Marie Skinner Sutton

Mathematics Dissertations - Archive

The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to earn such degrees motivates exploration of the appropriate use of technology that engages students in the first-year calculus classroom. Technology enhances our capacity to incorporate visualization into the teaching of mathematics, yet research suggests that high school mathematics students who prefer to visualize when solving mathematics tasks are not the “super stars” of their classrooms. In this qualitative study, nine students, five of whom prefer …

A Modeling Study In The Regulation Of Stress On Neuronal Plasticity, Pengcheng Xiao

Mathematics Dissertations - Archive

How stress can affect human cognitive functions has been a very popular topic for researchers from different fields including physiology, psychology, biology, neuroscience, and applied mathematics. Hypothalamic−pituitary−adrenal (HPA) axis plays an important role in response to stress by releasing hormones, and level of glucocorticoid has been widely considered to be one key factor to distinguish people with different stress disorder. Emerging evidence has shown that glucocorticoid act on glutamate neurotransmission system and consequently influences neuronal activities’s cognitive function. It changes in the glutamate release and induces synapse plasticity change. Spike-Timing Dependent Plasticity (STDP) is one of the important neuroscience foundations …

Nilpotent Lie Algebras And Nilmanifolds Constructed From Graphs, Allie Denise Ray

Mathematics Dissertations - Archive

The interaction between graph theory and differential geometry has been studied previously, but S. Dani and M. Mainkar brought a new approach to this study by associating a two-step nilpotent Lie algebra (and thereby a two-step nilmanifold) with a simple graph. We prsesent a new construction that associates a two-step nilpotent Lie algebra to an arbitrary (not necessarily simple) directed edge-labeled graph. We then use properties of a Schreier graph to determine necessary and sufficient conditions for this Lie algebra to extend to a three-step nilpotent Lie algebra.After considering the curvature of the two-step nilmanifolds associated with the graphs, we …

Determinantal Ideals From Symmetrized Skew Tableaux, Bill Robinson

Theses and Dissertations--Mathematics

We study a class of determinantal ideals called skew tableau ideals, which are generated by t x t minors in a subset of a symmetric matrix of indeterminates. The initial ideals have been studied in the 2 x 2 case by Corso, Nagel, Petrovic and Yuen. Using liaison techniques, we have extended their results to include the original determinantal ideals in the 2 x 2 case, as well as special cases of the ideals in the t x t case. In particular, for any skew tableau ideal of this form, we have defined an elementary biliaison between it and one …

Analysis And Constructions Of Subspace Codes, Carolyn E. Troha

Theses and Dissertations--Mathematics

Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …

Free Resolutions Associated To Representable Matroids, Nicholas D. Armenoff

Theses and Dissertations--Mathematics

As a matroid is naturally a simplicial complex, one can study its combinatorial properties via the associated Stanley-Reisner ideal and its corresponding free resolution. Using results by Johnsen and Verdure, we prove that a matroid is the dual to a perfect matroid design if and only if its corresponding Stanley-Reisner ideal has a pure free resolution, and, motivated by applications to their generalized Hamming weights, characterize free resolutions corresponding to the vector matroids of the parity check matrices of Reed-Solomon codes and certain BCH codes. Furthermore, using an inductive mapping cone argument, we construct a cellular resolution for the matroid …

Unimodality Questions In Ehrhart Theory, Robert Davis

Theses and Dissertations--Mathematics

An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal h^*-vector.Although various sufficient conditions have been found, necessary conditions remain a challenge. Highly-structured polytopes, such as the polytope of real doubly-stochastic matrices, have been proven to possess unimodal h^*-vectors, but the same is unknown even for small variations of it.

In this dissertation, we mainly consider two particular classes of polytopes: reflexive simplices and the polytope of symmetric real doubly-stochastic matrices. For the first class, we discuss an operation that preserves reflexivity, integral closure, and unimodality of the h^{* …}

Sobriety In Delta Not Sober, Joe Mashburn

Mathematics Faculty Publications

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

Multi-Term Linear Fractional Nabla Difference Equations With Constant Coefficients, Paul W. Eloe, Zi Ouyang

Mathematics Faculty Publications

We shall consider a linear fractional nabla (backward) fractional difference equation of Riemann–Liouville type with constant coefficients. We apply a transform method to construct solutions. Sufficient conditions in terms of the coefficients are given so that the solutions are absolutely convergent. The method is known for two-term fractional difference equations; the method is new for fractional equations with three or more terms. As a corollary, we exhibit new summation representations of a discrete exponential function, at, t = 0; 1; : : : .

Sixteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Riemannian Geometry (Abstract), Chikako Mese

Kenneth C. Schraut Memorial Lectures

Riemannian Geometry studies the geometry of curved spaces. It originated with the ideas of the Bernhard Riemann in the 19th century extending Gaussian geometry, or the study of geometry of curves and surfaces contained in 3 dimensional Euclidean space.

2015 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

The Graph Theory Origin Story (Abstract), Daniel Roberts

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Many research questions in pure mathematics arise from considerations of real world problems. Part of the job of a mathematician is to ask this type of question.

2015 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper

Theory & Applications of Graphs

The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from a recent paper of Amos, Caro, Davila and Pepper [2], while also answering an open problem posed by Meyer [9].

Spectral Theory For Gaussian Processes: Reproducing Kernels, Random Functions, Boundaries, And L2-Wavelet Generators With Fractional Scales, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by a host of applications, e.g., in mathematical physics, and in stochastic differential equations, and their use in financial models. In this paper, we show that, for three classes of cases in the correspondence, it is possible to obtain explicit formulas which are amenable to computations of the respective Gaussian stochastic processes. For achieving this, we first develop two functional analytic tools. They are: …

Formality And Informality In Cost-Benefit Analysis, Amy Sinden

Utah Law Review

Cost-benefit analysis (CBA) is usually treated as a monolith. In fact, the term can refer to a broad variety of decisionmaking practices, ranging from a qualitative comparison of pros and cons to a highly formalized and technical method grounded in economic theory that monetizes both costs and benefits, discounts to present net value, and locates the point at which the marginal benefits curve crosses the marginal costs curve. This article develops a typology that helps to conceptualize the multiple varieties of CBA along a formality-informality spectrum. It then uses this typology to analyze the treatment of CBA by the academic …

A Hamiltonian Approach To Wave-Current Interactions In Two-Layer Fluids, Adrian Constantin, Rossen Ivanov

Articles

We provide a Hamiltonian formulation for the governing equations describing the two-dimensional nonlinear interaction between coupled surfacewaves, internalwaves, and an underlying current with piecewise constant vorticity, in a two-layered fluid overlying a flat bed. This Hamiltonian structure is a starting point for the derivation of simpler models, which can be obtained systematically by expanding the Hamiltonian in dimensionless parameters. These enable an in-depth study of the coupling between the surface and internal waves, and how both these wave systems interact with the background current.

Will Oscillating Wave Surge Converters Survive Tsunamis?, Laura Cooke, P. Christodoulides, E. Renzi, T. Stefanakis, F. Dias

Articles

With an increasing emphasis on renewable energy resources, wave power technology is becoming one of the realistic solutions. However, the 2011 tsunami in Japan was a harsh reminder of the ferocity of the ocean. It is known that tsunamis are nearly undetectable in the open ocean but as the wave approaches the shore its energy is compressed, creating large destructive waves. The question posed here is whether an oscillating wave surge converter (OWSC) could withstand the force of an incoming tsunami. Several tools are used to provide an answer: an analytical 3D model developed within the framework of linear theory, …

A Cryptographic Attack: Finding The Discrete Logarithm On Elliptic Curves Of Trace One, Tatiana Bradley

Scripps Senior Theses

The crux of elliptic curve cryptography, a popular mechanism for securing data, is an asymmetric problem. The elliptic curve discrete logarithm problem, as it is called, is hoped to be generally hard in one direction but not the other, and it is this asymmetry that makes it secure.

This paper describes the mathematics (and some of the computer science) necessary to understand and compute an attack on the elliptic curve discrete logarithm problem that works in a special case. The algorithm, proposed by Nigel Smart, renders the elliptic curve discrete logarithm problem easy in both directions for elliptic curves of …

Modeling The Progress And Retention Of International Students Using Markov Chains, Lucas Gagne

Williams Honors College, Honors Research Projects

International students are a small and diverse student population present in any sizable American university. One of the greatest obstacles in their path is the acquisition of the English language. English for Academic Purposes (EAP) programs, such as the English Language Institute (ELI) at the University of Akron, attempt to address this problem. By studying how this student population progresses in their academic studies, EAP programs and their associated universities can make well-informed decisions on how best to serve their English Language Learners. One way to study International students is through the use of a Markov model based on university …

Mathematics In Contemporary Society Chapter 4, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11 …

The Unimodality Of Pure O-Sequences Of Type Two In Four Variables, Bernadette Boyle

Mathematics Faculty Publications

Since the 1970's, great interest has been taken in the study of pure O-sequences, which, due to Macaulay's theory of inverse systems, have a bijective correspondence to the Hilbert functions of Artinian level monomial algebras. Much progress has been made in classifying these according to their shape. Macaulay's theorem immediately gives us that all Artinian algebras in two variables have unimodal Hilbert functions. Furthermore, it has been shown that all Artinian level monomial algebras of type two in three variables have unimodal Hilbert functions. This paper will classify all Artinian level monomial algebras of type two in four variables into …

Pure Injective And *-Pure Injective Lca Groups, Peter Loth

Mathematics Faculty Publications

No abstract provided.

The Logical System Of Frege’S Grundgesetze : A Rational Reconstruction, Méven Cadet, Marco Panza

MPP Published Research

This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze . We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

Pruebas Entimemáticas Y Pruebas Canónicas En La Geometría Plana De Euclides, Marco Panza, Abel Lassalle Casanave

MPP Published Research

Dado que la aplicación del Postulado I.2 no es uniforme en Elementos, ¿de qué manera debería ser aplicado en la geometría plana de Euclides? Además de legitimar la pregunta misma desde la perspectiva de una filosofía de la práctica matemática, nos proponemos esbozar una perspectiva general de análisis conceptual de textos matemáticos que involucra una noción ampliada de la teoría matemática como sistema de autorizaciones o potestades y una noción de prueba que depende del auditorio.

Since the application of Postulate I.2 in the Elements is not uniform, one could wonder in what way should it be applied in Euclid’s …

Comparative Analysis Of Various Continuous-Time Deterministic Models Of Tumor-Immune Interactions, Robert Paul Childress

Mathematics Theses - Archive

Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 alone \cite{CDC},obtaining as complete an understanding as possible of cancer is obviously necessitated.I investigate deterministic ordinary differential equation models of increasingcomplexity simulating avascular tumor growth and interactions with the innate immuneresponse. After first establishing a baseline of tumor growth limited only by theavailability of local nutrients, I compare the effects on said growth of the nativeimmune system response, chemotherapy, immunotherapy, and various combinations ofthe aforementioned …

Some Multivariate Process Capability Indices, Rachel Lee Goodwin

Mathematics Dissertations - Archive

Process capability indices (PCIs) play an important role in the field of Statistical Process Control. Prior to the last 25 years, PCIs had been formulated to assess the quality of a single product characteristic. Product quality, however, is typically dependent on several related variables. Therefore, there is a great need for multivariate process capability indices (MPCIs). The quality of a product is almost always determined from sample data. Thus, it is imperative that an MPCI has a corresponding confidence interval. In that way, conclusions may be drawn regarding the capability of the process that makes that product. Of the MPCIs …

Numerical Solutions Of American Options With Dividends Using Finite Difference Methods, Nsoki Mavinga, Chi Zhang , '15

Mathematics & Statistics Faculty Works

We study the Black-Scholes model for American options with dividends. We cast the problem as a free-boundary problem for heat equations and use transformations to rewrite the problem in linear complementarity form. We use explicit and implicit finite difference methods to obtain numerical solutions. We implement and test the methods on a particular example in MATLAB. The effects of dividend payments on option pricing are also considered.

Positivity Of Equivariant Gromov–Witten Invariants, D. Anderson, Linda Chen

Mathematics & Statistics Faculty Works

We show that the equivariant Gromov–Witten invariants of a projective homogeneous space G/P exhibit Graham-positivity: when expressed as polynomials in the positive roots, they have nonnegative coefficients.