Mathematics Commons^™

Calculus Iii (Ung), Hashim Saber, Beata Hebda, Piotr Hebda, Benkam Bobga

Mathematics Grants Collections

This Grants Collection for Calculus III was created under a Round Seven ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Number Theory: Niven Numbers, Factorial Triangle, And Erdos' Conjecture, Sarah Riccio

Mathematics Undergraduate Publications

In this paper, three topics in number theory will be explored: Niven Numbers, the Factorial Triangle, and Erdos's Conjecture . For each of these topics, the goal is for us to find patterns within the numbers which help us determine all possible values in each category. We will look at two digit Niven Numbers and the set that they belong to, the alternating summation of the rows of the Factorial Triangle, and the unit fractions whose sum is the basis of Erdos' Conjecture.

Understanding Natural Keyboard Typing Using Convolutional Neural Networks On Mobile Sensor Data, Travis Siems

Computer Science and Engineering Theses and Dissertations

Mobile phones and other devices with embedded sensors are becoming increasingly ubiquitous. Audio and motion sensor data may be able to detect information that we did not think possible. Some researchers have created models that can predict computer keyboard typing from a nearby mobile device; however, certain limitations to their experiment setup and methods compelled us to be skeptical of the models’ realistic prediction capability. We investigate the possibility of understanding natural keyboard typing from mobile phones by performing a well-designed data collection experiment that encourages natural typing and interactions. This data collection helps capture realistic vulnerabilities of the security …

Probabilistic Modeling Of Student Interactions During A Passing Period At The University Of Dayton, Allyson Pacifico

Honors Theses

The University of Dayton is composed of five colleges and schools: College of Arts and Sciences, School of Law, School of Business Administration, School of Education and Health Sciences, and School of Engineering. The University of Dayton is composed of about 11,000 students on campus who all have distinct class schedules and paths they take between their classes. In this study, I wanted to know the probability of meeting my friends with a different class schedule as I walk between classes. The data consisted of one to two students from each college, except for the School of Law, who documented …

A Computational Method For Solving A Class Of Fractional-Order Non-Linear Singularly Perturbed Volterra Integro-Differential Boundary-Value Problems, Mohammed M. A. Abuomar

Mathematical Sciences Theses

In this thesis, we present a computational method for solving a class of fractional singularly perturbed Volterra integro-differential boundary-value problems with a boundary layer at one end. The implemented technique consists of solving two problems which are a reduced problem and a boundary layer correction problem. The reproducing kernel method is used to the second problem. Pade’ approximation technique is used to satisfy the conditions at infinity. Existence and uniformly convergence for the approximate solution are also investigated. Numerical results provided to show the efficiency of the proposed method.

Mathematics In Contemporary Society - Chapter 1 (Spring 2018), 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.

Mathematics In Contemporary Society - Chapter 2 (Spring 2018), 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 Odd Lindley Burr Xii Model: Bayesian Analysis, Classical Inference And Characterizations, Mustafa Ç. Korkmaz, Haitham M. Yousof, Mahdi Rasekhi, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its statistical structural properties including ordinary and incomplete moments, quantile and generating function and order statistics are derived. The odd Lindley Burr XII density can be expressed as a simple linear mixture of BurrXII densities. Useful characterizations are presented. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed. …

Dynamics For A Random Differential Equation: Invariant Manifolds, Foliations, And Smooth Conjugacy Between Center Manifolds, Junyilang Zhao

Theses and Dissertations

In this dissertation, we first prove that for a random differential equation with the multiplicative driving noise constructed from a Q-Wiener process and the Wiener shift, which is an approximation to a stochastic evolution equation, there exists a unique solution that generates a local dynamical system. There also exist a local center, unstable, stable, centerunstable, center-stable manifold, and a local stable foliation, an unstable foliation on the center-unstable manifold, and a stable foliation on the center-stable manifold, the smoothness of which depend on the vector fields of the equation. In the second half of the dissertation, we show that any …

A New Family Of Topological Invariants, Nicholas Guy Larsen

Theses and Dissertations

We define an extension of the nth homotopy group which can distinguish a larger class of spaces. (E.g., a converging sequence of disjoint circles and the disjoint union of countably many circles, which have isomorphic fundamental groups, regardless of choice of basepoint.) We do this by introducing a generalization of homotopies, called component-homotopies, and defining the nth extended homotopy group to be the set of component-homotopy classes of maps from compact subsets of (0,1)ⁿ into a space, with a concatenation operation. We also introduce a method of tree-adjoinment for "connecting" disconnected metric spaces and show how this method can …

Subtraction Games: Range And Strict Periodicity, Bryce Emerson Blackham

Theses and Dissertations

In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.

Crystallographic Patterns In Philippine Indigenous Textiles, Ma. Louise Antonette N. De Las Peñas, Agnes Garciano, Debbie Marie Verzosa, Eduard C. Taganap

Mathematics Faculty Publications

The aim of this study was to analyze a representative sample of Philippine indigenous textiles in order to capture the range of symmetries and color symmetries present. This paper examines the existence of symmetries in finite designs, and classifies the plane-group and frieze-group symmetry types of the repeated patterns in woven textiles. The tendency of a particular symmetry to be more or less common than another can indicate relationships between the symmetries and the weaving technique or the culture that produced them. This paper will also examine designs and patterns with color symmetry found in these textiles. The sample consisted …

Volume 10, Taylor Hogg, Tiffany Carter, Brandyn Johnson, Haleigh James, Josh Baker, Tyler Cernak, Kirsten Bauer, Allie Snavely, Mary Zell Galen, Eric Powell, Thomas Wise, Katie Kinsey, Beth Barbolla, Maeleigh Ferlet, Rebecca Morra, Michala Day, Alexandra Evangelista, Max Flores, Harley Hodges, Clardene Jones, Harrison Samaniego, Jamesha Watson, Abby Gargiulo, Heather Green, Haley Klepatzki, Juan Guevara, Dani Bondurant, Michael Joseph Link Jr., Pamela Dahl, Maeve Losen, Charlotte Murphey

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Roger A. Byrne

An Analysis of Media Framing in Cases of Violence Against Women by Taylor Hogg

Writing in the Discipline of Nursing by Tiffany Carter

Photography by Brandyn Johnson

The Hidden Life of Beef Cattle: A Study of Cattle Welfare on Traditional Ranches and Industrial Farms by Haleigh James

Bloodworth's by Josh Baker and Tyler Cernak

Prosimians: Little Bodies, Big Significance by Kirsten Bauer

Skinformed by Allie Snavely

Coopertition and Gracious Professionalism: The Effects of First Robotics Folklore and Culture on the Stem Community by Mary Zell Galen

Tilt by Eric Powell And Thomas Wise

The Millennial …

Operator Semigroups Induced By First-Order Differential Equations, Amy Adair

Honors Capstones

No abstract provided.

Sonscreen Film Festival Awards/Student Awarded Prestigious Scholarship, Andrews University

World Changers Made Here

No abstract provided.

The Impact Of Khan Academy Math Remediation On Ninth Grade Student Achievement, Sandra Kelly

Doctoral Dissertations and Projects

The purpose of this quasi-experimental study was to determine if using Khan Academy as math remediation for fifteen minutes per day during a ninth grade Math I class would significantly affect student math achievement as measured by the North Carolina READY Math I End-of-Course Assessment. This quantitative study conducted at two rural high schools in West Virginia used remediation theory to make a comparison against a control population with the independent variable being grade level instruction only or grade level instruction plus math remediation using Khan Academy. The participants in the study included 131 ninth grade high school students taking …

A Mathematical Analysis Of The Game Of Chess, John C. White

Selected Honors Theses

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …

Edge Induced Weightings Of Uniform Hypergraphs And Related Problems, Laars C. Helenius

Dissertations

The starting point of the research is the so called 1-2-3 Conjecture formulated in 2004 by Karoński, Luczak, and Thomason. Roughly speaking it says that the edges of any graph can be weighted from {1, 2, 3} so that the induced vertex coloring (as the sum of weights adjacent to a given vertex) is proper. The conjecture has attracted a lot of interest from researchers over the last decade but is still unanswered. More recently, the conjecture has been studied for hypergraphs.

The main result of this dissertation shows in particular that an analogous conjecture holds for almost all uniform …

Webwork Problems For Openstax Introductory Statistics, Scott Kersey, Stephen Carden

Mathematics Ancillary Materials

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.

Webwork Problems For Openstax Calculus Volume I, Scott Kersey, Stephen Carden

Mathematics Ancillary Materials

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant.