# Mathematics Commons™

## All Articles in Mathematics

11511 full-text articles. Page 1 of 302.

2016 Western Michigan University

#### The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

##### Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

2016 California State University - San Bernardino

#### Bio-Mathematics: Introduction To The Mathematical Model Of The Hepatitis C Virus, Lucille J. Durfee

##### Electronic Theses, Projects, and Dissertations

In this thesis, we will study bio-mathematics. We will introduce differential equations, biological applications, and simulations with emphasis in molecular events. One of the first courses of action is to introduce and construct a mathematical model of our biological element. The biological element of study is the Hepatitis C virus. The idea in creating a mathematical model is to approach the biological element in small steps. We will first introduce a block (schematic) diagram of the element, create differential equations that define the diagram, convert the dimensional equations to non-dimensional equations, reduce the number of parameters, identify the important parameters ...

2016 Washington University in St. Louis

#### A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with ...

An Introduction To Boolean Algebras, 2016 California State University - San Bernardino

#### An Introduction To Boolean Algebras, Amy Schardijn

##### Electronic Theses, Projects, and Dissertations

This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures ...

Regular Round Matroids, 2016 California State University - San Bernardino

#### Regular Round Matroids, Svetlana Borissova

##### Electronic Theses, Projects, and Dissertations

A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we give ...

Planar Graphs, Biplanar Graphs And Graph Thickness, 2016 California State University - San Bernardino

#### Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon

##### Electronic Theses, Projects, and Dissertations

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.

2016 University of Tennessee, Chattanooga

#### Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little

##### Honors Theses

Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes ...

Newton’S Third Law In Karmic Warfare, 2016 Claremont Colleges

#### Newton’S Third Law In Karmic Warfare, Kazmier Maślanka

##### The STEAM Journal

A work entitled "Newton's Third Law in Karmic Warfare" is a mathematical visual poem which is a perfect example of a technique, that I call The Paradigm Poem. This piece makes a direct connection with the concept of karma and Newton’s Third Law of motion. I will introduce the concept of “The Mathematical Paradigm Poem” to illuminate an example of how metaphor is used in mathematical visual poetry. I will also discuss much of the process in making this aesthetic expression.

Foundations Of Wave Phenomena, 2016 Department of Physics, Utah State University

#### Foundations Of Wave Phenomena, Charles G. Torre

##### Charles G. Torre

This is an undergraduate text on the mathematical foundations of wave phenomena. Version 8.2.

Density-Dependent Leslie Matrix Modeling For Logistic Populations With Steady-State Distribution Control, 2016 Western Kentucky University

#### Density-Dependent Leslie Matrix Modeling For Logistic Populations With Steady-State Distribution Control, Bruce Kessler, Andrew Davis

##### Bruce Kessler

The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity (see [1], [2], [4], [5], and [6]), with mixed results. In this paper we provide a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and the desired steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same ...

2016 Poly-disciplinary Faculty of Safi

#### Controllability And Nonsingular Solutions Of Sylvester Equations, Hamid Maarouf

##### Electronic Journal of Linear Algebra

The singularity problem of the solutions of some particular Sylvester equations is studied. As a consequence of this study, a good choice of a Sylvester equation which is associated to a linear continuous time system can be made such that its solution is nonsingular. This solution is then used to solve an eigenstructure assignment problem for this system. From a practical point view, this study can also be applied to automatic control when the system is subject to input constraints.

Potentially Nilpotent Tridiagonal Sign Patterns Of Order 4, 2016 North University of China

#### Potentially Nilpotent Tridiagonal Sign Patterns Of Order 4, Yubin Gao, Yanling Shao

##### Electronic Journal of Linear Algebra

An $n\times n$ sign pattern ${\cal A}$ is said to be potentially nilpotent (PN) if there exists some nilpotent real matrix $B$ with sign pattern ${\cal A}$. In [M.~Arav, F.~Hall, Z.~Li, K.~Kaphle, and N.~Manzagol.Spectrally arbitrary tree sign patterns of order $4$, {\em Electronic Journal of Linear Algebra}, 20:180--197, 2010.], the authors gave some open questions, and one of them is the following: {\em For the class of $4 \times 4$ tridiagonal sign patterns, is PN (together with positive and negative diagonal entries) equivalent to being SAP?}\ In this paper, a positive answer ...

Mathematical Optimization And Applications, 2016 Nova Southeastern University

#### Mathematical Optimization And Applications, Teodora Suciu

##### Mathematics Colloquium Series

This talk centers on mathematical optimization in the context of Calculus of Variations. Optimization involves choosing the best element from a set of choices, usually through mathematical approaches. Solving these kinds of problems is considered an essential tool in many areas of science and engineering. Additionally, various mathematics and business applications are discussed. Also explored is a real-life example with a detailed algorithm that is closely related to the Traveling Salesman problem.

Mathematical Relativity And The Nature Of The Universe, 2016 Nova Southeastern University

#### Mathematical Relativity And The Nature Of The Universe, Priscila Reyes

##### Mathematics Colloquium Series

In this talk, I will be discussing certain space-times, which can be used to model celestial objects and events in the universe. These are solutions to Einstein's field equations, which roughly describe the relation between matter, energy and the geometry of the universe. The concept of time in relation to an observer will be demonstrated. I will also include some interesting phenomena that arise out of the unusual mathematical structure of space-times , such as Lorentz contraction, reverse Cauchy-Schwarz, and the twin paradox.

Efficacy Of Math Video Tutorials On Student Perception And Achievement, 2016 Kennesaw State University

#### Efficacy Of Math Video Tutorials On Student Perception And Achievement, Carol R. Kahrmann

##### Doctor of Education in Teacher Leadership Dissertations

Abstract

The purpose of this mixed methods research study is to explore how teacher-made video tutorials in one middle school mathematics classroom are being used and what enables/impedes their effectiveness. A quantitative, quasi-experimental design investigates how video tutorial usage relates to students’ self-efficacy and achievement in mathematics. The sample consisted of 55 students in the experimental group and 65 students in the control group. Results found parents wanted the tutorials even if they did not view them. Students did actually use the video tutorials for remediation and learning. Videos longer than ten minutes impeded the effectiveness of the videos ...

2016 Missouri University of Science and Technology

#### Solvability Of Differential Systems Near Singular Points, Leon M. Hall

##### Leon Hall

"Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form zDy'(z) = A(z)y(z) + B(z)y(αz) + C(z)y'(αz) in the neighborhood of the singularity at z = 0"--Abstract, page 2.

2016 Selected Works

#### Inclusion Theorems For Boundary Value Problems For Delay Differential Equations, Leon M. Hall

##### Leon Hall

"In this thesis existence and uniqueness of solutions to certain second and third order boundary value problems for delay differential equations is established. Sequences of upper and lower solutions similar to those used by Kovač and Savčenko are defined by means of an integral operator, and conditions are given under which these sequences converge monotonically from above and below to the unique solution of the problem. Some numerical examples for the second order case are presented. Existence and uniqueness is also proved for the case where the delay is a function of the solution as well as the independent variable ...

2016 Missouri University of Science and Technology

#### Missouri Section Of The Mathematical Association Of America: Centennial History 1915-2015, Leon M. Hall

##### Leon Hall

"Compiling and writing the history of the Missouri MAA Section has been time-consuming, but it has mainly been rewarding and a wonderful learning experience. Both the Monthly and the MAA began with strong Midwestern and Missouri influences, something which our section can look back on with well-deserved pride. Missouri MAA members have consistently advanced collegiate mathematics, mathematics education, mathematics research and scholarship, and public appreciation for and understanding of mathematics in both Missouri and the nation. Looking to the future, the MAA and the Missouri Section can continue to be a great source of opportunities for leadership and service for ...

2016 Murray State University

#### Teaching Functions: The Good, The Bad, And The Many Ways To Do Better, Melanie Bayens

##### Honors College Theses

The way functions are taught in school needs improvement. Many times when students are introduced to functions in Algebra 2, the definition is glossed over, the instruction is lacking, and deeper understanding of the concept is lost. This causes problems when students are required to use this knowledge of functions in later classes, particularly, in Precalculus and Calculus. First, this paper will give the definition of a function and its role in mathematics. Second, this paper will delve into the problems of teaching functions the standard way. Finally, it will present multiple alternative methods for teaching functions. Specifically, it will ...

Calculus Students’ Ideas About Functions: Identifying Opportunities To Support Teacher Learning, 2016 Boise State University

#### Calculus Students’ Ideas About Functions: Identifying Opportunities To Support Teacher Learning, Laurie Overman Cavey, Patrick R. Lowenthal

##### Patrick R. Lowenthal

We describe the first phase of a study aimed at developing video-based instructional modules for secondary mathematics teachers. We began by consulting the literature on figural pattern tasks (c.f. Rivera, 2010) and teachers’ ability to interpret student work (c.f. El Mouhayar & Jurdak, 2012). Interpreting student work on figural pattern tasks requires awareness of different problem solving strategies, such as recursive and constructive, and how students might use them with tasks that require different levels of generalization (El Mouhayar & Jurdak, 2012).