Digital Commons Network^™

Mathematics Behind Machine Learning, Rim Hammoud

Electronic Theses, Projects, and Dissertations

Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …

Partial Representations For Ternary Matroids, Ebony Perez

Electronic Theses, Projects, and Dissertations

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a …

Sum Of Cubes Of The First N Integers, Obiamaka L. Agu

Electronic Theses, Projects, and Dissertations

In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …

The Effects Of Project Lead The Way Launch Curriculum On Elementary Girls’ Perception And Career Interests In Science, Technology, Engineering, And Mathematics, Mina Blazy

Electronic Theses, Projects, and Dissertations

The United States has examined the quality of science, technology, engineering and mathematics (STEM) education since before the turn of the century. STEM educators are still having the conversation around why more women are not joining STEM pathways. Girls and boys as early as birth are curious about the world; through their own lens they learn about gravity from dropping spaghetti on the floor or seeing a small insect on the wall. As children get older they are influenced by the perceptions of their parents and peers.

This study looked at the perception and career interests of girls in STEM …

Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham

Electronic Theses, Projects, and Dissertations

This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam.

A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had …

Indicators Of Future Mathematics Proficiency: Literature Review & Synthesis, Claudia Preciado

Electronic Theses, Projects, and Dissertations

The beauty of mathematics can arguably be found in the way in which all concepts are interrelated and interwoven to create a massive web of knowledge and in the ways this can be applied to all aspects of life and technology. Given this inextricable interrelationship amongst several mathematical topics, many students encounter issues in learning mathematics due to gaps in their understanding of previously taught material. As a result, mathematics education in the K-12 setting has emphasized the need for interventions in order to help students grasp the progressively complex concepts that are required by our current society and education …

On The Evolution Of Virulence, Thi Nguyen

Electronic Theses, Projects, and Dissertations

The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.

Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan

Theses Digitization Project

The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.

An Investigation Of Air Resistance On Projectile Motion From Aristotle To Euler, Michael Edward Clayton

Theses Digitization Project

From antiquity until today, mathematicians have tried to develop a theory of projectile motion. The development of a theory of projectile motion began with just a basic observation of motion by the great Greek mathematician Aristotle and has evolved to become more than conjecture or hypothesis, but a well developed science of prediciting the flight and accuracy of a projectile in motion. This thesis traces the development of the theory of projectile motion from Greek antiquity to about the mid 1700's.

Leonhard Euler's Contribution To Infinite Polynomials, Jack Dean Meekins

Theses Digitization Project

This thesis will focus on Euler's famous method for solving the infinite polynomial. It will show how he manipulated the sine function to find all possible points along the sine function such that the sine A would equal to y; these would be roots of the polynomial. It also shows how Euler set the infinite polynomial equal to the infinite product allowing him to determine which coefficients were equal to which reciprocals of the roots, roots squared, roots cubed, etc.

Teaching Mathematics In The Classroom With Powerpoint Software, Robert Ward Kopp

Theses Digitization Project

This study will look at at how to better student achievement in an Algebra II course. Specifically this study examines two different modifications made during the second semester of an Algebra II course taught at a high school in Riverside County. The modifications that were made were based on a detailed literature review that suggested looking at how students learn while using PowerPoint software as an instructional tool and at the same time investigate the consequence of rearranging a fairly common and predetermined curriculum pattern.

Assessing Online Assessments: A Comparison Study Of Math Assessment Tools For Third-Grade Students, Tina Kim Chan

Theses Digitization Project

The study reported here examined the move towards online assessments and addressed the question of whether or not different assessment tools affect student scores and student learning. The research activities covered a three-week period, from June 5, 2006 to June 23, 2006. During this time, seventeen third grade students served as their own control group by taking several math tests online and several math tests with paper and pencil. Results were compared to see if performance on computer-based tests would be more successful than pencil-and-paper tests. A follow-up survey to evaluate and interpret the quantitative results was also used. Findings …

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

The Development Of Curriculum For A High School Course Integrating Drafting And Mathematics, Diana Lynn Mcvicker

Theses Digitization Project

No abstract provided.

Arboreal Adventure: A Cross Curricular Unit On Trees, Anne Elizabeth Boshoven

Theses Digitization Project

No abstract provided.

Curriculum In Mathematics For Air Conditioning And Refrigeration, Darrow P. Soares

Theses Digitization Project

No abstract provided.

An Interdisciplinary Unit On The Renaissance, Sarah Elizabeth Hughes

Theses Digitization Project

No abstract provided.