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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Mathematics Behind Machine Learning, Rim Hammoud
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
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
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. …
Math 3100 - Mathematical Thinking: Communication And Proof - Week 1 Outline, Laura J. Wallace, Cory Johnson, Shawn Mcmurran, Min-Lin Lo
Math 3100 - Mathematical Thinking: Communication And Proof - Week 1 Outline, Laura J. Wallace, Cory Johnson, Shawn Mcmurran, Min-Lin Lo
Q2S Enhancing Pedagogy
As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …
Math 3100: Communication And Proof - Assessment, Shawn Mcmurran, Min-Lin Lo, Corrine Johnson, Laura Wallace
Math 3100: Communication And Proof - Assessment, Shawn Mcmurran, Min-Lin Lo, Corrine Johnson, Laura Wallace
Q2S Enhancing Pedagogy
As a group, we hope through this FLC project to develop a course that promotes departmental SLOs, as well as University learning outcomes for a writing-intensive course. We focused on our new foundational course (MATH 3100 Mathematical Thinking: Communication and Proof). This course, designated as a writing-intensive course, introduces students to disciplinary ways of thinking and communicating in mathematics with emphasis on the construction of valid mathematical arguments, critiques of arguments, and structure of professional mathematical writing including typesetting. We would like to develop a library of useful materials that faculty members can adapt in their classrooms in order to …
Reflection On Use Of The "Reacting To The Past" Pedagogy In A History Of Mathematics Course, Davida Fischman
Reflection On Use Of The "Reacting To The Past" Pedagogy In A History Of Mathematics Course, Davida Fischman
Q2S Enhancing Pedagogy
This brief report provides a reflection on the use of the "Reacting to the Past" (RTTP) pedagogy in a History of Mathematics classroom. The conclusion is drawn that the RTTP pedagogy is very successful in engaging students in active learning, and appropriate games may be utilized to help students learn about the role of mathematics in historical developments as well as in society today.
Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham
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 …
On The Evolution Of Virulence, Thi Nguyen
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
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
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
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.
Fundamental Theorem Of Algebra, Paul Shibalovich
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.
Arboreal Adventure: A Cross Curricular Unit On Trees, Anne Elizabeth Boshoven
Arboreal Adventure: A Cross Curricular Unit On Trees, Anne Elizabeth Boshoven
Theses Digitization Project
No abstract provided.