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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. …

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 …

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.

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.