Digital Commons Network^™

Algebra Tutorial For Prospective Calculus Students, Matthew Mckain

All Capstone Projects

Many undergraduate degrees require students to take one or more courses in calculus. Majors in mathematics, science, and engineering are expected to enroll in several rigorous calculus courses, but those majoring in social and behavioral sciences and business must also have some basic understanding of calculus. The goal of this project is to create a web-based tutorial that can be used by the GSU Mathematics faculty to reinforce the algebra skills needed for introductory or Applied Calculus. The tutorial covers the concepts of the slopes of lines, polynomial arithmetic, factoring polynomials, rational expressions, solving quadratic equations, linear and polynomial inequalities, …

The Four Color Theorem: A Possible New Approach, Matthew Brady

All Student Theses

The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.

Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind …

A Little Aspect Of Real Analysis, Topology And Probability, Asmaa A. Abdulhameed

All Student Theses

The body of the paper is divided into three parts:

Part one: include definitions and examples of the metric, norm and topology along with some important terms such as metrics l₁,l₂,l_∞ and vector norm |x|_p which also known as the L^p space. In case of the topology space this concept adjusted to be a unit ball that is distance one from a point unit circle.

Part two: demonstrate the measure and probability which is one of the main topics in this work. This section serves as an introduction for the remaining …

Trigonometry: An Overview Of Important Topics, Lauren Johnson

All Capstone Projects

The purpose of this project was to help students achieve a better understanding of Trigonometry, in order to better prepare them for future Calculus courses. The project is a tutorial that walks the student through important Trigonometry topics. The topics range from, but are not limited to, finding the measure of an angle to analyzing the graphs of Trigonometric Functions. Each topic allows an opportunity for the student to assess their understanding by working through practice problems and checking their solutions.

At any university, incoming students will have a wide variety of mathematical backgrounds. These students differ in age, in …

History Of Mathematics From The Islamic World, Asamah Abdallah

All Student Theses

Learning the history of mathematics is crucial to fully understanding the world of mathematics today. This paper will explore the history of mathematics from the Islamic world. It will focus on the contributions of well-recognized mathematicians including, Al-Khwarizmi, Al-Khayyam, Uqlidisi, Kushyar ibn Labban, and Abu Kamil. It will also concentrate on the contributions that the Islamic world had on algebra, beginning with Al-Khwarizmi and his contribution to the developmental of algebraic equations, and Khayyam and his contribution to the geometrization of algebra. This paper will also discuss the ways in which the Muslims applied the mathematics they learned into their …

The Impact Of Students’ Attitudes After Implementing A Leadership Collaborative Grouping Method In A Collegiate Technical Mathematics Class, Robert J. Belin

All Student Theses

This research paper explored students’ attitudes towards mathematics before and after the implementation of an experimental instructional method. The measurement tool that was used is the Mathematics Attitude Inventory for Students (ATMI). The experimental methodology implemented in the collegiate class is a leadership based cooperative learning model. Students were surveyed twice. The first installment of the ATMI was conducted prior to a mathematics unit that spanned three classes. The second installment of the ATMI survey was conducted after the unit was completed. Student surveys were assessed and determined if the experimental model had any impact of students’ attitudes towards mathematics. …

On Emmy Noether And Her Algebraic Works, Deborah Radford

All Student Theses

In the early 1900s a rising star in the mathematics world was emerging. I will discuss her life as a female mathematician and the struggles she faced being a rebel in her time. I will also take an in depth look at some of her contributions to the mathematics and science community . Her work in algebra and more specifically, ring theory, are said to be foundations for much of the work done since then. Her developments in abstract algebra helped to unify topology, geometry, logic and linear algebra. Also, Noether's theorem is a widely used theorem in physics along …

Nested Monte Carlo Tree Search As Applied To Samurai Sudoku, Laura Finley

All Student Theses

As Sudoku has come into prominence as a favorite logic puzzle, mathematicians and computer scientists alike have analyzed the game for interesting properties. The large search space presents a challenge for both generating and solving Sudoku puzzles without relying on techniques that simply permute a valid puzzle. These permutations result in puzzles that are essentially the same since they follow the same solution path. Many Sudoku generating or solving programs rely on brute-force methods to avoid this pitfall, but this is inefficient since there is no heuristic to navigate the huge search space. A nested Monte Carlo tree search has …