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Articles 121 - 150 of 242
Full-Text Articles in Mathematics
The Banach-Tarski Paradox, Matthew Jacob Norman
The Banach-Tarski Paradox, Matthew Jacob Norman
Theses Digitization Project
The purpose of this thesis is to establish the history and motivation leading up to the Banach-Tarski Paradox, as well as its proof. This study discusses the early history of set theory as it is documented as well as the necessary basics of set theory in order to further understand the contents within. Set theory not only proved to be for the mathematical at heart but also struck interest into the mind of philosophers, theologians, and logicians.
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.
Closure Operations In Commutative Rings, Chloette Joy Samsam
Closure Operations In Commutative Rings, Chloette Joy Samsam
Theses Digitization Project
The purpose of this study is to survey different types of closures and closure operations on commutative rings and ideals.
Orthogonal Polynomials, George Gevork Antashyan
Orthogonal Polynomials, George Gevork Antashyan
Theses Digitization Project
This thesis will show work on Orthogonal Polynomials. In mathematics, the type of polynomials that are orthogonal to each other under inner product are called orthogonal polynomials. Jacobi polynomials, Laguerre polynomials, and Hermite polynomials are examples of classical orthogonal polynomials that was invented in the nineteenth century. The theory of rational approximations is one of the most important applications of orthogonal polynomials.
Solutions To A Generalized Pell Equation, Kyle Christopher Castro
Solutions To A Generalized Pell Equation, Kyle Christopher Castro
Theses Digitization Project
This study aims to extend the notion of continued fractions to a new field Q (x)*, in order to find solutions to generalized Pell's Equations in Q [x] . The investigation of these new solutions to Pell's Equation will begin with the necessary extensions of theorems as they apply to polynomials with rational coefficients and fractions of such polynomials in order to describe each "family" of solutions.
Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet
Monomial And Permutation Representation Of Groups, Rebeca Maria Blanquet
Theses Digitization Project
The purpose of this project is to introduce another method of working with groups, that is more efficient when the groups we wish to work with are of a significantly large finite order. When we wish to work with small finite groups, we use permutations and matrices. Although these two methods are the general methods of working with groups, they are not always efficient.
Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Cassini Ovals As Elliptic Curves, Nozomi Arakaki
Theses Digitization Project
The purpose of this project is to show that Cassini curves that are not lemniscates, when b does not equal 1, represent elliptic curves. It is also shown that the cross-ratios of these elliptic curves are either real numbers or represented by complex numbers on the unit circle on the conplex plane.
Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez
Prouhet-Tarry-Escott Problem, Juan Manuel Gutierrez
Theses Digitization Project
The purpose of this research paper is to gain a deeper understanding of a famous unsolved mathematical problem known as the Prouhet-Terry-Escott Problem. The Prouhet-Terry-Escott Problem is a complex problem that still has much to be discovered. This fascinating problem shows up in many areas of mathematics such as the study of polynomials, graph theory, and the theory of integral quadratic forms.
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.
Symmetric Generation, Lisa Sanchez
Symmetric Generation, Lisa Sanchez
Theses Digitization Project
The purpose of this project is to conduct a systematic search for finite homomorphic images of infinite semi-direct products mn : N, where m = 2,3,5,7 and N <̲ Sn and construct by hand some of the important homomorphic images that emerge from the search.
A Comparison Of Category And Lebesgue Measure, Adam Matthew Moore
A Comparison Of Category And Lebesgue Measure, Adam Matthew Moore
Theses Digitization Project
This study, Lebesgue measure and category have proved to be useful tools in describing the size of sets. The notions of category and Lebesgue measure are commonly used to describe the size of a set of real numbers (or of a subset of Rn). Although cardinality is also a measure of the size of a set, category and measure are often the more important gauges of size when studying properties of classes of real functions, such as the space of continuous functions or the space of derivatives.
Symmetric Generation Of M₂₂, Bronson Cade Lim
Symmetric Generation Of M₂₂, Bronson Cade Lim
Theses Digitization Project
This study will prove the Mathieu group M₂₂ contains two symmetric generating sets with control grougp L₃ (2). The first generating set consists of order 3 elements while the second consists of involutions.
A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka
A Study On The Modular Structures Of Z₂S₃ And Z₅S₃, Bethany Michelle Tasaka
Theses Digitization Project
This project is a study of the properties of the modules Z₂S₃ and Z₅S₃, which are examined both as modules over themselves and as modules over their respective integer fields. Each module is examined separately since they each hold distinct properties. The overall goal is to determine the simplicity and semisimplicity of each module.
Symmetric Presentation Of Finite Groups, Thuy Nguyen
Symmetric Presentation Of Finite Groups, Thuy Nguyen
Theses Digitization Project
The main goal of this project is to construct finite homomorphic images of monomial infinite semi-direct products which are called progenitors. In this thesis, we provide an alternative convenient and efficient method. This method can be applied to many groups, including all finite non-abelian simple groups.
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
A Locus Construction In The Hyperbolic Plane For Elliptic Curves With Cross-Ratio On The Unit Circle, Lyudmila Shved
Theses Digitization Project
This project demonstrates how an elliptic curve f defined by invariance under two involutions can be represented by the locus of circumcenters of isosceles triangles in the hyperbolic plane, using inversive model.
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Constructible Numbers: Euclid And Beyond, Joshua Scott Marcy
Theses Digitization Project
The purpose of this project is to demonstrate first why trisection for an arbitrary angle is impossible with compass and straightedge and second how trisection does become possible if a marked ruler is used instead.
Geodesics Of Surface Of Revolution, Wenli Chang
Geodesics Of Surface Of Revolution, Wenli Chang
Theses Digitization Project
The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.
Morse Theory, Rozaena Naim
Morse Theory, Rozaena Naim
Theses Digitization Project
This study will mainly concentrate on Morse Theory. Morse Theory is the study of the relations between functions on a space and the shape of the space. The main part of Morse Theory is to look at the critical points of a function, and to find information on the shape of the space using the information about the critical points.
Ore's Theorem, Jarom Viehweg
Ore's Theorem, Jarom Viehweg
Theses Digitization Project
The purpose of this project was to study the classical result in this direction discovered by O. Ore in 1938, as well as related theorems and corollaries. Ore's Theorem and its corollaries provide us with several results relating distributive lattices with cyclic groups.
Snort: A Combinatorial Game, Keiko Kakihara
Snort: A Combinatorial Game, Keiko Kakihara
Theses Digitization Project
This paper focuses on the game Snort, which is a combinatorial game on graphs. This paper will explore the characteristics of opposability through examples. More fully, we obtain some neccessary conditions for a graph to be opposable. Since an opposable graph guarantees a second player win, we examine graphs that result in a first player win.
Symmetric Generators Of Order 3, Stewart Contreras
Symmetric Generators Of Order 3, Stewart Contreras
Theses Digitization Project
The main purpose of this project is to construct finite homomorphic images of infinite semi-direct products.
Symmetric Generation, Dung Hoang Tri
Symmetric Generation, Dung Hoang Tri
Theses Digitization Project
In this thesis we construct finite homorphic images of infinite semi-direct products, 2*n : N, where 2*n is a free product of n copies the cyclic group of permutations on n letter.
An Investigation Of Kurosh's Theorem, Keith Anthony Earl
An Investigation Of Kurosh's Theorem, Keith Anthony Earl
Theses Digitization Project
The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.
The Riesz Representation Theorem For Linear Functionals, Thomas Daniel Schellhous
The Riesz Representation Theorem For Linear Functionals, Thomas Daniel Schellhous
Theses Digitization Project
This study will investigate the Riesz representation theorem for linear functionals in relation to locally compact Hausdorff spaces. Two other theorems that are commonly called "Riesz representation theorem" are the theorem for finite-dimensional inner product spaces and the theorem for Hilbert spaces [BN00], and studying these interesting topics helps us to not only gain a better understanding of how linear functionals interact with vector spaces over which they are defined, but also to see faint threads that hint at a deep connection between the various fields of modern mathematics.
Homomorphic Images Of Progenitors Of Order Three, Mark Gutierrez
Homomorphic Images Of Progenitors Of Order Three, Mark Gutierrez
Theses Digitization Project
The main purpose of this thesis is to construct finite groups as homomorphic images of infinite semi-direct products, 2*n : N, 3*n : N, and 3*n :m N, where 2*n and 3*n are free products of n copies of the cyclic group C₂ extended by N, a group of permutations on n letters.
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
The Universal Coefficient Theorem For Cohomology, Michael Anthony Rosas
Theses Digitization Project
This project is an expository survey of the Universal Coefficient Theorem for Cohomology. Algebraic preliminaries, homology, and cohomology are discussed prior to the proof of the theorem.
The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas
The Fundamental Group And Van Kampen's Theorem, Aaron Christopher Thomas
Theses Digitization Project
This thesis deals with the field of algebraic topology. Basic topological facts are addressed including open and closed sets, continuity, homeomorphisms, and path connectedness as well as discussing Van Kampen's Theorem in detail.
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Geometric Theorem Proving Using The Groebner Basis Algorithm, Karla Friné Rivas
Theses Digitization Project
The purpose fo this project is to study ideals in polynomial rings and affine varieties in order to establish a connection between these two different concepts. Doing so will lead to an in depth examination of Groebner bases. Once this has been defined, step will be outlined that will enable the application of the Groebner Basis Algorithm to geometric problems.
On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean
On A Symmetric Presentation Of The Double Cover Of M₂₂: 2, Gabriela Laura Maerean
Theses Digitization Project
The purpose of this project is to construct finite homomorphic images of infinite semi-direct products. We will construct two finite homomorphic images, L₂ (8) and PGL₂ (9) of the infinite semi-direct product 2*³ : S₃. The main part of this project is to construct the double cover 2 - M₂₂ : 2 and the automorphism group M₂₂ : 2 of the Matheiu sporadic group M₂₂ as a homomorphic image of the progenitor 2*⁷ : L₃ (2).