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Articles 1 - 20 of 20
Full-Text Articles in Algebraic Geometry
Whitney's 2-Isomorphism Theorem For Hypergraphs, Eric Anthony Taylor
Whitney's 2-Isomorphism Theorem For Hypergraphs, Eric Anthony Taylor
Theses Digitization Project
This study will examine a fundamental theorem from graph theory: Whitney's 2-Isomorphism Theorem. Whitney's 2-Isomorphism theorem characterizes when two graphs have isomorphic cycle matroids.
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.
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.
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.
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.
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.
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 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).
Studies In Free Module And It's Basis, Hsu-Chia Chen
Studies In Free Module And It's Basis, Hsu-Chia Chen
Theses Digitization Project
The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property.
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah
Theses Digitization Project
The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.
Primary Decomposition Of Ideals In A Ring, Sola Oyinsan
Primary Decomposition Of Ideals In A Ring, Sola Oyinsan
Theses Digitization Project
The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.
Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren
Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren
Theses Digitization Project
The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.
Differential Geometry Of Surfaces And Minimal Surfaces, James Joseph Duran
Differential Geometry Of Surfaces And Minimal Surfaces, James Joseph Duran
Theses Digitization Project
No abstract provided.