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Articles 151 - 180 of 242
Full-Text Articles in Mathematics
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
The Composition Of Split Inversions On The Hyperbolic Plane, Robert James Amundson
Theses Digitization Project
The purpose of the project is to examine the action of the composition of split inversions on the hyperbolic plane, H². The model that is used is the poincoŕe disk.
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Using Non-Euclidean Geometry In The Euclidean Classroom, Kelli Jean Wasserman
Theses Digitization Project
This study is designed to explore the ramifications of supplementing the basic Euclidean geometry, with spherical geometry, a non-Eugledian geometry curriculum. This project examined different aspects of the impact of spherical geometry on the high school geometry classroom.
There Are Only Four, Danielle Josette Mccoy
There Are Only Four, Danielle Josette Mccoy
Theses Digitization Project
This paper is an investigation of finite-dimensional normed algebras over the reals from both an abstract and concrete point of view.
Construction Of Homomorphic Images, Stephanie Ann Hilber
Construction Of Homomorphic Images, Stephanie Ann Hilber
Theses Digitization Project
This thesis constructs several finite homomorphic images of infinite semi-direct products of the form 2*n:N.
Foundations Of Geometry, Lawrence Michael Clarke
Foundations Of Geometry, Lawrence Michael Clarke
Theses Digitization Project
In this paper, a brief introduction to the history, and development of Euclidean geometry will be followed by a biographical background of David Hilbert, highlighting significant events in his educational and professional life. In an attempt to add rigor to the presentation of geometry, Hilbert defined concepts and presented five groups of axioms that were mutually independent yet compatible, including introducing axioms of congruence in order to present displacement.
Operations In Hilbert Space, Dennis Michael Gumaer
Operations In Hilbert Space, Dennis Michael Gumaer
Theses Digitization Project
This thesis reviews some of the major topics in elementary Hilbert space theory. The theory of operators is developed by providing details regarding several types of operators, in particular compact operators. This study of compact operators is the start of the refinement of bounded linear operators to those which are also members of the Schatten p-class operators.
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.
Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto
Tessellations Of The Hyperbolic Plane, Roberto Carlos Soto
Theses Digitization Project
In this thesis, the two models of hyperbolic geometry, properties of hyperbolic geometry, fundamental regions created by Fuchsian groups, and the tessellations that arise from such groups are discussed.
Chinese Remainder Theorem And Its Applications, Jacquelyn Ha Lac
Chinese Remainder Theorem And Its Applications, Jacquelyn Ha Lac
Theses Digitization Project
No abstract provided.
Poincaré Duality, Christopher Michael Duran
Poincaré Duality, Christopher Michael Duran
Theses Digitization Project
This project is an expository study of the Poincaré duality theorem. Homology, cohomology groups of manifolds and other aglebraic and topological preliminaires are discussed.
Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader
Simulating Spatial Partial Differential Equations With Cellular Automata, Brian Paul Strader
Theses Digitization Project
The purpose of this project was to define the relationship and show how an important subset of spatial differential equations can be transformed into cellular automata. Contains source code.
Factorization, Di Phan Reagan
Factorization, Di Phan Reagan
Theses Digitization Project
The purpose of this thesis will focus on the two most efficient algorithms which are quadratic sieve and number field sieve. Background information such as definitions and theorems are given to help understand the concepts behind each method.
Symmetric Representation Of The Elements Of Finite Groups, Barbara Hope Gwinn-Edwards
Symmetric Representation Of The Elements Of Finite Groups, Barbara Hope Gwinn-Edwards
Theses Digitization Project
The main purpose of this thesis is to construct finite groups as homomorphic images of infinite semi-direct products.
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins
Theses Digitization Project
This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.
Stone's Representation Theorem, Ion Radu
Stone's Representation Theorem, Ion Radu
Theses Digitization Project
The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.
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.
Minimal Surfaces, Maria Guadalupe Chaparro
Minimal Surfaces, Maria Guadalupe Chaparro
Theses Digitization Project
The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.
Tutte Polynomial In Knot Theory, David Alan Petersen
Tutte Polynomial In Knot Theory, David Alan Petersen
Theses Digitization Project
This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.
Construction Of Finite Homomorphic Images, Jane Yoo
Construction Of Finite Homomorphic Images, Jane Yoo
Theses Digitization Project
The purpose of this thesis is to construct finite groups as homomorphic images of progenitors.
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Conics In The Hyperbolic Plane, Trent Phillip Naeve
Theses Digitization Project
An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.
Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Aspects Of The Jones Polynomial, Alvin Mendoza Sacdalan
Theses Digitization Project
A knot invariant called the Jones polynomial will be defined in two ways, as the Kauffman Bracket polynomial and the Tutte polynomial. Three properties of the Jones polynomial are discussed. We also see how mutant knots share the same Jones polynomial.
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Geodesic On Surfaces Of Constant Gaussian Curvature, Veasna Chiek
Theses Digitization Project
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
The Structure Of Semisimple Artinian Rings, Ravi Samuel Pandian
The Structure Of Semisimple Artinian Rings, Ravi Samuel Pandian
Theses Digitization Project
Proves two famous theorems attributed to J.H.M. Wedderburn, which concern the structure of noncommutative rings. The two theorems include, (1) how any semisimple Artinian ring is the direct sum of a finite number of simple rings; and, (2) the Wedderburn-Artin Theorem. Proofs in this paper follow those outlined in I.N. Herstein's monograph Noncommutative Rings with examples and details provided by the author.
Minimal Congestion Trees, Shelly Jean Dawson
Minimal Congestion Trees, Shelly Jean Dawson
Theses Digitization Project
Analyzes the results of M.I. Ostrovskii's theorem of inequalities which estimate the minimal edge congestion for finite simple graphs. Uses the generic results of the theorem to examine and further reduce the parameters of inequalities for specific families of graphs, particularly complete graphs and complete bipartite graphs. Also, explores a possible minimal congestion tree for some grids while forming a conjecture for all grids.
Gauss-Bonnet Formula, Heather Ann Broersma
Gauss-Bonnet Formula, Heather Ann Broersma
Theses Digitization Project
From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.
Freeness Of Hopf Algebras, Christopher David Walker
Freeness Of Hopf Algebras, Christopher David Walker
Theses Digitization Project
The Nichols-Zoeller freeness theorem states that a finite dimensional Hopf algebra is free as a module over any subHopfalgebra. We will prove this theorem, as well as the first significant generalization of this theorem, which was proven three years later. This generalization says that if the Hopf algebra is infinite dimensional, then the Hopf algebra is still free if the subHopfalgebra is finite dimensional and semisimple . We will also look at several other significant generalizations that have since been proven.
Hausdorff Dimension, Loren Beth Nemeth
Hausdorff Dimension, Loren Beth Nemeth
Theses Digitization Project
The purpose of this study was to define topological dimension and Hausdorff dimension, Namely metric space theory and measure theory. It was verified that in the sets of elementary geometry, the dimensions agree, while in the case of the fractals, the Hausdorff dimension is strictly larger than the topological dimension.
The Evolution Of Equation-Solving: Linear, Quadratic, And Cubic, Annabelle Louise Porter
The Evolution Of Equation-Solving: Linear, Quadratic, And Cubic, Annabelle Louise Porter
Theses Digitization Project
This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Investigation Of 4-Cutwidth Critical Graphs, Dolores Chavez
Theses Digitization Project
A 2004 article written by Yixun Lin and Aifeng Yang published in the journal Discrete Math characterized the set of a 3-cutwidth critical graphs by five specified elements. This project extends the idea to 4-cutwidth critical graphs.