Physical Sciences and Mathematics Commons^™

Intersection Numbers, Embedded Spheres And Geosphere Laminations For Free Groups., Suhas Pandit Dr.

Doctoral Theses

Topological and geometric methods have played a major role in the study of infinite groups since the time of Poincar´e and Klein, with the work of Nielsen, Dehn, Stallings and Gromov showing particularly deep connections with the topology of surfaces and three-manifolds. This is in part because a surface or a 3-manifold is essentially determined by its fundamental group, and has a geometric structure due to the Poincar´e-K¨obe-Klein uniformisation theorem for surfaces and Thurston’s geometrisation conjecture, which is now a theorem of Perelman, for 3-manifolds.A particularly fruitful instance of such an interplay is the relation between intersection numbers of simple …

Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.

Doctoral Theses

In everyday life, there arise many situations where two parties, sender and receiver, need to communicate. The channel through which they communicate is assumed to be binary symmetric, that is, it changes 0 to 1 and vice versa with equal probability. At the receiver’s end, the sent message has to be recovered from the corrupted received word using some reasonable mechanism. This real life problem has attracted a lot of research in the past few decades. A solution to this problem is obtained by adding redundancy in a systematic manner to the message to construct a codeword. The collection of …

Alternating Links And Subdivision Rules, Brian Craig Rushton

Theses and Dissertations

The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.

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.

Empirical Development Of An Instructional Product And Its Impact On Mastery Of Geometry Concepts, Donaldson Williams

Dissertations

Problem

Relatively poor levels of mathematical thinking among American school children have been identified as a major issue over the past half century. Many efforts have been made to increase the mathematics performance of children in schools. Additionally, out-of-school-time programs have attempted to address this issue as well. Holistic development is one of the distinguishing features of Seventh-day Adventist instructional programs. Yet, as of 2007, the Pathfinder program, an informal educational program operated by the world-wide Seventh-day Adventist church, had no instructional product designed to foster participants’ cognitive development in mathematics. This study focused on the empirical development of an …

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.

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.