The Impact Of Experience On Elementary School Teacher Affective Relationship With Mathematics, 2010 Olivet Nazarene University

#### The Impact Of Experience On Elementary School Teacher Affective Relationship With Mathematics, John Salzer

*Ed.D. Dissertations*

This study was designed as an exploratory examination of the impact of teaching experience on elementary school teachers’ affective relationships with mathematics. A self-reporting survey was used to examine a wide variety of experience factors, including factors related to quantity of experience, type of experience, and post-certification training opportunities (n = 275). Participants were also asked to identify services that might impact their affective relationships with mathematics. This study resulted in recommendations for seven follow-up studies to gain insight into factors that significantly correlated to teacher attitudes toward math or to their perceived changes in attitudes over time. Recommended practices for ...

Dynamics Groups Of Asynchronous Cellular Automata, 2010 Clemson University

#### Dynamics Groups Of Asynchronous Cellular Automata, Michael Macauley, Jon Mccammond, Henning S. Mortveit

*Publications*

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is *π*-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the *dynamics group*. We have previously shown that exactly 104 of the possible 2^{23 }= 256 cellular automaton rules are *π*-independent. In the article, we classify the periodic states of these systems and describe their dynamics groups, which are quotients of Coxeter groups. The dynamics groups provide information about permissible ...

Combinatorics And Topology Of Curves And Knots, 2010 Boise State University

#### Combinatorics And Topology Of Curves And Knots, Bailey Ann Ross

*Boise State University Theses and Dissertations*

The genus of a graph is the minimal genus of a surface into which the graph can be embedded. Four regular graphs play an important role in low dimensional topology since they arise from curves and virtual knot diagrams. Curves and virtual knots can be encoded combinatorially by certain signed words, called Gauss codes and Gauss paragraphs. The purpose of this thesis is to investigate the genus problem for these combinatorial objects: Given a Gauss word or Gauss paragraph, what is the genus of the curve or virtual knot it represents?

The Life Of Evariste Galois And His Theory Of Field Extension, 2010 Liberty University

#### The Life Of Evariste Galois And His Theory Of Field Extension, Felicia N. Adams

*Senior Honors Theses*

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible ...

Analyzing Fractals, 2010 Syracuse University

#### Analyzing Fractals, Kara Mesznik

*Syracuse University Honors Program Capstone Projects*

** **

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is *self- similar*, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the *Contraction Mapping Theorem* and shifted using *linear* and *affine* *transformations*.

Fractals live in something called a *metric space*. A *metric* *space*, denoted (*X, d*), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals we are only concerned with metric ...

Generalized Emp And Nonlinear Schrodinger-Type Reformulations Of Some Scaler Field Cosmological Models, 2010 University of Massachusetts Amherst

#### Generalized Emp And Nonlinear Schrodinger-Type Reformulations Of Some Scaler Field Cosmological Models, Jennie D'Ambroise

*Open Access Dissertations*

We show that Einstein’s gravitational field equations for the Friedmann- Robertson-Lemaître-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can be equivalently reformulated in terms of a single equation of either generalized Ermakov-Milne- Pinney (EMP) or (non)linear Schrödinger (NLS) type. This work generalizes or presents an alternative to similar reformulations published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T. Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.Williams. In particular we cast much of these authors’ works into a single ...

On The Frequency Of Finitely Anomalous Elliptic Curves, 2010 University of Massachusetts Amherst

#### On The Frequency Of Finitely Anomalous Elliptic Curves, Penny Catherine Ridgdill

*Open Access Dissertations*

Given an elliptic curve E over Q, we can then consider E over the finite field Fp. If Np is the number of points on the curve over Fp, then we define ap(E) = p+1-Np. We say primes p for which ap(E) = 1 are anomalous. In this paper, we search for curves E so that this happens for only a finite number of primes. We call such curves finitely anomalous. This thesis deals with the frequency of their occurrence and finds several examples.

Minimum Rank Of Skew-Symmetric Matrices Described By A Graph, 2010 University of Wyoming

#### Minimum Rank Of Skew-Symmetric Matrices Described By A Graph, Mary Allison, Elizabeth Bodine, Luz Maria Dealba, Joyati Debnath, Laura Deloss, Colin Garnett, Jason Grout, Leslie Hogben, Bokhee Im, Hana Kim, Reshmi Nair, Olga Pryporova, Kendrick Savage, Bryan Shader, Amy Wangsness Wehe

*Mathematics Publications*

The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank among all skew-symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We apply ...

Geometric And Combinatorial Aspects Of 1-Skeleta, 2010 University of Massachusetts Amherst

#### Geometric And Combinatorial Aspects Of 1-Skeleta, Chris Ray Mcdaniel

*Open Access Dissertations*

In this thesis we investigate 1-skeleta and their associated cohomology rings. 1-skeleta arise from the 0- and 1-dimensional orbits of a certain class of manifold admitting a compact torus action and many questions that arise in the theory of 1-skeleta are rooted in the geometry and topology of these manifolds. The three main results of this work are: a lifting result for 1-skeleta (related to extending torus actions on manifolds), a classification result for certain 1-skeleta which have the Morse package (a property of 1-skeleta motivated by Morse theory for manifolds) and two constructions on 1-skeleta which we show preserve ...

Solvability Of Commutative Right-Nilalgebras Satisfying (B (Aa)) A= B ((Aa) A), 2010 Universidad de Chile

#### Solvability Of Commutative Right-Nilalgebras Satisfying (B (Aa)) A= B ((Aa) A), Ivan Correa, Alicia Labra, Irvin R. Hentzel

*Mathematics Publications*

We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Our main result is that these algebras are solvable and not necessarily nilpotent. Our results require characteristic ≠ 2, 3, 5.

Construction And Properties Of Hussain Chains For Quotients Of Projective Planes, 2010 University of Tennessee - Knoxville

#### Construction And Properties Of Hussain Chains For Quotients Of Projective Planes, Lee Troupe

*Chancellor’s Honors Program Projects*

No abstract provided.

Some Classification Results For Hadamard Matrices Of Order 6, 2010 University of Tennessee - Knoxville

#### Some Classification Results For Hadamard Matrices Of Order 6, William Lee Tune

*Chancellor’s Honors Program Projects*

No abstract provided.

An Exploration Of Optimization Algorithms And Heuristics For The Creation Of Encoding And Decoding Schedules In Erasure Coding, 2010 University of Tennessee - Knoxville

#### An Exploration Of Optimization Algorithms And Heuristics For The Creation Of Encoding And Decoding Schedules In Erasure Coding, Catherine D. Schuman

*Chancellor’s Honors Program Projects*

No abstract provided.

Discrete Fractional Calculus And Its Applications To Tumor Growth, 2010 Western Kentucky University

#### Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

*Masters Theses & Specialist Projects*

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the *n*-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make *n*- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus while ...

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, 2010 Western Kentucky University

#### An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

*Masters Theses & Specialist Projects*

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(*n*) time where *n* is the number of crossings in ...

Khovanov Homology In Thickened Surfaces, 2010 University of Iowa

#### Khovanov Homology In Thickened Surfaces, Jeffrey Thomas Conley Boerner

*Theses and Dissertations*

Mikhail Khovanov developed a bi-graded homology theory for links in the 3-sphere. Khovanov's theory came from a Topological quantum field theory (TQFT) and as such has a geometric interpretation, explored by Dror Bar-Natan. Marta Asaeda, Jozef Przytycki and Adam Sikora extended Khovanov's theory to I-bundles using decorated diagrams. Their theory did not suggest an obvious geometric version since it was not associated to a TQFT. We develop a geometric version of Asaeda, Przytycki and Sikora's theory for links in thickened surfaces. This version leads to two other distinct theories that we also explore.

Endomorphisms, Composition Operators And Cuntz Families, 2010 University of Iowa

#### Endomorphisms, Composition Operators And Cuntz Families, Samuel William Schmidt

*Theses and Dissertations*

If b is an inner function and T is the unit circle, then composition with b induces an endomorphism, β, of L^{1}(T) that leaves H^{1}(T) invariant. In this document we investigate the structure of the endomorphisms of B(L^{2}(T)) and B(H^{2}(T)) that implement by studying the representations of L^{1}(T) and H^{1}(T) in terms of multiplication operators on

B(L^{2}(T)) and B(H^{2}(T)). Our analysis, which was inspired by the work of R. Rochberg and J. McDonald, will range from the theory of composition ...

C*-Algebras Of Labeled Graphs And *-Commuting Endomorphisms, 2010 University of Iowa

#### C*-Algebras Of Labeled Graphs And *-Commuting Endomorphisms, Paulette Nicole Willis

*Theses and Dissertations*

My research lies in the general area of functional analysis. I am particularly interested in C*-algebras and related dynamical systems. From the very beginning of the theory of operator algebras, in the works of Murray and von Neumann dating from the mid 1930's, dynamical systems and operator algebras have led a symbiotic existence. Murray and von Neumann's work grew from a few esoteric, but clearly original and prescient papers, to a ma jor river of contemporary mathematics. My work lies at the confluence of two important tributaries to this river.

On the one hand, the operator algebras ...

Classical Groups, Integrals And Virasoro Constraints, 2010 University of Iowa

#### Classical Groups, Integrals And Virasoro Constraints, Da Xu

*Theses and Dissertations*

First, we consider the group integrals where integrands are the monomials of matrix elements of irreducible representations of classical groups. These group integrals are invariants under the group action. Based on analysis on Young tableaux, we investigate some related duality theorems and compute the asymptotics of the

group integrals for fixed signatures, as the rank of the classical groups go to infinity. We also obtain the Viraosoro constraints for some partition functions, which are power series of the group integrals. Second, we show that the proof of Witten's conjecture can be simplified by using the fermion-boson correspondence, i.e ...

Relative Primeness, 2010 University of Iowa

#### Relative Primeness, Jeremiah N Reinkoester

*Theses and Dissertations*

In [2], Dan Anderson and Andrea Frazier introduced a generalized theory of factorization. Given a relation *τ* on the nonzero, nonunit elements of an integral domain *D*, they defined a *τ-factorization* of *a* to be any proper factorization *a = λa _{1} · · · a_{n}* where

*λ*is in

*U (D)*and

*a*is

_{i}*τ*-related to

*a*, denoted

_{j}*a*, for

_{i}τ a_{j}*i*not equal to

*j*. From here they developed an abstract theory of factorization that generalized factorization in the usual sense. They were able to develop a number of results analogous to results already known ...