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 ...

Developmental Understanding Of The Equals Sign And Its Effects On Success In Algebra, 2010 Boise State University

#### Developmental Understanding Of The Equals Sign And Its Effects On Success In Algebra, Ryan W. Brown

*Boise State University Theses and Dissertations*

For some students, the equals symbol is viewed as a directive to carry out a procedure, instead of a symbol expressing mathematical equivalence. The purpose of this study was to develop and to pilot a questionnaire to measure students’ understandings of relational equivalence as implied by their interpretations and use of the equals symbol. The results of this questionnaire were compared with student testing data with the goal of determining a correlation between understanding of symbolic equivalence and success in a typical algebra course. It was found that students who demonstrated an ability to define and articulate an appropriate meaning ...

Stably Free Modules Over The Klein Bottle, 2010 Boise State University

#### Stably Free Modules Over The Klein Bottle, Andrew Misseldine

*Boise State University Theses and Dissertations*

This paper is concerned with constructing countably many, non-free stably free modules for the Klein bottle group. The work is based on the papers “Stably Free, Projective Right Ideals" by J.T. Stafford (1985) and “Projective, Nonfree Modules Over Group Rings of Solvable Groups" by V. A. Artamonov (1981). Stafford proves general results that guarantee the existence of non-free stably frees for the Klein bottle group but has not made the argument explicit. Artamonov allows us to construct infinitely many non-free stably free modules. This paper will also construct presentations and sets of generators for these modules. This paper concludes ...

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 ...

On The Irreducibility Of The Cauchy-Mirimanoff Polynomials, 2010 University of Tennessee - Knoxville

#### On The Irreducibility Of The Cauchy-Mirimanoff Polynomials, Brian C. Irick

*Doctoral Dissertations*

The Cauchy-Mirimanoff Polynomials are a class of polynomials that naturally arise in various classical studies of Fermat's Last Theorem. Originally conjectured to be irreducible over 100 years ago, the irreducibility of the Cauchy-Mirimanoff polynomials is still an open conjecture.

This dissertation takes a new approach to the study of the Cauchy-Mirimanoff Polynomials. The reciprocal transform of a self-reciprocal polynomial is defined, and the reciprocal transforms of the Cauchy-Mirimanoff Polynomials are found and studied. Particular attention is given to the Cauchy-Mirimanoff Polynomials with index three times a power of a prime, and it is shown that the Cauchy-Mirimanoff Polynomials of ...

The Origins Of Mathematical Societies And Journals, 2010 University of Tennessee - Knoxville

#### The Origins Of Mathematical Societies And Journals, Eric S. Savage

*Masters Theses*

We investigate the origins of mathematical societies and journals. We argue that the origins of today’s professional societies and journals have their roots in the informal gatherings of mathematicians in 17th century Italy, France, and England. The small gatherings in these nations began as academies and after gaining government recognition and support, they became the ancestors of the professional societies that exist today. We provide a brief background on the influences of the Renaissance and Reformation before discussing the formation of mathematical academies in each country.

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 ...

A Criterion For Identifying Stressors In Non-Linear Equations Using Gröbner Bases, 2010 The University of Southern Mississippi

#### A Criterion For Identifying Stressors In Non-Linear Equations Using Gröbner Bases, Elisabeth Marie Palchak

*Honors Theses*

No abstract provided.

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 ...

Fractions Of Numerical Semigroups, 2010 University of Tennessee - Knoxville

#### Fractions Of Numerical Semigroups, Harold Justin Smith

*Doctoral Dissertations*

Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown.

Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is ...

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 ...