Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, 2010 Utah State University

#### Classical Foundations For A Quantum Theory Of Time In A Two-Dimensional Spacetime, Nathan Thomas Carruth

*All Graduate Theses and Dissertations*

We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.

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.

Computational Circle Packing: Geometry And Discrete Analytic Function Theory, 2010 University of Tennessee, Knoxville

#### Computational Circle Packing: Geometry And Discrete Analytic Function Theory, Gerald Lee Orick

*Doctoral Dissertations*

Geometric Circle Packings are of interest not only for their aesthetic appeal but also their relation to discrete analytic function theory. This thesis presents new computational methods which enable additional practical applications for circle packing geometry along with providing a new discrete analytic interpretation of the classical Schwarzian derivative and traditional univalence criterion of classical analytic function theory. To this end I present a new method of computing the maximal packing and solving the circle packing layout problem for a simplicial 2-complex along with additional geometric variants and applications. This thesis also presents a geometric *discrete Schwarzian* quantity whose value ...

Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, 2010 Western Michigan University

#### Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, Anirban Dutta

*Dissertations*

Pricing derivatives is one of the central issues in mathematical finance. The seminal work of Black, Scholes and Merton has been the cornerstone of option pricing since their introduction in 1973. Their work influenced the pricing theory of other derivatives as well.

This derivative pricing theory has two primary shortcomings. Firstly, the theoretical pricing in such theories are not accompanied by a stable trading strategy. Secondly, they often assume that the market agents use a uniform model for the underlying instrument and that the market prices of the derivatives reveal all the information about the underlying instrument.

Theoreticians like Grossman ...

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 ...

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?

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 ...

Dancing With Heretics: Essays On Orthodoxy, Questioning And Faith, 2010 Utah State University

#### Dancing With Heretics: Essays On Orthodoxy, Questioning And Faith, Darren M. Edwards

*All Graduate Theses and Dissertations*

While much has been written about the conflicts, supposed or actual, between logic and faith, science and religion, few accounts of the personal turmoil these conflicts can cause exist. Likewise, many of these nonfiction accounts are written from a distinctly polarized place leaning either to science or faith.

In this thesis, I mix research and history with memoir and a sense of poetry to explore my personal experience with this conflict. At its outset, I hoped for this project to capture my struggle as an orthodox member of The Church of Jesus Christ of Latter-day Saints (LDS) in dealing with ...

The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, 2010 Utah State University

#### The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, Fangjuan Hou

*All Graduate Theses and Dissertations*

Explicit timing and interspersal assignments have been validated as effective methods to facilitate students' math practice. However, no researchers have explored the combinative effect of these two methods. In Study 1, we extended the literature by comparing the effect of explicit timing with interspersal assignments, and interspersal assignments without timing. Generally, participants' rate of digits correct on easy and hard addition problems was higher during the explicit timing condition than during the untimed condition. However, the participants' rate of digits correct decreased after initial implementation of the explicit timing condition.

Motivation plays a crucial role in maintaining performance levels and ...

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.

Time Series Models For Computing Activation In Fmri, 2010 Iowa State University - Graduate Student

#### Time Series Models For Computing Activation In Fmri, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

No abstract provided.

Development Of A Discrete Mathematics Textbook And Guide For High School Teachers, 2010 Utah State University

#### Development Of A Discrete Mathematics Textbook And Guide For High School Teachers, Rebecca A. Stokes

*All Graduate Plan B and other Reports*

This project was to create the beginnings a textbook for teacher's to supplement instruction of a discrete mathematics course at the high school level. The development of the text was guided by past and current efforts to place discrete mathematics in high school curriculum. A review of the literature and experiences of instructors were viewed and analyzed to guide the construction of the textbook. The text was written with the goal to give teachers information about the topics of discrete mathematics, extra resources, lesson ideas , and optional worksheets for students. Several lessons were created and one was implemented in ...

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 ...

Carleson-Type Inequalitites In Harmonically Weighted Dirichlet Spaces, 2010 University of Tennessee - Knoxville

#### Carleson-Type Inequalitites In Harmonically Weighted Dirichlet Spaces, Gerardo Roman Chacon Perez

*Doctoral Dissertations*

Carleson measures for Harmonically Weighted Dirichlet Spaces are characterized. It is shown a version of a maximal inequality for these spaces. Also, Interpolating Sequences and Closed-Range Composition Operators are studied in this context.

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 ...

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 ...

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 ...

Analysis Of Discrete Data Under Order Restrictions, 2010 Georgia Southern University

#### Analysis Of Discrete Data Under Order Restrictions, Jeff Campbell

*Electronic Theses and Dissertations*

Strategies for the analysis of discrete data under order restrictions are discussed. We consider inference for sequences of binomial populations, and the corresponding risk difference, relative risk and odds ratios. These concepts are extended to deal with independent multinomial populations. Natural orderings such as stochastic ordering and cumulative ratio probability ordering are discussed. Methods are developed for the estimation and testing of differences between binomial as well as multinomial populations under order restrictions. In particular, inference for sequences of ordered binomial probabilities and cumulative probability ratios in multinomial populations are presented. Closed-form estimates of the multinomial parameters under order restrictions ...

Weighted Inverse Weibull And Beta-Inverse Weibull Distribution, 2010 Georgia Southern University

#### Weighted Inverse Weibull And Beta-Inverse Weibull Distribution, Jing Xiong Kersey

*Electronic Theses and Dissertations*

The weighted inverse Weibull distribution and the beta-inverse Weibull distribution are considered. Theoretical properties of the inverse Weibull model, weighted inverse Weibull distribution including the hazard function, reverse hazard function, moments, moment generating function, coefficient of variation, coefficient of skewness, coefficient of kurtosis, Fisher information and Shanon entropy are studied. The estimation for the parameters of the length-biased inverse Weibull distribution via maximum likelihood estimation and method of moment estimation techniques are presented, as well as a test for the detection of length-biasedness in the inverse Weibull model. Furthermore, the beta-inverse Weibull distribution which is a weighted distribution is presented ...

Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, 2010 Marquette University

#### Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, Leigh A. Van Den Kieboom, Marta Magiera, John Moyer

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the ...