Physical Sciences and Mathematics Commons^™

Change Bell Ringing And Mathematics: A High School Student Excursion Into Graph Theory And Group Theory, Kristi Carlson

Honors Theses

This unit was created as a way to introduce higher level mathematics concepts to advanced high school students. All five of the National Council of Teachers of Mathematics Process Standards are found in this unit. For most of the unit, students work within small groups

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen

Theses and Dissertations

Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described. Definitions of fusion rules and fusors are introduced, along with the functor categories of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researcher's choice. One such objective function, a functional on families of classification systems, and in particular, receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument that minimizes it …

Parity Theorems For Combinatorial Statistics, Mark A. Shattuck

Doctoral Dissertations

A q-generalization Gn(q) of a combinatorial sequence Gn which reduces to that sequence when q = 1 is obtained by q-counting a statistic defined on a sequence of finite discrete structures enumerated by Gn. In what follows, we evaluate Gn(−1) for statistics on several classes of discrete structures, giving both algebraic and combinatorial proofs. For the latter, we define appropriate sign-reversing involutions on the associated structures. We shall call the actual algebraic result of such an evaluation at q = −1 a parity theorem (for the …

Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis

Theses and Dissertations

This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo

Theses and Dissertations

The purpose of this paper is to provide new examples supporting a conjecture of Ash, Doud, and Pollack. This conjecture involves Galois representations taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant.

A Bayesian Approach To Wireless Location Problems, Ivan Zorych

Dissertations

Several approaches for indoor location estimation in wireless networks are proposed. We explore non-hierarchical and hierarchical Bayesian graphical models that use prior knowledge about physics of signal propagation, as well as different modifications of Bayesian bivariate spline models. The hierarchical Bayesian model that incorporates information about locations of access points achieves accuracy that is similar to other published models and algorithms, but by using prior knowledge, this model drastically reduces the requirement for training data when compared to existing approaches. Proposed Bayesian bivariate spline models for location surpass predictive accuracy of existing methods. It has been shown that different versions …

Building Efficient Systems From Data In A Computational Intelligence Framework, Debrup Chakraborty Dr.

Doctoral Theses

There are problems of interest for which precise mathematical or physical understanding is yet to come. Let us illustrate this with an example. Suppose, for a mining operation one needs to blast a certain portion of the soil/rock using some specific ex- plosives. Before the blast is made, the miners want to know the intensity of vibration that would be produced at a certain distance from the site of blasting. The intensity of vibration may de pend on several factors. For example, it will depend on the characteristics and quantity of the explosive used, the rock characteristics of the region, …

Analyzing The Combination Of Polymorphisms Associating With Antidepressant Response By Exact Conditional Test, Baofu Ma

Mathematics Theses

Genetic factors have been shown to be involved in etiology of a poor response to the antidepressant treatment with sufficient dosage and duration. Our goal was to identify the role of polymorphisms in the poor response to the treatment. To this end, 5 functional polymorphisms in 109 patients diagnosed with unipolar, major depressive disorder are analyzed. Due to the small sample size, exact conditional tests are utilized to analyze the contingency table. The data analysis involves: (1) Exact test for conditional independence in a high dimensional contingency table; (2) Marginal independence test; (3) Exact test for three-way interactions. The efficiency …

Hypersurfaces Of Prescribed Curvature In Hyperbolic Space, Marek Szapiel

Doctoral Dissertations

In this paper we consider the problem of existence of hypersurfaces with prescribed curvature in hyperbolic space. We use the upper half-space model of hyperbolic space. The hypersurfaces we consider are given as graphs of positive functions on some domain Ω ∈ Rⁿ satisfying equations of form

f (A) = f (κ₁, . . . , κ_n) = ψ,

where A is the second fundamental form of a hypersurface, f (A) is a smooth sym- metric function of the eigenvalues of A and ψ is a function of position. If we impose certain conditions …

The Classification Of Links Of Up To And Including Thirteen Crossings, Dylan Joshua Faullin

Masters Theses

The prime links of up to 13 crossings are classified up to unoriented equivalence.

Mathematics, Meaning, And Identity : A Study Of The Practice Of Mathematics Education In A Rural High School, Rick Anderson

Dissertations and Theses

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community.

The findings suggest that high school mathematics education is related to the rural …

A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson

Theses and Dissertations

This thesis presents a simple force-based model of moving and interacting cells that incorporates a realistic description of cell adhesion and applies it to a system of spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.

Principal Component Regression For Construction Of Wing Weight Estimation Models, Humberto Rocha

Mathematics & Statistics Theses & Dissertations

The multivariate data fitting problem occurs frequently in many branches of science and engineering. It is very easy to fit a data set exactly by a mathematical model no matter how the data points are distributed. But building a response by using a limited number of poorly distributed data points is very unreliable, yet necessary in conceptual design process. This thesis documents the lessons learned from fitting the wing weight data of 41 subsonic transports by three types of interpolation methods---least polynomial interpolation, radial basis function interpolation, and Kriging interpolation. The objective of this thesis is to develop an automatic …

Maximal Surfaces In Complexes, Allen J. Dickson

Theses and Dissertations

Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula …

An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson

Theses and Dissertations

I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.

Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus

Theses and Dissertations

In this thesis, we study the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup

Theses and Dissertations

Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.

Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle

Theses and Dissertations

A pension plan administrator promises certain benefits in the future in exchange for labor today. In order to budget for this expense and create more security for the participant, the administrator uses a pension cost method. Each cost method assigns a portion of the future liability to the current year. This is called the normal cost. We calculate the normal cost under three cost methods using different annuity, interest and inflation assumptions. Then we make comparisons between cost methods as well as between assumption changes. The cost methods considered in this paper are the unit credit cost method, projected unit …

Explicit Computations Supporting A Generalization Of Serre's Conjecture, Brian Francis Hansen

Theses and Dissertations

Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation.

Influences Of Surfactant On The Breakup Of A Fluid Jet In Viscous Surrounding, Muhammad Irfan Hameed

Dissertations

The effect of insoluble surfactant on the breakup of a fluid jet surrounded by another viscous fluid at low Reynolds number is studied both theoretically and experimentally. Equations governing the evolution of the interface and surfactant concentration are derived using a long wavelength approximation for the case of an inviscid jet and a slightly viscous jet surrounded by a more viscous fluid. These one dimensional partial differential equations governing the evolution of the slender jet are solved numerically for given initial interfacial perturbations and surfactant concentration. It is found that the presence of insoluble surfactant at the interface retards the …

Theory And Algorithms For Swept Manifold Intersections, Yuriy Mileyko

Dissertations

Recent developments in such fields as computer aided geometric design, geometric modeling, and computational topology have generated a spate of interest towards geometric objects called swept volumes. Besides their great applicability in various practical areas, the mere geometry and topology of these entities make them a perfect testbed for novel approaches aimed at analyzing and representing geometric objects. The structure of swept volumes reveals that it is also important to focus on a little simpler, although a very similar type of objects - swept manifolds. In particular, effective computability of swept manifold intersections is of major concern.

The main goal …

Electromagnetic And Acoustic Propagation In Strip Lines And Porous Media, Lin Zhou

Dissertations

Wave propagation in two physical structures is described and analyzed in this dissertation. In the first problem, the propagation of a normally incident plane acoustic wave through a three dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength λ and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the …

The Control Of Frequency Of A Conditional Oscillator Simultaneously Subjected To Multiple Oscillatory Inputs, Christina L. Ambrosio

Dissertations

A conditional oscillator is one that requires input to oscillate. An example of such is the gastric mill network of the stomatogastric ganglion of the crab Cancer borealis which requires modulatory input from outside the stomatogastric ganglion and fast input from the pyloric network of the animal in order to become active. This dissertation studies how the frequency of the gastric mill network is determined when it is simultaneously subjected to two different rhythmic inputs whose timing may be mismatched. We derive a mathematical model of the gastric mill network and deduce that the difference in timing between the pyloric …

The Lie Symmetries Of A Few Classes Of Harmonic Functions, Willis L. Petersen

Theses and Dissertations

In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the resulting transformations. In this paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with …

Hopf Bifurcations And Horseshoes Especially Applied To The Brusselator, Steven R. Jones

Theses and Dissertations

In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system.

Graph Theory For The Secondary School Classroom., Dayna Brown Smithers

Electronic Theses and Dissertations

After recognizing the beauty and the utility of Graph Theory in solving a variety of problems, the author decided that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in Graph Theory, namely Vertex Coloring, Minimum Spanning Tree, Domination, and Hamiltonian Paths and Cycles, which are appropriate for high school level.

Measuring Inter-Rater Agreement Among Pathologists In Cancer Screening Studies, Krystle S. Oates

Electronic Dissertations and Theses

Although cervical cancer is one of the most preventable forms of cancer in the United States, it still remains the leading cause of cancer mortality in El Salvador. This is attributed to poor cancer screening in El Salvador. The Pap smear test is the traditional screening method that pathologists use for the direction of cervical cancer in women, but the Thin Prep test is said to be an improvement to the Prep smear test. In this project, we will use the data from pathologists in the United States and El Salvador who analyzed the slides of 471 Salvadoran women who …

On The Nature Of Connectivity Types, Miao Xu

Honors Theses

No abstract provided.