Physical Sciences and Mathematics Commons^™

K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.

Doctoral Theses

This thesis discusses the K-theory of quadratic modules by studying Roys elementary orthogonal group of the quadratic space Q1H(P) over a commutative ring A. We estab- lish a set of commutator relations among the elementary generators of Roys elementary orthogonal group and use this to prove Quillens local-global principle for this elementary group. We also obtain a result on extendability of quadratic modules. We establish nor- mality of the elementary orthogonal group under certain conditions and prove stability results for the Ki group of this orthogonal group. We also prove that Roys elementary orthogonal group and Petrovs odd hyperbolic unitary …

Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.

Doctoral Theses

Completely positive (CP-) maps are special kinds of positivity preserving maps on C ∗ -algebras. W.F. Stinespring [Sti55] obtained a structure theorem for CP-maps showing that they are closely connected with ∗-homomorphisms. W. Arveson and other operator algebraists quickly realized the importance of these maps. Presently the role of the theory of CP-maps in our understanding of C ∗ -algebras and von Neumann algebras is well recognised. It has been argued by physicists that CPmaps are physically more meaningful than just positive maps due to their stability under ampliations. From quantum probabilistic point of view CP-maps are quantum analogues of …

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

All At One Point: The New Physics Of Italo Calvino And Jorge Luis Borges, Mark Thomas Rinaldi

Dissertations, Theses, and Capstone Projects

This work of comparative literary criticism focuses on the presence of mathematical and scientific concepts and imagery in the works of Italo Calvino and Jorge Luis Borges, beginning with an historical overview of scientific philosophy and an introduction to the most significant scientific concepts of the last several centuries, before shifting to deep, scientifically-driven analyses of numerous individual fictions, and finally concluding with a meditation on the unexpectedly fictive aspects of science and mathematics. The close readings of these authors' fictions are contextualized with thorough explanations of the potential literary implications of theories from physics, mathematics, neuroscience and chaos theory. …

Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.

Doctoral Theses

In this chapter, we explain the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. We introduce some notations and preliminaries that will be used in the subsequent chapters.Study of proximinality related properties and ball intersection related properties of Banach spaces have been an active area of research in the field of geometry of Banach spaces. In this thesis, we mainly study these two classes of Banach space theoretic properties.We consider only Banach spaces over the real field R and all subspaces we consider are assumed to be closed.1.1 PreliminariesFor a Banach …

On The Group Of Transvections Of Ade-Diagrams, Marvin Jones

Theses and Dissertations

In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kⁿ (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : G_f,S ! SL(Z)_n where g(X) = P⁻¹XP where P is the change of basis matrix for S to H.

Student Application Of The Fundamental Theorem Of Calculus With Graphical Representations In Mathematics And Physics, Rabindra R. Bajracharya

Electronic Theses and Dissertations

One mathematical concept frequently applied in physics is the Fundamental Theorem of Calculus (FTC). Mathematics education research on student understanding of the FTC indicates student difficulties with the FTC. Similarly, a few studies in physics education have implicitly indicated student difficulties with various facets of the FTC, such as with the definite integral and the area under the curve representation, in physics contexts. There has been no research on how students apply the FTC in graphically-based physics questions.

This study investigated student understanding of the FTC and its application to graphically-based problems. Our interest spans several aspects of the FTC: …

Cal Poly Women’S Basketball 2013-2014 Shot Selection Analysis, Noah Alexander Zwarg Mr.

Statistics

The initial goal of my senior project was to find some way to help the Cal Poly women’s basketball team score more efficiently. The first idea that came to my mind on how I could accomplish this goal was to look at the most important thing when it comes to scoring more points, the shot itself. I went with my initial idea and recorded each shot that a player took during the 2013-2014 season and categorized each shot by the distance it was taken (close, medium, long, or three), and whether the shot was open or guarded for a total …

On The Evolution Of Virulence, Thi Nguyen

Electronic Theses, Projects, and Dissertations

The goal of this thesis is to study the dynamics behind the evolution of virulence. We examine first the underlying mechanics of linear systems of ordinary differential equations by investigating the classification of fixed points in these systems, then applying these techniques to nonlinear systems. We then seek to establish the validity of a system that models the population dynamics of uninfected and infected hosts---first with one parasite strain, then n strains. We define the basic reproductive ratio of a parasite, and study its relationship to the evolution of virulence. Lastly, we investigate the mathematics behind superinfection.

La Vie De Blaise Pascal Et Son Heritage Mathématique Et Philosophique, Katherine Weeks

Honors Theses

This paper will discuss the life of Blaise Pascal, his philosophy and mathematics. We will first study the life of Pascal, by looking at his family, the success of his family, and how he was educated. We will then move onto study the history of the arithmetic triangle, which eventually becomes known as Pascal’s Triangle. Finally we will look at Pascal’s Pensées. Finally we will conclude that Pascal is not only known for Pascal’s Triangle but also his legacy in the Philosophic world. It becomes clear that Pascal would not have been the mathematician he was without the philosophy, and …

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

Teachers' Beliefs And Practices Regarding Homework: An Examination Of The Cognitive Domain Embedded In Third Grade Mathematics Homework, Pandora Dell Bedford

Theses and Dissertations

The purpose of this phenomenological study was to gain a better understanding of third grade math teachers''beliefs and practices regarding homework, to explain how teachers''beliefs and practices regarding homework aligned to the framework of the Revised Bloom's'Taxonomy Cognitive Domain, and to determine the administrative influences on homework practices. The data were collected during October and November 2013. Six third grade math teachers (primary unit of analysis) and four principals (secondary unit of analysis) were interviewed from Dell School District. Each participant (teacher and principal) was interviewed for approximately one hour. A second meeting was set at a later time with …

Convexity Properties Of The Diestel-Leader Group Γ_3(2), Peter J. Davids

Honors Projects

The Diestel-Leader groups are a family of groups first introduced in 2001 by Diestel and Leader in [7]. In this paper, we demonstrate that the Diestel-Leader group Γ₃(2) is not almost convex with respect to a particular generating set S. Almost convexity is a geometric property that has been shown by Cannon [3] to guarantee a solvable word problem (that is, in any almost convex group there is a finite-step algorithm to determine if two strings of generators, or “words”, represent the same group element). Our proof relies on the word length formula given by Stein and Taback …

Calculator Usage In Secondary Level Classrooms: The Ongoing Debate, Nicole Plummer

Honors College Theses

With technology becoming more prevalent every day, it is imperative that students gain enough experience with different technological tools in order to be successful in the “real-world”. This thesis will discuss the debate and overall support for an increased usage of calculators as tools in the secondary level classroom. When the idea of calculators in the classroom first came to life, many educators were very apprehensive and quite hesitant of this change. Unfortunately, more than 40 years later, there is still hesitation for their usage; and rightfully so. While there are plenty of advantages of calculator use in the classroom, …

Inversion Of The Broken Ray Transform, Roman Krylov

Electronic Theses and Dissertations

The broken ray transform (BRT) is an integral of a function along a union of two rays with a common vertex. Consider an X-ray beam scanning an object of interest. The ray undergoes attenuation and scatters in all directions inside the object. This phenomena may happen repeatedly until the photons either exit the object or are completely absorbed. In our work we assume the single scattering approximation when the intensity of the rays scattered more than once is negligibly small. Among all paths that the scattered rays travel inside the object we pick the one that is a union of …

Re-Analysis Of The World Data On The Emc Effect And Extrapolation To Nuclear Matter, Stacy E. Karthas

Honors Theses and Capstones

The EMC effect has been investigated by physicists over the past 30 years since it was discovered at CERN. This effect shows that the internal nucleon structure varies when in the nuclear medium. Data from SLAC E139 and JLab E03 103 were studied with the Coulomb correction and directly compared. The Coulomb distortion had a greater impact on the JLab data due to slightly lower energies and different kinematics. The EMC ratio was found to have a dependence on a kinematic variable, which was removed when Coulomb corrections were applied. The methodology was developed to apply Coulomb corrections, which had …

Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder

Senior Independent Study Theses

An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …

A Bayesian Model Of Fertility Decisions In Relationship To Female Labor Force Participation, Rebecca C. Wardrop

Senior Independent Study Theses

Due to the increasing number of women in the labor force, opportunity costs associated with labor force participation are becoming an important factor in fertility decisions. Further, these decisions are assumed to be dynamic as the opportunity costs change as a woman progresses through her career. A Bayesian statistical model , which allows the distribution of the likelihood of having children to be updated as information is gathered, lends itself to the dynamicity of the decision-making process. A generalized model for fertility decisions in terms of labor force participation is created. I also discuss potentials for implementation and furthering the …

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

Markov Chain Theory With Applications To Baseball, Cal D. Thomay

Senior Independent Study Theses

The applications of Markov chains span a wide range of fields to which models have been designed and implemented to simulate random processes. Markov chains are stochastic processes that are characterized by their memoryless property, where the probability of the process being in the next state of the system depends only on the current state and not on any of the previous states. This property is known as the Markov property. This thesis paper will first introduce the theory of Markov chains, along with explaining two types of Markov chains that will be beneficial in creating a model for analyzing …

The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen

Senior Independent Study Theses

The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …

Education And Women Mathematicians In The Middle East, Syeda Tooba Zahra

Legacy Theses & Dissertations (2009 - 2024)

Middle Eastern women have made important contributions in the field of Mathematics. The purpose of this thesis is to understand the educational background for women in the Middle East and look at the life and contribution of a sample of women mathematicians in representative Middle Eastern countries such as Turkey, Lebanon, Iran, and Pakistan.