Physical Sciences and Mathematics Commons^™

12. Kinesiology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

15. Pharmacy, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

19. Zoology, Northeastern State University

Oklahoma Research Day Abstracts

No abstract provided.

Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit

Williams Honors College, Honors Research Projects

In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.

Writing In The Geometry Classroom, Amy Lynn Rome

LSU Master's Theses

This study sought a time-efficient way to implement writing in ninth-grade Geometry. Students wrote responses to five expository writing prompts spread out over the spring semester of the 2014-2015 school year. Students’ first attempts were graded and returned to them along with feedback in the form of a teacher-written exemplar. Students rewrote assignments to improve their grades. All first and second attempts were collected and evaluated. We found that students were more successful after seeing the exemplar. Moreover, on assignments occurring later in the semester, more students were able to score in the top categories of the writing assignments on …

An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper

Theses and Dissertations

Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.

First, we create a …

Teacher Influence On Elementary School Students’ Participation In Science, Technology, Engineering, And Mathematics, Courtney Hartman

Honors College Theses

The purpose of this study is to explore the influence of elementary school teachers on encouraging students’ interest and participation in Science, Technology, Engineering, and Mathematics. The researcher sought to understand what methods teachers use in their classrooms to encourage students to participate in STEM subjects and programs. This mixed methods study consisted of a questionnaire to collect quantitative data, as well as an interview of selected teachers who participated in the questionnaire to collect qualitative data. The data was analyzed to determine the overall perceptions of teachers regarding the importance of encouraging students to participate in STEM. The qualitative …

Mathematics Education In A Multilingual And Multicultural Environment, Anjum Halai, Richard Barwell

Book Chapters / Conference Papers

No abstract provided.

I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch

Senior Independent Study Theses

This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.

Mathematics In Contemporary Society Chapter 4, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11 …

A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross

Department of Math & Statistics Faculty Publications

This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.

Non-Simplicial Decompositions Of Betti Diagrams Of Complete Intersections, Courtney Gibbons, Jack Jeffries, Sarah Mayes-Tang, Claudiu Raicu, Branden Stone, Bryan White

Articles

We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij-Soederberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences in such pure diagrams be totally ordered, we are able to define a multiplication law for Betti diagrams that respects the decomposition and allows us to write a simple expression of the decomposition of the Betti diagram of any complete intersection in terms of the degrees of its minimal generators. In the more traditional sense, the decomposition of complete intersections of codimension at most 3 …

Two Compact Incremental Prime Sieves, Jonathan P. Sorenson

Scholarship and Professional Work - LAS

A prime sieve is an algorithm that finds the primes up to a bound n. We say that a prime sieve is incremental, if it can quickly determine if n+1 is prime after having found all primes up to n. We say a sieve is compact if it uses roughly √n space or less. In this paper, we present two new results.

• We describe the rolling sieve, a practical, incremental prime sieve that takes O(n log log n) time and O(√n log n) bits of space.

• We also …

The Finite Embeddability Property For Some Noncommutative Knotted Varieties Of Rl And Drl, Riquelmi Salvador Cardona Fuentes

Electronic Theses and Dissertations

Residuated lattices, although originally considered in the realm of algebra providing a general setting for studying ideals in ring theory, were later shown to form algebraic models for substructural logics. The latter are non-classical logics that include intuitionistic, relevance, many-valued, and linear logic, among others. Most of the important examples of substructural logics are obtained by adding structural rules to the basic logical calculus FL. We denote by 𝖱𝖫𝑛 � the varieties of knotted residuated lattices. Examples of these knotted rules include integrality and contraction. The extension of �� by the rules corresponding to these two equations is …

Chaos And Learning In Discrete-Time Neural Networks, Jess M. Banks

Honors Papers

We study a family of discrete-time recurrent neural network models in which the synaptic connectivity changes slowly with respect to the neuronal dynamics. The fast (neuronal) dynamics of these models display a wealth of behaviors ranging from simple convergence and oscillation to chaos, and the addition of slow (synaptic) dynamics which mimic the biological mechanisms of learning and memory induces complex multiscale dynamics which render rigorous analysis quite difficult. Nevertheless, we prove a general result on the interplay of these two dynamical timescales, demarcating a regime of parameter space within which a gradual dampening of chaotic neuronal behavior is induced …

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.

A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr.

Georgia Educational Research Association Conference

The purpose of this qualitative study was to explain how ninth grade mathematics students at a rural high school in Georgia constructed knowledge through student talk when problem solving using Kapur’s (2012) productive failure design. An embedded case study design was used to understand how a group of students constructed knowledge through their use of talk, persistence during the task, and use of prior knowledge while working on a productive failure modeled task. Triangulation resulted from the collected data from multiple sources, which included videotaping, interviewing, and analyzing student artifacts. Utilization of the constructivist perspectives of Vygotsky (1934/1962), Piaget (1971), …

The Cosm Newsletter

The COSM Newsletter (2008-2018)

• The College of Science and Mathematics Welcomes New Administration in the Dean’s Office
• COSM Faculty and Staff Recognized at College and University Levels
• College Awards
• University Awards
• Summer SOAR Project: Books for Back Pack Buddies
• COSM Alum Honored in Promotion Ceremony at the Pentagon
• Altrusa partners with Georgia Southern Pre-Vet Students for First Annual Dog Wash
• Two COSM Undergrads selected for Prestigious Summer Research Programs
• The Department of Biology Welcomes New Faculty
• Dr. Ed Mondor Named 2014 Outstanding Advocate for First Year Students
• Distinguished Alumnus Chosen
• Honor’s Day Ceremony Resumes
• Professor Gives Talk at 11th Congress on the Biology of …

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 …

Mathematical Modeling Of Tick-Borne Encephalitis In Humans, Amanda Kriesel, Michael Meyer, Geoffrey Peterson

Journal of Undergraduate Research at Minnesota State University, Mankato

Tick-Borne Encephalitis is a virus that affects ones nervous system and is transmitted from tick to human through tick bite. In recent years, the number of cases of tick-borne encephalitis in Europe has been increasing. This mathematical biological model of Tick-Borne Encephalitis was created in order to further our understanding of such phenomenon, as well as study the relationship between vectors and their hosts. Specifically, we will investigate the population model of ticks in certain regions and its correlation to tick-borne encephalitis infections in the region.

Choosing Between Parametric And Non-Parametric Tests, Russ Johnson

Journal of Undergraduate Research at Minnesota State University, Mankato

A common question in comparing two sets of measurements is whether to use a parametric testing procedure or a non-parametric procedure. The question is even more important in dealing with smaller samples. Here, using simulation, several parametric and nonparametric tests, such as, t-test, Normal test, Wilcoxon Rank Sum test, van-der Waerden Score test, and Exponential Score test are compared.

On Sign-Solvable Linear Systems And Their Applications In Economics, Eric Hanson

Journal of Undergraduate Research at Minnesota State University, Mankato

Sign-solvable linear systems are part of a branch of mathematics called qualitative matrix theory. Qualitative matrix theory is a development of matrix theory based on the sign (¡; 0; +) of the entries of a matrix. Sign-solvable linear systems are useful in analyzing situations in which quantitative data is unknown or had to measure, but qualitative information is known. These situations arise frequently in a variety of disciplines outside of mathematics, including economics and biology. The applications of sign-solvable linear systems in economics are documented and the development of new examples is formalized mathematically. Additionally, recent mathematical developments about sign-solvable …

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.

Structure Of Lipid Bilayers, John Nagle, Stephanie Tristram-Nagle

Prof. Stephanie Tristram-Nagle Ph.D.

The quantitative experimental uncertainty in the structure of fully hydrated, biologically relevant, fluid (L(alpha)) phase lipid bilayers has been too large to provide a firm base for applications or for comparison with simulations. Many structural methods are reviewed including modern liquid crystallography of lipid bilayers that deals with the fully developed undulation fluctuations that occur in the L(alpha) phase. These fluctuations degrade the higher order diffraction data in a way that, if unrecognized, leads to erroneous conclusions regarding bilayer structure. Diffraction measurements at high instrumental resolution provide a measure of these fluctuations. In addition to providing better structural determination, this …

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: …

Transposing Noninvertible Polynomials, Nathan Cordner

Library Research Grants

In the class of invertible polynomials, the notion of dual polynomials W and W^T, as well as dual groups G and G^T is well-understood. In this paper we investigate finding dual pairs W and W^T for noninvertible polynomials. We find that in many instances, our intuition that stems from invertible polynomials does not extend to the noninvertible case.

Fields In Math And Farming, Susan D'Agostino

Journal of Humanistic Mathematics

A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.