Mathematics Commons^™

02. Animal Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

09. Environmental Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

07. Criminal Justice, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

11. Genetics, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

08. Engineering, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

13. Mathematics, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

14. Optometry, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

16. Physics, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

17. Psychology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

19. Zoology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

06. Computer Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

03. Biology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

05. Chemistry, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

10. Forensic Science, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

12. Kinesiology, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

15. Pharmacy, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

18. Statistics, University Of Central Oklahoma

Oklahoma Research Day Abstracts

No abstract provided.

Diophantine Geometry, Eulerian Number Theory, And Undergraduates, Christopher D. Goff

College of the Pacific Faculty Presentations

This talk will tell the story of how a geometry problem of Diophantus led all the way to a paper of Euler on number theory. Then we will describe how translating this work of Euler led ultimately to an undergraduate project in a History of Mathematics course last spring.

The Brave New World Of Open Access & Creative Commons: A Humanistic Experiment In Mathematical Publishing, Gizem Karaali

Pomona Faculty Publications and Research

In January 2011 the Journal of Humanistic Mathematics (JHM) published its first issue. JHM (http://scholarship.claremont.edu/jhm) is an online-only, peer-reviewed, open-access journal which has passed the all important ten-thousand-download barrier in its first anniversary. In order to remain faithful to the fundamental principles of open access, JHM uses Creative Commons licensing, where authors retain copyright of their work, but others are free to reuse them (with proper attribution). In this note I share and reflect upon our experience with open access and Creative Commons.

Measuring Habits Of Mind: Toward A Prompt-Less Instrument For Assessing Quantitative Literacy, Stuart Boersma, Dominic Klyve

Numeracy

In this study, we offer a new “prompt-less” instrument for measuring students’ habits of mind in the field of quantitative literacy. The instrument consists of a series of questions about a newspaper article the students read. The questions do not explicitly solicit quantitative information; students’ habit of mind is assessed by their use of quantitative reasoning even when it is not asked for. Students’ answers were graded according to a modified version of the Quantitative Literacy Assessment Rubric (QLAR) published in this journal (vol. 4, issue 2). We applied the instrument and rubric to assess pre- and post-intervention habits of …

Using A Media-Article Approach To Quantitative Reasoning As An Honors Course: An Exploratory Study, Stuart Boersma, Dominic Klyve

Numeracy

In this study, we investigate student performance on a basic skills assessment of percentages and ratios in two cohorts of students: the general (non-STEM) student body (cohort G) and (non-STEM) honors students (cohort H). Both cohorts used a media-article approach to the study of quantitative reasoning. A pre- and a post-intervention assessment were administered with a two-week intervention period consisting of critical analyses of the use of percentages and ratios in media articles. Using non-parametric techniques, no statistically significant improvement was measured in cohort G while cohort H students showed statistically significant improvement on several items.

The Scope Of Numeracy After Five Years, H. L. Vacher, Dorothy Wallace

Numeracy

The purpose of this editorial is to provide an efficient way for readers and potential authors to see (a) what type of papers are published in this journal and (b) what subjects are appropriate. The editorial consists mainly of about a dozen pages of tables including live links to the papers’ access/abstract pages to facilitate easy browsing. In the first table, the 85 papers that have been published in the journal’s first five years are classified into: review papers; research papers; case studies; essays; book reviews; columns; and editorials about the journal. In the second table, the papers are inventoried …

Full Stability In Optimization, Nghia Tran

Wayne State University Dissertations

The dissertation concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to

parametric variational systems including the well-known generalized equations and variational inequalities. Many relationships of full stability with the conventional notions …

Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications, Sean Michael Tilson

Wayne State University Dissertations

We construct Power operations in the K"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of the homotopy of relative smash products as being related to obstructions to having $E_infty$ ring maps. The operations in the $C_2$-equivariant Adams spectral sequence are a partial extension of the work of Bruner in cite{HRS} and have applications to motivic homotopy theory.

Discrete Littlewood-Paley-Stein Theory And Wolff Potentials On Homogeneous Spaces And Multi-Parameter Hardy Spaces, Yayuan Xiao

Wayne State University Dissertations

This dissertation consists of two parts:

In part I, We establish a new atomic decomposition of the multi-parameter Hardy spaces of homogeneous type and obtain the associated $H^p-L^p$ and $H^p-H^p$ boundedness criterions for singular integral operators. On the other hand, we compare the Wolff and Riesz potentials on spaces of homogenous type, followed by a Hardy-Littlewood-Sobolev type inequality. Then we drive integrability estimates of positive solutions to the Lane-Emden type integral systems on spaces of homogeneous type.

In part II, We establish a $(p,2)$-atomic decomposition of the Hardy space associated with different homogeneities for $0

Error Bounds For The Lanczos Methods For Approximating Matrix Exponentials, Qiang Ye

Mathematics Faculty Publications

In this paper, we present new error bounds for the Lanczos method and the shift-and-invert Lanczos method for computing e−^τAv for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos method will converge rapidly if the matrix A is well-conditioned, regardless of what the norm of τA is. Numerical examples are given to demonstrate the theoretical bounds.

Proof And Problem Solving At University Level, Annie Selden, John Selden

The Mathematics Enthusiast

This paper will be concerned with undergraduate and graduate students’ problem solving as they encounter it in attempting to prove theorems, mainly to satisfy their professors in their courses, but also as they conduct original research for theses and dissertations. We take Schoenfeld’s (1985) view of problem, namely, a mathematical task is a problem for an individual if that person does not already know a method of solution for that task. Thus, a given task may be a problem for one individual, who does not already know a solution method for that task, or it may be an exercise for …

A Proposal For A Problem-Driven Mathematics Curriculum Framework, Judith S. Zawojewski, Marta T. Magiera, Richard Lesh

The Mathematics Enthusiast

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework.

Maximum Principle Preserving High Order Schemes For Convection-Dominated Diffusion Equations, Yi Jiang

Dissertations, Master's Theses and Master's Reports - Open

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains …

Lattice Platonic Solids And Their Ehrhart Polynomial, Eugen J. Ionascu

Faculty Bibliography

First, we calculate the Ehrhart polynomial associated with an arbitrary cube with integer coordinates for its vertices. Then, we use this result to derive relationships between the Ehrhart polynomials for regular lattice tetrahedra and those for regular lattice octahedra. These relations allow one to reduce the calculation of these polynomials to only one coefficient.