Mathematics Commons^™

Making Explicit The Commonalities Of Msp Projects: Learning From Doing, Marilyn Strutchens, W. Gary Martin

The Mathematics Enthusiast

The seven projects discussed in the preceding articles are funded by the National Science Foundation (NSF) Math and Science Partnership (MSP) program (Hamos et al., 2009), which began in 2002. One of the main goals of the MSP program is to build capacity and integrate the work of higher education, especially its STEM disciplinary faculty, with that of K‐12 to strengthen and reform mathematics and science education (Hamos et al., 2009). Thus, the MSP program brought together three sets of people (disciplinary faculty, teacher educators, and school system personnel) who do not usually work together to reform the mathematics and …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Statistical Analysis Of Student Performance In Mathematics Courses, Katie Merkling, Hannah Dorman, Nicolle Kinzel

Symposium on Research and Creative Expression (SORCE)

We examined the effect of taking AP Calculus in high school on final letter grades in Calculus I, II, and III at Valparaiso University. The data used in our study was obtained from the registrar and included demographic information, entrance exam scores (ACT, SAT, AP, etc.), Valpo GPA for each semester, and final letter grades in all math courses from Spring 2008-Summer 2012. We performed multiple statistical analyses, such as chi-square tests, two-sample t-tests, and multiple regressions, using the statistical software package R. Our results show that students who took AP Calculus in high school on average received higher final …

Mathematical Habits Of Mind For Teaching: Using Language In Algebra Classrooms, Ryota Matsuura, Sarah Sword, Mary Beth Piecham, Glenn Stevens, Al Cuoco

The Mathematics Enthusiast

The notion of mathematical knowledge for teaching has been studied by many researchers, especially at the elementary grades. Our understandings of this notion parallel much of what we have read in the literature, but are based on our particular experiences over the past 20 years, as mathematicians engaged in doing mathematics with secondary teachers. As part of the work of Focus on Mathematics, Phase II MSP, we are developing, in collaboration with others in the field, a research program with the ultimate goal of understanding the connections between secondary teachers’ mathematical knowledge for teaching and secondary students’ mathematical understanding and …

Tme Volume 10, Number 3

The Mathematics Enthusiast

No abstract provided.

Phase Transition Of Boolean Networks With Partially Nested Canalizing Functions, Kayse Jansen, Mihaela Teodora Matache

Mathematics Faculty Publications

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the …

2013 (Summer), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Summer Colloquium.

Decoupling The Stationary Navier-Stokes-Darcy System With The Beavers-Joseph-Saffman Interface Condition, Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Differential Graded Contact Geometry And Jacobi Structures, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We study contact structures on nonnegatively graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and Jacobi manifolds. This correspondence allows us to reinterpret the Poissonization procedure, taking Jacobi manifolds to Poisson manifolds, as a supergeometric version of symplectization.

Toward An Mhealth Intervention For Smoking Cessation, Golam Mushih Tanimul Ahsan, Ivor D. Addo, Sheikh Iqbal Ahamed, Daniel Petereit, Shalini Kanekar, Linda Burhansstipanov, Linda U. Krebs

Mathematics, Statistics and Computer Science Faculty Research and Publications

The prevalence of tobacco dependence in the United States (US) remains alarming. Invariably, smoke-related health problems are the leading preventable causes of death in the US. Research has shown that a culturally tailored cessation counseling program can help reduce smoking and other tobacco usage. In this paper, we present a mobile health (mHealth) solution that leverages the Short Message Service (SMS) or text messaging feature of mobile devices to motivate behavior change among tobacco users. Our approach implements the Theory of Planned Behavior (TPB) and a phase-based framework. We make contributions to improving previous mHealth intervention approaches by delivering personalized …

Embedding And Nonembedding Results For R. Thompson's Group V And Related Groups, Nathan Corwin

Department of Mathematics: Dissertations, Theses, and Student Research

We study Richard Thompson's group V, and some generalizations of this group. V was one of the first two examples of a finitely presented, infinite, simple group. Since being discovered in 1965, V has appeared in a wide range of mathematical subjects. Despite many years of study, much of the structure of V remains unclear. Part of the difficulty is that the standard presentation for V is complicated, hence most algebraic techniques have yet to prove fruitful.

This thesis obtains some further understanding of the structure of V by showing the nonexistence of the wreath product Z wr Z^2 as …

Relations Between Distorted And Original Angles In Str, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Using the Oblique-Length Contraction Factor, which is a generalization of Lorentz Contraction Factor, one shows several trigonometric relations between distorted and original angles of a moving object lengths in the Special Theory of Relativity.

Genomic Analysis Of Stress Response Against Arsenic In Caenorhabditis Elegans, Surasri N. Sahu, Jada Lewis, Isha Patel, Serdar Bozdag, Jeong H. Lee, Robert Sprando, Hediye Nese Cinar

Mathematics, Statistics and Computer Science Faculty Research and Publications

Arsenic, a known human carcinogen, is widely distributed around the world and found in particularly high concentrations in certain regions including Southwestern US, Eastern Europe, India, China, Taiwan and Mexico. Chronic arsenic poisoning affects millions of people worldwide and is associated with increased risk of many diseases including arthrosclerosis, diabetes and cancer. In this study, we explored genome level global responses to high and low levels of arsenic exposure in Caenorhabditis elegans using Affymetrix expression microarrays. This experimental design allows us to do microarray analysis of dose-response relationships of global gene expression patterns. High dose (0.03%) exposure caused stronger global …

Spectral Stability Of Weak Detonations In The Majda Model, Jeffrey James Hendricks

Theses and Dissertations

Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that …

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …

Counting The Number Of Squares Reachable In K Knight's Moves., Amanda M. Miller, David L. Farnsworth

Articles

from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reach- able in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k-squared – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.

Nsf's Math-Science Partnership Projects- Measuring The Trickle-Down Effect Of American Tax Dollars, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Teacher Learning In Lesson Study, Jennifer M. Lewis, Davida Fischman, Iris Riggs, Kelli Wasserman

The Mathematics Enthusiast

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students’ autonomous problem‐solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among the teams’ composition, leadership, and content foci.

Supporting Middle School Mathematics Specialists’ Work: A Case For Learning And Changing Teachers’ Perspectives, Joy W. Whitenack, Aimee J. Ellington

The Mathematics Enthusiast

In this paper, we highlight one whole‐class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state‐wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge …