Physical Sciences and Mathematics Commons^™

Meaningful Distributed Instruction— Developing Number Sense, Edward C. Rathmell

Faculty Publications

What Is Number Sense?

The primary goal for elementary and middle school mathematics is to help students learn to use numbers meaningfully, reasonably and flexibly in everyday life. This means that students must develop a deep understanding of

-- numbers and operations,
-- when operations can appropriately be used to solve problems, and
-- judging the reasonableness of their solutions to problems.

They also need to develop attitudes so they

-- believe they can make sense of mathematics, and
-- habitually try to make sense of mathematics.

In other words, students need to develop number sense.

Understandings Needed for Number …

Health Literacy In The Mathematics Classroom: The Iowa Core Curriculum As An Opportunity To Deepen Students’ Understanding Of Mathematics, Elana Joram, Susan Roberts-Dobie, Nadene Davidson

Faculty Publications

By 2012, all high schools in Iowa will be required to incorporate the new Iowa Core Curriculum, followed by elementary and middle schools in 2014 (Iowa Department of Education, 2009). The Iowa Core Curriculum addresses the question: "How is Iowa's educational system preparing our youth for successful lives in the 21st-century global environment?" (Davidson, 2009). It consists of core content standards, and identifies essential concepts and skills for content areas. The Iowa Core Curriculum also includes the ―21st Century Skills‖ of ―health, financial, technology, and civic literacy, and employability skills. These skills are to be infused into existing subject matter …

Preferential Utilization Of Nadph As The Endogenous Electron Donor For Nad(P)H:Quinone Oxidoreductase 1 (Nqo1) In Intact Pulmonary Arterial Endothelial Cells, Robert D. Bongard, Brian J. Lindemer, Gary S. Krenz, Marilyn P. Merker

Mathematics, Statistics and Computer Science Faculty Research and Publications

The goal was to determine whether endogenous cytosolic NAD(P)H:quinone oxidoreductase 1 (NQO1) preferentially uses NADPH or NADH in intact pulmonary arterial endothelial cells in culture. The approach was to manipulate the redox status of the NADH/NAD⁺ and NADPH/NADP⁺ redox pairs in the cytosolic compartment using treatment conditions targeting glycolysis and the pentose phosphate pathway alone or with lactate, and to evaluate the impact on the intact cell NQO1 activity. Cells were treated with 2-deoxyglucose, iodoacetate, or epiandrosterone in the absence or presence of lactate, NQO1 activity was measured in intact cells using duroquinone as the electron acceptor, and …

A Compartmentalized Approach To The Assembly Of Physical Maps, Serdar Bozdag, Timothy J. Close, Stefano Lonardi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Physical maps have been historically one of the cornerstones of genome sequencing and map-based cloning strategies. They also support marker assisted breeding and EST mapping. The problem of building a high quality physical map is computationally challenging due to unavoidable noise in the input fingerprint data. Results: We propose a novel compartmentalized method for the assembly of high quality physical maps from fingerprinted clones. The knowledge of genetic markers enables us to group clones into clusters so that clones in the same cluster are more likely to overlap. For each cluster of clones, a local physical map is first …

The Kalman Filter On Time Scales, Nicholas J. Wintz

Doctoral Dissertations

"In this work, we study concepts in optimal control for dynamic equations on time scales, which unfies the discrete and continuous cases. After a brief introduction of dynamic equations on time scales, we will examine controllability and observability for linear systems. Then we construct and solve the linear quadratic regulator for arbitrary time scales. Here, we seek to find an optimal control that minimizes a given cost function associated with a linear system. We will find such an input under two different settings; when the final state is fixed and when it is free. Later, we extend these results to …

Holomorphic Extensions In Toric Varieties, Malgorzata Aneta Marciniak

Doctoral Dissertations

"The dissertation describes the Hartogs and the Hartogs-Bochner extension phenomena in smooth toric varieties and their connection with the first cohomology group with compact support and sheaf coefficients. The affirmative and negative results are proved for toric surfaces and for line bundles over toric varieties using topological, analytic, and algebraic methods"--Abstract, page iii.

On The Estimation Of Averages Over Infinite Intervals With An Application To Average Persistence In Population Models, Sean F. Ellermeyer

Faculty Articles

We establish a general result for estimating the upper average of a continuous and bounded function over an infinite interval. As an application, we show that a previously studied model of microbial growth in a chemostat with time–varying nutrient input admits solutions (populations) that exhibit weak persistence but not weak average persistence.

A Note On The Application Of Ec2sls And Ec3sls Estimators In Panel Data Models, Badi H. Baltagi, Long Liu

Center for Policy Research

Baltagi and Li (1992) showed that for estimating a single equation in a simultaneous panel data model, EC2SLS has more instruments than G2SLS. Although these extra instruments are redundant in White (1986) terminology, they may yield different estimates and standard errors in empirical studies with finite N and T. We illustrate this using the crime data of Cornwell and Trumbull (1994). We show that the standard errors of EC2SLS are smaller than those of G2SLS for this example. In general, we prove that the asymptotic variance of G2SLS differs from that of EC2SLS by a positive semi-definite matrix. Although this …

Testing The Fixed Effects Restrictions? A Monte Carlo Study Of Chamberlain's Minimum Chi-Squared Test, Badi H. Baltagi, Georges Bresson, Alain Pirotte

Center for Policy Research

Chamberlain (1982) showed that the fixed effects (FE) specification imposes testable restrictions on the coefficients from regressions of all leads and lags of dependent variables on all leads and lags of independent variables. Angrist and Newey (1991) suggested computing this test statistic as the degrees of freedom times the R2 from a regression of within residuals on all leads and lags of the exogenous variables. Despite the simplicity of these tests, they are not commonly used in practice. Instead, a Hausman (1978) test is used based on a contrast of the fixed and random effects specifications. We advocate the use …

Adaptive Nonparametric Distribution-Free Procedures In Factorial Data Analysis, Richard Nzagong Ferim

Mathematics Dissertations

Many statisticians have questioned the basic assumptions about underlying models which might dominate the analysis of the data in many cases. The assumption of normality without much thought is of concern to a growing group of statisticians. If wrongly assumed, the assumption of normality can lead in serious flaws in the analysis of data. It therefore becomes important to consider distribution-free procedures that don't have to rely on the normality assumption. This is where the adaptive procedures come into play. When data is skewed or light tailed, these adaptive methods produce better results than the regular Wilcoxon and parametric methods. …

Non-Traditional Socio-Mathematical Norms In Undergraduate Real Analysis, Paul Christian Dawkins

Mathematics Dissertations

This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative investigation of classroom instruction and interactions, student and instructor interviews, and class exams. The study explores the roles of each norm as the students constructed understanding of advanced mathematics and transitioned to advanced mathematical thinking. I define "non-traditional" according to research accounts of traditional instruction in proof-based mathematics courses and considerations on the culture of …

Large Deviation Principle For Functional Limit Theorems, Adina Oprisan

Mathematics Dissertations

We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an averaging limit theorem, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.We prove also a large deviation principle for a class of empirical processes associated with additive functionals of Markov processes that were shown to have a martingale decomposition. Functional almost everywhere central limit theorems are …

Testing The Equality Of Regression Coefficients And A Pooling Methodology From Multiple Samples When The Data Is Multicollinear, Fransell Riley

Mathematics Dissertations

Testing the equality of regression coefficients between two regression equations is a common practice in statistics today. The theory and methods are sufficiently developed under ordinary least squares (OLS) estimation. However, there is no method for conducting such tests when OLS estimation is not an appropriate method. For example, when multicollinearity exists in the data.Therefore, there is a need for a method to test the equality of regression coefficients when the data is multicollinear. In this research, we will present methods for conducting such a test using ridge regression coefficient estimators and principal component estimators. We will also present a …

Logistic Regression With Misclassified Covariates Using Auxiliary Data, Nathan N. Dong

Mathematics Dissertations

When standard regression methods are used, measurement errors cause a bias in parameters estimation. In dealing with discrete covariates, such measurement errors are known as misclassification and the corresponding discrete covariate is said to be misclassified. Even though the collected data may not be fully reliable, it may be possible to collect some sub-data with full precision called auxiliary data and the remaining data called primary data may contain misclassification. In this paper, in order to improve predictions from the primary data with misclassification, we propose a method based on the maximum likelihood approach; by using the prediction with auxiliary …

High-Order Numerical Schemes For High-Speed Flows, Maria Luisa Bambozzi Oliveira

Mathematics Dissertations

A numerical scheme with high order of accuracy is necessary to resolve small length scales in flow transition and turbulence processes. However, numerical simulation for shock-boundary layer interaction, shock-acoustic interaction, porous media flow and multiple phase flow, among others, also require a numerical scheme that can successfully capture discontinuities. To accomplish this, it is essential that an effective shock/discontinuity detector is implemented to reduce damping of physically important high-frequency waves.In this work, two high-order shock capturing schemes - the Weighted Essentially Non-Oscillatory (WENO) scheme and the Weighted Compact Scheme (WCS) - are investigated. Based on this analysis, a shock/discontinuity detector …

The Uniqueness Of Minimal Acyclic Complexes, Meri Trema Hughes

Mathematics Dissertations

In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of finitely generated free modules over a commutative local ring which share a common syzygy module. Although such uniqueness occurs over Gorenstein rings, the question has been asked whether two minimal acyclic complexes in general can be isomorphic to the left and non-isomorphic to the right. We answer the question in the negative for certain cases, including periodic complexes, sesqui-acyclic complexes, and certain rings with radical cube zero. In particular, we investigate the question for graded algebras with Hilbert series $H_R(t)=1+et+(e-1)t^2$, and such monomial algebras possessing a special …

A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán

Mathematics and Statistics Faculty Publications and Presentations

We introduce a new mixed method for linear elasticity. The novelty is a simplicial element for the approximate stress. For every positive integer k, the row-wise divergence of the element space spans the set of polynomials of total degree k. The degrees of freedom are suited to achieve continuity of the normal stresses. What makes the element distinctive is that its dimension is the smallest required for enforcing a weak symmetry condition on the approximate stress. This is achieved using certain "bubble matrices", which are special divergence-free matrix-valued polynomials. We prove that the approximation error is of order k + …

The Number Of Permutations Realized By A Shift, Sergi Elizalde

Dartmouth Scholarship

A permutation $\pi$ is realized by the shift on N symbols if there is an infinite word on an N-letter alphabet whose successive left shifts by one position are lexicographically in the same relative order as $\pi$. The set of realized permutations is closed under consecutive pattern containment. Permutations that cannot be realized are called forbidden patterns. It was shown in [J. M. Amigó, S. Elizalde, and M. B. Kennel, J. Combin. Theory Ser. A, 115 (2008), pp. 485–504] that the shortest forbidden patterns of the shift on N symbols have length $N+2$. In this paper we give …

Transformée En Échelle De Signaux Stationnaires, Daniel Alpay, Mamadou Mboup

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk.

Generalized Q-Functions And Dirichlet-To-Neumann Maps For Elliptic Differential Operators, Daniel Alpay, Jussi Behrndt

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized Q-function. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein type formulas for the difference of the resolvents and trace formulas in an H2-framework are obtained.

The Schur Transformation For Nevanlinna Functions: Operator Representations, Resolvent Matrices, And Orthogonal Polynomials, Daniel Alpay, A. Dijksma, H. Langer

Mathematics, Physics, and Computer Science Faculty Articles and Research

A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we find a Nevanlinna function np which is a fractional linear transformation of the given function n. The main results concern the effect of this transformation to the realizations of n and np, by which we …

Krein Systems, Daniel Alpay, I. Gohberg, M. A. Kaashoek, L. Lerer, A. Sakhnovich

Mathematics, Physics, and Computer Science Faculty Articles and Research

In the present paper we extend results of M.G. Krein associated to the spectral problem for Krein systems to systems with matrix valued accelerants with a possible jump discontinuity at the origin. Explicit formulas for the accelerant are given in terms of the matrizant of the system in question. Recent developments in the theory of continuous analogs of the resultant operator play an essential role.

Local-To-Global Spectral Sequences For The Cohomology Of Diagrams, David Blanc, Mark W. Johnson, James M. Turner

University Faculty Publications and Creative Works

We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings. © 2008 Elsevier B.V. All rights reserved.

A Comparison Of Methods For Generating Bivariate Non-Normally Distributed Random Variables, Jaimee E. Stewart

UNF Graduate Theses and Dissertations

Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they …

Addressing The Principles For School Mathematics: A Case Study Of Elementary Teachers Pedagogy And Practices In An Urban High-Poverty School, Robert Q. Berry, Linda Bol, Sueanne E. Mckinney

Educational Leadership & Workforce Development Faculty Publications

The extent to which four novice teachers assigned to an urban high-poverty school implemented the Principles of School Mathematics during their mathematics instruction program was investigated using a case study design. The research team conducted 36 unannounced observations of the participating teachers and utilized a developed assessment to guide their observations. Results indicated that only one teacher was judged proficient for all the principles. The remaining three teachers fell short in the implementation and direction of the principles. Detailed descriptions of the pedagogical practices of the teachers are provided.

Using A Mathematical Model Of Cadherin-Based Adhesion To Understand The Function Of The Actin Cytoskeleton, J. C. Dallon, Elijah Newren, Marc Hansen

Faculty Publications

The actin cytoskeleton plays a role in cell-cell adhesion but its specific function is not clear. Actin might anchor cadherins or drive membrane protrusions in order to facilitate cell-cell adhesion. Using a mathematical model of the forces involved in cadherin-based adhesion we investigate its possible functions. The immersed boundary method is used to model the cell membrane and cortex with cadherin binding forces added as linear springs. The simulations indicate that cells in suspension can develop normal cell-cell contacts without actin-based cadherin anchoring or membrane protrusions. The cadherins can be fixed in the membrane or free to move and the …

A Finite Volume Method For Solving Parabolic Equations On Logically Cartesian Curved Surface Meshes, Donna Calhoun, Christiane Helzel

Donna Calhoun

We present a second-order, finite-volume scheme for the constant-coefficient diffusion equation on curved, parametric surfaces described via smooth or piecewise smooth mappings on logically Cartesian meshes. Our method does not require analytic metric terms, shows second-order accuracy, can be easily coupled to existing finite-volume solvers for logically Cartesian meshes and handles general mixed boundary conditions. We present numerical results demonstrating the accuracy of the scheme, and then use the scheme to solve advection-reaction-diffusion equations modeling biological pattern formation on surfaces.

Visualdsolve: Visualizing Differential Equations With Mathematica, Second Edition, Stan Wagon, Antonin Slavik, Dan Schwalbe

Stan Wagon, Retired

No abstract provided.

Geometric Ergodicity Of Gibbs Samplers (University Of Minnesota), Alicia Johnson

Alicia A. Johnson

No abstract provided.

Using A Personal Response System, John Hawkins, Bruce Mclean

John B. Hawkins

Over the years, we have consistently used the latest technology in our classes. It has made us more organized and has increased the understanding of our students. Now we have combined our old presentations and drawings from the past and placed them in PowerPoint presentations with imbedded questions. These questions can be multiple choice or questions that have numerical answers. Our University has settled upon one company to provide a personal response system, eInstruction’s Classroom Performance System (CPS). The students answer each question as it appears and we are able to evaluate our lectures in real time. Applets can still …