Mathematics Commons^™

Ldpc Codes From Voltage Graphs, Christine A. Kelley, Judy L. Walker

Department of Mathematics: Faculty Publications

Several well-known structure-based constructions of LDPC codes, for example codes based on permutation and circulant matrices and in particular, quasi-cyclic LDPC codes, can be interpreted via algebraic voltage assignments. We explain this connection and show how this idea from topological graph theory can be used to give simple proofs of many known properties of these codes. In addition, the notion of abelianinevitable cycle is introduced and the subgraphs giving rise to these cycles are classified. We also indicate how, by using more sophisticated voltage assignments, new classes of good LDPC codes may be obtained.

Average Min-Sum Decoding Of Ldpc Codes, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker

Department of Mathematics: Faculty Publications

Simulations have shown that the outputs of minsum (MS) decoding generally behave in one of two ways: the output either eventually stabilizes at a codeword or eventually cycles through a finite set of vectors that may include both codewords and non-codewords. This inconsistency in MS across iterations has significantly contributed to the difficulty in studying the performance of this decoder. To overcome this problem, a new decoder, average min-sum (AMS), is proposed; this decoder outputs the average of the min-sum output vectors over a finite set of iterations. Simulations comparing MS, AMS, linear programming (LP) decoding, and maximum likelihood (ML) …

Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park

Mathematics and Statistics Faculty Publications and Presentations

Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report …

A Numerical Analysis Approach For Estimating The Minimum Traveling Wave Speed For An Autocatalytic Reaction, Erika Blanken

Electronic Theses and Dissertations

This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the auto-catalyst. The diffusion coefficients for A and B are given by DA and DB. These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, v* and v*, depending on DB/DA, where for speeds v ≥ v*, a traveling wave solution exists, while for speeds v < v*, a solution does not exist. Moreover, if DB ≤ DA, and v* and v* are similar to one another and in the order of DB/DA when it is small. On the other hand, when DA ≤ DB there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining …

Fractal Interpolation, Gayatri Ramesh

Electronic Theses and Dissertations

This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton s, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley s paper, Fractal Functions and Interpolation. I also mention results on iterated function system …

Analysis Of Kolmogorov's Superposition Theorem And Its Implementation In Applications With Low And High Dimensional Data., Donald Bryant

Electronic Theses and Dissertations

In this dissertation, we analyze Kolmogorov's superposition theorem for high dimensions. Our main goal is to explore and demonstrate the feasibility of an accurate implementation of Kolmogorov's theorem. First, based on Lorentz's ideas, we provide a thorough discussion on the proof and its numerical implementation of the theorem in dimension two. We present computational experiments which prove the feasibility of the theorem in applications of low dimensions (namely, dimensions two and three). Next, we present high dimensional extensions with complete and detailed proofs and provide the implementation that aims at applications with high dimensionality. The amalgamation of these ideas is …

Comparing Assessment Methods As Predictors Of Student Learning In Undergraduate Mathematics, Nichole Shorter

Electronic Theses and Dissertations

This experiment was designed to determine which assessment method: continuous assessment (in the form of daily in-class quizzes), cumulative assessment (in the form of online homework), or project-based learning, best predicts student learning (dependent upon posttest grades) in an undergraduate mathematics course. Participants included 117 university-level undergraduate freshmen enrolled in a course titled "Mathematics for Calculus". Initially, a multiple regression model was formulated to model the relationship between the predictor variables (the continuous assessment, cumulative assessment, and project scores) versus the outcome variable (the posttest scores). However, due to the possibility of multicollinearity present between the cumulative assessment predictor variable …

Numerical Analysis Of Elliptic Inverse Problems With Interior Data, Mark Gockenbach

Department of Mathematical Sciences Publications

A number of algorithms have been proposed and analyzed for estimating a coefficient in an elliptic boundary value problem when interior data is available. Most of the analysis has been done for the simple scalar BVP

-Δ a Δ u = f in Ω,

a (∂ u / ∂ n) g on ∂ Ω

However, some methods and the associated analysis have been extended to the problem of estimating the Lamé moduli in the system of linear, isotropic elasticity. Under certain idealized conditions, convergence of estimates to the exact Lame moduli has been proved for two techniques, the output …

An Introduction To Systems Biology For Mathematical Programmers, Evind Almaas, Allen G. Holder, Kevin D. Livingstone

Mathematics Faculty Research

Many recent advances in biology, medicine and health care are due to computational efforts that rely on new mathematical results. These mathematical tools lie in discrete mathematics, statistics & probability, and optimization, and when combined with savvy computational tools and an understanding of cellular biology they are capable of remarkable results. One of the most significant areas of growth is in the field of systems biology, where we are using detailed biological information to construct models that describe larger entities. This chapter is designed to be an introduction to systems biology for individuals in Operations Research (OR) and mathematical programming …

Best P-Simultaneous Approximation In Some Metric Space, Mona Khandaqji, Wasfi Shatanawi

Turkish Journal of Mathematics

Let X be a Banach space, (I,\mu) be a finite measure space, and \Phi be an increasing subadditive continuous function on [0,+\infty) with \Phi(0)=0. In the present paper, we discuss the best p-simultaneous approximation of L^\Phi(I,G) in L^\Phi(I,X) where G is a closed subspace of X.

Some Characterizations Of Rectifying Curves In The Euclidean Space E^4, Kazim İlarslan, Emilija Nesovic

Turkish Journal of Mathematics

In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement N^{\perp} of its principal normal vector field N. In particular, we study the rectifying curves in E^4 and characterize such curves in terms of their curvature functions.

Nonexistence Of Stable Exponentially Harmonic Maps From Or Into Compact Convex Hypersurfaces In R^{M+1}, Jiancheng Liu

Turkish Journal of Mathematics

In this paper, we study the nonexistence problems for stable exponentially harmonic map into or from compact convex hypersurface M^m \subset R^{m+1}, and show that every nonconstant exponentially harmonic map f, between M^m and any compact Riemannian manifold, is unstable if (4) holds.

Primary Finitely Compactly Packed Modules And S-Avoidance Theorem For Modules, Arwa Eid Ashour

Turkish Journal of Mathematics

In this paper we introduce the concept of primary finitely compactly packed modules, which generalizes the concept of primary compactly packed modules. We first find the conditions that make the primary finitely compactly packed modules primary compactly packed. Also, several results on the primary finitely compactly packed modules are proved. In addition, the necessary and sufficient conditions for an R-module M to be primary finitely compactly packed are investigated. Finally, we introduce the S-Avoidance Theorem for modules.

A Study Of Boundary Layer Fflow With No-Slip And Slip Boundary Conditions, Sandra B. Spillane

Doctoral

This thesis involves solving the two-dimensional boundary layer equations for axially symmetric fluid flow along a circular cylinder using the no-slip and slip boundary condition, and along a flat plate with the slip boundary condition. Initially, historical results in both areas are summarised. The research section of this thesis is concerned with extending these historical results. In the first research chapters, a Pade approximation and an Euler transformation are used to greatly extend the region of validity of the historical results. Following that is an investigation of the relaxation of the traditional no-slip boundary condition, which usually occurs when there …

Adaptive Hp-Fem For Elliptic Problems In 3d On Irregular Meshes, David Andrs

Open Access Theses & Dissertations

This work deals with adaptive hp-FEM on irregular meshes. It shows the advantage of completely irregular meshes, using the arbitrary level hanging nodes. The above is demonstrated on a numerical example with distribution of electrical potencial.

Reaction To The Reactors, Ted Eisenberg

The Mathematics Enthusiast

1. A comment. I discussed the contents of my paper with colleagues on many different occasions. By their reactions they seem to divide themselves into two camps. One camp takes the stance of: Are you crazy to mention such things in the classroom? We are charged to teach mathematics, and that’s it. Who cares if Einstein never learned to swim? The other camp however takes an opposite stance: Such items are really important for students to know because they help students to think about the lives and times of the men who created the material they are studying; our lessons …

Comments Provoked By "Flaws And Idiosyncrasies In Mathematicians: Food For The Classroom?", Brian Greer

The Mathematics Enthusiast

In mathematics classes, it is appropriate for many reasons to discuss mathematicians as people with lives, personal problems, both influenced by and influencing cultural movements and societal issues. Mathematics is a human activity, and mathematicians are human. Eisenberg's paper raises important and fascinating issues, such as the extent to which intellectual achievements can be kept separate from the personality and actions of their creator (such as Wagner). However, in my reactions, I suggest ways in which I believe the discussion needs to be broadened and refocused.

Values In Mathematics And Science Education: Similarities And Differences, Alan Bishop

The Mathematics Enthusiast

literacy and expertise from their citizens than ever before. At the heart of such demands is the need for greater engagement by students with school mathematics and science. As the OECD/PISA definition of numeracy puts it:

“Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen”(OECD, 2003)

Values are an inherent part of the educational process at all levels, from the systemic, institutional macro-level, …

Critique On Eisenberg's Article, Renuka Vithal

The Mathematics Enthusiast

I enjoyed reading the article and learned some interesting (and disturbing) information about well known mathematicians that is not so well known. However in its current form it is more appropriate for the popular media rather than as an academic or scholarly article.

Having said that it does raise some serious questions of ethics and values that all mathematics educators should be engaging. The increasingly popular view that mathematics teaching be socially contextualised means that this kind of historical information may be communicated in lecture rooms and classroom with little understanding or awareness of the "hidden curriculum" being enacted.

Doin' The Math: On Meaningful Mathematics-Ethics Connections, Kurt Stemhagen

The Mathematics Enthusiast

In this essay mathematics is conceived of as intentional human activity. Since intention implies choice, there are ethical dimensions to making mathematical choices. Embracing these dimensions requires acknowledging the contextual nature of mathematics. First John Dewey’s philosophy of mathematics and a reconsideration of mathematical empiricism are posited as ways to foster a context sensitive understanding of mathematics. Next, I address the ways in which existent conceptions of mathematics—even those which support reform in mathematics education—are insufficient with regard to their ability to recognize its human dimensions. The essay concludes with a distinction between mathematics education that ethically applies existing versions …

The Action Map As A Tool For Assessing Situated Mathematical Problem Solving Performance, Murad Jurdak

The Mathematics Enthusiast

The aim of this paper is to investigate the appropriateness, concurrent and construct validity of action map as a tool for assessing situated problem solving performance. Action map is rooted in activity theory whose stipulations are compatible with situated problem solving. Thirty-one last year secondary students were given three tasks with real –world context. Based on the analysis of the written solutions and interviews, evidence is presented on the appropriateness and validity of action map as an instrument to assess situated problem solving performance.

A Reflection On Mathematical Cognition: How Far Have We Come And Where Are We Going?, Kristin Umland

The Mathematics Enthusiast

Any theory of mathematical cognition and learning must ultimately articulate with our current understanding of how the mind works and with current theories of how knowledge is acquired from both an individual and social perspective. Certainly the human mind is very complex; understanding how it works in general and identifying the components that contribute to “doing mathematics” in particular is no easy task. To understand how the mind does mathematics, we must identify what mathematicians actually do in the context of everyday cognition. Here we discuss some of what is known and about this and point out directions for future …

Relationship Of Some Psychological Variables In Predicting Problem Solving Ability Of In-Service Mathematics Teachers, M. K. Akinsola

The Mathematics Enthusiast

This paper examines some psychological variables in predicting problem solving ability of inservice mathematics teachers. The sample consists of 122 in-service teachers enrolled in degree programme. Five standardized instruments were used to collect the data on teachers’ mathematics anxiety, mathematics teaching efficacy belief, locus of control, study habits and problem solving ability. Multiple regression, Chi-square analysis,and Pearson moment correlation coefficient were used to analyze the data. The results show that mathematics anxiety, mathematics teaching efficacy belief, locus of control and study habits all have significant relationships with problem solving ability with mathematics anxiety having the highest and study habits the …

How Is Mathematics Education Philosophy Reflected In The Math Wars?, David M. Davison, Johanna E. Mitchell

The Mathematics Enthusiast

Throughout the duration of what has been termed the “math wars”, many overlygeneralized statements by both sides have detracted from the quest for a solution to the conflict between conceptual and procedural approaches to mathematics study. In terms of philosophies of mathematics education, the absolutist view posits that mathematical knowledge is certain and unchallengeable while the fallibilist view is that mathematical knowledge is never beyond revision and correction. We suggest that the major mathematics education reforms have been absolutist in focus and have not reflected the changing nature of the discipline. Thus we believe that true reform will reflect changing …

Teaching Proof At Ks4, Sue Waring

The Mathematics Enthusiast

Proof is a fundamental component of mathematics and so, in my opinion, it should be part of mathematical education in schools. It is an important link between topics and so can help pupils achieve a deeper understanding of the “wholeness” of mathematics and, moreover, it is vital for able pupils if they are to be inspired by mathematics and given a firm basis for future mathematical studies.

Consecutive Numbers, Steve Humble

The Mathematics Enthusiast

The hidden secrets of our number system can often reveal the magical quality of mathematics. Through the process of discovery and discussion with fellow classmates, the hidden depths of maths takes on new appeal. Consecutive numbers is one such area that gives this excitement.

New And Noteworthy Books From Sense Publishers

The Mathematics Enthusiast

No abstract provided.

Tme Worldwide Daily Circulation [Dec 6-11, 2007]

The Mathematics Enthusiast

No abstract provided.

Statistical Issues In The Normalization Of Multi-Species Microarray Data, John R. Stevens, Balasubramanian Ganesan, Prerak Desai, Sweta Rajan, Bart C. Weimer

Mathematics and Statistics Faculty Publications

Several species of bacteria are involved in the production of cheese, including Lactobacillus brevis and Lactococcus lactis. A custom-designed Affymetrix microarray was recently developed to study gene expression in three organisms on a single chip. This array contains only perfect match features for the coding and non-coding regions in the genomes of all three sequences. The multi-species nature of this array version raises interesting questions regarding the preprocessing or normalization strategies for the analysis of gene expression data. We present and evaluate several possible strategies using both cDNA dilution data and experimental expression data from a repeated measures design. …

Estimates Of Positive Solutions For Higher Order Right Focal Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (p;n - p) right focal boundary value problem. A new set of upper and lower estimates of positive solutions for the boundary value problem are obtained. These estimates implement and improve the ones in the literature.