Mathematics Commons^™

Using Manipulatives In Mathematical Problem Solving: A Performance-Based Analysis, Catherine A. Kelly

The Mathematics Enthusiast

This article explores problem solving in elementary classrooms while focusing on how children use (perform tasks) manipulatives and/or tools in problem solving while working on mathematical tasks. Ways for teachers to assess children’s learning through performance-based tool (manipulative) use will also be examined and suggested. Current research reveals that teachers need to teach and assess children’s mathematical knowledge in ways that will allow them to show (perform) what they really understand. And, teachers must be able to see beyond obvious correct or incorrect answers into children’s thinking processes by testing with “tests that allow students the opportunity to show what …

Frames Of Reference And Achievement In Elementary Arithmetic, Eddie M. Gray, Demetra Pitta-Pantazi

The Mathematics Enthusiast

This paper considers the relationship between 8-11 years old students’ numerical achievement and a possible disposition towards the construction of particular frames of reference. The paper uses the characteristics of a variety of kinds of images to focus upon frames of reference and explores a possible relationship between children’s verbal descriptions of concrete and abstract nouns and the different ways they respond to aspects of elementary arithmetic. It seeks to establish whether or not children towards the extremes of arithmetical achievement (low and high achievement) have a disposition towards different kinds of frames of reference. The analysis suggests that at …

How Students Conceive Function: A Triarchic Conceptual-Semiotic Model Of The Understanding Of A Complex Concept., Iliada Elia, Panayotis Spyrou

The Mathematics Enthusiast

This study explores conceptions for function amongst 164-second year students of the Department of Education at the University of Cyprus and their relationship with students’ abilities in dealing with tasks involving different modes of representations of function. The test that was administered to the students included recognition tasks given in various representations and questions requesting definition and examples of function’s applications in real life situations. Results have shown that students’ definitions and examples of the notion are closely related to their ability to use different modes of representations of function. These three factors, i.e., definitions given by the students, functions …

Sunrise… Sunset…, Alex Friedlander, Tzippora Resnick

The Mathematics Enthusiast

Sunrise and sunset are obviously a part of our everyday life. Our connection to the movement of celestial bodies, including the Sun, has been somewhat diminished by modern life, in contrast to the practical interest, fascination or even awe of earlier civilizations. Mathematics and astronomy have a long history of cooperative work, but due to their complexity and technical difficulty, usually those who participated in this endeavor were at the advanced studies level, or occupied high religious positions.

Tme Volume 3, Number 2

The Mathematics Enthusiast

No abstract provided.

Numbers And Polynomials- 50 Years Since The Publication Of Wittgenstein's Bemerkungen Über Die Grundlagen Der Mathematik (1956): Mathematical And Educational Reflections, Giorgio T. Bagni

The Mathematics Enthusiast

According to L. Wittgenstein, the meaning of a mathematical object is to be grounded upon its use. In this paper we consider Robinson theory Q, the subtheory of firstorder Peano Arithmetic PA; some theorems and conjectures can be interpreted over one model of Q given by a universe of polynomials; with respect to nonconstant polynomials some proofs by elementary methods are given and compared with corresponding results in the standard model of PA. We conclude that the creative power of the language can be pointed out in how the language itself is embedded into the rest of human activities, and …

Tme's Worldwide Circulation Statistics

The Mathematics Enthusiast

No abstract provided.

Charactarizations Of Linear Suboptimality For Mathematical Programs With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we …

Adding Depth To The Discussion Of Capital Budgeting Techniques, Tom Arnold, Terry D. Nixon

Finance Faculty Publications

The subject of capital budgeting generally encompasses a significant percentage of any beginning finance course with net present value (NPV) often receiving the most attention. Even after this substantial time allotment, critical assumptions and comparisons of the different techniques (such as payback period, discounted payback period, NPV and IRR) are frequently glossed over due to time constraints. Consequently, the goal of this paper is to present these non-NPV techniques in a manner that allows the beginning finance student to expeditiously see the intuition, inherent assumptions, and any connection with the more popular NPV calculation. A small portion of this paper …

Editorial: A Global Intellectual Collage, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

A Classification Of Strategies Employed By High School Students In Isomorphic Combinatorial Problems, Martina Janácková, Jaroslav Janácek

The Mathematics Enthusiast

The aim of the paper is to discuss some aspects of the combinatorial thinking of high school students. We took one student - Jane and gave her 4 isomorphic testing problems. Then we tried to classify the different strategies the students took in their solutions.

Detectable Coloring Of Graphs, Henry E. Escuadro

Dissertations

A basic problem in graph theory is to distinguish the vertices of a connected graph from one another in some manner. In this study, we investigate the problemof coloring the edges of a graph in a manner that distinguishes the vertices of the graph. The method we use combines many of the features of previously introduced methods.

Let G be a connected graph of order n ≥ 3 and let c : E (G ) [arrow right] {1,2,...,k } be a coloring of the edges of G (where adjacent edges may be colored the same). For each vertex …

Admissible Sequences, Preprojective Modules, And Reduced Words In The Weyl Group Of A Quiver, Mark Kleiner, Allen Pelley

Mathematics - All Scholarship

This paper studies connections between the preprojective modules over the path algebra of a finite connected quiver without oriented cycles, the (+)-admissible sequences of vertices, and the Weyl group. For each preprojective module, there exists a unique up to a certain equivalence shortest (+)-admissible sequence annihilating the module. A (+)-admissible sequence is the shortest sequence annihilating some preprojective module if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. These statements have the following application that strengthens known results of Howlett and Fomin-Zelevinsky. For any fixed …

Quadratic Forms And Height Functions, Lenny Fukshansky

CMC Faculty Publications and Research

The effective study of quadratic forms originated with a paper of Cassels in 1955, in which he proved that if an integral quadratic form is isotropic, then it has non-trivial zeros of bounded height. Here height stands for a certain measure of arithmetic complexity, which we will make precise. This theorem has since been generalized and extended in a number of different ways. We will discuss some of such generalizations for quadratic spaces over a fixed number field as well as over the field of algebraic numbers. Specifically, let K be either a number field or its algebraic closure, and …

Hole Dynamics In Polymer Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Lu Zou

All HMC Faculty Publications and Research

This article develops a model for the closing of a gaseous hole in a liquid domain within a two-dimensional fluid layer coupled to a Stokesian subfluid substrate, and compares this model to experiments following hole dynamics in a polymer Langmuir monolayer. Closure of such a hole in a fluid layer is driven by the line tension at the hole boundary and the difference in surface pressure within the hole and far outside it. The observed rate of hole closing is close to that predicted by our model using estimates of the line tension obtained by other means, assuming that the …

Fibroblast Migration And Collagen Deposition During Dermal Wound Healing: Mathematical Modelling And Clinical Implications, S. Mcdougall, J. A. Sherratt, P. K. Maini, J. C. Dallon

Faculty Publications

The extent to which collagen alignment occurs during dermal wound healing determines the severity of scar tissue formation. We have modelled this using a multiscale approach, in which extracellular materials, for example collagen and fibrin, are modelled as continua, while fibroblasts are considered as discrete units. Within this model framework, we have explored the effects that different parameters have on the alignment process, and we have used the model to investigate how manipulation of transforming growth factor-b levels can reduce scar tissue formation. We briefly review this body of work, then extend the modelling framework to investigate the role played …

François Viète, Between Analysis And Cryptanalysis, Marco Panza

MPP Published Research

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same …

Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational …

The Thermodynamic Formalism For Almost-Additive Sequences, Anna Mummert

Mathematics Faculty Research

We study the nonadditive thermodynamic formalism for the class of almost-additive sequences of potentials. We define the topological pressure PZ(Φ) of an almost-additive sequence Φ, on a set Z. We give conditions which allow us to establish a variational principle for the topological pressure. We state conditions for the existence and uniqueness of equilibrium measures, and for subshifts of finite type the existence and uniqueness of Gibbs measures. Finally, we compare the results for almost-additive sequences to the thermodynamic formalism for the classical (additive) case [10] [11] [3], the sequences studied by Barreira [1], Falconer [5], and that of Feng …

Timelike Surfaces Of Constant Mean Curvature ±1 In Anti-De Sitter 3-Space H31), Sungwook Lee

Faculty Publications

It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space H³ ₁(−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL₂R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E ³ ₁. The hyperbolic Gauß map of timelike surfaces in H³ ₁(−1), which is a close analogue of the classical …

Linear And Log-Linear Models Based On Generalized Inverse Sampling Scheme, Soumi Lahiri

Dissertations

This dissertation explores the development of novel statistical techniques and the applications in modeling rare events using generalized inverse sampling scheme. The Poisson model can be used for independent frequency count data. Also negative binomial and negative multinomial (NMn) models are applicable when there is only one rare category in the population. Here, a new model, based on generalized inverse sampling scheme, is introduced to study several rare events simultaneouly. The generalized inverse sampling scheme is used to study several rare categories of a population. Samples are drawn until a predetermined number of the total of the rare events occur. …

Mathematical Problems Arising In Interfacial Electrohydrodynamics, Dmitri Tseluiko

Dissertations

In this work we consider the nonlinear stability of thin films in the presence of electric fields. We study a perfectly conducting thin film flow down an inclined plane in the presence of an electric field which is uniform in its undisturbed state, and normal to the plate at infinity. In addition, the effect of normal electric fields on films lying above, or hanging from, horizontal substrates is considered. Systematic asymptotic expansions are used to derive fully nonlinear long wave model equations for the scaled interface motion and corresponding flow fields. For the case of an inclined plane, higher order …

Automatic Recognition Of Printed And Handwritten Mathematical Expressions., Shri Sahadeb Garain Dr.

Doctoral Theses

This thesis presents a systematic study on recognition of printed and handwritten mathematical expressions. Automatic recognition of printed expressions is an essential requirement for efficient Optical Character Recognition (OCR) of scientific paper documents. On the other hand, recognition of handwritten expressions has been tried for online environment. Here expressions are written using electronic data tablet/stylus providing a convenient alternative to keyboard or mouse used for data entry into a computer.The previous studies dealing with different aspects of expression recognition are, at first, reviewed. Next, the scope of the present thesis, its layout and contributions are outlined. Discussion on OCR of …

Design Of Iteration On Hash Functions And Its Cryptanalysis., Mridul Nandi Dr.

Doctoral Theses

No abstract provided.

Basic Properties Of Sobolev's Spaces On Time Scales, Ravi P. Agarwal, Victoria Otero-Espinar, Kanishka Perera, Dolores R. Vivero

Mathematics and System Engineering Faculty Publications

We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of functions defined on an arbitrary open interval of the real numbers are derived.

Latin Squares With Forbidden Entries, Jonathan Cutler, Lars Daniel Öhinan

Department of Mathematics Faculty Scholarship and Creative Works

An n × n array is avoidable if there exists a Latin square which differs from the array in every cell. The main aim of this paper is to present a generalization of a result of Chetwynd and Rhodes involving avoiding arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for arrays with arbitrarily many entries per cell. In particular, we prove that if m ∞ N there exists an N = N(m) such that if F is …

Double Domination Edge Critical Graphs., Derrick Wayne Thacker

Electronic Theses and Dissertations

In a graph G=(V,E), a subset S ⊆ V is a double dominating set if every vertex in V is dominated at least twice. The minimum cardinality of a double dominating set of G is the double domination number. A graph G is double domination edge critical if for any edge uv ∈ E(G̅), the double domination number of G+uv is less than the double domination number of G. We investigate properties of double domination edge critical graphs. In particular, we characterize the double domination edge critical trees and …

Trees With Unique Minimum Locating-Dominating Sets., Stephen M. Lane

Electronic Theses and Dissertations

A set S of vertices in a graph G = (V, E) is a locating-dominating set if S is a dominating set of G, and every pair of distinct vertices {u, v} in V - S is located with respect to S, that is, if the set of neighbors of u that are in S is not equal to the set of neighbors of v that are in S. We give a construction of trees that have unique minimum locating-dominating sets.

On The Chromatic Number Of The Ao(2, K , K-1) Graphs., Navya Arora

Electronic Theses and Dissertations

The alphabet overlap graph is a modification of the well known de Bruijn graph. De Bruijn graphs have been highly studied and hence many properties of these graphs have been determined. However, very little is known about alphabet overlap graphs. In this work we determine the chromatic number for a special case of these graphs.

We define the alphabet overlap graph by G = AO(a, k, t, where a, k and t are positive integers such that 0 ≤ t ≤ k. The vertex set of G is the set of all k …

Math Anxiety: What It Is And How It Can Be Prevented By Elementary Classroom Teachers, Amy Christenson

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.