Physical Sciences and Mathematics Commons^™

A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks

Bridgewater Review

No abstract provided.

Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce

The Mathematics Enthusiast

Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students …

Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi

The Mathematics Enthusiast

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students …

Instrumented Techniques And Reflective Thinking In Analytic Geometry, Nurit Zehavi, Giora Mann

The Mathematics Enthusiast

In a previous study that explored epistemological perspectives on solving problems with Computer Algebra Systems (CAS) we concluded that awareness of the special ways that the software utilizes symbols in algebraic manipulations and in implicit plotting should be encouraged (Zehavi, 2004). Such awareness is required for, and encouraged by treating geometry analytically with a symbolic-graphical system. In this paper we compare a traditional solution of a problem in analytic geometry with CAS-based solutions to the same problem. The discussion will focus on the role of reflective thinking, namely selection of techniques, monitoring of the solution process, insight, and conceptualization, play …

Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

A Comparison Of The Danish And The Virginia Secondary Teacher Education System: Their Values And Emphasis On Mathematics Content Knowledge, Bettina Dahl

The Mathematics Enthusiast

In this paper I will first examine an example of secondary mathematics teacher education in the USA, namely Virginia, then compare it with the secondary teacher education in Denmark. The purpose is both to investigate how much mathematics the students get in the respective systems and secondly to see what this type of teacher education communicates about the values emphasized in the various countries’ education systems. I spent more time on explaining the Danish education system than that of the USA and the single states since it is assumed that the reader is familiar with these systems. One cannot necessarily …

Tme Statistics

The Mathematics Enthusiast

No abstract provided.

Von Neumann And Computers, Steve Humble

The Mathematics Enthusiast

The title of this paper should not be Von Neumann and computers, but Von Neumann and the Von Neumann machine. Von Neumann may be famous for many things but humility was not one of them. Yet no one had anything bad to say about 'good time' Johnny Von Neumann; he just was too likeable. He gave massive parties and loved women, fast cars, jokes, noise, Mexican food, fine wine, and, most of all, mathematics. 'Unbelievable', said one of Von Neumann's old friends, 'He knew how to have a good time. His parties were once if not twice a week at …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Tme Volume 2, Number 2

The Mathematics Enthusiast

No abstract provided.

Taxi Cab Geometry: History And Applications!, Chip Reinhardt

The Mathematics Enthusiast

We will explore three real life situations proposed in Eugene F. Kraus e's book Taxicab Geometry. First a dispatcher for Ideal City Police Department receives a report of an accident at X = (-1,4). There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third …

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Action: Tell Me More Albert!, Jerry T. Baty, Virginia A.H. Mcclendon

The Mathematics Enthusiast

The new school year opens with the instructor cheerfully announcing to the students on the first day, “Good morning, class! Welcome to the fun of a new language called algebra”. He continues, “Today we are going to have a conversation about your success in this classroom. First, is the area of mathematics called algebra, necessary for your future?"

None of the students responds.

A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott

The Mathematics Enthusiast

The National Council of Teachers of Mathematics (NCTM) has taken a very firm stand on the issue of equity in mathematics education. Not only is equity incorporated in the Curriculum and Evaluation Standards for School Mathematics (1989) and Principles and Standards for School Mathematics (2000), equity is the first plank of NCTM’s legislative platform.

Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein

The Mathematics Enthusiast

It is a pleasure, challenge, and an honor to respond to the thoughtful and innovative debate started by Braver, Micklus, Bradley, van Spronsen, Allen, & Campbell on teaching mathematics for social justice. They take seriously the issues in, and raise many interesting views about, my article, Teaching and Learning Mathematics for Social Justice in an Urban Latino School (JRME, January, 2003). I would like to respond to (connected) two points in particular: the relationship of functional to critical literacies, and the relationship of “critical thinking” in mathematics to learning mathematics for social justice. However, I would first like to clarify …

Gutstein Generalized- A Philosophical Debate: A Critical Commentary On Gutstein's (2003) Thesis For The Incorporation Of Social Justice In The Mathematics Curriculum, Seth Braver, Jane Micklus, Sheila Bradley, Hillary Van Spronsen, Samantha Allen, Vicki Campbell

The Mathematics Enthusiast

The Scene: A Courtroom
The Year: 2004 (old style), 15 (new style - After Standards)

The Grand Inquisitor mounts the podium, and addresses the Debaters standing silently before him. A large crowd fills the hall.

Inquisitor:
Ladies and Gentlemen! You have been summoned here today to present the final arguments for and against these propositions which have so vexed our society in recent months. Each of you represents a vision of the future of mathematics education. Ere the sun sets we shall fix our resolve to one vision or the other. The victors, I doubt not, shall lead us into …

Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou

The Mathematics Enthusiast

Through this research into the solution of the cubic, I hope to learn the thoughts of mathematicians during this period of history. This knowledge must be conveyed in a way that is historically and mathematically accurate, yet comprehensible and readily available to use in a class of eighth grade math students. It is my wish that as we begin to delve into the world of algebraic and graphical solutions to the problems in the eighth grade text, students will be able to make a connection with this information to that they are currently using to solve their problems. They should …

Commentary On Ballou's Paper: Galois - The Myths And The Man, Catherine Degrandpre

The Mathematics Enthusiast

mathematics curriculum. As seen in her paper, the solution of the cubic essentially involves the use of a clever substitution in the general cubic in order to reduce it into a cubic without the square term, which in turn is factorable as a quadratic provided one makes another substitution. A natural question to ask ourselves, which mathematicians in the colorful theory of equations undoubtedly did as well, is how far can we push this technique of cle ver substitutions to solve higher degree equations. These substitutions are called Tschirnhaus transformations and have a pattern of the form x = y …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Tme Volume 2, Number 1

The Mathematics Enthusiast

No abstract provided.

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson

Inquiry: The University of Arkansas Undergraduate Research Journal

No abstract provided.

Asymptotic Formulas For The Resonance Eigenvalues Of The Schrödinger Operator, Sedef Karakiliç, O. A. Veli̇ev, Ş. Atilgan

Turkish Journal of Mathematics

In this paper, we consider the Schrödinger operators defined by the differential expression Lu= - \Delta u + q(x)u in d-dimensional paralellepiped F, with the Dirichlet and the Neumann boundary conditions, where q(x) is a real valued function of L_2(F). We obtain the asymptotic formulas for the resonance eigenvalues of these operators

The Basis Number Of The Semi-Composition Product Of Some Graphs I, M. M. Jaradat, E. A. Rawashdeh, M. Y. Alzoubi

Turkish Journal of Mathematics

The basis number of a graph G is defined to be the least integer d such that there is a basis \mathcal{B} of the cycle space of G such that each edge of G is contained in at most d members of \mathcal{B}. We investigate the basis number of the semi-composition product of two paths and a cycle with a path.

Self-Adjoint Boundary Value Problems On Time Scales And Symmetric Green's Functions, Gusein Sh. Guseinov

Turkish Journal of Mathematics

In this note, higher order self-adjoint differential expressions on time scales, and associated with them self-adjoint boundary conditions, are discussed. The symmetry peoperty of the corresponding Green's functions is emphasized.

On Groups With The Weak Wide Commensurable Property, Ayşe Berkman, Mahmut Kuzucuoğlu, Erdal Özyurt

Turkish Journal of Mathematics

An infinite group with the weak wide commensurable property is shown to be abelian, provided that it is locally finite or locally graded or non-perfect or linear. We also investigate the properties of infinite non-abelian groups with the weak wide commensurable property. Moreover, we describe completely the structure of infinite locally finite groups whose p-subgroups have the weak wide commensurable property. (AMS MSC: 20F50, 20E34).

Valuations Of Polynomials, Sorasak Leeratanavalee

Turkish Journal of Mathematics

A tree is a connected (undirected) graph that contains no cycles. Trees play an important role in Computer Science. There are many applications in this field. Ordered binary decision diagrams are trees in the language of Boolean algebras. For the applications, it is important to measure the complexity of a tree or of a polynomial. The complexity of a polynomial over an arbitrary algebra can be regarded as a valuation. The concept of the valuations of terms was introduced by K. Denecke and S. L. Wismath in [5]. In [6], the author defined the depth of a polynomial which is …

Corrigendum Uniqueness Of Primary Decompositions [Turkish J. Math. 27 (2003), 425--434], Patrick F. Smith

Turkish Journal of Mathematics

No abstract provided.

Maximum Entropy-Based Fuzzy Clustering By Using L_1-Norm Space, Mohammad Ghorbani

Turkish Journal of Mathematics

One of the most important methods in analysis of large data sets is clustering. These methods are not only major tools to uncover the underlying structures of a given data set, but also promising tools to uncover local input-output relations of a complex system. The goal of this paper is to present a new approach to fuzzy clustering by using L_1-norm space by means of a maximum entropy inference method, where, firstly, the resulting formulas have more beautiful form and clearer physical meaning than those obtained by means of FCM method and secondly, the obtained criteria by this new method …