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Full-Text Articles in Physical Sciences and Mathematics

Chess And Problem Solving Involving Patterns, Dores Ferreira, Pedro Palhares Jul 2008

Chess And Problem Solving Involving Patterns, Dores Ferreira, Pedro Palhares

The Mathematics Enthusiast

In this paper we present the context and results from a study, with 3rd to 6th grades children, about the relationship between chess and problem solving involving geometric and numeric patterns. The main result of this study is the existence of a relation between strength of play and patterns involving problem solving. We have included in the beginning an analysis of chess as a context for elementary mathematics problems, also showing its richness historically.

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Mathematics For Middle School Teachers: Choices, Successes, And Challenges, Linda Martin, Kristin Umland Jul 2008

Mathematics For Middle School Teachers: Choices, Successes, And Challenges, Linda Martin, Kristin Umland

The Mathematics Enthusiast

The opportunities for mathematics department faculty from institutions of higher education (IHEs) to work with middle school mathematics teachers are on the rise; the U.S. Department of Education has allocated almost $800 million for mathematics and science partnerships since 2004 that require collaboration between faculty from IHEs departments of arts and sciences and school districts. Changes in credentialing requirements due to the No Child Left Behind Act of 2001 mean that middle school mathematics teachers must take more mathematics content courses, yet current offerings for teachers in many mathematics departments typically focus on elementary or high school mathematics and often …

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Early Insurance Mechanisms And Their Mathematical Foundations, Amy Minto Jul 2008

Early Insurance Mechanisms And Their Mathematical Foundations, Amy Minto

The Mathematics Enthusiast

This article gives a historical survey of early insurance mathematics and its development in relation to the maritime industry and the origins of the life insurance industry. The history of the probability and statistics and its intricate connection to the actuarial sciences and modern insurance can be traced to the time period described in this paper.

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Guest Editorial: Reaction To The Final Report Of The National Mathematics Advisory Panel, Brian Greer Jul 2008

Guest Editorial: Reaction To The Final Report Of The National Mathematics Advisory Panel, Brian Greer

The Mathematics Enthusiast

In 2006, President Bush appointed the National Mathematics Advisory Panel (NMAP henceforth) which issued its Final Report on March 13, 2008. The Final Report (summary), plus reports of three subcommittees and five Task Groups, together with two appendices containing the Presidential Executive Order setting up the panel, and details of the panel membership and other personnel, can be downloaded from www.ed.gov/about/bdscomm/list/mathpanel/index.html

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Chopping Logs: A Look At The History And Uses Of Logarithms, Rafael Villarreal-Calderon Jul 2008

Chopping Logs: A Look At The History And Uses Of Logarithms, Rafael Villarreal-Calderon

The Mathematics Enthusiast

Logarithms are an integral part of many forms of technology, and their history and development help to see their importance and relevance. This paper surveys the origins of logarithms and their usefulness both in ancient and modern times.

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Meet The Authors Jul 2008

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

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Tme Volume 5, Numbers 2 And 3 Jul 2008

Tme Volume 5, Numbers 2 And 3

The Mathematics Enthusiast

No abstract provided.

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Introduction To Thinking As Communicating, Anna Sfard Jul 2008

Introduction To Thinking As Communicating, Anna Sfard

The Mathematics Enthusiast

This book is a result of years-long attempts to change my own thinking about thinking, a task seemingly as improbable as breaking a hammer by hitting it with itself. In this unlikely undertaking, I have been inspired by Lev Vygotsky, the Byelorussian psychologist who devoted his life to “characterizing the uniquely human aspects of behavior,”2 and by Ludwig Wittgenstein, the Austrian-British philosopher who insisted that no substantial progress can be made in this kind of endeavor unless the ways we talk, and thus think, about uniquely human “forms of life” undergo extensive revisions.

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Positive Solutions Of A Third-Order Three-Point Boundary-Value Problem, Bo Yang Jul 2008

Positive Solutions Of A Third-Order Three-Point Boundary-Value Problem, Bo Yang

Faculty Articles

We obtain upper and lower estimates for positive solutions of a third-order three-point boundary-value problem. Sufficient conditions for the existence and nonexistence of positive solutions for the problem are also obtained. Then to illustrate our results, we include an example.

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Criteria For Components Of A Function Space To Be Homotopy Equivalent, Gregory Lupton, Samuel Bruce Smith Jul 2008

Criteria For Components Of A Function Space To Be Homotopy Equivalent, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

We give a general method that may be effectively applied to the question of whether two components of a function space map(X, Y) have the same homotopy type. We describe certain group-like actions on map(X, Y). Our basic results assert that if maps f, g: X → Y are in the same orbit under such an action, then the components of map(X, Y) that contain f and g have the same homotopy type.

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Mathematical Cognition And The Final Report Of The National Mathematics Advisory Panel: A Critical, Cultural-Historical Activity Theoretic Analysis, Wolff-Michael Roth Jul 2008

Mathematical Cognition And The Final Report Of The National Mathematics Advisory Panel: A Critical, Cultural-Historical Activity Theoretic Analysis, Wolff-Michael Roth

The Mathematics Enthusiast

In its Final Report, the National Mathematics Advisory Panel has depicted a stark image of mathematical competencies and achievement among U.S. students. The Advisory Panel notes the lack of research with “truly scientific” rigor and, mentioning Vygotsky’s cultural-historical activity theory in passing, suggests its utility to be untested. In reading the report, I noted the limited understanding of the mathematics education literature it articulates and a complete failure to draw on established, “tried and proven,” theory and practice in mathematics education founded upon an encompassing culturalhistorical activity theory. This theory is comprehensive and encompassing, because it retains activity in its …

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Three Strikes, Tom O'Brien, Marianne Smith Jul 2008

Three Strikes, Tom O'Brien, Marianne Smith

The Mathematics Enthusiast

The first part of the paper describes and comments upon three aspects of the back-to-basics movement: the make-up and mindset of the National Mathematics Advisory Panel (NMP), the movement’s history in California, and recent “grassroots” activities of the movement in the state of Washington. The second part reports and comments on the principal findings of the NMP report.

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Editorial: 2 To 3- An Omnibus Of Features & Policy Issues In Mathematics Education, Bharath Sriraman Jul 2008

Editorial: 2 To 3- An Omnibus Of Features & Policy Issues In Mathematics Education, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

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A Case Study Using Soft Systems Methodology In The Evolution Of A Mathematics Module, Jon Warwick Jul 2008

A Case Study Using Soft Systems Methodology In The Evolution Of A Mathematics Module, Jon Warwick

The Mathematics Enthusiast

This paper describes the application of Soft Systems Methodology as a tool for facilitating the review of a taught mathematics module so that the views of those engaged with the module could be captured and conflicting expectations and views highlighted. Checkland’s Soft Systems Methodology is used since it enables the capture of stakeholder views and addresses both ‘hard’ and ‘soft’ aspects of the learning experience. Stages in the application of Soft Systems Methodology are illustrated including the development of a rich picture and conceptual models and the work was conducted using a stakeholder group that included students taking the module …

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Inverses - Why We Teach And Why We Need Talk More About It More Often!, Woong Lim Jul 2008

Inverses - Why We Teach And Why We Need Talk More About It More Often!, Woong Lim

The Mathematics Enthusiast

This article examines the key role that the notion of inverses plays in numerous mathematical concepts.

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A Simplex Model For Layered Niche Networks, Philip Fraundorf Jul 2008

A Simplex Model For Layered Niche Networks, Philip Fraundorf

Physics Faculty Works

No abstract provided.

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Enumerating Constrained Non-Crossing Minimally Rigid Frameworks, David Avis, Naoki Katoh, Makoto Ohsaki, Ileana Streinu, Shin-Ichi Tanigawa Jul 2008

Enumerating Constrained Non-Crossing Minimally Rigid Frameworks, David Avis, Naoki Katoh, Makoto Ohsaki, Ileana Streinu, Shin-Ichi Tanigawa

Computer Science: Faculty Publications

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints, which we call constrained non-crossing Laman frameworks, on a given set of n points in the plane. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in O(n4) time and O(n) space, or, with a slightly different implementation, in O(n3) time and O(n2) space. In particular, we obtain that the set of all the constrained non-crossing Laman …

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Magic Math Cards, Steve Humble Jul 2008

Magic Math Cards, Steve Humble

The Mathematics Enthusiast

Starting lessons with a good story, captures students imagination. The story then leads nicely into a magic card experiment which can be used to help teach the topic. I have used magic with a variety of age groups and found that they ask different questions of the task, and search for different levels of answers.

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New Titles In Mathematics Education Jul 2008

New Titles In Mathematics Education

The Mathematics Enthusiast

No abstract provided.

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"Obeying A Rule": Ludwig Wittgenstein And The Foundations Of Set Theory, Giorgio T. Bagni Jul 2008

"Obeying A Rule": Ludwig Wittgenstein And The Foundations Of Set Theory, Giorgio T. Bagni

The Mathematics Enthusiast

In this paper we propose some reflections on Wittgenstein’s ideas about grammar and rules; then we shall consider some consequences of these for the foundations of set theory and, in particular, for the introduction of major concepts of set theory in education. For instance, a community of practice can decide to follow a particular rule that forbids the derivation of arbitrary sentences from a contradiction: since, according to Radford’s perspective, knowledge is the result of thinking, and thinking is a cognitive social praxis, the mentioned choice can be considered as a form of real and effective knowledge.

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Algebra For All?, Brian Greer Jul 2008

Algebra For All?, Brian Greer

The Mathematics Enthusiast

In 1957, the director of one of the major math curriculum projects in the UK was quoted in a newspaper as saying: "Up went Sputnik and down came all the pure mathematicians saying we must do sets and be saved". The corresponding message from the National Math Panel Final Report is "Up went the economic performance of China and India and down came all the pure mathematicians saying we must do algebra and be saved".

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Unfolding Manhattan Towers, Mirela Damian, Robin Flatland, Joseph O'Rourke Jul 2008

Unfolding Manhattan Towers, Mirela Damian, Robin Flatland, Joseph O'Rourke

Computer Science: Faculty Publications

We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthogonal polygon. The algorithm cuts along edges of a 4×5×1 refinement of the vertex grid.

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A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich Jul 2008

A Review Of Fibroblast Populated Collagen Lattices, J. C. Dallon, Paul H. Ehrlich

Faculty Publications

Bellaes introduction of the fibroblast populated collagen lattice (FPCL) (1) has facilitated the study of collagen-cell interactions. As a result of the numerous modifications of the casting of FPCL's, the in vivo applications of these in vitro findings has been confusing. Here experimental FPCL contraction findings are viewed in regard to three proposed mechanisms responsible for lattice contraction. The cellular mechanisms responsible for generating FPCL contraction are: cell contraction, cell tractional forces related to cell locomotion, and initial cell elongation and spreading.

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Integer Ratio Logarithm Based Edge Detection For Runway Hazard Detection, Sri Satya Vardhan Gogineni Jul 2008

Integer Ratio Logarithm Based Edge Detection For Runway Hazard Detection, Sri Satya Vardhan Gogineni

Electrical & Computer Engineering Theses & Dissertations

As air traffic is growing in leaps and bounds every day, flying safe has been a major concern in day to day life. Aviation safety is always dependent on the performance of the pilot and air traffic controllers. The very involvement of human discretion introduces judgment as a component of a safe takeoff and landing. A convenient and immediate alternative would be the use of technology to alleviate the problem. Several algorithms have been developed to solve this problem. However, most computer vision algorithms leave the task of interpreting the end data unaddressed. Juggling the myriad tasks during landing and …

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A Symbolic Operator Approach To Power Series Transformation-Expansion Formulas, Tian-Xiao He Jun 2008

A Symbolic Operator Approach To Power Series Transformation-Expansion Formulas, Tian-Xiao He

Tian-Xiao He

In this paper we discuss a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalizations, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed.

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Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen Jun 2008

Fusion Of Character Tables And Schur Rings Of Dihedral Groups, Long Pham Bao Nguyen

Theses and Dissertations

A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We investigate the case where H is the dihedral group. In many cases, G can be completely determined. In general, G can be proven to have many interesting properties. The theory is developed in terms of S-ring …

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A Sharp Bound For The Reconstruction Of Partitions, Vincent Vatter Jun 2008

A Sharp Bound For The Reconstruction Of Partitions, Vincent Vatter

Dartmouth Scholarship

Answer in g a question of Cameron, Pretzel and Siemons proved that every integer partition of n >= 2(k + 3) (k + 1) can be reconstructed from its set of k-deletions. We describe a new reconstruction algorithm that lowers this bound to n >= k(2) + 2k and present examples showing that this bound is best possible.

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Analysis On The Strip-Based Projection Model For Discrete Tomography, Jiehua Zhu, Xiezhang Li, Yangbo Ye, Ge Wang Jun 2008

Analysis On The Strip-Based Projection Model For Discrete Tomography, Jiehua Zhu, Xiezhang Li, Yangbo Ye, Ge Wang

Xiezhang Li

Discrete tomography deals with image reconstruction of an object with finitely many gray levels (such as two). Different approaches are used to model the raw detector reading. The most popular models are line projection with a lattice of points and strip projection with a lattice of pixels/cells. The line-based projection model fits some applications but involves a major approximation since the x-ray beams of finite widths are simplified as line integrals. The strip-based projection model formulates projection equations according to the fractional areas of the intersection of each strip-shaped beam and the rectangular grid of an image to be reconstructed, …

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An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern Jun 2008

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed …

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Algorithms For Some Geometric Facility Location And Path Planning Problems., Sasanka Roy Dr. Jun 2008

Algorithms For Some Geometric Facility Location And Path Planning Problems., Sasanka Roy Dr.

Doctoral Theses

The facility location problem is a resource allocation problem that mainly deals with adequate placement of various types of facilities to serve a distributed set of demands satisfying the nature of interactions between the demands and facilities and optimizing the cost of placing/maintaining the facilities and the quality of services.The facility location problem is well-studied in the Operations Research literature and recently has received a lot of attention in the Computer Science community. For a company, the facility location problem provides more strategic decisions than just giving importance to locate the lowest cost space for storing its products. While identifying …

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