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2010

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Articles 151 - 180 of 690

Full-Text Articles in Mathematics

Poset Pinball, Gkm-Compatible Subspaces, And Hessenberg Varieties, Megumi Harada, Julianna Tymoczko Jul 2010

Poset Pinball, Gkm-Compatible Subspaces, And Hessenberg Varieties, Megumi Harada, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

This paper has three main goals. First, we set up a general framework to address the problem of constructing module bases for the equivariant cohomology of certain subspaces of GKM spaces. To this end we introduce the notion of a GKM-compatible subspace of an ambient GKM space. We also discuss poset-upper-triangularity, a key combinatorial notion in both GKM theory and more generally in localization theory in equivariant cohomology. With a view toward other applications, we present parts of our setup in a general algebraic and combinatorial framework. Second, motivated by our central problem of building module bases, we introduce a …

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Fastmedusa: A Parallelized Tool To Infer Gene Regulatory Networks, Serdar Bozdag, Aiguo Li, Stefan Wuchty, Howard A. Fine Jul 2010

Fastmedusa: A Parallelized Tool To Infer Gene Regulatory Networks, Serdar Bozdag, Aiguo Li, Stefan Wuchty, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Motivation: In order to construct gene regulatory networks of higher organisms from gene expression and promoter sequence data efficiently, we developed FastMEDUSA. In this parallelized version of the regulatory network-modeling tool MEDUSA, expression and sequence data are shared among a user-defined number of processors on a single multi-core machine or cluster. Our results show that FastMEDUSA allows a more efficient utilization of computational resources. While the determination of a regulatory network of brain tumor in Homo sapiens takes 12 days with MEDUSA, FastMEDUSA obtained the same results in 6 h by utilizing 100 processors. Availability: Source code and documentation of …

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On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke Jul 2010

On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke

Computer Science: Faculty Publications

We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n3) time for polygons whose gluings are specified by n labels.

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A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert Jul 2010

A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert

Theses and Dissertations

Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into 3-dimensional space and can be very complicated. Twist and bitwist are simple constructions that provide an easy path to both creating and understanding closed, orientable 3-manifolds. By starting with simple face pairings on a 3-ball, a myriad of 3-manifolds can be easily constructed. In fact, all closed, connected, orientable 3-manifolds can be developed in this manner. We call this work a tool kit to emphasize the …

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Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas Jul 2010

Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas

Department of Mathematics: Dissertations, Theses, and Student Research

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of …

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A Hybrid Radial Basis Function-Pseudospectral Method For Thermal Convection In A 3-D Spherical Shell, Grady Wright, Natasha Flyer, David A. Yuen Jul 2010

A Hybrid Radial Basis Function-Pseudospectral Method For Thermal Convection In A 3-D Spherical Shell, Grady Wright, Natasha Flyer, David A. Yuen

Mathematics Faculty Publications and Presentations

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral methods in a “2 + 1” approach is presented for numerically simulating thermal convection in a 3‐D spherical shell. This is the first study to apply RBFs to a full 3‐D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface‐based coordinate system such as spherical coordinates. As a result, when used in the lateral directions, as in this study, they completely circumvent the pole issue with the further advantage that nodes can be “scattered” over …

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Comprehensive Peroxidase-Based Hematologic Profiling For The Prediction Of 1-Year Myocardial Infarction And Death, Marie Luise Brennan, Anupama Reddy, W.H. Wilson Tang, Yuping Wu, Danielle M. Brennan, Amy Hsu, Shirley A. Mann, Peter L. Hammer, Stanley L. Hazen Jul 2010

Comprehensive Peroxidase-Based Hematologic Profiling For The Prediction Of 1-Year Myocardial Infarction And Death, Marie Luise Brennan, Anupama Reddy, W.H. Wilson Tang, Yuping Wu, Danielle M. Brennan, Amy Hsu, Shirley A. Mann, Peter L. Hammer, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background— Recognition of biological patterns holds promise for improved identification of patients at risk for myocardial infarction (MI) and death. We hypothesized that identifying high- and low-risk patterns from a broad spectrum of hematologic phenotypic data related to leukocyte peroxidase-, erythrocyte- and platelet-related parameters may better predict future cardiovascular risk in stable cardiac patients than traditional risk factors alone. Methods and Results— Stable patients (n=7369) undergoing elective cardiac evaluation at a tertiary care center were enrolled. A model (PEROX) that predicts incident 1-year death and MI was derived from standard clinical data combined with information captured by a high-throughput peroxidase-based …

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Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts, Dorothy Wallace Jul 2010

Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts, Dorothy Wallace

Numeracy

Variation is a natural result of any process, including education. Understanding how variation propagates and increases is necessary for designing educational interventions that work for the intended population. We show how common strategies such as setting standards and tracking can accidentally produce unintended and undesirable results due to the way variation moves through a system.

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Creating A Masters In Numeracy Program, Eric Gaze Jul 2010

Creating A Masters In Numeracy Program, Eric Gaze

Numeracy

The Master of Science in Numeracy program at Alfred University received full approval from the New York State Education Department (NYSED) in May of 2007. This first-of-its-kind program seeks to provide teachers at all levels, from across the curriculum, the skills, and more importantly the confidence, to introduce relevant quantitative concepts in their own disciplines. Created to be a complement of the MS Ed. in Literacy, the 30-hour MS in Numeracy program consists of four required core courses (Teaching Numeracy, Teaching with Data, Assessment and Learning Theories in Numeracy, and Doing Science and Numeracy), five electives from a list of …

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Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner Jul 2010

Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner

Numeracy

This paper introduces Spreadsheets Across the Curriculum, a workshop-based educational materials development project to build a resource to facilitate connecting mathematics and context in undergraduate college courses where mathematical problem solving is relevant. The central idea is “spreadsheet modules,” which, in essence, are elaborate word problems in the form of short PowerPoint presentations with embedded Excel spreadsheets. Students work through the presentations on their own, making and/or completing the spreadsheets displayed on the slides in order to perform calculations or draw graphs that address the issue (context) posed in the word problem. The end result of the project is the …

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Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman Jul 2010

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman

Numeracy

This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …

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Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman Jul 2010

Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman

Numeracy

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …

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Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison Jul 2010

Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison

Numeracy

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …

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Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi Jul 2010

Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi

Numeracy

Colby-Sawyer College has adopted a mission for quantitative literacy (QL) to give students the “necessary skills to understand and use quantitative information in their personal and professional lives.” We have implemented an across-the-curriculum approach to develop these skills. As part of this QL program, we administer two assessment tests, one in basic mathematical skills and one that applies those skills, plus an attitude survey to both freshmen and seniors. Three years of data show that seniors score about 10 percentage points higher than freshmen on these tests. However, seniors still scored below 55 percent on both tests, and many cannot …

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Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk Jul 2010

Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk

Numeracy

Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …

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Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels Jul 2010

Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels

Numeracy

Science Literacy requires numeracy as part of its foundation, and much of Numeracy draws on examples and applications from the sciences. They share the goal of creating a society that is mathematics numerate and science literate, and are interrelated. National priorities to strengthen both among all our students are driven by practical considerations of economic competitiveness that increasingly depend on technological innovation. It is also critical to each individual for long-term job opportunities and for informed citizenship. With up to 80% of 21st century jobs requiring mathematics and science skills, a large majority of the 2,900,000 students who graduate from …

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Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi Jul 2010

Extension Of Plurisubharmonic Functions With Growth Control, Dan Coman, Vincent Guedj, Ahmed Zeriahi

Mathematics - All Scholarship

Suppose that X is an analytic subvariety of a Stein manifold M and that varphi is a plurisubharmonic (psh) function on X which is dominated by a continuous psh exhaustion function u of M. Given any number c > 1, we show that varphi admits a psh extension to M which is dominated by cu on M. We use this result to prove that any omega-psh function on a subvariety of the complex projective space is the restriction of a global omega-psh function, where omega is the Fubini-Study Kahler form.

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Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher Jul 2010

Rules Without Reason: Allowing Students To Rethink Previous Conceptions, Mary Mueller, Dina Yankelewitz, Carolyn Maher

The Mathematics Enthusiast

This paper reports on the strategies chosen by a group of sixth-grade students in an urban informal learning program as they worked to solve an open-ended, nonroutine task. In particular, the paper focuses on the ability of these students to rise above their previous, procedure-based misconceptions and arrive at a mathematically reasonable solution. Aspects of the problem task, the problem-solving environment, and, importantly, of the nature of the teacher’s interventions are analyzed to determine the conditions that encouraged students to approach mathematics as a logical, meaningful, sense-making activity.

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Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn Jul 2010

Climbing And Angles: A Study Of How Two Teachers Internalize And Implement The Intentions Of A Teaching Experiment, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this innovative teaching experiment, the context of climbing is used to induce the teaching and learning of angle concepts. This article reports on the outcomes of a three day teaching and climbing experiment and the impact of this experience on the teacher’s understanding of meso and micro embodiments of mathematics, angle representations, as well as shifts in their attitudes about teaching/learning geometry.

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Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams Jul 2010

Rehearsal Or Reorganization: Two Patterns Of Literacy Strategy Use In Secondary Mathematics Classes, Anne Adams

The Mathematics Enthusiast

This study presents two critical cases illustrating distinct patterns in teachers' use of literacy strategies in secondary mathematics classes. The cases are part of a professional development project designed to enhance teachers' pedagogical skills by developing content literacy strategies for use in secondary mathematics and science classrooms. Teachers' beliefs about teaching mathematics, their uses of writing and vocabulary development strategies, and goals for student learning were examined via interviews, classroom observations, reflections on teaching, and teacher posts to an online discussion forum. Results show patterns of literacy strategy use were related to teachers' views of pedagogy and of mathematics. Ned, …

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Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker Jul 2010

Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.

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Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit Jul 2010

Cultural Conflicts In Mathematics Classrooms And Resolution: The Case Of Immigrants From The Former Soviet Union And Israeli "Old Timers", Miriam Amit

The Mathematics Enthusiast

This paper describes a singular process that has been transforming mathematics education in Israel over the past 20 years, as a result of a massive influx of mathematics teachers from the former Soviet Union (FSU). It traces the key points of conflict that marked the initial contact between Israel's mathematical and educational culture and the codes and values brought with the immigrant teachers from the FSU. It then shows how this conflict is gradually becoming resolved, as the two disparate cultures merge into a single, new culture, based on 'the best of both worlds.' This case, we claim, can serve …

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Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried Jul 2010

Some Reflections On Hernández And López’S Reflections On The Chain Rule, Michael N. Fried

The Mathematics Enthusiast

To shed light on how history of mathematics can play a role in mathematics education, Hernández and López chose well in focusing on the chain rule as a case study. Generally speaking, it is, as they point out, a topic students find difficult to grasp: it is a rule involving a different order of complexity than, say, the rule for differentiating functions of the form f(x)=xn, and, although it can eventually become intuitive, it is far from intuitive at the start. Harel et al. (2009) have pointed out that students’ difficulties with the chain rule involve: “...coordinating three or more …

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Magic Circles In The Arbelos, Christer Bergsten Jul 2010

Magic Circles In The Arbelos, Christer Bergsten

The Mathematics Enthusiast

In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software.

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Vectors In Climbing, Anne Birgitte Fyhn Jul 2010

Vectors In Climbing, Anne Birgitte Fyhn

The Mathematics Enthusiast

In this article, the work on mesospace embodiments of mathematics is further developed by exploring the teaching and learning of vector concepts through climbing activities. The relevance and connection between climbing and vector algebra notions is illustrated via embedded digital videos.

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The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe Jul 2010

The History Of Mathematics As A Pedagogical Tool: Teaching The Integral Of The Secant Via Mercator’S Projection, Nick Haverhals, Matt Roscoe

The Mathematics Enthusiast

This article explores the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics. In particular, we draw on the mathematically pedigreed but misunderstood development of the Mercator projection and its connection to the integral of the secant function. We discuss the merits and the possible pitfalls of this approach based on a teaching module with undergraduate students. The appendices contain activities that can be implemented as an enrichment activity in a Calculus course.

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Problem Posing From The Foundations Of Mathematics, Libby Knott Jul 2010

Problem Posing From The Foundations Of Mathematics, Libby Knott

The Mathematics Enthusiast

This reflective paper develops a repertoire of questions for teachers to use in their classrooms during episodes of mathematics discussions with and among students. These questions are motivated by an examination of questions posed by Wittgenstein in Zettel, and are connected to underlying tacit assumptions about mathematics, most of which lie subtly below the generally accepted milieu of math-talk. Once classrooms norms have been established to encourage participation by all students in a democratic and just classroom environment, these questions can be used effectively to stimulate meaningful discourse. These questions provide important examples of problem posing designed to encourage student …

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A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez Jul 2010

A Semiotic Reflection On The Didactics Of The Chain Rule, Omar Hernandez Rodriguez, Jorge M. Lopez Fernandez

The Mathematics Enthusiast

According to (Fried, 2008), there is an intrinsic tension in trying to apply the history of mathematics to its didactics. Besides the widespread feeling that the introduction of didactic elements taken from the history of mathematics can detract the pedagogy of mathematics from the attainment of important goals, (Fried, 2008, p. 193) describes a pair of specific pitfalls that can arise in implementing such historical applications in mathematics education. The description in (Fried, 2008), is presented in the parlance of Sausserian Semiotics and identifies two semiotic “deformations” that arise when one fails to observe that the pairing between signs and …

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The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer Jul 2010

The Influence Of A Multidisciplinary Scientific Research Experience On Teachers Views Of Nature Of Science, Jerine Pegg, Edith Gummer

The Mathematics Enthusiast

This study examined a professional development project for K-12 science teachers that engaged participants in an authentic scientific investigation along with explicit-reflective attention to nature of science (NOS). The Views of Nature of Science (VNOS) and Views of Scientific Inquiry (VOSI) Questionnaires (Lederman, Abd-El-Khalick, Bell, & Schwartz, 2002; Schwartz, Lederman, & Thompson, 2001) were used to examine the relationship between teachers’ views of NOS and specific aspects of the professional development project. Results of the study show that teachers’ views of NOS were influenced by the multidisciplinary, primarily non-experimental research that they engaged in, the opportunity to observe interactions of …

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Epilogue, Bharath Sriraman Jul 2010

Epilogue, Bharath Sriraman

The Mathematics Enthusiast

The table of contents of this double issue included the above quote from the historian Howard Zinn which might seem puzzling to the reader. Why was this quote included and what is it supposed to mean? In the opening editorial, I mused over the whole enterprise of scholarly publishing and what it amounts to in the grand scheme of things. Zinn’s quote reminds us that academia is a cloistered unit and many of the things we place importance on in the academic culture of publish or perish seem insignificant when viewed through the lens of real problems that occur outside …

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