Physical Sciences and Mathematics Commons^™

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 …

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 …

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 …

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 …

Tme Volume 2, Number 2

The Mathematics Enthusiast

No abstract provided.

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

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

The Mathematics Enthusiast

No abstract provided.

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Tme Statistics

The Mathematics Enthusiast

No abstract provided.

An Analysis Of The Chemical Processes In The Smoke Plume From A Savanna Fire, Jorg Trentmann, Robert J. Yokelson, Peter V. Hobbs, Tanja Winterrath, Ted J. Christian, Meinrat O. Andreae, Sherri A. Mason

Chemistry and Biochemistry Faculty Publications

[1] Photochemistry in young plumes from vegetation fires significantly transforms the initial fire emissions within the first hour after the emissions are injected into the atmosphere. Here we present an investigation of field measurements obtained in a smoke plume from a prescribed savanna fire during the SAFARI 2000 field experiment using a detailed photochemical box-dilution model. The dilution used in the model simulations was constrained by measurements of chemically passive tracers (e.g., CO) near and downwind of the fire. The emissions of the dominant carbonaceous compounds, including oxygenated ones, were taken into account. The field measurements revealed significant production of …

Preparation, Structural Characterization, And Dynamic Properties Investigation Of Permalloy Antidot Arrays, Andriy Vovk, Leszek M. Malkinski, Scott L. Whittenburg, Charles O'Connor, Jin-Seung Jung, Suk-Hong Min

Chemistry and Biochemistry Faculty Publications

Regular nanosized structures are considered to be promising materials for magnetic information storage media with high density of information. Recently attention was paid to static and dynamic magnetic properties arising from dimensional confinement in such nanostructures. Here we present an investigation of permalloy antidot arrays of different thicknesses. Thin permalloyfilms of thickness ranging from were deposited on nanoporous membranes with a pore size of . It was found that additional ferromagnetic resonance peaks appear for film thicknesses below , while films with larger thicknesses show resonanceproperties similar to continuous films. A comparison between the filmsdeposited onto Si wafers and porous …

Wave Field Migration As A Tool For Estimating Spatially Continuous Radar Velocity And Water Content In Glaciers, John H. Bradford, Joel T. Harper

Geosciences Faculty Publications

Normal-moveout velocity analysis can lead to significant overestimates of the velocity structure of temperate glaciers since most englacial reflectors approximate point scatters and violate the assumption of planar flat lying reflectors. Migration velocity analysis (MVA) is a tool that does not depend on the assumption of flat lying reflectors. MVA can provide laterally and vertically continuous velocity estimates from conventional common-offset radar sections. In a study of temperate Bench Glacier, Alaska, we used MVA coupled with dielectric modeling to estimate the distribution of water content along a cross-section of the glacier. We found the glacier has two layers, an upper …

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.

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 …

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Tme Volume 2, Number 1

The Mathematics Enthusiast

No abstract provided.

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 …

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.

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 …

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 …

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 …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Assessing The Accuracy Of Respondents Reports Of The Location Of Their Home Relative To A National Forest Boundary And Forest Cover, John D. Baldridge, James T. Sylveste, William T. Borrie

Society and Conservation Faculty Publications

This paper assesses the accuracy of responses to a question that asks the location of respondents’ homes relative to a National Forest boundary. The analysis also assesses the accuracy of respondent reports on forest cover in the area surrounding their home. We find non-ignorable error in the responses to both questions. The remainder of this paper is divided into three sections. First, the methods used for this study are described as are limitations of the study. Second, we illustrate the study’s results. Finally, we discuss our results and conclusions.

State Aggregation And Population Dynamics In Linear Systems, Jonathan E. Rowe, Michael D. Vose, Alden H. Wright

Computer Science Faculty Publications

We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a …

Diurnal Water-Pressure Fluctuations: Timing And Pattern Of Termination Below Bench Glacier, Alaska, Usa, T. J. Fudge, Joel T. Harper, Neil Humphrey, W. Tad Pfeffer

Geosciences Faculty Publications

Observations from basal water-pressure sensors along the length of Bench Glacier, Alaska, USA, show that diurnal fluctuations of water pressure are seasonal and restricted to summer. Most notable about these fluctuations is their disappearance in the late summer and early autumn, long before the seasonal end of diurnal meltwater input. Here we present data documenting the end of diurnal water-pressure fluctuations during the 2002 and 2003 melt seasons. The end of diurnal fluctuations occurred abruptly in multiple boreholes spaced meters to kilometers apart. There was no obvious spatial progression of termination events, and a clear correlation with meteorological forcing or …

Evolution Of Subglacial Water Pressure Along A Glacier’S Length, Joel T. Harper, Neil Humphrey, W. Tad Pfeffer, T. J. Fudge, Shad O'Neel

Geosciences Faculty Publications

Observations from along the length of Bench Glacier, Alaska, USA, show that the subglacial water-pressure field undergoes a multiphase transition from a winter mode to a summer mode. Data were collected at the glacier surface, the outlet stream, and in a network of 47 boreholes spanning the length of the 7 km long glacier. The winter pressure field was near overburden, with low-magnitude (centimeter to meter scale) and long-period (days to weeks) variations. During a spring speed-up event, boreholes showed synchronous variations and a slight pressure drop from prior winter values. Diurnal pressure variations followed the speed-up, with their onset …

Historical Context And Hazardous Waste Facility Siting: Understanding Temporal Patterns In Michigan, Robin Saha, Paul Mohai

Environmental Studies Faculty Publications

This article tests the proposition that, beginning in the 1970s, historic growth of public environmental concern and opposition to waste facilities, as well as changes in the policy environment increasingly encouraged hazardous waste facilities siting to follow the path of least (political) resistance and resulted in environmental inequities. Our longitudinal analysis of sitings in the State of Michigan from 1950 to 1990 reveals a distinct temporal pattern supporting our hypotheses. Whereas significant racial, socioeconomic, and housing disparities at the time of siting were not in evidence for facilities sited prior to 1970, patterns of disparate siting were found for facilities …