Mathematics Commons^™

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 …

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Tme Statistics

The Mathematics Enthusiast

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Discrete Approximations Of Differential Inclusions In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study discrete approximations of continuous-time evolution systems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "broken lines." This result allows us to establish the value and strong solution convergences of discrete approximations of the Bolza problem for constrained infinite-dimensional differential/evolution inclusions under natural assumptions on the initial data.

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

The Mathematics Enthusiast

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 …

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 …

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 …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Tme Volume 2, Number 2

The Mathematics Enthusiast

No abstract provided.

A Bayesian Approach To Wireless Location Problems, Ivan Zorych

Dissertations

Several approaches for indoor location estimation in wireless networks are proposed. We explore non-hierarchical and hierarchical Bayesian graphical models that use prior knowledge about physics of signal propagation, as well as different modifications of Bayesian bivariate spline models. The hierarchical Bayesian model that incorporates information about locations of access points achieves accuracy that is similar to other published models and algorithms, but by using prior knowledge, this model drastically reduces the requirement for training data when compared to existing approaches. Proposed Bayesian bivariate spline models for location surpass predictive accuracy of existing methods. It has been shown that different versions …

Thermal Imaging Of Circular Inclusions Within A Two-Dimensional Region, Shannon Talbott, Hilary Spring

Mathematical Sciences Technical Reports (MSTR)

The ability to study the interior of an object without destroying it is an important industrial tool. One method of recent interest is steady-state thermal or impedance imaging. In this paper we will use the steady-state heat equation to locate one or more circular inclusions within a two-dimensional region, where the boundaries of the inclusions have partially disbonded from the surrounding material; this disbond is modelled as between the heat flux and jump discontinuity at the disbonded interface.

A Survey On Intrusion Detection Approaches, A Murali M. Rao

International Conference on Information and Communication Technologies

Intrusion detection plays one of the key roles in computer security techniques and is one of the prime areas of research. Usages of computer network services are tremendously increasing day by day and at the same time intruders are also playing a major role to deny network services, compromising the crucial services for Email, FTP and Web. Realizing the importance of the problem due to intrusions, many researchers have taken up research in this area and have proposed several solutions. It has come to a stage to take a stock of the research results and project a comprehensive view so …

Building Efficient Systems From Data In A Computational Intelligence Framework, Debrup Chakraborty Dr.

Doctoral Theses

There are problems of interest for which precise mathematical or physical understanding is yet to come. Let us illustrate this with an example. Suppose, for a mining operation one needs to blast a certain portion of the soil/rock using some specific ex- plosives. Before the blast is made, the miners want to know the intensity of vibration that would be produced at a certain distance from the site of blasting. The intensity of vibration may de pend on several factors. For example, it will depend on the characteristics and quantity of the explosive used, the rock characteristics of the region, …

Specific Ige Response To Purified And Recombinant Allergens In Latex Allergy, Viswanath P. Kurup, Gordon L. Sussman, Hoong Y. Yeang, Nancy Elms, Heimo Breiteneder, Siti Am Arif, Kevin J. Kelly, Naveen K. Bansal, Jordan N. Fink

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

In recent years, allergy to natural rubber latex has emerged as a major allergy among certain occupational groups and patients with underlying diseases. The sensitization and development of latex allergy has been attributed to exposure to products containing residual latex proteins. Although improved manufacturing procedures resulted in a considerable reduction of new cases, the potential risk for some patient groups is still great. In addition the prevalent cross-reactivity of latex proteins with other food allergens poses a major concern. A number of purified allergens and a few commercial kits are currently available, but no concerted effort was undertaken to …

Investigation Of Laser Beam Induced Current Techniques For Heterojunction Photodiode Characterization, Weifu Fang, David A. Redfern, Kazufumi Ito, G. Bahir, Charles A. Musca, John M. Dell, Lorenzo Faraone

Mathematics and Statistics Faculty Publications

A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P-n HgCdTe heterojunction photodiode structures. In particular, the question of …

Lebesgue ▼-Measure And Riemann ▼-Integration, Heather Bjorum

Masters Theses & Specialist Projects

Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided.

Direct Numerical Simulation For Flow Transition Over A Flat Plate, Shutian Deng

Mathematics Dissertations - Archive

In this paper, direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number of 0.5 and a Reynolds number of 1000 based on the free stream velocity and inflow displacement thickness has been carried out. The time-dependent Navier-Stokes equations are solved directly by a third-order TVD Runge-Kutta method from Shu(1998). A sixth order central compact scheme from Lele (1992) that facilitates high resolution of the flow field is used for spatial discretization together with a sixth order implicit compact filter. To avoid possible non-physical wave reflection from the boundaries, the non-reflecting boundary conditions …

On The Image Of The Totalling Functor, Kristen Ann Beck

Mathematics Theses - Archive

Let A denote a DG algebra and k a field. The totalling functor, from the category of chain complexes over the graded A-modules to the catagory of DG modules over A, can be extended to one between their derived categories. If this extension were onto, the derived category of the category of DG modules would be superfluous. This paper investigates the image of the extension of Tot in the fundamental case when A is the polynomial ring in d variables over k. When d is at least 2, there are semifree DG modules of rank n, where n is at …

Upper Estimates For The Energy Of Solutions Of Nonhomogeneous Boundary Value Problems, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We establish upper bounds for the energy of critical levels of the functional associated to a perturbed superlinear elliptic boundary value problem. We show that the perturbed problem satisfies the estimates obtained by Bahri and Lions (1988) for the symmetric problem. We use these estimates to prove the existence of nonradial solutions to a radial elliptic boundary value problem. Our results fill a gap in an earlier paper by Aduén and Castro.

A Constructive Proof Of Ky Fan's Generalization Of Tucker's Lemma, Timothy Prescott '02, Francis E. Su

All HMC Faculty Publications and Research

We present a proof of Ky Fan's combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan's lemma to allow for triangulations of Sⁿ that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker's lemma that holds for a more general class of triangulations than the usual version.

Construction Of M^4 Run Linear Graphs By Finite Geometries, Chung Yi Suen

Mathematics and Statistics Faculty Publications

Finite projective geometries are used to obtain some series of Taguchi's linear graphs involving m^4 runs, where m is a prime or a prime power. The concept of maximal linear graph is introduced to reduce the number of nonisomorphic linear graphs. Some 81-run maximal linear graphs are given as examples. A table of 27 nonisomorphic 16-run maximal linear graphs, which is believed to be complete, is provided.

On The Construction Of Mixed Orthogonal Arrays Of Strength Two, Chung Yi Suen, Warren F. Kuhfeld

Mathematics and Statistics Faculty Publications

The generalized Kronecker sum was used by Wang and Wu (J. Amer. Statist. Assoc. 86 (1991) 450) and Dey and Midha (Statist. Probab. Lett. 28 (1996) 211; Proc. AP Akad. Sci. 5 (2001) 39) to construct mixed orthogonal arrays. We modify their methods to obtain several families of mixed orthogonal arrays. Some new arrays with run size less than 100 are found.

Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal

Mathematical Sciences Technical Reports (MSTR)

This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects.

Two-Dimensional Self-Assembly In Diblock Copolymers, Anette E. Hosoi, Dmitriy Kogan '03, Caitlin E. Devereaux '02, Andrew J. Bernoff, Shenda M. Baker

All HMC Faculty Publications and Research

Diblock copolymers confined to a two-dimensional surface may produce uniform features of macromolecular dimensions (∼10–100  nm). We present a mathematical model for nanoscale pattern formation in such polymers that captures the dynamic evolution of a solution of poly(styrene)-b-poly(ethylene oxide), PS-b-PEO, in solvent at an air-water interface. The model has no fitting parameters and incorporates the effects of surface tension gradients, entanglement or vitrification, and diffusion. The resultant morphologies are quantitatively compared with experimental data.

A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson

Theses and Dissertations

This thesis presents a simple force-based model of moving and interacting cells that incorporates a realistic description of cell adhesion and applies it to a system of spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.

Positive Solutions For The Beam Equation Under Certain Boundary Conditions, Bo Yang

Faculty Articles

We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established

Some Analogs Of Zariski's Theorem On Nodal Line Arrangements, A.D. Raza Choudary, Alexandru Dimca, Ştefan Papadima

Mathematics Faculty Scholarship

For line arrangements in P² with nice combinatorics (in particular, for those which are nodal away the line at infinity), we prove that the combinatorics contains the same information as the fundamental group together with the meridianal basis of the abelianization. We consider higher dimensional analogs of the above situation. For these analogs, we give purely combinatorial complete descriptions of the following topological invariants (over an arbitrary field): the twisted homology of the complement, with arbitrary rank one coefficients; the homology of the associated Milnor fiber and Alexander cover, including monodromy actions; the coinvariants of the first higher non-trivial …

Differentials In The Homological Homotopy Fixed Point Spectral Sequence, Robert R. Bruner, John Rognes

Mathematics Faculty Research Publications

We analyze in homological terms the homotopy fixed point spectrum of a T–equivariant commutative S–algebra R. There is a homological homotopy fixed point spectral sequence with E^2_(s,t) = H^(−s)_(gp) (��;H_t(R;��_p)), converging conditionally to the continuous homology H^c_(s+t)(R^(h��);��_p) of the homotopy fixed point spectrum. We show that there are Dyer–Lashof operations β^ϵQ^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E^(2r)–term of the spectral sequence there are 2r other classes in the E^(2r)–term (obtained mostly by Dyer–Lashof operations …