Physical Sciences and Mathematics Commons^™

Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski

Mathematics Faculty Publications

A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult …

A (Not So) Complex Solution To A² + B² = Cⁿ, Arnold M. Adelberg, Arthur T. Benjamin, David I. Rudel '99

All HMC Faculty Publications and Research

No abstract provided in this article.

Random Walks On The Torus With Several Generators, Timothy Prescott '02, Francis E. Su

All HMC Faculty Publications and Research

Given n vectors {_i} ∈ [0, 1)^d, consider a random walk on the d-dimensional torus ^d = ℝ^d/ℤ^d generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*^k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*^k) ≥ C₁k^−n/2, where C₁ = C(n, d) is …

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Analogies And Mathematics: What Is The Connection? Book Review Of Mathematical And Analogical Reasoning Of Young Learners, Bharath Sriraman

The Mathematics Enthusiast

Lyn English (Ed). Mathematical and Analogical Reasoning of Young Learners. New Jersey: Lawrence Erlbaum & Associates, 2004. ISBN 0-8058-4945-9.

In the last decade and a half mathematics education literature has shown a rapid increase in books and articles that focus on the social and cultural issues related to mathematics learning and teaching. Although the social and cultural dimensions are important and relevant, the cognitive dimension of mathematical learning is equally important and received less attention. Mathematical and Analogical Reasoning of Young Learners takes us back to the very roots of learning and investigates foundational questions on the nature of …

The Nature Of Proof In Today's Classroom. Book Review Of The Nature Of Proof, Erica Lane

The Mathematics Enthusiast

Harold Fawcett. The Nature of Proof. New York City: Bureau of Publications, Columbia University, 1938. Re-printed by the National Council of Teachers of Mathematics in 1995.

Throughout the world, children are taught new ideas and concepts in a variety of ways, and the advocates of the different approaches claim that their method is the most effective and profitable for the students. In addition to the different teaching styles, each individual learns the material in a distinct manner. Teachers, therefore, must be aware of the diverse techniques of both teaching and learning in an effort to optimize the learning experience …

Computational Approaches To The Design And Analysis Of Stability Of Polypeptide Multilayer Thin Films, Bin Zheng

Doctoral Dissertations

The focus of this research is the development of computational approaches to understanding the physical basis of layer-by-layer assembly (LBL), a key methodology of nanomanufacturing. The results provided detailed information on structure which cannot be obtained directly by experiments.

The model systems chosen for study are polypeptide chains. Reasons for this are that polypeptides are no less polyelectrolytes than the more usual polyions, and one can control the primary structure of a polypeptide on a residue-by-residue basis using modern synthetic methods. Moreover, as peptides constitute one of the four major classes of biological macromolecules, research in this direction is expected …

Modulation Of Airway Inflammation By Immunostimulatory Cpg Oligodeoxynucleotides In A Murine Model Of Allergic Aspergillosis, Banani Banerjee, Kevin J. Kelly, Jordan N. Fink, James D. Henderson Jr., Naveen K. Bansal, Viswanath P. Kurup

Mathematics, Statistics and Computer Science Faculty Research and Publications

Allergic aspergillosis is a Th2 T-lymphocyte-mediated pulmonary complication in patients with atopic asthma and cystic fibrosis. Therefore, any therapeutic strategy that selectively inhibits Th2 T-cell activation may be useful in downregulating allergic lung inflammation in asthma. In the present study, we developed a CpG oligodeoxynucleotide (ODN)-based immune intervention of allergic inflammation in a mouse model of allergic aspergillosis. Four different groups of mice were used in a short-term immunization protocol. Three experimental groups of animals (groups 1 to 3) were sensitized with Aspergillus fumigatus antigens. Animals in group 1 were immunized with A. fumigatus antigen alone, while those in group …

Deadline Analysis Of Interrupt-Driven Software, Dennis Brylow, Jens Palsberg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Real-time, reactive, and embedded systems are increasingly used throughout society (e.g., flight control, railway signaling, vehicle management, medical devices, and many others). For real-time, interrupt-driven software, timely interrupt handling is part of correctness. It is vital for software verification in such systems to check that all specified deadlines for interrupt handling are met. Such verification is a daunting task because of the large number of different possible interrupt arrival scenarios. For example, for a Z86-based microcontroller, there can be up to six interrupt sources and each interrupt can arrive during any clock cycle. Verification of such systems has traditionally relied …

Vector Operations In Superscalar Architectures, Nathan Daniel Flinn

Electrical & Computer Engineering Theses & Dissertations

Vector calculations are very prevalent today. Though the vector-processing computer is quite an old concept, superscalar processors lack hardware support for vector operations. This thesis investigates whether an ordinary superscalar computer architecture can be designed to include hardware support for improved vector operations without drastically changing the existing superscalar design and behavior. A computer architecture design was created and implemented that included the vector multiply (dot product) operation. The design includes a Vector Operations Unit that captures incoming vector operations and generates the necessary set of machine instructions to complete the vector operation internally. It then delivers these instructions to …

Heights And Diophantine Problems, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at Rice University, September 2004.

Distinguishing Numbers For Graphs And Groups, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

A graph G is distinguished if its vertices are labelled by a map φ: V(G) → {1,2,..., k} so that no non-trivial graph automorphism preserves φ. The distinguishing number of G is the minimum number k necessary for φ to distinguish the graph. It measures the symmetry of the graph. We extend these definitions to an arbitrary group action of Γ on a set X. A labelling φ: X → {1, 2,..., k} is distinguishing if no element of Γ preserves Γ except those which fix each element of X. The distinguishing number of the group action on X is …

Entire Pluricomplex Green Functions And Lelong Numbers Of Projective Currents, Dan Coman

Mathematics - All Scholarship

Let T be a positive closed current of bidimension (1,1) and unit masson the complex projective space Pⁿ. We prove that the set Valpa(T) of points where T has Lelong number larger than alpha is contained in a complex line if alpha ≥ 2/3, and |V alpa(T ) \ L| ≤ 1 for some complex line L if 1/2 ≤ alpha < 2/3. We also prove that in dimension 2 and if 2/5 ≤ alpha < 1/2, then |V alpha (T ) \ C| ≤ 1 for some conic C.

Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh

Mathematical Sciences Technical Reports (MSTR)

This paper develops an algorithm for finding one or more non-insulated, pair-wise disjoint, linear cracks in a two dimensional region using boundary measurements.

Homology Over Local Homomorphisms, Luchezar L. Avramov, Srikanth Iyengar, Claudia Miller

Mathematics - All Scholarship

The notions of Betti numbers and of Bass numbers of a finite module N over a local ring R are extended to modules that are only assumed to be finite over S, for some local homomorphism phi: R -> S. Various techniques are developed to study the new invariants and to establish their basic properties. In several cases they are computed in closed form. Applications go in several directions. One is to identify new classes of finite R-modules whose classical Betti numbers or Bass numbers have extremal growth. Another is to transfer ring theoretical properties between R and S in …

Subgradients Of Distance Functions At Out-Of-Set Points, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics Research Reports

This paper deals with the classical distance function to closed sets and its extension to the case of set-valued mappings. It has been well recognized that the distance functions play a crucial role in many aspects of variational analysis, optimization, and their applications. One of the most remarkable properties of even the classical distance function is its intrinsic nonsmoothness, which requires the usage of generalized differential constructions for its study and applications. In this paper we present new results in theser directions using mostly the generalized differential constructions introduced earlier by the first author, as well as their recent modifications. …

Putnam, Pizza & Problem Solving, Andrew J. Bernoff, Francis E. Su

All HMC Faculty Publications and Research

Ok, here's a difficult question for you.. How can you get roughly 10% of the student body at your college to get up early on a Saturday and spend six hours working on an incredibly difficult exam for which many will get a score of zero?

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

Pitchfork Bifurcations Of Invariant Manifolds, Jyoti Champanerkar

Dissertations

In a parameter dependent, dynamical system, when the qualitative structure of the solutions changes due to a small change in the parameter, the system is said to have undergone a bifurcation. Bifurcations have been classified on the basis of the topological properties of fixed points and invariant manifolds of dynamical systems. A pitchfork bifurcation in R is said to have occurred when a stable fixed point becomes unstable and two new stable fixed points, separated by the unstable fixed point come into existence.

In this thesis, a pitchfork bifurcation of an (in- 1)-dimensional invariant submani-fold of a dynamical system in …

Numerical Simulation Of Microwave Heating Of A Target With Temperature Dependent Electrical Properties In A Single-Mode Cavity, Hoa Kien Tran

Dissertations

This dissertation extends the work done by Hue and Kriegsmann in 1998 on microwave heating of a ceramic sample in a single-mode waveguide cavity. In that work, they devised a method combining asymptotic and numerical techniques to speed up the computation of electromagnetic fields inside a high-Q cavity in the presence of low-loss target. In our problem, the dependence of the electrical conductivity on temperature increases the complexity of the problem. Because the electrical conductivity depends on temperature, the electromagnetic fields must be recomputed as the temperature varies. We then solve the coupled heat equation and Maxwell's equations to determine …

The Adjoint Of An Even Size Matrix Factors, Ragnar-Olaf Buchweitz, Graham J. Leuschke

Mathematics - All Scholarship

We show that the adjoint matrix of a generic square matrix of even size can be factored nontrivially, answering a question of G. Bergman. This note is a preliminary report on work in progress.

On The Dressing Method For The Generalised Zakharov-Shabat System, Rossen Ivanov

Articles

The dressing procedure for the Generalised Zakharov-Shabat system is well known for systems, related to sl(N) algebras. We extend the method, constructing explicitly the dressing factors for some systems, related to orthogonal and symplectic Lie algebras. We consider ’dressed’ fundamental analytical solutions with simple poles at the prescribed eigenvalue points and obtain the corresponding Lax potentials, representing the soliton solutions for some important nonlinear evolution equations.

Some Statistical Contributions To The Analysis Of Human Genome Diversity And Evolution., Analabha Basu Dr.

Doctoral Theses

The work embodied in this thesis pertains to human population genetics. In particular, the overarching goals of this thesis are to contribute to the understanding of genomic diversity of human populations and to the development of statistical methods for making inferences in genome diversity studies. With these two goals in mind, we have carried out a detailed statistical analysis of genomic data on a large number of ethnic populations of India, generated in the laboratory of the Anthropology & Human Genetics Unit, Indian Statistical Institute, Kolkata. Additionally, wherever relevant, we have compared our data with those collated from the published …

The Birational Isomorphism Types Of Smooth Real Elliptic Curves, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

In this note we determine all birational isomorphism types of real elliptic curves and show that it is the same as the orbit space of smooth cubic real curves in real projective space under linear projective equivalence. There are two families, each depending polynomially on a real parameter in a open subinterval of R. We further show that the complexification of a real elliptic curve has exactly two real forms. Thus the real elliptic curves come in pairs which are isomorphic over C. Finally, the map taking a real elliptic curve to its j-invariant maps the two families …

Explicit Lower Bounds On The Modular Degree Of An Elliptic Curve, Mark Watkins

Mathematics - All Scholarship

We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation of zero-free regions for Dirichlet L-functions, but here, due to the work of Goldfield-Hoffstein-Lieman, we know that there are no Siegel zeros, which leads to a strengthened result.

Basin Of Attraction Of Periodic Orbits Of Maps On The Real Line, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

We prove a conjecture by Elaydi and Yakubu which states that the basin of attraction of an attracting 2 ^k -cycle of the Ricker's map is where E is the set of all eventually 2 ^r -periodic points. The result is then extended to a more general class of continuous maps on the real line.

Conic Blocking Sets In Desarguesian Projective Planes, Leanne D. Holder

Mathematics Faculty Research

a conic blocking set to be a set of lines in a Desarguesian projective plane such that all conics meet these lines. Conic blocking sets can be used in determining if a collection of planes in projective three-space forms a flock of a quadratic cone. We discuss trivial conic blocking sets and conic blocking sets in planes of small order. We provide a construction for conic blocking sets in planes of non-prime order, and we make additional comments about the structure of these conic blocking sets in certain planes of even order.

Difference Equations Versus Differential Equations, A Possible Equivalence For The Rössler System?, Christophe Letellier, Saber Elaydi, Luis A. Aguirre, Aziz Alaoui

Mathematics Faculty Research

When a set of non linear differential equations is investigated, most of the time there is no analytical solution and only numerial integration techniques can provide accurate numerical solutions. In a general way the process of numerical integration is the replacement of a set of differential equations with a continuous dependence on the time by a model for which these time variable is discrete. When only a numerical solution is researched, a fourth-order Runge-Kutta integration scheme is usually sufficient. Nevertheless, sometimes a set of differential equations may be required and, in this case, standard schemes like the forward Euler, backward …

Corrective Greedy Algorithm For Finding The Straight Line Skeleton Of A Simple Polygon, Amit Parnerkar

Culminating Projects in Computer Science and Information Technology

No abstract provided.