Mathematics Commons^™

Tanzania, Mathematics, And Me: Reflections From My Work With Tanzanian Teachers, Mandi Maxwell

ACMS Conference Proceedings 2007

In June 2006 I had the privilege of participating in a four-day teacher training workshop in Mumba, Tanzania. In this paper I will discuss the challenges and triumphs of working with Tanzanian Secondary Mathematics teachers. We will discuss the educational environment, teaching strategies, and curricular issues that affect mathematics teachers in rural areas of Tanzania and contrast that with the American educational experience. We will also discuss some of the goals of the Teacher Training workshop that my colleagues and I led and look at some of the specific mathematical ideas and applications that I shared with the Mathematics teachers …

Mathematical Knowledge And Leibniz' Epstemology, Jonathan Zderad

ACMS Conference Proceedings 2007

No abstract provided.

Integrating Ethics Into The Database Course With A Focus On Data Modeling And Normalization, James F. Glasgow, Ph.D

ACMS Conference Proceedings 2007

No abstract provided.

Optimize Your Matth Services Through Networking, Patrice Conrath

ACMS Conference Proceedings 2007

No abstract provided.

Modeling Growth In Christian Evangelism, Marvin Bittinger

ACMS Conference Proceedings 2007

No abstract provided.

Breathing Life Into The Liberal Arts Math Course: Ten Teaching Tips, Mark Colgan

ACMS Conference Proceedings 2007

Teaching the liberal arts math course for general education students presents unique challenges, but the course also offers exciting life applications and opportunities for integrating faith with a variety of creative topics. I try to make the course interesting by actively involving students and relating mathematical topics to their lives. In this paper I will discuss some things I have tried in the liberal arts math course I teach at Taylor University: using students' names, use of undergraduate teaching assistants (T As), group guessing games, handout booklets, hangman, group projects, memory verses, reflection papers, and life lessons.

Six Ways, Yea Seven, That Scripture Is Integral To Our Science And Math Classes, Sean Bird

ACMS Conference Proceedings 2007

This paper looks at the ways the Bible informs mathematics and its role in guiding our stewardship of God’s creation.

Voltaire: A Study In Finding A Needle In A Haystack, Andrew Simoson

ACMS Conference Proceedings 2007

In Euler’s popular notes to a German Princess of 1837, he describes Voltaire as laughing about the idea of a hole going to Earth’s center. Did Voltaire actually write about this idea? Herein we describe the answers to be found upon searching through the huge opus of Voltaire’s written work. The result has links to Newton’s 1687 Principia discoveries and the French Academy’s early eighteenth century international scientific expeditions to Lapland and Peru establishing the veracity of those discoveries.

The Beautiful And Sublime In Mathematics, Paul Zwier

ACMS Conference Proceedings 2007

A précis of Paul Zwier's talk presented at the meetings of the ACMS Conference at Messiah College on June 1, 2007.

Connection-Oriented Computer Science Education, Kim Kihlstrom

ACMS Conference Proceedings 2007

Computers play an important role in every area of our society and are integral in every academic discipline. Today's computer science students need a background that will prepare them for the expanding range of computing opportunities. The opportunities for computer professionals are varied and increasing in diversity. However, undergraduate computer science programs tend to be narrowly focused on programming and related technical skills. Female students in particular tend to be highly interested in exploring connections between computer science and other fields.

How can we leverage these observations at a liberal arts college, where interdisciplinary connections are highly desirable, and where …

Exploring Loci In Geometry, Owen Byer, Deirdre Smeltzer

ACMS Conference Proceedings 2007

No abstract provided.

Measures Of Travers Ability In Graphs, Futaba Okamoto

Dissertations

For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …

The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui

Dissertations

In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dv_s ), where dv_s ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …

Introduction (2007), Angela Hare

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2007), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2007

Sixteenth Conference of the Association of Christians in the Mathematical Sciences

Which Chessboards Have A Closed Knight's Tour Within The Cube?, Joseph Demaio

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. When the chessboard is translated into graph theoretic terms the question is transformed into the existence of a Hamiltonian cycle. There are two common tours to consider on the cube. One is to tour the six exterior n x n boards that form the cube. The other is to tour within the n stacked copies of the n x n board that form the cube. This paper is concerned with the latter. In this paper …

Some Results Of Backward Itô Formula, Guiseppe Da Prato, Jose-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We use the notion of backward integration, with respect to a general Lévy process, to treat, in a simpler and unifying way, various classical topics as: Girsanov theorem, rst order partial differential equations, the Liouville (or Lyapunov) equations and the stochastic characteristic method.

Existence Of Minimizers And Necessary Conditions In Set-Valued Optimization With Equilibrium Constraints, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study set-valued optimization problems with equilibrium constraints (SOPEOs) described by parametric generalized equations in the form 0 is an element of the set G(x) + Q(x) where both G and Q are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the PalaisSmale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.

Suboptimal Minimax Design Of Constrained Parabolic Systems With Mixed Boundary Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in mixed (Robin) boundary conditions. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We design and justify an easily implemented suboptimal structure of the feedback boundary regulator and compute its optimal parameters ensuring the required state performance and robust stability of the nonlinear closed-loop control system on the infinite horizon.

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Mathematics Faculty Publications

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

Variational Analysis In Bilevel Programming, S Dempe, J Dutta, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of advanced tools of modern variational analysis and generalized differentiation to problems of optimistic bilevel programming. In this way, new necessary optimality conditions are derived for two major classes of bilevel programs: those with partially convex and with fully convex lower-level problems. We provide detailed discussions of the results obtained and their relationships with known results in this area.

The Time Invariance Principle, Ecological (Non)Chaos, And A Fundamental Pitfall Of Discrete Modeling, Bo Deng

Department of Mathematics: Faculty Publications

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.

Approximations Of Continuous Newton's Method: An Extension Of Cayley's Problem, Jon T. Jacobsen, Owen Lewis '05, Bradley Tennis '06

All HMC Faculty Publications and Research

Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size h=1, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots

Hartman-Grobman Theorems Along Hyperbolic Stationary Trajectories, Edson A. Coayla-Teran, Salah-Eldin A. Mohammed, Paulo Régis C. Ruffino

Articles and Preprints

We extend the Hartman-Grobman theorems on discrete random dynamical systems (RDS), proved in [7], in two directions: For continuous RDS and for hyperbolic stationary trajectories. In this last case there exists a conjugacy between traveling neighbourhoods of trajectories and neighbourhoods of the origin in the corresponding tangent bundle. We present applications to deterministic dynamical systems.

Variational Principles For Set-Valued Mappings With Applications To Multiobjective Optimization, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which~being certainly of independent interest are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang formulated via an appropriate subdifferential notion for …

Step-Up Simultaneous Tests For Identifying Active Effects In Orthogonal Saturated Designs, Samuel S. Wu, Weizhen Wang

Mathematics and Statistics Faculty Publications

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given alpha level in the strong sense.

Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich

Mathematics Research Reports

We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modi- fied one-sided Lipschitz condition imposed on the right-hand side (i.e., on the velocity sets) of the differential inclusion, which is a significant improvement of the conventional Lipschitz continuity. Our main attention is paid to establishing efficient conditions that ensure the strong approximation (in the W^1,p-norm as p greater than or equal to 1) of feasible trajectories for the one-sided Lipschitzian differential inclusions under. consideration by …

A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler

Mathematics Faculty Publications

If a large number of educated people were asked, ``What was your most exciting class?'', odds are that very few of them would answer ``Trigonometry.'' The subject is generally presented in a less-than-exciting fashion, with the repeated caveat that ``you'll need this when you take calculus,'' or ``this has lots of applications'' without ever really seeing many of them. This manuscript addresses how the author is trying to change this tradition by exposing casual students from kindergarten to college to Joseph Fourier's secret, that nearly any function can be built out of sine and cosine curves. And music serves as …

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Journal 2007

From a Christian perspective, both modern and post-modern approaches to the philosophy of mathematics have significant shortcomings. This paper explores an alternative. It summarizes Augustine of Hippo’s views on the four classical themes of the philosophy of mathematics-the ontology of mathematical objects, their epistemology, the nature of truth in mathematics, and how we account for the effectiveness of mathematics in describing the natural world. It then traces what has happened to Augustine’s perspective in the roughly 1600 years since it was written concluding with a discussion of some spiritual and intellectual problems with the currently dominant secular perspective.