Mathematics Commons^™

Trigonometry Without Sines And Geometry Without Angles, Phillip Lestmann

ACMS Conference Proceedings 2007

In his book, Divine Proportions, N. J. Wildberger advocates for a "rational" trigonometry by substituting the squares of the common trigonometric ratios for those ratios themselves. This presentation examines and critiques the claims of the book by evaluating its presented methods.

Portrayls Of Mathematics In Culture, Jeremy Case

ACMS Conference Proceedings 2007

This paper looks at various portrays of mathematicians in culture, and how that can influence perceptions of mathematics.

Integrating Moral And Spiritual Themes In Middle School And High School Mathematics Teaching Units, Dave Klanderman, Sean Bird

ACMS Conference Proceedings 2007

In 2006, the Kuyers Institute published a total of nine math lessons for the middle school and high school which incorporate a Christian perspective. This paper examines the impact of teaching all of these lessons at a the high school level as well as selected lessons at the college level with preservice elementary and secondary mathematics teachers.

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Conference Proceedings 2007

Enlightenment thinkers saw the universe as mechanistic and mathematics as the language in which the universe is written. They viewed mathematics as eternal, as transcending human minds, and as comprehensible by human beings. Thus mathematics, from their perspective, is our best tool for understanding the secrets of nature. This outlook was nicely summarized by Morris Kline: (Kline, 1953) In brief the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. From a Christian perspective, however, the Enlightenment outlook is flawed. It privileges …

Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Jongerius

ACMS Conference Proceedings 2007

While most biographical works on C.S. Lewis give passing reference to Lewis' problems with elementary mathematics, few have made an attempt at diagnosing the difficulty or exploring its impact on his writing. A careful study of family correspondence, however, makes it clear that his learning difficulties were not with mathematics alone and suggests connections between attitudes toward and abilities in both mathematics and language. This paper will make these connections clear and will illustrate their ties to Lewis' effective mathematical references.

Counting Tulips: Three Combinatorial Proofs, Eric Gossett

ACMS Conference Proceedings 2007

A gardener has r ≥ 1 red tulips and b ≥ 1 blue tulips, each in its own pot. She plans to plant them in a line along the edge of her driveway. In how many visually distinguishable ways can she arrange them?

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.

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennet

All HMC Faculty Publications and Research

No abstract provided in this article.

A Hexagon Result And Its Generalization Via Proof, Michael De Villiers

The Mathematics Enthusiast

This paper presents the discovery of a hexagon result on Geometer’s Sketchpad and its generalization via proof for any 2n-gon. The result is : If ABCDEF is a hexagon with opposite sides parallel (not necessarily equal), then the respective centroids G, H, I, J, K and L of triangles ABC, BCD, CDE, DEF, EFA and FAB, form a hexagon with opposite sides both equal and parallel.

Introduction Of A New Construct: The Conceptual Tool "Flexibility", Mette Andresen

The Mathematics Enthusiast

This paper presents a new construct: the conceptual tool ‘Flexibility’. The construct was a result of an attempt to extract experiences of teaching and learning with the use of laptops. It was further developed and refined on the basis of four small-scale teaching experiments. The teaching experiments, being part of a development project in upper secondary school mathematics, investigated the use of laptops for teaching differential equations from a modeling point of view. The research was double-aimed: one objective was to conclude the project with some recommendations for the design of teaching, in the form of guidelines suitable for a …

New And Noteworthy Books From Sense Publishers

The Mathematics Enthusiast

No abstract provided.

Tme Volume 4, Number 2

The Mathematics Enthusiast

No abstract provided.

The Probability Of Relatively Prime Polynomials, Arthur T. Benjamin, Curtis D. Bennett

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

Editorial: New Horizons-Four Years Later, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Objective Truth Versus Human Understanding In Mathematics And In Chess, Olle Häggström

The Mathematics Enthusiast

This paper begins with a review of the collection 18 Unconventional Essays on the Nature of Mathematics edited by Hersh (2006). Inspired especially by the contribution by Thurston to that collection, I then go on to discuss, by means of a couple of thought experiments involving computer "oracles", the nature of mathematics as a human activity, hopefully providing some balance to the simplified view (sometimes held by research mathematicians such as myself) of the discipline as purely a quest for objective truth.

The Philosophy Of Mathematics, Values And Keralese Mathematics, Paul Ernest

The Mathematics Enthusiast

This paper explores the philosophical significance of the Keralese and Indian subcontinent contribution to history of mathematics. Identifying the most accurate genesis and trajectory of mathematical ideas in history that current knowledge allows should be the goal of every history of mathematics, and is consistent with any philosophy of mathematics. I argue for the need of a broader conceptualization of philosophy of than the traditional emphasis on scholastic enquiries into epistemology and ontology. For such an emphasis has been associated, though I add need not necessarily be so, with an ideological position that devalues non-European contributions to history of mathematics. …

The Stabilizing Effect Of Noise On The Dynamics Of A Boolean Network, Christopher S. Goodrich, Mihaela Teodora Matache

Mathematics Faculty Publications

In this paper, we explore both numerically and analytically the robustness of a synchronous Boolean network governed by rule 126 of cellular automata. In particular, we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system. This noise is introduced by changing the states of a given number of nodes in the system according to certain rules. New mathematical models are developed for this purpose. We use MATLAB to run the numerical simulations including iterations of the real system and the model, computation of Lyapunov exponents, and generation of …

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 …

A Complexification Of Rolle’S Theorem, J. P. Pemba, A. R. Davies, N. K. Muoneke

Applications and Applied Mathematics: An International Journal (AAM)

A new version of the classical Rolle’s theorem is proved for any complex-valued differentiable function of the complex variable on an open connected convex subset of the complex field. The associated Mean-Value theorem follows naturally. A few explicit illustrative examples are provided in the closing section of the paper.