Applied Mathematics Commons^™

Can Critical Thinking Be Redeemed?, Jeremy Case

ACMS Conference Proceedings 2009

We often claim that mathematics develops critical thinking skills. Critical thinking has many different definitions, but problem solving, deduction, analyzing arguments, and identifying assumptions are all certainly a part of critical thinking. As the trend in higher education moves away from focusing exclusively on content towards assessment and learning outcomes, we can justify our endeavors since mathematics and critical thinking align themselves well.

However, when examining the ultimate purpose of critical thinking in higher education, we must take care. If there is no agreed upon content knowledge in our postmodern age, the focus of education falls elsewhere. How one thinks …

Exploring The Limits Of Computing Through Exhaustive Search, Jeffrey L. Lehman

ACMS Conference Proceedings 2009

Many computing problems can be solved by identifying all possible moves or combinations of events and then picking the best solution. Problems in this domain provide fertile ground for exploring problem representation, storage requirements, and computational complexity. The problems and solution approaches are easy to understand, yet quickly push the memory and storage limits of a personal computer. This paper describes insights from a preliminary investigating of two exhaustive search problems, the 15-puzzle and Rubik’s cube. The insights gained by looking at exhaustive search problems can be integrated into classroom discussions and projects.

Monoids For Math Majors, Brian D. Beasley

ACMS Conference Proceedings 2009

Inspired by an MAA PREP workshop on “The Art of Factorization in Multiplicative Structures”, this paper will treat the basics of congruence monoids and arithmetical congruence monoids with their potential for a Modern Algebra or capstone course.

Supplemental Vocabulary Acquisition In The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham

ACMS Conference Proceedings 2009

DeSymbol is a program that translates first-order predicate logic expressions into English. It is designed to help students practice when learning or reviewing symbolic logic: students begin by translating English sentences into symbolic logic notation, and then they can use DeSymbol to translate the logic back into English to check their work.

The newest version of DeSymbol adds the ability for the user to expand the system’s vocabulary, using a web interface. The user can enter new nouns, verbs, or adjectives, specifying each word’s part of speech, its singular and plural forms, and (for verbs) whether the verb takes an …

Professor Peacock's Symbolical Algebra: Glimpses Into The Life And Work Of A Mathematical Reformer, Richard Stout

ACMS Conference Proceedings 2009

In his 1859 obituary of George Peacock (Royal Society of London, 1859),the nineteenth century mathematician and Dean of Ely Cathedral, his friend and long-time colleague J. F. W. Herschel not only lists Peacock's accomplishments as an educator, a churchman, and a mathematician, but also describes a man who embodies warmth and wisdom, the kind of person you would enjoy knowing and having as a colleague. Writing about Peacock in the Memoirs of the Royal Astronomical Society, Augustus DeMorgan echoes these sentiments when he says that "Whenever a man of safe judgment was wanted, who united kindness and courtesy to a …

The Development Of Mathematical And Spiritual Maturity In The Undergraduate Mathematics Curriculum, Angela Hare

ACMS Conference Proceedings 2009

Colleges and universities that teach mathematics have a responsibility to develop in students an appreciation of the powerful tools they are studying in the mathematics curriculum. Beyond this fundamental responsibility, the Christian college or university has the richer task of equipping mathematics graduates to use their mathematical knowledge and skills to sharpen their spiritual insight, to serve others, and to promote justice and freedom in society. The growth in mathematical maturity that occurs during the undergraduate years is an asset that enables Christian students of mathematics to participate in the redemptive work of Jesus Christ through their discipline of study. …

Approximating Sums Of Infinite Series, Kara Garrison, Thomas E. Price

ACMS Conference Proceedings 2009

The Euler-Maclaurin summation formula is frequently used to efficiently estimate sums of infinite series of the form $\sum_{j=1}^{\infty}f(j)$. The purpose of this article is to describe a modification of this numerical technique designed to simplify and reduce the computational effort required to obtain an acceptable estimate of the sum. The modified formula is obtained by replacing $f\left( x\right) $ with an easily constructed polynomial like interpolating function $a\left( x\right) $ designed to simplify the calculation of the integral and derivatives associated with Euler-Maclaurin. This approach provides a more tractable algorithm which can be written as a matrix equation. Examples are …

Integrating Dynamic Software Into Geometry Courses At Middle School, High School, And College Levels: Ten Lesson Plan And Instruction Material Units Incorporating Geometer's Sketchpad Version 4.07, Jamie Blauw, Lauren Zylstra, Dave Klanderman

ACMS Conference Proceedings 2009

This paper explores the use of dynamic geometry software (Geometer's Sketchpad) in the teaching and learning of Geometry at the high school and college level. As part of an honors project, two of the authors created a series of lesson activities to address specific geometric concepts. Each lesson implements Geometer's Sketchpad to create an engaging student-centered learning environment.

A Vision For Acms, James Bradley

ACMS Conference Proceedings 2009

This paper applies McGrath's and Heller's approach to the consideration of mathematics. It assumes that mathematics is not self-interpreting, but that, looked at from a framework informed by the Christian scriptures, it can be seen as having significant meaning and value and a transcendent purpose. In particular, it presents a classical interpretation of mathematics broadly conceived, presents two approaches to providing warrant for such an interpretation, and explores some implications. It argues, by means of the example of the classical interpretation, that the relationship between mathematics and theology is a viable area of scholarly inquiry encompassing profound and fascinating questions. …

Arithmetic Sequences, Diophantine Equations And The Number Of The Beast, Bryan Dawson

ACMS Conference Proceedings 2009

Revelation 13:18 invites anyone with "understanding" to "calculate the number of the beast". This session reviews historical attempts using arithmetic sequences and gives conditions by which a name is "beastable" by those methods. Do these approaches make it reasonable to identify the beast based on such calculation alone?

A Quick Way To Find The Arc Length Between Between Two Points Of The Logarithmic Spiral, Peter Rothmaler

ACMS Conference Proceedings 2009

No abstract provided.

Algebra Investigator, Al Hibbard

ACMS Conference Proceedings 2009

No abstract provided.

About Furuta's Inequality And Aluthge Transform On Pseudo-Hilbert Spaces, Loredana Ciudariu

ACMS Conference Proceedings 2009

No abstract provided.

Paper Abstracts (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

Introduction (2009), Terry Perciante

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

The Heavens And The Scriptures In The Eyes Of Johannes Kepler, Dale L. Mcintyre

ACMS Conference Proceedings 2009

The heavens declare the glory of God… Ps. 19:1 Acclaimed as one of the most accomplished and influential scientists of his time, the subject of this paper was also a passionate defender of the Christian faith who believed he had been called by God to glorify Him in the study of His Creation. We see a man who was so immersed in both the Scriptures and his exploration of the heavens that his scholarly writings often burst forth with biblical quotations and songs of praise for God the Creator. Though always magnanimous and tolerant of others, he suffered persecution from …

Table Of Contents (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2009), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2009

Seventeenth Conference of the Association of Christians in the Mathematical Sciences

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

ACMS Journal 2008-2009

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.

Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman

ACMS Conference Proceedings 2007

Many mathematics instructors at the college level are looking for a curricular option that has the potential to serve a number of different constituencies. It could be to encourage more students to take math courses, or to give worthwhile options to students who need to take math but who are not ready for calculus (or its sequence). On the other hand, one may wish to add a new course for majors outside of the typical offerings, or even to prepare students for undergraduate research. The mathematics of voting and choice is ideally suited to meet all these needs in the …

Bach (To The Calculus Of) Variations, Charles R. Hampton

ACMS Conference Proceedings 2007

While it is quite common for professionals (doctors, lawyers, academics, etc) to be talented in many ways, including musical talent, there is a special connection between music and mathematics. Musicians collectively are not more talented in mathematics than other professionals and other academics. This paper examines the connections between math and music, particularly calculus and the music of Johann Sebastian Bach.

Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky

ACMS Conference Proceedings 2007

This paper will begin by introducing the issues that arise from chaos theory for the Christian mathematician and scientist: What is at stake in this debate? It will then briefly review chaos theory, by means of two examples. It will then introduce the metaphysical interpretations given to chaos theory by three different scientist-theologians. The paper will conclude with a brief introduction to open theists, and analyze their use of chaos theory to supper their theological claims.

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.