Mathematics Commons^™

A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker

ACMS Conference Proceedings 2009

As professors, we all want our students to succeed, and to be motivated to study. We all get questions from students that can be boiled down to, "What can I do with X degree?" Certainly, a quick answer is to point students to career websites, or to send them to the career services department on campus. However, we want to do better than that. We want students to learn how to investigate these future directions, and to have them think about their future more holistically--not just an effort to find a job. To that end, we have developed a course …

History Of Mathematics In The Service Of School Mathematics Education, Calvin Jongsma

ACMS Conference Proceedings 2009

This slide presentation outlines the author's use of history of mathematics in teaching a mathematics-content course to prospective middle school mathematics teachers. A pedagogical rationale for using history of mathematics is given, along with a case study illustrating its use for teaching the topic of ratio and proportion drawing upon the numerical and geometrical theories of such found in Euclid's Elements.

Galileo's Solution To Dante's Riddle, Andrew Simoson

ACMS Conference Proceedings 2009

In Dante’s Inferno, several riddles are posed regarding the relative sizes of ordinary men versus giants versus Lucifer—all of which Galileo solves in his first public lecture—which we review herein.

Sage: Math In Your Dorm Room, From Calculus To Research, Karl-Dieter Crisman

ACMS Conference Proceedings 2009

As computers have revolutionized math research in disciplines as disparate as number theory and bioinformatics, it is natural for us to introduce our students to technology in ways beyond mere homework-checking. However, most familiar programs are either not comprehensive enough to encompass all the math in our curriculum, or are very expensive and accessible only in a lab or with a student license. The open source software package Sage addresses all of these issues.

Sage is suitable for discovery and computation in introductory courses such as calculus or linear algebra, while also being ideal for use in upper-level courses or …

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

Elementary-Level Mathematics Content In Comic Book Format, Bruce Kessler, Janet Tassell, Mary Evans, Cathy Willoughby, Melissa Zimmer

Mathematics Faculty Publications

No abstract provided.

Extending The Support Theorem To Infinite Dimensions, Jeremy J. Becnel

Faculty Publications

The Radon transform is one of the most useful and applicable tools in functional analysis. First constructed by John Radon in 1917 [9] it has now been adapted to several settings. One of the principle theorems involving the Radon transform is the Support Theorem. In this paper, we discuss how the Radon transform can be constructed in the white noise setting. We also develop a Support Theorem in this setting.

Migration And Mixing Between Populations In Disease Models, David Burger

Theses, Dissertations and Culminating Projects

The goal of this thesis is to model the spread of disease between populations and find ways to prevent its continued epidemic. This thesis studies disease spread as a function of migration in epidemiological models. The models are constructed using the compartmental approach, and we compare discrete and continuous time approximations. In the discrete model, we will look at ways that induced migration can cause an epidemic case to turn into a dieout case. It will be shown that migration can only effect the size of an outbreak, but cannot create or destroy one. For the continuous cases, we will …

Metric Regularity And Lipschitzian Stability Of Parametric Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns the study of variational systems described by parameterized generalized equations/variational conditions important for many aspects of nonlinear analysis, optimization, and their applications. Focusing on the fundamental properties of metric regularity and Lipschitzian stability, we establish various qualitative and quantitative relationships between these properties for multivalued parts/fields of parametric generalized equations and the corresponding solution maps for them in the framework of arbitrary Banach spaces of decision and parameter variables.

Ethnomathematics In The Dominican Republic: A Mathematics Education Approach To Knowledge And Emancipation, Sofia Pablo-Hoshino

Renée Crown University Honors Thesis Projects - All

This focus of this project was to look at the extent to which ethnomathematics is being used in the mathematics curriculum in theDominican Republic. Broadly described, ethnomathematics emphasizes that the culture, history, and experiences of the students are significant and therefore should be infused into the mathematics curriculum.

I read articles and books as well as traveled to theDominican Republicto conduct qualitative research. I interviewed 32 professionals consisting of mathematics teachers, mathematics professors, and mathematics education professors from theSantiagoandSanto Domingoareas. I then volunteered at the Dominican Republic Education and Mentoring (DREAM) Project where I was able to observe and participate …

Using Maxwells Z Model To Determine Lunar Mare Lava Thickness, Autumn Wille

Honors Capstones

Capstone submitted as a graduate requirement for the BSU Honors Program.

Weak Sharp Minima On Riemannian Manifolds, Chong Li, Boris S. Mordukhovich, Jinhua Wang, Jen-Chih Yao

Mathematics Research Reports

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and obtain their complete characterizations in the case of convex problems on finite-dimensional Riemannian manifolds and their Hadamard counterparts. A number of the results obtained in this paper are also new for the case of conventional problems in linear spaces. Our methods involve appropriate tools of variational analysis and generalized differentiation on Riemannian …

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.