Mathematics Commons^™

Life Lessons From Leibniz, Andrew J. Simoson

ACMS Conference Proceedings 2013

The tri-centennial of Leibniz’s death is nigh (2016). And 2013 is not too early to begin a special celebration of this man of mathematics. Besides being the co-discoverer of calculus and the implementer of binary numbers, formal logic, and formal languages, all of which foreshadowed the computer age, Leibniz is said to be one of the last to know almost everything that was known about almost anything. Professionally, his occupation was librarian in the princely court of Hanover in oldGermany. Serving under three different princes, the last of whom became George I of England, Leibniz had to continual lyre-invent himself—somewhat …

Al-Khwārizmī: Founder Of Classical Algebra, Calvin Jongsma

ACMS Conference Proceedings 2013

Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior toal-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess thehistorical importance of al-Khwarizmi’s contributions for developments in European algebra.

Expanding Jonathan Edwards’ Typology Program: The Bell Curve As A Type Of Christ, Jason Wilson

ACMS Conference Proceedings 2013

Over two hundred years after his death, an unfinished notebook of Jonathan Edwards’ was published for the first time in1993. Edwards was a father of the Evangelical movement, but because his work on typology was not published until recently, it has received almost no attention. In his notebook, Edwards makes an explicit argument for extending biblical typology to nature in a biblically grounded manner. This study is an attempt to extend that research program into mathematics/statistics.We will consider the following proposition, “The normal distribution (the graph of which is the bell curve) is a biblical type of Christ.” The basic …

Delaware, Dickeson, Assessment And How You Can Help, Greg Crow, Maria Zack

ACMS Conference Proceedings 2013

How much release time should a chair receive? What is the cost per unit for a particular academic program? What is a student credit hour (SCH) anyway and why would anyone care? Why are so many boards enamored of Delaware, Dickeson and Assessment? The answer to these and many related questions will be presented in this talk. Analytics and various“efficiency measures” are becoming increasingly important in higher education and mathematicians and computer scientists are being regularly recruited to help university administrators make meaning from large volumes of data. Come and learn about this trend and how you can be of …

Explore Global Opportunities For Mathematics Scholarship, Teaching, And Service, Ron Benbow

ACMS Conference Proceedings 2013

There are numerous overseas opportunities in which to apply your knowledge and interest in mathematics. These international experiences allow you to expand your scholarship, to extend your teaching skills, to offer professional services to K-12 teachers or other university instructors, and to provide much personal enrichment as well. Examples from recent professional experiences in Liberia, Haiti, Guatemala, and Ecuador will be shared to illustrate the connections to teaching, scholarship, and service. Information regarding MAA Study Tours, Fulbright Specialist grants, and other relevant organizations will be provided.

Euler And The Ongoing Search For Odd Perfect Numbers, Brian D. Beasley

ACMS Conference Proceedings 2013

Leonhard Euler, after proving that every even perfect number has the form given by Euclid, turned his attention to finding odd perfect numbers. Euler established a basic factorization pattern that every odd perfect number must have, and mathematicians have expanded upon this Eulerian form ever since. This paper will present a brief summary of Euler’s result and some recent generalizations. It will also note connections between odd perfect numbers and the abundancy index (the abundancy index of a positive integer is the ratio of the sum of its positive divisors to itself). In particular, finding a positive integer with an …

Computing Foundations For The Scientist, Catherine Bareiss, Larry Vail

ACMS Conference Proceedings 2013

There is a need for a new style of supporting a computer course. Although it is widely recognized that computer technology provides essential tools for all current scientific work, few university curricula adequately ground science majors in the fundamentals that underlie this technology. Introducing science students to computational thinking in the areas of algorithms and data structures, data representation and accuracy, abstraction, performance issues, and database concepts can enable future scientists to become intelligent, creative and effective users of this technology. The intent of this course is not to turn scientists into computer scientists, but rather to enhance their ability …

A Different Approach, Catherine Crockett

ACMS Conference Proceedings 2013

This paper discusses an approach used to encourage science majors to rethink their attitudes and study habits in a first semester calculus course. Two activities were used to enhance study habits. They are outlining concepts and in-class quizzes designed for self-evaluation of skills. After using both methods in two sections of the calculus course, the students were surveyed to determine if these activities were successful. A majority of the students felt the activities were helpful and wanted to continue them.

Reading Assignments And Assessments: Are Your Students Reading Math Texts Before Class, After Class, Both, Or Neither?, David Klanderman, Mandi Maxwell, Sharon Robbert, Bill Boerman-Cornell

ACMS Conference Proceedings 2013

In his recent book What the Best College Students Do [Bain, 2012], Ken Bain defines a number of different types of students including “surface learners,” “strategic learners,” “routine experts,” and finally, “deep learners.” In our mathematics courses at Trinity, we have found examples of all of these student types. A major determinant of their preferred approach to learning appears to be the ways and degrees to which mathematical texts and other written materials are read prior to class sessions. Each full-time member of the department both assigns and assesses the reading of mathematical materials prior to class sessions. Assessment methods, …

Philosophy Of “Spinning Wheels”, Loredana Ciurariu

ACMS Conference Proceedings 2013

In this material I will speak about some well-known mechanisms studied by students and engineers emphasizing the impact which “spinning wheels” had and have in development of the society, on Christians and the church. Also the discovery of the machineries determines major changes in the people’s outlook and leads to new trends in philosophy and Christianity. Then, I will give some examples from the Bible where “spinning wheels” it seems to appear: Judges 16:21, Ezekiel 1 and Revelation. It is also interesting to see 2 Kings 2:9-12, 2 Kings 6:13-18 and maybe Daniel 7:9.

In addition, an avi file where …

An Investigation Of Hi Ho! Cherry-O Using Markov Chains, Nicholas C. Zoller

ACMS Conference Proceedings 2013

In the children’s board game Hi Ho! Cherry-O, players attempt to move 10 cherries from their trees to a bucket in the center of the game board. A spinner determines whether a turn includes moving cherries from tree to bucket or bucket to tree. The winner of the game is the first player to move all of her cherries from her tree to the bucket. We model the gameplay using a Markov chain and calculate the expected number of turns needed to complete one game. Then we investigate what happens when the rules are changed. We discover that rules …

The Structures Of The Actual World, Walter J. Schultz, Lisanne D’ Andrea Winslow

ACMS Conference Proceedings 2013

Scripture teaches that God has a plan for the universe. In this paper we argue that in order for it to function as a plan, it must have a temporal structure, a representational structure, and a proto-causal structure. This paper presents a formal model of the these three structures. As it turns out, the structures of God’s plan are best understood as the structures of a musical composition. We, then very briefly describe its implications. The first is that this model (based ultimately in the doctrine of God) grounds a metaphysics of science. Second, it grounds a structuralist philosophy of …

Perspectives On Chaos: Reflections Of A Mathematical Physicist, Kyle Spyksma

ACMS Conference Proceedings 2013

Chaos Theory, the mathematical media darling of the ’90s, has become less of a societal fad and research interest over the past couple of decades. However, from a mathematical physicists’ perspective, issues surrounding Chaos Theory can be valuable aides in forming views on how mathematics, science and reality relate. In this talk, I will briefly explore how Chaos Theory can shape views of these relationships, with a focus on the language we use and (perhaps unintentionally) abuse when doing science and mathematics.

Galileo's Muse: Renaissance Mathematics And The Arts (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Galileo's Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Cambridge, MA: Harvard University Press, 2011, 336 pages. ISBN 9780674059726.

Introduction (2013), Eric Gossett

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Schedule (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

Al-Khwarizmi: Founder Of Classical Algebra, Calvin Jongsma

Faculty Work Comprehensive List

Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior to al-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess the historical importance of al-Khwarizmi’s contributions for developments in European algebra.

19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Association of Christians in the Mathematical Sciences 19th Biennial Conference Proceedings, May 29 - June 1, 2011, Bethel University.

Coble And Eisenhart: Two Gettysburgians Who Led Mathematics, Darren B. Glass

Math Faculty Publications

In 1895, there were 134 students at Gettysburg College, which was then called Pennsylvania College. Of these students, two of them went on to become president of the American Mathematical Society. In this article, we look at the lives of these two men, Arthur Coble and Luther Eisenhart, and their contributions to mathematics and higher education, as well as look at what mathematics was like at Gettysburg at the end of the nineteenth century.

Volume 05, Ian Karamarkovich, Jessica Cox, Kyle Fowlkes, Allison Pawlowski, Kaitlin Major, Carrie Dunham, Kelsey Scheitlin, Kathryn Grayson, Ashley Johnson, Jennifer Nehrt, Kelsey Stolzenbach, Kristin Mcquarrie, Sara Nelson, Melisa Michelle, Jessica Sudlow, Perry Bason, Danielle Dmuchawski, Mariah Asbell, Matthew Sakach, Timothy Smith Jr., Annaliese Troxell, T. Dane Summerell, Sarah Ganrude, Malina Rutherford, Hannah Hopper, John Berry Jr., James Early, Colleen Festa, Chelsea D. Taylor, Michelle Maddox, Kaitlyn Smith, Sarah Schu, Cabell Edmunds, Katherine Grayson, Kayla Tornai

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

The Tallis House as an Extension of Emily Tallis in McEwan's Atonement by Ian Karamarkovich

Graphic Design by Jessica Cox

Graphic Design by Kyle Fowlkes

Graphic Design by Allison Pawlowski

Incorporating Original Research in The Classroom: A Case Study Analyzing the Influence of the Chesapeake Bay on Local Temperatures by Kaitlin Major, Carrie Dunham and Dr. Kelsey Scheitlin

Graphic Design by Kathryn Grayson

Graphic Design by Ashley Johnson

Facing the Music: Environmental Impact Assessment of Building A Concert Hall on North Campus by Jennifer Nehrt, Kelsey Stolzenbach And Dr. Kelsey Scheitlin

Art by Kristin …

Propeller, Joel Kahn

The Transdisciplinary STEAM+ Journal

This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.

How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons

Journal of Humanistic Mathematics

A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.

Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz

Journal of Humanistic Mathematics

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …

Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 806. Ciphering book, 1822-1827 (40 p.), of James M. Brown, Butler County, Kentucky, which also contains a few pages of account entries and other various notations, (806a). Photocopy of ciphering book is also included. Also letter, 1989, from donor relating family data.

The Brave New World Of Open Access & Creative Commons: A Humanistic Experiment In Mathematical Publishing, Gizem Karaali

Pomona Faculty Publications and Research

In January 2011 the Journal of Humanistic Mathematics (JHM) published its first issue. JHM (http://scholarship.claremont.edu/jhm) is an online-only, peer-reviewed, open-access journal which has passed the all important ten-thousand-download barrier in its first anniversary. In order to remain faithful to the fundamental principles of open access, JHM uses Creative Commons licensing, where authors retain copyright of their work, but others are free to reuse them (with proper attribution). In this note I share and reflect upon our experience with open access and Creative Commons.

Methods In Visual Mathematics: Reductionism In Researching Mathematical Principles In Art, Lauren N. Colie

AUCTUS: The Journal of Undergraduate Research and Creative Scholarship

People traditionally rely on visual arts as an effective communication tool and medium of self-expression for when words fail to convey abstract concepts. Thera Mjaaland, anthropologist and professional photographer, writes, “Art is capable of negotiating conceptual gaps caused by a dichotomized epistemology” (393). In essence, Mjaaland asserts that art helps relate different modes of thinking by illustrating the abstract and difficult to grasp—privileging the communicative value of an image over that of text. Within this method of communication is a collection of works acknowledged by public consensus to be of an elevated status or value. The art world is deeply …

Hannum Family (Sc 746), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 746. Ciphering book containing problems using the British pound system, which also contains accounts of John Hannum, Jr., and Richard Hannum, and writings of Penelope Hannum, Logan County, Kentucky. Also clippings, chiefly from newspapers of Russellville, Kentucky, 1820-1860.

Research On National Culture Effects On Human Failures In Container Shipping, Kai Jiang

World Maritime University Dissertations

No abstract provided.