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ACMS Proceedings Editor Association of Christians in the Mathematical Sciences PROCEEDINGS ACMS May 2020, Volume 22 Introduction (Howell) From Perfect Shuffles to Landau’s Function (Beasley) The Applicability of Mathematics and The Naturalist Die (Cordero-Soto) Marin Mersenne: Minim Monk and Messenger; Monotheism, Mathematics, and Music (Crisman) Developing Mathematicians: The Benefits of Weaving Spiritual and Disciplinary Discipleship (Eggleton) Overcoming Stereotypes through a Liberal Arts Math Course (Hamm) Analyzing the Impact of Active Learning in General Education Mathematics Courses (Harsey et. al.) Lagrange’s Interpolation, Chinese Remainder, and Linear Equations (Jiménez) Factors that Motivate Students to Learn Mathematics (Klanderman et. at.) Teaching Mathematics at an African University–My Experience (Lewis) Faith, Mathematics, and Science: The Priority of Scripture in the Pursuit and Acquisition of Truth (Mallison) Addressing Challenges in Creating Math Presentations (Schweitzer) A Unifying Project for a TEX/CAS Course (Simoson) Is Mathematical Truth Time Dependent? (Stout) Charles Babbage and Mathematical Aspects of the Miraculous (Taylor) Numerical Range of Toeplitz Matrices over Finite Fields (Thompson et. al.) Computer Science: Creating in a Fallen World (Tuck) Thinking Beautifully about Mathematics (Turner) Replacing Remedial Mathematics with Corequisites in General Education Mathematics Courses (Unfried) Models, Values, and Disasters (Veatch) Maximum Elements of Ordered Sets and Anselm’s Ontological Argument (Ward) Closing Banquet Eulogies for David Lay and John Roe (Howell, Rosentrater, Sellers) Appendices: 1-Conference Schedule, 2-Parallel Session Abstracts, 3-Participant Information Indiana Wesleyan University Conference Attendees, May 29 - June 1, 2019 Table of Contents Introduction Russell W. Howell.................................... iv From Perfect Shuffles to Landau’s Function Brian Beasley.......................................1 The Applicability of Mathematics and The Naturalist Die Ricardo J. Cordero-Soto ................................. 14 Marin Mersenne: Minim Monk and Messenger; Monotheism, Mathematics, and Music Karl-Dieter Crisman................................... 24 Developing Mathematicians: The Benefits of Weaving Spiritual and Disciplinary Discipleship Patrick Eggleton..................................... 40 Overcoming Stereotypes through a Liberal Arts Math Course Jessica Hamm....................................... 47 Analyzing the Impact of Active Learning in General Education Mathematics Courses Amanda Harsy, Marie Meyer, Michael Smith, and Brittany Stephenson.... 55 Lagrange’s Interpolation, Chinese Remainder, and Linear Equations Jesús Jiménez....................................... 70 Factors that Motivate Students to Learn Mathematics Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, and Patrick Eggleton........................ 76 Teaching Mathematics at an African University–My Experience Kathleen Lewis...................................... 90 Faith, Mathematics, and Science: The Priority of Scripture in the Pursuit and Acquisition of Truth Bob Mallison........................................ 93 Addressing Challenges in Creating Math Presentations David Schweitzer..................................... 116 A Unifying Project for a TEX/CAS Course Andrew Simoson..................................... 127 – ii – Is Mathematical Truth Time Dependent? Richard Stout....................................... 137 Charles Babbage and Mathematical Aspects of the Miraculous Courtney K. Taylor.................................... 143 Numerical Range of Toeplitz Matrices over Finite Fields Derek Thompson, Maddison Guillaume Baker, and Amish Mishra....... 151 Computer Science: Creating in a Fallen World Russ Tuck......................................... 159 Thinking Beautifully about Mathematics James M. Turner..................................... 172 Replacing Remedial Mathematics with Corequisites in General Education Mathematics Courses Alana Unfried....................................... 189 Models, Values, and Disasters Michael H. Veatch.................................... 203 Maximum Elements of Ordered Sets and Anselm’s Ontological Argument Doug Ward......................................... 214 Closing Banquet Eulogies for David Lay and John Roe ................ 218 Appendix 1: Conference Schedule ............................. 224 Appendix 2: Parallel Session Abstracts .......................... 228 Appendix 3: Participant Information ........................... 261 – iii – Introduction The twenty-second biennial conference of the Association of Christians in the Mathematical Sciences was held at Indiana Wesleyan University from May 29 until June 1, 2019. Thanks go to Melvin Royer and his colleagues at IWU for all their efforts that went into hosting it. Many thanks also to the three invited speakers: • Ken Ono (University of Virginia) – Why does Ramanujan, “The Man Who Knew Infinity,” Matter? – The Jensen-Pólya Program for the Riemann Hypothesis Ken Ono (B.A., University of Chicago; Ph.D., UCLA) is the Thomas Jefferson Professor of Arts and Sciences at the University of Virginia. He has been awarded an NSF CAREER grant, a David and Lucile Packard Fellowship, a Presidential Early Career Award, and a Guggenheim Fellowship. He is currently a Vice President of the American Mathematical Society. He is a renowned expositor with recognition as the MAA George Pólya Distinguished Lecturer, and recent winner of the Prose Award for Best Scholarly Book in Mathematics. His passion for developing and sharing the ideas of Ramanujan is illustrated by his recent role as associate producer of the film The Man Who Knew Infinity. • Joan Richards (Brown University) – From Theology to the Negative Numbers in the World of William Frend – The Foundations of Calculus in the World of Augustus De Morgan Joan Richards (B.A., Radcliffe College; Ph.D., Harvard University) is the Director of the Program of Science and Technology Studies and Professor of History at Brown University. She received a Guggenheim Fellowship, and served as fellow at the Max Planck Institute. Her book Mathematical Visions: Non-Euclidean Geometry in Victorian England focuses on the reception of a geometrical theory in the wider culture of nineteenth century England. Her book Angles of Reflection is at once a memoir and an exploration of the logical work and family life of Augustus De Morgan. Her projects are linked by an abiding interest in the ways that mathematics has served as a model of human thinking. • Michael Alford (FBI, Cyber Division) – Threats and Successes of Cybersecurity Michael Alford has been a Special Agent with the FBI in Indianapolis for over ten years. Special Agent Alford has a Master’s of Science in Digital Forensics from the University of Central Florida, and has over 15 years of experience in computer security and computer forensics. Special Agent Alford routinely investigates complex computer intrusions, including national security intrusions and intrusions into industrial control systems. – iv – Two workshops were offered on May 29. Ryan Botts, Judith Canner, and Alana Unfried organized a seminar on using R Studio, and in a parallel session Greg Crow, Lori Carter, Catherine Crockett, Matt DeLong, Derek Schurrman, and Amanda Harsy Ramsey discussed early career issues for new faculty and graduate students. Many thanks to them, not only for organizing the sessions, but also for the helpful information they provided. The conference schedule is presented in Appendix 1, Appendix 2 gives the abstracts for the parallel sessions, and Appendix 3 lists information for the individual participants. There were a total of 79 papers presented by the 138 conference attendees. Not every paper was submitted to these Proceedings, but the following pages contain the ones that made their way through the single-blind review process, each having been scrutinized by a minimum of two reviewers. Thanks go to the authors for their good work. Too numerous to mention are all the referees that were involved, but heartfelt thanks go to them for their diligence. The twenty-third biennial conference for ACMS, set to be hosted by Azusa Pacific University, is slated for June 23–26, 2021. Plans are to hold it in conjunction with the Christian Engineering Society. Details can be found at acmsonline.org, which is the official ACMS website. Russell W. Howell (Westmont College) ACMS Proceedings Editor – v – From Perfect Shuffles to Landau’s Function Brian D. Beasley (Presbyterian College) Brian Beasley (Ph.D., University of South Carolina) has taught at Presbyterian College since 1988. His professional interests range from number theory and history of mathematics to problems sections in various journals. Recently he has helped recruit mentors for ECM and Project NExT fellows on behalf of the MAA Southeastern Sec- tion. Brian and his wife Kathy are now in the empty nest stage, thankful that both sons are gainfully employed college graduates. Abstract If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This paper will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will
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