Association of Christians in the Mathematical Sciences Eighteenth Biennial Conference Proceedings, June 1{4, 2011 Westmont College, Santa Barbara, CA Edited by Russell W. Howell Table of Contents Introduction.......................................... ii Conference Schedule.....................................1 Abstracts of Presentations..................................4 Brian D. Beasley, Where, Oh Waring? The Classic Problem and its Extensions .... 15 Ryan Botts, Lori Carter, Lesson's Learned: A Journey in Computational Science ... 22 Robert L. Brabenec, Thinking Philosophically about Mathematics ............ 29 Jeremy Case, PK Mathematicians ............................. 35 Loredana Ciurdariu, Pascal's Thoughts Seen in the Light of Scripture ......... 53 Eric Gossett, The Search for Hamilton ........................... 66 Nathan Gossett, The Need for a Graphics Programming Course in CS ......... 74 Wayne Iba, Real Simulations and Simulated Reality .................... 81 Stephen Lovett, Bringing Undergraduate Research into the Classroom ......... 90 Nathan Moyer, Connecting Mathematics Students to Philosophy and Faith ....... 95 Judith Palagallo, Calculus Communication Circle ..................... 103 Doug Phillippy, The Study of Mathematics: A Text from a Christian Perspective ... 107 Donna Pierce, Math History Study Abroad Program .................... 120 Michael Rempe, Google and the Mathematics of Web Search ............... 131 Gordon A. Swain, The History of the Area between a Line and a Parabola ....... 138 Mary Walkins, History of Mathematics: An Exercise in Strengths ............ 154 Samuel P. Wilcox, A Bayesian Secondary Analysis in an Asthma Study ........ 158 Josh Wilkerson, What we can Learn from Process Theology ............... 166 Nicholas J. Willis, Two Faith Integration Projects for Freshman Majors ........ 184 Maria Zack, Using Original Historical Mathematics Texts in the Classroom ...... 189 Nicholas C. Zoller, The Mathematics of Cubic Sudoku .................. 199 Participant List........................................ 207 Conference Photos...................................... 210 { i { Introduction Ninety participants, eight spouses, and three children came to Westmont College for the eigh- teenth biennial conference of the Association of Christians in the Mathematical Sciences. They enjoyed superb weather during the conference dates of June 1{4, 2011. Unfortunately, those who chose to spend some extra time in Santa Barbara and stayed through June 5 experienced a rare day of rain. Coincidentally, the last time ACMS convened at Westmont (1993) there was another rare rain event. It might be helpful to California if ACMS could schedule yet another meeting at Westmont when the state is in the midst of its next drought! Among those attending, about ten were at their very first ACMS meeting. All participants enjoyed two presentations given by each of the the three invited speakers: Art Benjamin (Harvey Mudd College), Fred Brooks (University of North Carolina), and Glen Van Brummelen (Quest University). As the conference schedule indicates (page1), there were thirty-three contributed papers in parallel sessions dealing with a variety of topics in mathematics and computer science. Abstracts for the invited addresses and the contributed the papers can be found beginning on page4. Twenty of the contributed papers, which begin on page 15, are part of these Proceedings. There were also two panel discussions relating to the interaction between mathematics and computer science: within institutions, and within ACMS. A final panel session gave an an overview of a recently-completed ACMS book project: Mathematics Through the Eyes of Faith. This project involved eleven ACMS members and was published by HarperOne, San Francisco. Several informal activities complemented the scheduled sessions. On Thursday evening about fifty delegates enjoyed viewing the skies from Westmont's observatory, which houses the largest telescope between Los Angeles and San Francisco. Early on Friday morning twenty-one hikers make a trek up the foothills to Montecito Overlook.A picture of their venture can be found in the conference photos section, which begins on page 210. The traditional conference banquet took place on Friday evening. After Saturday morning parallel sessions dealing with faith integration issues the conference concluded with a worship service. We at Westmont considered it a privilege to host this event. We wish you every blessing in your respective vocations and look forward to seeing many of you again in 2013 at the nineteenth biennial ACMS conference. Bethel University (St. Paul, Minnesota) has agreed to be the host site. In 2015 the conference is planned to convene in Canada for the first time, hosted by Redeemer University College (Ancaster, Ontario). Russell Howell Conference Coordinator { ii { ACMS 18th Biennial Conference Schedule Westmont College, June 1{4, 2011 Wednesday, June 1 5:30 { 6:30 p.m. Dinner 7:00 { 8:30 p.m. Opening Session (Winter Hall, Room 210) Introduction of first-time participants Invited Address: Art Benjamin, Harvey Mudd College Mathemagics! 8:30 { 9:30 p.m. Refreshments Thursday, June 2 7:45 { 8:45 a.m. Breakfast 9:00 { 9:30 a.m. Welcome from Gayle Beebe (President of Westmont); Devotional (Room 210) 9:30 { 10:30 a.m. Invited Address: Art Benjamin, Harvey Mudd College (Room 210) Combinatorial Trigonometry (and a method to DIE for)! 10:30 { 11:00 a.m. Break 11:00 { 12:00 p.m. Invited Address: Fred Brooks, University of North Carolina (Room 210) The Computer Scientist as Toolsmith 12:00 { 1:00 p.m. Lunch (ACMS board meets during this time) 1:30 { 2:30 p.m. Contributed Papers: Assorted Mathematical Topics, I (Room 106) Nicholas Zoller: \The Mathematics of Cubic Sudoku" Brian Beasley: \Waring's Problem and Extensions" Bryant Mathews: \Tropical Mathematics" Contributed Papers: Assorted Computer Science Topics (Room 216) Nathan Gossett: \The Need for Graphics in Computer Science" Gene Rohrbaugh: \The Moral Status of Intelligent Machines" Wayne Iba: \Real Simulations and Simulated Reality" 2:30 { 3:30 p.m. Break 3:30 { 4:30 p.m. Contributed Papers: Faith and the Mathematical Sciences, I (Room 106) Jason Wilson: \Natural Law in the Secular vs. Biblical Mind" Jeremy Case: \Preacher-Kid Mathematicians" Loredana Ciurdariu: \Pascal's Thoughts and the Scriptures" Contributed Papers: Mathematics and Pedagogy, I (Room 216) Kristen Camenga: “Reflections on a Capstone Course" Rebekah Yates: \Linear Algebra as a Discussion Class" Steve Lovett: \Bringing REU into the Classroom" 4:30 { 5:30 p.m. Discussion with Fred Brooks (Room 210) 5:30 { 6:30 p.m. Dinner 7:00 { 8:00 p.m. \Divide and Conquer or Merge and Maximize?" (Panel/Discussion, Room 106) Joint vs. separate Mathematics and Computer Science Programs Phillip Lestmann, Michael Stob, David Stucki, Maria Zack 8:00 { 9:00 p.m. \Computer Science and ACMS" (Discussion, Room 106) Led by Matt DeLong and the ACMS board 9:00 { 10:00 p.m. Observatory Viewing ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 1 Friday, June 3 7:45 { 8:45 a.m. Breakfast 9:00 { 9:30 a.m. Devotional and Announcements (Room 210) 9:30 { 10:30 a.m. Invited Address: Glen Van Brummelen, Quest University (Room 210) Mathematics Across Cultures: How Can Worldview Affect Mathematics? 10:30 { 11:00 a.m. Conference Photo (Winter Hall Lawn) and Break 11:00 { 12:00 p.m. Contributed Papers: Mathematics and Statistics (Room 106) Mike Stob: \R on the Cloud" Sam Wilcock: \A Bayesian Secondary Analysis in an Asthma Study" Talithia Williams: \The Misapplication of Statistics in American Life" Contributed Papers: Computer Science in the Liberal Arts (Room 216) Gene Rohrbaugh: \The Place of Computing in the Liberal Arts" Ryan Botts: \Lessons Learned: A Journey in Computational Science" Lori Carter: \Lessons Learned: A Journey in Computational Science" Open Discussion: \Computer Science in the Liberal Arts" 12:00 { 1:00 p.m. Lunch 1:30 { 2:30 p.m. Invited Address: Glen Van Brummelen, Quest University (Room 210) Trigonometry, Ancient Astronomy, and the Birth of Applied Mathematics 2:30 { 3:30 p.m. Break 3:30 { 4:30 p.m. Contributed Papers: Assorted Mathematical Topics, II (Room 106) Michael Rempe: \The 25 Billion Dollar Linear Algebra Problem" Justin Marks: \Pattern Recognition in Large Data Sets" Jonathan Leech: \Skew Lattices in Algebra and Computer Science" Contributed Papers: Philosophical/Historical Topics, I (Room 216) Gordon Swain: \History of the Area Between a Line and a Parabola" Robert Brabenec: \Thinking Philosophically about Mathematics" Maria Zack: \Using Original Historical Texts in the Classroom" 4:30 { 5:30 p.m. Contributed Papers: Faith and the Mathematical Sciences, II (Room 106) Mark Colgan: \Connecting Calculus with Biblical Ideas" David Stucki: \Teaching Infinity, and Beyond!" Josh Wilkerson: \Faith, Mathematics, and Process Theology" Contributed Papers: Mathematics and Pedagogy, II (Room 216) Mary Walkins: \History of Mathematics: An Exercise in Strengths" Judy Palagallo: \Calculus Communication Circles" Nicholas Willis: \Two Integrative Projects for Freshman Majors" 6:00 { 7:30 p.m. Conference Banquet (Founders' Room in the Dining Commons) ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 2 Saturday, June 4 7:45 { 8:45 a.m. Breakfast 9:00 { 10:00 a.m. Contributed Papers: Book Projects Relating Faith and Mathematics (Room 106) Doug Phillippy: \A Text with a Christian Perspective" Panel: \ACMS Project: Mathematics Through the Eyes of Faith" Jim Bradley,