Abstracts of Papers Presented at MathFest 2018 Denver, CO August 1 – 4, 2018 Published and Distributed by The Mathematical Association of America Contents Invited Addresses 1 Earle Raymond Hedrick Lecture Series by Gigliola Staffilani . 1 Nonlinear Dispersive Equations and the Beautiful Mathematics That Comes with Them Lecture 1: Thursday, August 2, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 2: Friday, August 3, 10:30–11:20 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 3: Saturday, August 4, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 AMS-MAA Joint Invited Address . 1 Gravity’s Action on Light: A Mathematical Journey by Arlie Petters Thursday, August 2, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 MAA Invited Address . 1 Inclusion-exclusion in Mathematics: Who Stays in, Who Falls out, Why It Happens, and What We Should Do About It by Eugenia Cheng Friday, August 3, 11:30–12:20 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Snow Business: Scientific Computing in the Movies and Beyond by Joseph Teran Saturday, August 4, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 1 Mathematical Medicine: Modeling Disease and Treatment by Lisette de Pillis Thursday, August 2, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 2 MAA James R.C. Leitzel Lecture . 2 The Relationship between Culture and the Learning of Mathematics by Talitha Washington Saturday, August 4, 9:00–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building . 2 AWM-MAA Etta Z. Falconer Lecture . 2 Finding Ellipses by Pamela Gorkin Friday, August 3, 9:30–10:20 AM, Plaza Ballroom A, B, & C, Plaza Building . 2 MAA Chan Stanek Lecture for Students . 2 FAIL: A Mathematician’s Apology by Laura Taalman Thursday, August 2, 1:30–2:20 PM, Plaza Ballroom A, B, & C, Plaza Building . 2 Pi Mu Epsilon J. Sutherland Frame Lecture . 3 The Singular Uniformity of Large Random Systems by Peter Winkler Wednesday, August 1, 8:00–8:50 PM, Plaza Ballroom A, B, & C, Plaza Building . 3 NAM David Harold Blackwell Lecture . 3 Continuous, Discrete, or Somewhere in Between: An Introduction to Time Scales with Applications by Raegan Higgins Friday, August 3, 1:30–2:20 PM, Plaza Ballroom A, B, & C, Plaza Building . 3 Alder Awards 4 Alder Awards Friday, August 3, 2:30–3:50 PM, Plaza Ballroom, A, B, & C, Plaza Building . 4 Creativity Amidst Adversity by Mohamed Omar Friday, August 3, 2:30–2:50 PM, Plaza Ballroom, A, B, & C, Plaza Building . 4 Way to Fail! by David Clark Friday, August 3, 3:00–3:20 PM, Plaza Ballroom, A, B, & C, Plaza Building . 4 Mathematics by Design by Chad Awtrey Friday, August 3, 3:30–3:50 PM, Plaza Ballroom, A, B, & C, Plaza Building . 4 iii iv Contents Invited Paper Sessions 5 The MAA Instructional Practices Guide in Action Thursday, August 2, 3:00–5:30 PM, Plaza Ballroom E, Plaza Building . 5 Bridging Network Science and Graph Theory Thursday, August 2, 1:30–4:20 PM, Grand Ballroom II, Tower Building . 6 Geometric Ideas and Where to Find Them Friday, August 3, 1:30–4:20 PM, Plaza Ballroom D, Plaza Building . 7 Modeling Biological Rhythms Friday, August 3, 1:30–4:50 PM, Plaza Ballroom E, Plaza Building . 8 Strategies to Synergize Culture in the Learning and Doing of Mathematics Saturday, August 4, 1:30–3:20 PM, Plaza Ballroom E, Plaza Building . 10 Category Theory for All Saturday, August 4, 1:30–4:20 PM, Plaza Ballroom D, Plaza Building . 11 Contributed Paper Sessions 13 A Number is Never an Answer: Developing Mathematical Thinking and Communication Through Writing Part A: Thursday, August 2, 1:30–5:45 PM, Governor’s Square 10, Plaza Building . 13 Part B: Friday, August 3, 9:00 AM - 12:15 AM–12:15 PM, Governor’s Square 10, Plaza Building . 15 Advancing Women in Mathematics: On the Ground Initiatives Thursday, August 2, 1:30–5:25 PM, Governor’s Square 14, Plaza Building . 17 Best Practices and Innovation in the Teaching of Discrete Mathematics Friday, August 3, 1:30–4:45 PM, Governor’s Square 10, Plaza Building . 20 Encouraging Effective Teaching Innovation Part A: Thursday, August 2, 9:00–11:55 AM, Governor’s Square 12, Plaza Building . 22 Part B: Thursday, August 2, 1:30–6:05 PM, Governor’s Square 12, Plaza Building . 24 Fostering Undergraduate Interdisciplinarity Friday, August 3, 1:30–6:25 PM, Governor’s Square 15, Plaza Building . 27 Great Circles, Great Problems Thursday, August 2, 1:30–5:25 PM, Governor’s Square 15, Plaza Building . 30 Inquiry-Based Learning and Teaching Part A: Friday, August 3, 9:30 AM–12:25 PM, Governor’s Square 14, Plaza Building . 32 Part B: Friday, August 3, 1:30–5:45 PM, Governor’s Square 14, Plaza Building . 34 Part C: Saturday, August 4, 9:00 AM–12:15 PM, Governor’s Square 14, Plaza Building . 36 Mastery Grading Part A: Thursday, August 2, 1:30–4:05 PM, Governor’s Square 11, Plaza Building . 38 Part B: Friday, August 3, 1:30–5:05 PM, Governor’s Square 11, Plaza Building . 40 Part C: Saturday, August 4, 1:30–3:05 PM, Governor’s Square 11, Plaza Building . 42 Mathematical Themes in a First-Year Seminar Thursday, August 2, 1:30–5:05 PM, Governor’s Square 16, Plaza Building . 43 Mathematics and the Life Sciences: Initiatives, Programs, Curricula Saturday, August 4, 1:30–3:25 PM, Governor’s Square 17, Plaza Building . 46 Mathematics Research Experiences for K–12 Teachers and Students Thursday, August 2, 1:30–3:45 PM, Governor’s Square 17, Plaza Building . 47 Modeling-Based Teaching and Learning in Differential Equations Courses Saturday, August 4, 1:00–4:55 PM, Governor’s Square 15, Plaza Building . 49 Priming the Calculus Pump: Fresh Approaches to Teaching First-Year Calculus Part A: Friday, August 3, 9:30 AM–12:25 PM, Governor’s Square 16, Plaza Building . 51 Part B: Friday, August 3, 1:30–5:25 PM, Governor’s Square 16, Plaza Building . 54 Part C: Saturday, August 4, 9:00–11:35 AM, Governor’s Square 16, Plaza Building . 56 Ready or Not: Corequisite Courses and Just-in-Time Review Friday, August 3, 1:30–5:05 PM, Governor’s Square 17, Plaza Building . 58 Recreational Mathematics: Puzzles, Card Tricks, Games, Gambling and Sports Part A: Friday, August 3, 10:30 AM–12:25 PM, Grand Ballroom II, Tower Building . 60 Part B: Friday, August 3, 1:30–5:15 PM, Grand Ballroom II, Tower Building . 61 Part C: Saturday, August 4, 9:00–11:35 AM, Grand Ballroom II, Tower Building . 63 Contents v Research in Undergraduate Mathematics Education (RUME) Thursday, August 2, 1:30–4:45 PM, Plaza Ballroom D, Plaza Building . 65 Teaching Undergraduate Mathematics with Primary Historical Sources Part A: Friday, August 3, 1:30–4:45 PM, Governor’s Square 12, Plaza Building . 67 Part B: Saturday, August 4, 1:30–5:30 PM, Governor’s Square 12, Plaza Building . 69 The Capstone Experience for Mathematics Majors Saturday, August 4, 1:30–3:45 PM, Governor’s Square 10, Plaza Building . 70 General Contributed Poster Sessions 73 General Contributed Poster Session I Thursday, August 2, 1:30–3:00 PM, Plaza Exhibit Hall . 73 General Contributed Poster Session II Thursday, August 2, 3:30–5:00 PM, Plaza Exhibit Hall . 79 General Contributed Poster Session III Friday, August 3, 1:00–2:30 PM, Plaza Exhibit Hall . 85 Graduate Student Session 93 Great Talks for a General Audience Saturday, August 4, 1:00–5:00 PM, Governer’s Square 9, 10, 14 . 93 PosterFest 2018 97 PosterFest Friday, August 3, 3:00–4:30 PM, Plaza Exhibit Hall . 97 Index of Speakers 101 Invited Addresses 1 Invited Addresses Earle Raymond Hedrick Lecture Series Gigliola Staffilani Massachusetts Institute of Technology Nonlinear Dispersive Equations and the Beautiful Mathematics That Comes with Them s Lecture 1: Thursday, August 2, 11:00–11:50 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 2: Friday, August 3, 10:30–11:20 AM, Plaza Ballroom A, B, & C, Plaza Building Lecture 3: Saturday, August 4, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building In these lectures I will give an overview of the rich mathematical structures that characterize the wave solutions of some of the most important nonlinear partial differential equations, such as the Schrodinger¨ equation. In doing so I will illustrate how beautiful pieces of mathematics, developed using different tools, not just coming from analysis, have been generated over the years in order to answer some of the most fundamental questions for these equations, such as existence and uniqueness of solutions for example. Along the way I will formulate open questions and possible new directions of investigation. AMS-MAA Joint Invited Address Thursday, August 2, 10:00–10:50 AM, Plaza Ballroom A, B, & C, Plaza Building Arlie Petters Duke University Gravity’s Action on Light: A Mathematical Journey The gravitational fields of stars, black holes, and galaxies act on light propagating near them, casting magnification patterns in space. Such optical phenomena have wide-ranging physical applications, including detecting extrasolar planets and testing for a fifth dimension of the universe. Assuming no background in astrophysics or cosmology, this talk will take you on a mathematical journey unveiling the intriguing properties of these beautiful magnification patterns. MAA Invited Address Friday, August 3, 11:30–9:50 AM, Plaza Ballroom A, B, & C, Plaza Building Eugenia Cheng School of the Art Institute of Chicago Inclusion-exclusion in Mathematics: Who Stays in, Who Falls out, Why It Happens, and What We Should Do About It The question of why women are under-represented in mathematics is complex and there are no simple answers, only many contributing factors.