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MAA Mathfest 2013 Abstracts of Papers.Pdf Jul 31-Aug 3, 2013 Abstracts o f Papers Hartford, CT Abstracts of Papers Presented at MathFest 2013 Hartford, Connecticut July 31–August 3, 2013 Published and Distributed by The Mathematical Association of America Contents Invited Paper Sessions 1 Open and Accessible Problems in Knot Theory Thursday, August 1, 1:00–5:00 PM,MarriottBallroomA ............................. 1 Developments in Commutative Algebra Thursday, August 1, 2:00–4:50 PM,MarriottBallroomB ............................. 2 Complex Geometry Research and Accessible Problems Friday, August 2, 2:00–4:50 PM,MarriottBallroomA............................... 3 AMS-MAA Special Session: Coding Theory and ... Friday, August 2, 2:00–4:50 PM,MarriottBallroomB............................... 4 Recent Developments in Mathematical Finance Saturday, August 3, 1:00–4:45 PM,MarriottBallroomB ............................. 5 Climate and Geophysical Modeling Saturday, August 3, 2:00–3:50 PM,MarriottBallroomA ............................. 6 Contributed Paper Sessions 7 Best Practices for Teaching Online Courses Thursday, August 1, 1:00–4:55 PM ......................................... 7 History and Philosophy of Mathematics: Euler’s Mathematics Thursday, August 1, 9:00–10:30 AM,Room27 .................................. 9 History and Philosophy of Mathematics: Seventeenth and Eighteenth Centuries Thursday, August 1, 1:00–5:30 PM,Room27 ................................... 10 History and Philosophy of Mathematics: Nineteenth Century Friday, August 2, 8:30–10:00 PM,Room26 .................................... 11 History and Philosophy of Mathematics: Twentieth Century, Part 1 Friday, August 2, 8:30–11:30 AM and 2:30–3:00 PM,Room27 .......................... 12 History and Philosophy of Mathematics: Twentieth Century, Part 2 Friday, August 2, 2:30–4:00 PM,Room26..................................... 13 History and Philosophy of Mathematics: Using History and Philosophy in Teaching Mathematics Friday, August 2, 3:00–5:30 PM,Room27..................................... 14 History and Philosophy of Mathematics: The Arc of Time Saturday, August 3, 8:30–10:30 AM,Room27................................... 15 Interactions Between History and Philosophy of Mathematics Part 1: Saturday, August 3, 10:30–11:30 AM, Room 27 Part 2: Saturday, August 3, 2:30–5:00 PM,Room27................................ 16 My Favorite Geometry Proof Friday, August 2, 1:00–4:55 PM,Room14..................................... 17 Inquiry-Based Learning Best Practices Part 1: Friday, August 2, 3:20–5:15 PM,Room16 ................................. 20 Part 2: Saturday, August 3, 8:30–11:25 AM,Room16............................... 21 Part 3: Saturday, August 3, 1:00–4:55 PM,Room16................................ 22 Undergraduate Research Activities in Mathematical and Computational Biology Thursday, August 1, 1:00–3:55 PM,Room15 ................................... 25 Research in Mathematics for High School and Community College Students Friday, August 2, 1:00–2:55 PM,Room16..................................... 27 iii iv Contents The Mathematics of Planet Earth in Research Friday, August 2, 1:00–2:15 PM,Room15..................................... 28 The Mathematics of Planet Earth in the College Mathematics Curriculum Friday, August 2, 3:05–3:55 PM,Room15..................................... 29 Recreational Mathematics: New Problems and New Solutions Part 1: Thursday, August 1, 1:00–4:15 PM,Room10 ............................... 29 Part 2: Friday, August 2, 8:30–10:45 AM,Room16 ................................ 31 Curriculum Development to support first year mathematics students Part 1: Saturday, August 3, 8:30–11:25 AM,Room14............................... 32 Part 2: Saturday, August 3, 1:00–4:55 PM,Room14................................ 34 Math Circles: Best Practices Thursday, August 1, 1:00–4:15 PM,Room17 ................................... 36 General Contributed Paper Sessions 38 GCPS Session 1: History and Philosophy of Mathematics Thursday, August 1, 8:30–10:10 PM,Room14................................... 38 GCPS Session 2: Research in Graph Theory or Combinatorics Thursday, August 1, 8:30–10:10 AM,Room15 .................................. 39 GCPS Session 3: Probability or Statistics Thursday, August 1, 8:30–9:40 AM,Room16 ................................... 40 GCPS Session 4: Teaching Advanced Mathematics Part 1: Thursday, August 1, 8:30–10;10 AM,Room26............................... 41 GCPS Session 5: Research in Linear Algebra or Geometry Thursday, August 1, 1:00–4:25 PM,Room26 ................................... 42 GCPS Session 6: Assessment, Mentoring, or Outreach Friday, August 2, 8:30–11:25 AM,Room14.................................... 45 GCPS Session 7: Teaching Calculus Part 1: Friday, August 2, 8:30–10:25 AM,Room15 ................................ 47 GCPS Session 8: Other/Research in Applied Mathematics Friday, August 2, 8:30–11:30 AM,Room17.................................... 49 GCPS Session 9: Teaching Introductory Mathematics Part 1: Friday, August 2, 1:00–3:55 PM,Room17 ................................. 51 GCPS Session 10: Research in Algebra or Topology Saturday, August 3, 8:30–9:55 AM,Room15 ................................... 53 GCPS Session 11: Teaching Calculus Part 2: Saturday, August 3, 8:30–10:40 AM,Room21............................... 54 GCPS Session 12: Teaching Introductory Mathematics Part 2: Saturday, August 3, 8:30–10:25 AM,Room22............................... 55 GCPS Session 13: Modeling/Applications Saturday, August 3, 8:30–10:45 AM,Room26................................... 57 GCPS Session 14: Teaching Advanced Mathematics Part 2: Saturday, August 3, 1:00–4:10 PM,Room21................................ 59 GCPS Session 15: Research in Number Theory Saturday, August 3, 1:00–2:25 PM,Room22.................................... 61 GCPS Session 16: Mathematics and Technology/ Research in Analysis Saturday, August 3, 1:00–3:25 PM,Room26.................................... 62 Graduate Student Session 64 Great Talks for a General Audience: Coached Presentations by Graduate Students Saturday, August 3, 1:00–5:30 PM,ConnecticutConventionCenter,Room11 . .. 64 PosterFest 2013 Saturday, August 2, 3:30–5:00 PM,ConnecticutConventionCenter,Pre-functionarea 66 Index of Speakers 70 Invited Paper Sessions Open and Accessible Problems in Knot Theory Thursday, August 1, 1:00–5:00 PM, Marriott Ballroom A Colin Adams Williams College ([email protected]) Turning Knots into Flowers A triple crossing is a crossing in a projection of a knot that has three strands of the knot passing straight through it. We will show that every knot K has a triple crossing projection and then investigate c3.K/, which is the minimum number of triple crossings in a projection of K. In joint work with students, we also considerextensions to cn.K/.In particular we show that for any knot, there exists an n such that cn.K/ 1. That is to say,every knot has a projection with only a single multi-crossing, and in fact that projection looks just like a daisy. This opensD up a variety of directions for further research. Lew Ludwig Denison Universtiy ([email protected]) Knot Mosaics In 2008, Lomonaco and Kauffman introduced knot mosaics, which have been shown to be equivalentto tame knot theory. This topic is easily accessibleto undergraduate students as it is very hands-on.We explore severalareas of this new approachto knottheory including the mosaic number (the smallest integer n required to fit a given knot on an n n mosaic board). We also consider the mosaic number for different families of knots. Several open questions will be posed. This presentation is for a general mathematical audience. Sandy Ganzell St. Mary’s College of Maryland ([email protected]) The Forbidden Number of a Knot Virtual knot theory has a useful diagramatic approach: two diagrams represent the same knot if and only if they differ by a sequence of extended Reidemeister moves. But some moves are forbidden. So, like many forbidden things, we should do them, and find out what the consequences are. It turns out they’re pretty interesting. Elizabeth Denne Washington & Lee University ([email protected]) Folded Ribbon Knots in the Plane Knots and links are modeled as folded ribbons lying flat in the plane. The ribbonlength of a knot is the length of a polygonal knot divided by the width of the ribbon around it. In this talk we’ll give examples of folded ribbon knots and their ribbonlength. We’ll also discuss the topology of folded ribbons and the problem of minimizing ribbonlength for a given knot type. There are a number of open questions related to this problem. Joel Foisy SUNY Potsdam ([email protected]) Graphs that are Intrinsically Linked with an Unused Vertex We say that a graph is intrinsically linked with an unused vertex provided it contains, in every spatial embedding, a pair of non-split linked cycles, as well as a vertex that is not part of the non-split link. In this talk, we will discuss three operations that can be used to obtain graphs with this property, as well as several open questions about graphs with this property. Laura Taalman James Madison University ([email protected]) Sequences, Spiral Knots, and the Elephant in the Room Spiral knots are generalizations of torus knots in which certain overcrossings in the standard braid representation are changed to undercross- ings. Previous work with undergraduates about the determinants of various classes of spiral knots has uncovered a suprising menagerie of patterns, each of which hints at a still unknown pattern
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