2014 Section Meeting

Invited talks

Frank Farris, Santa Clara University

Polyhedral Symmetry in the Plane?

Abstract: When we classify plane patterns by their symmetries, there is a famous trichotomy: Plane patterns may be rosettes, friezes, or wallpaper patterns. The symmetries of a rosette all share a single fixed point; a frieze pattern is invariant under translation in one direction, a wallpaper pattern in two. In this talk, we undercut tradition, which normally insists that symmetries must preserve distances. We allow certain distance-deforming transformations to play the role of symmetries. In particular, we show how the polyhedral groups can act on the plane. To make patterns with these new transformations as symmetries, we construct functions invariant under the polyhedral actions. One of these is shown below. Do you believe that it has the same symmetries as a tetrahedron? This talk, accessible to undergraduate mathematics students, combines a little group theory, a little complex analysis, and several other ingredients in the service of mathematics and art.

Colm Mulcahy, Spelman College

Martin Gardner: Man of Mathematics, Magic & Mystery

Abstract: The theme of Mathematics Awareness Month 2014, which launches on April 1st, is "Mathematics, Magic, and Mystery", which is closely patterned after the title of a classic 1956 Dover paperback by the legendary Martin Gardner (1914--2010).

Martin was without a doubt the best friend mathematics ever had, and it's fitting that in his centennial year we seize the opportunity to leverage his extensive written legacy---over 100 books---to turn new generations on the magic and mystery of mathematics, and the joys of problem solving and rational thinking. The goal is to inspire many "Aha!" moments, and add to Gardner's record of turning innocent youngsters into mathematics professors (and mathematics professors into innocent youngsters).

Mathematics Awareness Month will provide people with multimedia opportunities to explore the kinds of topics Martin made famous via his famous "Mathematical Games" columns for Scientific American, and associated books. These range from hexaflexagons, magic squares, geometric vanishes, mobius bands, and mathemagic, to juggling, Penrose tiles and the connection between card shuffling and fractals.

We'll preview some of the Mathematics Awareness Month activities, while surveying Martin Gardner's achievements, and highlighting the potential for major outreach into the nation's youth.

Twitter users may enjoy following @MathAware (Mathematics Awareness Month), @WWMGT (What Would Martin Gardner Tweet?) and @MGardner100th (Martin Gardner Centennial).

Robin Lock, St. Lawrence University

Statistical Inference Using Scrambles and Bootstraps

Abstract: Does drinking beer attract mosquitoes? What's the average asking price for all used Mustang cars for sale on the web? Is the "malevolence" of a sports team's uniform related to the number of penalties it gets? These are questions of statistical inference -- reasoning from the data in a sample to say something about an entire population. Can we address such questions with just simple ideas (like random sampling and visual displays) that are easily accessible to students, before introducing lots of technical machinery and theoretical distributions that may hinder understanding key concepts like what a p-value really measures? We'll illustrate how we can use intuitive simulations, implemented with freely available, web-based software (StatKey), to address the opening questions and help students appreciate core ideas of statistical reasoning.