The spring 2015 meeting was held March 14, 2015 at Franklin & Marshall College.
- Ezra (Bud) Brown (Virginia Tech)
The Many Names of (7,3,1)
- In the world of discrete mathematics, we encounter a bewildering variety of topics with no apparent connection between them. There are block designs in combinatorics, finite projective planes in geometry, round-robin tournaments and map colorings in graph theory, (0, 1)-matrices in linear algebra, difference sets in number theory, error-correcting codes on the internet, and the torus at the doughnut shop. But appearances are deceptive, and this talk is about the (7,3,1) design, a single object with many names that connects allof these topics. Along the way, we'll learn how Leonhard Euler was once spectacularly wrong, how P. J. Heawood was almost completely right, and what happened when Richard Hamming got mad at a computer.
- Frank Farris (Santa Clara University)
Polyhedral Symmetry in the Plane?
- When we classify plane patterns by their symmetries, we meet a time-honored trichotomy: These 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, by allowing 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 symmetry 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.
- Aparna Higgins (University of Dayton)
Sequences of Polygons
- At a mathematics meeting several years ago, two students who attended different schools and who did not know each other presented talks that were variations of the same problem. The student from the University of Dayton spoke of the result of alternately inscribing regular polygons and circles, while the other spoke of the result of alternately circumscribing regular polygons and circles. Recently, I heard a talk on other variants of this theme, and I found myself still intrigued by the questions. I am delighted when I see problems that are simple to state, yet have an element of surprise. I will use GeoGebra to help us explore some of these problems. This talk will be accessible to undergraduates.
Faculty Contributed Paper Session
Faculty talk schedule (PDF)
Faculty talk abstracts (PDF)
Student Contributed Paper Session
Student talk schedule (PDF)
Student talk abstracts (PDF)
Section Governor, Annalisa Crannell, Franklin & Marshall College
Of course, the biggest news of the year is that 2015 marks the 100 year anniversary of the MAA. What started with a tiny group who wanted support a new journal called the American Mathematical Monthly has grown into a vibrant organization with nearly 12,000 members. What a transformation!
The MAA prides itself on being the foremost association dedicated to expository mathematics; we're the largest association whose mission is to support math at the collegiate level. So it was exciting for me to see that the MAA now has 16 funded proposals, worth $8.5 million, that help to support faculty in bringing mathematics to our students and to the world.
Keep your eyes peeled for the upcoming CUPM report on the curriculum, and also on the nifty “Ingenious” brochure which highlights the way that mathematics can and should be an orientation to careers. This summer's PREP workshops for faculty promise to be excellent!
Also looming on the horizon is the new departmental membership structure! Starting next year, departmental memberships will not be tied to journals; but rather, they will allow departments to nominate unlimited numbers of students. The institutional memberships come also with a discount on hosting WebWorks. The MAA is excited to think that this might help institutions expose our students to mathematics and introduce them into a wonderful mathematics community.
Speaking of our wonderful community, if you or your department has an interesting mathematics story to share, send it into the MAA Focus. They are always looking for interesting ideas for stories, and also for news of what our members are doing.
Registration for MathFest opens on March 1. This summer's program is going to be so wonderful that MathFest will actually run one extra day, closing with a musical produced and directed by your very own Governor. I hope to see you there!
The MAA is about to enter its 100 Year Celebration. Woo-hoo!
Annalisa Crannell, Governor