Liz McMahon, Lafayette College
Error Detection and Correction in the Card Game SET™. (Friday, April 12, 8:00PM - 9:15PM)
We begin with a variation of the game of SET™, which makes use of a parity check. This allows us to detect (but not correct) one error made in the play of the game. More analysis of this situation leads us to define a Hamming distance on the deck of cards; we can use this distance to classify different categories of non-sets, three cards that do not form a set. The metric also gives us a perfect single error-correcting code.
Mathematics in the Game of SET™. (Saturday, April 13, 8:30PM - 10:00PM)
The card game SET™ is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game. We’ll look at questions in combinatorics, probability, linear algebra, and especially geometry. The deck is an excellent model for the finite affine geometry AG(4,3) and provides an entry to surprisingly beautiful structure theorems for that geometry. If you’d like some practice before the talk, go to www.setgame.com for the rules and a Daily Puzzle.
Liz McMahon is a professor in the Department of Mathematics and also teaches in the Women’s and Gender Studies Department. Her research interests are in combinatorics (polynomial invariants), finite geometry (complete caps in AG(4,3), visualized using the card game SET®), and Cayley graphs. Her PhD was in non-commutative rings. Liz grew up in Chapel Hill, NC, so she is "a Tar Heel born and bred. Go Heels!" She graduated from Chapel Hill High School (there was only one of them back then) in 1971. She earned her AB from Mount Holyoke College in 1975, her MS from the University of Michigan in 1978, and her PhD from the University of North Carolina in 1982. "I love biking, rock climbing, hiking, travel and music. My sweetie and mathematical partner is Gary Gordon; he’s got some family photos that are fun. Our two daughters are Rebecca and Hannah. They are both math teachers."
Frank A. Farris, Santa Clara University
Undercover Symmetry. (Saturday, April 13, 9:30AM - 10:30AM)
Spend some time with the images shown, which, according to the usual classification, have exactly the same symmetry type. Something seems different about the right-hand image: Why do the yellow/pink bowties seem to have mirror symmetry, which are not symmetries of the pattern as a whole? Why are they set at such strange angles relative to the orientation of the grid of red dots? These strange features led me to discover new types of symmetry in wallpaper patterns, with unexpected connections to such things as eigenvalues of a Laplacian and the length spectra of orbifolds.
Frank Farris has taught at Santa Clara University since 1984. He served as Editor of MathematicsMagazine from 2001 to 2005, and again in 2008. In Fall, 2011, he spent a quarter at CarletonCollege as Benedict Distinguished Visiting Professor. While at Carleton, he taught a senior seminar “Creating Symmetry,” covering much of the material in this talk. The course also led to an exhibition at Carleton of Farris’s mathematical art, “Seeing Symmetry,” which has since traveled to the University of Minnesota and now appears at the University of St. Thomas. A new version of the exhibition opened at Pomona College in February.
David Kung, St. Mary's College of Maryland
Symphonic Equations: A Mathematical Exploration of Music. (Saturday, April 13, 2:00PM - 3:00PM)
Mathematics and music seem to come from different spheres (arts and sciences), yet they share an amazing array of commonalities. We will explore these connections by examining the musical experience from a mathematical perspective. The mathematical study of a single vibrating string unlocks a world of musical overtones and harmonics - and even explains why a clarinet plays so much lower than its similar-sized cousin the flute. Calculus, and the related field of differential equations, shows us how our ears hear differences between two instruments - what musicians call timbre - even when they play the same note at the same loudness. Finally, abstract algebra gives modern language to the structures beneath the surface of Bach's magnificent canons and fugues. Throughout the talk, mathematical concepts will come to life with musical examples played by Willamette students and the speaker, an amateur violinist.
David Kung fell in love with both mathematics and music at a very early age. More successful with one than the other, he completed three degrees from the University of Wisconsin - Madison, none in music, before joining the faculty at St. Mary's College of Maryland. A recently promoted Professor of Mathematics, he still enjoys playing violin with students and in the local community orchestra. He has authored a variety of articles on topics in harmonic analysis and mathematics education, and is the recipient of numerous awards including the 2006 Teaching Award from the MD/VA/DC section of the MAA. He is co-writing a book about college math teaching entitled, "What Could They Possibly Be Thinking? Understanding Your College Math Students." His upcoming Great Courses lectures on Mathematics and Music will be released in January of 2013.