Barbara Ashton, Borough of Manhattan Community College, City University of New York
“A Sampler of Topics from Mathematics and the Arts”
Three different topics from current publications that illustrate how mathematics can be used to model artistic endeavors will be discussed. The first two topics, from the Journal of Mathematics and the Arts, include how to calculate the area and volume of gothic structures using single variable calculus and how contra dancing is related to finite groups. Professor Ashton will also discuss an algorithm she has developed for modeling and generating heraldic designs.
Barbara Ashton was a faculty member at Wittenberg University and a former President of the Ohio MAA. She is currently an associate professor of mathematics at Borough of Manhattan Community College,– The City University of New York where she recently completed directing the Science and Technology Entry Program, a college prep program for historically underrepresented and economically disadvantaged high school students. Ashton is a nationally recognized expert on the mathematics of Frank Lloyd Wright’s architecture. Her current research focuses on the relationships between mathematics, religion and art. In her spare time, she scouts out locations in New York City where her border collies can play Frisbee.
Michael Henle, Oberlin College
“Can You Hear the Mathematics?”
Connections between mathematics and music range from the mathematics of acoustics and sound itself, through the theory of scales and temperaments, to the use of mathematics in musical composition and analysis. This talk focuses on music composition. Many composers, including some quite famous ones, have been accused of using mathematics. Some arguably have done so consciously. In other cases the presence of mathematics in their works has only been detected by some kind of ex post facto analysis. Either way, the question we ask here is: is the mathematics audible?
Musical composition can be aided by mathematics in numerous ways. Mathematics can be used to determine overall proportions and other large-scale parameters of a piece. It can provide tools for the manipulation of musical materials already composed. It can also generate from scratch the smallest details of a composition, namely, the notes themselves: pitches, dynamics and durations. But can the mathematics be heard? This talk will present a number of very short case studies, almost exclusively based on classical music composed in the last 100 years. Don’t expect any grand conclusions, but at least we will raise some basic issues.
Michael Henle is the current editor of The College Mathematics Journal. He has taught for 40-some years at Oberlin College having gone there directly from graduate work at Yale. He started his mathematical life as a functional analyst and then became a bit of a combinatorialist. He is the author of two texts: A Combinatorial Introduction to Topology (Dover) and Modern Geometries: Non-Euclidean, Projective and Discrete (Prentice-Hall). A lifelong interest in music led him to the topic of this lecture. He plays piano a bit and is a sometime composer. He avoids, however, employing mathematics in music himself as far as possible.
Dave Sobecki, University of Miami (Hamilton)
“Of Elephants, Fuzzy Dogs and Teaching Backwards: A Story About Making Your Course Engagin’”
The traditional method of teaching math goes something like this: Definition; Theorem; Example; Example; Example; Application. Many of us feel pretty comfortable with that - hey, it worked for us. But does it work well for the average student? I propose a backward method: starting with applications to motivate the math. When you start to think this way, it opens up a world of possibilities. I'd like to share some of my world of possibilities.
Dave Sobecki was born and raised in Cleveland, and started college at Bowling Green State University in 1984 majoring in creative writing. Eleven years later, he walked across the graduation stage to receive a PhD in math, a strange journey indeed. After two years at Franklin and Marshall College in Pennsylvania, he came home to Ohio, accepting a tenure-track job at the Hamilton campus of Miami University. Dave has won a number of teaching awards in his career, and more recently has turned his attention to writing textbooks. He has written or co-authored either five or nine textbooks, depending on how you count them, as well as several solutions manuals and interactive CD-ROMS. Dave is in a happy place where his love of teaching meshes perfectly with his childhood dream of writing. Dave is also a former coordinator of Ohio Project NExT. He lives in Fairfield, Ohio with his lovely wife Cat, and fuzzy dogs Macleod and Tessa. When not teaching or writing, Dave's passions include Ohio State football, Cleveland Indians baseball, heavy metal music, travel, golf and home improvement.
John Stillwell, University of San Francisco
“From Perspective Drawing to the Eighth Dimension”
The discovery of perspective drawing in the 15th century led to projective geometry, in which points and lines are the main ingredients. Even with this simple subject matter there are some surprises, where three points fall on the same line or three lines pass through the same point, seemingly for no good reason. The big surprises, or "coincidences", of projective geometry are the Pappus theorem, Desargues theorem, and the little Desargues theorem. Even more surprising, these purely geometric theorems were found (by David Hilbert and Ruth Moufang) to control what kind of *algebra* is compatible with the geometry. Compatible algebras live in 1, 2, 4, and 8 dimensions.
“Hits and Memories: 1940-1970”
Some reminiscences of mathematics and mathematics books from the middle of last century set against the cultural background of the time. In particular, I will explain which comic book hero had the most influence on my mathematical development.
John Stillwell was born in Melbourne, Australia in 1942. He was educated at Melbourne High School (1956--1959) and Melbourne University (1960--1965), before going to MIT for his Ph. D. (1965--1970). From 1970 to 2001 he taught at Monash University in
Melbourne, during which time he wrote his best known book, Mathematics and Its History, and gave invited talks at the ICM in Zurich in 1994 and the Joint Meetings of the AMS and MAA in Baltimore in 1998. Since 2002 he has been at the University of San Francisco, where he continues to write mathematics books, most recently Naive Lie Theory (Springer 2008) and Roads to Infinity (A K Peters 2010). He received the MAA's Chauvenet prize for mathematical exposition in 2005.