### Some of my Students

One of the most rewarding activities for me at Bates is working with students on their senior theses. Sometimes they choose the topics, other times I do. We may meet from two to five hours a week. Students study on their own, and then we discuss the work. Sooner a later, a "problem" to investigate arises, and becomes the focus of the thesis. Nearly all the students I have had have written theses that involve some new mathematics. All involve good writing. I am proud of the work my students have done, and enjoy the working relationships that always develop. They leave Bates as my friends, and I continue to hear from them fairly often.

Here are some photos of my students and me from the past few years. Click on any photo for a bigger version.
The math department's experiment with one-semester theses began its second year in 2003/04. In the winter, I was Erica Dodd's advisor as she worked on modeling the population of India's Bengal tiger. Starting with the standard predator-prey model from a differential equations course, Erica tried to find coefficients that made the model match the actual statistics of these endangered tigers and their prey, gaur. One of the biggest challenges Erica faced was actual finding reliable numbers on tiger and guar populations. Erica also figured the effects of poaching into her model.
In the fall, Jer Brown studied Bessel functions in an ambitious project. Among other things, Bessel functions can be used to model the motion of a bob on a pendulum whose length changes at a constant rate. Jer studied the development and theory of these functions, wrote a C++ program to solve the involved DE's numerically and built a lengthening-pendulum from which to collect data. The data Jer got off this device was amazing. Jer wisely chose to turn this thesis into a two semester honors thesis through the physics department, and was indeed awarded honors in physics in the spring.
In 2002/03 I supervised two thesis students, Sarah Cremer and Mark Prelli. We're pictured at the end-of-year celebration party held in the math department. Sarah wrote a two-semester thesis on the relationship between Q and P curves and their interactions; this was an extension of Meredith Odell's work (Meredith appears below). Mark wrote a one-semester thesis about locating repelling periodic points of Julia sets, and supplemented his thesis with a computer program that illustrates graphically two very different ways of finding such points. (One semester theses were new to the math department this year).
 Sarah and Mark each presented their work at the second annual "Mount David Summit", an opportunity for all Bates students to share their thesis work with the college community. Pictured with Sarah is Dean of Faculty Jill Reich.
I advised two thesis students in 2001/02. Here Sam Hawes and Meredith Odell are all smiles after their final thesis presentations in May.
Here's Meredith just before that presentation. She looks worried, but it was all just an act. She gave a fine talk, to a room full of math faculty, other senior math majors, Math Campers, and a dozen or so of her friends. In her thesis she proved that Q-curves and P-curves are tangent at C-values for which 0 is on a super attracting periodic cycle, and that these curves intersect but are not tangent where 0 is pre-periodic. We hope to publish the results as a follow up to a paper called "The road to chaos is filled with polynomial curves" published in 1996 in the American Mathematical Monthly.
Sam investigated the locations of repelling periodic points for Julia sets sporting Siegel disks, inparticular doing a discrete Fourier transform on the way the distance and angle change as one moves around one of the disks. The result was terrific. His investigations were done using a program he wrote and continually modified as needed to give us insight into the behavior of these objects.
Chris Danforth wrote a joint physics/math thesis in 2000/01; I was advisor for the math part. Chris built a "thermosyphon" to demonstrate the kind of behavior in a fluid moving as modeled by the Lorenz equations. The device was very touchy and Chris nearly melted it into a mass of plastic junk, but it worked! And when he plotted the data collected from the way the fluid rolled this way, then that way, it was indeed very similar to the plot of the numeric solutions of the Lorenz equations. The 3D reconstruction plots were especially revealing. Chris is now a graduate student at the University of Maryland, working in chaotic dynamical systems.
Chris was also one of the stars on the Bates tennis team. He's spent several summers on Squirrel Island, where his family has a residence, and he teaches tennis. Chris is rightfully regarded as a tennis god on the island; when my family and I visited him there in the summer after his Bates graduation, most of the island's population turned out to watch Chris in a late afternoon doubles match with various family members and friends.

Earlier in the day, I got to play tennis with Chris on those wonderful clay courts, and while ultimately giving me the expected trouncing, he can never forget that I did win my first game against him that day! (Thanks Chris!) I hope he is able to realize his dream of being a highly regarded professor at some good school, with his summers off to play tennis and study on the idyllic, beautiful, Squirrel Island.

In 2000, because of my sabbitacal leave during the spring, I was unable to serve as Melissa Borr's thesis advisor. I am sorry for this missed opportunity. But I still helped her work on it. Missy and I built a device for studying the frequencies at which nodes form on a square membrane, fixed along its four boundaries. To see and photograph the nodes, we poured a small bit of salt on the membrane - a stretched rubber sheet about 4" square - as it was set into motion by a large speaker vibrating underneath it. The resulting patterns appeared at nearly exactly the identical frequency ratios as predicted by the numeric solutions of our mathematical model of this system. Very Cool! Look for more about this on a future page.
Chris Santillo and I enjoyed studying the mysteries of Siegel Disks during his senior year, 1997-98. We started working in August before the semester started; the sound of the pounding-in of Pettingill Hall's first pylons was a constant background during our discussions in room 207. Chris and I enjoyed playing various CD's for one another; he introduced me to the delightful music of Tipsy, and I got him interested in the amazing guit-steel playing of Junior Brown. In the summer of 1999, I visited Chris in Massachusetts, and we saw Junior play a show in Cambridge.
Carl Landry '98 didn't write a thesis with me, but he took a number of classes with me and we became very good friends. I served as his math major advisor, and in fact, his advisor for many things about life, money, marriage, happiness. We enjoyed many discussions about everything. Carl spent many hours student-teaching at Lewiston High, and I visited his class one day for an evaluation. Carl's a natural teacher, and indeed, has wisely chosen to make a career out of it.
In 1997, Brian O'Conner wrote a thesis based on a study of Feigenbaum's paper "Quantitative Universality for Nonlinear Transformations". The picture of us was taken at the 1997 Hudson River Undergraduate Mathematics Conference, held in April, 1997 at Williams College - Brian is standing behind me while to his left are Bates students David Chamberlain, Jamie McDowell and Else Kyyro. My colleague Bonnie Shulman is in the middle of the photo. All of us gave talks at this event.

 Return to Chip's Home Page © 2004 by Chip Ross Associate Professor of Mathematics Bates College Lewiston, ME 04240 email: sross@bates.edu (note: the first letter is an "s"!)