Working in the spring of 1997, Julie began by reading an early paper by Ronald L. Graham (one of the great combinatorists of our times), and discovered an error in one of the proofs. We set about exploring whether the theorem was in fact true. We found that it was true, and were able to correct the proof. This involved providing the details for a case that was ommitted in Graham's orginal proof. Julie's work was published in the Pi Mu Epsilon Journal (vol 10, no 10, Spring 1999), and she presented her result at the national MAA summer meeting in Atlanta with financial assitance provided by Pi Mu Epsilon. Coincidentally, Ron Graham gave a keynote address at this meeting, and Julie got to meet him first hand. The photo below shows (left to right) Julie, Professor Torrence, and Ron Graham.
Julie completed her Ph.D. in mathematics in 2002, and is now an assistant professor of mathematics at Sam Houston State University in Texas.