Stacey Lamont and Chester Lipka are studying a mathematical question that has eluded a complete solution for 66 years.

Their project involves something called the “Graph Reconstruction Conjecture”, an informal description of the problem is as follows: if shown pieces of a network (subnets if you like), can you reconstruct the entire network from having seen the pieces?

The project grew out of a trip to Victoria last winter. Five students accompanied Dr. Rick Brewster, Associate Professor of Mathematics TRU, to the 8th Coast Combinatorics Conference. Dr. Wendy Myrvold from UVic gave a talk on graph reconstructions. Dr. Brett Stevens from Carleton University asked a question at the end of her talk, which she said was as yet unanswered.

Chester Lipka

“So far we have settled the question of Dr. Stevens and in the process identified some generalizations of recent work in the field,” Brewster said. “It has been a very successful summer so far.”

That undergrads can tackle such complex problems – and have success is a credit to Brewster and his mentorship. At the Victoria conference faculty from UVic and SFU commented on Brewster’s initiative for taking undergrads to a function geared for doctoral students and professors.

Lamont, from Revelstoke and Lipka from Williams Lake both agree that it was the opportunity to attend the conference that set their academic career paths. Both undergrads are from small towns and had no concept of researching and learning at such advanced levels.

For few days in July they took a break from researching in the Old Main Math lab to attend the Canadian Math Society’s Undergraduate Conference on Mathematics at Simon Fraser University.

“I’m pretty sure that if I hadn’t attended these conferences that I wouldn’t be planning to go to grad school,” Lamont said. “Grad school before (the conference) was just a dream. Now I need to go.”

Chester Lipka’s summer research is funded by TRU’s Comprehensive University Enhancement Fund and from Rick Brewster’s NSERC grant. Stacey Lamont’s by NSERC’s Undergrad Student Research Assistance program.

“I know that if I had gone to a large university I wouldn’t have had to opportunity to attend conferences and conduct summer research,” Lipka said. “Here I talk to my prof, I know him, not a teaching assistant.”

“I’ve had a good introduction to different areas of discrete math and the conferences make me want to learn more about it. I’m learning how much further I can go with the discipline.”

Brewster has co-authoured four papers in various academic journals with undergrads, and hopes to submit the work with Lamont and Lipka this fall. “The reason we are getting papers published is because our undergrads are exposed to research problems at conferences and in the summer research term,” he said. “At the upper levels we have small classes and take on those students who wish a taste of research.”

“In our small classes, I notice which students have the work ethic, organization skills or pure talent. If I was teaching a class of 300 or 400 hundred, with TAs, I wouldn’t.”

As they head back for the final year of their BSc Mathematics degree, both Lamont and Lipka will be adding applications to graduate schools and for scholarships to their course work.

For more information contact Dr. Rick Brewster by email at rbrewster@tru.ca or by phone 828-5215.