Mathematics and Statistics undergraduate student Emilia Alvarez wins Canadian Math Society award

An undergraduate student from the department of Mathematics and Statistics is celebrating a recent award win from the Canadian Math Society, for a project she worked on with her professor, Robert Raphael.

The project began in class. “This summer I asked professor Raphael a question, largely because I'd misread a homework question, to be perfectly honest!” says Alvarez.

The question concerned infinite series (which are sums of infinitely many terms) that one can regroup and rearrange in a series. Alvarez had a question about how a series could be regrouped which wasn't addressed in the textbook nor in any other mathematical resource.

Together, Alvarez and Raphael began to discuss the problem, and worked on it throughout the summer and into the fall. “Essentially, we found that you can regroup a conditionally convergent series to make it absolutely convergent!” Alvarez explains.

They extended the result in a joint paper which professor Raphael encouraged Alvarez to present at the Canadian Mathematical Society's Winter Meeting from the 2 – 3 of December.

Alvarez participated in the poster session alongside a dozen other undergraduate and graduate students, winning the prize for best student poster. “People were very receptive to the work,” she notes.

Raphael praises the “nuanced, advanced” ideas of his student. “Emilia thinks about ideas and then raises questions boldly. Emilia also has great technical skills, hence the beautiful poster.”

Alvarez plans to extend her research into the series of functions, which are more elaborate.

“It's a very rewarding opportunity to work with professor Raphael; the work is challenging, motivating and one of the most enriching experiences of my studies.”