“This milestone is the culmination of years of effort, planning and re-planning, as well as a fair bit of dreaming. So, it is one of the most rewarding experiences I have had,” said Azam, a student in USask’s College of Arts and Science. “On the other hand, remembering all the wonderful moments with my professors and friends, I feel nostalgic and sad that my life at this wonderful university is drawing to an end.”
Azam, who was born and raised in Dhaka, Bangladesh, began his studies at USask in January 2016. He is now set to receive a Bachelor of Science (double honours) degree in mathematics and computer science during 2021 Spring Convocation.
Azam has consistently excelled throughout his undergraduate studies, earning numerous scholarships and awards along the way. Recently, the high-achieving student was named the winner of the Best Thesis Prize in Mathematics and Statistics (for mathematics) for his thesis titled “Quantum Information Through Topological Quantum Field Theories,” supervised by Dr. Steven Rayan (PhD), a faculty member in the Department of Mathematics and Statistics. The award was presented during a virtual event hosted by the department in April 2021.
“This was the most awe-inspiring event of my life,” said Azam. “Getting such a recognition from professors who I so deeply admire gave meaning to everything I had done so far. I don’t think I can do justice to my feelings surrounding this event with words.”
“Mahmud’s bachelor thesis is really something to behold. It could easily be a master’s-level thesis, if not a chapter in a PhD thesis,” said Rayan. “What impresses me is not only the level of mathematical and scientific sophistication, but also how well written it is. It was publication quality on the first try. I’m so proud of Mahmud. Watching his growth as a mathematician and seeing his talent emerge has been very rewarding.”
Throughout his studies at USask, Azam has had the opportunity to work directly with several professors as the recipient of three Natural Sciences and Engineering Research Council (NSERC) Undergraduate Student Research Awards (USRA)—one in computer science and two in mathematics. Rayan said earning three NSERC awards as an undergraduate student is “an atypical feat” that speaks to the high quality of Azam’s work and academic abilities. This summer, Rayan and Azam will work together to develop a novel approach to quantum computing and information theory using techniques from areas in mathematics such as geometry, topology and category theory.
“His thesis work and his upcoming NSERC USRA work are an attempt to discover new possibilities in the emerging subject of quantum computing—possibilities that can only be detected by examining a part of mathematics called topology, which is the study of shapes and how they stretch and squeeze,” said Rayan. “This is a paradigm shift. If you think of computing as being built from 0s and 1s, there doesn’t seem to be a lot of room there for stretching and squeezing. But quantum computing has more freedom, and that is best expressed through topology. Mahmud is ahead of the curve, trying to make precise the connection between quantum computing and this kind of math, and trying to find new ways to compute that are able to solve difficult real-world problems in shorter amounts of time.”
Azam’s first NSERC USRA was in 2017, working with Dr. Christopher Dutchyn (PhD) in the Department of Computer Science. Together they examined different ways of writing computer programs with guarantees of correctness using a specialized programming language that allows one to write logical proofs about the correctness of programs that can then be verified by a computer.
In the summer of 2019, alongside a computer science internship, Azam conducted research in number theory with two former faculty members in the Department of Mathematics and Statistics, Dr. Cameron Franc (PhD) and Dr. Jenna Rajchgot (PhD). Azam described the project as “one of the most fascinating experiences” he had at USask.
“Dr. Franc and Dr. Rajchgot introduced me to some of the most advanced and beautiful mathematics I had seen so far, which ultimately inspired me to commit fully to doing the double honours,” he said. “This project also inspired me take some of the most beautiful upper-year reading courses in mathematics and computing that I would not otherwise think of taking. These include CMPT 498: Topos Theory, which was jointly planned and taught by Dr. Dutchyn and Dr. Franc, and MATH 450: Algebraic Geometry Through Moduli and MATH 460: Galois Theory and Topology, both taught by Dr. Rayan.”
In 2020, Azam worked with Dr. Ebrahim Samei (PhD), a faculty member in the Department of Mathematics and Statistics, for his second NSERC USRA. Together they tackled an open problem concerning the classification of a certain collection of objects in an area of mathematics called geometric group theory.
“This research, which we hope to publish before the end of the summer, has implications for another area of mathematics called functional analysis, which ultimately connects to quantum mechanics,” said Azam, who noted that doing research with his professors for summer projects and for his thesis was the best part of his USask experience.
“I feel that the level of depth that a student can reach in a topic through just one summer of research under a great professor is amazing. I don’t think one can fully appreciate the beauty of a subject like mathematics or computing without delving into such depths. I consider myself extremely lucky to have gotten the opportunity to do this four times in my undergraduate life. However, I must say that working with friends past midnight on that one assignment problem that nobody was able to solve, and then collectively and organically solving it, missing the last bus and walking home after that—these are just as enjoyable and meaningful experiences.”
Outside of the classroom, Azam served as an executive member of the Math & Stats Student Society (MS^3) and was also a member of the Computer Science Student Society during his second year of studies. Looking to the future, following several competitive graduate school offers in both mathematics and computer science, Azam will begin graduate studies in mathematics at the University of Toronto this fall.
Azam said he would like to thank his teachers and friends for making his undergraduate journey at USask “so wonderful.”
“I would like to especially thank all my supervisors for giving me the opportunity to work with and learn from them, and for nurturing my passion for mathematics and computing,” he said.