Math is a core part of the EngSci program. The rigorous training and deep theoretical foundation students receive in Year 1 and 2 foundation courses help them to develop formal logic and algorithmic thinking, and strong problem-solving skills.
It should come as no surprise then that the program exerts a certain kind of pull for many highly skilled math enthusiasts.
“Having taught first year engineering science students over my career, I can attest that it certainly attracts some of the best high school mathematics students,” says Professor Emeritus Ed Barbeau (Math). Barbeau is the organizer of the annual University of Toronto Undergraduate Mathematics Competition where the university’s top students test their problem-solving skills in a timed contest.
This year, EngSci students Robert Li (PEY) and Hshmat Sahak (Year 1) placed 3rd and 5th, respectively, an impressive feat in a field of 38 students mostly from the math and applied math programs. In the 2019 competition, EngSci student Jennifer Guo (PEY) also received an honourable mention.
For these students, this was not their first time at the math rodeo. Each started entering math competitions in elementary school. In high school, Li placed 1st in the Canadian Team Mathematics Contest, while Guo was one of 16 finalists for Canada’s team for the International Math Olympiad over three years, and Sahak was invited to write the Canadian Math Olympiad last year.
“Many Engineering Science students have a level of mathematical maturity that is unparalleled in other programs, and they routinely excel in International math competitions,” says Professor Ashish Khisti, Chair of the Machine Intelligence major. “Many of our graduates are recruited by the best graduate schools internationally, precisely due to these reasons.”
We sat down with the three students to find out what they get out of this unique type of competition, and what advice they might share with students considering entering one themselves.
What happens at the competition?
Li: This competition included ten problems, and you are expected to write full solutions in 3.5 hours. Your five highest-marked problems have to earn a total of 30 marks or more for your other problems to be considered. In other words, you want to briefly go over all the problems, identify the ones you can solve, then try your best to solve them. This encourages you to reach the core of at least a few problems.
Guo: The problems in the contest are very different from exam problems, they are more often proof-style where you have to prove if something is true or not. They are most similar to calculus exam questions and linear algebra.
How do you prepare?
Guo: Practice is key, doing lots of repetition and review to build familiarity.
Li: You can attempt problems from past years, look at problems from the North-America wide Putnam competition, or attend Putnam preparation sessions, if they’re offered where you are.
Sahak: I had very little opportunity to practice due to my course load and other commitments.
What do you get out of competing in math contests?
Sahak: I find writing math contests to be an incredibly rewarding endeavour. They allow me to challenge myself, to push myself to my intellectual limits, and to apply mathematical concepts outside the scope of a classroom. I also get to meet new people who have the same interests as me, build my network.
Li: One main reason for me to write the U of T Mathematics Competition was to see two friends who went into the math program, while I went into engineering. We hadn’t seen each other in two years. The contest is like a microcosm of life: fun, friends and a welcomed bit of challenge.
What advice do you have for other students thinking of entering a math contest?
Li: Don’t stress if you find any of these too hard. I remember Prof. Stangeby, who taught us calculus, saying: in repetitively attempting to solve a problem and failing, you are exercising the muscles in your brain. In the end, solving problems involves trying different things. The two most important things are to know what things to try, and to try things faster. That said, don’t hesitate if you just want to write this competition for fun and friends, because that’s what I had in mind that day.
Sahak: Just go for it. You have nothing to lose. Also, it’s a great way to challenge yourself, and to gauge where you stand with regard to university-level math. It’s an incredible learning experience and a surprisingly enjoyable one at that.
What are your future goals?
Sahak: I plan on majoring in either Robotics or Machine Intelligence in my third year of study. Grad school is a viable option afterwards, where I can see myself invested in the progression and evolution of robotics/control systems through the application of artificial intelligence and machine learning algorithms.
Li: I’m graduating next year in the Machine Intelligence major of Engineering Science, and I’m looking to do graduate studies. Right now, I am doing research in computer vision and deep learning as part of my PEY Co-op at the Vector Institute.
Guo: I recently completed my PEY Co-op at Uber ATG where I learned a lot about how machine learning is done “in real life”. I am considering a more pure-math focused career. To learn more about that, I will be doing summer research under Prof. Khesin from U of T’s Department of Mathematics.
Any final thoughts?
Li: I want to bring attention to Prof. Barbeau for organizing this Competition for the past 20 years. EngScis in previous years had the luck to have him as their Calculus teacher. Aside from mathematician and Professor Emeritus at U of T, he is also one of the three members of Team U of T, which placed 3rd among all North American Universities in the 1960 Putnam Mathematical Competition.