Rigorous Proofs at Waterloo


The challenges of mathematics at the University of Waterloo…

After completing my IB exams in May of 2018 and a summer in the US, I started at the University of Waterloo (Mathematics) in Canada. 

When I began my classes and had a look at the first Algebra and Calculus assignments, I knew that this was going to be a difficult and demanding semester. While the work I had done in IB Further Mathematics certainly helped a little, we began Algebra and Calculus “from scratch” in a sense. The approach these courses took when teaching the content was nothing like I had seen in IB. 

We learned the importance of rigorous proofs in the Algebra course, which involved proving very basic statements such as 0 + x = x (using a computer program to validate our justification) and building up to more difficult ones such as proving that there is an infinite number of primes. In Calculus, we started by learning the formal definitions of real numbers, limits and continuity with proof techniques which I have never seen in IB. Overall, Waterloo takes a more formal and rigorous approach when teaching Mathematics than any high school course does. This approach is important in teaching students how Mathematics works as opposed to simply doing it. While this is indeed challenging, it is very satisfying.

In terms of life at university apart from academics, I would recommend everyone to go into residence their first year. I was initially reluctant to do so, but have no regrets. It’s very useful to be in a trusting community where friendships which can last an entire lifetime can be easily built. Additionally, different friendships entail different activities shared amongst them. For example, my friend MK and I spend our time playing football and going to restaurants around town, while my friend Kianna and I enjoy watching Anime in the evenings. While there are certainly some ups and downs in University, I believe that you can always count on the friends you have made to be there for you.

I have found that Waterloo reminds me of Bangkok Patana in some respects, it’s not a big University (like Toronto, for example), so going to class doesn’t feel intimidating whatsoever. Most of the professors I have had have very interesting backgrounds and are humorous during lectures as well, which can help make students feel more comfortable.

Liam McQuay, Class of 2018