The above question is a demonstration of number theory, a favourite of SMUS mathematician Andrew Kang. In honour of Pi Day, we have two student perspectives on the joys of math competitions. Below Grade 11 student Andrew talks about his competitions thus far, and in our second post, up-and-comer Jonathan reports on the Middle School mathematics team.
When did you first start taking part in math competitions?
My first math contest was Math Challengers, and although it is only a contest for Grades 8 and 9, I was allowed to participate in Grade 7. I got my first glimpse of competitive math that day, and I even got to play in the face-off round – a buzzer-round in the style of Jeopardy. Through the sweat and adrenaline that dominated me during those intense five minutes, I first developed my love for math contests, and I ended up taking first place in the regionals.
What do you like about contests?
Contrary to what most people would expect, math contests are exciting. (Big surprise, I know.) But in all seriousness, when I write a math contest, for the one hour that I am drawing and erasing little triangles or bubbling in what (I hope) are the correct answers, I feel like I am in some sort of twisted race, where if I want to get further, I need to solve another problem. The best part is the satisfaction and relief that comes after solving an especially difficult problem, given the tough time restraints. Knowing that all that staring blankly at the page and doodling diagrams on the paper, hoping that at least some hint comes to mind, came to fruition is an indescribable joy that one has to experience to truly understand.
Which contests have you written this year, and how were they different (difficulty, content, form, etc.)?
I took a multitude of contests this year. Perhaps the hardest and longest was the Canadian Open Mathematics Challenge (COMC). A total of 12 questions in two and a half grueling hours, the COMC was increasingly difficult, with the last question almost untouchable. I ended up qualifying for the Canadian Mathematics Olympiad (CMO), which the top 50 students that wrote the COMC can write, and I will be taking the CMO in March. I also wrote the Canadian Senior Mathematics Contest, which was similar to the COMC. On the other hand, I recently took two multiple choice tests on consecutive days: The American Mathematics Contest (AMC) and the Fermat, each consisting of 25 multiple choice questions. The AMC requires much more mathematical knowledge and gets impossibly difficult as the test progresses, while the Fermat depends more on logic and intuition.
What do you like about mathematics?
Above all, math makes sense to me. Generally, I enjoy every subject, but math really sticks out because the processes I go through in my head are somehow magical. I remember when, in calculus class, I learned the concept of the derivative and its applications. In those classes I felt as if I was given a key to open my eyes to a whole new world, previously unexposed to my naïve self. It blew my mind that mathematicians were actually able to size every curve down to a set of infinitesimally small portions, and then add these portions back up to get results that I never knew were possible to achieve. Not only that, but I was able to take the step-by-step journey to learning this new concept – I was not simply given a formula to memorize and told to accept facts, but instead I could learn each concept piece by piece, and eventually mold them all into a fundamental yet totally sensible conclusion. That is what I love about math.
What’s your proudest math moment thus far?
My proudest moment would probably be qualifying for the USA Junior Mathematics Olympiad (USAJMO) near the end of Grade 10. It was an unbearable nine-hour contest, thankfully split over the course of two days, with three very mind-boggling questions each day. Each year, the people who do well on the American Mathematics Contest are invited to write the American Invitational Mathematics Exam (AIME), and those who do well on the AIME are then again invited to the USAJMO. I was thus selected as one of the top 270 students in North America, and I was one of only five Canadians who qualified for the contest. I also recently qualified for the Canadian Mathematics Olympiad – I was invited to write because I was one of the top 50 students in Canada that wrote the Canadian Open Mathematics Challenge.
What do you plan to do with your mathematical talents in the future?
I am hoping to major in robotics engineering in university – although I love math, I want to apply my skills into practical uses instead of diving into pure theoretical math. I love science as well as math, particularly physics and chemistry, which is why I want to go into engineering, in the hopes that I can dedicate my life to a comprehensive field involving problem-solving, a skill that I have greatly developed through writing math contests.