Ralph McDougall, a second year engineering student from Stellenbosch University, was the overall winner of the ninth South African Tertiary Mathematics Olympiad (SATMO), held for the first time via an online platform on 22 August, due to the COVID-19-pandemic.
Lourens van Niekerk, a BScHons student in mathematics at SU, was the joint winner of the Honours students. All in all, 19 SU students competed with over 290 students from eight South African universities.
Both Ralph and Lourens are old-time participants in maths Olympiads. Lourens says he has been participating since Grade 4, and in 2018 he was part of the SU team that participated in the International Mathematics Competition for tertiary students in Bulgaria. Ralph has twice represented South Africa at the International Mathematics Olympiad while still at high school. In 2018 he won the South African Mathematics Olympiad for high school students.
Ralph, a former learner from Curro Durbanville High School, says that these days he is only participating for the fun of it: “I really enjoy the thrill of finding solutions to seemingly hard problems. Whatever your score, one should enjoy the challenge and try to learn something new in the process."
His advice to fellow participants is to develop the skill of being able to identify when a method is going to take too long to be feasible: “The types of problems in these competitions often have multiple ways of getting to the same answer, but only a few of them can be done by hand without pages of tedious calculations. Probably the most frequent thought while solving Olympiad-type problems is: There must be a better way. This is something that comes with experience."
Lourens, who grew up in Kimberley and matriculated from Hoërskool Diamantveld, says he is not by any standard the best mathematician out there: “I just like competing!" He has completed a BCom- Mathematical Sciences degree, with a focus on computer science, and is now pursuing a BScHons-degree in mathematics.
His advice to students is to think outside of the box: “Relate questions to objects you are comfortable with. Create easier examples, look for patterns, and be creative. These questions usually require playing around a lot and incorporating ideas that you probably never thought to put together before. I love them because many of the questions are made fun with tangible examples. For example: A 20x20 cm board must be tiled with seven colours such that ...". I mean, how many ways are there to do this? This is fun!"
Needless to say, Lourens plans to continue with this MSc in Mathematics next year, while Ralph is thinking of specialising in signal processing.
Dr Dirk Basson, a lecturer in SU's Department of Mathematical Sciences and SU's SATMO-coordinator, says Olympiads are different from a normal mathematics exam: “ The problems rarely involve knowing large amounts of knowledge, but rather asks students to solve unusual problems using existing and commonly known tools. In order to solve the problems, students need to have a deeper than average understanding of all high school and first year mathematics, and a broad view of the connections between ideas and the kind of problems they solve."
The question paper consists of 20 problems and has been hosted by the South Africa Mathematical Society since 2012.
On the photos above, Ralph McDougall (left) and Lourens van Niekerk. Photos supplied