Math Through Interesting Problems

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By Yin Xzi – 1st year student

Last month I took my first ever math course at Quest – it was called “Math Through Interesting Problems” taught by the wonderful Asia Matthews. The course overview promised that we were going to explore advanced mathematical thinking through basic mathematics in geometry, origami, puzzles, number theory, amongst other things.

I’d heard great things about math at Quest – how phenomenal the tutors are (I can now also add my testimony to the ever growing list), how they absolutely change you as a person (even if you don’t like math), and how it kind of (like most Quest courses, really) takes over your life. Nothing I’d heard or read, however, prepared me for the math block that was.

Let me backtrack a little. The math philosophy here doesn’t follow the convoluted progression of pre-algebra, algebra, geometry, and calculus that exists and is perpetuated by the standard mathematical curriculum worldwide. Instead of memorizing formulas and learning the situations in which some formulas can (and should) be used, Quest math focuses on mathematical thinking – the process by which you approach a problem (any kind of problem, whether it involves numbers or not) and systematically solve it.

Folding hexagons out of squares

Math is put into context – equations that are vague and floaty (a2 + b2 = c2) are grounded in the person (or group of people) who discovered the concept. It turns out that the Pythagoreans didn’t eat beans and had such intense laws regarding the secrecy of everything that they found that members who released information were drowned.

With this in mind, class began with the number 19 and a scheduling problem. The task given was to create 6 sets of unique groups such that no one individual in the class works twice with another person, with a minimum of 3 people per group. We rotated numbers, shuffled seats, assigned letters to each person. All strategies were underpinned by the sense that: this should be possible. (Try this question – you’ll learn a lot about mathematical thinking by the time you solve it)

We went on to solve magic squares and come up with the beginnings of graph theory. We played around with non-isomorphic graphs, folded squares out of squares, and all the while I started to see math more and more often in my everyday life.

Just a tetra-tetraflexagon with its hexa-hexaflexagonal pals

Bathroom tiles became 4×4 magic squares, chess boards. Windows became evidence of the golden rectangle. Patterns and number sequences that we chanced upon in week 1 of class came up in week 2, week 3, and even in the final three days. Tetra-hexa-flexa-hedrons and an octahedronal shape, with each consisting of 8 triangles, that could be ‘squashed’ into a flat plane from any direction became my favorite past times.

For the final assignment of the class I ended up attempting to create a strategy for Settlers of Catan that would maximize your chances of winning. For a game that emphasizes chance a lot, it sure has a lot of strategies that can be mathematically explored and supported.

The math behind Settlers of Catan is worth spending five days on, trust me

Math Through Interesting Problems challenged me beyond what I thought I was capable of doing – it turns out that I’m a lot better at mathematical thinking than I thought I was, and that I like math a whole lot more than I thought I did.

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