CCA Previews ’22: Mathematics Club

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By Lai Pengchong (22S06D), Chairperson, Edmund Xiao (22S02A), Vice-chairperson, Liu Fenghua (22S06P), Secretary-cum-treasurer

A mathematics club?

Yup, math club! Have you ever been fascinated by the genius behind a math concept? Or are you a hardcore buff who spends all your time grinding away at puzzles or messy geometrical diagrams? Are you craving for the same sparks of enlightenment and fulfilment that once ignited your interest in math? If your answer to any of the above is yes, you’ll understand why there’s a whole CCA built around math, and joining it won’t disappoint you!

…. Well, now you’ve got me interested. How do I know that it’s really for me?

Simply put, if you’re interested in math, math club is perfect for you. The math you’ll find here will be very different from the JC curriculum (we admit, sometimes it can get boring). Instead, we go much deeper into elegant and mind-blowing concepts that can, and will, satisfy your intellectual cravings. In essence, we explore problems similar in spirit to our favourite logical puzzles or brain teasers, with more mathematical rigour and greater difficulty to truly sate our sense of curiosity. 

If you really want a teaser, here’s a famous but nonetheless interesting puzzle:

Let’s say you’re playing a very special chess game with an evil wizard. Both players get to move twice on each turn instead of once, and you play as black. Is it possible for you to devise an algorithm, so that you always win? Answer is at the end :)

Alright, but what does a typical session look like?

Great question! The best aspect of math club is our freedom to do whatever we want during our regular sessions (provided that it’s tangentially related to, well, mathematics). Our sessions are conducted (and chosen) by our members and can come in a range of forms—including sharings or even games! A large breadth of topics can be covered with technical accuracy, depth and most importantly, fun, thanks to many knowledgeable and passionate club members. We’ve covered “chim” topics in number theory along with more light-hearted ones, like how to get better at mental math or games. There is no doubt that there will be something for everyone. 

Beyond just teaching and learning math, we’re also a tight-knit community. Here, we’re all free to bond not only over our interest in the subject, but also in a more carefree, comfortable, and cozy environment. Amidst heated discussions, arguments, or just loud banter (not necessarily math-related), you will learn and make friends. 

Hah, to have read this far into the article, I’m mildly interested! Tell me the schedule.

There is only one session per week from 4:00 to 6:00 pm on Tuesdays, and we are never obliged to do extra work beyond our club time (unless we want to, of course!). Otherwise, you can simply just come, have fun and relax! You’ll still have time and energy for your own pursuits, be it mathematical or not—another great perk. While it is really unfortunate that many of our plans were disrupted by Covid-19, we did hold a range of events in previous years! This included holiday Math Club camps (combined with RI Y1-4 and RGS), learning journeys to NUS, as well as inter-CCA collaboration activities. Members also took part in a range of competitions throughout the year such as the American Mathematics Competition, Shanghai TI Cup, and SMO.

Alright, thanks for the information! I’ll keep it in mind and look around for a while more.

Here’s the solution, if you’re interested:

Sadly, you can’t guarantee a win. Let’s suppose you, playing as black—and hence moving second—have a winning strategy. White simply moves his Knight out and back in the first turn. The board remains the same, but it’s your turn to go next. It’s as if the game has restarted, but this time you go first—you have switched colours with the wizard! We initially assumed that the second player to move can win, but now anyone can be the “second player” to guarantee a win by “skipping” their turn using the above moves. This is absurd, as there can only be one winner, so our supposition that black has a winning algorithm is false. 

The solution may appear simple, but the question is in no way easy, requiring that one stroke of genius. Math is full of deceptively simple problems like these, which act as gateways to concepts with a variety of exciting applications. If this sounds like your cup of tea, math club would be a great choice for you!

*Cover image taken in accordance with SMMs during the prior phase of Covid-19 measures.

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