Effective Thinking Through Maths

I was very excited for another edX course, so far I have really enjoyed their platform, it keeps me focused more than a book and the production quality is really good. I was skeptical for this course “Effective Thinking Through Mathematics”. Looking at the content, I thought it would be a breeze, I am an engineer by education and trade, what else could it teach me about problem solving? I put my ego aside and dove in.

Organized over five different “weeks” (though each “week” you could do in a day or two), the course is not highly technical and the lessons are broad. The lecturer, Prof. Starbird, is engaging, the content is fun, and the format of small clips with work in between really helps me learn. He describes 5 elements of effective thinking, which I will try to keep in mind during my coding journey. My favorite quote of his is “failure leads to success”, if we learn effectively from our failures the success will follow. Here is the quote I have put on a post-it near my laptop:

Fail to succeed. Intentionally get it wrong to inevitably get it even more right. Mistakes are great teachers — they highlight unforeseen opportunities and holes in your understanding. They also show you which way to turn next and they ignite your imagination. — Professor Starbird

My number one problem when coding/designing is that I jump into a problem a bit too quickly, and fail to write down ideas, gather my thoughts, or break the problem down into smaller pieces. I am especially nervous for the upcoming challenge for a “Towers of Hanoi” solver, which seems like a massive undertaking. However, in going through this course I have already started thinking about the problem in smaller, more manageable steps. An important lesson I learned is to break a problem down to its simplest form, even if it seems trivial. For Towers of Hanoi that means starting with a 1-disk problem, then a 2-disk problem, and so on. This way we can see how patterns emerge that will help us successfully solve an 8-disk problem.

The next two “weeks” of the course focus on cardinality/ set theory and infinity. The professor does an excellent job of allowing us to prove to ourselves different parts of set theory by first using concrete examples before discussion the abstractions. I won’t get into any details of it, but it really made me miss mathematics from university.

I recommend this course for anyone and everyone, it is light-hearted, challenging, and thought-provoking. It is short and simple while still addressing core topics in problem solving. 5/5!

Onward!

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