Mathematical Thinking

Yay! I handed in my last assignment for the semester yesterday, and I am feeling great! The best thing about the holidays is that I have 3 weeks completely free to pursue something that interests me; these holidays it is going to be set theory. I’ve got a couple of interesting resources on set theory that I am going to work my way through, and I am going to do a course on Coursera, “Introduction to Mathematical Thinking”, taken by Keith Devlin.

In the introduction (to the Introduction to Mathematical Thinking) Prof. Devlin has stressed the difference between real mathematics and high school maths. He describes high school maths as being procedural, following sequential steps from A -> A1 -> A2, …, -> Ai, -> B. While this is perfectly reasonable (especially for pre-20th century maths) Devlin suggests that the real world of mathematics is nothing like this, that it is abstract and requires the ability to think outside the box, which is a valuable commodity in today’s world. I thought it was interesting that I could almost have run Devlin’s introduction alongside Clare’s introduction of SYD 701 and they would have been near identical. Like SYD 701, it is about understanding more than it is about doing, and at times it may seem slow but there is some real nuggets of gold buried within the process.

For set theory, I have a couple of great teaching documents, one in particular by Glynn Winskel at Cambridge University. Its quite funny, I hadn’t intended to blog about this journey I am on – but I am only into the first chapter of Winskel’s paper and I am already beginning to see how the combination of these two projects is going to force me to think in entirely different ways. There are some (seemingly) simple exercises in Winskel’s paper that are challenging my approach to problem solving, which is great! Even in this early stage, it is apparent that I don’t have to tools to approach these challenges and I am going to have to find new ways of tackling them.

And that is why I am blogging. Throughout SYD 701, Clare challenged us and opened up opportunities to explore different views and perspectives. It was really enjoyable, and I feel more capable as a result. But I blogged last month, about it being an ‘odd’ process and not being able to pinpoint exactly what we were learning. This holiday project feels the same, I am not really sure where it is going to lead but I hope it will challenge the way I approach problems and find solutions and therefore, be one of the best learning experiences this year. It would be silly not to record this journey, because it could be something truly transformative.

3 thoughts on “Mathematical Thinking”

1. Thank you for blogging about this – I shall enjoy reading it and sharing a bit of the journey with you 🙂 And thank you for your comments too – there are times when I wonder if I take things a little too far with SYD701 and then I am so heartened by what you have written and to know that I am in line with academics a lot more reputable than me 🙂

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• btw have you considered putting up some of your favourite links in your blog sidebar? I am sure you are gathering quite a few now and they could prove useful in the weeks to come !

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• lol – the parallel between the approach you have taken to SYD 701 and what Devlin described was incredible. And to be honest, I am not sure I would have been prepared to embrace the process fully without the preparation of SYD. So, thank you very much Clare 🙂

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