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Diagramming Maths Topics - 2014/11/22
An impossible task, but wouldn't it be useful to have some sort of diagram of topics in maths, connected somehow to show the links between topics? How could such a diagram been created? How could it be explored? How could it be dynamic? Maintainable? Usable?
Maths is an incredibly wide subject, covering a vast, vast number of topics. There's a huge variety of topics within the subject, and so many of them connect with each other.
Studying complex numbers can be assisted by knowing about vectors, but learning about vectors can be assisted by knowing about complex numbers! Each can support the other, so which should we regard as more fundamental?
Or what about calculus versus adding fractions? Without being able to add fractions it's almost impossible to learn the fundamentals of calculus, and yet we can do calculus without being able to add fractions. Well, sort of.
And then there's the sheer complexity of the connections, and the number of topics. The granularity is also a challenge - how detailed should we be when we specific a topic? We can talk about "algebra," but then we can talk about details such as rearranging and solving equations, linear equations, cubics, completing the square, surds, factorisations, and so much more. How deep do we go? How detailed should we be?
But there are already so many pages and sites already out there that it's obvious this is important, and potentially incredibly useful. It's also completely obvious that this is hard.
The challenge is to make something useful. Navigable, connected, explorable, maintainable. I think it can be done. I think it should be done.
I know that teachers have worse than zero time. They have huge amount of negative time - over-committed, over-worked - but if we can work together, perhaps we can make something that ultimately will help.
I'll start to collect links to pages that already have something and I'll put them here:
I've decided no longer to include comments directly via the Disqus (or any other) system. Instead, I'd be more than delighted to get emails from people who wish to make comments or engage in discussion. Comments will then be integrated into the page as and when they are appropriate.
If the number of emails/comments gets too large to handle then I might return to a semi-automated system. That's looking increasingly unlikely.
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