Maths for Humans: Linear, Quadratic and Inverse Relations

The final week of my Future Learn MOOC called: Maths for Humans: Linear, Quadratic and Inverse Relations is about to go live tomorrow. This feels like all I have been doing for the last three or four months, and I am very glad that it is now coming to a close.

A MOOC is a Massive Open Online Course. This is free online education, run potentially on a large scale. Future Learn is a relatively new MOOC platform run by the Open University in the UK, and they have vast experience with distance education over many decades. Maths for Humans is a course that Daniel Mansfield and I have put together at UNSW, supported by UNSW Learning and Teaching Funds from UNSW L&T.

Currently we have about 8500 people registered, but as is typical in such MOOCs only some fraction of that are actively learning — perhaps around a third or so. Which is still a decent number.

And why is a pure mathematician who is re-configuring modern geometry, and also trying to steer the Ship of Mathematics to safer, more placid waters, spending his energies this way? Well one reason is that I have got some grant funding for this, and so some teaching relief. So actually I have not been teaching this semester, because I also have another big project going on to revamp some of our first year tutorials, which I must tell you about some other time.

I happen to think mathematics is far and away the most interesting subject. I reckon a lot of people would be both pleased and enriched to have an opportunity to learn more mathematics in a systematic, structured, and thought-out way. Courses like the one Daniel and I have put together are exactly in this direction. And also they should help high school students and teachers, which is always a good thing from my point of view.

But you might be surprised that, in addition, I actually learn a lot of important things by trying to figure out how best to present material to people who are not necessarily very advanced in mathematics. That motivates a lot of my YouTube channel too. It turns out that having to explain something to someone who perhaps really has no idea about the subject forces me to think hard about what the essence of the matter is, what the key examples are, what to say and what not to say. And invariably I learn something.

What did I learn putting this MOOC together? A lot. I learnt about power laws in biology, about allometry, the study of scaling in biology, about Zipf’s law, thought some more about Benford’s law (which I have mused on from time to time), and reviewed some basic supply and demand kind of elementary economics that I had more or less forgotten. I had a chance to review lots of things that officially I know, but that it is good to solidify. And I also learnt that the bowhead whale is the longest living mammal, with a record lifespan of 211 years.

And I believe that I also learnt the right way to think about the quadratic formula. Let me share with you what I would like to call al Khwarizmi’s identity:

ax^2+bx+c=a(x+b/(2a))^2+(4ac-b^2)/4a

This is the heart of the matter as far as I am now concerned. The usual quadratic formula is just a sloppy consequence that results if one is cavalier about taking “square roots”, which I hope none of you are any more. Geometrically this formula allows us to identify the vertex of the parabola ax^2+bx+c. It is this identity, I’ll bet, that students will learn when they study quadratic equations, one thousand years from now.

The course is lasting only another week, but if you register before the end, then the course contents will be available to you after it closes. So check it out! This link ought to work:

https://www.futurelearn.com/courses/maths-linear-quadratic/

Some thanks: Laura Griffin has a been a big help as our project manager, and Iman Irannejad has done a cracker job with the videos. Ruslan Ibragimov has been splendid with technical assistance, and Joshua Capel and Galina Levitina have both been a big help running the course. Thanks to them, and to the folks at UNSW L&T who have supported the project from afar.

 

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