In the preceding five parts of this book there is a lot to digest and each part focuses on a different way of thinking like a mathematician. Putting them all together and applying them effectively takes time and practice. It is not easy to think like a mathematician; there is no set of rules to follow, though many techniques have been given. Doing mathematics is certainly more of an art than a science.

Therefore, in this chapter I will pick out some interesting points from earlier chapters and see how we can integrate the methods.

Getting started

The biggest hurdle with any mathematics problem is getting started. I set weekly exercises for my students and when a student says ‘I am stuck on question X’ my standard reply is ‘Well, what have you done so far?’ Their reply is often ‘Nothing. I can't get started. I don't even know where to start.’

The advice in many Study Aid type books is to look for previous worked examples. However, my students don't need to have this pointed out to them, they have probably already looked in their notes for a similar problem. And in fact this study book advice may be the cause of their difficulties.