I will be in Portugal next week, and one of my colleagues has offered to take the lectures in the final week of term. But I managed to get to where I wanted to get; the last few lectures will be responses to comments from students and tutors about things that need more discussion.
This was one of the parts of the course I was most looking forward to do: debugging dodgy proofs. There are quite a few examples in the lecture notes, the supplementary material, and the homework problems. Some involve fairly standard mistakes, such as dividing by zero in a hidden way, or treating divergent series as if they had well-defined values; some involve structural errors, like running a proof backwards and getting the converse of what you are after; and then there are the classics, such as “all horses have the same colour” and “all triangles are isosceles”.
Also, in a discussion of how to approach an unfamiliar problem, we talked about the locker problem, which is conveniently posed here by Emily Allman. Unless you are a genius, first you have to work a small example to discover what it is that you actually have to prove.
After my last lecture, I was delighted to get this comment in an email from a student:
You made the transition from A-level to University much easier for me, you taught me to look at mathematics in a different way and I feel I am now able to approach this course in the way I should after learning Mathematical Structures. Every single lecture you gave was so intriguing and I didn’t realise how much I had learnt from them until the mid-term exam.
This is what makes teaching such a worthwhile profession. Something has been achieved!
A reminder of the LMS Gresham Lecture on Tuesday 14 May 2013, at 6pm in the Museum of London Lecture Theatre. It will be a look at this module, how it was designed and delivered and what reaction it had. See you there.