Additional Useful Topics coming next

I have finally decided to start work on the Additional Useful Topics section that I have had planned for some time, especially after a number of you emailed to request it!

These are methods and ideas that I think are particularly useful for TMUA preparation. Technically, it is possible to solve TMUA questions without explicitly knowing some (or maybe all) of them, and an examiner could reasonably argue that a competent student might arrive at some or all of these conclusions naturally through their mathematical studies.

In my experience, however, this is often not the case. For many students, these ideas remain unfamiliar, overlooked, poorly understood, or understood only superficially. This is not really the fault of students or their teachers! As many of these ideas simply receive relatively little attention in the mainstream mathematics curriculum. So my aim of this section is to address as many of these gaps as possible in detail, to help students further prepare for the TMUA.

Here is the current planned list — which I made into a poll so that you can indicate whichever you would most like me to write first.

The list is subject to change, expansion or omission as I work through it, and is intended to give you an idea of what I currently have in mind.

You are also very welcome to suggest further topics that you think would be useful!