Most of the advice on writing mathematics in the previous posts is aimed at the postgraduate student or those writing papers. Yet many of us are all too keenly aware that undergraduate students are in even greater need of help. For example,
- misuse of the equals sign; I’ve lost count of the number of times have I told students that both sides of = must be of the same type so a function doesn’t equal a point in and ‘equals’ is not a synonym of ‘therefore’ or ‘implies';
- sentences that are missing one or more of subject, verb, object;
- steps in a proof that have no relation to what has gone before;
- etc …
I am pleased to say that Dr Kevin Houston of Leeds University has written to me to tell me how he is trying to help students to write properly:
- I am writing a book called How to Think Like a Mathematician which includes a bit about writing mathematics at university (but can be applied at lower levels). This is aimed at first degree students – I notice that a lot of advice about writing maths is aimed at PhD students, for example, the video of Serre.
The sample chapter on writing is on my website along with the full booklet that we give to our first year maths students here at Leeds.
A couple of quotes taken at random:
- An equation involves saying that two expressions are equal, for example, . Note that an inequality, such as , is not an equation.
‘The number of people over 40 = 5′, which reads all right, but the eye is drawn to the (erroneous) expression 40 = 5.