How To Write Mathematics Badly 3

Friday 16 March 2007 at 4:44 pm | In Articles | 8 Comments

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 R^2 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, 3x^2-7x = 4x. Note that an inequality, such as x \leq 5, 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.

Well-worth reading!


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  1. I’m guilty of a few/most of the examples that you have mentioned! (especially the proof one!) Although, now I had learnt that if you do have the quadratic and want to solve it, you don’t use the equals sign but iff!

    I guess I’ve had that ‘habit’ since school. But I haven’t actually got the grasps of proofs yet (still waiting to one day waking up and being able to do them!).

    Just wondering- is there anything wrong with using the three dots for therefore, and writing ‘iff’ instead of ‘if and only if’?

    Comment by beans — Saturday 17 March 2007 12:14 am #

  2. Forgot to mention- like the new look. It’s cool! (and would you ever know if we do the sums that it asks us to do incorrectly??!! )


    Comment by beans — Saturday 17 March 2007 12:16 am #

  3. Hey, the layout has changed, very nice.

    Comment by MIke — Saturday 17 March 2007 1:41 am #

  4. Beans: I often use \therefore but it seems to be going out of fashion. Similarly I use \Leftrightarrow instead of iff which I think looks nicer. But if you are writing words rather than sentences it is better to use if and only if otherwise it begins to look a bit like txt spk 🙂

    So I would write x^2=1\Leftrightarrow x=\pm 1, or x is a solution of the equation x^2=1 if and only if x=\pm 1.

    Comment by steve — Saturday 17 March 2007 10:29 am #

  5. I think I’ll stick with the three dots as well! I normally use that symbol for iff, but I guess you have a fair point about using ‘iff’ in sentences! So in theorems or proofs, it’s best to write it out in full I suppose. (I got a big fat circle around iff on my work!)

    Grrr, I can’t even write s.t anymore! (It’s all for the best, but its much quicker to just write iff and s.t!)

    Comment by beans — Saturday 17 March 2007 12:49 pm #

  6. Whoa nice new theme.

    @beans: the reason it asks you to do the sum is to prevent automatic spamming by bots.

    Comment by Adeel Khan — Wednesday 21 March 2007 3:05 pm #

  7. Very tempting to ask instead for a solution to the partial differential equation \dfrac{\partial ^2 z}{\partial x^2}-\dfrac{\partial ^2 z}{\partial y^2}=\dfrac{2z}{x}

    Comment by steve — Wednesday 21 March 2007 3:28 pm #

  8. Grrr, I had ‘forgotten’ to answer the question and hence lost my reply!!

    Adeel: I was just asking whether Steve would know it I had done the sum incorrectly! :p 😮

    BTW Steve, that’s not fair! I haven’t done them yet, although it’s a good plan if you want me to shut my yap!

    Comment by beans — Wednesday 21 March 2007 9:31 pm #

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