Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Say you are writing a mathematical modeling paper in a science journal. How do you write your variable and parameter definitions in paragraph form so that you keep active voice but do not sound repetitive. For example

"$x$ is the average rate of change of ..."

Variable name followed by "is" sounds correct, but this must be frowned upon due to capitalization issues. Perhaps you could write,

"The average rate of change of ... is [called] $x$"

This is passive voice. We tend to use in proofs,

"Let $x$ be the rate of change of ..."

But this gets repetitive fast if you are writing in paragraph form. My guess is that this is more of an issue for applied mathematicians writing for non-math audiences.

share|cite|improve this question

closed as off-topic by Najib Idrissi, Claude Leibovici, Tom Oldfield, egreg, Jonas Meyer Mar 22 '15 at 16:42

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – Najib Idrissi, Claude Leibovici, Tom Oldfield, egreg
If this question can be reworded to fit the rules in the help center, please edit the question.

This is something I think one learns in time. I reread my first (and thus far only) paper a few weeks ago and noticed that I was very repetitive. It's not easy to be precise and not repetitive but the best authors manage to do it with plenty of experience. Try reading some of the heavyweights in certain fields, like Rudin or Lee, and see how their prose is. It might help. – Cameron Williams Feb 2 '14 at 2:03
By the way, "The average rate of change is $x$" is not passive voice, though "The average rate of change is called $x$" arguably is. In any case, there's no reason not to use the passive voice here. – ShreevatsaR Feb 2 '14 at 2:45
up vote 2 down vote accepted

Repetition is actually not that bad. It certainly is better than elegant variation. A collection of all the typical linguistic constructions used in mathematics can be found in Jerzy Trzeciak's Writing Mathematical Papers in English.

share|cite|improve this answer
Additionally, the passive voice is actually not that bad. It has a bad reputation because it allows its users to avoid allocating responsibility for some particular action, but in this case that's exactly what you want. We don't care who called a particular value "x", only that that is what they chose. – Jules Feb 2 '14 at 9:28

One of the great things about the English language is that there are so many different ways to say the same thing. So, avoiding repetitiveness should not be too difficult. Here are a few different ways to phrase your example sentence:

(1) Let $x$ be the rate of change ...

(2) Using $x$ to denote the rate of change, ...

(3) Let's use $x$ to represent the rate of change ...

(4) If $x$ is the rate of change, then ...

And, of course, you can get other variants by putting this clause later in the sentence:

(5) We will show that $y = kx$, where $x$ is the rate of change ...

And so on. Bear in mind that this sort of flexibility is often a source of confusion for readers whose native language is not English. If we use different words, this suggests to them that the meaning might be somehow different, too. There is a nagging fear, for example, that "denote" and "represent" might have two different meanings. For this audience, repetition is good, sometimes. So, don't go overboard with the thesaurus.

share|cite|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.