Basic Guidelines for good mathematical writing
2023/02/21
Insoo Park(TA)
IMEN 260: Operations Research Ⅰ
Guidelines for good mathematical writing
▪ This presentation closely follow the following:
• Su, Francis. "Guidelines for Good Mathematical Writing." (2015).
▪ It is not only for good mathematical writing, but also for high scores on your assignments.
▪ Furthermore, it is expected to be helpful not only in this course, but also in every courses with
assignments that need to be written mathematically.
▪ I will try to give you a generous score!
▪ However, I have the right to deduct points for assignments that ignore the guidelines that I will
show you from now on.
IMEN 260: Operations Research Ⅰ
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Guidelines for good mathematical writing
1. Know your audience
▪ You may confuse about the reader(=TA)’s background about this course.
• ‘what background can we assume of the reader?’
• ‘what terminology should we define?’
▪ A good rule of thumb is to assume that you are writing to another student in the course who
has not yet done the assignment.
• Even though she has attended all the same lectures and has read the same textbook, it is a standard
courtesy to remind your reader of any relevant items that she has recently learned in class or
from the textbook, or things she should know but might have forgotten.
IMEN 260: Operations Research Ⅰ
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Guidelines for good mathematical writing
1. Know your audience
𝑛
𝑚
▪ For instance, consider the situation that we want to say that 𝑥 is rational and denote 𝑥 = .
(1) Since 𝑥 is rational, we can set 𝑥 =
𝑛
𝑚
where 𝑚 and 𝑛 are integers.
(2) Recall that a rational number can be expressed as a fraction. Since 𝑥 is rational, we can set
𝑥=
𝑛
𝑚
where 𝑚 and 𝑛 are integers.
→ (2) is better.
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Guidelines for good mathematical writing
2. Set an invitational tone.
▪ It is traditional to create an inviting atmosphere in one’s mathematical writing.
▪ You can regard mathematical writing as an inviting readers to join us in our reasoning
process by writing in the present tense.
1. Use pronoun “We” instead of “I”.
• “We construct the dual problem as …”
2. Direct the reader with gentle commands.
• “Let 𝑛 be the…”
• “Recall that …”
• “Consider the set of …”
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Guidelines for good mathematical writing
3. Use complete sentences.
▪ Consider this piece of writing:
▪ What’s being assumed?
▪ What’s being proved?
▪ What’s the relationship between these phrases?
▪ The reader(me…) should not have to figure out what the writer was thinking.
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Guidelines for good mathematical writing
3. Use complete sentences.
▪ Consider the work of another writer who has attempted the same problem:
▪ I do not expect rigorous writing like the above, but you need to describe your own path from a
problem to a solution.
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Guidelines for good mathematical writing
4. Learn the etiquette.
▪ It is customary to avoid starting sentences or phrases with a number or symbol.
• 𝐴 is a subset of ℝ. (X)
• Let 𝐴 be a subset of ℝ. (O)
▪ It is also customary to emphasize unfamiliar words that we are about to define, either by
italicizing or underlining them.
▪ Other rules of etiquette can be learned through observing the norms of textbooks in this course.
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Towards Elegance..
1. Decide what’s important to say.
• A well-written solution will present just enough details and highlight the most interesting or unexpected
parts of the argument.
2. Highlight structure.
• If your argument is going to be a long one, with lots of technical details, then try to help the reader by
summarizing the outline of your argument at the beginning.
3. Choose good examples.
• A difficult idea may be easier to digest if accompanied by an example.
4. Avoid red herrings.
• A red herring is something that misleads or distracts from a relevant or important question.
• For example, if you say “We express the rational 𝑟 as 𝑛/𝑚 where 𝑚 and 𝑛 have no common factors”,
then you will use the “no common factors” idea. If you never use that fact, you should omit saying it.
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