Common mistakes

- Pay attention to “less than” versus “no more than”: One is <, the other is \leq (or \le). Pay attention to “decreasing” versus “nonincreasing” too.
- Do not use contractions in formal writing. Don’t –> do not. Can’t –> cannot. Note that I am not saying to eliminate apostrophes! They are needed for possession (a problem’s optimal solution, for instance).
- Punctuate your equations. For instance, consider a line like,

This equation is given as follows:

\begin{equation}

\label{e:myeqn} 3x + 2y = 6

\end{equation}

Now, consider the following proof…

You shouldn’t have this. The sentence preceding the equation was ended by “3x + 2y = 6,” and so it should end with a period (“…3x + 2y = 6.”) Now, suppose you were continuing your sentence:

\begin{equation}

\label{e:myeqn} 3x + 2y = 6,

\end{equation}

where $x$ and $y$ are both nonnegative.

This is correct. Of course, if there’s no call for punctuation, don’t add it. But there often is. - Something that comes up in combinatorics: less vs. fewer. Less is devoted to floating point items, fewer is devoted to integer objects. First, let’s not make it too complex: If you have two variables $x < y$, you’d always say “$x$ is less than $y$.” Now, if you were comparing extreme points of P and Q, you say that P has fewer extreme points than Q. (Not “less” extreme points.)
- You can get into trouble using “the” in your papers, believe it or not. You should not refer to “the optimal solution” unless you know it’s unique. Use “an optimal solution” instead. You may safely refer to “the optimal objective function value, if one exists” (with the latter caveat not necessary if you did know that an optimal solution exists).
- For section titles, be consistent with your capitalization rules. If one section title is “Computational Results,” then another section title should not be “Conclusions and future research.” (It should be “Conclusions and Future Research” instead.) It does not appear that every journal treats capitalization of sections the same way, so just be consistent with how you write them within a paper. The same principle goes for captions of tables and figures, and so on.
- Passive vs. active voice is an interesting choice in technical writing. I was taught (and subsequently untaught) a long time ago not to use first person (I, we, our, etc.) in formal papers. The problem is that when you do that, you have to write much of your paper in passive voice. Consider the following alternatives. “We then compute the optimal solution” versus “The optimal solution is then computed.” The former is more direct and less stilted, and experts say that active voice is easier to read. So there’s probably no right answer here, but it seems very common to use first person plural in your paper to avoid passive tense. Note that it’s not necessary to remove all passive tense from your paper, but in general I want to avoid it. Also, even if you sole-author a paper, it is very uncommon to see “I” or “my”; first-person plural seems to be used even in this case.
- A raging debate is “because” versus “since” versus “as” when they are used to mean the same thing. Consider this phrase: Problem P has an optimal solution [because, as, since] $\hat{x}$ is feasible. What word in the [ ] should we choose? I prefer “since,” and a friend of mine prefers “as.” Yet some strongly prefer “because,” noting that “since” and “as” have alternative meanings that can confuse readers. That might be true especially for non-native English speakers.