Of course, a rule is never without exceptions ...

General

  • Use a hyphen between adjectives to indicate when an adjective describes another adjective: "red spotted trousers" describe trousers that are red and spotted (the trousers can be described as "red trousers" and "spotted trousers") and "red-spotted trousers" describes trousers that have red spots (red describes spots, not trousers). This comes up frequently in technical writing. We have a two-connected graph because two describes how the graph is connected, not the graph itself. I would like to use brackets as well in technical writing to be clear. In "two-edge-connected graph" does "two" describe edge, edge-connected or connected? We could say "two-(edge-connected) graph" ...
  • "et al." is short for "et alia", so "et. al." and "et. al" and "et al" are incorrect.
  • Active voice is generally easier to read and so preferable to passive voice. Of course, there are exceptions. See this handout from UMN Δ for an explanation and examples.

Mathematical

  • Do not start a sentence with a lower case variable. Use "Edge e is ... " instead of "e is ..."
  • Use lower case variable names for elements, upper case for sets and \mathcal for collections.
  • Use variable names that invoke what they represent. Hence P for a path, C for a cycle and G for a graph.
  • Only define or denote something if it clarifies the writing. If you only use something once or twice in the paper, then consider not defining it, or defining it "locally" (for example within the proof of a lemma, within a paragraph, etc.).
  • References to particular lemmas, theorems, etc are proper nouns and so should be capitalized. Hence, "By Lemma 1, we get the following lemma."
  • State a lemma for something that you will use later in the paper. State a theorem for something you expect or hope others will refer to.
  • Proofs are local. You should not refer to the contents of a proof outside of the proof or inside a different proof.

References

  • Give credit where credit is due. If you rely heavily on the work of people, then use their names in the text, don't relegate them purely to the list of references. Even if a paper has many authors, give all their names at least the first time you refer to their work in your paper. There may be some number at which point you use et al. right from the start, but we rarely have more than 5 authors in mathematics.
  • Do not use a reference number in brackets as a noun. Examples:
    • "Doe shows that blah [13]." rather than "[13] shows that blah".
    • "The techniques of Doe and Smith are ... [13]" rather than "The techniques of [13] are ... "
    • "See Ref. 13 for a more detailed description." rather than "See [13] for a more detailed description."

Latex

  • Use as few latex packages as possible; strange packages may not be available for camera-ready production.
  • To cite a reference without the square brackets, \usepackage{cite} and \citen{XX}.
  • Use bibtex and maintain a "global" repository of bibtex citations. When working with others, cut and paste the relevant citations into a local .bib file. When uploading a paper for publication or for arXiv, replace \bibliographystyle{???} \bibliography{???} with the contents of the final .bbl file.