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[Writing for CS] 9. Mathematics

  • Clarity
    • "Any" sometimes means "all" and sometimes means "some"
    • An algorithm or problem is "intractable" only if it is NP-hard, that is, the asymptotic cost (or computational complexity) is believed to be worse than polynomial.
    • "Formula" and "expression" are not necessarily an "equation"; that latter involves an equality
    • Two things are "equivalent" if they are "distinguishable" with regard to some criteria. It can mean they are best "similar".
    • "Element" is a member of a set. And a set is "partitioned" into subsets.
    • "Metric" is expected to satisfy conditions. In mathematical contexts, use "measure" unless metric is intended.
  • Theorems
    • Even if there are only two or three of each in the paper, you should consider numbering key examples.
  • Readability
    • Use parentheses of appropriate size
    • Mathematics/digits should not be used at the start of a sentence.
      • ex. 7 of the runs were ~ => There were 7 successful runs ~
    • Avoid letting a number, symbol, or abbreviation appear at the start of the line, particularly if it is the end of a sentence. You should not let a quantity become detached from its unit.
    • Mathematics should have motivation. Straightforward mathematics is daunting.
    • Avoid unnecessary subscripts: use x and y than x_1 and x_2
    • Mix subscripts and superscripts with caution
  • Numbers
    • Don't mix number modes. ex. four and 32 processors => 4 and 32 processors
    • Fractions are only rarely used for values, and should not be used as abbreviations.
    • It is more logical to represent quantities to the same number of decimal places.
    • Guesses and approximations should be clearly indicated as such, with words such as "roughly", "nearly", "approximately", "about", "almost" or "over".
  • Units of Measurement
    • Units should be typeset in the font used in the paper for text, even when they are part of a mathmatical expression.
    • Put white space between values and units.

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