1. Run a spell-checker.
  2. If you use \(X\) or \(i\) as variables, don’t write them as X or i.
  3. Write \(\log(n)\) instead of \(log(n)\), \(\arg\max\) instead of \(argmax\), \(\Pr(E)\) instead of \(Pr(E)\)), etc. You can use the “\operatorname” command for non-standard operators.
  4. For inner product notation, use \(\langle x,y \rangle\) instead of \(<x,y>\).
  5. Make sure all parentheses, brackets, curly braces, etc. are matched, and also properly sized, e.g., \[ \left( \frac{x+y}{2} \right) \] rather than \[ ( \frac{x+y}{2} . \]
  6. Be consistent in your use of calligraphic (e.g., \(\mathcal{X}\)), blackboard (e.g., \(\mathbb{P}\)), and other font styles.
  7. If you have a “tall” mathematical expression like \(\left( \sum_{x=0}^{2^n-1} \frac{2^{2^x}}{3} \right)\), it is better to put it in a separate equation display, like \[ \left( \sum_{x=0}^{2^n-1} \frac{2^{2^x}}{3} \right) . \]
  8. If you need to use some text expression inside an equation, use the “\text” command, e.g., \[ \{ x \in [0,1] : \text{$1/x$ is a prime integer} \} . \]
  9. Mathematical expressions and equations should generally be written as if part of a complete sentence. For example, I define a set \(S\) by \[ S := \{ x \in [0,1] : \text{$1/x$ is a prime integer} \} , \] and there is a comma at the end of the display to separate the independent clauses.
  10. In \(\LaTeX\), it is better to use “double-backtick” for opening quotation marks and “double-apostrophe” for closing quotation marks.
  11. Make sure notation and jargon is properly defined before use.
  12. Define “theorem” environments as needed (e.g., using the amsthm package).