some notes on professional writing

1. should use punctuations in equations.
2. Avoid starting a sentence with a mathematical expression, seperate symbols by puncutation marks or words.
3. "the" is inapproprieate when the object referred is not unique or does not exist
4. write "the kth term", not "the k-th term"
5. two types of ellipsis, vertically centered and ground level. The latter is used between a list of symbols or to indicate a product. A_1...A_n. i = 1, 2, ..., n
6. Several commonly used abbreviations, e.g., i.e., et al.,

7. avoid using the adj or advs. very, rather, quite, nice, interesting (all these are imprecise). So is "essentially"