Listed here are the frequent tips when I proofread papers from master or phd students. They are numbered for convenient indexing. When I see a problem, I marked its corresponding number on the paper that I proofread to save my time. The correctness is not guaranteed.
[1]. The usage of a hypen, en-dash, and em-dash
They are different, but often abused by fresh authors. In "trade-off", "-" is a hyphen. In "pp. 134–150", "–" is an en-dash, indicateing a pertinent range. While an em-dash is graphically denoted as "—", it is called a punctuation, used in a sentence.
In LaTex, "-" generates a hyphen, "--" gives an en-dash, and "---" yeilds an em-dash.
[2] A comma cannot connect two sentences
[W] Samy is good at math, Sana is good at English.
[C] Smay is good at math and Sana is good at English.
[C] Samy is good at math, Sana is good at English, and Grace does not like Latin.
[3] The usage of that
[W] Assume p is an integer.
[C] Assume that p is an integer.
[C] Assuming that p is an integer, 2p+q must be a real number.
[W] We conclude p is an integer.
[C] We conclude that p is an integer.