-> wants proof, rather than just examples, that something you claim to be true in general is indeed true in general.
-> wants to follow the logic of your reasoning.
-> wants to understand conceptually as well as follow logically (so would appreciate examples, in addition to proof, if they help in understanding).
-> wants to know the main points (but not too much gory detail) of how you figured out your solution: what led you to take the path you did?
-> Check for correctness of mathematics, including reasoning.
-> Reorganize and reword to improve clarity and flow of explanation.
-> Be precise, not vague.
-> Put the paper aside, then reread it as if someone else had written it. If you have trouble following, so will your reader, so revise some more.
-> If possible, have someone else read and critique the write-up. (The student who consistently had the best write-ups of any student I have ever had in this class said she always tried them out on a friend who had little math background.)
|a2 +b2 = c2
|| a2 +b2 = c2,
where c is the length of the hypotenuse of a right triangle, and a and
are the lengths of the legs.
"To find it, multiply it by three, then add two to it."
The word "it" stands for three different things in this sentence! The reader may need to be a mind reader to understand what the writer intends. And writing this unclear often indicates that the writer is confused, too, or will be soon.
"To find f(x), multiply x by three, then add two to the result."
Incorrect: Since m and n are both odd numbers, m = 2k + 1 and n = 2k + 1.
(Does the writer really understand, or have they just mindlessly applied a rule?)
Correct: Since m and n are both odd numbers, m = 2k + 1 for some integer k and n = 2l + 1 for some integer l.
Incorrect: Since x = 2, therefore x2 = 4.
Correct: Since x = 2, x2 = 4.
therefore, thus, hence, consequently, besides, moreover, furthermore, however, likewise, similarly, accordingly, still, however, nevertheless, otherwise, afterwards, later, earlier, indeed