Academic Writing

To be updated (regularly if possible) ..

How to write and publish a math paper? (by Ansgar Jüngel)

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The Grammar According to West" (by Douglas B. West)

• 5. It would be better to consider notational expressions as single objects (that is, nouns).
  
  

• 14. It would be better to take a comma before "hence", "thus" and "therefore".
  Sometimes, there is no comma after "hence" and "thus" (single syllables) to enhance mathematical understanding.  
  "Therefore" would be treated the most formal, introducing a major conclusion. Thus, it is better to take a comma after "therefore". 
  
  

• 18. A statement that is assumed is an axiom, considered througout to be true. Something supposed is a hypothesis. If you want to introduce an argument by contradition, it would be better to use "suppose". Not "Assume for a contradiction", Use "Suppose to the contrary that".
  
  After words of hypothesis or conclusion ("suppose", "assume", "implies", "conclude", etc.), use "that" when what follows is a clause with an English verb. Omit "that" when what follows is just a noun unit. For example, "Suppose x+y<10" and "Suppose that f is a function..".
  
  

• 57. "Left hand side, left-hand side" should  be "left side". There is no "hand".
  
  

• 60. "Which" vs "that"
  I have two shirts that need cleaning; two of my shirts need cleaning.
  I have two shirts, which need cleaning; I have only two shirts.
  
  

• 65. It is better to avoid "i.e." and "e.g.". Use "that is" and "for example".
  
  

• 77. "Above" and "Below" are adverbs. They do not directly modify nouns. Hence, "the above graph" and "the below figure" are incorrect. We can write "the graph above" as a short form for a "the graph shown above".
  
  

• 79. "In Section 4, we show" rather than "In Section 4, we will show"; the justification for this is viewing ther entire article as a unit, happening in the present.
  
  

• 88. "a theorem", "a result" but not "a work" and "a joint work". Just "work" and "joint work". Note that "work" is an abstract noun and does not take the indefinite article "a". Also, not "a joint research".
  
  

• 92. "a same argument" => "the same argument" or "a similar argument"

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Writing Mathematical Papers in English (by Jerzy Trzeciak)

• p46: Not "In 1964, Lax has shown...". Use "In 1964, Lax showed..."  (Use the past tense if a date is given.)

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Practical suggestions for mathematical writing, Notices Amer. Math. Soc.

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Others

• "1,\ldots,N" would be better than "1,\cdots,N". 

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