Jerzy Trzeciak. Writing mathematical papers in English: A practical guide


CONTENTS
Part A: Phrases Used in Mathematical Texts
Abstract and introduction………………………………………4
Definition…………………………………………………….6
Notation……………………………………………………..7
Property……………………………………………………..8
Assumption, condition, convention……………………………..10
Theorem: general remarks……………………………………..12
Theorem: introductory phrase………………………………….13
Theorem: formulation…………………………………………13
Proof: beginning……………………………………………..14
Proof: arguments…………………………………………….15
Proof: consecutive steps……………………………………….16
Proof: “it is sufficient to……………………………………..17
Proof: “it is easily seen that …………………………………..18
Proof: conclusion and remarks…………………………………18
References to the literature…………………………………….19
Acknowledgments…………………………………………….20
How to shorten the paper……………………………………..20
Editorial correspondence………………………………………21
Referee’s report………………………………………………21
Part B: Selected Problems of English Grammar
Indefinite article (a, an, —)……………………………………23
Definite article (the)………………………………………….24
Article omission………………………………………………25
Infinitive…………………………………………………….27
Ing-form…………………………………………………….29
Passive voice…………………………………………………31
Quantifiers…………………………………………………..32
Number, quantity, size………………………………………..34
How to avoid repetition……………………………………….38
Word order………………………………………………….40
Where to insert a comma……………………………………..44
Some typical errors…………………………………………..46
Index……………………………………………………….48



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writing mathematical papers

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