## Writing Mathematical Papers in English: A Practical Guide |

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### Contents

Phrases Used in Mathematical Texts | 4 |

it is sufficient to | 17 |

Passive voice | 31 |

Where to insert a comma | 44 |

### Common terms and phrases

Adjective ADVERBIAL CLAUSES adverbs apply assertion assume assumption Banach space bounded bounded function bounded set Comma compact set compact support completes the proof compute Consequently constant construction converge convex defined definition density derivative described Direct sums disjoint boxes element entries zero equal to G equation equivalent examples expressions F and G F is greater fact finite number function G is dense gives Hence holds hypotheses implies ING-FORM integral interest least lemma limit exist linear linear operator mathematical measurable functions method negative clauses norm notation Note the infinitive Note the inversion Note the plural noun obtain open subset Ordinal numbers paper passive voice positive positive-definite precise problem properties random variables reader Replacing the structure restriction satisfy Section self-adjoint sentence shows similar smallest smooth Studia Mathematica subject and verb subset symbol Taylor's formula theorem theory true unique solution g word order write e.g.