By Jerzy Trzeciak
Read or Download Writing Mathematical Papers in English: A Practical Guide PDF
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Extra info for Writing Mathematical Papers in English: A Practical Guide
Example text
7. Multiples: The k -fold integration by parts shows that ..... We have shown that F covers M twofold. It is bounded by a multiple of t a constant times t . This distance is less than a constant multiple of d. Note that G acts on H as a multiple, say n, of V . 8. Most, least, greatest, smallest: Evidently, F has the most the fewest points when ..... In most cases it turns out that ..... Most of the theorems presented here are original. The proofs are, for the most part, only sketched. Most probably, his method will prove useful in .....
G. between two symbols. 1. Comma not required: We shall now prove that f is proper. The fact that f has radial limits was proved in [4]. It is reasonable to ask whether this holds for g = 1. Let M denote the set of all paths that satisfy (2). There is a polynomial P such that P f = g. The element given by (3) is of the form (5). Let M be the manifold to whose boundary f maps K. Take an element all of whose powers are in S. We call F proper if G is dense. There exists a D such that D ∼ H whenever H ∼ G.
Or : surprised to find out] Their study resulted in proving the conjecture for ..... The success of our method will depend on proving that ..... To compute the norm of ..... amounts to finding ..... We should avoid using (2) here, since ..... [Not: “avoid to use”] We put off discussing this problem to Section 5. It is worth noting that ..... [Not: “worth to note”] It is worth while discussing here this phenomenon. ] It is an idea worth carrying out. [Not: “worth while carrying out”, nor : “worth to carry out”] After having finished proving (2), we will turn to .....